カテゴリー別検索
Soils and Foundations 2006年
出版
soils and Foundations
| タイトル | 表紙（Soils and Foundations） | ||||
| 著者 | |||||
| 出版 | soils and Foundations | ||||
| ページ | -〜- | 発行 | 2006/10/15 | 文書ID | 20937 |
| 内容 | |||||
| ログイン | |||||
| タイトル | Contents（Soils and Foundations） | ||||
| 著者 | |||||
| 出版 | soils and Foundations | ||||
| ページ | -〜- | 発行 | 2006/10/15 | 文書ID | 20938 |
| 内容 | |||||
| ログイン | |||||
| タイトル | Elasto-Plasticity of Unsaturated Soils: Laboratory Test Results on a Remoulded Silt | ||||
| 著者 | F. Geiser・L. Laloui・L. Vulliet | ||||
| 出版 | soils and Foundations | ||||
| ページ | 545〜556 | 発行 | 2006/10/15 | 文書ID | 20939 |
| 内容 | 表示 SOILS A.ND FOUNDATIONS ¥,'ol 46. N'a 5. 545-556. Oct 2006Japanese Geotechnlcal Societ}ELASTO-PLASTICITY OF UNSATURATED SOILS= LABORATORY TESTRESULTS ON A REMOULDED SILTFRAiN OISE GEISERi), LYESSE LALOUli} and LAURE 'T VVLLI Ti)ABSTRACTCurrent models of the elasto-plastic behaviour of unsaturated soils contain important underlying assumptions thathave not been tested due to a lack of adequate experimental data. To address this issue, the objectlve of this paper is topro¥'ide a comprehensive set of experimental data. An extensive experimental program has been performed on arernoulded unsaturated silt. To characterise its elasto-plastic behaviour, samples vere taken through various stresspaths, including wetting, dr_vin*' and compression. Experirnental results vere analysed to provide (1) evidence ofsuction-induced preconsolidation; (2) dependence of' cohesion and shear strength at failure on suction; (3) stiffness inrelation to suction and (4) uniqueness of the critical state line.Key words: deformation, Iaboratory tests, partially saturated soil, plasticity, shear strength, silts (IGC: D5/D6)behaviour of soils at a gi¥'en external loading pressureINTRODUCTION(e.g. Croney and Coleman, 1954; Blight, 1966; BiarezExperimental data showin_ : all aspects of the behaviourof a particular unsaturated soil are scarce. This is mainlyet al., 1988; Zerhouni, 1991; Fleureau et al., 1993). On afirst-time drying path the saturated sample is initially verydue to the many (well-knolvn) experimental difficultiescompressible and then, beyond a suction close to s*, itbecomes less compressible, sho¥ving a quasi-reversiblebeha¥'iour. These observations do not correspond ¥viththe assumptions made in the elasto-plastic frame¥vorkproposed by Alonso et al. in 1990 and extended by otherauthors (Wheeler and Sivakumar, 1995; Wheeler, 1996).and the time-consuming nature of testing unsaturatedsoils. Earlier research work studied the shear strength(Fredlund et al., 1978; Escario and Saez, 1986) andisotropic compression of unsaturated soil at differentinitial suction ¥'alues (Matyas and Radhakrishna, 1968)separately. More recently, significant progress has beening volume measurement by e.g. Alonso et al. (1990),In this videly-used model, it is assurned that the suctioneffect is similar to the effect of a mean effective stressunder isotropic loading conditions (i.e. with initial elasticbeha¥'iour follo¥ved by an elasto-plastic response).In this paper ¥ve contribute to a complete experimentalkno¥vledge of the stress-strain relationship of unsaturatedWheeler and Sivakumar (1995) both on compactedsoils by examing the behaviour of remoulded Sion silt.kaolin, C*ui and Delage (1996) on Jossigny silt, andfinally, Ma touk et al. (1995) on Trois-Rivieres silt.Samples ¥vere subjected to various stress paths including:(i) isotropic compression at controlled suction and (ii)drying-wetting by means of increasing and decreasing thesuction at a controlled external pressure. Both of these¥vere follo¥ved by shearing the sample to critical state.made in an attempt to better understand the link betlveenshear strength and volume change, and to characterise it¥vithin a single framework. In these ¥vorks the experimental results examined the stress-strain relationship, inciud-Ho¥vever, none of these ¥vorks addressed the relevance ofthe suction value, s*, at ¥vhich air enters into the pores ofsoils. If the suction applied to the soil is less than thisair-entry value, s*, the behaviour of the soil can accurate-As in previous research ¥ve assume the behaviour ofly be interpreted using the standard effective stressconcept (Fleureau and Indarto, 1993; Fleureau et al.,unsaturated soils can be fully described by two stress statevariables. It has been sho¥ 'n by Fredlund and Morgen-1995; Karube and Kawai, 2001; Kohgo et al., 1993).stern (1977) that the tot.al stress, the pore air pressure andVVhen the suction ¥'alue exceeds the air-entry value,the pore ¥vater pressure can be expressed in any t¥voho¥vever, t¥vo stress state variables may be necessary for aindependent stress combinations in order to characterisethe mechanical behaviour of unsaturated soils. Typically,the net stress and the matric suction are chosen as statevariables. In this paper, ho 'ever, the results are alsocomplete description of the soil. This dependency of thestress-strain relationship on suction is further examinedin this paper using experimental data obtained on Sionanalysed usmg the combmatron of the "saturated effective" stress and the matric suction. Such a combinationsilt .Other researches have examined the drying-1vettingi' Soil'Iechanics Laborator)*, S¥viss Federal institu e ofTechnoiog)*EN. c-EPFL, slvitzerland (1)'esse.lalouie epfl.ch).The manuscript for this paper ¥1'as recei¥'ed for revie v ort Januar}' l l, ,_005; approved on h'ta}, 29, 2006.¥vritten discussions on thls paper should be submitted before ¥. ,la ' I , 2007 to lhe Japanese Geotechnical societ ', 4-38-2, sel goku. Bunk}'o-ku,Tok.vo I 12-001 l, Japan. Upon request the closing da e may be exteuded or e month.545 GE SER ET AL.,)'*4(3"dlymq¥ ettm"' paths (Fig. i, A-H-H'). The sampleo¥vn ¥veight vas assumed to be negligible. The effectivepressure p' ¥vas kept constant and equal to zero. Thesamples (diameter 40 mm and height - 9 mm) ¥vere placedG FEon a saturated high air entry ceramic disc and subjectedI,AH' 45to a positive air pressure by increasing the cell pressure,p'iSH,,,1,'1,1c¥vhile the pore ¥vater' pressure u,, remained unchanged.In this ¥vay, the capillary suction s ¥vas equal to theimposed air pressure u*. For each suction le¥'el, at leastfour samples lvere prepared. ¥ rhen the variation of the¥vater content tends to be negligible, the hydraulicDFrg. 1. H¥. dro-mechanical stress pati]s foltowed in this stud .equilibrium is reached (usually after 200 to 1000 hours ondrying paths and took significantly longer on ¥vettingpaths). Two samples vere used to determine the ¥vatercontent and the other t¥vo samples ¥vere used for volumemeasurement. To determine the volume change, theallo vs continuity in the modelling of the saturated andunsatur'ated states,samples ¥vere removed from the pressure plate and placedfor four hours in petroleum in order to fill the air pores.Because petroleum is hydrophobic, it can be assumedMATF.RIAL PRF.PARATIONThe soil examined in the research reported her'e is asandy silt (USCS classification: CL-lvlL) from the regionof Sion (S¥vitz,erland). The density of solid particles isp,=2.794 Kg/m3. The index properties of the soil are:TvL=25.40/0, }t'l'=16.70/0, Jp=8.70/0. The grain sizethat this procedure causes no ¥vater volume change in thesample (preliminary obser¥'ations sho¥ved no significanttotal volume variation at this stage). The total ¥*olume¥vas then measured using a picnometer (L.agny, 1996;Geiser', 1999). Details on this technique as ¥vell as theaccuracy values are available in Peron et al. (2006).For the t/'icl.1"ia! tests, the samples (50 mm in diameter,care ¥vas taken in sample preparation to ensure the100 mm in height) ¥vere fir'st consolidated to a gi¥'enconfining pressure, p', (Fig. 1, A-B) under' saturatedreproducibility of the initial state. The sample preparation procedure consisted of mixing a kno¥ "n mass of drysoil lvith de-aired and demineralised vater to an initialone-dimensional loadin_*," history of the sampie, as theconfining pressure ¥vas al¥vays higher than the equivalent¥vater content lv=1.5 Tt'L. This ¥vater content ¥vasassumed large enough to produce a slurry that has nomean effecti¥'e stress applied during one-dimensionalloading. When the consolidation ¥vas completed, samplesinternal structure. To remove air bubbles trapped in thevas ¥'ibrated. It ¥vas then placed inside a¥vere subjected to drying path (B-C) at constant "saturated effecti¥'e pressure" p' by increasing u. ¥vhile maintain-hermetica]ly closed box for '_4 hours. The initial voiding constant total pressure, p, and u,.. Finally, ¥vhenratio eo at the slurry state varied bet¥veen 0.9 and 1. Forthe triaxial tests the samples lvere prepared in a mouldingequilibrium ¥vas reached (usually after one to threetube (K{) condition) subject to a vertical consolidation･ Path C-D: isotropic compression. This path ¥vasdistribution is 80/0 clay, 7,-o/o silt and 200/0 sand. Specialslurry, the soilstress of 100 kPa. This led to samples having initlal ¥'oidratios bet¥ *een 0.69 and O.76, and water content bet¥veen24.80/0 and 27.60/0.TF.STING PROGRAMMF, A¥. 'D PROC_F.DURF,SThe saturated beha¥*iour of the Sion silt ¥vas firstcharacterised. A total of 15 tests (on 89 samples) in thepressure plate apparatus and 44 saturated and 30 unsatu-conditions. This ¥vas assumed to erase the pre¥'ious¥veeks), samples ¥vere taken through various str'ess paths:obtained by increasing the confining pressure p ¥vhilekeeping both u^ and u,,, constant (thus allolving freeflo¥v of air and ¥vater). Pressure ¥vas applied in stepsand ¥vas maintained until equilibrium ¥vas achie¥'ed(usually after several days)^･ Path C--E: fully drained shearing (see Table i). Thispath l 'as achie¥'ed by increasing the deviatoric stressq = (71 - (T3 ¥vhile keeping both t/* and u,, constant. Thepaths (see Fig. 1). In the follo ving, a con7p/'ession patllrate of shearin*' varied from 0.0012 to O.O018 mm/mln(see next paragraph for details). For most tests, unloading-reloading ¥vas performed at an axial strain ofrepresents a path obtained by applying a total externalel = '-o/o .rated triax.'ial tests ¥vere performed using different stressstress (T] or cT3 (axial or lateral stress, respecti¥'ely) atconstant suction and a dryiilg-tt'etting path correspondsto a path obtained internally by modifying either u*, thepore air pressure or u,., the pore ¥vater pressure. We ¥villlater define the mean total pressure, p= (1 /3)((TI +2(T3),the mean eff cti¥'e pressure, p' =p - uw' and the mean netpressure, p>:< = p - u*.A pressure p!ate apparatu,s ¥vas used to study the･ Path C-F: constant ¥vater content shearing (seeTable '-). In this case the shearing vas carried out under¥vater-undrained conditions ¥vhile maintaining a constant pore air pressure u=,, thus alio¥ving air drainage.The pore ¥vater pressur'e u,, ¥vas measured during theshearing so that the suction ¥vas kno¥vn. The appropriate shear rate ¥vas 0.06 mm/min for these tests.･ Path C-G: constant mean effective pressure. This ELASTO-PLASTICiTY OF U*NSATURATED SOiLSlable l,eTUnsaturated drained shear testss = u* (r{A-B# B-C* C-D or C-G*=Tesilic]1 lp'(kPa) (kPa) (kPa)400NS-D 1 400450503I OOi¥'S-D-' 450NS-D3ler 500ei n:llTS*()("'O)(O. )o.801 o 6615 66619.583o.72 1 o.645 oo3NS-D4 600o.666003o.788 o.64NS-D5NS-D6NS-D7NS-D96005004004ao2006005003003o.7 o.65NS-D I l600600600NS-D 1 2NS*D 1 3100lOO1 OO33f_600600500502SO1 OO333S.* iei:1 '(-)lOOl OO547o.70 o.66r' = :l I .616.877l I .4niLlslcr49O 25O IlO.283O 1733o 334802o 724o.74o 33o.25O_755 O 62O_712 0.67O.712 O 6320 46.6, 7o.08o 4714. l620291* see paths in Fig. 1_Table 2. Unsaturated constant water content shear tests (path A-B-C-measured using pressure-volume controllers. Very fe¥vF' in Fig. 1)ex'perimental data exist in the literature for this method.((T ),i!*Test A-B and C-E B-C and C-E l"j *'al (sla!)ejnil(-)(kPa) (Ol'a)*n tUNS-U1 1200O O 74 23 O30 O.735 2 1 . I O. 15200(kPa)NS-U2 200U2NS-U3300300NS-U4 300NS-U5 300U51000NS-U6 300NS-U7 300NS-U8 30060 O 71 20.8 O.3O 0. 7 1 22 OlOO O.718 18.6 O 33200 O 738 lO.6 O.66280 O 712 8.2 O_93O O.748 20.5 Ol OO O.7 1 2 1 7_6 O. 1200O 743 O.2280 O 712 7 6 O.289*3consisted of increasing the deviatoric stress vhilekeeping both the mean effective pressure and the suction constant.Cell pressure, air pressure andOur tests have shown that temperature and atmosphericpressure changes, as ¥ 'ell as air leaks, considerablyinfluence the results. An impro¥'ed configuration isintroduced here by usin_ : a rnixed ¥ *ater and air controller: the air ¥'olume is limited t.o that present inconnection tubes only. With this modification, thevolurne change of the sample can be satisfactorilymeasured. Ho¥ve¥'er, undetectable air leaks are stillpossible. The precision of such an improved system isestimated atO.?_･_ cm3 representing O. 1 IC/o of a conven-tional sample volume of 200 cm3.For the results presented in the follo¥ving, all triaxialcells l 'ere also calibrated to deduce the sample volumechange from the cell volume change (follo¥ving Head,1986), to allo¥ " a rough doubie check. For some tests,only the ¥vater volume changes A V,. and the initial andfinal degrees of' saturation (S* * ** and S* n , respectively)were determined. The value of tS*"*¥vas estimated fromthe hydric path results using the Tv-S* cur've and S* fwas'ater pressure ¥veremeasured using GDS pressure controllers. Suction to thesample ¥vas applied or measured using the axis-translation technique (f'or details see Fredlund and Rahardjo,1993), usin_g: high air-entry ceramic disc ¥vith air-entryvalues of 100, 300, 500 and 1500 kPa.measured at the end of the test. The volumetric changesVolulne ChangesMeasurement of volume changes in triaxial tests isindicates that the complete equalisation of' pore waterpressure throughout the sample is possible if the timeessentialrequired to fail the sample is set to:could then bevritten as A V=A V,. /S*.Shea/ RateThe shear rate for the drained unsaturated tests (pathC-E) was determined in accordance ¥vith the classicalGibson and Henkel method (1954). This approachvhen analysing the mechanical behaviour of asoil. In the case of a saturated test, volurne change is onlydue to vater exchange and can easily be measured ¥vith aburette or a pressure-volume controller. In the case ofunsaturated samples, however, sample voiume change istf= H21(llc.(1 - Ur)) (1)¥vheret : tirne required for' the sample to fail,H : half height of the sample (5055 mm),n: numerical factor depending upon the extent andrelated to both ¥ 'ater and air volurne changes and cannotbe measured so readily (Laloui et al., 2006). The air-¥vatervolume method has been used in this ¥vork for the volumelocation of the drainage boundary. For our tests since thechange measurement. In this approach, the volumetricwater drainage ¥vas only performed at the bottom of thechange of' the sample is obtained by simply adding the airsample via the high air value ceramic, ll = 0.7 ,and water ¥'olume changes. Both ¥'olume changes areUf: average degree of dissipation of t.he induced pore GEISER ET AL.,)'*48¥vater pressure at failure. CeneraHy O.95 is assumed to besuf lcient to find the soil intrinsic charac eristic uncierdrained conditions,c*: consolic.iation coefficient, calculated usin_"*. Head's(see Figs. )-(ci) and 2(e)). Note that, no hysteresis ispresent for the oven-dried samples. This result confirmsthat there is a behavioural difference bet¥veen o¥*en-driedrelationship (1986):cnature of the beha¥*iour that occurs, ¥vhen the samples are¥vetted after ha¥*in : been cirieci at a suction of 300 kPa= T9*)(2H)2/r,)o (2)t,)o corresponds to the time at ¥vhich the soil reaches 900/)of its consolidation for a :iven load. This ¥vas cleterminedfrom the isotropic consolidation path (C-D) at differentvalues of suction. By proceeding in this fashion, thee¥'olution of the soil permeability vith suction, thepermeability of the high air entry disc and the drainageboundary ¥vere already taken into account.samples and samples subjected to high suctions (¥vhereconsiderable hysteresis lvould be expected).Figure '-(b) sho¥vs the suction consolidation plane. Thescatter of the data is quite important, as an error of ,_01on t,he volume measur'ement implies an error of about 5010on the void ratio value. Starting: from initial void ratio of0.9-1.0 for s=0 (not sho¥vn in this logarithmic plane),the void ratio reduces to about O.7 for suction ¥'alues oflOOkPa. Due to the data scatter, the compressibilityFor example, for a consolidation stress of 400kPa,¥vith a high air entry disc of 500 kPa and a suction oflOOkPa yields: r90=72000s, T,;t)=0.848 and ,_H=110mm c, =0.14,5 mm2/s. According ro Eq. (1), t*"= (1 101index cannot be determined. Note that fitting a straightline through the triangle mar'ks (¥vetting path) yields aslope of around O.017. This ¥'alue can be compared lviththe unloading sarurated compressibility from isotropic,-)2/0.75 ･ O. 1425 ･ (1 - O.95) = 56608 Is * 1 57/1 . Assumin_ ,_compression (/t-* O.004 to O.OI 1).The shrinkage curve (Fig. '-(a)) confirms the obser¥*ations of other authors (Biarez, et al., 1988; Fleureau andthat failure occurs for an axial strain of almost 100/0, ashear rate of l.2 um/min has to be set. In the tests, therate ¥'aried bet¥veen I .'_ and I .8 /Imlmin depending on thepermeability of the high air entry ¥'alue ceramic and onthe applied stress and suction level These values are inIndatro, 1993).Vhen the ¥vater content decreases, thevoicl ratio first follows a line close to the saturation curve(i.e, e= ()'</y,.) It.') and then c.lecreases slight]y.agreement ¥vith those used by Ho and Fredlund (198,_)and later bv_ Delage et al. (1987).Isotl'opic Col77pressiol7 Tests ol7 U/7saturatec! Sclnlp!es(Path C-D)RESULTS AND INTERPRF.TATIONDlying- 'Vetting Bellavioul' (Pat/7s A -H-H' )Figure '_ sho¥vs the characterisation of silt in relation topaths A-H-H', performed under zero net pressure p=i=.The simultaneous measurement of vater contents andIsotropic compression tests lvere conducted by increasing the pressure in steps at pre-selected ¥*alues of suctionbet¥veen O and ?_80 kPa (Fig. 3(a)). Only ¥vater volumetricstrains 8., (defined as the variation of the water ¥*olumeA Vw over the initial total volume V , 8,,, =A V,, / VO) ¥vererecorded in this first series. All samples ¥vere preconsoli-¥'olume changes anci their representation, as suggested byBiarez et al, (1988), gi¥'es the complete state of the soil.dated under saturated conditions to an effecti¥*e meanpressure of 300 kPa and then dried to a given le¥'el ofThis representation includes: (a) the shrinkage curvesho¥ving the void ratio e as a function of ¥vater content It',suction (O, 100, 200 and 7_80 kPa) ¥vhile keeping p' (saturated effecti¥'e pressure), at 300 kPa, before starting the(b) the consolidation plane sho¥ving e as a function ofisotropic compression (path ABCD, Fig. 1). Thesuction (logarithmic scale), (c) the degree of saturation S*(logarithmic scale), and (e) the usual retention curvesho¥ving }t' as a function of the suction (logarithmicesrimated yield points (in a p' Iogarithmic representation)are identified by a change in slope. For the case of s= 100kPa, no clear yield point is detectable. Plotting the yieldpressure in terms of both p* (net pressure) and p' versusscale).suction allo ¥'s the examination of the variation of .vielciThree different symbols are represented: (i) the circlescorrespond to dryin_"* of the samples, ¥vith a slurry at anlocus (Fig. 3(b)). Up to the suction corresponding to theair-entry ¥'alue, one ¥vould expect the yield cur¥'e to beinitial ¥vater content of I .51'vL, (ii) the triangles representsamples first dried to a gi¥'en suction of 300 kPa and then¥*etted by decreasing the suction, (iii) the crosses cor-¥'ertical in the s-p' plot (because beha¥*iour under saturated conditions is governed solel_v by p-u, ) and inclined at45' from the vertical in the s p=i= plot (p= =p'-s). There isrespond to samples first dried in the o¥'en at 105'C anda simple mapping bet veen the tlvo curves separated bythen ¥vetted by decreasin_a* the suction.the magnitucie of suction applied.Isotropic consolidation tests gi¥'e information on theas a function of w, (d) S* as a function of suctlonFi ure 2 demonstrates that this soil remains almostsaturated on a drying path belo¥v the air-entry suction, s*,vhich is approximately 50 kPa (see Fi :. '_(c) and )_(d)).Further increasing: the suction led to a sig:nificant reduc-tion in S*, though such reduction rapers off above a suction value of 400 kPa (Fig. 2(d)). Note that the relation-variation of the compressibility ¥vith suction. ),' is definedas the elasto-plastic slope in the In (p') versus e plane and).=:< as the corresponding compressibility in a In (p*)versus e plane. The ¥'alues are summarised in Fig. 4 forthe Sion silt and also for other soils frorrl the literature:ship bet¥veen ¥¥*ater content and degree of saturation is theJossigny silt (Vicol, 1990), Trois-Rivi res silt (l¥,Iaatouksame in all three cases (Fi . ?(c)).et al., 1995), kaolin (¥¥rheeler and Sivakumar, 1995 andThe experimental results also re¥*eal the hystereticSivakumar, 1 993), Steerbeek silt (Leclercq and rlELASTO-PLASTICITY OF UNSATURATED SOILS5- C).1i(b)a(L)d' O 8 :08CQLoA A:,_>Al06402030A : i-Aia06o1011_(c)1 041 ooo1 oo¥ (d)Air entry(/)coCQ0505 -CQ(1)o(D(:)a)(DOo40102030Water content, w [o/o]oo1o1 oo I oao I oooo40(e)30 - ¥¥Drying path (w jt = I .5 wL)p ( jw jtWetting ath= dried)^ Wetting path(initia[ly dried at 300 kPa)c:(D- 20c:ooL(D(Is 10 -:a1i O I oooo1 oo1 oooSuction, s [kPa]Pig. 2.Behaviour of the Sion silt uDder drying 2lnd wetting paths (pressure plate)Velbrugge, 1985), kaolln (Matyas and Radhakrishna,1968). For se¥'eral of the soils sho¥¥'n in Fig. 4(b) an initialconfining pressure of (7 =600 kPa and at different suction levels (s=0, 50, 100, '_OO and 280 kPa). The initialincrease of ),* at low suction value is noticed, follo¥ved byrnodulus and the maximum deviatoric stress tend toa reduction.gradually increase ¥vith increasing suction. In saturatedsoils, suction and p' (under isotropic loading conditions)D/'ained Shear Tests (Pat/Is C-E)Figure 5 sho¥vs the stress and strain data for triaxialdrained shear tests at a constant "saturated effective"have sirnilar' effects on the volume cham e and shearstrength (Laloui et al., 2005). Each sample sholved a peakde¥'iatoric stress ¥vhich ¥vas then follo¥ved by a gradual CJEISER ET AL55 oo06*(a)[> (oe(aj/e )/>.C:_CL'U)o/ /E 02o:5O-HCsat (s=0kPa)H HCNSI (s = 100 kPa)3e)400300600l 'I/'"Ii '/.... .-r..---/ "-- e'lHCNS3 (s = 280 kPa)4/d :..-"-'"'3-HCNS2 (s = 200 kPa)'(S/B . !/ ;' ' _ '*CLE>/2'e)5/O800 Iooo2CO 600800400oSaturated eftective mean pressure, p' [kPa]Suction, s [kPa]03300(b)p'>' 02._:(u)(,)e)oo 10a :sHF Kaolin (Wheeler et al ')E- Steerbeek silt ',/ r' - ¥-y- Kaolin (Matyas et al )/ >;"U)i(/EO O.1 Rl __1___"_'l eO(Ds o:Cli:'¥(b)"{3-' Jossigny silt*$- Trois-R'v'eTes silt*(p*CL 200 -- S'on silt_' :: : ' **s-::L A_'o600500400preconsolidation pressure [kPaJFig. 3. Unsaturatcti isotropic tests: (a) experimental resu!ts and)･ielding points and (b) evolution of the preconsolidution pressurewith suctionreduction to¥vards critical state. Visual obser¥'ation of thesamples has sho¥vn that the decreasing stress after thepeak coincides ¥vith the development of shear bands. Thetest at s= '_80 kPa (corresponding to S,* 300/0) PresentedO200 600400Suction, s [kPa]800Fig. 4. Conlpressibilit _' as a function of sucrion in (a) a saturatedeffective stress approach and (b) a net mean stress approach fordiffercnt soilspressure (T3: '-OO, 300 and 1000 kPa. The rele¥'ant stressstrain relationships are sho¥vn in Fig. 7.Shear bands appear before the peak in deviatoric stresswhen the ratio between the initial suction s and ((7 )i i* isa dlfferent behaviour, in ¥vhich shear bands started tolarge (typically, for Sion siit, ¥vhen the ratio s/((T )i i, isdevelop early in the test and the stren_._"th could not bemobilized.Figure 5(b) illustrates the ¥'olumetric strain, in ¥vhichthe samples sho¥ved compression ¥vhich lvas follo¥ved byover 0.45). For ratios do¥vn to O.3, Iocalisation can stillappear, but this occurs after the peak. For ratios smallerthan 0.3 (Fig. 7(c)), no significant suction-induced effectsdilation as the shearing progressed. The amount ofnegligible in comparison to the compression effects.The relationship bet¥veen 81 and uw (and s), representeddilation increased ¥vith increasing suction.Drained shear tests at the constant net confinin9:pressure of (T =400 kPa and at different suction levels(s=0, 50, 100 and 200 kPa) are plotted in Fig. 6. As inthe previous tests, the initial modulus and the maximumde¥'iatoric stress gradually increase ¥vith suction^ Thiscan be observed implying that the drying effects arein Fig. 7, mainly shows that the built up pore-¥vaterpressure is smaller for unsaturated than for saturatedsamples, as the fluid in the unsaturated case is a mixtureof air and ¥vater and thus is more compressible.behaviour is similar to that observed in saturatedE!astic Behaviourcondition for tests performed under increasing confiningpressure. Ho¥vever, in this case even for a large value ofaxial strain, q never reaches a unique residual value.In order to describe the elastic behaviour of Sion silt,an unloadin*' path was usually performed at about 20/0 ofaxial strain during the shearing tests. T¥vo different "elas-tic" moduli are defined: (i) the secant modulus E* definedCor7st(?/7t ,Vater Coi7tent Shear Tests (Paths C-F)In this series of tests, samples ¥vere consolidated tothree different ¥*alues of saturated effecti¥*e confinementas the slope in the el - q graph at a given axial strain 8i of0.50/0 and (ii) the unloading modulus E defined as theaverage slope in the 81-q plane durin*' unloading. lELASTO-PLASTICiTY OF UNSATURATED SOILS1 5001 60a(a)CQCUi- 1200- r-u)u)a)/ ¥ _-r *.lu)4Lc'):- ll'l' } -u)(D(13 = 600 kPa (s = 50 kPa)(13= 600 kPa (s= 100 kPa)400 ･*?-' - ( 3 = 600 kPa (s = 200 kPa)C-i -･cF3 = 600 kPa (s = 280 kPa)ooo"::oas 500' Satvrated (s = O kPa)H ' NSD2 (s = 50 kPa)- NSD3ter (s = 100 kPa)-- NSD5 (s = 200 kPa)'5; - k!･;(1)a1 5 255 10e-* -- - ' __ll+---( 3 = 600 kPa (s = O)o 'oICOO " /-i-co 800oas//CT"/CLD_551o205 Io 15OAxial strain, 81 [o/o]2aAxia[ strain, 81 [o/,]-1o(b)'** "- O>KOOes--s::- '1"c(Q*co++oCQ2Oe) 3E*C::(b)r;$> 1u)¥¥*oot2¥.eL- ______( ----t. ; ---- ...¥ ___-(3r-"- Ie- -'L¥ " x 14¥E4>'_"> / "$ _¥ *¥6¥(1)+'(1;55 10 20 25ric strain 8*10oAxiai strain, 81 [o/o]Fig. 5. Drained shearing tests at an effective confining pressure (T of600 kPa and at different suction levels (s=0, 50, 100, 200 and 280kPa): Ax'iat strain 81 versus (a) deviatoric stress q and (b) volumet-¥ *¥¥e8i5o(',,¥*75x-20Axial strain, 81 [o/o]Frg. 6. Drained shearing tests at a net confining pressure a3* of 400kPa and at different suction levels (s=0, 50, 100 and 200 kPa):Axial strain 51 versu s (a) tlevialoric stress r/ and (b) ,vater volumetric strain 8***Figure 8 sho¥¥'s these rnoduli as a function of suction atcase is represented by the critical state line at saturationels of "saturated effectrve" , p' , and net mean(CSL), as the peak strength and the strength at criticalstress, p*. As ¥vould be expected, suction increases thestate are close for normally consolidated tests on saturat-stiffenin*' of the soil at a gi¥'en confinin*" stress a or cT .ed samples. Lines are plotted through the peak stren*'thpoints determined at the same suction level. The presentdata on the Sion silt sho¥v that intercept a (a rneasure ofdifferent leSimilar observations ¥vere made by Fleureau (1992), Cui(1993) and Lagny (1996).cohesion) increases ¥vith suction, Ivhile the slope (/1p**k)Peak Strengthremains almost constant.Peak strength qp**k obtained from constant ¥vater content tests are plotted as function of suction in Fig. 9. Itcp**can be seen that qp**k increases with suction for lolv valuesof effecti¥'e confining pressure ((7 i i* = 200 kPa) but slight-figure is based on a surnmary proposed by Delage andGraham (1995), the data on Al-Agoza clay (Mashhourly decreases for high values of effective confining pressureet al., 1995) and our o 'n resu[ts. No clear trend can beobser¥'ed for the variation of the friction angle cp*.k. Forthe silts, it appears that cp**k decreases ¥vith suction,particula '1y for Trois-Rivi res silt, which is a relativelycollapsible soil. In comparison, Sion silt is not collapsibleand cp**k is almost constant. The cohesion as a functionof suction (Fig. 11(b)) is similar for all the soils (exceptTrois-Rivieres silt), Ieading to some simplifications in themodelling of shear strength of unsaturated soils.When the peak shear strength points are plotted, in a(cr3i*it=1000 kPa). (T j*,j*=300 kPa represents an inter-mediate state. In Fig. 9(b), the results are scaled bydividing qp*"k by the effective confining pressure. Notethat a rnaximum value of qp*<*klcr i it = '3' I is found close toa suction value equivalent to the air-entry ¥'alue (s*=50kPa).The points representing the peak deviatoric stress versus the corresponding net mean pressure p* are plotted inFig. 10 for tests on unsaturated samples. The saturatedFigure 1 1(a) sho¥vs, as a comparison, the f'riction angleas a function of suction for diff;erent soils. This 552GEISER ET ALLo(¥,o(1CQorQcLo!': iOLlsa ao-aLr- aeoo::;C')'l',(c¥{c¥lc¥1I il:a,CL0c')(!)u)cco r¥eou):) :):)Lr)(!);c:OCe,* ;-t!) ;'O:;CLU)cl)(1):)Z fzzf･ , .. ,,{=0C:CQu)-OT-75o><<"･:1-tr)¥a__. _.: -faaooo oo l!)ao 'oaalr)C tc:]ar ' A-* 'aLoooc:)oa ooLooc,Lr)C ( J-- Lr)c¥Lr)c¥::)V)z:)(1)Z(1)Zr)[ed ] "n 'eJnsseJd-ieseN¥ eJOdLr)c¥oc:[E?d ] S 'UO!;onS([ed ] b 'SSeJ;S O!JOle!Aear):)OCQCLO,( 'o_:x 'xocoao c lCu)u)Q)F(:),- oOLc J2(Qc:0f-tOro¥o1'Q, ;LOa::CLCl)"'C:;(1)cl'as' :oo oCLoU)CQt[:')c!)f', ,:: ,d<_ (:) _I **_ t=_ oo o a o oUDtf)C[ 3d ] b SSeJ;S OVOIE;lAea [8d ] s uol ons,[ d ] n 'eJnsse.Jd-Je; /V¥ eJOdac¥11 ro_o_:J-ooll !1 -- Lr) __ r)(o:):)oco(O:) z z",,)Z if 'a)Q,- tr)Lr)o- a) !- 0Q):;s-::' :e e- o 'l::a<C. .='ooo o o oce o [edC ] S a'uo!}onSoc¥Ct[ed ] b sseJ;S OiJO elAea!***[ed ] n 'eJnsseJd-Je e,V¥ ejOdFig. 7.Constant watcr content shearing tcsts: (a) (cT ) n t = 200 kPa, (b) ((T!) =300 kPa and (c) ((T ) = 1000 kPa' ni* n 553EL．ASTO−PLASTICITY OF UNS．ATURAT狂D SOILS2500200UnめadingmodulusE s司80kPa ！㊥ ノ㌔ ！■，o 20GO” ！／150住而首儀襲国φ田σ筆00SecantmodulusE（ε＝05％）、 き で U甲｝辱』一P＿…／1一⑦；＝＝＝醐88臨“・D”■響’”餅コ℃o稠18撃：； ゆ・埴． 一＠一一σ『載600kPa50 ’㎜壕 ・・直1｝6岬甲・◆ 一一●一一σ｝＝400kPa 匪3言1 一・慨一σ’＝500kPaののΦ s瓢200kPa ノ’ ’／1500・一 ㊧ん τ1灘13 ノろ』 畔 ル／ ／諺のQ 1…1 ！髪＼C＄Lats＝。kPao ノ彰 S雷5ひ55kPa讐ノニ☆言講避c口）Φo rトP☆＝400kPa。a／00 50o250 300100 150 200Suction，slkPalFiσ8．2000500 1000 1500Net rnean pressure，P★［kPaIE盟9stic mod面as a function ofsucIion for Sion si賑Fig．10． Pe貸k s重reほgIh for di『ferent suαions in theρ牝17p鳳ane（individり 副valuesofsuctionaregive賎inFig、12）2500（a〉團 60「一 ↑・2000圏囹3iRit＝200kPa十σ鵬 3init襯300kPa”毎一げα． 1500一邑 焉 の 攣 Madridciayedsand層一「緬幅Guadalix cIay『冨・唖J。sslgnysilt （a） 1 ×．一50一Φ1⑳に．・一。一掌rois−Rivi合res sllt、 、・一・響・一AトA9Qza ciay“Sionsilt㌧骨σ甲 3init 篇屡OOO kPaσ億1000＝｝ 、o 、8ε 1一印ゆ砥500革 爾鯉、◎塞30K00 50100 150 200250 300、 卜 』 甲 ■騨 』ゾ ド 2010Suction，s lkPa】500 10001500Suction，s lkPal35500（b）（b） ｝・3 400− 1 三の 2．5−0◆髭3・・∋ 1b 闘 雷蕊 ・ 。’國 ユσ 2翻O 、 ，の 一 ，’。1・・1〆§20叶②！メ樗⑧1，5一一◆1 諺ソ0 50歪OG 150 200250 300Suction，s lkPa】 0齢一0500 10001500Suction，＄【kPa】Fig。9．Pe段kdeviatorics亘ressasaf照cIionofsuction（cons重anIwater con｛en韮重esIS）K9．11．罪「riαlonangle（幻andcohesion（b）a重peakstreP9芝hversus suc額o臓（netmeanstressinterpre雌io臓）グー（1p1＆ne（Fig．12），the slope connecting them，ηp，、k，canQnce more be assumed to be coast＆nt。The cohesion alsoC1・i！iごα1S！α！（∼increases（a1豆thepoints wit紅s〉O ares圭芝uated on or＆bove While signlncαnt rese＆rch e貸brts have addressed thethe cSL line at s鱗o）．Qu＆n重itatively the effect is 正essre1εttionship between s難ear strength＆nd suc宅ion，only apronounced重han in theρ＊一（1plane．few have exam量ned｛he e9奄ct of suction o11critical sta重e（e、g。Tol119901Wheeler and Sivakumar，1995；Maatouket al．，1995）．The tests on saturaξed samp正es are p至otted in GEISER ET AL.554Fig. 13 for the Sion silt: the Critical State Line (CSL,) hasa slope of M= I .3 ¥ 'ith a correlation coefficient r of O.99.A11 the points corresponding to unsaturated samples(solid dots) are close to the CSL, Iine. The scattering of theexperimental points is similar to that observed in saturated conditions. This ¥ 'ould mean that the critical state isuniquely defined in a p' interpretation for the consideredle¥'els of suction. Taibi (1994) has obtained similar resultsfor unsaturated soils,Figure 14 sho¥vs the critical state points in a p* interpretation, ¥vhere a unique line can no longer descrlbe theCSL. The results seem to be similar to those described byMaatouk et al. (1995), ¥vith a decreasing slope M and anincreasing cohesion ¥vith suction, respectively.25001 23Yie!c!ing13(Q20ao -s = O kPa1500 --100 eO_x200 n"' =CTa,(1)3iour. Fe¥v experimental r'esults are available in theliterature for the determination of yield locus in the case50 50e)c,,o laoo oCQ>e)OThe kno¥vledge of the shape of the yield locus and its¥'ariation ¥vith suction is an important aspect of beha¥'-i aoof unsaturated soils (Zakaria et al., 1995; Cui andDela>"e, 1996; Geiser et al., 1998). The procedure used todetermine the yield surface is as follo¥vs. The samples arefirst loaded isotropically ¥vith a consolidation pressurep = 400, respectively 600 kPa. They are then unloaded todiff rent values of confining pressures prior to shearin*".1 OO7127 .83 )soo -o55o I ooo50D5002000Saturated effective mean stress, p' [kPa]The defined yield limit then corresponds to the highestvalue of the mean effective stress (400, respectively 600kPa) and a specific ¥'oid ratio. The unloadin*' steps movedthe stress state inside this yield surface. Since the stressPeak strength for different stlctions in the p'-q planeFig. 12.250030ao: Norma]ly consolid drained (s=0 kPa): Normaily consol undrained (s=0 kPa)Overconsolidated drained (s=0 kPa)25aoCUe Unsaturaied samples (s>0 kPa)-cr 2aooe) 15aoe>e)C 50a -e' 501 OO71 l'CSL at s = O kPa1 oo,^ep'" e e 83500*e551s = 100 kPa4ooooooO1 50aCritical state line for saturated anti unsoturated statesFig. 14.300225ol1 oooOO _O 1_'vv _O 210¥*tl-o 350}Oo 2 4 i;0 (yo 108Fig. 15.50020aoCritical state line for different suctions in the p *q planeO20CQCL ( 15cr500Net mean pressure, p [kPa]Effective mean stTess, p' [kPa]ril:F. 13.i oo100oaoO*23ioo. p;'oOtQ>e)CUOM=1 32aoe ' i'v)u)oo 10ao -15ao -u)e)M=13c,)13cl)eci2aoofCLicyCri 'oal State Line at s=0 kP lCL-o 41 oo, =i150200p (kPa)ldentification of the yielti point in the case of a triaxial tcst[illlll FLAS'TO-PLASTI(,TY OF UNSATURATED SOILS6co5ao- - s = O kPc p* =40akP40a -cr300 -_}D06p ¥D08scocL! ( 200 -s=iOOkPacr 40a' s = 280 kPaDO1cTD02D018pDOIO100 rD019¥*7; 300 ool i 200-NSD13l(O l'a100 -D09/NSD4>¥¥¥ ¥NSDi iNCNS12,7 __O200400Saturated effective rnean stress, p' [kPa]1*1l.bo400200NSD9e)o014p¥oNSD{;, A s=200kPacl)- D012pi) ¥ ¥lD¥017oo 6 ¥¥rNSDi2¥u)l D07DO 5pv;C4CSL at s = O kPa;¥:CSL at s = O kP500 e s=50kPao p' = 600 kPafOoo600p' [kPa], dsP800Fig. 17. Yield points under unsaturated conditions in an saturatedeffective stress representation for a saturated preconsolidationpressure of 600 kPaFig. 16. Stress paths, yield points and plastic strain vector incrementsunder sa$urated conditionspoint ¥vas ¥vithin the yield surface, initial strains due to apaths, it ¥vas found that the behaviour is different interms of volume variation ¥vhen the suction increasesabove the air entry value. Isotropic compression tests atshear stress ¥vould be mainly elastic, until the stress pointconstant suction revealed that the preconsolidationreached the yield surface, and after that it becarne plastic.pressure increases ¥vith the suction in the "effectivestress" approach. This increase is not as pronouncedrather limited in the net stress approach. Frorn thetriaxial shear test, an increase of stiffness and peakstrength ¥vith suction at constant mean effective or netThe combination of pre-yield and post-yield linearitypermits bilinear extrapolation techniques for identifyingthe yield point (Graham et al., 1982). Yield points aredetermined from a stress-strain criterion by using variousprocedures, all consisting of identifying a change of slopepressures is only sholvn for lo¥v confining stress. Suctionin the stress-strain planes (Fig. 15).Figure 16 sho¥vs the yield points in saturated conditionsappears to ha¥'e an effect similar to that of mechanicaloverconsolidation vhen representing the results in therepresented in the p'-q plane, together with the plasticeffective stress plane. Softening appears post-peak for thestrain increments at the onset of yielding. In this figure,cases of high suction or lolv net mean pressure. In thethe yield locus corresponding to t¥ 'o consolidationpressures are dra vn by interpolation. The behaviourp'-q plane, the critical state line is shol 'n to be independ-vould clearly be represented by a non-associated flo¥vent of suction (in the studied range of stress and suction);this is not the case in the p*-q plane. Finally, it is sho¥vnthat the yield locus increased ¥vith suction.rule.Figure 17 sho¥vs the effect of suction on the yield sur-face at a saturated preconsolidation pressure pof 600kPa. Although a complete determination of the yieldlocus is not possible based on so felv points (includingdata points for isotropic loading q= O), the general trendof suction hardening is clearly visible (see continuouslines). The effect of suction can be seen as a result of asuction-induced preconsolidation. Similar results wereobtained for compacted unsatur'ated soils (Zakaria et al.,1995; Cui and Delage, 1996). Similar r'esults are observedin a p* representatlon (Geiser, 1999).CONCLUSIONSA remoulded silt has been subjected to various loadingpaths, and the interpretation of the r'esulting datacontribute to our understanding of the behaviour of'unsaturated soils,The drying-¥vetting tests confirmed the hystereticnature of the behaviour. Under more general loadingACKNOWLEDGEME_NTSThis ¥vork ¥vas funded by the Swiss NSF, grantGruaz'_1-42360.94. The authors gratefully thank lvlr. G.for his help in performing the laboratory testing.REFERENCESl) Alonso, E. E., Gens, A. and Josa, A. (1990): A consriiu ive modelfor partially sa urated soils, Gdotecllnique, 40(3), 405-430,2) Biarez, J_. Fleureau, ,J. N'I., Zerhouni, N,1. I. and Soepandji, B. S,(1988): Variarions de volumes des sols argileux lors de cycles dedrainage-humidification. Revue F,'an a!se c!e Gdotechilique, 41,637 13) Blight, G_ E(1966): Strength characteristics of dessicated cla_¥*s,ASCE J. Soil N'Iech. Fourld. Engrg. Div., 92, 19-37.4) Croney, D. and (,*oieman, J. D. (1954): Soil structure in relarion tosoil suc ion, J, Soi! Science, 5, 75-84.5) C ui, Y. J (1993): Etude du comportement d'un limon compactnon satur et de sa modelisation dans un cadre elasto-plastique,PhD Thesis, Ecole nationale des Poms et Chauss6es, Paris 556GEISER ET、AL、6）Cui，Y．，LandDelage，P，（1996）IY1eidingandplasτlcbehaviourof a鷺unsa【urated co【npacτed silt，（360∼εc／7’∼i（1”〔∼，46（2），291−311．7）Delage，P、and Graham，J．（1995）＝Mec｝1anlcal behaviour of 五’1913．，19（3），2H−24L25）Kohgo，Y。，Naka！lo，M、andMiyazak1，τ，（玉993）二Theore庶aI aspec【sofcons【imtive1nodel1ngforunsaIし星rateδso1ls，50’Z∫αnゴ unsaturated so澱s：Undersζanding t鮭e behav1our of unsaturated soils Fo朋ゴα1’01∼∫，33（4），49−63． requires concep田al models，Pro‘。1n∫．Co11∫ U1∼，∫碗’”α’ωSo礁，26）Lagny，C．（1996）＝Comporteme賊 mεca自ique des sols 且ns sous Par1s，1223−1256． fortesco離a醸esαfortespressionsn6gat1ves，P1のr1∼θ5’∫．狂cole8）Deiage，P．，Suraj de S1lva，G．P．R．and de Laure，狂．（三987）：Un Cenτrale Parls、 nouvei apPare“甘iaxiai pour les sols【10n sat柱r（｝sラP／10ご．9∼1r E∼〃「ト．27）Laloui，L．and Nuth，！〉i、（2005）：Anin［roduc“on toIhecoほsti篭utive Co1ザ5M圧，Dublin，1，26−28． modeHingofuns＆turaτedsoils，REOC‘Eε〃’，ノ．C’v’1だ119’11θθ1”’119ノ．9〉 Escario，V．and Saez，J．（1986）：The shear s芝rengt為of par雛y satu− 9（5−6），651−670、28）Laloui，L，，P6ron，｝｛．，Gelser，F、，Rifa’1，A．andVu騰eξ，L（2006）： ra｛edsolls，Gゴo’θc／11殉肥，36（3），453−456．10） F玉eureau，」．r〉1，（1992）＝Conヒr玉butioa a1ラ（箕ude eτa la mod（｝蕪sat玉on 、へdvances ln volume measllremen芝 in u：｝satura吃ed 毛riaxial tes！s， des materiaux polyPllasiques，ノノ‘7わ’〃∼‘π’0117γ∼θ5’∫，Ecole Ce【貰rale So’Z5αη（ノFoε〃∼4α”017∫，46（3），34玉一350． Paris．29）Leclercq，J．a員dVerbmgge，J．C．（1985）：Prop説t6sg60m6can1queslI）Fleureau，、L M．and lndaゴto（1993）l Comporteme郎du疑mQn de Jossignyremanl6sQumlsaunepressioninterstitiellen6ga［ive，…2〉 Fleureau，、1、NI．，K鮭eirbek−Saoud，S．，Soemi芒ro，R，andτa玉bi，S。 （1993）： Bellav玉or of c！ayed so甜s on dry1ng−wetting Pa芭hs， Cαη．豆3） F玉eureau，J．KI．，K｝｝eirbek−Saoud and Taibi，S、（1995）＝Exper霊men− talaspectsandmodelllngoω1ebe無avlourofso1isw1由anegative14） Fredlu職d， D． G． a簸d レlorgerlsτern， N． R． （三977）＝ Stress s［ate variablesfo田nsaturatedsoils，擁5C五一G万，447−465． Variatio頁ofしmsa田ratedsollshearstrengthparameterswi出suc− t1on，P1’oご，1’π，Con∫Uη5ρ’”昭’θゴSo’Z5，Par1s，1487−1493． cぬaracIeristlcsofpartiallysa田raτedsolls，04αθぐh17ゆθ，茎8（4）， 432−448．三5）Fredh鵬d，D．G．arld Rahard30，H．（1993）l So’1A4e‘hρ11’c5弄011 U1∼5θ∼ど〃窟θαF So〃5，Jolm WiIey and Sons．（1978）： Thesllearstreng由ofu職samratedsoils，Cθπ．0θαθぐ11．ノ．，15，andLaloul，L．（2006〉：A鷺improvedvolume measurementindetermi漁gsoilwaterre【entioncし星rve，0θ01θc1∼．33）Peron，H，，｝｛uecke1，T， 琵5’．／，，20（1），34）Sivakumar，V．（1993）＝Ac蹴icalsta【eframeworkforuIlsaturated soils，PhZ）7γ1θ5’∫，Un玉versi【y of Shef盗eld． 313−321．i7）Gelser，F．（玉999）：Comporteme猷繭can即ed’unllmonnon6ωde exp6rimentale et mod61isatio厳co“s虚田i、・e，PhOSwissFederaIlns【iτuteofτechnology，Lausan鷺e．F，，Laloul，L a賎d Vulllet，L （1998）：Yield1ng of a18）Ge1ser， 45（3），465−477．32）M飢yas，E、L．and Radhakrishna，H．S．（1968）：Vo1ロme change pressure，Pヂoc、∫1π、Coη∫Uη，∫α1ま〃門α∼θゴ50’Z∫，Paris，57−62， τ11θ5’∫， cr玉嫉ca王sτa葛e of a co賛apsible unsaturated si1［y soil．Gゴo∫θc／111’‘7∼’θ，31） 汽4ashhour，1〉L 親1．，lbrah1mラ汽’1．L aRd EトEmanラ魏L 氏・L （1995）： Gθ01θ‘1∼、／、，30，287−296、 saエur61 so1，Facu116des Scie昆ces Agro…10m1ques Gembloぴx、30）Maa芝ouk，A．，Leroue員，S．and la Rochelle，P．（1995）：Yielding and Rεv置’θだノ「ロ’∼9傭θゴθGゴαθchlliσ‘’θ，62，59−66．16）Fred1闘d，D．G．，Morge“stem，N．R．and W1dger，R、A， des sols【10【｝satur6s、Compteイe【玉dus dロCo玉loqし【e su「Ie t「avail du35） Soii∼loisτure Equ圭pmen覧Corporat1oほ（1985）：Coτnmercial pub11ca一 【io職s，P．O．Box30025，Sanτa Barbara，CA，USA、36）Taib1，S．（1994）：Comportementm6caniqueed1》・draul1quedessols parI1e！lemerlt satur6sラPhZ）71hε∫’∫，Ecole Centrale Paris． remoulded sandy s玉1【ln saturaτed and u昆saζurated sIates， P’・00 211ゴ37）To註，D．G．（玉990）：Aframeworkfor糖nsaturatedsoilbehaviour， ∫’π．Co／4．Un5θ’∼！1’θ’留So1Z∫， 1，Beijing，54−59． Gだo’（∼ch171（1∼’θ，40（1），31−44・F、， Lalo虚， L・and Vu1韮et， L・（2000）：On the volume38）Vicol，T、（1990）l Comportemem bydraulique et m6canique d’un 加unsaturated仁r1axial teSt，U’15α’∼〃’α’θ4So〃5、ブoノ貯 measureme数t limonnonsatur6．ApPllcatio自alamod611s煎on，P1∼07hθ5Z5，Ecole19〉 Geiser， ．451α（eds． by Rahardjo，ToH and Leo119），Balkema，669−674．20） Gibson，R． E。andHe臓kei，D．，L（1954）＝ln創uenceofdurationof ξesτs a【COnStant rate Of Stra1n On meaSUred drained Sτren9由． Na“onale des Ponts et Cl玉a越ss6es，Paris．39） V▽lleeier，S。」．（1996）：王nc1駄sionofspec1員cwatervolume、vid擁n an elasto−plasticmodelforunsaτurate〔isoi1，Cσ11．Gθo’θごh．ノ、，33， G40’θch吻∼擢，4（1），6−15． 42−57．2玉）Gra恥am，」、，Pinkney，R，B．，Lew，K．V，a鷺d Tra玉nor，P．G、S、 （1982）；Curve踊ngandlaboratorydata，Cαη．Gθo’θ‘17．ノ，，19，40〉 、Vheeler，S．」、andS1vakumar，V．（1995）：An e！asto−plas【1ccri篭ical 201−205．41） Zakar玉a，L、Vhee玉er，S。J．andAnderson，∼V．F．（玉995）：Yieldingof22）Head，K．H．（1986）lA4α17置’θ10ゾ50〃五αウoノ“θ’01アrε5r∫11g，Pentec｝藁 u簸sa芝ura葛ed compacted kaoli員．Pヂ Press． 223−228、23）Ho，D，Y．FandFredlund，D「G、（1982），Amu1τistagetr1axialtes〔 forunsaヒuraIedsolls，0θ01ech、ル5’．ノ．，5（1），18−25．42｝Zerllouni，M．L（199玉）：R61edelapressionl瓢ers面ellen6gative dans le comporξeme蹴des sols−ApPllcaほon aux ro臓es。ρ1の24） Karube，D．and Kawa1，K、（200玉）＝The role of pore water玉自tile 7「hθ5Z5，Ecoie Centrale Par玉s。 mecha虚cal b曲aviorofunsatura［ed soi蓋s，Gθo’θご1r，Gθ0109． state framework for unsa［urated soi1，Gごo’θcノ〃1’（1∼！θ，45（1），35−53．o‘、 Uη∫01∼〃η’θゴSo’Z∫，Paris， | ||||
| ログイン | |||||
| タイトル | seepage Failure Mechanism of The Gouhou Rockfill Dam during Reservoir Water Infiltration | ||||
| 著者 | L. M. Zhang・Q. Chen | ||||
| 出版 | soils and Foundations | ||||
| ページ | 557〜568 | 発行 | 2006/10/15 | 文書ID | 20940 |
| 内容 | 表示 SOILS AND FOUND¥TiONS¥*ol46, N'o )* 557-56s, Oct. 2006Japanese C; eotechnical Socie }SEEPAGE FAILURE MECHANISM OF THE GOUHOU ROCKFILLDURING RESERVOIR WATER INFILTRATIONL. M. ZHANGi) and QUNDAMCHEN ii)ABSTRAC.TThe catastrophic failure of the 71-m high Gouhou concrete-f'aced rockfill dam in Qinghai Pro¥'ince, China, hasdra¥vn many studies. This paper aims at providing ne¥v understanding on the modes and process of this failure, whichcould be applicable to similar dam failures. The geometrical and hydraulic criteria for internal erosion in rockfillmaterials are assessed. Unsaturated-saturated seepage theory is used to analyze the Gouhou dam since the rockfillmaterials of the dam ¥vere unsaturated before reser¥'oir ¥vater infiltration. The ¥vater infiltration is simulated by severalcases of transient seepage analyses. According to the study, a perched-water table formed in the dam ¥vhen thereservoir lvater infiltrated into the rockfill from the top of the concrete face. The perched water spread nearlyhorizontally along stratifications in the rockfill and exited from the downstream slope at a hi**h elevation as observedbef'ore the breach of the dam. The hydraulic gradient of the perched ¥vater table ¥'as the highest near the wetting front,vhich might pro¥'ide necessary hydr'aulic conditions to trigger internal erosion and piping failure. Based on thegeometrical conditions of the rockfill materials and the hydraulic conditions in the dam, the susceptibility of internalerosion is e¥'aluated and the possible modes and process of seepage failure of the dam are described.Ke _'vords: intemal erosion, piping, rockfill dam, seepage analysis unsaturated soils, water infiltration, vetting front(IGC: D6/E6/E7)the Gouhou dam since the rockfill materials of the damI_r JTRODUCTION¥vere at an unsaturated condition bef'ore reservoir fillin9:On 27 August 1993, a catastrophic failure of the 71-mThe lvater infiltration process and associated hydraulicconditions ar'e simulated by several cases of transientseepage analyses. Based on the geometrical conditions ofthe rockfill materials and the hydraulic conditions in thedam, the susceptibility of internal erosion is evaluatedand the possible modes and process of the seepage failureof the dam are described.high Gouhou rockfill dam occurred in Gonghe County,Qinghai Pro¥'ince, China during the first high reservoirle¥'el operation of the dam. The dam is one of manyrockfill dams that failed due to seepage problems duringreservoir fillin_ :. According to the statistics (Fell et al.,1992; ICOLD, 199) ; Foster et al., ,_002), other thanovertopping, internal erosion and piping are the primarycauses of failures and major hazards in embankmentdams. Many dam failures due to erosion have beenreported, e.g., Teton and Fontenelle dams (USCOLD,1988). Panshet dam (Singh and Varshney, 1995), andGEOMETRICAL AND HYDRAULIC CRITERIA FORSEEPAGE EROSIONSchuler (1995) summar'ized sever'al criteria f'or internalerosion and suggested tlvo steps to assess the susceptibility of internal erosion. First, geometrical conditions forseveral European dams (Charles, 1998).Although many studies on internal erosion of damsha¥'e been carried out (e.g., Charles, 1998), the processinvolved in internal erosion is still not vell understood.internal erosion should be checked according t.o ge-The objective of this paper is to provide ne¥v understanding on the modes and process of dam failures thatSecond, hydraulic conditions should be assessed according to hydraulic criteria for a critical seepage force tocause the inner erosion of movable grains.Many geometrical criteria can be used for the assessment of internal erosion of soils. Some criteria are basedon filter rules. A ¥vell-kno¥vn filter criterion, DI5F/ornetrical criteria for particle motion in the soil skeleton.may occur during reservoir filling such as the failure ofthe C}*ouhou dam. The geometrical and hydraulic criteriafor internal erosion in rockfill materials are assessed.Unsaturated-saturated seepage theory is used to analyze*] Associate Professor, Departmenof Civil Errgineering, The Hong Kong Universit} of Science and Technology, Hong Kong (cezhangl@"ust.hk).**)Associate Professor, S a e Key Laboratory of Hydraulics and i¥,Iountain Ri¥'er Engineering, C ollege of Hydraulic and HydroeiectricEngineering, Sichuan University. C'hina (cqfqe sina.com).The manuscrlpt for this paper ¥vas received for revielv on September _1", 2005; approved on July 26, 2006.¥Vritten discussions on this paper should be submitted before May I , 2007 to the Japanese Ceo echnical Society, 4-38-2, Sengoku, Bunkyo-ku,Tokyo I 12-001 l, Japan. Upon request the closing date may be extended one momh.oO7 ZHANG AND558C_HEN0870P otection pebblTO,P r pet war'3282.0_! Norrna!wat er:eyel_3 7 *Ol;7T 3 ..*-;3281=0Water stopConorete faceAl'=3267 '$¥CoRcrete face:･ '¥･¥TT 3260 Ol/. 7.(5:) ¥' fO ,;;3240.pl ¥ I ll'S Ciose-up view A- 3220 OI *3214.20*rT 32 o a-+ 321 2 20Gr nod )riteCurtain groutinFig. 1.Riverbed GraveiMaximum cross-section of the Gouhou dam (after Gouhou Dam Faihlre Investigation Team, 1996): A l unitsD85B4, ¥vas proposed by Terzaghi and Peck (1948) usingthe filter material diameter D15F (the diameter of filterparticles at ¥¥'hich 150/0 by ¥veight are finer) and the baseinmetersbased on numerous seepage stability tests of soilsconvex shaped grain-size distributions:O. 76(DIoglos)D90+ (b!;I << )D90, 15･ IoglO(b,:)1 86vith+ I (2)material diameter Ds5B (the diameter of base particles atwhich 850/0 by ¥veight are finer). Although the criterion¥vas developed for uniform soils, it is often used in prac-¥vhere D90, Dls, and D60 are the particle diameters attice for graded soils as ¥vell. Sherard et al. (1984) defined a¥vhich 900/0, 150/0 and 600/0 by ¥veight are finer, respec-nar'ro¥v boundary Dl5F/D85B=9 between erosion failureand filtration success using these t¥vo parameters.Tomlinson and Vaid (,_OOO) also concluded that a soil-tively.filter system ¥vith Dl5F /DSSB < 8 ¥vould not fail based on angations by the United Sates Bureau of Rec]amationexperimental study. of piping erosion. Several other(Mantei, 1985) for the sand ., surface soils at Calamusdam sho¥ved that the up¥vard seepage resulted in tinygeometrical criteria define internal erosion using moreparameters, such as D95B, and D75B (the diameters of thebase particles at ¥vhich 950/0 and 750/0, respectively, byweight are finer) (e.*".. Honjo and Veneziano, 1989).Vaughan and Soares (1982) presented an experimentalHydraulic criteria for internal erosion are usually indicated by a critical hydraulic gr'adient. Labor'atory investi-pipes at hydraulic gradients as lo¥v as 0.23. Skempton andBrogan (1994) gauged critical gradient values of 0.2 toO.34 for up vard flo¥v conditions. Den Adel et al. (1988)measured critical gradient ¥'alues of 0.16 to 0.17 for arelationship between the permeability of a filter and thesize of particles that pass through the filter. A boundaryfor stable filtration (i.e., for the filter to retain thesmallest particles that ¥vould be ¥vashed a¥vay durin_',_steady flow of fines driven by horizontal water fio¥vs.erosion) was expressed as k = 6.7 x 10-6 ! '2, in ¥vhich k isthe coefficient of permeability and 6 is the size of theThe Gouhou dam ¥vas a concrete-faced rockfill dam 71m high Detalls of design, construction, operation, andparticle that ¥vould just pass the filter.failure of the dam have been reported by the GouhouAnother category of geometrical criteria is proposed toassess vhether the physical nature of a soil allo¥vs themotion of its finer particles ¥vithin its o vn pore space.Dam Failure In¥'estigation Team (1996). The rockfill ¥vasdirectly founded on a sandy gravel of approximately 10 mSherard (1979) divided hetero_ eneous embankmentmaterials into t¥vo parts, a coarse fraction and a finefraction represented by DssFi * and Dl5c.****, respecti¥'ely.FAILURE OF THF. GOUHOU DAMthick. The dam crest ¥vas 265 m long, 7 m ¥vide at anelevation of 3281.00 m. The design, normal and check¥vater levels lvere all 3278.00 m and the correspondingreservoir volume was 3.1 million m3. The upstream andThe DI*c.**>*IDs5Fi** ratio of the embankment materialsshould be less than 4 to 5 to be stable. Kenney and Lau(1985) developed a technique ¥ 'ith ¥vhich a *"rain-sizeThe maximum cross-section of the dam is sho¥vn indistribution curve can be interpret,ed as the ratlo of thethe cushion material supporting the concrete face and itspercentage increment H corresponding to the gradationbet¥veen a diameter D and its fourfold 4D to F, themaximum design particle diameter ¥vas 100 mm. Zone IIpercentage finer than D. Internal erosion is not likely todo¥vnstream slopes ¥vere 1:1.61 and 1:1 .50, respectively.Fig. I . The rockfill ¥vas divided into 4 zones. Zone I ¥vaslvas a transition z,one ¥vith the maximum design particlediameter bein 400 mm. Zones 111 and IV ver'e the main1.3 (1)rockfill ¥vith the maximum design particle diametersbeing 600 mm and 800 mm, respectively.Reservoir filling began in September 1989 before thedam was completed. ¥Vhen the construction of the damBurenkova (1993) pr'oposed an empirlcal cnterlon¥vas completed in October' 1990, the reservoir ¥vater leveloccur ¥vhenHF SEEPAGE FAILURElvIECH AN I S559l¥vas as hlgh as 3'-74. 10 m (,3.90 m below the normal ¥vaterlevel) and seepage fio¥v ¥vas obser¥'ed at both the do¥vnstream slope at elevation 3'_'_3.00 m and the riverbed. Theseepage flo¥v disappeared in 1991 and 19921vhen the¥vater levels lvere only bet¥veen 3260.70 rn and 3262.60 m,¥vhich indicated that there ¥vas leakage in the dam aboveselevation ,326,_.60 m, but no leakage belo¥v elevation3,_67_.60 m.' i ;Startin*' from 14 July 1993, the reservoir lvater level-c.ts** .'rose continuously from 3261.00m to 3277.00m. Thevater le¥'el reached 3277.00 m at noon 27 August 1993.According to measurements of the traces of ¥vater level,the highest vater le¥elas 3'77 30 m, Ivhich ¥vas O.70 mlo ver than the normal ¥vater level. In¥'estigations afterthe dam failure re¥'ealed that water had flo¥ved into thedam frorn the joint bet¥veen the bottorn platform of theparapet vail and the concrete face since noon, 27 August.The ele¥'ation of the bottom of the parapet vail ¥vas{a) Govhouock !i dam 3fter breach13277.00 m, ¥vhich ¥vas 0.30m lower than the designedelevation 3277.30 m due to settlement of the dam. At"about 20:OO hours the same day, t¥vo children in Gouhouvillage witnessed water seeping out from the do¥vnstreamslope of the dam at a high ele¥'ation of 3260.00 m (seeFig. l). At ?_1:OO hours, the reservoir management staffheard loud noises and salv protection pebbles rollingdo¥vn from the upper portion of the do¥vnstream slopemixing ¥vith ¥vater flo¥vs and mist. One hour fortyminutes later, the dam breached at '_'_:40 hours. Aphotograph of the remnant of the dam is sho vn inFig. 2(a). The middle part of the darn breached. The(b) Close-up of the defeotive connection betweenthe pa apet wall and the concrete faceFig. 2. Photos of the Goulrou dam after failure (after Gouhou DamF'ailure Investigation Tcam, 1996)breach ¥vas trapezoidal. The top ¥vidth of the breach ¥vasi38m. The bottom of the breach ¥vas 28 m wide atele¥'ation 3'_50.00 m.particles during construction. Chen and Zhao (1996)Many studies have been carried out after the disastrousfailure in order to find the causes of the failure. AccordIn*' to the findings of the Gouhou Dam Failure Investigation Team (1996), there ¥vere se¥'eral structural problemsanalyzed the stability of the darn slope and conductedsteady-state seepage analyses using a saturated-onlyanalysis method. The dam vas considered to be uniformwith the dam. First, the ¥vater stops at joints of' concrete-Chen and Zhang (2006) conducted a three-dimensionalface panels did not function properly, especially at theupper part of the concrete face. Second, the connectionbetween the concrete parapet ¥vall and the concrete face¥vas not maintained pr'oper'ly in a segment along the damaxis (see Fig. 2(b)), ¥vhich left a concentrated flo¥vchannel frorn the reservoir to the rockfill. Third, theconcrete face ¥vas separated from the transition materialseveral rneters belo¥v the parapet ¥vall. Finally, theanalysis of ¥vater infiltration into the Gouhou dam usin_a,_embankment materials ¥vere evident.ly stratified o¥ving tosegregation of rockfill particles during construction,especially near the crest of the dam. These structuralimperfections created leakage channels. The resultedinternal erosion by seepage ¥vas considered as a directcause that triggered the dam failure.Liu and Miao (1996) conducted permeability tests andseepage stability tests ¥1'ith the darn rockfill materialstaken from the remnant of the breached darn using a300 mm-diameter permeability cell. Liu et al. (1998)conducted a model test to study the failure mechanism ofthe dam. The model rockfill was stratified with fine andcoarse layers to simulate the segregation of the rockfilland the'hole concrete face ¥vas assumed ineffective.saturated-unsaturated seepage theory. The three-dimensional characteristics of seepage through the dam bound-ed by step abutments ¥vere studied. The geometricalconditions of the rockfill materials and the hydraulicconditions in the dam, as lvell as the modes and mechanisms of seepage f'ailure of the dam associated with theprocess of ¥vater infiltration into the originally unsaturat-ed rockfill, however, have not been sufficient.1y studied.These will be the focus of study in this paper.CONCEPTUAL I? ITFILTRATION MODEL ANDMATERIAL PROPERTIESGove/'ning Equations jbr Seepage through UnsaturatedSatu/'atec! Soi!sSeepage flo¥v in unsaturated soils, as seepage in saturat-ed soils, is governed by Darcy's law and the continuityequation. The governing equation for water flow throughunsaturated-saturated soils can be obtained by introducin_ Darcy's la¥v into the continuity equation. In the ZHANG AND CHEN5601 oo10{)90908080.' 70> .' 70e)c; 60r:a:cl'; 60o 50c 50c:e,e,CLc:Q;40e,o*302040302010oooco10a iOolaiooe1 aoGrain size (mm)Fi(;. 3. GFain-size distribution curves of the materia!s in the 4 zones(Based on data from Gouhou Dam Faiiure Investio*ation Team*1996)study, total stress changes and deformation of the soilskeleton are not considered. Taking the total hydr'aulichead ll as the unkno¥vn and the soil as a transverselyanisotropic material, the governing differential equationfor t¥vo-dimensional flow throug:h an unsaturated soil isas follo¥vs (Fredlund and Rahardjo, 1993):a:¥' (¥k.) +aay (k)OOGrain size (mm):!ae,a/7 (3)y** aVl at¥vhere y, is the unit wei{)ht of water; e,,, is the volumetricwater content; V/ is soil suction; t is time; k* and kv are thecoefficients of permeability In the x- and y-direction,respectively and are functions of the soil suction.Sin7p!rfied Profi!es for A na!ysisThe Gouhou dam as sho¥vn in Fig. I is a z,oned rockfilldam. According to results of an in¥'estigation of theremnant of the dam after failure (Gouhou Dam FailureInvestigation Team, 1996), the maximum grain sizes ofthe materials in zones I, II, 111, and IV ¥vere approximately 100, 400, 600 and 800 mm, respectively. Se¥'eral **rain-size distribution curves of these materiais are sho¥vn inFig. 3. Except for the mater'ial in zone I, the grain-sizedistribution curves of the materials in other 3 zones donot differ considerably. As large boulders ¥vere fe v at theborro¥v site, the dam ¥vas in fact not e¥'identl _, zoned.Ho¥vever, the field investigation revealed that the rockfilllvas seriously segregated durin_g: construction due to the¥videly-graded nature of the materials and insuf cientquality control. Therefor'e the grain-size distributions ofthe rockfill materials are highly scattered. Figure 4 sho¥vsFig. 4. Grain-size distribution curves of the finest, medium, andcoarsest rockfi i materials (Based on data f rom Gouhotl DamFailure Investigation Team, 1996)Considering the fact that horizontal sand¥viches ofcoarse layers and fine layers ¥vere present in the dam butthe dam lvas not e¥*idently zoned, four cases of transient¥vater infiltratlon analyses (i.e., Cases I, II, 111 and IV)are performed in this study to simulate possible conditions of the Gouhou dam. The simplified profile for CasesI-III is sho¥vn in Fig. 5(a). Case I invol¥'es a uniformrockfill dam ¥vith the concrete face not effective aboveelevation 3260.00 m. The g:rain-size distribution of thefinest rockfill (see Fig. 4) is taken as the material for zone1 in this case. The riverbed gravel (zone 3) is the same inall four cases. Cases 11 and 111 both include a sandwichlayer (zone 2) of 10 m thick between elevations 3260.00and 3270.00 m. The grain-siz,e distribution (see Fig. 4) ofthe medlum rockfill is taken as the material for zone I inthese two cases. The sandwich layer is the finest rockfill inCase 11 but the coarsest rockfill in Case 111 (see Fig. 4).Case IV represents a fully stratified dam and the simplified simulation profile is sho¥vn in Fig. 5(b). The lvholedam is divided into 7 Iayers, sand¥viched aiternately bylayers of the coarsest rockfill and the finest rockfill. Allthe rockfill materials are assumed isotropic in the seepagesimulation. The simulation cases and the correspondingzoning and materials are summarized in Table 1.M:ateria! P/-opertiesFour materials, that is, the finest, medium, and coarsest rockfill and the riverbed gravel, are involved in theseepage analyses (see Table 1). The index properties ofthese materials are listed in Table 2 and the grain-sizedistributions of these materials have been plotted inthe grain-size distributions of the finest, medium, andcoarsest rockfill samples obtained from the field duringFi**. 4.construction and after failure. The segregation resulted intic curve and the permeability function, need to besandwiches of coarse layers and fine layers in the dam.The coarse layers ¥vere about 0.3 to O.4 m thick each anddefined to solve the partial differential equation (Eq. (3))for the transient seepage analysis. The soil-¥vater charac-extended from the upstream to the downstream. Theteristic cur¥'e is a relationship between the volumetricsaturated coefficients of permeability of the coarse layers¥vater content and the soil suction in the soil. Aswere as high as 0.02 to O.44 m/s, ¥vhich ¥vere 13 ordersof magnitude greater than those of the fine layers.experimental data ¥vere lacking, the cur¥'e in this paper¥vas estimated from the g:rain-size distributions and indexT¥vo soil property functions, the soil-¥vater characteris- SEEPAGE FAILUREly561¥. IECH NIS 11 Zero ux80!ee'Av )o )60B^fAl+328i oo/ one '- 3270_oo;e .- // Zone 2 (Sandwich)e,v 604,1 eB:260.00^(o );(¥ :" ･-4a1 eto $¥>d.Zane I (Uniform rock jl)Tota head H=10 rrl20cInitial water tab e I O¥TnZone 3 (Riverbed gravel)o322a oa, .32i o ooZero fux boundaryoi ao i sc502acx250(a) Cases 1-Ill801 yl Zero ux boundary)o ^s: ¥ " /+ - -3281 Oa:e60 _BA(: /f _ . >¥¥- ･' e e8;?)O/c 1 e_3_ 273_,0_o_3265 oos SS .B40Totai head H=10 m20 _3220 OO/321 O aooZe.lo_ilux boundary50 1 OOoFig. 5.Table 1.X1 50 200 250(b) Case IVSimpiified prof'lles and bounda , conditions for transient seepage analysis of tho four casesSimulation cases and their corresponding zoning and materi･-alslable 2.Index propertics of the four materials used in seepage ana!}-sisCaseI (Hon ogeneous)ZoninlIII (Coarse sandlvich layer)Finest rockfill3Same as zone lRiverbed ravell*¥1edium rockfill,II (Fine sandrvich iayer)i¥,Ialerial2Finest rockfill3Rh･erbed1lvledium rockfillravelN+1aterialFinest rockfillSpecificInitial waterg:ra¥'it¥.'contentG,Tt' ( , )Coarsest rockfili2 682.682 68Riverbed2.71N"ledium rockfillravelSaluratedcoe cient ofPorosit yperrneabi ityn (7･ )k._,t ( x lO 5 mls)5O.,-12.,)O 21l I .63* )O.2 l12 *3O 27:).23 l74Coarsest rockfill3IV (S ratifted dam)RiverbedravelThe 2nd, 4th, 6lh layers Coarsest rockfiHThe rest laversRiverbed g:ravelFoundation. Fincst rockfillmated soil- ¥'ater characteristic curves and permeabilityfunctions for the soils considered are sho¥¥'n in Fig. 6.Initia! Conditions alrd Boundaly ColrditionsThe initial ground ¥vater table is set at the base of thedam and the 10 m-thick riverbed is submerged. Abo¥'e theproperties of the soil (Fredlund et al., 2002). Thepermeability functlon is a relationship bet¥veen theinitial ¥vater table, the initial soil suction increases linear-coefficient of permeability and the soil suction. In thispaper, the permeability functions for the materials ¥vere14.2kPa, ¥.vhich is the suction in the rockfill thatcorresponds to the average compaction ¥vater content ofestimated using the Fredlund et al. (1994) predictionmethod. The caiculations vere assisted by a prograrnSoilVision (SoilVision Systems Ltd., ,_OOl). The esti-3.50/0 during construction.ly ¥vith the elevation. The maximum suction is 1lmited toThe boundary conditions for the seepage analyses aresholvn in Fig:. 5. It is assumed that the concrete face is ZHANG AND CHEN562impervious belo¥v elevation 3260.00 m in C_ases 1-III andbelo¥v elevation 3265.00 in Case IV, but is ineffbcti¥'eabove these specified ele¥'ations because of the defecti¥'econnection bet¥veen the parapet ¥vall and the concretedefined as a rising: ¥vater le¥'el from elevation 3277.00 m atthe base of the parapet ¥vall to the maximum ¥vater levelof 3'_77.30 m ¥vithin the first day and a constant ¥vaterlevel of 3277.30 m after¥vards. A zero fiux boundar'y isface and the separation bet veen the concrete face and thetr'ansition zone. Therefore, the boundary condition of theapplied along the dam crest. The do¥vnstream slope isupstream slope surface of the dam is divided into t vois less than the elevation head and other¥vise a freeparts: a zero flux condition belo¥¥' elevation 3'_60.00 m inoutflo¥v boundary. The bottom of the r'iverbed is definedas a zero flux boundary due to the lo¥v permeability of thebedrock beneath it.Cases IIII or 3265.00m in Case IV and a total headcondition above the elevations. The latter condition isdefined as a zero fiux boundary condition if the total headANALYSIS OF WATER INFll,TRATION INTO THF,o 30ROCKFILLo 25e,oThe transient infiltration analyses ¥ 'ere carried outusing the finite element progr'am SVFlux (SoilVision020Systems Ltd., 2003) together ¥vith a partial diff renceq,equation solver FlexPDE (PDE Solutions Inc., '_003).The program SVFlux can be used to analyz,e both steady0.1Sq,E O Ostate and transient flo¥vs throug:h saturated and unsatu->orated soils.o 05Case I-Umforll7 DanlO OO1 E-02 1 E O{1 E+00 1 E+01 1 E 02 1 E+03 1 E+04 1 E+05 i E 0eMatrie suetio:( ) Soii-water e(kPa)r oteristio curvesA uniform rockfill dam is studied in this case considering that there is no evident difference among the materialzones. The finest material in Fig:. 4 is considered in thetransient seepage analysis for easy convergence. The1 E )2process of ¥vater infiltration, as indicated by the pore-¥vater pressure contours obtained by the analysis, isshown in Fig. 7. The contours ¥vith zero pore-¥vatereS:.._ I E-OSs)pressur'e represent the transient vetting fronts. Waterfio vs into the dam from the upper part of the upstreamce,8 1 E-08slope where the concrete face is ineffective. The vettingfront advances do¥vn¥vards ¥vith time. Before the ¥vettingJatee)1 E- ie'front reaches the initial ground ¥vater table in the1 E-14E-02 1 E-O11E+00 1 E+0I E+02 1 E+03 1 E+041E+051E+06MatFic suetion (kPa)(b) Pemleability funotionsrig. 6. Esrimated soil-watcr characteristic cilrves and per leabilityfunctions for the four soilsriverbed, the rockfill is divided into t¥vo z,ones by¥¥'erting front. One is the saturated z,one ¥vithin¥¥'etting front; the pore ¥vater pressures ¥vithin itpositi¥'e. The other is the unsaturated zone outsidethethearethe¥vettmg front the pore ¥vater pressures ¥vithin it arenegative. The maximum pore- "ater pressure occurs atthe upstream slope face at elevation 3260.00 m. The3277 30 m2i6a() t = 2 days( ) t = 5 days3277 30 mo;7¥"a *{ j';;;'1: !;;;1{;; o0/;(o) t = 8 daysFig. 7.(d) i = 18aysPore-water pressure contours (in l{Pa) during ihe infiltration proecss, Case I SEEPAGE FAILURE56'olvIECHANIS*¥Ipore- vater pressures decrease gradually f'rom thevater table, a fio¥v channel forms and the veloclty atmax'imum at the slope surface to zero at the vettingfront. The rnaximum negati¥'e pore pressure outside thepoint C* in the flo¥v channel increases abruptly. Also thevelocity at the dam toe increases ¥vlth time graduaHy. Att= 13 days, the velocity at point C increases substantiallyperched-1vater table depends on the limit imposed on themaximum initial soil suction in the dam.again because the previousl"v unsaturated zone near theAfter 5 days, the bottorn of the ¥vetting front joins theupstream face is completely saturated and the infiltrationground ¥vater table in the riverbed (Fig. 7(b)) and alvater can only fio¥v do¥vnstrearn. After '-O days, the¥'elocities at the t¥vo points approach constant vaiues,vhich indicate that the flolv field nearly arri¥*es at aseepa_ :e channel from the upper portion of the upstreamslope to the rlverbed f'orms in the dam (Fig. 7(c)). Afterl 8 days, the ¥vater pressures increase monotonically fromthe phreatic surface to the bottom of the dam and thesteady-state condition.T¥vo additional analyses ¥vere also conducted assumin_"*.flo v nearly reaches the steady-state condition (Fig. 7(d)).that k* is t¥vo times k! and four times k , respecti¥*ely. TheThe evolution process of the seepage flow sho vs that theperched ¥vater table does not exit from high ele¥'ations atthe do vnstream slope but flows do vmvards to joint theinitial g:round ¥vater table. If the reservoir vater levelpersists, then the steady-state fio¥v condition ¥vill bereached and ¥vater exits frorn the do vnstrearn slope toeand the riverbed. This is not the seepa*'e pattern observedflo v patterns obtained ¥vere all sirnilar to those in Fig. 7except that the rates of ¥vetting front development werefaster. The 2 to 4 times increase in k* did not change thedo¥vn¥vard flo¥v pattern in the uniform darn.Cclses II-IV-Effect OJ StranficationTo include the effect of material stratification in theon the site.dam, a horizontal sand¥vich layer located bet¥veenThe changes in flo¥v ¥'elocity at the dam toe 'rand pointC on the base (see Fig. 5) ¥vith time are shown in Fig. 8.The velocities at the darn toe and point C are nearly zeroelevations ,3 _60.00 rn and 3270.00 m as sho¥vn in Fig. 5(a)is considered. The sand¥vich layer f'or Case 11 is the finestbefore the wetting front merges lvith the ground watersaturated coefficients of permeabillty of the fine sand¥vichand the coarse sand vich are O. 19 and 19.9 times, respec-table in the riverbed at t= 5 days as sho¥vn in Fig. 7(b).Once the ¥vetting front merges lvith the initial ground2 OE-05and for Case 111 the coar'sest. In Cases 11 and 111, thetively, of the coefficient of permeability of the mediurnrockfill, as shown in Table '-.The pore- vater pressure contours during the infiltration process in Case 11 vith the finer sand¥vich layer are1 eE-osshown in Fig. 9. There are t¥¥*o dominant flo¥ * directions.One is the down¥vard flo¥v to the riverbed and the other is1 205the horizontal fio¥v along the inter'face betlveen theuniform rockfill and the finer sandwich. Cornpared with_oa, 8{} -06the results of Case I, nevertheless, the horizontal flo¥v ino>this case with a finer sandlvich is much more pronounced.4Frgure 10 shows the pore-¥vater pressure contoursE*aduring the infiltration process in Case 111 ¥vith the coarserO OE+005 10o1520Tirne t (day)Fig. 8. Changes in fiolv velocity at the tlam toe r and point C* on thebase lvith time, Case I3277 03 m(a) t = O I dayssandl¥'ich layer. In Fig. lO, the do vn¥vard flo v plumediminishes and there is only one dominant fio¥v direction,i.e., the horizontal direction along the interface betweenthe coarser sand vich and the uniform rockfill. Thehorizontal fiow to the do¥vnstream slope surface is much3277 09 m(b) t = O 3 days255a(o) t = O 5 daysFig. 9.(d) t = O 8 daysPore-water pressure contours (in kPa) during the infiltration process, Case 11vith a finer sandwich la)'er ZHA iG36=iA¥. DCHEiN7327! al5 m.(1_¥t¥SOJiil!; 50.¥L/50o50(b) t = O 15 days(a) t = D G5 d ys3277 090 rn_.7 3277 D4S m.T7 3277 135 m*--li i i 50 ¥¥¥*':,(/¥50 .+.o¥(d) f = O 45 days(c) t = a 3 daysFig. lO. Pore-water pressure contours (in kPa) tiuring the infiltration process, Case HI Ivith a coarser sandwich la)er1and the finer rockfill belol ' (Fig. 10) can be explained bythe transfer condition in the seepage theory (Craig, 1997).04l _ -- -''1 2 -04oE*a4¥Vhen ¥vater flo¥vs across a boundary between t¥vodissimilar soils, the direction of fio¥v ¥vill chan_ e to¥varclsthe normal direction of the boundary as ¥vater' flo¥vs fromF 8 aE-05a soil ¥vith higher permeability ro a soil ¥vith lowerio 6CE*OSe,>- =--- __ __ _ i4 O -a5-*2 oE*a5permeability and vice ¥'ersa. The flo¥v direction dependslargely on conditions at the ¥vetting front where soil isinitially unsaturated. As can be seen from Fig. 6(b), acoarser soil ¥vill ha¥'e a smaller coefficient of permeabilityo a *eaOO I 0Tllrne t ( ay)O 4 O 503Fig. Il. Changes in f ow velocit at point D on tiownstream siope andthe (iam toe T with time, Case 111faster than the vertical fio¥v to the riverbed. After 0.15days (3 6 hrs), the ¥vetting front reaches the surface of the¥¥*hen the soil is desaturated. Ther'efore, ¥vhen ¥vater fio¥vsfrom the finer sand¥vich do vn into the rockfill, thedi 'ection of the flo v ¥vill turn more to¥vards the ¥*erticaldirection as sho¥vn in Fig. 9. Con¥'ersely ¥vhen ¥vater flo¥vsfrom the coarse sand¥vich do¥vn into the rockfill, the fio¥vdirection ¥vill turn more to¥vards the horizontai directionas sho¥vn in Fig. 10. The lateral spread of fluids at theintei'face of t¥vo media ¥vas also observed in centrifugemodeling of the mobility of dense non-aqueous phasedo vnstream slope at e]e¥*ation 3260.00 m as sho¥vn inFig. lO(b). Ho¥vever, the ¥vetting front has not reachedliquids in saturated soils (Pantazidou et al., ,_OOO).A stratified rockfill dam (Case IV in Fig. 5), ¥vhich hasthe ri¥*erbed after O.45 days (10.8 hrs). This reproduces7 alternating coarse and fine layers, is analyzed toqualitatively the phenomenon obser¥*ed at the Gouhourepresent better the effect of se*'re_"*,ation of rockfill duringdam ¥vhere the perched-¥vater first flolved out from thedo¥vnstream slope near elevation 3260.00 m and eventual-construction. In this case, the finest and the coarsestrockfill material are used for the alternating layers assho¥vn in Fig. 5(b). Figure 12 sho¥vs the pore-¥vaterpressure contours during the infiltration process in CaseIV. At first, the infiltration ¥vater spreads along theinterface bet¥veen the second coarse layer and the thirdl.¥' Ieci to the catastrophic failure of the dam.The changes in the ¥'elocity at point D on the do¥vnstream slope and the dam toe T (see Fig. 5) Ivith time inCase 111 are sho¥vn in Flg. 1 1 . The ¥*elocity at point D is¥+ery small before the ¥vetting front arrives at the do¥vnstream slope at r=0.15 days as sho ,'n in Fig. 10(b). The¥'elocity at the exit point D increases abruptly at t= O. 15days, ¥vhich Indicates that the lvetting front arri¥*es at thefine layer in the horizontal direction. The horizontal flo¥vto¥vards the do¥vnstream slope surface is faster than the¥'ertical flolv to¥vards the riverbed. After I day, the¥vettin front almost reaches the surface of thedo¥vnstrearn slope and a flo¥v channel forms from theupstr'eam slope to the do¥vnstream slope. Ho¥vever, thedo¥vnstrearn slope at elevation 3265.00 m as shown inFig. 12(b) ¥vhile the do¥vn¥vard mo¥'ement of seepagevelocity at the dam toe keeps at a lo¥v value ancl does notlvater is still limited. Therefore, this case also reproduceschange much during the infiltrarion process, vhichthe phenomenon observed at the Gouhou dam lvhere theperched- vater first exited from the do vnstream slopeindicates that the fio¥v through the toe is not likely tocause seepage failure.The dominant horiz,ontal seepage fio¥vs along theinterface bet¥veen the rockfill and the finer sand vich(Fig. 9) and t.he interface bet¥veen the coarse sand¥vichnear ele¥*ation 3260.00 m. SEEP GE FAILURE565¥iECHANIS¥. I(aj t = a 5 days(b) t= I a d3y3277 30 m7 3277 30 m5050(c) t = 1 5 d ysFig. 12.(d) t = 2 4 d ysPore*wateF pressure contours (in kPa) during the inflltration process, Case IV (stratified darn)1POSSIBLE FAILURE MECHANISMS OF THE DAMThe infiltration analyses descr'ibed in the previoussections sholv that the seepage ¥vater can indeed flolvthrough the dam and exit from the do¥¥'nstream slope at ahigh elevation (see Figs. 10 and 1'_), as observed in thefield. The possibility of seepage failure of' the dam thendepends on ¥vhether or not the geometrlcai and hydraulicconditions for internal erosion failure are met.C:)1:)- F'n:est-o-. Med'urr!08･-t - Coarsests:cH+F=1O--- - H/F:::i 3c:e) 0 5Q,S:)o a4c:SStable 'u)CQ 02c')Geolnetl'icct! Conditions foi' Seepage Fai!ureIn or'der to assess the susceptibility of internal erosion,the geometrical conditions f'or internal erosion should be:r:aevaluated first. T¥vo g:eometrical criteria mentionedearlier for assessing the possibility of int.ernal erosionproposed by Kenney and Lau (1985) and Burenkova(i993) are used in this study because these criteria aresuitable for soils ¥vith smooth gradations (Schuler, 1995).In a smooth gradation, the soil is neither gap-graded norcomposed of' t¥vo distincti_¥* diftbrent size fractions. TheUnstab eo 0204Oc81F mass fraction smaile than DFig. 13. Relaiionship between H and F corresponding io variousdiamcters D or ti]e ihree orain-size distriblrtions accordin" toKennev and Lau (1985)fore, the three rockfill-materials are all likely to suffergrain-size distributions of the three rockfill-materialsfrom internal erosion if' necessary hydraulic conditionsadopted m the translent seepage anal ses (i.e., theare present and the seepage exit is not lvell protected.grain-size distributions of the finest, medium and coarsestrockfill in Fig. 4) are smooth distributions. According toHyc!rau!ic Conclitions f'ol' Seepage Fai!ul'ethe method of Kenney and Lau (1985), the F¥'alue used inthis criterion should be less than O.'_ because the uniformity coefficients U* of the rockfill materials are largerthan 3.0 and the rockfill materials are videly graded. Thevalues of H and F corresponding to various diametersD for the three g:rain-size distributions are calculated andThe hydraullc gradients in the dam during the reser¥'oir- vater infiltration process are obtained by the ti'ansient seepage analyses. Figure 14(a) sholvs the horizontalhydraulic gradients along the do¥vnstream slope surface(see Flg. 5) for the four simulation cases at times t= 18are also plotted in Fig. 13. Within the F ¥'alues bet¥veendays (Case I, vater exits from the slope toe), t= 0.8 days(Case II, the per'ched ¥vater is about to mel"ge ¥vith theground ¥vater table), t=0.1 5 days (Case 111, the perchedO and 0.2, some H/F values of all the three rockfill-¥vater just reaches the dolvnstream slope), and t='-.4materials are less t.han the criticai value of' I .3. Therefore,days (Case I¥r, the perched ¥vater is about to arrive at thethe three rockfill-materials are susceptible to internal erosion.elevation 3230.00 m are greater than 0.5, but the mode ofpresented in Fig. 13. The lines F+H= I and H/F= 1.3The geometrical criterion (see Eq. (2)) of Burenkovado¥vnstrearn slope). In Case I, the gradients belolvperchedvater movements in this case is not the one(199,3) is another criterion recommended by Schuleroccurred in the field. In Case II, the perched ¥vater does(1995) for soils ¥vith smooth gradations. The parametersin Burenko¥*a's criterion for the three rockfill-materialsare calculated and listed in Table 3. All values of D901D6anot reach the do¥vnstream slope surface; therefore, thehydraulic gradients along the A-A section are very small.for the three rockfill-materials exceed the respectiveare ..*areater than 1.0. The maximum h.vdraulic gradients,¥ 'hich are 1.04 and 1.35, respecti¥'ely, both occur at thevalues of 1.86 Ioglo(D9(}/D15) + I in the criterion. There-In Cases 111 and IV, the _",_radients near the ¥vetting f'ront Z,HANCJ AND566Tabie 3.c!l¥,iaterialCalculated parametcrs in Burenkova's criterion for the three rockfill-materiais(mm) c! o (mm) dl= (mm)Finest rockfi l20.2N,Iedlum rockfill50.0Coarsest rockfill240.03l22.044 O-e- Ca5e l'1(Ll: ;l 'c;n H:6.52,6 8,2.821 .65.45?_.65sO 8 days3260,aco>Q)3250&i4 965 465^05hydraulic gradient values near the ¥vetting front and insome regions of the dam are greater' than the allo¥vablegradient in the four cases. Particularly in Cases 111 andIV, failure may initiate in the sand¥vich at the do¥vnstream slope ¥vhere the hydraulic gradients are as high asO.9 and 1.49.ec:. 62l0.1'_-0.32. According to Fig. 14(b), the horizontalCase iV t::2 4 d ys32TOFl S6 l*(d {)/c! *)According to results of permeability tests by L,iu andlvliao (1996), the allowable hydraulic gradient of thecoarse rockfill to prevent seepage erosion ¥vas onlyH}- case lii' t=0 15 days'O.76 lg(c!,;o/cl <) + 1O 6s 18 d ysI - Case li'c!,;)/d6]O.I_ "32903280CHEN@ Wetting front3240Process of Fai!tlreAccording to the transient seepage analyses, stratifications of coarser and finer layers are a trigger that acceler-32303220OO-o 5051015Horizontal hydrau!ic gradient(a) Section A-A in Fig 56-e-Case i t=18 days- - Case li, t=0 82 121:)H: Case !ii, t=0possible failure process of the dam can no¥v be illustratedin Fig. 15. First, the rockfill materiais are susceptible tointernal erosion according to the geometrical criteria of5 days-h Case iV, t=2 4 days08Kenney and Lau (1985) and Burenko¥'a (1993). At noon27 August 1993, the reser¥'oir ¥vater level exceeded thebottom platform of the parapet ¥vall. Water flo¥ved Intothe dam throu*'h the channel bet¥veen the parapet ¥valll:'>J:c:04oNo:C Oslope at a high elevation and indeed creates the hydraulicconditions for seepage failure^ If the rockfill of the damwere perfectly uniform, the dominant seepage fio¥v ¥vouldbe do¥vn¥vards to¥vards the r'iverbed.Based on the aforementioned extensi¥'e analyses, theaysQ)vates the perched ¥vater to spread along the horizontaldirection. The perched ¥vater exits from the do¥vnstreamO 102030 SO 6a40Distance from upstream sur ace (m)( ) Sectian B-B in Fig 5Fig. 14. Horizontal hydratllic gradients along tlre dolvnstream slopesurfaee (Section A-A) and the horizonta:1 section B-Band the concrete face and filled the gap bet¥veen therockfill and the concrete face (see Fi**s. 2(b) and 5).Driven by *'ra¥'ity, ¥vater infiltrated into the rockfill andwould have ad¥'anced nearly horiz,ontally from theupstream slope to the do¥vnstream slope along stratifications formed during construction (see Figs. 10 and 12). Aiarge unsaturated zone lvould still be present belo¥v theperched ¥vater. The propagation of the ¥vetting front¥vould be associated ¥vith a hydraulic gradient (seeinterface between the coarse layer and the fine layer.The horizontal hydraulic gradients along B-B section atelevation 3265.00 m (the middle section of the sand¥vichin Fig. 5(a) for Cases l-III and the interface bet¥veen thecoarse layer and the fine layer in Fig. 5(b) for Case IV) atthe same times as in Fig. 14(a) are sho¥vn in Fig. 14(b). Inall the four cases, the hydraulic gradients are large nearthe ¥'etting front, reaching O.72, 0.31, 0.9 and 1.49 inFig. 14(b)) that exceeded the criticai gradient for internalCases I, II, 111 and IV, respectively. In Cases I and II, thezone vould then fall and roll down along the slope¥vettin_ : fronts do not reach the do¥vnstream slope surfaceand seepage failure at the sand¥vich elevation is not likely.together ¥vith ¥vater and mist. Finally, after a large part ofIn Cases 111 and IV, the maximum hydraulic gradients arebreached as ¥vas observed in the field.both located at the do¥vnstream slope sur'face, i.e. the exitof the infiltration ¥¥'ater.erosion. Once the ¥vettlng front reached the do¥vnstreamslope surface, the fine particles in the rockfill would belost gradually under the action of the seepa*'e force. Apiping channel would form progressively across the dam.The fio¥v rate ¥vould then incr'ease significantly, ¥vhich¥vould cause ¥vashout of the rockfill at the do¥vnstreamslope. Large slope protection pebbies above the erodedthe downstream slope ¥vas ¥vashed a¥vay, the dam iSEEPACE FAILURE IECHANIS 1A3277.30 ,(m ¥e ¥;･."." "(1 ) . '"T 326i .OC m l,4567l* + (6)(2)¥. :¥- -F ;:,- - +j: _ (5):;(4)Concrete face;= .-¥rT 3260,00 m(3)(2) Water infiltration into rockfill(4) Progressive development of piping(5) Washout of slope and falling of pebbles(3) Initiation of internal erosion(6) Dam breach(1 ) Water level risingFig. 15.Postulated seepage failure process based on rational anal)sesACKNOWLEDGEME_NTSCONCLUSIONSThe f'ollo¥vin*' conclusions can be dra¥vn based on thene¥v understanding obtained from the analysis of ¥vaterinfiltration into the Gouhou rockfill dam, the fio¥v patterns and hydraulic gradients in the dam, as vell as thegeometrical characteristics of the rockfill materials:(1) Based on the *'eometrical criteria of Kenney and Lau(1985) and Burenko¥'a (1993), the rockfill materialsof the Gouhou dam ar'e susceptible to internal erosion if necessary hydraulic conditions are present.( _) A perched-water table formed in the dam ¥vhen thereservoir ¥vate, infiltrated into the rockfill from thetop of the concrete face. The vettin*' f'ront advancedThe described ¥vork is substantiall), supported by agrant from the NSFCIRGC Joint Research Schemebet¥veen the National Natural Science Foundation ofChina and the Hong Kong Research Grants Council(Project No. N-HKUST61 1 /0,3). The authors ¥vould alsolike to thank Prof. D. G. Fredlund for his ¥'aluablecomments on this lvork. The permission from Prof. Z. Y.Chen of' China Institute of ¥Vater Conservancy andHydropo ver Research. Beijing, to use the t¥vo photos inFig. 2 is also gratefully ackno¥vledged.¥vith time and divided the dam into t vo zones: aREFERENCESsaturated zone inside the ¥vetting f'ront and an unsaturated zone outside the ¥vetting front.l) Burenkova, V V(3) If the rockfill of the dam ¥vere perfectly uniform(Case 1), the dominant infiltration plume vouldmove do¥vn¥vards to join the ri¥'erbed and ¥vould notexit from the do¥vnstream slope surface at highele¥'ations.(4) The dam ¥'as in fact stratified due to segre*"ation ofsoil particles during construction. Stratifications inthe dam, ¥vhether' fine or coarse layers, could causethe horizontal spreading of infiltration plumes toaccelerate (Cases II, 111, and IV), In particular, t.heperched ¥vater ¥vould spread nearly horizontallyalong the interface betlveen a coarser sandrvichmaterial and the finer rockfill mater'ial belolv. Assuch, the perched ¥vater ¥vould fiolv through therockfill and exit from the dolvnstream slope at ahi*･h elevation as observed before the breach of theGouhou dam. The lateral spreading can beexplained by the theory of seepage across the interface of t vo dissimilar rnedia.(1993): Assessment of suffbsion in non-cohesionand graded soils . Filters iil Geotec'llnica! ailc! H_vc!rau!ic En*"ineering(eds. by Brauns. J., Heibaum, ¥. ,and Schuier, U_), A. ABalke-ma, Ro erdaln, Netherlands, 357-360.2) Charles, j. A. (199S): Internal erosion in European embankmentdams-progress report of ¥vorkinroup on inlernal erosion Inembankmem dams. Danl Sc{fer_v (ed. by Berga, L^), A. A. Balkema,Rotterdam, Netherlands, 2, Ij 67l576.3) Chen, Q and Zhang, L. h,i. (2006): Three-dimensional anaiysis of¥vater infiltration into the Gouhou rockfill dam using: saturatedunsaturated seepage theory. Can Georech. J., 43(5), 449-461.4) Chen, Z. Y. and Zhao, Y_ Z. (1996): Slope stability anaiysis of theGouhou dam-deterministic model. Goi!hou Conc'rete*Fclcec!Rockfi!l Dam-Desi*"n. Construction. Opera!ion, and Faihu'e (ed.by China National Flood and Drought Pre¥'ention Ofi ce), ¥¥*aterC*onservancy and Hydropower Press, Beijing, 55-60.5) Craig, R. F. (1997): Soi! Afechanics, 6 h ed., E & FN Spon, London.6) den Adel. H,. Bakker, K J. and Breteler, M K_ (1988): Internalstabili "v of minestone. ProcIn!. S_1'mp !Vfode!!ing Soi!-rilaterStructure In!erac!ions (eds. by Kolkman, P. A , Lindenberg. J. andPilarczyk. K. ¥V.), A. A. Balkema. Rotierdam. Netherlands,225-23 1 .7) Fell, R., , 'Iac(J*regor. P, and Stapledon, D (1992): Geotechniccll¥'ith a hydraulicEn*"ineering of Enlbankment Danls. A. A. Baikema, Rotterdam,Netherlands*'radient that is higher than the critical ¥'alue needed8) Fos er, *¥,1., Fell, R and Spannagle, i¥,1. (2000): The s atis ics of(5) The wetting front lvas associatedto cause internal erosion. When the wetting frontembankmem dam failures and accidems, C(In. Ceotechreached the do¥vnstream slope surface, pipingl OOO- I 024 .failure would be triggered since the geornetricalconditions of the rockfillerosion.vere susceptible to internalJ., 37(5),9) Fredlund, D. G. and Rahardjo, H. (1993): Soi! IVlecllanics forUlisatiira!ecl Soi!s, John ¥¥rjley & Sons, inc_, Ne¥v YorklO) Fredlund, D. G., Xing. Aand Huang, S. (1994): Predicting hepermeabili y func ion of unsatura ed soils using soii*water charac- 568Z｝｛、へNG．へND C騒EN11） Fredlund，NI，D、，∼Vilson，G、∼y、and Fred1し【nd，D G．（2002）＝Use20）PDESoluεlonhlc、（2003）∫1avPOど3R師θ1で11cd癒〃7∼’θ1，Antloch， Callfomla，USA、 of こhe grain，size dis［ribution for estlmatio鳶 of 芝he so藍一、vater21） Schuler，U．（1995）：How ［o deal、、Fith ［he probiem of suαuslon， cllaraCterisdccurve，Cαノ1、（｝θαθch．／，，39（5），lio3−m7． Rθ5θα1でhα’1ゴ五）（∼vθ！oρ11∼θ1∼’〃1’hθF’θ1ゴ（∼ズ五）α〃15，SNCLD，Crans− ［eristiccurve，Cσ11．Gεo’θぐ11．ノ．，31（4），533−546．12）GouhouDamFailure…nvestigationTeam（19％）1Technicaldetails Nlo爲tana，Sw髭zerian（玉，1−15， of dle Go曲ou dam，Gα！11α！Cα∼c1’αθヂαcθ41∼ocんガ〃0α1η一22）Sherard，、ヌ．L．（197∼））：S1nklloles1n dams ofcoarse，broad玉y grained ρε∫’91∼， Co11∫11一∼’ぐ1’011， 0Zフθ’日α”011， θ11ご ノ『θ〃∼〃ぞ （ed． by Chhla soils，ηα11∫θα’0115Qブ／3’1∼∫ノπ．Coη9，加rg8加1η∫，1飢emaIioIlal Na｛ional Flood and DrQught Preve【1tion Of資ce），∼Vater Conservan− CommlssiononLargeDams，Paris，France，2，25−35． cy and｝畷ydrQpower Press，Beijing，111−245，23）Sllerard，」，L，，Dほnn1gan，L、P，andTalbα，，」13）Ho頃o，Y．andVeΩez1ano，D．（1989）l Improved熱ltercr紅er1on for cohesiolllessso1ls，ノ 0θ01θc11、五11913．，H5（1），75−94．14）1COLD（1995）：Dam fa1沁resl stat1stic analysis，β正’〃α”∼99，∫1r1θノR（玉984）：Baslc l》roper［ies of sa【｝d and gravel良lters，．1．Gθo∫θごh、ど1191宮．，110（6）， 684−700．− no’10ηα1Coノη1η’5∫10η011加19θDσ〃∼∫，1皿ema【io良aICommlsslon on Large Dams，Par1s．15）Keほney，T．C，and Lau，D．（1985）l I厭emal s【abi比y ofgranωar 51Iers，Cαη．0θo’θc11，／、，22（2），215−225．16）Liu．，LandMiao，L．L（1996）＝蔦xperlmen｛alstudyofseepageand24）Singh， B． and Varshney， R、 S、 （玉995）＝ Eng’1∼θθ1””1g ／10r ∬1η加1∼ん1ηθ’π0αη15，A．A．Ralkema，Brook丘eld，USA，25） Skempζon，A，、V．and Brogan，J，｝〉i σ994）：ExperimeaIs on p1pl【｝9 insandygravels，G80’θc／1吻z’θ，44（3），449−460．26） Soi1V1sioa Systen｝s Ltd．（2001）：So〃VZ5’011 U5∈∼r’∫（3∼”ゴθ Vθ1510η 3．0，Saskatoon，Canada・ seepages〔abilityofGouhourock翻maIer1als，Gα’hα’Co11α門θ1θ一27）SoiiVisionSystemsL【d．（2003）：3Vノマ∼！xU∫θ1・1∫イ、伽π’013．12， 汽α‘θ‘1Roご勺5〃ρα’n−0θ5191∼，Coノ∼，∫’ノw‘’10’r，OPθ’“α110’1，θノ1げノ『α〃”1で 5館’”αθ4／U’∼、∫副〃一α’θび月11”θE！θ1ηθ1π2五）／3P5θθpαgθご》o礁〃11g， （ed．byChlnaNa柔1onalFlooda“dDroughtPreve【1tiα10伍ce）， Saskatoon，Saska芝chewan，Canada． ∼Vater Conservancy a琵d Hydropower Press，Be1jing，18−25．17）Liu，」．，Dlng，L。Q．．M玉ao，L．」、and Yan9，K．｝｛、（1998）：Mo〔墨eI28）τerzag厩，K．and Peck，R，（1948〉＝So〃A（1θc11αηic5”∼Eng’ηθα1ng P1’αα’ぐθ，John Wiley and Sons，Inc、，New York． s｛面yonfail肝emechan1smso琶heGoullourock611dam，C／71η．ノ、29）τomh簸son，S．S．and Va1d，Y．P。（2000）＝Seepage forces an（玉 ∫ノ』｝，4”，ノ『η9’9．，（王D，69−75． confin玉ng Pressure effects on piping erosion， Cα11， （フθ01θc11、 ，1．，18）Ma肌el，C，L．（1985）：Seepageco蹴rol forembanKmentdamsUSBR prac【iceラ SθθP‘∼9θ αノ7ゴ五，＆7ん‘19‘∼ノ》o〃1 ∠ ‘7171∫ ‘∼114 ／11∼ρo‘〃1ゴ〃1θ1r15 （eds。 by Volpe， R。 L． arld Ke鰻y， ∼V． E．）， ASCE， New York， 37（王），1−B．30｝ USCOLD（1988）：Lesso自s fronl dan11ncidents，USA−II，Prepared by τhe subcomn貰圭uee of Dam hlddents a貧cl Acc1dents of tbe Cen〔rifuge s田dy of DNAPL transport in granしElar media，ノ． Commi貰ee on工）am Safe［y of由e U．S．Com搬iRee oΩLarge Dams （USCOLD），American Socie［y of C1vll Engineers，New York・31）Vaughan，P．R．andSoares，H．F．（三982）：Desig頁of負iters forclay Gθo’θごh「Gθoθ17v〃’011，E∼7918。，韮26（2），105−ll5「 coresof（玉ams，／．（｝θo’εc1∼、どノ1grg，0’v、，108（1），17−31． 299−305、19）PanIazidoロ，M．，Abu−Hassane1n．Z。S、alld Riemer，M、F、（2000）： | ||||
| ログイン | |||||
| タイトル | The Role of Nature of Particles on The Behaviour of Rockfill Materials | ||||
| 著者 | A. Varadarajan・K. G. Sharma・S. M. Abbas・A. K. Dhawan | ||||
| 出版 | soils and Foundations | ||||
| ページ | 569〜584 | 発行 | 2006/10/15 | 文書ID | 20941 |
| 内容 | 表示 SOILS AND FOU¥_*DATIONS ¥;ol46, NTo, ),569584, Oct. 2006Japanese GeoLechnical Sociel)THE ROLE OF NATURE OF PARTICLES ON THE BEHAVIOUR OFROCKFILL MATERIALSA. ¥rARADARAJANTi), K. G. SHAR IAii), S. M. ABB sii!) and A. K. DHA ¥*A 'iY)ABSTRACTThe nature of' the particles of se¥'en allu¥'ial rockfill materials and three quarried rockfill materiais are expressed interms of uncompacted void content and unconfined compressive strength of each of the rockfill materials. Drainedtria.¥'ial tests are conducted on modeled rockfill materials. The beha¥'iour of' the r'ockfill materials is related to theunconrpacted void content and unconfined compressive strength of the rockfill materials. A predlction procedure isproposed to determine the angle of shearing resistance of the rockfill materials using uncornpacted void content andunconfined compressive strength of these materials.Key words: rockfill materials, triaxial tests, uncompacted void content, unconfined compressi¥'e strength (IGC: D3/D6)particles as the basis. This procedure assumes implicitlyINTRODUCTIONthat all the factors affecting: the stren9:th of the rockfillmaterial can be related to the size of the part.icle. But, it isRockfill dams are constructed using materials mostlyobtained by blasting rocks in quarries. These materialsconsist of angular to subangular particles. Rockfill damsare also constructed ¥vith materials collected frornkno¥vn that the factors such as shape, surface roughnessand strength of the particles also affect the strength of' thematerials are a¥'ailable in the riverbeds of the tributariesrockfiH materials. This paper deals ¥vith laboratory testing of rockfill materiais collected from ten project sitesand correlation of the behaviour of these materials*ithof the major ri¥'ers, Ganges and Indus in India. These¥'arious characteristics of the particles.ri¥'erbed in some cases. Large quantities of thesealluvial rockfill materials consist of rounded andsubrounded particles as a result of impact, rolling andREVIEWsliding action in the ri¥*erbed. Rockfill materials consistof particles as large as 1200 mm. It is known that theParticles of' rockfill materials are primarily derivedfrorn quarries b), blasting rock or collected from riverbeds. The characteristics of the particles are expressed byinterparticle contact stresses increase ¥vith the size of theparticles ¥vhen they are subjected to loading in anengineering structure such as rockfill dam The lalgethe mineralogy, size, shape and surf'ace texture. Themineralogy depends on the parent rock from ¥vhich thecontact stresses cause breakage of particles. The natureof particles such as shape and roughness also affect thebreakage of particles. The behaviour of rockfill materialsparticle is deri¥'ed. The size is defined by the size of thesquare hole in a screen of a sieve in GeotechnicalEngmeering. The rockfill particles are mostly equidimen-are affected by the breakage of particles besides all otherfactors that aft ct the behaviour of' granular rnaterialsconsisting of smaller sized particles.sional. The degree of roundness of the particles is qualita-tively described as angular, subangular, subrounded,rounded and well rounded (Lambe and Whitman, 1969).As the sizes of the rockfill materials are large, somekind of rnodeling technique is often used to reduce theSurf'ace texture of the particle refers to minor features ofsize of particles so that the samples prepared ¥vith smallersize particles can be tested. The material parameters froma surface of a particle, independent of size, shape, ort.he tests are used to get the parameters f'or large sizeprototype particles by extrapolation usin_ : the size of thetexture are dull, polished, smooth or rough, striated,frosted, etched or pitted (Lambe and Whitman, 1969).*) Head, Dept, of Ci¥'il Engineering. Dr.de2:ree of' roundness. Sorne terms used to describe surface,1.G, R_ Educational and Research Instituie (Deemed University). Chennai 600095, Tamil Nadu, India(formerly Dogra Chair Professor. IIT Delhi).*=} Professor and Head. Dept of C*i¥'il Engineering, Indian Insritute of 'Technolog), Hauz Khas, Nelv DelhiIOOi6, India (kgsharma@civil.iltd_ernet_in).**=} Reader, Dept. of Civil Engineering, Jarnia N,Iillia Islamia, Jarnia Nagar, iNew Delhi I 10025, India**u Director. CSivIRS, Hauz Khas, tNe¥v Delhi 1 100i6, India.The manuscript for this paper ¥vas received for revie¥v on November 1, 2004; approved on N,Iay 29, 2006¥Vritten discussions onhis paper should be submitted before ¥. ,Iay I ,*007 to the Japanese Geo echnical Socie v, 4-38-2. Sengoku. Bunkyo-ku,Tokyo I 12-001 l, Japan_ Upon request the closing date may be extended one month.56C)_ VARADARAJAN ET AL.570Youd (1973) used the ratio of minimum radius of theR mJlt Sa lrDam Slte !r 1" ' 111' lr"rlparticle edges to the inscribed radius of the entire particle_¥;.:TT 1'/tr:tf ; ';' !x'r'r'14 t"; /"_ +1;: s '; !_ !;tl"(ol Dsrl' Siteto depict the roundness of the particle. Over the yearsrseveral tests have been evolved for measuring coarseag*'regate quaiity in High¥vay Engineering in terms ofYes[erm Y:ImuF n Can' ] Sito f'/"'/rl :1 _ r ' T $ : P:lrbati Dsn] Siteparticle shape, angularity and sur'face texture. Standardised tests include percentage of fractured par'ticles(ASTM D5821-1995), fiat and/or elongated particles inr J' ^' th :: 'fl;1:: j;i /d;;-if /'h /i' r) ;･j::;I'; ';:/:;;; '/ti/'_i iare*'ates and it is similar to the uncompacted voids testfor fine aggregates (ASTM C1252-1998). This test is moreobjective and less labour intensive and less time consum-'"' ';( 4' 'trlli " s "; t s;- ;:7: F Ft1"I 1 " .,/ ! '; '_ I:sij l: rJ4*; !Q'; ;uYiEl/TGhri D:lrn Sit::i ,;r'-l; fxr!coarse aggregates (ASTM D4791-1999), and index ofparticle shape and texture (ASTM D3398-2000). Alhrich(1996) proposed an uncompacted voids test for coarse' * =1' __'r"$-4 : ;/ r _ v'cL/f' '- x'! T; s' { '" ""/r'$1 't' :¥:"J'f ' ;s; . , _ 'i/ i' ;'1 ' 'T;";' l ;fecki ]n l iaterialsl * r)'tuarTTied(T r Rockl" u la e isBoth T} es orl ockfln ¥' Ialerinls'P "" ";1;) , lling (Hossain et al., '_OOO).Rockfill materials contain particles of large size and itis dif cult to test them. Therefore, the siz,e of the rockfill!' + ^-! ti';'fss i _'::L:'::'::'1 :.':;::,:/:i:::'Si2;;;i;r/':''{ ';)"_ ir';) t'J:mater'ials is reduced using modeling technique. Four!!"modeling techniques are used to reduce the siz,e of the; 'I_"AFrockfill materials viz. the scalping technique (Z.eller and2 ;f' 'Li" ' 'l '! J;{:? .::;H"i i ] _ltl' J#:llF ""; I -": ; rl';,. I -11 R:/rWullimann, 1957), parallel gradation technique (Lo¥ve,1964), generation of quadratic _ rain size distributioncurve (Fumagalli, 1969), and replacement technique(Frost, 1973). The parallel gradation technique ¥vas)f! " l'uriln D:] siteFig. 1. Location of the project sites on the mapconsidered the most appropriate out of these four tech-the prediction of the angle of shearing resistance forniques (Ramamurthy and Gupta, 1986).Rockfill materials have been tested using lar_"*e scaletriaxial testing equipment. Specimen diameter in thesetests ranged from 15.2 mm to 500 mm, the maximum sizeprototype rockfill materials using the character'istics ofthe particles.of the particles ran>'ed from 3.8 to 100 mm and themaximum confining pressure ranged from 0.69 to 13.8MPa (Hall and Gordon, 1963; Marsal, 1967; Fumagalli,ROCKFII,L MATERIALS1969; lvlarachi et al., 197,_; Thiers and Donovan, 1981;sites in India. The locations of the projects are sho vn inAnsari and Chandra, 1986; Venkatachalam, 1993;Fig. I . Six of the sites are located in the states of Punjab,Varadarajan et al., 2003). These researchers conductedtests on a wide ran*'e of rockfill materials. They haveconcluded that (i) the stress-strain behaviour of theUttranchal, Uttar Pradesh and Har'yana in the northernpart of India. One site is in West Bengal state in theeastern part of India. Seven alluvial and three quarriedrockfill materials ¥vere chosen for the study. A briefrockfill material is nonlinear, inelastic and stressdependent, (ii) an increase in confinin_pressure causesincrease in the ¥'alue of peak deviatoric stress, axial strainand volumetric strain at failure, and (iii) an increase inthe size of the particles results in an increase in volumetricstrain at the same confining pressure. They found that thebehaviour of the rockfill materials depends on mineralcomposition, particle siz,e, shape, gradation, and relativedensity of the rockfill materials.The material parameters for the large prototype siz,erockfill materials were obtained from the materialparameters of the modeled rockfill materiais usin_ *Rockfill materials ¥vere collected from seven projectdescription of the location and the rocks are presented inTables 1(a) and 1(b). The alluvial rockfill materials ¥verefrom the beds of the tributaries of the t¥vo major riversGanges and Indus. Representative rockfill materials ¥verecollected from the project sites. The grain size distribution cur¥'es of all the materials are sho¥vn in Fi :. '_. Themaximum particle size ran_9:es from 200 to 1200 mm. A¥vide ran_"*e of gradation characteristics is observed int.hese materials.The photographs of typical allu¥'ial and quarriedrockfill materials are sho¥vn in Fi_"._s. 3 and 4. Strikingextrapolation techniques ¥vith the maximum particle sizeof the rockfill materials as the basis (Venkatachalam,differences in composition and nature of particles are1993; Var'adar'ajan et al., 2003).each alluvial rockfill material consists of roundedSCOPF,particles ¥vith rounded and smooth surfaces of ¥'ar'iousrock types, each quarried rockfill material consists ofparticles ¥vith angular and rough surfaces of same rockThe scope of the in¥'estigation lvas to determine thecharacteristics of the particles of the rockfill materialsfrom various project sites, to conduct triaxial tests onmodeled rockfill materials and to propose a procedure forobserved in the tlvo types of rockfill materials. Whereastype. THE ROLE OF NATURE OF ROCKF LL iATERiALS571lOO-h Rs!80e,-hsr tisnl ( 3 2O rurF] l/_bah ie sr { OO ru/}/-- r- Puru! ia {ianl ( I L0V rTlnl l/¥VYC (SE] (25 mnl mo eled)L////VYC (SE] (SO nna mo eled)- - YYC (SE) (5C mrl mo s]ed)e)//- ･ Psrbatl d2;n (700 mm}, , 40///-- - h oi d2m (600 mnl}60eeJ:t S-i -Tehr: dsm (2:S rllnl'-1 - VYC (SE) (2L}O n]m'--c- ¥YVC ( BS) (250 rnm)/20oO,llO1lOOOlOOMaximum Particle Size (mm)Fig. 2.'Table 1(a).SNo.l.A luvial rockfill materials usedProject nameTehri DamGrain size distribution curve for the rockfill materialsLocationName of the rocksOld DobataQuar zite, phyllite,borro¥v area,sandstone, graniteDistrict 'TehriTehri DamS. NoNew DobataQuartzite, phylliie,borro¥v area,District Tehrishaie, IirnestoneProject namel . Kol DamQuarried rockfill materials usedLocatiorlKol, District Bilaspur,Name of the rockLirnestoneHimachai Pradesh Stale2Garhl"al,Uttaranchal State, *Table 1(b).Purulia Dam Purulia, ¥Vesi BengalHornblande-Siate = quartz-schist3. Parbali Dam Kartah quarry, Sainj, QuartziteDis rict Ku lu, HimachalPradesh StateGarh¥val,Uttaranchal S ate3*Kol DamKol, DistrictQuartzite, Iirnestone,Bilaspur,shale, sandstoneHimachal PradeshThe nature of the particles primarily refer to size,shape, sur'face texture and mineralogical composition ofState4RanjiSagarDam)+Shah NeharShahpur Kandi,Quartzite, jasper,the particles. The sizes of the particles and their distribu-Districtshale, con_"..lomerate,Gurdaspur,Punjab Stateclaystoue, sands one,tion in a rockfill material are determined by sieveAt running:,¥,Iicaceousdistance (RD)7410, nearsandstone,rlts of chartTerrace, DistrictKangra, HimachalHosain et al. (,_OOO), has been adopted herein for rockfillquartz tePradesh Statematerials. The test apparatus proposed by Alhrich (1996)was fabricated and is shown in Fig. 5(a). With thisVesternFoundation ofYamunabridge, DistrictCanalYamuna Nagar,Quartzite, marbel,limestoneHaryana Staie7Foundation of siltYamunaejector site,CanalDistrict YamunaphylliteNagar, HaryanaStateapparatus, material vith maximum particles size of 19.0mm can be tested. The apparatus and the test procedureare briefiy described in the follo¥ving.Quartzite, Iimestone,shale, sandstone,Vesternanalysis.The shape, surface texture and gradation of fineaggregates are quantitatively expressed by a singleproperty kno¥vn as Uncompacted Void Content (UVC)(ASTM C1252-1998). The sarne concept, ¥vhich has beenextended to coarse aggregates by Alhrich (1996) andSansarpur6.NATURE OF PARTICLESThe apparatus consists of a top and a bottom cylinder.The bottom cylinder called cylindrical measure, is oneside open on the top. The top cylinder which functions asa funnel, is fitted lvith a conical cylinder at the bottom.The opening at the bottom is provided ¥¥'ith a lid ¥vhichcan be opened suddenly to pour the material in thecylindrical measure (Fig. 5(b)).The upper cylinder is filled freely with 5 kg of rockfillmaterial after striking off the excess material. The bottomlid is suddenly opened to allow the material to freely fall VARADARAJAN ET AL.57_v'=":}j{ist.,!;* :."*. ,(-"'* ";S i'*.: .{(a)Frg 3. A]luvial rockfi 1 matcrials obtained from bridge sitc. ¥VesternYumuna CanalFig. 5(a).Apparatus useti to determine Uncompacted Void CoutentH4Jl ;n m!s*d.=}I60i'F'I +l a2 mm1 smm!L*- H I=+Fig. 4. Quarried rockfill materials obtained from Ko] Dam Site(b)in the cylindrical measure. The material collected is¥vei hed after le¥*elinFig. 5(b).l,ine diagram of UVC apparatusthe surface. The IJVC is calculatedas :UVC = V-F/G x 100 (1)V¥vhere,V=Volume of the material collected in the cylinch･icalmeasure in ml,F=Net ¥vei**ht of the material collected in cylindricalmeasure in gm,G = Specific gravity of the materialthe maximum particle size. Also the value of UVC_ forRanjit Sagar material is less than that for Puruliamaterial for the same maximum part.icle siz,e. Lo¥¥'ervalue of UVC indicates more material (particles) per unitvolume (i.e. higher density) (Eq. (1)).A material having different average particle sizes but¥vith same uniformity coefficient (i.e. parallel gradation)and shape and surface texture ¥1*ill attain lo¥ver void ratio¥vith larger a¥'erage particle size, provided the compactionTo study the effect of size, three modeled rockfillmaterials ¥vith maximum sizes of 19.00, 9.50 and 4.75mm ¥vere prepared from each rockfill material usingeffort is same (Lambe and Whitman, 1969). The decreaseparallel gradation technique (L.o¥ve, 1964). The ¥'alues ofRanjit Sagar and Purulia rockfill materials are ¥vellgraded ¥vith uniformity coefficient 131 and 15 respectively. But, for the same maximum particle size. Puruliarockfill material sho¥vs higher value of UVC than RanjitUVC for each materialvere determined. Semi log plotsbetween the maximum particle sizes of the modeledmaterials and UVC ¥ver'e plotted. Typical plots for t¥vorockfill materials from Ranjit Sagar dam site and Puruliadam site are sho¥vn in Fig. 6. The plots are found to belinear and may be used to determine t.he value of UVC forlar_ :er particle sizes as sho¥vn in Fig. 6. In Fig. 6, it isobserved that the value of UVC decreases with increase inin the UVC value ¥vith increase in particle siz,e obser¥'ed inthis study (Fig. 6) also confirms this finding.Sagar rockfill material (Fi_ :. 6). This may be attributed tothe fact that the particles of Purulia rockfill material ¥vithangular and rough surfaces attain lo¥ver density (higherUVC) than the particles of Ranjit Sagar rockfill material¥vith rounded and relati¥'ely smooth surfaces. Therefore, r=THE ROLE OF NATURE OF ROCKFILL ivIATERIALS573ss40sou30's>120>< ioe)::: ** :3sos'lOv>- :es:o:4lMaximum Particle Size (mm)10o :o 40 eo so 1:o i40 160 Iselo{)UCS (Fig. 6. T)pical plot of uncompacted void content vs max'imumparticle sizePa)Fig. 7. Variation of UVC with UCS for aiiuvial and qilarricd rockfilimateriaisthe ¥'alue of UVC may also be used for comparing theshape and surface characteristics of the particles bet¥veent¥vo rockfill mater'ials having similar gradation curves.2.5 k**) is loaded in a drum of 700 rnm diameter andThus, the value of UVC may be used to quantitatively500 mm length alongrepresent size asof particles.1 i cast h･on balls. The drum is rotated about its axisymmetric axis on the vertical plane at a speed of 30 to 33 rpmupto 500 re¥'olutions. The aggregate is then taken out andvell as shape and surface characteristicsIndividual particle strength is one of the factors thatafi ct the shear strength of **ranular materials and therockfill materials in particular as the particle is subjectedto hi**h interparticle stresses durin*' shearing. In thisstudy, the strength of the particle is represented by thevith abrasive charge consisting ofsieved through 1.7 mm Indian Standard (IS) sieve. TheLos An*'eles Abrasion value, expressed in percentage, iscalculated f'rorn the ratio of the material passed through1 .7 mm IS sieve of total weight of the materiai taken. TheUnconfined Compressive Strength (UCS) of the rockLos Angeles Abrasion value (LAV) for alluvial rockfillfrom ¥vhich the particle is derived. The UCS value formaterials are also plotted in Fig. 7. It is remarkable tonote that the nature of' variation of LAV of the alluvialmaterials ¥vith respect to UCS is similar to that of UVC.each rockfill material is determined as f'ollolvs.Blocks of representative rock vere collected from theproject sites. At least five cylindrical specimens of sizes38.1 mm in diameter and 76.2 mm in length ¥ 'ere coredfrom the rock. Each specimen lvas tested in a compression testing machine with a constant stress rate of O.) tol .O MPa/s till failure (ASTM D _938-95). The failure loadas expressed in stress is the UCS of the specirnen. Anavera*"e of' UCS values of the five specimens is taken asthe UC.S value of the rock.Three modeled rockfill materials with rnaximum particle sizes 25, 50 and 80 mm were obtained using parallelThe LAV of quarried materials also shovved similarbehaviour (not sho vn in figure).It is noted in Fig. 7 that there is scatter of points andthere is no specific trend for ¥'arious alluvial rockfillmaterials in the plot between UCS and UVC/LAV. Thevalue of UVC for an alluvial rockfill material isdependent on the roundness and the smoothness besidesthe size of the particles. Incr'eased roundness and smooth-ness ¥vill result in reduction in the UVC value for therockfill material consisting of sarne sized particles. Thegradation technique (Lo¥ve, 1969) for each rockfillmaterial. Typical gradation curves for the modeleddegree of roundness and smoothness may not be same formaterials of a rockfill material are shomaterials considered in this study are derived from therocks of Himalayas and are the product of the riverbed'n in Fig. 2. Thesemodeled materials ¥vere used later in triaxial tests. Theall the alluvial rockfill materials. The alluvial rockfillvalues of UVC for these maximum particle sizes wereobtained by extrapolation from the UVC values alreadyaction during ¥ "ater fio¥v in the tributaries of the majordetermined for smaller maximum particle sizes.The values of UVC vere plotted against the values ofUCS for all the modeled rockfill materials as shown incarry broken rock pieces of various sizes producedFig. 7. As observed ear'lier, it is found that the ¥'alues ofUVC decreases with increase in particle size and the valueof UVC is high for quarried rockfill material as comparedto the value of UVC for alluvial rockfill rnaterial for thesame maximum particle size.An abrasion test ¥vas also conducted on the rockfillparticles to determine Los Angeles Abrasion Value (IS:2386: Part 4: 1963). In this test an aggregate of 5 kg¥veight (20l2.5 mm size, 2.5 kg and 12.5-10mm size,rivers Indus and Ganges (Fig. 1). These snow-fed riversprimarily by glaciation and ¥veathering of rocks/boulders. The impact, rolling and sliding actions of the rockpieces in the ri¥'erbed during ¥vater fio¥v cause roundnessand smoothness to the rock pieces. The riverbed-actionson the rock pieces depend essentially on the ¥'elocity of¥vater fio¥v and the nature of the riverbed. As theseactions are not same for all the rivers, the roundness andsmoothness of the rock particles are different for eachrockfill material and this is reflected in the scatter of thepoints in the plots bet veen UCS and UVC/LAVobserved in Fig. 7 for various alluvial rockfill materials. ¥rARADARAJAN ET AL.574OTable 2. Details of drained triaxial testsgQu eSNo.ilvlaleria]s from .Maximum Confining pressure,particle (rl (¥. ,{Pa)size CJP:ston, ****(mm)HYd rc JiLC ch(sTr,berdreEnog ?lRanjit Sagar Dam Site = 25, 50, SO 0.35. O.70 1 10 1 40)80Tehri Dam Si 25,e 50,O_352.O 704,-hYdQvilc oii too {(both borro¥v areas) I .056, I .4083SeQling ctornps¥Vestem Yamuna C_anal 25, 50, 80 O.2, 0.4, O 6, O 8ond outerm e m brenes(both sites)4+Shah Nehar Si e 25, 50, SO ; 0.2, O.4, O^6, O 8)Kol Dam Si e 25, 50, 80 O.3> O 6, O.9, l.2orik38 1 cm c x 81.,3 cm height)(both ma erials)6.Puru ia Dam Site 25, 50, 80 O.3, O 6, O.9, l^27^Parbati Dam Site 20. 40. 80 O.3, 0.6. O.9, l._)See:]na clernp5Tabte 3. Details of the triaxial cel!ParticularsApplied byCapacityFrorn Wetero ,vrrette ferC_onfining pressureAir- va er pressure s.vstem 3 lv{Pa9erv o I rmeesVr nci*Yo t umeFechQnQeAxial loadSpecimen sizeH .'draulic pressure unitiQtereipressure875 7 kNLen_ .*th = 813 mm, Diameter = 38 1 mmFig. 8. Trislxia] test setupIn Fig. 7, it is noted that bet¥veen the t¥vo rockfillmaterials from Tehri dam site (points corresponding toUCS ¥'alues 106.47 and 136.96 MPa) the mater'ial ¥vithhigher UCS sho¥vs lo¥ver UVC/LAV though they belon'_to the same area and might have been subjected to similarriverbed action. As such, it appears that the effect ofriverbed action on the material ¥vith higher UCS is moregiven by Abbas ('-003). A brief description of theexperimental procedure is presented in the following.The quantity of various sizes of rockfill materialsrequired to achieve the gradation of the modeled rockfillmaterial for preparing the specimen at specified relati¥'edensity ¥vas determined by weight. The sample ¥vasthan the one ¥vith lo¥ver UCS for comparable riveTbedprepared using a split mould. The sample ¥vas prepared infive layer's in the split mould by compacting each layer byaction. Therefore, it is probable that there is a generala ¥'ibrator. The sample ¥vas saturated by allo¥ving ¥vater totrend, as sho vn by a¥'erage linear lines in Fig. 7, that aspass through the base of the triaxial cell, and using a topdrainage sy. stem for removing air voids. The sample ¥vassubjected to the required consolidation pressure and thensheared by applying axial loading ¥vith a rate of loadingUCS increases UVC decreases provided the riverbedaction is similar for all the alluvial rockfill materials.TRIAXIAL TESTSConsolidated drained triaxial tests ¥vere conducted onthe modeled rockfill materials. A dry density corresponding to 870/0 of relative density ¥vas adopted forof I mm/min. Readings of vertical displacement, volumechange, and axial loads were recorded at periodic intervals.testing. The confining pressure ranges for the tests ¥vereF,XPERIMF.NTAL RESULTSchosen depending upon the dam/abutment hei*･ht in eachSti'ess-St/'ail7- Vohune Change Re!ationsllipsproject. Details of the tests are presented in Table '-.Large size triaxial testing facility at the Central Soil andMaterials Research Station, Ne¥v Delhi, India, a Government of India Research Station ¥1'hich pro¥'ides laboratory and field testing services for most of the river valleyprojects in the country, ¥vas used for testing. Specimensize of 381 mm in diameter by 813 mm in length ¥vas usedfor testin*'. Details of the triaxial cell used for thespecimen size is sho¥vn in Fig. 8. Details of the equipmentused are g:iven in Table 3.The complete details of the experimental procedur'e areStress-strain-volume change relationships of themodeled alluvial rockfill materials are sho¥vn in Figs. 9 to15. It is observed that, in general, axial strain at failureincreases ¥vith increase in confinin*" pressure andmaximum particle size. Volume change r'esponse sho¥vscompresslon for three of the alluvial rockfill materialsfrom Tehri dam site (Old Dobata), Kol dam site, andRanjit Sagar dam site. The ¥'olume compression increases¥vith confining pressure and maximum particie size inthese materials. Three of the remaining alluvial rockfillmaterials from Shah Nehar site, and Western Yamuna THE ROLE OF NATURE OF ROCKFiLL IATER ALS757566:,--"Iw'i} : Inl d::::^*:))r:4:e,4')/.'e,Cl).ox-X'x E Eh9'5rF'; E. '-,S-E(1 3. ! 3r(f 71.s 'te 1>e,> *,e,:x_{4r/ .x -l.Ar-r Jef}_ J:A:r A-A1A.a. ' ef e- e- ' h o:.o -o *e *o -o1l?'OO15l_:)*Ax'ial Strain ((Vo)Axiai Strain (o/o)(i) Stress-Strain Behaviour(i) Stress-Strain BehaviourOOes -0.4e:: -O.4(,), -08c,. ,_e.**- 11)_ _0.8o>>- I .6-1.215Axial Strain (olo)(ii) Volume Change BehaviourFig.9. Stress-strain-volume chan"e behaviour of aliuvial rockfi lmaterial obtained from old dobata borrow area, 'Tehri Dam Site15Axial Strain (olo)(ii) Volume Change BehaviourFig. lO. Stress-strain*volume chan"e behaviour of alluvial rockfiiimaterial obtained from new dobata borrolv aFea. T=ehri Dam SiteCanal (Bridge site and Silt Ejector site) sho¥v volumecompression initially and some dilation latter duringbreakage factor, Bg. The value of B* is calculated byshearing. The dilation nearly vanishes ¥vith increase insie¥'ing the sample using a set of sieves (80 to 0.075 mm)confining pressure and maximum particle size. The netvolumetric strain is compressive in all the cases. Therockfill material from Tehri dam site (Ne¥v Dobata)sho¥vs mixed trend in the volume change behaviour.before and after testin*'. The percentage of particlesretained in each sieve is determined at both stages. Dueto breakage of particles, the percentage of particlesretained in large size of sieves will decrease and theStress-strain-volume change relationships of the threepercentage of particles retained in small size sieves ¥villincrease. The surn of decreases will be equal to the sum ofquarried rockfill materials are sho¥vn in Figs. 16 to 18. Inthese materials also, axial strain at failure increases ¥¥'ithconfining pressur'e as ¥vell as maximum particle size. Allthe quarried materials sho¥v compression in the initialincreases in the percentage retained. The decrease (orincrease) is the value of the breakage factor B_* (Marsal,1967).part of shearing and dilation in the later part of shearing.The relationships bet¥veen UCS and B* for all theThe dilation in volumetric strain decreases considerablymodeled rockfill materials ¥vith the maximurn particle size¥vith increase in confining pressure and the maximumof 50 mm for three confining pressures, 0.4, 0.6 and0.8 MPa are sho¥vn in Fig. 19. It is observed that theparticie size.Efi ct oj' UVC and UCS on B/'eakage Factol'Breakage of particles ¥vas obser¥'ed during triaxialtests. The breakage is expressed quantitatively by thebreakage increases ¥vith increase in confining pressure,(T3 for both alluvial and quarried rockfill materials. Theincrease in confining pressure causes an increase incontact stresses leading to an increase in particle break- lVARADARA JAN HT AL.57G93.0)-.5,,*:62.Ov')' c'):,e;(/)(/,Oi^**;,*.:,O3.l.O>e,e):0.5O0.01215Axial Strain (o/o)Axiai Strain (o/o)(i) Stress-Strain Behaviour(i) Stress-Strain BehaviourOO): -*s -O.4-1,(,e, -0,8. ,,, _7_S -1.'>>-1 .6-315{5Axial Strain (o/o)Axial Strain (olo)(ii) Volume Change Behaviour(ii) Volume Change BehaviourPi*. 11. Stress*strain-volume chan*e behaviour of alhlvia rockfilimaterial obtained from Ranjit Sagnr Dam Siteage.In Fi**. 19 it is also noted that the quarried rockfillmaterials ¥vith higher UVC ¥'alues (Fig. 7) sholv higher B*Fi(p.12. Stress-strain*volume chan"e behaviour ofaliuviai rockfi ln{atertal obtajned from Shah Nehar S tein density (Fi_ . 6). Increase in density causes increase ininterparticle contact stresses leading to increased particlevalues than the alluvial rockfill materials. The higherUVC ¥'alues in the quarried rockfill materials are due tobreaka_ e. Similar effects of size of the particles andconfining pressure on breakage factor ¥vere obser¥'ed byMarsal (1965), Vesic and Clou*'h (1968), lvlarachi et al.an_9:ular and rough particles as obser¥*ed earlier and as a(1969), Venkatachalam (1993) and Varadarajan et al.consequence they undergo higher breakage than the(2003 ) .allu¥'ial rockfill materials.The rate of increase of Bg ¥ 'ith (T3 is sho¥vn in Fig. '-Ofor the same materials. It is found that the quarriedrockfill materials ha¥'in** particles of angular and roughsurface sho¥v hi_"*,her rate of breakage than the alluvia]rockfill materials ha¥'in*' particles of rounded and smoothsurface.The effect of maximum particle size on B* is sho¥vn inFi . ,_1 for the samples tested at the same (73 equal to 0.8MPa. It is observed that the breakag:e increases ¥vith theincrease in the maximum particle size for both t.¥'pes ofrockfill materials. Vith the increase in the size of theparticles, the ¥'alue of UVC decreases indicating increaseAs the breakage factor is related to the UVC, thescatter of points observed in Figs. 19 and 21 is attributedto the scatter of the points in the relationship bet¥veenUCS and UVC in Fig. 7 for the alluvial rockfill materials.Also, the avera_",_e lines indicated in these figurescorrespond to the average lines sho¥vn in the relationshipbet¥veen UCS and UVC in Fi_"._. 7.Effect of UVC ancl UCS ol7 Vohnnerric Stl'air7The effects of the maximum particle size and theconfining pressure on the volumetric strain at failur'e aresho¥vn in Figs. 2,_ and 23 for the t¥vo types of rockfillmaterials. It is observed that volumetric strain at failure 「577THE ROLE OF N．へTURE OF ROCKFILL M、へTERi、へLS3。03．5 ③③φ⇔φ⇔ φゆ3．0姦菱 2，5Φ舜轟 2．5筐峯 ヂ 囲魁鼠し 4φ竃2．0 ゆ訂一一講ぞ｝萌’弩1．5 繧礁鴇誰2・or一『 『一「 ゴ㎜旧㎜ 一蝉一 一溌韮．3．乞溺 ム齢ム 一一燃匿艶一 盒合 ．憲1．o4〉㊤’鐸㊤ 1。Oo1 β鋤O Gミー92MPユ00ム噺司4MP＆臓G汗o尊MPユ o．5X σこ訓）SMP，乞 ：5mmd一吋、一一 憩ロtIud隅、0。5 s臼mmd。n、、o．o0．000E5亘0，，1015Axial Strain（（％）Axi3置Straln（％）（i）Stress−S辻ギainBeh謎、1iour（i）Stress−Strahl Be垂1av量OUr （1．0 oOσ汗02MPユ△侮累り4MPa× o罫口硫初く・MP翁）一〇．5 oo￠㎜×G轡OSMP．一⑧σこ塁G鉢陸】aAσfooMPa駕 一（1．12−o．2 ムムa＆こ一1．o口σザ〔｝oMPax σゼ1）8MPa 25mmd、諏需鳳 50m期d『』レ、、）一 sommd，二4．5一 Sl与mmd＝、一 一 一goユ5mmd．．，りO G；一Q2MPa△鰍甥u4MPa一一 5「｝mmd一、、麗σr編GOMP＆⇔σぜi2MP註の o田警厨躍一2．oφ亀⇔％軸⑳⑧￠￠＞＞ 一2，5 一〇．3051015Axi21Sむ’ain（％）（童産）Vo翌ume Change Behavio騒roさ1（1ま5Axla嚢Str段藍n（％》）（li）VolumeChangeBellaviourFig．13。Stress勒sIrain騨vo加mecha鰍gebeh賃viourof謎量1賎via汁oc酬l ma亀eri賃lob芝ained舞om擁dgeSitegWesこer羅YamunaCanalf「19・玉4・S｛ress・s症rain【・d礪echangebella、Plourof“賎uvi田rock韮銭increases with maximum partlcle size and the con行ningfailure envelopes for e＆c紅 maximum p＆rticle size of m“乳er亘ε監量ob載ai無ed from SilεKjedor Si症e，、、▼es重er鳳Yε毫π田na Canalpressure for bo宅h the niaterials．These負ndings on volu−rock徹l material passed througll the origin as shown inmetriC Strain at failUre are，in general，Simllar tO thOSethe Fig．24 for the tyP呈cal rockfill mate1’重als．From t熱enoted for breakage factor．τhat is，lower the UVC，angle of t熱e s玉ope，αofthe fa玉lure envelope，the angle ofhigher is the breakage factor leading to higher volumetricShearingreSiSξanCe，φWaSCalCUlatedaSφ一Sia㎜1（taηα）str段in at failure．As noted in the previous sectlon，the（Lambe and Whitman，玉969）for ea曲rock薮H material．scatter iR the points in the relationship be重、veen UCS andB、in Figs．19and2玉宝s related to the scatter of points in雌∼α（ゾPαπic1εShσP召011φtherela￡ionships between UCS alldUVC in Fig．7for由ealluvlα1materials．Therefore，由e scatter of points ThevariationofφwithUCS圭sshownin｝7ig．25forthethτeesizesofmodeled＆lluvlalan（lquarriedrock創Iobserved in Figs．22an（123is a豆so due to the sca賛er ofmε粍erials．hisobservedthatξhevaluesofφforquarriedmaterialsarehlgher山anthoseforalluvialmaterials．ThepointsinFig．7．quarried rock創l materials wi由higher value of UVC！41191θoゾ’Shθαノ●加g Rθ5Z5’‘7n6θφ From the stress−strain cur、ノes the values of（σ1一σ3）atfailure for each con負ning Pressure，σ3，were determinedand with these values the plots ofρ（；（σ1十σ3）／2）vs（1（襯（σ1一σ3）／2）weremade foreach rock長II maξerlal as shownin Fig．24for typical alluvia1（01d Dobata，Tehrl Dam）＆nd quarried （Paruliε1 Dam） rockfi11 materials． 丁王1e（F玉g．7） are 豆ooser than the aHuvial rockfill ma【el’ials．Therefore，a looser quarried rock負ll material wouldprovide lower interlocking resistεしnce during shear圭ngthan an alluvial rock行11m飢erial．However，the natureof par盤cle shape and surface texture also εし9奄ct theinterlockingreslstanceduringshearing．瓢ghervalueofUVC for quarried materi＆I also iadicates more angular l¥,ARADARAJAN ET ALOi S3.s:,3 * ()4'--::¥j:.;'cL' 2.f)e,.'C!), ! 5.Oe3;･l .O>e)'pQO . 50.0o15OAxial Strain (( ())5 1 o15Ax. ial Strain (olo)(i) StressStrain Behaviour(i) Stress-Strain BehaviourO.O1¥- -O.s- I .Oi.,eso-c -1._:)(1e,t,= -2.0, _l>-, .515>,Axial Strain (94,)(ii) Volulne Change Behaviourrig. 15. Stress-s,rain-volt me cl]ange behaviour of alluvial rockfillmaterial obtained from Kol Dam SiteAx ial Strain (olo)(ii) Volume Change BehaviourFig. 16. Stress-strain*voltlme change behaviour of quarriedinateria! obtajned from K*ol Dam Sitcrockfil!and rougher particles than the allu¥*ial rockfili material asalready noted in Fig. 7. Due to this, quarried rockfillmaterial ¥vould provide higher interlocking resistancedurin9: shearing: than the alluvial rockfill material,et al. (2003) have sho¥vn that the c value increases ¥viththe increase in maximum particle size for alluvial rockfillFurthermore, in the case of quarried rockfill materials the(2003) have reported decrease in the c value ¥vith increasein maximum particle size for quarried rockfill materials.As sho¥vn in Fig. 7, the ¥'alue of U¥rC decreases ¥vith theincrease in maximum particle siz:e for both allu¥'ial anddilatancy caused by the angular and rough particlesduring shearing as sho¥vn by the ¥'olume change behaviour in Figs, 16, 17 and 18 Ieads to higher shearingresistance. Considering the net eff'ects of density andnature of the particles for the t¥vo types of rockfillmaterials, it is e¥*ident that the eff ct of shape and surfacetexture of particle is more dominant than the effect of thedensit.v of the rockfill material leading to higher angles ofshearing resistance for the quarr'ied rockfill materialsthan those for the allu¥'ial rockfill materials.E.fi;ect of Partic!e Size oil cIn Flg. 25, it is observed that the c value decreases ¥viththe maximum particle size for quarried rockfill materialand it increases lvith the maximum particle for allu¥'ialrockfill material. Venkatachalam (1993) and ¥raradarajanmaterials. Marachi et al. (1969) and Varadarajan et al.quarried rockfill materials. A Iarger sized rockfill material1 'ith lo¥ver value of UVC_ ¥vould be denser and ¥vouldexhibit higher interlocking resistance during shearing.It is observed from Fi_g:. 21 that larger siz,ed rockfillmaterials ¥vith lo¥ver UVC value also undergo higherbreakage during shearing. The effect of breakage is torecluce the resistance during shearing. Therefor'e, the neteffect of denseness and breakage on shearin_"_ resistance¥vill decide the nature of change of c ¥vith respect to t,heincrease in the maximum particle siz,e. It is noted that therate of averag:e increase in breaka e factor ¥vith incr'easein confining pressure is higher for quarried rockfillmaterials than that for alluvial rockfill materials THE ROLE OF NATURE OF ROCKFILL hIATERIALS:)579:)O cr ;$03 lPsA (;;06 lPaa l;:;[ o .Ipe I t eX o;:: 1 2 IP(tll44J- o mrn d:::;X:3X)(.-3]XC1ealIS1s:'C,,1X'--' SO mm d:? i' Xr¥le. ･i: 1'X5 rTIFTI d:?11 I?,e,k(le,AC:1oo246 8ltl'OeeeOc:olO4 6 8oAxial Strain (o/*)lOAx'iai Strain (olo)(i) Stress-Strain Behaviour(i) Stress-Strain BehaviourQ.Oo.oeeee c:o::l'-0.5s: -1.0Cl)vcs,.e, _lOO cJ1=0i .rpae, _2.0A (T =06 {Pa as * O, ¥.1Pa::X c>-1.5= 1 2 iPa*･*mnl d***.- sO n]I l d 's'>- SO mrn d=: '-3.0lOlOAxial Strain (ol*)Axial Strain (o/o)(ii) Volume Change Behaviour(ii) Volume Change BehaviourFig. 17. Stress-strain-volume ciranoe bel]aviour of quarried rockfillFio. 18. Stress-strain*volume cl]anoe behaviour of quarried rockfiilmaterial obtained from Parbati Dam Sitema eriat o ]tained frorn Purulia Dam Site(Fig. 20). Therefore, the effect of breakage on the shearing resistance of quarried rockfill materlal is higher thanthat for' alluvial rockfill material. Therefore, the effect of15¥*"-¥breakage on the c value appears to be more dominant inS lOthe case of quarried rockfill materials than that in the caseOof alluvial rockfill rnaterials. Therefore, the valuedecreases with the increase in the maximum particlefor quarried rockfill mater'ials ¥vhereas the valueincreases with the increase in the maximum particleof csizeof csizefor allu¥'ial rockfill materials as sho¥vn in Figs. 25 and 26.- -Allullai (O 6 ¥. rpn)A- O.lL*-rried tQ 8 1Pa)Llnear (A]luFi**. 27. It is significant to note that the value of c as ¥vellas the average r'ate of increase in the value of c. IPa))L--･-･ ･ ･---*¥'>-- Bl 1raeEr (Ailt 1 n! (O S ;¥. rpa )i !.:)=__--1..,_ :_ !:'1,:$J:*'- 0e:tI t",* 'e]i;,, -_;__ e*o･_-o 75 Ioo 125The avera*'e rate of change of c ¥'alues ¥vith respect tomaxirnum particle size has been plotted ¥vith UCS valuesfor both types of the rockfill materials as sho¥ 'n inal (O 4- - 1_Inear {Ailullsl {O e ¥. Ipa))r]Jo IEffect of UCS on cA!lu l; i (O 4 1Pn}'*- A[lu la! (O S ¥. IPa}e QL:err;ed (rJ 4 , Ipn]-B O, arr:ed (O 6 ¥. IPa]Fig. 19. Variation of B,150l 75UCS (MPa)vith UCS for the twoty pes of rockfillmaterials¥'ithrespect to maximum particle size increase with theand 21 on the average, the value of' UVC decreasesincrease in the UCS value for alluvial rockfill materials assho¥vn in Fi**s. 26 and 27. As already observed in Fi**s. 7(denseness increases) ¥vith the increase in the UCS valueand the breakage factor increases ¥vith the increase in the i580 ¥*ARADARAJAN ET ALs2.5¥-¥12.0t)'*.*** 6A: l･S$es,e J:i5s>b<- - * }Iu"isl t25l.OHil. 5_nrn)A! it*11; i i s ) mrn)!ll '1 { I s{) mm)¥-O.:'_* - -e-QL;: rr:edt:5m:1 )cSH - ( ts3rr eti ( s j nlmO.o r'='****'i QO 1 2060140**l OOl 60l :)_:)-OUCS (MPa)UCS (MPa)Fig. 23. Variation of voiumctric strain at failure witl] UCS at threerig. 20. varlation of average ratc of change of B,, wiul rospecto a*ma¥. imum particle sizeswith UCS123-- 1022^s:8ee64ot)*2p ( , IPa)o5 o7:):)-l OOl 2550rig. 24. p-q diagram for t)'picarig^ 21. variation of B,, 1 'ith UC_S for the tlvomaterialsalluvia] and quarrled rockfillmatcrialsUCS (MPa)l. pGS of rockfillje 'I r =' !,..___"__ -- ,,- -'=itil**' t= l*i=*=1)**'* **+ r)<' *=:* *h== )**};**1 I **=*J(* * -! *=*f= : +*'* } i***hr *'- .f'li :'i*:****- ;*=*1**}"'s ; _ * ? *=* +t* IY**'t h=i: !== 2.04: },;t*c**'*I*<:' '-=. 'H - !* *' ** r *='*-s- !'**h*1* i)*=n +*=*'1.:).:)-i{***ki i:'f, 1,0s(( ss Q.5eS O.oj1 rF-o.520oi ]7 1i l" m m i':]rtio]e size {n'm)loo(] 50 l_･ O 200UC_S (l rpa)Fig. 22. Variation of volt nretric strain at fai!ureconfining pressuresrig. 25. Variation of c-value with nraximum particle sizevith UCS ai threeUCS ¥'alue for the alluvial rockfill materials (Figs. 19 and_1). As discussed in the previous section, the effect ofincrease in denseness (lo¥ver UVC value) is to increase theshearin : resistance during shearin due to hi9:her interlocking, but the effect of increase in denseness is also todecrease the shearing resistance due to the damage causedb_¥' high breakage of particles. It appears that the effect ofdenseness in increasing the shearing resistance duringshearing is more domlnant than the effect of breakage ofparticles in decreasin_cT._ shearing resistance. As a result, thec value as ¥vell as the rate of increase in c value ¥vithrespect to the maximum particle siz,e increases ¥vith theUCS value. ¥Vith regard to quarried rockfill materials, ithas not been possible to arrive at any conclusion on theeffect of UCS due to limited data.PREDICTION OF c FOR PROTOTYPE ROCKFILLMATF.RIAl,Shear strength of geologic materials has been expressed THE ROLOF NATURE OF ROCKFILL ¥1ATERIALS5Sl5 Orockfill materials from the triaxial test results. The value45of (x' ¥vas found to be nearly constant and ¥vas equal to0.937.e,e,The parameter B' has been expressed as a function ofthe baslc characteristics of the rockfill materials that;b4 Qe,3 :)-affect their behaviour. These characteristics includee,particle size, nature of particle shape ancl surface, particle30strength, gradation and relati¥'e density, In this study, theparticle size, the nature of particle shape and surface and2050 Ioo 150O2 (] (}UCS (rvlPa)gradation are expressecl in terms of UVC and the particlestrength Is represented by the UCS of' the representativerock f'rom ¥vhich the particles are cierived. Accordingly,the value of' B' is expressed as:B' = Cl P '=rrg 26, Variation of c-vaiue witi] UCS of thrce max'inlL m particlesizeswhere CI' C , pl and pC2(UVC) " (4)are constants,P normalized UCS value. In this study the UCS isnormalized ¥vith UCS ¥'alue of' Ranjit Sagar rock-(].20fill rnaterial ¥vhich is the highest ¥'alue. Any otheri¥*alue could ha¥*e also been usecl for normaliza-O.15tion,UVC uncompacted void content expressed as fraction.1 O.1(]The relative densit.v has not been included in the abo¥'e<:,relationship (Eq. (4)) as all the modeled rockfill materialsvere tested vith the same relative density.eJ0.05<The ¥'alues of the constants C!, C , pl and p¥veredetermined as follolvs.().ooo50 Ioo 150The value B' ¥vas determined using Eq. (4) at four200UC*S (tvrpa)Fig. 27. Variation of average rate of change of c-valuc witl] respect toconfining pressure with UCSconfining pressures for each modeled rockfill material.The avera :e of f'our values¥'as calculated. This ¥*alue ¥ 'asused in Eq. ( -) along ¥vith the ¥*alues of' P and UVC ofthat material. Thus three equations ¥vere formed for thethree modeled materials for each rockfill material.T¥venty one of such equations ¥vere f'ormed for se¥'enas a f'unctional relationship bet¥veen shear strength andnormal stress or principal stresses by various researchersallu¥'ial rockfill materials and nine equations lvere f'ormedfollo¥ving Mohr-Coulomb failure criterion (deMello,constants Cl, C , pl and pl ¥vere foLmd using least squaresfitting method for alluvial and quarried r'ockfill materialsseparately. With these constants, the relationships for theprediction of the B' value ¥vere found to be:1977; Yoshinaka and Yamabe, 1981; Franklin andDusseault, 1989; Ramamurthy, '-OO1). Herein, the following relationship is proposed for the rockfill materialstested under triaxial condition("(71 (7 =B cTl+2cr (_.)P* Pafor the three quarrled rockfill materials. The fourB' = 0.85016PO I - 2 14964(UVC) (5)for alluvial rockfill materials and,B' = O.58072Po iwhere, B' is a non-dimensional parameter based on indexproperties of the rockfill materials, c ' is non-dimensionalparameter, CTI and cr3 are the major and minor principalstresses and p* is atmospheric pressure expressed in thesarne unit as the principal stresses.The parameter, a' can be determined by conducting atleast t¥vo triaxial tests with two different confiningpressures as:log ((Ti-(73)iae' log= (al- CT3)j - I (3)((71+2(73)iO.59167(UVC) (6)for quarried rockfill materials.The validity of' these Eqs. (5) and (6) ¥vas ¥'erified asfollo¥vs:Using the Eqs. (5) and (6), the value of B' ¥vas predicted f'or each modeled rockfill material. The values of al atfailurevere then predicted using Eq. (2) for the fourconfining pressures, (T3 used in the triaxial tests. F=romthese vaiues of crl and (T3 at failure, the ¥'alue of c ¥vascalculated. The ¥'alues of c predicted for all the modeledrockfill materials have been compared ¥vith the observedvalues from the tests in Figs. '-8 and 29. It has been((Ti + '-CT3)i- l¥vhere subscripts i and j+ I indicate tlvo triaxial tests.The values of' ( '¥'ere determined for all the rnodeledobserved that the error bet¥veen the predicted andobserved c-¥'alue is in the range of -8 to + 1'_(olo). Assuch the predlction may be considered satisfactory. Using ¥IARADARAJAN ET AL.5s24550c Tehri Dam ( Old Dobaie)Tehri Dam (N+el¥'Dobata)c Koi D ulll puru]ia DamA P arbat i DamA Kol D mX Ranjit Sa_ ar Damc Sl]ab Nellar45ooVestern Yamuna Canal (Brid*._,e Site)+ ¥ *estern Yamtlna Canal {Silt Ejecto te),o pancheshlr. ¥.epalXes>*i-*e, 40X.,1iddie Siang,+e +cc';>42eyc ie,35coAAoB4AooAoAe,39304030:,:, o4239Obs e]'¥ed 4hVal ue4:,.-Obs e r¥ed c･Val ueFig. 28. Comparison of observed and predicted c-values for alluvia]Fig. 29. Comparison of observed and predicted c-values for quarriedrockfill materialsrockfill materiaisTable 4.Comparison of c-values of prototype rockfill materialsc-values basedc-vahles based onDifferenceon po ver la liu c-¥'alues(degree)index properties(degree)51 441 9Tehri Dam(New Dobata)46 , i39 7- 6.5- i 4 07Kol Dam41 .636.35.3- 12.74Ranjit Sagar Dam63 34 1-7- 17 6Shah Nehar43 ,240.52 7- 6 25¥Ves ern Yamuna Canal50 343 .4- 6 9- 13.7245.843.5- 2.3- 5 .02Kol Dam38.8473,59 . 02Purulia Dam37l3 8 ,, 8l4.58Parbati Dam40.440.0h,laterial siteTehri DamDifference(o,6)(degree)- 1 8.68(O d Doba a)AHuvial- 2780(Bridge Sile)¥¥restern Ya nuna Canal(Silt Ejector Si e)QuarriedEqs. (5) and (6), the values of c ¥vere predicted for analluvial obtained from Panchesh¥var Hydro-electric37- o 99The value of c for prototype siz,e rockfill material ¥vasdetermined ¥vith the Eq. ('-) using B' values as calculatedPo¥ver Project, Nepal and a quarried rockfill materialfrom Eqs. (5) and (6) for the corresponding values ofobtained from Middle Siang Hydro-electric Po¥verUVC of the prototype size. The values of c predicted fora prototype size of 300 mm for all the rockfill materialsare presented in Table 4. For comparison, the values ofc vere predicted for all the rockfill materials using thecommonly used extrapolation technique using po¥ver la¥v(Varadarajan et al.. 2003). Significant differences arenoted bet¥veen the predicted c ¥'alues by the t¥vo procedures. It is believed that the c ¥'alues predicted by theprocedure used in the present study is realistic as itincludes most of the basic characteristics of the rockfillProject, Arunachal Pradesh (materials not included forthe determination of constants in Eqs. (5) and (6)) andare sho¥vn in Figs. '-8 and 29. The predictions appearquite satisfactory.As more data are a¥'ailable ¥vith time, constants in Eqs.(5) and (6) may be further refined. Equations (5) and (6)can then be used ¥vith confidence to predict the angle ofshearing resistance of rockfill materials for the design ofdams . TRE ROLE OF N．へTURE OF ROCKHLL M．へTERI．へLSma芝eriaiwhereasthecommonextrapo1＆tionprocedureused collsiders ollly the maximum particle size of由erock負llmateriaL58316／1NcGE−35／99from出eMlnistryofwαterResources，ResearcllandDevelopmentDlvisiol1，Govemmentofln（iia．The assistaace provided by various project aut熱oトitlesisgratefullyacknowledged．CO翼CLUSIONS The c紅aracteristics of particles from seven alluviaIrockfill nlaterials aud three quarried rock且11 買1aterialshave been quautltatively expressed by ullcompacted voidcontent and uncon負ned compressive strength of the rockparticles．王）ecre＆se in the ullcompacted void content withdle maxinユum par￡icle size and average（iecrease圭n theuncompacted void content with uncon負ned compressivestrength of the particles are observed．Angularαnd roughsurfaced pεtrticles ofquarried rock負互1materials are foundto hεtve higher uncompacted void co陰tent than宜he roundREFERENCES D 、へbbas， S、 釣「1、 （2003）：Test三ng and n｝odeling the bel｝avioしlr of riverbed and quarried rock自11nla乳e藝als，Pノ∼五） Tノ∼θ5’5，RT Delh1， New Delhi，王ndia．2》．へ組rich，R、C、（1996）：Inf沁enceofaggregatepropert1eso【1perform− ance Qf heavy−du｛y hQt−mix asphal【 pave道1ellts， 71’α’∼∫po1マα1’o∼7 1∼θ5θα’℃h1∼θco1｝イ1547，Transl）ortatioll Research Board，Nationai Researcll Cou疏c11，Washingτoll D、C3》．Ansa嫉，K、S、andCilandra，S、（1986）：｝穫owoughtolletodeternli【｝e so貢parameters to be used ia【he clesign of ear〔妻1aad rock撮l dam？， Pヂoぐ，／’1伽nGθo’θ‘一11，Co／1∫．，NewDelhi，2，1−6、4）ASTM C l252（1998）：S礁∼ゴαヂゴT25’A／θ∼hoゴ．五〇r Uノ∼co11∼ρααθ4and smoo由 surfaced particles of alluvial rock負ll 歓「o’ゴCo’∼‘θ1∼ωゾF加ε、4ggrθ9αθ妨／ノ漁ε1κ’θゴαvp‘’1『’1ぐ1θ51即θ，materialS． S‘〃プ汝c（∼7εY1‘”｝θ，αノ14（フ’”α4’1∼9ノ，．へST｝〉正S［andard、 From the drai貧ed tri＆xial tests on山e mQdeled rock負llIIlaterials of alluvial and qua…』ried rockfil塁Rlaterials，thefOllOwingCOnCIUSiOnS＆redraWa． i） The axial stra玉n，volumetric str3in and breakage5）．へSTM D 2938 （！995）：S’α11ゴα1『4 Tθ5’Mθ∫ノ∼04∫oノ『U1∼co1｛！『’∼e4 Co〃∼ρ∼（ぞ55’yθ 511ぞ∼19∫h ￠ブ1∼∼’θご’ 1∼oごん Co∼ぞ 5ρ（∼c1〃1θn5， ．へSτ！∼・1 Standard6）ASTM D3398（2000）＝∫襯伽・ゴτε5’Mθrhoゴ、戸01・／ノ1ゴαq〆 。499∼θ9α1θρθ∼’1’（ゾθ5ノ∼oρθ【∼’∼oF7ε』Yπ〃｝θ，、へSτ）》I Standard． factor increase wit益 col1負aing Pressure and7）ASTMD479i（1999｝：S∼α1∼ゴαノゼTθ5’A／θ’1∼oゴ∫01’F1α’Pα1一”（b1θ5， maximumparticlesize。 li）丁負e average rate ofbreak＆ge factor witll 五101∼9α副Pα航ゾθ5，01。F1醒αノz‘1五ノo刀9α’θ‘1PαノYic1θ∫加Co鷹θ cQn食n呈ng Pressure is higher for（lual−r圭ed rockf｝ll materiahhan that for a11uvial rock最11material． iii） The angles of shearing resistance for quarried rocknl至nlaterials are higher than those for a重luvi− al rock負ll materials with compar＆ble unconaned compressive stl’eng書h of rock particles． lv）Theangleofshearingresistanceforalluvi＆l ！1gg’ぞgα18，AST｝〉I Standard．8）ASTM D5821（1995）13’α1r‘1α1’ゴ7’θ5’、・》θ11∼04∫01・0θ’θ1・〃1加〃∼g〃∼θ Pθ’｝c8∼∼1α9（∼ oゾ」F1て∼c1ど’1署‘ノ ραノ7’c1θ5 111 Coα1写（∼。499ノ“‘∼9‘r∫θ， ．へST∼㌧I Standard，9） de卸1ello，V．F、B．（！977）：Re負ectio【｝ondes1gndecisionsof i）rac巨cal significance ｛o embankrllen［ dan】s， 17’1∼ Rα’1ん’1∼θ 五θc’μ∼θ， Gθo’εc／11瞭’θ，27（3），281−354．10）Franklin，」．A、andDusseaしElt，M、B、（王989）IRo欲五1∼911∼θθ∼”1∼8． McGraw−Hiil Publ三slliug Company，New York，237−269、11）Fro黛，R、」、（1973）：So〃1θ7θ∬’〃g五』vρθ∼・’θncθ5α1∼4Cノ∼αrθc1θ1へi∫”cs rock行ll materiαls lncreases with the maximum oゾβα’1ゴ8ヂー（31甲αvθ！F1〃∫11∼五απh∠）α〃1∫，刈STど∼イ1，SτP523＝207， particle size and opPosite trend is noted for quar−ま2） Fumaga目i，E．（1969）：Tests o騒 collesiollless materials for rockfill ried rock且ll materials． v） The angles of shearing resistance as we圭l as the rate of 圭11crease in angle of resistance ㍉v疑h maxlmum particle size incre＆se with the increase dams，／．3MF五，ASCE，95（SM1），313−332、王3） Hali，E，B and Gordon，B．B、（1963）：τr1ax1a1毛esting usiag large scale high r）ressure eq糠ゆment，〆iS7込／，STP36王，315−328、14）Hossain，氏・L S、，Parker，F．aud Kandha1，P、S、（2000）：Compar1son aΩdevaluatiolloftesζsfQrcoarseaggregate，湘S7M／、τθ5’，Evα1、， in the ullcon行ned conlpressive strengtぬ of t紅e JTEVA，28（2），77−87、 rockparticlesforallu、・ialrock且llmateri＆1s．15） 至S 2386： Part 4 （1963）： A／θ’hoゴ5 0Lブ 71θ5’ノ10r 、4gg1’θgα’ε∫ノlo〆 vi） The behaviour of rock行ll m＆terials，in general， 買玉ay be exp圭a玉ned呈n tel’ms of the uncompacte（i Conぐ〆αα Aグθc1∼σ刀1cα1 P1臼oρθ1’”ε5， Bureau of Indian Stalldard， India、16） L【ambe，丁 ∼V、alld∼V11貢man，R，V，（1969）：So11A／θぐ1∼α’11c5，3rd ed、， void content and ullcol1且ned conlpressive 、V疑ey EasterΩLtd．，New Delhi、 strength of the rock particle．17）Lowe， 」 ， （1964）： Shear strerlgt暴 of coarse embankment dam vii）Arelationshiphasbeendevelopedtopredictthe an黛le of s紅ear圭ng resista！1ce of mo（1eled rockhl正 m飢erials using the uncompacted vold coatent of materiais，P”of．8〃∼∫1∼∼．Co’∼9．五αrgθ五）α1115，3，745−761．18）Maracili，N、D．，GlanC、K、，Seed擁、B、andDuncan，J．養L（1969）： S〃’θ∼1g！11α’∼406∫01’〃1α”oηCソ1α照αθだZ5”c50ゾ9Roc姻”A1α∫（∼がαな， RePort No、TE69（5），C1vil Engineering Depar【nlent，University of 由e rock負ll materlals and ullcon伽ed compressive Ca墨ifornia，Berkeley，US、へ、 strength of the rock particles．It is believed that19）Marac撤，N、D．，Chal1，C，K．andSeed，R．B，（1972）：Eva！職io自of thls method is superior to the existing method properties of rock自ll materla垂s， 、ノ． 5A4F五， ASCE， 98 （S｝》11）． based on maximum size of particlesαnd may be used to predict theαngle of s封earing resistance of 95d玉4．20）Marsa1，R．」、（1965）l Discuss1on，Pノ・o（・、，6’h ICSAグ■E，3，310−316．，So〃21）Marsal，R．J、（1967）：Largescaleこestingofrock良Uma芝erials，ノ prototype size rockhll materials．It鼓as potential A4θc1∼、α’∼4Fα∼ノ∼ゴ五）’v．，ASC狂，93（2），27−43、 to beused fortheprediction oft紅e ang至eofshear−22）Ramam穏rこhy， T、 （200D： Sllear strength response of some geologicalmaterialsi田rlaxlalcompression，1n1．ノ．RocんMθご1∼、 iPg resistance for the des呈gn of rockfi至l dams． A伽’∼∼gSc、，38，683−697、23）Ramamurthy，T．and Gur）芝a，K，K （1986）：Response r）aper to熱owACKNOWLEDGEMEMST｝1e researc至l work∼vas pαrtly supPorted by Gr＆nt No． ougllt one【o determine soil parameters【o be used in the design of ear樋1and rock丘駐dams，P”oc，∫（｝C，2，15一三9．24） τねiers，G、R、and DQnovan，T．D、（1981）：Field densi｛y grada￡ion 58婆V、へR、へD、へR、へ」．へN ET．へL， 51∼eθrS〃マθ119’hρブεo’／，〆当S7ン》，STP740（eds、byR。N、Yo臼gandE ma芝eria！stmde湘ghsIresses，／、＆》π，滋SCE，94（SM3），661−688．28）Yosh1naka，R、a自dYamabe，τ、（i981）＝Astゴengthcri毛eriopofrocks C．To、mse自d），American Society of Tes［ing and Nlaterials， a厳（irockmasses，P／90ぐ．1’π．＄L”71ρ．馳αんRoぐた，Tokyo、 315−325．29｝You（i，丁、L．（1973）：Factorscomro目ingmaximし三ma臓dminimLml25）Varadarajan，A．，Sl｝arma，KG ，Venkatachalam．K、alldGし騨a， AK，（2003）：Tesii睦ga竃1dmodelhlgIworocknIlmaterials，ノ． deロsities ofsa！lds，Sρθc’α1τθclr111cσノP置’δ！’ぐσ’1011No．523， 0θo∼θclr。Gθoθ’1v．￡1∼91召．，ASCE，129（3），206−21830）Zeller，JandWulllma…1n，R．（1957）汀hesbearstre丘9dloftheshell26）Venkatachalam．K．σ993）：Prediction of mechallical behaviour of IllateriaIs for tbe GQ−Sche除e【｝alp Dam． SwiIzerlaad， PIPoc． 4 rock鼓11nlater1ais，Ph．0． r／1θ515，i1，τ Delh1， ∫CSA’1Fε．London，2．399−404、 and柔rlaxiai【est玉11gofiarge−sizerock角ll forlittlebluerundam，乙αZ）．27）Vesic，A Bandqough．G W、（1968）：Eehaviourofgranular 月1ηθ’ソcθη∫oぐ紐γ〆ひ1厚々5”ngo∫．、如θ1ソαな．98−122． | ||||
| ログイン | |||||
| タイトル | An Investigation of Diffuse Failure Modes in Undrained Triaxial Tests on Loose Sand | ||||
| 著者 | J. Desrues・I.-O. Georgopoulos | ||||
| 出版 | soils and Foundations | ||||
| ページ | 585〜594 | 発行 | 2006/10/15 | 文書ID | 20942 |
| 内容 | 表示 rSOILS Ai¥'D FOUi¥TDATIOi¥TS Val 46. No^ISI )94 Oci '006Japanese Geo echnicai Societ}AN INVESTIGATION OF DIFFUSE FAILURE MODES IN UNDRAINEDTRIAXIAL TESTS ON LOOSE SANDJACQUES DESRUEsi) and loAN'i¥1'Is-OREsT s GFORGOPOULOsii)ABSTRACTIn this paper ve present an experimental study perf'ormed as an attempt to exhibit non-localized, diffuse failuredef'ormation modes in sand specimens submitted to test conditions leadlng to unstable failure. In particular, we areinterested in diffuse modes ¥vhich may appear in common triaxial compression tests on undralned loose sand specimens. A special series of triax'ial compression tests are repor'ted. These tests resemble the comman triaxial compressiontests but are modified in such a ¥vay that after the peak in the stress-strain curve, test control is changed from straincontrol to stress-control. More precisel_¥', a special kind of load-control is used, based on an original device ¥vhichallo¥vs to recover displacement-controi after a dynamic step in the post-peak regirne. It is sho¥vn that the control usedallo¥ "s f'or the obser¥*ation of the failure modes occurring in the unstable branch of the test.Kev lvords: difiuse failure, dynarnic instability, Iocalization, shear band, stress-strain controlled triaxial compressiontests (IGC.:D6/F6)Chambon ('-OOO) and others- have sho¥vn that shearINTRODUCTIONbanding can be predicted solely on the basis of the con-A proper description and understanding of failure institutive la¥v that describe the beha¥'iour of the material.g:eomaterials is a rnajor concern in natural hazardmitig:ation. Localized failure is kno¥vn to control aOn the other hand, other theoretical investigations-Dar¥'e et al. (2000), Nova (1994)- suggest that insome loading conditions, Ioss of stability can occur fornumber of catastrophic ruptures obsel'¥'ed in the field(among other references, "Failure" by Scott (i987), buteft ctive stress states far bef'ore the plastic failure stressthere are cases in ¥vhich rupture seems to concern all or alar*'e part of the volume of the material involved in thecondition or the shear banding: bif'urcation criterlon ismet, and lead to diffuse rather than localized failure.problem. In the laboratory, a number of experimentalGajo ('-OOO, 2004) in¥'estigated theoretically and experimentally the onset of the instability in saturated,loose sand samples and analyzed the infiuence of loadingsystem compliance on the instability under stress-con-studies, e.g. Vardoulakis et al. (1978, 1985), Drescher(198,_), Han (1991), di Prisco ('-OOO), Desrues et al. (1985,1989, 2004), Tatsuoka et al. (1986, 1990), Yoshidatrolled conditions. The tests ¥vere performed undeldrained conditions rather than undrained, but special(1994), Kato et al. ('_OO1), Arthur et al. (1977, 1982),Finno et al. (1995, 1996) and others, have shown thatstrain localization is obser¥'ed in a large range of testbands ar'e likely to occur even in lvell refined tests,including: slenderness reduction and careful end lubrication (Desrues, 1996, ,_004). In loose sand and elevatedmean effective stress, Iocalization can be delayed sig-loading paths ¥vere follo¥ved, starting from an anisotropicstate of stress (cl, p') with q de¥'iatoric stress and p' meaneffective stress. The loading paths in¥'ol¥'ed imposed increase of the pore pressure in order to reduce p' at constant cl, or other stress path control in¥'olving a decreaseof'p' as an intermediate phase in the test. These tests leadto catastrophic failure, or limited failure ¥vith a dynamicnificantly but it remains the final deformation mode(Desrues, 1989). Shear bands are observed also in un-strain jump, depending on the deviatoric loading systern(dead loads or pneumatic piston). This study shares somedrained tests, in vhich the deformation is constrained topoints vith the one discussed in the present paper, but thelatter ¥vas concerned more ¥vith the question of diffuse orlocalized failure. Vaid and Si¥'athayalan (2000) in a veryconditions for geomaterials. In dense sand specimenstested under lo¥ ' to moderate mean effective stress, shearan isochoric deformation mode due to the pore fluidtrapped in the specimen (Han, 1991), (Mokni, 1999).Theoretical studies in the frame vork of BifurcationTheory-Rice (1976), Vardoulakis (1995), Desrues andChambon (1989), Chambon et al. (2000), Desrues anddetailed study of the fundamental factors that affect theobserved liquefaction susceptibility of saturated sands,discuss among other factors the effect of loading tech-*' Direcleur de Recherche, CNRS-Universit6 de Grenoble. FrancePhD Student, Naiional Technicai University of Athens, Greece (IGeorgopoulosC,mechan ntua.gr)^The manuscript for this paper ¥vas received tor revie¥v on November 12, 2004; appro¥'ed on July 26, 2006_¥Vritten discussious on this paper shou d be submiited beforeTokyo I 12-001 1 , JapanUpon reques,Ia.v I , 2007 to the Japanese Geotechnical Society, 4-38-2, Sengoku, Bunk_vo-ku,the closing date may be ex ended one month.585 DFSRUES AND GEORGOPOULOS58(,+'r '//';/ 'rii:-" : "(d)i (e) r$1 s :'t'¥- ;Irt;[i.(e)iL 'x::tl'(a)(oF g. 1, General synopsis of the triaxia] installationniques on the apparatus-specimen interactions in monotonic liquefaction tests. The techniques studied includestrain-controlled, dead ¥veight, pneumatic piston andFig. 2.General vielv of the triaxial installationpneumatic piston plus a volume booster. Ho¥ve¥'er, no experimental information is gi¥'en about localiz,ed or non-localized nature of the deformation process during thebe adjusted in the range 0.0001-5.9999 mm/min. Theunstable deformation phase, neither in CJajo (2000, '_004)nor in Vaid and Si¥'athayalan ('_OOO). In fact, deforma-axial load is measured by a load celllring (c), Ivhosecapacity is - 30 kN. An L,¥IDT is used for measuring thetion modes can hardly be characterized experimentallysince they are supposed to occur along unstable loadingaxial deformation of the specimen and it is placed on thebranches for ¥vhich the brutal acceleration of the deformation process does not allolv to obser¥'e the transientdeformation modes of the specimen.top of the cell. The cell pressure is controlled by amechanical valve and the pore pressure by a mercury potsystem (e), ¥vhich allo¥vs at the same time for volumechange measurements during the drained phases of theIn the follo¥ving ¥ *e present a simple, prospecti¥'e,tests (consolidation). Both the cell pressure and the poreexperimental study performed as an attempt to observepressure are measured by pressure gauges. A11 themeasurements are recorded using a data acquisitioneither localized or non-10calized, diffuse failure deforma-tion modes in sand specimens submitted to tests conditions typically leading to unstable failure. A special testsystem under computer control (f).In order to achieve the special test control describeddevice is used to let the system jump into the dynamicmode after load peak, but only for a short whlle. Afterthat, displacement control is restored, allo¥ving for acharacterization of the kinematics the specimen under-above in section I , a slight modification ¥vas made to the¥¥'ent during the unstable, quasi instantaneous part of themainly stems from the necessity to be able to control thepath.stress and not the strain in a triaxial test, after the peak intriaxial apparatus. The modification consists of theinstallation of a spring bet¥veen the piston of the cell andthe load cell/ring. The purpose of such a modificationthe stress-strain cur¥'e in the softenln_"._ region. TheF,XPERIMENTAL SF,T-UPIn the follo¥ving, a short description of the triaxialapparatus used is given and the special device developeddescribed system consists of an elastic spring of A'* stiffness, vhich has a metal box on one of its ends. The metalbox is connected to the one end of the spring via a boltis described. Further information and details on theand a nut. The bolt is scre¥ved at one end of a piston. Thespring itself can freely slide along the piston, ¥vhich goesprocedure of triaxial testing for soils can be found in soilthrough the spring. What can prevent the spring frommechanics handbooks, e.g. Bishop and Henkel (1957), ormore recently Bardet (1997), Head (1992).sliding is a nut at the one end of the piston. A metal box isThe triaxial apparatus used is a basic strain-controlledaxisymmetric triaxial apparatus. Figures I and 2 sho¥v thethrough the spring up to the load cell/ring. At the sametime the box ¥vith the nut serves as a re ulator for themain features of the installation. It is made of t¥¥'opre-stress le¥'el of the elastic spring. This means that, bykeeping the other end of the spring fixed (i.e. scre¥ved atindependent components, namely (a) a loading frame50 kN in capacity, manufactured by Wykeham Farrance,including a frame and a motorized scre¥v jack controllin_"_.the displacement of the bottom platen of the system and(b) a home-made triaxial cell. The displacement rate canused to transfer the axial forces fr'om the specimenthe load cell) and by scre¥ving the nut at the other end,one can compress the spring at a desired level. This ¥villlatei' on prove out to be useful. Figure 3 shows a typica]vie¥v of the described system. A photo of this system is U+¥,DRAINED TRIAXIAL TESTS ON LOOSE SANDESpeeirn ro+ e+)/""I_*. t st5587--xSp ngFig. 5.Schematics of the specimen-spring s,stemr･.'IT¥+** *_'*/ o.esD_*oQ 4INSTABILITY CO_NDITION FOR 1'HE SPECIMENSPRI_NG SYSTEMe.;Let us consider the systern specimen-spring described*//*'i ;J: 2lE.l I ' '//"/*.s*.__J:; Ii 1; S s e242s.: 1' i[ ,j ¥'¥,. : r¥'in Fig.denotedpcnnt Adepends,o, . . .) = f'( xA, . . .)* '* : 2,*+r! * : o *r'*. oe1;2_Z--ee¥--'¥.f '; /' 'The force applied by the specirnen on polnt A isFs */A, and the force applied by the spring ondenoted as Fsp,;A. The response of the specimenthe history of xA, including the present state:Fs ./A = f (xA - . ( I )i ¥ "'-_'-',- ; f: / i'oi5.asrson+_..')4 .::j/with xo = O.The response of the sprlng is linear, ¥vith a constant stiffness K,:= - K,(xA - _¥"B)Frg. 3. Side vielv of ihe spring system.Assuming that the mass of the system is concentrated atpoint A, the fundamental equation of dynarnics reads:F ' F nls **iA+ sp,iA=.(3)Usm' Eqs. (1) and (2) in (3):f (xA, . . .) - K*( XA - xB) = lni!.Let us consider a given state ¥ *hich has been reachedfollo¥ving a quasistatic loading path. Up to this state, theacceleration A is zero.f(x ) K(x xB)=0 (4)The system becomes unstable as soon as a small perturbation of the system does not lead to small oscil}ations(which in practice ¥vill decay due to imperfections likefrictionai and/or ¥'iscous eft cts), but to increasing dis-placement (either oscillating or monotonous) from therest position x. . Addin*' a small incrementai displacementu* to x* in Eq. (3) ¥ve *'et:J'(x. , + uA,. . .) -K*(XA + uA -xB) = n7( iA T tiA) = miiA (5)Frg. 4. Metal box, nut, eiastie spring and load cel!Substracting Eq. (4) from (5) gives:f(x. +LlA,...)-j'(xA,...)-K*ualso gi¥'en in Fig. 4.The device works in the following way: as long as theload transmitted to the spring-box system is lower thanthe pre-stress level, nothing happens to the spring: thesystem behaves as a rigid block. As soon as the axial loadexceeds the pre-stress level, the sprin (' starts to compress,i.e, it stores additional elastic energy. When the instabil-ity condition for the sprin a-specimen system is reached-nlu (6)The expansion of f(xA + uA,. . .) is a difficult task, as soonas non-elastic behavior is considered, due to the strongnon-1inearity of the constitutive equation. The study ofthe stabillty of an equilibrlum state can be restricted tothe beginnin*' of the rno¥'ement after a perturbation ofthe equilibrium, ¥vith a discussion of the different cases¥vith respect to loading and unloading.this condition is discussed in detaii in section 3, the sys-As illustrated in Fig. 6, in the general case (not elastic),tem jumps into a dynamic mode and the spring releasesthe energy stored by stretching back. Ho¥vever, the boxthe specimen has t¥vo possible responses. Depending onthe sign of the incremental stretch undergone, ¥vithrespect to the state, ¥¥'e have loading for continueddeformation process, and unloading for reverse deforrna-does not allow more energy release than the amountstored after the pre-stress level ¥vas over passed. So thedynamic part of the test is limited in ter'ms of specimendeformation, depending on the pre-stress level.tion.Considering that the present equilibrium state is a DESRUES AND GEORGOPOULOS588, +*,oAxFspe!AthenAe /T7; i:(,A)/"" ' Be /r ･ TT 7(A A)/"'!=A+Band using Eq. (8) for t=0 ¥ve get:A + B = t/ok l03din9/r- ' -peak._On the other hand, using It=0 for t O l eselastic. / Io{din*' ¥¥^kunioadin9e.kt' = /･i -[Ae'=/T- ;TTrBe ;:,i (K= A1 },"""I. elsstie= 1 /Y [A Bl Ok Unloading5ticelastic'/*-(XA-Xo)then A -B=0These conditions on A and B can be met with A = B=u0/2, then we have from Eq. (8):Fig. 6. Force-stretch characteristics of the specimen, vith loadingunioading branches in pre-peak and post-peak regimeu=.uo[ei /77;TT7;;7(A A )/"'tTe (9)compression state, the initial phase of later mo¥'ementIt is time no¥v to discuss the respective values of thetangent stlffness of the specimen K* and the stiffness ofthe spring K*. If the specimen exhibits a characteristicioad-stretch response ¥vlth a peak follo¥ved by a decrease¥vill be either loading, Ivhich corr'esponds to negative uA,or unloading, ¥vhich corresponds to positive uA. Depending on the sign of uA, the load increment corresponding toa small incremental displacement uA ¥vill read:f(xA + uA) -f (x. ) = - K:u,uA<,O Ioadingu, >0 unloadinf(x, +LlA)-f(xA)= -A'**uvith A': the tangent stiffness of the specimen for loadingand K:' the tangent stiffness of the specimen for unload-/Tx-xiTT';;(A -K,)/"'!]in the load like in Fig. 6, then one has to distinguish prepeak from post-peak states, and in both of them loadin_'_.from unloading (in the sense defined above).Before Peak: u<0 Ioadmg Ke=K:>. O (a)u>0 unloadin a A'* K**>0 (b)After Peak' u<0 Ioading K K <0 (c)u>0 unloading A'. K**>0 (d)mg.The equation for tlA (denoted u for concision) durin_"._the initial phase of the movement is then:mu J- ( KK*)u = O (7)¥vith A'*=K: or K:' dependin_g: on the sign of u.In cases (a), (b), (d), ¥ve have K*A',> O. Then the squareroot / ,T 77; is real and the general solution Eq. (9)of the differential equation involves only imaginary expo-nents. We have:u = uo cos (l¥/･ t)Classically the solution of this differential equation islooked for in the form:u = e ""'then ii= - O)2u and Eq. (7) becomes:(A' +K co2)u=0and for non-z,ero u:¥vhich is an oscillatin_g: movement, indicating that perturbations do not _g:row. The equilibrium is stable. Ho¥ve¥'er,in case (c), K:+K* can be negative if: K:<, -A'* ¥vhichmeans that the tangent stiffness of the specimen is nega-tive, Ivith a modulus higher than the stiffness of thesprin c'. ThenK K co2=0The t¥vo roots of the equation (possibly complex) are:/K* + K*co = +_ ,'/" ln/Y /r.T T l. /llK: A',!l/¥ //71/ I - n7-" """ - l. --and Eq. (9) becomes:u = uo /2 [e'rr T7 ? t + e'/K;-K, !"' tJ( I O)u=Ae"!{K.+f() ,,,t Be '/?rTT7 ,(,( A) ,,,, (8)in ¥vhich the second term gro¥vs exponentially ¥vith time,¥vhile the first decays exponentially. Neglecting the firstone ¥ve have:L,et us assume that the initial conditions (arbitrary pertur-u=uo/- e'/ A']. A "'i (11)and the general solution of the Eq. (7) is:bation applied) are: for t=0, u=uo and tt=0. For t=0¥ve have:e'/{A:.-A),,,r e "(A 'i)"'!/ =1We can conclude that a sufficient condition for instabilityof the system is:K..< -K* (1_7) fUNDRAINED TRIAXIAL TESTS ON LOOSE SAND589is, up to a certain level, and by keeping the other end ofthe spring firmly scre¥ved at the load cell. By this setout,Consolidated undrained tr axi21 oompression test (Hostun Sss]¥ve predefine the initial pre-stress level force of the sprin'_.This means, in other¥'ords, that the spr'in*' Ivill be pre-stressed up to a certain point f'rom the very first beginningof the test, ¥vhich ¥vill allolv us later on to investigatevarious cases of difitlse modes of' failure.Let us no¥v follo¥v ¥vhat happens if the spring is pre-<compressed. In the beginning of the undrained triaxialcompression test and up to the point ¥vhere the axial loadAxjal deformitiorl 'is less than the pre-stress f'orce level, the spring ¥vill not be,Tlmjadditionaily compressed.Fig. 7. Specimen's force-displacement curve for loose Hostun sand S:sUp to no¥v, the test itself resembles the comrnonundrained triaxial compresslon test. As soon as the axialforce is passed, this means that ¥ve have exceeded theSpring Stlffness' Se!ectionOne major point that is ¥vorth mentioning is the selec-tion of the elastic spring. The main purpose of thisexperimental investigation is to be able to be st.ress-con-pre-stress force level, the spring ¥vill start get compressedfrom its initiai state.At the peak in the load-displacement cur¥'e, K*=0 andthe instability condition K,< -K is not met immediatelytr'olled af'ter the peak, in the stress-strain curve of the soil(and cannot have been met before). After passing thespecimen, in a strain-controlled test. In order to achievethis, ¥ve ha¥'e to choose a spring ¥vith stiffness matchingEq. (1 '_), ¥vhich can be reformulated as: K* < - K keepingpeak in the stress-strain cur¥'e, K* becomes negati¥'e, ¥vithin mind that K* is the slope of the load-displacementcurve of the specimen in its softening branch, i.e.essentially a negative quantity, vhile the rigidity of thespring K; is essentially a positi¥'e one. This value of K* isassumed to go¥'em the post-peak behavior of the specimen considered as a ¥vhole, in its softening branch, aslong as the test remains non-dynamic (negligibleacceleration, Iow strain rate). Indeed, ¥vhatever thedeformation of the specimen is, diffuse or localized, itspost-peak axial force-displacernent characteristics can becharacterized by a K* value for' the specimen consideredas a structure. We discuss the behavior of the systemspring-specimen vith r'espect to the rat.io of Kand K .an increasing absolute value llK*:1. If the spring has beenproper'ly selected (proper stiffness K*), Iater or sooner thecondition will be met. Then the system specimen-sprin_ ,_vill start accelerating. The axial load continues todecrease and the spring to extend. However, ¥vhen theinitial pre-stress force is reached on this load-decreasin_",_branch, the system of the metal box-bolt-nut pre¥'ents thespring from fully extending to its original length. Fromthis point, the specimen will not r'eceive any more energyfrom the spring. Depending on the conditions, the systemmay or may not return to a strain-controlled behavior.Indeed, although a part of the potential (elastic) energytransrnitted to the system during the dynamic jump hasbeen dissipated in plastic deformation, another part hasbeen conver'ted to kinetic energy. This part has to beTo determine the relevant stiffness, we performed adissipated by plastic deformation also, before thestrain-controlled undr'ained triaxial compression tests onloose Hostun S28 sand. The steepest (negative) post-peakmovement stops. Thus, depending on the pre-load level,the specimen may be completely destroyed in the subse-inclination of the curve in the axial force-deformationquent rnovement, or recover some ri*･idity after thedynamic step-accelerating then decelerating phases.In the belo¥v experimental analysis, an attempt toexplore the various modes of failure is given, and thediagram ¥vas found to be K*= - 1.782 kN/mm (seeFig. 7). Thus, in order to fulfill inequality 12 sooner orlater after the peak, the stiffness of the elastic springvhich ¥vas selected, ¥vas smaller than K* (K,= 0.257 kN/rnm) .effect of the pre-stress force level to the failure mode isdiscussed.The smaller the stiffness of the spring, the sooner ¥villcome the dynamic jump after the peak. Ideal load control(dead load) is equivalent to a spring ¥vith vanishin_g:EXPERIMENTAL RESULTSstiffness. In this case the instability ¥vould occur just atTesting P/'ogi'canpeak load, but practical difficulties ¥vould result frornA series of five undrained triaxial compression tests¥vas performed in order to investigate the aforementionedextrernely lar_ :e -¥'irtually infinite indeed- deformat.ionof the spring.P/'e-st/'es's Level Se!ectionBy using the aforementioned system of the metal boxbolt-nut at the one end of the spring, we can control theelastic energy that ¥vill be given to the specimen in thesoftening region. This is easily accornplished by scre¥vingthe nut at the one end of the sprin_g:, where t.he metal boxdiffuse modes of failure. Loose specimens prepared bymoist tamping technique (50/0 Ivater content) fromHostun sand S28 were subjected to undrained triaxialcompression. According to previous ¥vork done by Hanand Vardoulakis (1991), the preparation of sand specimens vith the moist tarnping technique inevitable leads toa stratificarion of the sand specimen. X-ray tomographieshave clearly shown the existence of such layers inside the DFSRUES AND GEORCOPOULOS590Table l. U ldrained triax. ial compression tests in Hostun sand S2sDeformatioF}Void Relal 've SaturarionNo. Porosit}degreeratio denstest e [ -] n [ I Dr [CUSPROI053CUSPR02 1 .OS9C_ USPR03 1 . i 22CUSPR04 1 . 1 2 lCUSPR05 1 .40O 513O.52iO.529O.528O^533_ _ rate.t¥'] S. [ . ]- 4.999 499- 25_o- 24. 5599,699,699 7[mm/min]2.02 OVar'ious ratesl .OTable 2.No testUntirained triaxial conlpressionh,10bilized frictionangle ctests inPre -stressC_USPROlC_USPR02)_3 5040016_2e850CUSPR03CUSPR049 3e9.7e16.308 S o.t)C_USPR059 8 o,/o96 'ble¥*elHostun sand S'sTolalliquefaclionNOYESNONONOlOspecimen. It is quite possible that the tested specimenspossess some degree of orthotropy, but according to theresults obtained from biaxial tests this stratification doesnot seem to infiuence the geometric characteristics offailure modes in a significant manner. lvforeover, accord-ing to Han and Vardoulakis (1991), the observed shearband thickness does not seem to be related to the thickness of the layers. The ratio of height to diameter of thespecimen ¥vas kept constant for all tests (H/D= l, D=100.0 mm). Enlarged lubricated end platens ¥vere usedboth in top cap and pedestal. The application of the axialload lvas achieved through a loading r'am, ¥vhich cameinto contact with the top cap of the specimen through asphere, in order to avoid the de¥'elopment of bendin_"._moments to the specimen. Elastic membranes of 0.40 mmof direct observation. The specimen ¥vas obser¥'ed andphotographed through the pressure cell during the test,but the last observation and photo*"raph was done aftercell removing. In case of ¥vell-developed shear band(s)reachin*' the outer boundary, the lines of the grid ¥vouldhave been distorted in the ¥vell-kno¥vn figure illustratedby biaxial tests available in the literature (e.g. Desrueset al., 198_ , 1989, 2004; Vardoulakis et al., 1978, 1985;Tatsuoka et al., 1986, 1990). This of course is not enoughto guarantee that no localization took place inside thespecimen, since inner localized deformation modes mayexist, as sho¥¥'n by Desrues et al. (1996) using X-raytomography, and confirmed later by Alshibly et al.(2003) .R esu!tsthickness and 100.00 mm in diameter ¥vere used. AnAs already mentioned a series of five undrained triaxialestimate of the minimum and maximum ¥'oid r'atio for theHostun S2s sand has been previously given b_v Combecompression tests on loose Hostun sand S2s ¥vere performed in order to verify the modes of failure In the(1998) (e f*'=0 689 e = I 036). The "rain solid densitysoftening re*'ion. The effect of the pre-stress force level ofp* is '-.65 gr/cm3. The ¥'alues of porosity n and void r'atiothe spring to the total loss of the specimens' resistance iscritically investigated. For this reason, fi¥'e sand specimens ¥vere tested in undrained triaxial compression test,each one at a different pre-stress force level of axial force. , ",** . >e in Table I of the five specimens are calculated after theisotropic consolidation. A11 specimens ¥vere fully saturated (degree of saturation S,=99.4 99.70/0) and ¥vereisotropically consolidated up to p' =800 kPa, under aback pressure equal to u = 50 kPa. The confining pressure¥¥'as kept constant during the test, equal to (7.= 850 kPa.Table I summariz,es the five undrained triaxial compression tests. As far as strain rates are concerned, it shouldbe stressed that, as soon as the pre-stress le¥'el selected isreached, the spring starts takin*' a part of the overalldeformation rate imposed to the specimen-spring system;consequently the strain rate is reduced at this point, andthe strain rate reduction lvith respect to the overall defor-of the spring system. In this ¥vay we are able to controlthe ener*'y given to the sand specimen after the peak inthe softening: reg:ion.Table 2 summarizes the results of the triaxial tests. InTable 2 the first column is the No. of the test. The secondcolumn is the mobilized friction angle c in degrees, ¥vhilethe third sho¥vs the ratio in percenta*'e of the pre-stressforce level of the spring to the maximum axial forcemeasured durin_g: the test. If this percentage is equal tozero, this means that the spring is not at all pre-stressed,mation rate is depending on the currem tangent stiffnessof the specimen. Consequently, since the stiffness of thespecimen is monotonously decreasing along the test, thewhile a value of 1000/0 or more means that the springstrain rate reduction is maximum lvhen the pre-stresslevel is first reached, and decreases continuously fromthe spring. Finally, in the last column, ¥ve indicate¥ 'hether or not the sand specimen lost completely itsthis point. The reduction vanishes at the peak stress, andbecomes negative as the axial load start decreasing; i.e^the strain rate increases after the peak, due to the exten-resistance, meanin_ :, ¥¥*hether itsion of the sprin_._". h is easy to sho¥v that the strain rateremained soiid after the dynamic deforuation phase,becomes infinite when the criterion for a dynamic jump ismet. As far as strain field monitoring is concerned, onlyjump. Only one test, namely CUSPR-02, ¥vas completelyactually does not compress itself during the test, as theaxial force can not go beyond the pre-stress force level of¥'as fully liquefied or not.Figure 8 presents the shape of the five specimens in t,hefinal state. In four among the five tests, the specimensretainin*' the geometry of the final state after the dynamicdirect naked-eye observation and photography of thedestroyed by the deformation under¥vent during theouter surface of the cylindrical specimen ¥1*as performed.jump. The experimental pro*"ram ¥vas conducted in theHo¥vever, a grid vas dra¥vn on the membrane beforefollo¥ving lvay: first confirm that the over-pre-stressedspecimen preparation, in order to improve the efficiencyspring does not play any role (test CUSPR-Ol). Then･l r. ;U 'DRA NED TRIAXIAL TESTSOiNLOOSE SAND591Canso!idated Undrained Triaxiai CorTlpression Test (H0Stun Sia)sOl[:3'*o'iflff]¥.r2 0¥J: evs ?ol-h evs Fe2-x-eus R 03* evs pR (>4-{r- evspn e52ee/' -' '1 ;D,:ruspR-031 OO/5e,oo o I D O e20eee o eosAxia*= I,o O oo 025o ol 5strain sl [**#'*:i'"'** *F'ia. 9. Deviatoric stress versus axial slrain response for all fivespecimensConso idated Undra ned Tr axiai Cofnpres$ion Test {Hostun Sis)Fig. 8. Final configuration of the difrerent specimens: The specimenwithout label on tl]e photograph is tes CUSPR-024, [;*"o* -j3 e¥'alidate the ef iciency of the spring in promoting a jumpin the dynamic regime as soon as the theoretical conditionin Eq. (12) is met (test CUSPR-02) Then find empiricallythe threshold in the pre-stress force to apply to the springbefore testing, in order to avoid the complete destruction2se rlimit the amount of energy relaxed by the spring in thespecimen after the start of the dynamic jump. The finalshape of the specimens in the tests CUSPR-03, CUSPR04 and CUSPR-05, illustrated in Fi_"_.. 8, sho¥v that thiscondition could be met ¥vith pre-stress force above 88010CVSFR G102-; -cvspR03 'e- euspp' e45'=_I ; F :･ "' ': )_ ehll:1't 4 ETlo'4i'2 ' j; ; ,2 ! :' f : J.._l/'lIso - :l't'Ieo i + ,' I'o 1o ilt/1/ : i::-cuspp'e5 '2 ) tl'1 L{1 9s s't}/ :;e-- -- -of the specimen after the dynamic jump. In fact, asexplained in section '_, pre-stressing the spring allo¥vs to=- ---- cvsp_-so1!ee2$4 es 07Msan erteetivo prQs5t,ro p'Fio. lO. Deviatoric stress versusspecimensmean*eekPajeffective stress for all fiYeof the peak load of the tes . This exact value is notconsidered of particular significance. Indeed, both thepeak bef'ore the jump seem to be controlled by thevariability of the specimen preparation and the uncertain-responsible for the ¥'ariability of these features.ty on the exact behaviour of the spring-box system nearIn the same way, q versus p' curves sho ¥'n in Fig. 10indicate that, except in test CUSPROl, all the tests jumpthe pre-stress load, due to imperfections in the rather sirn-ple mounting of the experimental device, are responsibleof not really well controlled experimental response of thesystem as the axial load approaches the pre-stressed loadof the spring. Ho vever, the objective of the set of tests isfulfilled ¥vith the demonstration of the possibility (i) totri_ :ger a dynamic jump in the post-peak part of the testand (ii) to control it to recover a def'ormed but still solidconfigui'ation of the specimen after the jump.pre-stress level. In fact, the imperfections in the tests areat some point after the peak, directly to the near-liquefiedstate ¥vith ¥'anishing de¥'iatoric stress and near-vanishingmean effective stress. The scatter in the curves is large,and it can be seen that the initial stage of the deviatoricloading, represented here by the gray triangle, is veryconfused. This is attributed to the fact that the isotropicIn the follo¥ving, the stress-strain response of thecompression of the ¥'ery loose sand deposit obtained bymoist tamping is unstable and induces large fluctuationsin the undrained pore pressure at the beginning of thedifferent tests are discussed in detail. Figure 9 presents thedeviatoric loading. Even at larger de¥'iatoric stress ievel,deviatoric stress versus axial strain curves for the fi¥'ee.g. test CUSPR03 and CUSPR05 sho¥v sudden decreasestests. As mentioned above, due to the extra mechanicallinks introduced in the loading system by the springof the mean efi ctive stress p', not leading to the specimen collapse ho¥vever since the deviatoric stress startsincreasing again after a ¥vhile.Hence, all t.he tests did lead to more or less completeliquefaction. Figure 1 1 shows that in all the cases, poredevice, some scatter appears in the cur¥'es. Ho¥ve¥'er, aslong as the peak in the stress-strain curve is not reached,all curves are limited betlveen t¥vo straight lines, as in theFig. 9. Past the peak, the curves diverge each fromothers. In test CUSPRO1, a progressive decay of themobilised de¥'iatoric stress with increasing axial strain isobserved. In all other tests, a brutal drop occurs. Thisdrop corresponds to the spring suddenly uncompressing.Ho vever, neither the peak load nor the delay after thepr'essur'e becornes almost equal to the cell pressure,indicating near complete loss of mechanical strength ofthe material of the specimen. In this figure, the porepressure is plotted against strain of the specimen, ¥vhichallo¥vs to see the different phases of the test. In only onetest (CUSPR-O'_), the loss of mechanical strength is 1DESRUES AN TD592GEORGOPOULOSConsafidated Undr ined Triaxia Compression Test (Hostun S2a)DISCUSSIONlesc- .- ?･ -QeThe above ¥vork ¥vas performed in order to in¥'estigate, r r-f- tl :-Fthe modes of failure in geomaterials in undrainec.i' 7ce-Eee-see-s see- aD,c-br,/::compression tests on very loose specimens of Hostun S xsand. No strain localiz,ation could be observed in any of"_ _ _ _ev$1- - c ;E: p. 02{xevs i:2c lY -- r'clseTe- -- evsFco *ss= eL;c3ses- s 0 ;;oe r.",e e o o o ois o c20 o eico e2so oe5Axial 5S･ain sl -]Fio*. 11. Evolution of specimen's pore pressure ngainst total axialdeformationthe five specimens tested, so tlley are consic!e/'ed 1lavin*(ullcle/1gaone dlffuse nlodes offai!Lli'e. It should ne¥'ertheless be mentioned that in triaxial tests on loose, contract-ing sand specimens, it is usually difficult to decide1¥'hether a mode of failure is diffused or localized. Usin :X-Ray Computed Tomography on sand specimens testec.iin drained conditions, Desrues et al. (1996) have sholvnthat complex strain localization patterns can be hidden tothe naked eye observation of the outer membrane of thespecimens. Thus a more extensive triaxial program istotal since the pore pressure reaches the cell pressure.needed so as to ¥'erify and in¥'estigate the deformation ofHo¥vever, the difference bet¥veen the recorded cellthe specimen around the q peak. Whether or not shearbands occur in tests in loose specimens, drained orpressure and pore pressure may not be the most rele¥'antcriterion to decide bet¥veen total and near-liquefaction;indeed, ¥vhen approaching liquefaction, the differencebecomes small vith respect to both pressures so it may beaffected by small instrumental discrepancies like e.g. zerodrift of the pressure cells. For example, in a preliminarypublication (Ser¥'ant, 2004), test CUSPR-03 ¥vas quotedas totally liquefied, but re-evaluating the data for thedifferent tests, the authors consider that the most relevantundrained, in biaxial or a.¥'is.vmmetric triaxial or even Intrue triaxial tests, has been addressed by quite a fe¥vauthors in the past, ¥vith contradictory results in fact.Lade et al. (1988) concluded that instabilitycharacterlzed by a runoff of stress-carrying capacity ofthe specimen-can occur in saturated loose sand prior toattaining the failure stress state, ¥vithout formation ofshear bands. Chu et al. (1993), perfomling tests vithliquefaction in the present case is more the final shape ofstrain-path testing i,e. controlling the ¥*oiumetric versusaxial strain increment in axisymmetric tria.¥'ial tests reportthe specimens.runa¥vay instability occurring in an number of cases andIn fact, the essential difference bet¥veen the differentcases is shown in Fig. 8 ¥vhich presents the shape of thefive specimens in the final state. In four arnong the fiveindicate that in a!! il7stabi!ity tests, fOl･n7ation of sheai-indicator of tota! Iiquefaction ¥vith respect to /7ear-tests, the specimens remained solid after the unstabledeformation phase, retaining the geometry of the finalstate ¥vhen the testing machine ¥vas stopped. Onl.v onetest, namely CUSPR-02, ¥ 'as totally destroyed by theba/7ds c/id llot occu/'. Han and Vardoulakis (1991) sho¥vthat in undrained displacement-controlled biaxial tests onloose sand specimens no loca!ization tt*as obse/-ved, vhilefor load controlled tests and for large strains the c!efornlatiol7 Ioca!izes inside !he /'apid!_}, c! fol'n7ing zol7e. Katoet al., in a study of undrained shear characteristics ofdeformation under¥vent during the dynamic jump, andsaturated sand under anisotl opic compression, usingcould not even be dismounted from the testing cell. Thisis ¥vhat happens In common load-controlled tests alon'_sands from contractive to dilati¥'e, r'eport that at 300laa;(:'ia! strain, though shear bands It'as not obsei'vec! illunstable loading paths: nothing can be said about theactual deformation process during the initiation of thesa/77p!es, tllere seenl to be non-hoi710gelleities ill tl7e straincatastrophic fio¥v, because the only observable state issa/7lp!e. As for axisymmetric triaxial tests, De Gennaro etal. ('_004), in a study of the infiuence of loading path oncompletel"¥' distorted.c!istribution due nlain! y to ,fl'iction at botll enc!s of tl7eV rhat can be said from the observations illustrated bythe undrained behavior of a medium loose sand, reportphotographs presented in Fi**. 8 is that the specimensundrained triaxial compression and extension tests, bothCUSPR-Ol, CUSPR-03, CUSPR-04, and CUSPR-05strain-controlled and load-controlled, vithout anyapparent necking or strain localization. Conversely,lvlokni and Desrues (1999), in undrained displacememseem to ha¥*e undergone a diffuse mode of plastic defor-mation during the dynamic step, ¥vithout any obviousstrain localizations (shear bands or localized zones).Nothing can be said from the photograph of specimenCUSPR-02, but there is no reason ¥vhy the behaviour ofcontrolled biaxial tests, did obser¥*e localization in loosethese specimen lvould have been different in the initialand very loose sand, occurring lvhen the stress sTatereaches the line of maximum mobilized friction determined from drained tests on the same sand. Finno er al.sta*'e of the dynamic failure. Indeed the difference in thefinal shape bet¥veen this test and the others is that the(1996) in displacement-controlled undrained biaxial testson loose sand observed localization also; they state thatamount of energy delivered by the spring in test CUSPR-t/7e stl'ess state tvllen t/1e !ocedi atioll begins is vely closeO'_ ¥vas larger, due to the lo¥v pre-stress force used in thisto, yet precedes that col'/'esponcling to !17e /7la; :'inlum/770bi/ized friction. In the early stages of the tests, theyspecific case.described non persistent shear bands. Finally, for load- 593UNDR．へ亙N狂D TR更．へXI．へL T狂STS ON LOOS狂S．へNDcolltrolledulldraiaed【es｛，tllePresents葛udycollcludes芝〇三1011−localizedfai沁rlewl｝且eHanalldVa1’doulakls（1991）reportedlocalizatiorloccurrillgadargestraia。Fromthesedi働rellts芝udiesandprobablyafewo出ernotcltedlluhis brief ove王』、4ew，it apPearls thanloαgreeme飢lsAC藝《残▼OWL猛》G覧餌’狸鋸τIS 丁姦e audlors would韮ike to acknowledge the EU project五）θ9ノ＾σ‘／σ1io’∼ α114 11∼5F！αわ11々i（95「 ill G（∼011∼α∼θ々σZ5 w々ノ1、！4ρρ1’ω1io11’o H砿σ1’ごA4’／1g鷹ノ01∼（DIGA）iR the frame．work ofτhe Humaa Pαe厳ial P1’ogram，Research Train−foundon出epresenceorabsenceofstrainlocalizado王1in由etestsdesqlibedi王1volvingloosesandspeclmells． ingNetworks（｝｛PRN−CT−2002−00220）。However，it should be Roted that the st旦dies re至）ortiRg noloca至ization（lnduding t韮1e present one）were pel』formedwithout any specia1 π1easurlng efモort ξo char＆cterizes芝rain負eld taking place、vitl≧ia由e specimens；the state−ment of absence of evidence of locε盛izatio自was foundedon simple，direct naked−eye observation of the outersurfaceofthespecimens．Conversely，漁esmdiesco11−cluding to由e preseace of shear bands ln tl康e speclmenswere using advanced measurlng methods，Ilke X−ray pho一こograplまy（｝｛an and V＆rdou1＆kis）or stereophotogram−111etry（で〉lo裟ni arld Desrues，Fillno et al．）．Consequendy，鼠EF￡R配銅〒c氾s里）．組shibli，K、A、，Badste，S，N、andS【ure，S、F、（2003）＝S正rainlocali− z撮ion iasand：Pla【1esζrai【｝versus【rlaxialcompressloll，ノ．G（∼01θc！r， 五ηg’2、，、へSC狂．129（6），483−494、2）、へrthし【r，」、R．F、a【1d DunsζaΩ，丁、（1982）：Rupturelayersiagrar1目la重・ media，／U7．4AICo／1／1∠）4、Fα〃、θノー‘〃∼、．、1θ‘1’α，（eds、byVem僕eer． P、．A and Luger，H、」、），Baikeala，453−459、3）．へrしhur，J，R．F、、Dunstan．τ、，．へ1一．氏lli，Q、．へ，J，L、and．へssa磁，．へ． （1977）l Plasζic delomlatiQII and faHure in gral湘lar media， ααθc111∼蜘θ，27，53−74．4）Bardet，J P、（1997｝：εApθ1『’〃∼θ1∼’α1So’1・、1θごノ1‘’ノ∼’（5．Prelltice Hall、the conclusioas dτawn from the la貰er can be conside王・ed5）Bishop，、へ、W、and｝｛enkel，D、」．（1957）：7ノ尼A／θα5ど’1うθ111θnでoゾ∫α1tohavestl’ongerlfoundations． P1’oρθノー1嬬’11’hθ7ノ”α．v’α1rθ5∼．狂dward．叛moldL［d、6）C無ambon，R、，CrQchepeyre，S、a正1d Desmes，∫、（2000）l Loca巨za− doncri｛erialQrllQI1巨薯1earcons［i｛utiveequatioΩsQfgeoma芝erials．CONTCLUSION ∠、1θぐhCo1∼，ヂノ”ぐ’，．、如．，5，61−82、 A！1experimel宜al smdy was pelqformed，uslllg an origi一 soils under Stra1n∫〕a［h【eStin9、ノ、G〔∼01θぐh、オシ∼9ノ習、，．叛S（二⊃E，玉19（5）．王1alsimplemechanicaldevice，Ioilwestigatethemodesoffailure along unstable Ioading Paths III ulldr＆illed室ri＆xialcomやressiOmests． Tllecollcep芝ofasprll19−boxdeviceprove（hobesuc−cessfuhn t｝lat lt aUowed for recordillg specinlen deforrrla−tionevenalongullstable，dynamlcalp袖s．lndeed，wewereable芝operfor簸1actualuustable（leformationincre−Inents呈n the unload圭n黛bral・1ch of芝he箸est in undrεtinedllquefyhlgspecimel主s，stillkeepirlgtllepossibilitytoobserve tlle k呈nemat玉cs of the specinlen during theseinCrements． As far as the kirlema亘cs chal’acterizatio鶏is concemed，a烈且vesandspeclmensapParentlyu茱1derwentdi仔usemodes of failure and no s甘aln localizatioa、vas observedwlthnakedeye．ltshouldneverthelessbementionedth飢量n a t婁i＆xial test it is usua墨ly di伍cult to dec玉de whether amode of fallure is digused or localized．One ofthe malordenc猛ofthe triaxial test，＆s far as the characte1’izatioII ofthe mode ofdeformatioll is concemed，is the fact that theobservat玉on of the specimen during and afterξhe test isllmited to its o臓er boundary．Previous studies，uslngadvanced full岨eld meαsurillg teclmiques1汰e X−raytomography（Desrues et aL，1996），11ave shown thatフ）Chu，」、．Lo，S、一C、R、alldLee，1，K．（i993）：lnsこab11iこyof『grallu1＆r 874−8928）Combe，A．｛、（19981：Coml）or〔eIIlemdusabled『90stuI∬二sau triaxiaiax1sym6【rique．ComparaisonaveclesabledラHos硫mRF． ノ∼αρρo／Y‘！θ51α9θ，Universi【y Joseph FOur1er、9｝Darve．F andLaouafa，F、（2000）；Insしabllldesi【｝graaularmaterlais alld ap【）蕪cadoll tQ landslides．．、∫θch、Coノ∼，」Frlc’、、、／σ1、．5，627−652．10）DeGe【marQ，V、，Canou．、1、．Dupla，J．CalldBenahmed，N． （2004）：hl自ueace ot IQadiIlg Path QΩtlle ulldra1lled bellaviour of a mediumloosesallcl，c研、Gθorθc／1．／．．41，166−180、I D Desrues、」．and ChambQn，R （1989）：She訊r ba【圭d analysis for grall目lar nlateriais＝ ほ｝e ques［ion oゼ incl’enlenτal Ilon lilleari［y． ／ノ∼9θ’1’8三〃㌧鍾1℃1∼’y．，59，187週96、12） ￡）esrues、J，and ChamboI1．R、（2000）：Shear band allaiysis alld shear modulicalibration，／’1！、ノ、501’455∼η’（・1、．39，13−14，3757−3776、13） Desl’ues，」、and Hanlnlad，∼V （里989）＝Shear bancling del）endellcy oll nlean s芝ress level ill sand，P1＾o（一、21∼4／1π、耳Fo16た31∼oρ01r五〇cα1Z5‘∼一 ”o〃 αノ1‘ノ θヴセ〃ヤα！”01∼， Gdallsk、 57−68 （eds、 by Dembicki， E，， Gudehus，G and Sikora，Z、），Techn、U【11v，Gdansk、i4） Desrues，」、and V199ia【li．G、（2004）：Strain localiza【ion ill salld：an overvlew Qf the exぎ）erinlenこal resu1芝s ob【ailled in Grellob！e 目si自g SleI’eOPhoしogran㌶11elry，1η’、ノ．八「疋！〃∼ ’i1∼α’．A4θ’1∼、Gε01ηθ（・ノ∼‘7n’（5， 28（4）．279−321、15）Desrues，J，Lanier．」、andSωtz，P（1985）：Localizationofthe deforma［ionimestsollsalldsampie、E’∼91gFノ’αc1、．、／θ（レノ∼、，21， 909−921、16）Desrues J，Ch＆mboほ，R、，Mok【雀i，M aIld Mazerolle，F．（1996）： Void rat1o evok耗ioII i籍side shear baIlds in tri＆xial sal1〔I specinlensstrainlocalizationcallremal曲iddentothe！1akedeyein studiedbycomPu芝edtQmograplly，0σ01θぐ1r1瞭昭，46（3）、529−546、17）diPriscQC、．正mposimato．S．andVar（loulakis，1、（2000）：Medlal1レsu由test conditions，An interesting directio王l to extend cal n｝odeling Qf drailled creep triaxia1【es【s on loQse sand，Gゴo∼θぐ1∼一山isstudyistoperformblaxialcompressio厭ests，w良erethe霧10des of fai互ure are easier c紅ar＆cterized．Such testscou豆d be，for exaτnple，performed in the biaxia韮apPara− ノ瞭’θ，50（1），73−82、18） Drescher ．へ．aΩd Vardoulakis． 1 （1982｝：Geonle【ric soften1ng ia triaxiahes50ngranu！armaterial，040∼θ（’ノ11r1σ肥，32（4），291−303、重9｝ Drescher， ！X、， Vardoulakis， 1． alld ｝逼an， C、 （1990）： 、へ bi−axialtus proposed and designed by Varclo艮lakls and Drescher apparamsforこestlngsoils，Gθo’θ‘・1r、τθ5∼、ノ、，GTJODJ，13．（1990）orinthebiaxialapPara宅usdeveloped＆nddeslgned 226−234、by Desrues（1985）．Both of由em allow for free shearbandformation，wbilethesecondoneinadditlQnallowsforfulレ負eldillcrementalstralnmeasuremeatmonitorlngcluring tlle test．20痔inno，RJ，，Harr臨，W，W、Mooney，M、、へ．a【1dViggialli，G、 （1996）＝Strai員locεdiza［IQn a【1d undrained s芝eady state of sa臼d5，ノ． 0θ01θ（・ノ∼．五1rg／3、，ASCε．122（6｝，462−473、2i）Gajo，A（2004）＝Thein飾enceofs》一stemcomplianceollcollapseot tr1axial sa【1d sarnples，Cα’1，（3θo’θぐ11、ノ、，41，257−273、22｝Gajo，A，Pif1をr，L．and De Polo，F （2000）；．へ11alysis Qヂcerta1…｝賑、一 凋594DESRUES．へNDGBORGOPOULOS factors a貿ect玉ng t蝕e unstabie beha、・iour of saturated loose sand，32）Servant，G．D、F．，Darve，F，，Desrues，，LandGeorgopoulos，LO． Mεc11．Co1了， （2004）＝D縦use modes of failure ln geomaterials，p401・1ησ∫’oηE1一’α。Mθ’．，5，21シ237． C12α’・ααθ1・’5”‘50ゾPGθ01norθパ（7Z5（eds．by Di Benede艮o，Swe【s and23）Hlaa，C．a簸d Vardoulak1s， 1， （玉991）：Plane−s［rain compress叢Qn experlmentsonwaτer−sa芝ura［ed鋤e−gra1ne（isand，0σo’θc／111ゆ’θ， Ze琵linger）． 41（1），49−78．33）Tatsuoka，F，，Sakamoto，M．，Kawamura，τ、andFukushima，S．24）Harr1s，W、W．，Viggia廊，G。，MooΩey，Mi A、 and F魚no，R．」L （1995）：UseofstereoP！10togrammetryこoanab・ze由edevebpmen【 （肇986）：Stre【㌃gth and deforma｛ion characterist1cs of sand玉n plane of shear bands in sand，（3ε01θoh．τε5∼．ノ．，GTJODJ，18（4）， Fo∼’1∼4σ！’0115，26（1），65−84・ strain compression at extremely low pressures．SoiZ∫α’∼ゴ 405−420、34）Ta覧suoka，F．，Nakamura，丁．，Hua鷺9，GCand鉛鷺i，K．（1990）：25）Head，K、H（1992）＝A如1∼∼σ10∫50’1加ひ01’σ∼o’ツrθ∫’〃19，3跡ective StrengthanisotropyandshearbanddirectlQn1nplanestraln［estof Stress■eSts，、Joぬn∼V蔵ey a員αSo陰s，｝｛玉目，R． sand，Soiz∫σn‘ノFo∼〃rゴα’10η・∫，30（i），35−54．26）Kato，S。，lshihara，K．a職dTQwhata，1．（2001）IUn（玉ra1nedshear characterist1csofsatuτatedsa鷺du員deranlsotropicconso照a芒lon， a霞ec竃ing鮭quefactlon susceptibil玉ty of sands，Cα1∼．0θo’8c1L／1，37， So’なσ1∼4だα〃1ゴσ1’oη∫，41（1）ラレ1L 592−606．35）Vald，Y，P．and S1va出ayalan，S、（2000）：Fu艮damental faαors granular malerlals with non assoc1ated gow，／．だη913．∫》θぐ13F36）Vardoulakis，La職dGraf，B、（1985）＝CallbraIio臓ofcons伽t1ve modelsforgra臓ularmateriais賢slngdatafromb1ax1alexperlments， ASCE，韮14（12），2173−219L28）Mok頭，M andDesrues，」、（1999）＝Sζrai自10calizationmeasure−37）Vardoulakis，璽．a簸dSulem，J．（1995）：βψ〃でσ∫’oη瀦’1ψ5Z5’1127）Lade，P．V，Ne夏son，R．B、and ko，Y．NL（玉988）：1昆stab員ity of， ments1n undra玉ned plane＿strain b1ax三al｛esこs on Hostun RF sand， ！、4eぐノ∼。Co1∼、ノ『’”01、ルノα’．，4，419−441． G60’θごh11ゆθ，35（3），299−317， Gθo’nθc11απ’c5，Blackie．38）vardoulakis，L，Goldsc姓eider，M．andGudehus，Q』G（1978）l29）Nova，R，（韮994）：Corltrollabilityofζheincreme猷airesponseofsQil Fornla芝ion of shear ban（重s玉n sand bo〔玉les as a bifurcation prob蓋em， specimons subjec［ed εo arb貢rary load玉ng ρrogram蹟es，ノ・・、グθぐh． ／〃．／．劫〃ア1．〆4ηθノ．ノ、4θ’1∼、（沁o〃1θ‘／7．，2，99一玉28． βθ加v。ル1α’、，5（2），193−201，30）Rice，．L R．（1976）l The localiza【lon of plast1c deformatio目，39）Yos短da，τ。，τalsuoka，E，S1ddlque，M、S．A．and Kamegal，Y、 （玉994）：S無ear band1ng l鷺sand observed1n plane strain compres− 7＝ノ1θo’で”‘01α11（ゴ〆置ρ∫ン〃θびA4θ‘1’α11’c5（ed．by Koiter，、V．丁．）．Nortb− sion，ゐo‘θ〃ξ醒’011‘71∼ゴ81舜〃℃θ”o’1771θ01二γ，弄019So’1∫αη4Rocκ∫ Ho駐and Publisl1頭g Company，207−220， （eds，by Cha瓢bon，R。，Des田es，J．Vardou蓋akis，L），Balkema，3玉）Sco［t，R。F．（198フ）：Falkire，（％αθごh1∼iσμθ，37，423−466、 三65−179． | ||||
| ログイン | |||||
| タイトル | A Practical Numerical Model for Seepage Behavior of Unsaturated Soil | ||||
| 著者 | Kazunari Sako・Ryosuke Kitamura | ||||
| 出版 | soils and Foundations | ||||
| ページ | 595〜604 | 発行 | 2006/10/15 | 文書ID | 20943 |
| 内容 | 表示 r}SOILS AND FOUi¥DATIOi¥'S Vol46. N'o. 5, 595-604, Ocl. 2006Japanese C; eotechnical Societ}A PRACTICAL NUMERICAL MODEL FOR SEEPAGE BEHAVIOROF UNSATURATED SOILKAZUNARI SAKoi) and RYOSUKE KITA IURAii)ABSTRACTIt is irnportant to estimate the seepage proper'ties of unsaturated soils lvhen performing an unsaturated-saturatedseepage analysis, ¥vhlch is used to clarify the slope failure mechanism and predict the occurrence time of slope failuredue to rainfall. Kitamura et al. (1998) proposed a numerical model to quantitatively estimating the seepage propertiesof unsaturated soils. And they ha¥'e compared numerical results vith laboratory soil tests in order to examine thevalidity of the numerical model. Consequently, it has been found that the numerical model must be impro¥'edmoreover. In this paper a practical numerical model for seepage behavior of unsaturated soil is proposed to improvethe previous model proposed by Kitamura et al. (1998). Firstly, the basic theories of the previous model are explained.Calculation results are compared ¥vith those obtained from the laboratory soil tests in order to examine the validity ofthe previous model. Then, ve perfor'm sorne improvernents of the previous model based on hydro-mechanicalproperties, and propose a ne¥v parameter, named "parallel translation index ( Ipt)" ' From the results ¥ve showed thatthe relationship between the ne¥v parameter and the uniformity coefficient (U*), expressed by logarithm is linearrelation. Therefore, the reasonable seepage pr'operties of soils can be computed from the impro¥'ed nurrrerical modelusing only the popular soil parameters.Ke,_' ,vords: grain size distriction, soil-¥ 'ater characteristic curve, uniformity coefficient, unsaturated soil, void sizedistribution (IGC.: E7)seepage behavior of unsaturated soil is p 'oposed for theINTRODUCTIONimpro¥'ement of the previous model by Kitamura et al.(1998). First, the basic theories of the previous model areSoils located above the ground ¥¥'ater table are generally in an unsaturated condition. For' such soils, changes innegative pore-¥vater pressure have significant influence onmechanical properties, e.g, the coefficient of permeabil-re¥'ie¥ved. Secondly, calculation results are compar'ed¥vith those obtained from the laboratory soil tests in orderto examine the validity of the previous model. Then, ¥veperform some irnpro¥'ements in the previous model basedity, the shear strength, the compression index etc.on hydro-mechanical properties, and propose a ne¥vparameter, ¥vhich is named "parallel translauon mdexTherefore such changes may result in many geotechnicalproblems (e,g, mounding belo¥v ¥vaste retention pound,slope f'ailures, ground movements involving expansi¥'e(Ip,)".soils, and collapsing soils etc.) (Fredlund and Rahardjo,1993).THE NUMERICAL MODEL FOR SEEPAGEBEHAVIOR OF UNSATURATE SOILThe seepage proper'ties of unsaturated soils (i.e. thesoil-water characteristic curve (SWCC), and the relationships between degree of saturation ( S*), and unsaturatedsaturated permeability coefficient (k)) play key roles inUnsaturated soil is composed of three phases, viz. thesolid phase (soil particles), the liquid phase (pore-1vater)and the *'as phase (pore-air). Figure 1(a) shows a soilunsaturated-satur'ated seepage analysis. van-Genuchten(1980) pr'oposed numerical methods for obtaining theelement ¥vith a f'e¥v soil particles. This soil-mass situationseepage properties. He has proposed a close-formcan be modeled as shown in Fig, 1(b), ¥vhere voids filledequation for the hydraulic properties of unsaturated soil.with ¥¥'ater and air are represented as a pipe with adiameter (D), and an inclination angel (6). The soilKitamura et al. (1998) have proposed a numer'ical modelfor seepage behavior of pore-¥vater in unsaturated soilbased on some mechanical and probabilistic considera-particles are represented as the other impermeable partsof the model minus the space occupied pipe. Figure 2sho¥vs cross section of the element in Fig. 1(b). Thetions on the scale of soil particle size.In this paper a practical numerical modei of thevolume of' the element ( V*), and that of the pipe ( Vp), are*' Ritsumeikan Universi y, shlga, Japan (kaz-sako( ;+fc_ritsurnei.ac.jp).= Kagoshima Universil)', Kagoshima. Japan.=,The manuscript for this paper vas received for revie¥v on December 13. 2004; approved on June 7, 2006,¥Vritten discussions on tlris paper should be submi ted before i¥,Iay I . 2007 to the Japanese Geotechnical Socie y, 4-38-2, Sen_(',*oku, Bunkyo-ku,Tokyo 1 12-001 l. Japan. Upon requesl the closing date may be extended one month.595 SAKO AND596KITA *lLJRAThe shape of voids in soil is complex because the shapeand siz,e of soil particles are random, and the structureof their assembly is irregular. Therefore, D and e areregarded as random variables. Consequently, probabilitydensity functions for D(Pd(D)) and e(p*(e)), can beintroduced to esrimate the void slze distribution in a soilmass.First, Pd(D) is described. It is kno¥vn from the grainsiz,e analysis that the grain size distributions are approxi-mately expressed by the lognormal distribution. Thedistribution of void in a soil mass ¥vas measured by the(a)mercury intrusion proximity apparatus (Sato et al.,199'_); Yamaguchi et al., 1993). From these experimentalresults it ¥vas found that the ¥'oid size distributlon couldD!,be expressed by the lognormal distribution. Therefore,the use of the lognormal distribution can give Pd(D) asf ollo¥vs:- 'J(]n D - )., )P (D) i l Jr', 'D exp 2 : (3)j¥' In/1. 2: (4)(5): =!In +(1lcr,)2jI ,1(b)Fig, l. ¥_ iodeling of parric]es and voiti in soil mass: (a) a containerlvit!1 a few soil particles and (b) Pipe and the other impermeabieparts¥vhere, ).* =mean value of the lognormal distribution+ = standard deviation of the lognormaldistributionDD,,!1*= mean ¥'alue of D(7* = standard deviation of D.s in etan O/!+ and ( , are obtained from correlation of the grainsize distribution lvith the void size distribution. The siz,eof D is related to that of soil par'ticles because the size ofvoids is related to that of soil particles. The void siz,edistribution can be correlated ¥vith theSLDDlrain size distribu-tion based on the follo¥ving three assumptions.(1) The height of container in Fig. 1(b) (Di,) is set toDlo' It ¥vas found from the previous research ¥vork(Akai, 1969) that Dlo is one of factors that infiuencethe permeability coefficient:Dj* = Dlo (6)f)(2) !1, is expressed by the follolving equation:Fig. 2.Cross section of ihe container shownin Fi('^ l(b)represented by the follo¥ving equations respecti¥'ely:D , DhV*=D sine' tane Dh (1)D) D !'Vp (= -/T _, sin e (2)¥vhere. V..=volume of the container in Fig. 1(b)V0=¥*olume of the pipe in Fig. l(b)D= diameter' of the pipee=inclination angle of the pipeDh= height of the element in Fig. 1(b).fl= Di, ' P** (7)¥¥hele P,,= parameter used to fit the void ratio obtainedfrom calculation ¥vith that of experiment.(3) The coefficient of va 'iation ofthe void siz,e distribution is equal to that of the grain size distribution. Unoet al. (1998) have studied measurement methods ofvoid size distribution for sandy soil It has beendescribed in their paper that the void size distributionfor drying process of the SWCC is parallel to the grainsize distribution. Therefore, this result is applied torelate the void siz,e distribution ¥vith the g:rain sizedistribution:= * (7, (8)u* ,u* NU ,1ERICAL JvlODEL FOR ¥*OIDSvhere,Using Pd(D) and P*(O), voic.i ratio (e), volumetric= coefficient of var'iation,lvater content (TV,), suction (s*,), and unsaturated-saturated permeability coefficient (k), are deri¥'ed based onu* = mean value of the grain size,cr*= standard devlation of the grain size.The above three assumptions give 1, and (7.. Thus, Pd(D)can be computed by using the data of grain size distributlon.Next, P*(e) is described. A relationship bet¥veen acontact angle of adjacent soil particles (fi) and e issome mechanical and probabllistic consideration on thesoil partlcle size (Kitamura et al., 1998).Since the vold ratio is defined as the ratio of the ¥"olumeof voids to the ¥'olume of soil particles, It is expressed asfollo¥vs:=J -. ldefined in Fig:. 3. The distribution of e is related to that of'fi (i.e. the conjugate relation). Oda (197,_) has measuredthe contact angle at a contact point of adjacent particlesby optical microscope and sho¥vn the fr'equency distribu-tion of contact angle. Kitamura (1985) assumed a pentagon shape sho vn in Fig. 4 as P*(e) based on these results.p*(e) can be expressed as:217r-'Tr/2:i c'i- i'efr 12 ' fto ,_Equation (10) Indicates the expected ¥'alue, Ivhich ¥vasderived based on the probability theory, and the integration inter¥'al is expressed from O to f_. Ho¥vever, in thecalculation, the function is integrated from ()., -4Lj,) toInitially the ¥'oid ratio Is computecl from Eq. (10) ¥vhere, 7t( <e<0-)p (e) - 2/Jr --? 'cl,.__ V,-V Pd(D) P(e)c!ec!D()., + 4c , ).0+ '7z59 //!, is gi¥'en by Dlo. The calculation result is compared,? ( ITo e(9), )viththe ¥'alue obtained from the laboratory soil test. In orderto ag:ree ¥vith the actual void ratio obtained from thelaboratory soil test, iterati¥'e method is used by applyin_"._where, .= Iolvest height of' P*(e).j* is determined to be O. 159 ¥vhen the ratio of the mini-mum height to the maximum height of P*(a) is 1:3.*=O. 159 is used in the numerical experiment.change in P*, in Eq. (7). Finally, P*, in Eq. (7) is determined, and Pd(D) (i.e. ¥'oid size distribution) is obtainedfor a void ratio obtained from the laboratory soll test.The volumetric lvater content is defined as the ratio ofthe volume of the pore- vater to the total volume of soiland it is expressed as follolvs:I f'i '/2 VpI /e(c!)J j V.--V Pd(D) P (O)dec!D1+e 1+e o *'(11)¥vhere, e= ¥*oid ratio (Eq. (lO))e(c!) = ratio of' the ¥*olume of' the pore-¥vater to thevolume of the soil (In saturated condition,e(d) is equai to e.)c/=maximum diameter of pipes filled lvith¥vater.The suction is defined as the diff rence bet veen poreair pressure (u*1)' and pore-1vater pressure (u,.), (i.e. u* -u,,) Fl(rure ) sho¥ s a capillar) phenomenon. ForceFig. 3. Relationsl]ip between conta:ct angle of adjacent soil particles,P, and inclination angle, eequilibrium in the vertical direction can be expressed bythe follo ving equation:p,( e )P( j ' )*Co!p- :,l･_o(a), : ;!-- 7L12ofT;-,(b)Fig. 4. Distribution of contact angle, P, and inclination angle. O: (a) Probabilit)･ densit) function of contact angle, P(fl) and (b) Probabilit)density function of inclinarion angle, P*(O) 1 i59sSAKO AND KITA ･1URAD4 . sin e'A l! ' JzO-P 128 ･ /1 ' Dh ( 1 7)On the other hand, flux of water through the soilelement in Fig. 1(a) per unit time (Qe) is also expressed bythe follo¥ving equation in ¥vhich Darcy's lo¥v is applied:, Dh' tanO (18)Qe=k"i'A=k'i'D Dsinewhere. A =cross section area of the container inFig. l(b)7=average hydraulic gradient of soil mass inFig. 1(a).The average hydraulic gradient of the soil mass inFig. l(a) can be expressed as follo ¥'s:7= 4 ! / y,. ( 1 9)Capillary phenomenonFig. 5.DhQ. is equal to Qp. Combining Eqs. (17), (18), and (19)Jr ' d 'JZTs' COS (x= - ' d 2 . /1c ' ylv(12)4gives the follo¥ving equation:k-= y,. ' D i ' 7z ' sin e (_.O)D , D!*[ l¥vhere, T==surface tension128･/1 sin e ' ran e( = contact angle of meniscus at a contact pointof soil particlesSince D and e are random variables, the unsaturated-h* = pressure headsaturated permeability coefficient is expressed as follo vs:y*+ = unit ¥veight of lvater.Rearranging Eq. (12) gi¥'es /1c as sho¥vn in Eq. (13):/7 4 T coscyw ^ dk=J 'lj**/2_. -(13)o -.,!2y . 'D3 ' Tz ' sin e[[ D , D ' IJ1'_8 ･/J 'sin eT tan e('_1)The suction in the nearby meniscus is equal to the ¥vaterpressure that corresponds to pressure head. So, suction isexpressed as follo¥vs:s = y,, h 4' T='cos ce (14)dThe unsaturated-saturated permeability coefficient ¥villNUMERICAl. PROCEDIJREThe numerical procedure for the above model isdescr'ibed as follo¥vs;1) Dj,, P･ and a. are obtained from the grain siz,edistribution by using Eqs. (6), (7) and (8) in lvhich P,= isbe described by the follolvin_9::set to I .O. 2) ).Flux of laminar flolv in the pipe per unit time (Qp), isand (T into Eqs. (4) and (5). Then. Pd(D) can be comput-expressed using the Poisseuille la¥v as follo¥vs:ed from Eq. (3). 3) P*(e) is obtained from Eq. (9). 4)= )( 2･1･Op!;;;･D 4 (15)fz¥vhere, /! =viscous coefficient of ¥vateri = hydraulic gradient,In Fig. 1(b), i for the laminar' fio¥v in the pipe is definedas follo¥vs:._ Aul),,, (16)l Dh Isin eand. can be calculated by substituting !!,Using Pd(D) and P*(e), e can be calculated fromEq. (10). Follo¥vin_2: that, this calculatlon result is compared ¥vith the labor'atory soil test result. 5) The value ofP** is changed, and then the procedure from 1) to 4) isrepeated until the ¥'alue of e is corresponds to theexperimental result. 6) The saturated volumetric ¥vatercontent (W.***) is given by 'V.,**=e/(1 +e). 7) The valueof W. from O.O to W *** is substituted into Eq. (1 1), andthen d, ¥vhich corresponds to each value, can be obtained.8) Substituting d, ¥vhich correspond to arbitrary volumetric ¥vater content, into Eqs. (14) and (21) ¥vill result in s¥vhere, Au=difference of pore-¥vater pressur'e bet¥veenthe top and the bottom of the container inFig. 1(b).Substituting Eq. (16) into Eq. (15) gives the follo¥vin_"._equation:and k.NUMF,RICAI. EXPF.RIMENTTable I sho¥vs values used for the numerical experiment. The input parameters include T,, /!, e, the density NUivIERICALTable l,¥. *10DELFOR VOIDS599Values used for 2 numerical experimentSampleShirasuDenslty of soil particle (g/cm;)2.62873_4S x 10 ;Surface tensioll (Nlrn) ( ¥!ater temperaiure is 15'C)138x lO ;Coef cient of viscosity (Pa's) (¥ 'a er temperature is 15'C)Lo¥vest height of probabilhy density function of e, (*O. 1 59¥roid ratiol.71Grain size dislrlbutionPercentage finer by ¥veight (9/0) Grain size (mm))_if;t}Percemage finer by weiglGrain size (mm)( !.)I37.9o_05291*+135 3o 037632.7o,023930 lO 0139lO0.019 OO98 29.5095,84.75l91 22.00i=86 1o.8501.-27.4o 009974.40.4,_5l24.so 007063,0o.2501.(20.9o 003646 oO 106It/14.4O O0154 1 .4o 075of soil particle (p*) and the grain size distribution. Theseparameters are obtained from simple soil tests andcrcommon scientific tables.The values of the input parameters are obtained fr'omsoil tests on Shirasu and applied in the numerical experi-fail ¥vith heavy rainf'all.Figure 6 sholvs the grain sizesize distribution that have beenthe parameters expressed in Tableshow the grain size distributionThe dash line represents the approximate gr'ain sizedistribution due to the 18 dots, and this is expressed bythe lognormal distribution. The solid line is the void sizedistribution, and it is given as the cumulative distributionC:str i but i enstr I'' 0Ca i cu i aii c,[r*oe9080ejO70,/(U4:oe)c6050404Jdistribution and the voidcalculat.ed by the use ofI . In Fig. 6, the 18 dotsobtained from soil tests.soornent. Shirasu is defined as a non-cemented part ofpyroclastic flo¥v deposits and one of the famous volcanicproducts. Shirasu particles are porous and their density isless than that of the usual sandy soils. Therefore Shirasuground is easily eroded and Shirasu slopes often easilyIZe L r[cQ30::::3,:)2010o1 o 71 O s I 0 50-4Gra n s zeFig. 6.1 0 3 1 0 2{ ODiameter of the1{Ol1 Oop I pe(n1 02)Grain size distribution and void size distributionfunction based on P (D) as sho¥vn in Eq. (3). The voidbecause it has been assumed that the coefficient ofthe soil test results, the values of k computed by themodel appear to have been overestimated.In the numerical experiment, it is regarded that allvariation of the void size distribution is equal to that ofthe grain size distr'ibution. The seepa*'e pr'operties (i.e.pore-¥vater included in the soil mass contributes to generate the suction and the flo¥v ¥vater lvhich relates to thethe SWCC and the r'elationship between S* and k) ofper'meability coefficient. Ho¥vever, part of pore-watercontained in voids probably does contribute to the actualseepage behavior. Taking account of the hydro-mechani-size distribution (i,e, the solid line in Fig. 6) is parallel tothe grain size distribution (i.e, the dash line in Fi**. 6)Shirasu as sho vn in Table i are calculated using Pd(D).Figure 7 shows the SWC*C obtained from the numericalexperiment and ¥vater retention test on Shirasu. It isfound from Fig. 7 that the suction values calculated bythe proposed model are smaller than that obtained fromsoil test at the same degree of saturation. Figure 8 sho¥vsthe relationship between S*, and k. In comparison ¥vith--cal properties, ¥ve ¥vill rnodif'y the proposed model in thenext section. 1 iSAKO A¥.(]*oaD KITA*¥,IURA1 ooSoil p ulicie90 -A i i'C8 cLi a L on8070 -C(60ei._-i: $ "=50 --O:40 -+J30 -cl)20 -10Absorbed ¥vaterFree ¥ 'ateroo20 30 40 50 60 70 80 90 10010Fig. 9.Conceptl!al statcs of pore1'atcr and air in unsaturated soilDegree of saturation, S. (";)Fig. 7.Soil*water charactcristic eurveimprove the previous model.In the previous model, it is assumeci that all pore-¥vater'included in the soil mass contributes to g:enerate thesuction and the flo¥v ¥vater estimated by the permeabilitycoefncient. Using the parameters of the proposed numerical model, the ¥'olume of all pore-¥vater included in the1 02C-q)¥(1)::S;(1)･ ;+J101 i.100 =08 c ; at'onsoil mass (V,.) is e,x'pressed as follo¥vs:1 O 11 0 2j J::.iV,, = Vp Pd ( D ) P( (e )clec!D (22)( S *1 O 3CU *cl?a1 0 5On the other hand, part of the pore-¥vater contained inQ)L{-1 O 6voids probabl"v actually contributes to the seepage behav-CQO1 0 7ior as mentioned above. Therefore, c! In Eqs. (14) andL+J:SCJQ);Lh+,Q,LO,>(Q,Jc,) "-::)-OCQQ,Q,t) -{ 0 4(21) is reduced to obtain the reasonable value of SLI and k-.10 8The volume of the por'e- ¥'ater that contributes to thesuction (V,.,u) is expressed by the follo ving equation:10 9 " - -10 1a10-11= I 'rlI "*="-V,, ,u V1012o10 20 30 40 50 60 70 80 90 100Degree of saturation, S. ("t)Pd ( D ) Pc (e )d ec/D (23)*o '--,l¥vhere, V,.su=volume of the pore-¥vater contributlng tothe suction (V ,sL < V,.),d,i =maximum diameter of pjpes filled ¥vithFig. 8. Relationship between the de,*,_ ree ofsaturation andtlns tt ratcd-saiuratcd permeabilii, coefi cientvater that contFibutes to suction (c! u<, cl).And, the volume of the pore-¥vater that contributes to thepermeability coefFicient (V,.k) is as follo¥vs:IMPROVEMF.NT OF PREVIOUS iviODF.LFigure 9 sho¥vs a conceptual picture of soi} particles,pore-¥¥'ater and pore-air in unsaturated state. Pore-¥vat.eris divided into absorbed vater and free ¥vater. Free ¥vateris further subdivided into static and dynamic free ¥vater.Static free vater probably contributes to the suction asmeniscus ¥vater. Dynamic free ¥ ;ater probably contributes to the permeability coefficient as fio¥v ¥vater. InV,.k=j l:: (24)(iVp Pd ( D ) Pc (e )c!edDO 2¥vhere, V,.k=¥'olume of the pore-¥vater that contr'ibutesto the permeability coefficient (V,.k < V,.),c/k=maximum diameter of pipes filled ¥vithhvater that contributes to the permeabil;tycoefncient (c!k < d).conformity ¥vith the above-mentioned concept, an im-When d**, and c/k are used instead of d in Eq. (14) andprovement of the proposed numerical model is discussed.Eq. (21), respecti¥'ely, the following equations areobtained as the modified model:In this section an improvement in the ¥'old siz,e distribt, -tion is performed for static and dynamic free ¥vater. Inthis paper, ¥ve notice he ¥'oici size distribution, and i¥]fL'N'IERICTable 2.L N･IODELThe paFameter used io calculate ihe void size distribution¥,'oid size dis rlbuiionTest resultsDegree of,1aximum diameter ofSuclionsaturaLion pipes filled lvi h waterlaximum diameier of pipes filled wi hCumula ive percentages¥ 'aleror Yoid size distributlonhacontributes tohe suciions,, (kPa)c! (mm)92 so 988_07 x lOi3.00 >< lO92 5967.66 X lO !l 50X lOI96.2S. ((l601FOR ¥,OIDS)c!,u (mm)(?･ )i96.3384.54*92.S4 x lO16 oo x l0 292 44S2 . l4.912 28 x 10 !5_99x lO l91.36S19.Sl8_3.00 x 10 i84 243.749 20_1 .98 x lO ;71 26I x lO2.24 x lO :1 OOd 1ir ibL]t7Cc n r ;[ itt tJczi'llOO -90 =go lc60,)50C:,:)OoL 50( );'hth; r.:jsir o vel Od8 1_404J'O:e) 40>(1,+JcT: 3060=¥ I'Y11'70c:J:K} '*c cLi 8t en {b' J /F804J:* ･ 8= i80 i2020 '___/ ____. _ _______ _ ___10 /"I"ljJooO1 0 7 1 O e I O s I 0 4 1 0 3 { 0 2 1 O 1Diamete30:#;o lo 20 30 40OO { OI { 02of the piPe ( lll)Degree of5060safu rat i on70s.80go1 oo(*+.)Fi*. 10. Void size distributionFig. 11. Soil-water characteristic curve (aftcr tl]e improvement of thenumerical model)s'** =4 ･ T* ' cos Oi (_,5)cl * **=Jo'J"'I -"),,..D3'7z'sinek -- --*' P[ ( DD Df*-) J' P. (a )d edD1_'8･// sin e tan e(, 6)cl and c/***, ¥vhich correspond to the experimental resultssolid line. Therefore, 6 of the dash line is equal to that of'the solid line. The dash line is derived by a change in ), inEq. (3) under the constant coefficient of ¥'ariation.The result that vas obtained using the modified voidsize distribution of the dash line in Fig. 10 is sho¥vn inFrg 11. In this figure, it can be seen that the resultscomputed by the use of the improved ¥'oid size distr'ibu-Because the results for the cases ¥vhere S* is 90.70/0 andtion is in good agreement ¥vith the soil test results.94.70/0 in Fig. 7 probably have an influence of the airentry value, Table 2 does not include the calculationestimate d*** ¥vas applied to calculate dk, and the result isresults for these cases.Fig:u 'e 10 sho¥vs void size distributions. The solid linesho¥vn in Fig:. 12. Here it can be seen that the calculationresult agrees ¥vell ¥vith the soil test result. Ho vever, sincein this figure represents the void size distribution that isthere is only one saturated permeabiiity test result, thecalculated in the case sho¥¥'n in Table 1. The circularpoints sho¥v the distribution of d and the triangular¥'alidity of k cannot f'ully be examined. So, it is necessarypoints sho v that of d, . It is assumed that the cumulativepercentages of void size distribution of c!s are equal tothose of c!. The dash line in Fig:. 10 sho¥vs the void sizetests in the near future.distribution contributing to suction. The curve that*-_lognormal distribution. The dash line is parallel to therespectively. And these results are shown in Table 2.in Fig. 7 are calculated by the use of Eqs. (11) and (･- _ ),1approximates to the trian*'ular points ¥vas fitted usin_",_Therefore, the sarne improvement method used toto carr'y out many unsatur'ated saturated permeabilityThe proposed practical numerical model aims tocalculate the S¥ rCC and the relationship bet¥veen S* andk by the use of the parameters obtained fr'om some soil 瀦602SAKO AND KITAMURAtests．newparameteriscalle（i‘‘paralle至translationin（iex（1P【）”． As in the above−mentioned explanatlon，the void size ∼Ve 芝ake the case， 、vhich is shown in F圭9． 11 fordistribut圭on contr量buted to suction（i．e．the dash line ininstance，andcalculαte／pt．Figure13shows由eprocedureF圭9．10）is parallel to the void s茎ze distribution（i．e．theforobtalning1P、．ltisfolmdfromFig。13thatthemeanvalue of the void size distribut量on，which coτresponds tosolid line in Fig．10）．And由ey have由e same coef五cientof variation．The diEerence in each void size distribution50％of the cumulative percentage，contrlbuted to suction（the dash line）is equivalent to31。9％dlameter of the voldis expressed by the di牙er』ence among those mean values．Estimating由e d湿erence ln each mean value ofvoid size sizedistrlbution（thesolidline）（tbeallow①）．Thevaluedistr疑）ution gives a new parameter，which is proposed inofthepercentageisne∼、11yde負nedas／P、．lnthiscase，／P、isset to31．9（to aIlow②）．The same method ls also used inorder to improve the previous model ln this paper．Thethe relationship between S，andた．102 Table3shows the populaτsoil parameters an（i IP［forlol l o ①繍儲篇繍篇C窪lcじi飢…α官byてh3preViousmodei1001 の祠’避1α2レ㊦10−3巳． ゑ申」 ①Zき」賦r馴こ脚OaiC乳li就瑠緯暮し、＝…駈ぽfro轟・εO愛夢＝5 蝶」一瀦−CaiculatiGn（byτhθi窩1proved蹟ode1） ＼ 籠 o 10”11でΦ蛍噂の ol・胴一 ①10090、lo冒4忌・“5 0』 o聾邸一の・一￠一＝：）・一 』 邸 Φ 鰭 』 ① 血 “一τ㎜…㎜…｝ヲ7 ！』10樽6①10−7制10需8obO邸篇①①10−9706050Ω．①＞10寵10邸10”11コ匠03io−12 0一≦て，餌宅 下3〕 2銭r80lO−5蓬一 ＞，Z5 d i str i bUt l cn contr I鶉し美tεj to SuCt lOn 穆 臼厨“昌竃一℃｝①嚇曹”−磨一’10i d40一一』蕊』．諸翌30、農／．2010璽0 20 30 40 50 60 70 80 90 望000Degreeofsaturation，5（％）1σ7 iO幕6 10葡5 10廊4 10冒3 1σ2 10−I loo lol 102 ！F Diameter of the pipe （㎜）F童9，12、 Re嚢段霊量onship be琶ween tbe degree of s段重ura“on aηd the u願s飢腿ra霊e6印sat毛照｛edperme段bili重ycoe餓cienI（af吐er！heimpro、一e・Fl9，13。VoidsizedisIribu重lonIha“わeprocedareforo漁ining吐he me煎ofdlenu贈rlc田modeり P徽lieltr段臓sl頗onindex，1PIjsadded重oTable3・ V段hies o郵Ihe some general parame｛ers費nd蕪1e p段rallel｛r3nslation index Ciassif㌔cation ofSample ρ、 geomaterlals for θ｝ （9／cm3）eng玉臓ee【ing purposes ／Pl ／P軍o［1） （abOUt perm1abi1琵yu￠（about suct1o員）（cm） coe鰍ient）玉Shirasu SV−G2，52三、93至．49×10隔326，3415．12Shirasu SV−G2．551．267，88×豆0』高50、1529。3B．63Shirasu SV−G2，51豆、371、05×10湘335、4022。37．54S厩rasu2。621，691，95x10−494．豆739。05S｝擁rasu SV−G2，441．245、85x玉0葡459．7528．19．5Sh三rasu SV−G2．421，276．97x豆0即嵩55．9228、88，1S｝玉玉rasu SV−G2．63夏、7夏2，06×10㎝485．8331．9Ω．0S｝1叢【aSu SV−G2．541．754．08x10−459．0137、411，6Sh玉rasu SVG2461、46叢、41×10皿333．4718、32、681、42玉，86×10−56789SVVS3．618．82、710Shlrasu11Shirasu SV−G2、491．294．12XIO而482，8932．67、812Sむ1rasu SV−G2．581、577，24×10−448．2129．36「313S量1圭rasu SVG2、5444．8521．814Si11rasu豆5Sl1玉rasu1、501。44x10楠3VS2 72玉．662「89×玉〇一6sv2．581、142。73x玉0−4260．53457．1553．7846．017，06，656．2夏8。846．01玉6銘 NU ,IERICAL lvIODEL FOR ¥,OIDSpermeabilit"¥' coefncient, respectively. From these figures,it could be seen that the influence of' the void ratio on the¥'alue of lp* is small; ther'efore, the proposed rnodel can be15 samples. It is found from Table 3 that lp= is related tohe uniformity coefficient. The relatlonship bet¥veen U*and lp, about suction is sho vn in Fig. 14. The horizontalaxis is U* and is expressed ¥vith logarithm. On the otherhand, the vertical axis sholvs lpt' These t¥vo parametershave a linear relation as shown in Flg. 15.The relationship betlveen U* and 1 '* about permeabilityalso applied to the soil samples, which have the samegrain size distr'ibution and the different value of voidratio, in order to estimate lp* by using the ¥'alue of U*.coefficient is sho vn in Fig. 15. The horizontal axis is U*CONCLUSIONSand is expressed by logarithm. On the other hand, theIn this paper, the practical numer'ical model forvertical axis sho¥vs lp*. Fi_･._ure 1 5 also sho¥vs that these t voseepage beha¥'ior of unsaturated soil lvas proposed inorder to improve the numerical model. Firstly, the basictheories of the previous model vere re¥'ie¥ved. Thenumericai r'esults ¥vere compared ¥vith those obtainedfrom the laboratory soil tests in or'der to examine thepararneters ha¥'e a linear relation.From Figs. 14 and 15, it vas found that lpt can be deter-mined from the grain size distribution curve. Therefore,the S¥ fCC and the relationship bet¥veen S* and k can becomputed from the proposed practical numerical model¥'alidity of the previous model. It ¥vas found from theseresults that the suction values calculated by the previousmodel ¥vere smaller than those obtained f'rom soil test atthe same degree of saturation. In addition, it vas alsodetermined that the values of k calculated by the pre¥'ioususin_-' only some popular' physical and soil parameters assho¥vn in Table 1.Next, the applicability of l , to samples, ¥vhich aremade by the soil lvith the same grain size distribution andhave different value of void ratio, is examined. Table 4sho¥vs the ¥'alues of some general parameters and l forrnodel ¥vere overestimated in comparisonvith the soil testShirasu and Toyoura sand. These parameters areresults. Therefore, improvements of the previous modelrepresented in Figs. 16 and 17. These Figures sho¥v therelationship bet¥veen e and lp* about the suction and the¥vere needed to estimate the r'easonable seepage propertiesof soils.1 oo1 oo909080:¥70><Q)><8070 -a:)c:lc:c:60co60c:o50+-50+Jc:CQ40(,,('oz:cco30+Je)+'･ ,*+ '+' -20e)*** "++:Q3020*CQ10C40'(Q: ,*; !}10 -c:*..,"*oo1 OO{10Un i f orm i t yFig. 14. Relationship between the parallel translation index and theuniformit, coefficient about suction'Table 4.Classification oengineering purposesShirasu2 .4534)15. Relationship between the paralle! translation index and theuniformity coeffieient about permeabilit) coefficientID I o(cm)UfToyoura sandI p*(about suction)(aboutpermeabi itycoefiicien )30.9o.531.80.41 .3730.8o.5o 7420 61 .817 5l 4J .5 llcoefficient u.Values of lp* ,vith difference in void ratioSample = geomaterials for= P* e(g/cm3),Fi,,.ooo1 OOUniformity coefficient, l/.L=_603l .472 64o 803_16 x lO i1 37 x lO:ll.36l .62 SAKO AND KITAlvIURA60450from the Ministry of Eclucation, Sports, Science andTechnology, .Japan.i Te c} Jr sanri_,*¥1;40Shi asuNOTATIONxQ)c!::;:30 -c!k:to peFmeabi it_v coefficiemc:oc!u 'J(Ec:CQD:hc:diameter of pipeheight of the element in Fig. l(b)pressure headIP :parallel lranslarion indexD,,:+Ja,10p,(e):CQP ( D ) :cCLP,< :O 608 1 1 4 1 6O1.2su 'r<:V'V.:V k:)c:-* ;o8Sh"3 s f "_iasuJCQ(D:cT+Je)V -u'I"( :(x:7fi:3:6cc:c::othe soil elemeut in Fig_ l(a) per unitflu¥.' of laminar flo¥v in the pipe per unh timesuctionsurface ensionvolume of the container in Fig. l(b)¥'olume of the pipe in Fig. l(b)¥'olume of all pore-¥vater included in soil mass¥'o ume of pore-wa erhat contributeso permeabiliivcoefricient9cl)hrouglrimeV '10parameter in order o fit the void ralio obtained fromflux of ¥¥'atero_eO_p:Fig, 16. Relationship between tlre parallel translation inclex and thevoid ratio about suctionprobabi]ity density funclions for eprobabilit_v density functions for Dcalcula ion lvith that obtained from experimentVoid ratio, e:maximum diameter of pipes filied ¥vith ¥vaier lhat contributesto suction20 -(,,><maximum diameter of pipes fi]led ¥vith ¥vatermaximum diameter of pipes filled with ¥vater that comribmesvolume of pore-¥va er contributing to suction¥'oiumetric ¥vater contentcomact angle of meniscus at a co tact poincontact angle of adjacent soil parliclescoefncient OF Yariarionof soil particleslo¥vest height of P*(e)4/'* :standaFd deviation of l0 nor nal dis rlbutioninclination angle of pipemean value of lo :normal ciislribution3u<:mean ¥'alue ofu* :mean vaiue of D5cy:e:(J,:2(T* :rain sizestandard deviation of rain sizestanciard devialion of DcCQ1CLO.6 1 1.4 1 6O1 28Void ratio, eREFF,RF,NCESl ) Akai, K(1 969): Eve,1!s on Seepage, Soi! ,Vfechanics (ed_ by hJogami,T.), Gihodo, 99l02 (in Japanese).2) Frediund, D. G. and Rahardjo, H, (1993): Soi! fVechanics forFig. 17. Relationship bet veen the parallel translation index' and thevoid ratio about permeabilrty c08ff]cientWe performed the improvement of the previous modelbased on the hydro-mechanical properties, and proposedlp* Then, it ¥vas sholvn that the relation bet¥veen lp* andU* expressed by logarithm lvas a linear relation. Conse-quently, reasonable seepage properties of soils could becalculated from the proposed practical numerical modelusing only. some popular physical and soil parameters assholvn in Table I . Therefore it can be concluded that theproposed practical numerical model can contribute tomany geotechnical problems.U]Is(Ituratec! Soi!.s, ohn ¥¥?iley & Sons, 39.3) Kilamura, R. (1985): A h,1arko¥' model of particulate material lvithan isotropic fabrics, Proc. In! Con f. 1¥runl * fe!h. Engr'g^, rheor.App!. (!¥TU! ,JETAS.)"), 455-4644) Kiiamura, R., Fukuhara, S., Uemura, K , Kisanuki, J. arl;d Sevama,¥. ,1. (1998): A oumerical model for seepage through unsaturated soil,So!! and Founc!a!ions, 38 (4), 261-26_5) Oda, ¥.,1. (1972): Ini ial fabrics and their relations to mechanic.alproperties of granular malerial, Soi!s anc/ Founc!ca!on.s, 12 (1).17366) Sato, K., Soba> T , Ku¥vayama, T, and Uno, T. (1992): hlercuryintrusion echnique for macro pore measurement of particulate soil,Proc JSCF, (430/Ill-18), 39-142 (in Japanese).7) Uno, T^= Kamiva, K. and Tanaka, K. (1998): The distribution ofsand ¥*oid diameter by air in rusion method and moisture characleTistic cur¥'e method, Proc. JSCE, (603/lll-44), 35-44 (in Japanese)8) Yan-Genuchten, h,l Th. (1980): A closed-form equation for predictirrg the hydraulic conducrivit)' of unsa uraled soil, Soi! Sci. A,11. ,J.,ACKNOWl,F.DGEMF.NTThis research ¥vork vas supported by the Grant-in-Aidfor Scientific Research (No. 1'_79)_009, No. 13450196)44 (5), 892898.9) Yamaguchi, H^, Hashizume, Y and lkenaga, H (1992): C_hange inpore size distribulion or peat In shear processes, Soi!s anc!Fou,1c!ation.s, 32 (4), -16 | ||||
| ログイン | |||||
| タイトル | Uplift Capacity of Pile Groups Embedded in Sands: Predictions and Performance | ||||
| 著者 | K. Shanker・P. K. Basudhar・N. R. Patra | ||||
| 出版 | soils and Foundations | ||||
| ページ | 605〜612 | 発行 | 2006/10/15 | 文書ID | 20944 |
| 内容 | 表示 rSOILS AND FOUii¥]'DATIONS¥*ol46,NO), 605-6 1 2 ,Oct 2006Japanese Geotechnical Soclel}UPLIFT CAPACITY OF PILE GROUPS EMBEDDED IN SANDS:PREDICTIONS AND PERFORMANCEK. SHA TKERi), P. K. BASUDHARii) and N. R. PATRAiii)ABSTRACTThe paper pertains to the development of a simple semi-empirical method of analysis for predicting the upliftcapacity of pile groups embedded in sand assuming an irrverted truncated rectangular pyramidal f'ailure surface.Various pile and soil parameters such as length, diameter of the pile, group configuration, spacing of the piles and thesoil properties such as density, angle of' internai friction and the pile-soil interface f'riction angle ha¥'ing direct influenceon the uplift capacity of the pile group are incorporated in the analysis. The predicted values of uplift capacity of pilegroups ¥vith different configuration and length to embedment ratio are then compared ¥vith model test results carriedout as a part of the present investigation and also ¥vith the values reported in literature. The predictions are found to bein good agreement ¥vith the measured values validating the de¥'eloped method of analysis.iKewords limrtmg equilibrium, model test, pile,pile _",_roup,sand, uplift (IGC.: E4)embedment length, number of piles in a group and spac-INTRODUC.TI0_NPrediction of uplift capacity of' single piles anding of piles in a group. Madha¥* (1987) studied the interaction betlveen t¥vo identical piles in tension using bound-especially of pile groups is one of the most interestin_ ._ary integral technique. The reduction in individual pileareas of research in geotechnical engineers. Some of thestudies conducted on the behavior of single piles undercapacity due to the existence of another pile is quantifieduplift loads are due to So¥ 'a (1970), Vesic (1970),and it is found to depend on the spacing and length toRao and Venkatesh (1985), Chattopadhyay and Pisediameter ratio of piles.It is evident from the literature as cited abo¥'e that mostof the available studies are limited to single piles onl_v.But increasing use of **roup of piles to resist and sustain(1986), and Ramasamy et al. (2004). These studies areuplift loads requires accurate assessment of upliftvery helpful in understanding the behavior of piles undertensile loads and predicting the value of uplift capacity ofsin*'1e piles. But, Iiterature on such studies on the upliftcapacity of pile *'roups embedded in sand are scanty (Daset al., 1976; Siddamal, 1989; Chattopadhyay, 1994; Patr'aresistance for safe and economical design of' pile founda-and Pise, '-003). The theories to predict the upliftshape, spacing, embedment length to diameter ratio oflv:1eyerhof' (1973), Das and Seeley (1975), Isrnael andKlym (1979), Das (1983). Levacher and Sieffert (1984),tions. As such, there is a need to develop methods topr'edict the uplift capacity of pile groups and such ananalysis is presented in this study. The uplift resistance ofpile groups depends on several ¥'ariables like group size,capacity of piles ¥vere developed mostly by extending theanalysis of horizontal plate anchors under uplift loadspiles, soil type and its density and soil-pile friction an*'1e.Considering some of the above parameters a simplifiedanalysis based on limiting equilibrium is proposed toassuming development of failure surfaces starting fromthe edges of the anchor. Based on experimental observation and test data, lvleyerhof and Adams (1968) proposedpredict the uplift resistance of the group of piles. Labora-a general theory of uplift resistance for a strip footing intory rnodel tests on group of piles were conducted inmedium dense sand under axial uplift loads at differentsoils with the assumption that soil mass having approxi-pile spacing and lvith varying embedment length tomately truncated pyramidal shape is lifted up and forshallo¥v footing the failure surface extends up to theground surface. The theory ¥vas further' modified todiameter ratio. The predicted values of uplift capacitywere compared ¥vith the model test results so obtainedand vith other published experimental data to check thevalidity of the developed method of analysis.analyze circular footings and square and rectan*"ular pilegroups. Das et al. (1976) and Chattopadyay (1994)concluded that the efficiency of a pile group variesi:li tvithResearch Scholar, Ci¥'il Engineering Depar ment, Indian Institu e of Technology Kanpur, Kanpur 208016, India.Professor, di to, (pkbde=iitk.ac.in).Asst. Professor, ditto.'The manuscript for this paper ¥vas received for review on July 25, 2005; approved on ivlay 29, 2006.Vritten discussions on his paper should be submitted before " ay I , 2007 o the Japanese Geolechnical Society, 4-38-2, Seugoku, Bunkyo-ku,Tokyo I i2-001 l, Japan Upon request the closirrg date may be extended one month.605 lSHANKER ET AL.606¥vedge and its fr'ee body diagram are sholvn in Fig. 1.*,J ''UI*iThe mobilized shear resistance AT along: the fai]urefL__J'l)yrsurface of length zl L, at limiting condition is,A T=A R tan c (1)"" lL_illiL'p!IAZI"+tII]I'!'!!!'- r!v "I*::lli T TTWhere AR=Normal force acting on the failure of the¥vedge' Q?i r& ;iQ1";:rTT7TrFl;r'fl I1: I [ f'Pil :- Il _ LLll_Lz/'1 eLL----zlAR IOcose+KAQsine (2)( I,-AQ=yV rherezlZ ll (3)- Z-.)Following Chattopadhyay and Pise (1986) the coefficientof lateral earth pr'essure within the ¥vedge is taken as,tan 6Fig. 1. Free body diagram of lvedgeSTATF,MF,NT OF THF, PROBLEMK (1 sin c) tan c (4)Substituting Eq. (3) and Eq. (4) into Eq. (2) ¥ve get,Zi R = y (1, - Z(cos- e+A'zi.Z)sine ( )sin e) AZFigure I sho¥vs a typical general pile group (a 2 x '_ piiegroup is sho¥vn here) of diameter d and length L embedded in soil. The plan dimensions of the pile group are aSubstituting Eq. (5) into Eq. (1), ¥ve get(and b. The friction angle of the soil is c and the pile-soilinterface friction angle is 6. The object is to determine the)AT=y AZI, - Z(cos e Ksln e)AZtanc (6)ultimate uplift capacity of the pile group.Considerin*' the vertical equilibrium of the ¥vedge andANALYSISIn studying the per'formance of piles ¥vith enlargedbase, Dickin and Leun'* (1990) critically discussed thevarious possible types of slip surfaces namely the verticalslip surface model, inverted truncated cone or pyramidalmodel, curved slip surface model considered by severalassuming that the *eight of the pile group of the lengthA Z is equal to the total weight of the soil correspondln_"..to the volume occupied by each pile in the group for thelength IZ.( p + A P) - P+ q(a + 2x)(b + '_x)- (q + Aq )(a + _x + 2A x)(b + 2x+ 2ZI x)investigators in estimating the pile capacity. It is observedthat the analysis is relatively simpler if the slip surface isassumed to be linear making: an an2:le ¥vith the verticalthat depends on the factors like friction angle and angle-A W- 2(a+ b + 4x+ 2A x)ll Tsin e = O (7)Substituting Eq. (6) into Eq. (7) and on simplificationgetof dilatancy (V/), which is a function of the relativec/. '= 2q(a + ' ,)dZdensity of the soil. From literature it is found that forsingle piles this angle has been assumed to be equal to anyc!Z dZ+ 2(a + b + 4x) )'(L - Z) M (8)(Vermeer and Sutjiadi, 1985), c/2 (Clemence andVeesaert, 1977), c (Murray and Geddes, 1987) or a funcBased on the above discussion, in the present analysisan expression for the uplift capacity of pile group isderived based on the assumption that under limitin_"..condition, soil mass around the pile group fails as aninverted truncated pyramidal solid body havin*" similarcross section as that of the pile group extending up to theground surface passin*' through the tip of the pile at anangle fi from the vertical.Derivatiol7In the limiting equilibrium condition, ultimate capacityof the pile is attained ¥vhen the mobilized shear strengthalong t,he failure surface and the vei*･hts of the soil andpiles balance the applied forces. A ¥vedge of thickness A Zat a height Z above the tip of the pile is consider'ed; the'_q(b + '_x)+ (a + 2x)(b + ?_x) dq + d Wone of the follo¥ving namely the dilatancy angle (V/)tion of c (Sutherland et al., 198,_).ve¥vhere M=(cos e+Ksin e) tan cReferrin*' to Fig. I the follo¥ving relations are obtained,c!x cote x=ZcotedZdq= yq y(I-Z) c!"' ' ' ' ･ -This on substitution into Eq. (8) yields,dPdZ- = 2q(a + 2Z cot e) cot 0+ '_q(b + '_Z cot e) cot e+ (a+ 2Z cot g)(h + 2z cot e)( - }')+d W+ _'(a + b + 4Z cot e ) y( L - Z) I I (9)dZs- UPLIFT C APACITY OF PILE G ROUPS60T1dW c!Z=(a+'x)(b 'x)y (lO)here3Setting q=y(L-Z) and Kl=a+b and substitutingEq. (10) into Eq. (9) the Eq. (9) can further be simplifiedto a form as gi¥'en belo¥vdPdZ=2yLKI cot e + 8yLZ cot I e- 2yZA'I cot e- 8yZ2 cot I e + '_KI yLM '_KI yZM+ 8,yZLK cot e- 8),MZ2 cot e(11)that on integration yields an expi'ession for the grossultimate uplift capacity as,89PLegends= 2yL2A'I cot 6+ 4y cot 2 eL3 - yKl cot eL2L3- 8y cot2 e 3 + ,_Kl yL2M-K yML2L34yMcot eL 8yMcot e 3 (1_')P.=K}'(cot e+M)L * 43 y cot 6(cot 6+M)L3 (13)The net uplift capacity of pile group is,P*** = yL2(CI K! + c2L) - ,V,. (14)V,rhere, Cl and C2 are the dimensionless constants equalto (cot e M) and4- cot e (cot e+M) respectively.3n ylrd2W,._,_, is the self ¥vei**ht of the pile group = 4¥*ire rope11)Aluminum strip6 Pile capiodel Pile7.,Pulle)8.4¥* {agnelic base plale9 Dead 1 i htDizrlFig. 2,･fodel lankau eEx.'perimental set*upinfiuence of the piles and loading there on is reported tobe in the range of 3-8 pile diameters (Kishida, 196,3).Model piles ¥vere prepared from mild steel rod of7_O mm x 20 mm cross section. The length of embedmentof pile, L in sand bed ¥vas 400 mm, 600 mm and 800 mmresulting L/d as 20, 30 and 40 respectively. The pile-soilinterface friction angle ( ) Ivas f'ound to be 26' from thedirect shear test. Pile caps ¥vere prepared for '_ x 1, 3 x 1,2 x '_, 3 x 2 and 3 x 3 pile groups (at 3d, 4d and 6d spac-ing) using 12 mm thick mild steel plate. As most of theWhere, n is the number of piles in a group.For L/d> ?-O the failure surface is assumed tangentialto the pile surface up to 0.3L from the tip of the pile.Hence Eq. (1 1) is integrated bet¥veen the limits O to 0.7Land added to the skin friction developed in the remaininglength.It is to be noted that the pile group capacity will be theminimum of the values predicted by considering grouppreviously studied model test were conducted for L/dratio ranging from 12 to '_Ovith only a fe¥v tests conduct-ed ¥vith higher L/d values, in the present study the samehas been taken on higher side i.e 20, 30 and 40. With theaddition of data ¥vith hi**her L/cl ratio the data bankrepresented short, intermediate and long piles. The spacing ran*"ing from 3d to 6d is generally adopted in design.As such, the same 1¥*as chosen representing piles ¥vithaction or the capacity of an individual pile multiplied bythe number of piles in the group. Hovvever, it. is obser¥'edcloser' to large spacin*".that only for spacin*' beyond 6d piles in a group actsindividually. The present paper is concerned vith the*'roup action only that is consistent with experimentalsand bed (made by rainfall technique) composed ofresults. In recommending the capacity that is to bemum and minimum dry densities of the sand ¥vere foundadopted in design one must consider' ¥vhich one of theto be 16.2 and 14.74 kN/m3 respectively. Sand ¥vasabove two mechanisms *'ives the minimum value andadopt the same.The above predictive model is validated by experimen-poured uniforrnly into the tank throu*'h the slot hopperkeepin*' the height of fall of 300 mm. By using abo¥'etechnique medium dense bed ¥vas prepared ¥vith a dry unittal studies made on model piles, ¥vhich are as follows.¥veight (y) of 15.8kN/nf, corresponding to relativeThe model piles were embedded in horno*'eneous dryuniformly graded Ennore sand having uniformitycoefficient of I .71 and specific gravity of ･_.69. The maxi-density (D,) of 54.30/0 and angle of shearing resistanceEXPERIMENTAL DETAILSTests on model pile groups ¥vere conducted in a steeltank (size 990 mmx975 mm x 970 mm). The tank ¥vassufficiently large enough to take care of the effect of theedges of the tank on the test results as the zone of(c) of 38'.Piles were subjected to tensile loading through a pulleyarrangement ¥vith a fiexible wire whose one end ¥vasattached ¥vith the pile cap and the other end lvith aloadin*' pan over which dead loads are gradually placed insta*'es. A schematic dia*'ram of the complete experimen- 60sSHANKER ET AL.tal set-up ¥vith the loading system and pile in place andready for test is sho¥vn in Fig. '-. T¥vo dial gauges ¥vithmagnetic base ha¥'ing sensitivity of O.OI mm ¥vere used tomeasure the displacement placing them on the pile cap at180' apart and equidistant fr'om load axis.RF.SUL,TS AND DISCUSSIONSeries of tests ¥vere conducted in medium dense soil tostudy the effect of pile spacing (s), Iength to diameterratio (Llc!) and number of piles in a group (ll) on theuplift capacity of model pile groups. The load ¥'ersusdisplacement curves lvere plotted for all the pile groupsand some of them presented in Figs. 3(a), 3(b) and 3(c).The load-displacement curves sho¥v similar beha¥'ior fordifferent spacing and length to diameter ratio. By usingthe double tangent method the gross ultimate uplift load¥vas found. The net ultimate uplift load of a pile group(* )Pig. 3(a). Upiift load versus displacement curves (3 x I pile group with4d spacing)¥vas re¥vorked by subtracting the corresponding self¥veight of piles and cap.Variations of group efficiency ¥vith respect to pilespacing for different pile groups ¥vith I,/d ratio being: ?_O,30 and 40 are presented in Figs. 4(a), 4(b) and 4(c)respectively. From these figures it is obser¥'ed that there isa definite trend of Increase in the gr'oup efficiency ¥vith theincrease of pile spacing. From Fig. 4(b) for a 3 x 3 pilegroup the efficiency is increasing from 490/0 to 600/0 as thespacing changing from 3d to 6d. Similar trend has beenobser¥'ed for other pile groups. Further, it is observedthat the group efficiency is ciecreasing ¥vith the incr'easingnumber of piles in a group. For any given spacing themaximum efficiency has been observed for 2 x I pilegroup and minimum efficiency for 3 x 3 pile group. From(b)ri"_* . 3(b). Upiift foad vers s dispiacement curves (3 x 2 pile group with3d spacing)Figs. 5(a) and 5(b) it is obser'ved that the group efficiencyis significantly affected bv_ Iength to diameter ratio of thepile group. For any gi¥'en pile group and spacing thegroup efficiency is decreasing as the length to diameterratio of the pile group increasing. From Fig. 5(a), for a3 x I pile group at 3d spacing as the L/c! ratio increasesfrom '_O to 40 the reduction in the group efficiency isaround 140/0.The theoretical ¥'alues of the net uplift capacities fordifferent group of piles considered for experimentalstudies ¥vere estimated from Eq. (14). Different trialvalues of fi, the angle that the slip surface makes ¥vith thevertical ¥vere taken to estimate the theoretical pile groupcapacity and compared the same ¥¥'ith experimental(c)observations. It vas obser¥'ed that an angle equal to c14gi¥'es values that are in good agreement ¥vith experimentalFig. 3(c). Uplift load versus displacement curves (3 >< 3 pile group lvitl]results. The same is adopted for further predictions. A4d spacing)comparison of the predicted and measured values assho¥vn in Figs. 6(a), 6(b) and 6(c) demonstrates a closeagreement as most of the data points lie very close to theideal line. A quantitative comparati¥'e study ¥vasconducted to estimate the deviation of the predicteduplift capacity from the measured one. It ¥vas observedthat for 890/0 of the data (40 out of 45) the deviation ¥vas¥¥'ithin 300/0 and for 550/0 of the data (26 out of 45) theerror ¥vas even less than 100/0. Thus the absolute relativeerrors bet¥veen the predicted and measured values lie ingeneral in a range lvhich may be considered to be ¥vell¥vithin the range of experimental error and errorsinherent to the models. Ho¥vever, for the sake of spaceand brevity these computations are not presented here.While doing the model testing, an attempt ¥vas made tocheck the validity of the assumption of plane fai]ure UPLIFT CAPACIT " OF PILE GROUPS1iOO -･-6a9O1¥l); o')>C'i:,¥l- -8C -jL)(!'(1;Ov3¥S [)ac ing ( s/d )8064e)e;60 -l::r SO-,, ,,:;S(j)4a2a 3a 40406L'd*as8tioSpadng (s/d)(a)(a)Fig. 5(a).Variation of group efflciencyvith L/cl ratio, 3 x I pile groupVariarion of group efiiciency witi] pile spacing, Llc!= 20Fig. 4(a).oO -____ _G.J_r_o_Llp_hl7-eiaox Ixo:h-l118aVc:ov3xq,O8c;; -'60e;SOQ,oC:sO404020a2 3 4620 3C 40soud r8'*iaSpacing (s/d)(b)(b)Variation of group efficieuc, wil 1Fig. 4(b).le spacing, L/d=30Fig. 5(b).Variation of group efrrcienc, wiih L/d ratio, s/d=6lvere further checked ¥vith the experimental data reportedby various investigators as follolvs.leoG roLlp size8a -vefficiency of pile groups of size 2 x I , 3 x I , 4 x I , 2 x '_, 3x '_, 3 x 3. Rough wooden piles of diameter 12.7 mm andLlc!= 24 were used as model piles. lvledium condition ofsand ha¥'ing y = 15. 10 kN/m3, c = 31 ' and D*= 21 /o ¥vas3 :1eo --e'3¥3ceDas et al. (1976) reported net uplift capacity in terms of3¥11¥,ve)x l40used as the soil media. Pile-soil interface friction angle 620234S8rSp cing ( _!d)(c)Flg. 4(c).Variation of group efficienc) with pile spacing, L/d=40¥vas taken as 19.3' (Das, 1983). The measured values of'the net uplift capacity of pile groups lvere indirectlye¥'aluated from the reported efficiency diagram. Themeasured values of the net uplift capacities for differentgroups and the corresponding predicted uplift capacitiesusing Eq. (14) are plotted in Fig. 7. Most of the data lievery close to the ideal llne. The percentage of error in thepredicted values from the measured one is found to beless than 300/0 for 830/0 of' the total data (10 data pointssurface by introducing wet soft tissue papers at differentlevels in the soil strata. Ho¥vever, the adopted techniquedid notvork and the verification of the assumptionre*'arding the slip surface could not be made.out of 1'_ data points).Siddarnal (1989) reported axial uplift test results onmodel mild steel pile groups of size 2 x I and ,_ x 2 having,After comparing the predictions made by using theL/d=20 and 40. The spacing of 2, 4 and 6 times the pilepresent method vith the experimental data obtained fromthe present investigation, the correctness of the modeldiarneter for 2 x I pile groups and ,- and 4 pile diameterfor 2 x 2 pile groups vere used. The dlameter of the pile 1*i!."SHANKER ET AL.610120 -80a *7aolcat-60Gz 80z- 5CalC40aA +,:: 60'; 300CL 40!20a201 ooaoa 100 2aO 3aa 4aO 500 6aa 7CO 8aaa 20 40Me sLsred Pnu (N)60 80 1 oO 1 20Measured Pnu (N)(a)*- 2xl 2dx 2x2 2 5dComparison vith present model test resuiis, I./d= 20Fig. 6(a).- 3x 1 2do 3x2 2d1 200Fig. 7.-4=2xl 3d--x- 2x2 4d･ 2xi 4d+ 2x2 6d= :4d- - 3xl 6d- 3x2,4d3x2 6d,3xComparison with Das et al. (1976) model test resultsOOoZ8aoO*e)l 1'6aov1Q,_ r;- o-'lLF '400+1400DA 2i200e I-Iooo>< >K-o' 800200 *e)lcieal line6001oQ;CLO 2ao 40a eOO 8ao laao 1200400" easvred Pn (N)200( b)aoComparison lvith present model tcst results, L,/d=30Fig. 6(b).200 400 600 8co loao i200 14aoMe sLJrBd Pnv (N)-.= Lld=20 2xl 2d* L/d=20 2x I ,6d2aoo-L/d=40 2x I ,4d+ L/d=20 2x2 2d3 L/d=40,2x2 ,2dc}- ud=2a 2x 4dB ud=40,2x ,2d-4 ud=4a 2xl 6d-S: L/d=2a.2x2,4d-e L!d=40 2x2 4d1 500Fig. 8.zCLeColnparisonvith Siddamal ( 983) model test resultsoaO¥vas 20 mm. Dry sand havin*' y= 16.1 kN/m3, c=40.5'v::e,and= 23' ¥vas used as the foundation medium. Figure 8sho¥vs the comparison bet¥veen the predicted values ofuplift resistance by the present theory ¥vith the measuredc500ovalues of uplift test results. It is seen that the predictedO 500 150a 20ao1 OOOvalues are in reasonable agreement ¥vlth the experimentalMe sured Pnu (N)values with 700/0 of the data having error, Iess than 300/0.2x I-x,6ds 2xl.3d A 2xl 4d -x3xl.3d- 3xl,4d +-3xl,6d2x2,3d- - 2x2,4d-4 2x2.6d {;- 3x2,3d - 3x2.4d3x3,3d c - 3x3,4d :E- 3x3,6d3x2,6dChattopadhyay (1994) repor'ted limited uplift test resultsfor model pile groups of size '_ x I and '_ x2 and I,/d=15.78, 23.68 and 31.57. Aluminium tubes of outer diameter 19 mm ¥vere used as piles. The groups ¥vere tested(c)Fig. 6(c).Comparison with present model tcst resu ts, I,Id=40for spacing 2.3d, 4d, 5d and 6d. Coarse to medium sand¥vith D60=0.95 mm, Dl0=48 mm, C = I .98, c=40' and6=25' (,-13c) and unit lveight of y= 17.00 kN/m3 ¥vereused. From the load dlsplacement diagrams, the nets UPLIFT C APACITY OF PILE GROUPS61130a50a40az:_ 2003aa:,Q,5,2aaI aoC1 aaOOa 3ao 400 Sao1 OOr, easured Pn1 OO 2aao2002xl ,Lld=23 68-- 2xlX4 5dH - 2x - 3d2x- ,8d-h, 2xi L/d=31 57 ･ 2x2,L/d= 5 78a 2x2,Lld=2368 E 2x2,Lfd=31 573x ,6d-- 2x2 3d-+- 3xl 4- 5d-4 2xl Ud=15 78 -Fig. 9. Compariso}1 wrth Chattopadya)' (1994) model test resultsuplift capacity of pile and pile *"roups ¥vere measured.The theoretical and measured net uplift capacities areplotted in Fig. 9 sho¥ving the predictions to be in closeproximity to the ideal line ¥vith 670/0 of the data (4 out of6) having error, Iess than 300/0.Patra and Pise (2003) conducted model test on pilegroups of' size 2 x 1, 3 x 1, '_ >< '_, 3 x 2 using dry Ennoresand as f'oundation medium. The specific gravity anduniformity coefficient of the sand ¥vere '_.64 and 1.6respectively. The unit weight of' the sand during testin_',_¥vas 16.4 kN/rn3 (D, = 800/0). The corresponding angle ofshearing resistance c = 37'. Aluminum alloy tubes of 19mm outer diarneter, 0.81 mm wall thickness were used asmodel piles. To increase the ¥vall friction of pile, fineEnnore sand was **lued around the pile by adhesive. Thelengths to diameter ratios of piles were 12 and 38. Thepile-soil interface friction angiebetween smooth androu*'h surfaces of piles and sand ¥vas evaluated from thedir'ect shear test results and reported as 20' and 31'respectively. The theoretical and measured net upliftcapacity of rough pile groups for L/d ratio of 12 areplotted for comparison in Fig. 10. lvlost of the data (9 outof 12 i.e 750/0) is very close to the ideal line ¥vith error, Iessthan 300/0. Thus, it is seen that the semi-empirical modeldeveloped presently acquits itself quite ¥vell in predictinthe values of uplift capacity of pile groups that are inclose agreement ¥vith measured values.3aoMeasured Pnu' (N)(N}2x2 6dFig. lO.-4- 3xl 3d2x2 4 5d3x2 3d - - 3x2 4 5d -O 3x2 6dComparison wrth Patra and Pise (2003) model tcst resultsconsidered to be permissible in such predictions.However, the predictive model needs to be verified ¥vithfield tests and for spacing beyond 6d.NOTATIONThe follo¥ving symbols are used in this paper.a and b=plan dimensions of the pile groupC1 and C2= dimensionless constan sD* = relative densityc!= pile diarne erK= Iateral earth pressure coefficienL = embedded length of pileLlc!= ratio of embedded length io diame er of pileP** = ultima e uplift capacity of pileP *= net ullimate uplift capacity of pile1 'V=¥veight of the elementai strip'; . = self lveight ofhe pile groupA Z= thickness of ¥vedge elememe= angle of failure surface ¥vith horizoulalfi= angle of failure surface ¥vith ver icalc =angle of internal friction of the soil= pile-soil interface friccion an".__le)'= unitveight of the soilREFERENCES1) C hauopadyay. B_ (, . (1994): Uplift capacity of pile groups, Proc.!3th ICSIVIFE, Ne¥v Dethi, India, S39-5422) Chattopad),ay. B. C and Pise, P. J. (1986): Uplift capacit)' of pilesin sand, J. Geotech. E,1gr*". Div , ASC E, 112 (9), 888904.3) C*lemence. S. P, and Veesaert, C. J. (1977): Dynamic pullovtresistance of anchors in sand, Proc. IntS_1'nlp- Soi! Stl'ucrure Inter-action, Roorkee, India, 389397.CONCLUSIONSBased on the studies reported in the previous sections itcan be concluded that the pr'oposed model has excellentpotential in predicting the uplift capacity of pile groupsembedded in sand. The error mar*'in between the predict-ed values and the experimentally observed values ingeneral is ¥vell ¥vithin 300/0 (which may attribute to eitherexperimental error or error' due to the model) and may be4) Das. B. M. (1983): A procedure for estimation of uplift capaciiy ofrou_ :h piles, Soils ailc! Fbunc!a!iolis, 23 (3), 122126.5) Das, B, h,l and Seele.v, G R. ( 975): Uplift capacity of buriedmodel piles in sand. J. Geo!ech. Eng. Dil' . ASC'E, 101 (G TIO),l0911094.6) Das. B. i¥,1., Seelev, G. R. and Smith, E. J. (1976): Upllft capacilof group piles in sand, J. Geotech. Eng Dil' , ASCH, 102 (GT3)282-286.7) Dicking. E. A. and Leung. C. F_ (1990): Perfofrnance of piles ¥vithenlarged bases subjected to uplifl forces, Can Ceotec'h J., 27 (5), 612SH、へNK蕪R狂丁、へL． 546−556．16）Ramasamy，G、，Dey，B．and Indrawn，E．（2004）l Studies on skin8） Isη1ael，N、F．and Kiym，T、、V、（1979）＝Up！ift and be＆rillg capacity frlCt1oniロpileSunde口ensileandcompressiveload，∫’∼伽1∼ of shor［plers1【1san（三，ノ、Gθo’θ‘h，五ン∼9’8．0’V．，ASC三．105（GT5）， Gθo’ech，、／、，．34（2），276−289． 579−594．17）Rao，K．S．and Venkatesh，K H．（互985）：UI）11f【behavlor of short9）Kishida，｝4。（1963）：Stress dis【rlbほtion by model piles in sand，So’1∫ αηゴFo』〃τ‘1‘πノ0／15，4（1），1−23，10）Levadler，D．R、and Sie圧er【，，」、G，（1984）：Tes董onmodeherlslon piies i自u賢iform sand，So’Z∫απ4Fo”114α1’0113ラ25（4〉，1−7・18）S1ddama1，U，V、（1989）：Be！1aviQrofpilegroupsunderupli田oads， ル4、7セ‘1∼、771θ∫’∫，1至丁，民11aragpur，lndia。 P1】e5，、ノ．0θ01θch。￡η813．D疵，ASCE，玉10σ2），1735−1748，i9） Sowa，V．A．（1970）＝Pulling capacity of co員creτe cast in−s1しu boredmMadav，M「R、（1987）：班clencyofpilegroupsimellsion，Cθn． piles，Cα1∼・（7θo’θ‘1∼．ノ、，7，482−493・ Gθo’θc11、ノ．，24，149−153．20）Sutherland，H B、，Raalay．τ．、V、and Fa（H，M．0，（i982）：Up11ft12）Meyerhof，G．G．（1973）IUpll負resisζa員ceofincli簸eda良chorsa頁（1 capacity of embedded anchors in sand，Proc．31ゴ∫n’．Co1ゾβθ1∼θ、・、 piles，P’qoc、8’1r∫CSハ4FE，Nloscow，2，167−172． α岱1ro1でS”・zκ’∼’1巴∫，Cambridge，MA，2，451−463。i3），〉茎eyerhof，G、G．and Adams，、L L （1968｝：丁藍e ulti【nate upli負21）Vermeer，P．A、a巖d Su頃ad1，W、（1985）：τ11e up鮭食res1s〔ance of capacityoffoundations，Cα’LGθo∫θc／L．∫．，5（4），225−244。 shal正ow embedcled andユors，P1’oc。 1111置∫CεA4ノ『E，San Fra旨dsco，14）Murray，三．，1，andGeddes，JD．（1987）：Upllfτofancllorpla【esin CA，3，1635一1638．22）Veslc，A。S．（1970）＝Testso郎nstrumen！edplles，ogeecheerivers1［e， sa賑d，ノ、Gθo’θc11、五17g’8．，ASCE，113，202−215．15）Patra，N、R．a駐d Plse，P J、（2003）：Up蕪fξcapaciτ｝・ofpile groロps in ／．、∫o’1∠、4θ（r1∼．roε’ηθ「．Eηg’8、0’v．，ASCB，96（S鼓12），561−584． sand，E！θ‘’〆011．．／．（｝θo’θch．E’∼91習．，8，Bundle．B．鑑 | ||||
| ログイン | |||||
| タイトル | An Elastoplastic Model for Unsaturated Soils under General Three-dimensional Conditions | ||||
| 著者 | M. M. Farias・M. Pinheiro・M. P. Cordao Neto | ||||
| 出版 | soils and Foundations | ||||
| ページ | 613〜628 | 発行 | 2006/10/15 | 文書ID | 20945 |
| 内容 | 表示 rSOILS AND FOU*¥DATIONS Vol, 46.N'o ), 6 1 3-628 . Ocl. '*006J2',panese Geolechnical SocieL}AN ELASTOPLASTIC MODEL FOR UNSATURATED SOILS UNDERGENE.RAL THREE-DIMENSIONAL CONDITIONSM. M. FARL ¥si) M. PINHEIRoii} and M. P. CORDAO NETOiii)ABS'I'RACTEngineering problems concerned either directly or indirectly ¥vith unsaturated soils ar'e more and more common,ranging f'rom aspects related to seepage to those related to shear stl ength and volume change. A fe¥v constitutivemodels have been conceived to describe and quantify these problems all of them ¥vith some ad¥*antages and ch"a vbacksRegarding mechanical behavior, the so-called Barcelona Basic Model (BBM) has achieved ¥vide acceptance ingeotechnical engineering, basically due to its simple mathernaticai formulation and good description of phenomenaassociated ¥vith unsaturated soils, especialiy collapse. Another concept that has emerged as a po verful frame¥vork totackle three-dimensional states in granular materiais is that of a modified stress tensor, such as tjj. In this paper bothBBlvl isotropic structure and tjj concepts are combined to pr'opose a ne¥v elastoplastic model for unsaturated solls,called tjj-unsat. Modifications and generalizations for unsaturated states are introduced to accommodate thoseframelvorks and o¥'ercome some inherited ch･a vbacks. At the end of' this lvork, experimental data gathered fromspecialized geotechnical literature is used to support the theoretical framework. The satisf'actory agreernent bet veensirnulations and tests results emphasizes the applicability of the proposed formulation to real boundary valuegeotechnical problems.Ke¥.' "ords: collapse phenomenon, constitutive la vs, elastoplasticity, tjj concepts, unsaturated soils (IGC:D6/EO/E 1 3 /E 1 4)DO/D,3/D5/hand, the keystone of tjj-unsat three-dimensional stressINTRODUCTIONframe¥vork is related to the concept of SpatiallyMobilized Plane (SMP) and concepts associated to thatThis paper presents an alternati¥'e constitutive modelfor describing the mechanical behavior of soils, particularly at unsaturated states. The model, named tjj-unsat, isbased on the classical theory of plasticity, inasmuch as itplane, such as the modified stress tensor tjj andMatsuoka-Nakai f'ailure criterion. In order to grasp themeanin*' of these concepts, Iet a soil sample be submittedto three dift rent principal stresses until complete soiluses concepts such as yield and plastic potentialfunctions, flo¥v rules, hardening la¥vs. It is also foundedfailure is achie¥'ed. If three Mohr circles and theiron the critical state theory, vhose legitimization forunsaturated states has been extensi¥'ely supported bymany authors, to name but a fe v, Alonso et al. (1990),respective failure envelopes are plotted for each pair of"principal stresses (al-(T2), (al-(T3) and ((T2-a3), thenthree planes of mobllized shear strength can be defined.Axelsson et al. (1989), Toll (1990), lvla touk et al. (1995),The SMP will simply represent a composition of theseWheeler and Sivakumar (1995), Adams and Wulfsohnmobilized planes. In other ¥vords, SlvlP ¥vill represent the(1998) and Wang et al. (2002).The model adopts t¥vo ¥vell-established frarne vorks:one for Isotropic stress-suction conditions and anotherone for true three-dirnensional stress conditions. For theplane ¥vhere soil particles are considered most mobilizedon the a¥'erage in a 3D stress space (lvlatsuoka and Nakai,former, the isotropic frame¥vork of Barcelona BasicModel (BBM) is assumed. This model, vhich became abenchmark in literature for unsaturated soils, vasinduced by stress state (Nakal and Mihara, 1984).1977). The modified stress tensor tjj is regarded as arnechanical quantity able to account for the anisotropyFinally, Matsuoka-Nakai is a purely frictional failurecriterion based on the stress invariants related to theSMP. In a simple manner, it takes into consideration thedeveloped by Alonso et al. (1990) in order to reproduceseveral characteristics of the mechanical behavior ofinfluence of intermediate stress on soil strenth.Modifications to BBM f'rame vork ¥vere performedunsaturated soils. It offers a simple guideline to representand quantify soil collapse due to saturation. On the other¥vith the aim to o¥'ercome some dra¥vbacks associated to*' Professor, Dept. ofCivil and Environmental Engineering, University of Brasilia, Brasilia. DF, 70910900. Brazil (rnunizC ."S unb br),PhD Student, Dept, of Civil Engineering, Universitv of C*algar}', Calgary, AB, T2N IN4, Canadaiii] phD. Dept_of C'ivil and Environmental Engineering, Universlt}' of Brasilia, Brasilia, DF, 70910900, BrazilThe manuscript for this paper ¥vas recei¥'ed for revie v on November 2, 2005; ap )roved on June 13, 2006¥¥･'ritten discussions on thls )aper should be submitted before lvla ' l , 2007 to the Japanese Geotechnical Societ y, 4-38-2, Sengoktl, Bunkyo-ku,Tok)'o I 12-001 1 , Japan. Upon request the closing date ma)' be extended one month**]613 FARIAS ET AL.614r:.. '//" '/ipl' !)hI(cr )ipnff'h 3r-¥¥¥3!,(TO O Y(],,,,hA¥¥¥ '¥.･ cr5'¥- nr r (. l + (Ti] ): :]･:¥<'=i'::!=7/ ¥'i 'j.:.:=aGene 'aliz,ed! SMSMP(T, (Tj (TFig. 1. Mobi ized planes due to stress state, natural cohesion and soilsuction(. +. )Cthe description and estimation of soil collapse; ¥vhereasgeneralization of SMP, modified stress tensor tjj andlvlatsuoka-Nakai failure criterion vere proposed in orderto encompass unsaturated states of soil.In this paper, the stress tensor a is regarded to as thenet stress ((1=c total u*1), ¥vhere (Tto *1 stands for totalIII ((T, )Fil:r. 2. Generaiized SMP in the tl]ree-dimensionai principal stressspacestress tensor and I is the second order unit tensor(Kronecker's delta). The term suction refers to matricsuction (s=u -u, ), ¥vhere ua and uw are pore air andpore ¥vater pressures, respecti¥'ely.and the generalized SMP turns into the original SMP. Onthe other hand, for hypothetically high values of suction,the soil tends to an isotropic stress state, and as a conse-quence, the generaliz,ed SMP tends to the octahedralGF.NF.RALIZF.D SPATIALLY MOBll,IZF.D PLANF,plane.From Figs. I and 2, it can be shown that theThe concept of Spatially lvlobilized Plane (SMP)generaiiz,ed SlvlP intercepts the axis I, 11 and 111, (¥vhichaddressed in this paper is a generaliz,ation of t.hatcorrespond to the principal stresses (71' (T2, and cT3,originall.v conceived by lvlatsuoka and Nakai (1974) forcohesionless saturated soils-see aiso ¥vorks of Matsuokar'espectively) at points proportional to the square root ofthe principai stresses shifted by cTa The direction cosinesof the normal to this plane can be ¥¥'ritten as:and Nakai (1977, 1982) and Nakai and Matsuoka (1983).This generalization is established upon the extensiondj=lproposed by Ohmaki (1979) and Matsuoka and SunI 2(199'_, 1995), ¥vhich accounted for the effect of naturalcohesion of soil. Lat,er, other authors, based on theinterpretation of soil suction as a sort of apparentcohesion, developed constitutive models for unsaturatedsoils using SMP concepts (Kato et al., 1995; Kato, 1997;Matsuoka et ai., 2002).The idea herein suggested only accounts for theapparent cohesion due to soil suction. It can be readilyfigured out through Fig. 1, ¥vhich illustrates three Mohrcircles and their respecti¥'e failure envelopes shifted by cro./ - (-')(i= 1, 2, 3)iwherei are the principal values of the tensor stress(=(1+(701), and I._ and 13 are, respectively, the secondand third invariants of 6. For' clarity, the three stressinvariants are expressed as follows:I 1 = tr ( ) = I! + 3(70I. = - [tr (- 2)2 - tr ( 2)1 = J._ + 211 (TO + (TI 3 = det ( ) = I_.. + I._cro + Il (T(3)+ (7This shift-term can be concei¥'ed as a Cauchy stress actin_ :isotropically on the soil structure. In a general form, (70can be expressed as follo¥vs:(TO = k*s ( I )¥vhere k* is a soil parameter and s is the soil suction. Thesuction effect vas assumed in accordance lvith Alonsoet al. (1990). This linear relationship is simple andadequate from a practical engineering standpoint. Otherauthors, namely, Sun et al. (2000), proposed a morein ¥vhich ll' I._, and I..･, are, respectively, the first, secondand third invariants of the ori_defined in the previous section.inal stress tensor a, asGENERALIZF,D MEC_HANICAL QUANTITY tijAn immediate outcome of above extension is also thegeneralization of the concept of tensor' t, a mechanicalquantity that reflects the induced anisotropy of granulareffect.materials under saturated states (Nakai and Mihara,1984). In a general form and under unsaturated condi-It is important to note that the infiuence of a truecohesion could be easily incorporated by adding the termtion, it can be ¥vritten as a function of the second-ordertensors (1 and a (Pinheiro, '_004):sophisticated non-linear equation for expressin*' such an(c'cot c) to the right-hand side of Eq. (1); ¥vhere c standsfor true cohesion, and c stands for internal frictionalangle of the soil under saturated condition.Particularly ¥vhen the soil is fully saturated (70 ¥'anishes,t = aa (4)where a is a tensor computed from direction cosines ofthe normal to the generalized SMP. This dimensionless 7 ..,ELASTOPLASTIC< IODEL FOR UNSATURATED SOILS615invariants depend on (7a, i,e. they are infiuenced by the!state of soil suction as ¥vell.Gener'alizedASMP31 + 71, (TO + Il (tabo + bl ao + b2(TtD .ts co + cl (TO + c2 crB(9)tN = I, + 211 aa + 3crt a+ b3(7+ c3 (T+ b4(r5' !/2c4 (r40( I O)¥vhere the coefficients bi and ci (i=0, 1,...,4) areex'pressed as follolvs:bo = Il I. 13 - 91cbl = 11 1h+ ,_1= 31 j I1･. - 1) 1_.1*911 13 - 61!b3 = '_1 "IFrg. 3. Generaiized SMP and modified stress invariantsb4 = 21) II I_. - 913- 61._c0=1cl = 41! I,symmetric tensor is obtained through reverse transformation from its eigenvalues a as sho¥vn belo¥v:a = QaQ Tc. = 41(5)c3 = I '_Ilc4 = 9vhere the components of tensor a are g)iven by:[o did' O o] oa=OOd *In Eq. (5), Q is the orthogonal transformation rnatrix,numerically determined from the eigen¥'ectors of stresstensor (1 using, for instance, Jacobi rotation procedure.The definition of modified stress tensor t is the same asthe original one used by Nakai and lviihara (1984); there-fore the same terminology is adopted here. The onlydifference for unsaturated conditions is the cohesiveeffect produced by suction (s), 1¥'hich is incorporated intothe tensor(=a+(701) with (To(=k,s) and this affectsonly the direction of the generalized SMP, via the valuesof dj in Eq. (2). Under saturated conditions, this effect¥'anishes and the generalized Spatially Mobilized Planeand therefore the modified stress tensor t coincide ¥viththe original concepts.The modified stress invariants tN., and ts, respectively,normal and shear stresses acting on the generalized SMP,as for tjj-clay model (Nakai and Matsuoka, 1986) are+ 61.It can be easily verified by simple inspection that forcohesionless soils under saturated condition, i.e. (r0=0,Eqs. (9) and (10) reduce to those used in tj -clay model.Finally, just to emphasize, a different concept ofgeneralized SMP is advocated in this ¥vork in contrast¥vith Kato (1997) and Matsuoka et al. ('_OO'_). Theseauthors conceived a new modified stress tensor based on atranslated stress tensor(= (1 :- (rol). Here, ho¥ve¥'er, thistranslated tensor is not directly used to define themodified stress tensor t, but is only applied to calculatethe direction cosines of SMP (al, a2, a3), i.e. the effect ofsuction acts indirectly at t by adjusting the SMP direction.STRAIN INCREMENTsStl'ain Increlnents on the Gene/'a!i< -ec! SMPThe strain increments c/8N., and des, nor'mal and shearstrains on the generalized SMP, respectively, are thestrain invar'iants in the modified str'ess space t. In *'eneralterms, they can be expressed as follo¥vs:d8N = c!8:a (1 1)defined as:t , = t:a (6)d&s = il deD Il (1 2)tD = t - t ,a (8)where de is the total strain incrernent tensor and deD is the¥vhere ll･[i = /T denotes the norm of a tensor and tDstands for the deviatoric stress tensor related to thegeneralized SMP. Together with modified stress invariants, those strain increments play an important role onmodified stress space t (Fig. 3).The modified stress invariants on the orig:inal SMP canthe stress-dilatancy relationship to be delineated in thets = lltD Il (7)also be redefined as functions of the conventional stressinvariants II' I._ and 13 (Nakai and Matsuoka, 1986); thesame can be stated for the generalization introduced here.Ho 'ever, in that case, those extended modified stressc!8D = ci8 - dea ( 1 3)deviatoric strain increment tensor referred to thesequence.Strain Increlnent 'rensorsBased on concepts of the classic theory of Plasticity,the total strain increment tensor is split into t¥vo 1 !ET AL.compouents, according to the additive decompositionl' ::: Ierule:!c/8 = c!e* + c!sP ( 1 4)! t) Ill !T*¥vhere c!8* denotes the elastic strain, ¥vhich can bel '"'*1:'!..: '/, (s)(a)obtained from the generalized Hooke's la¥v; ¥vhereas cl8denotes the plastic strain determined according to anassociated fio¥v rule referred to t-space.c/8* = (D*) - I :c/a ( 1 5)' ::: i + (::)deP = c!y af ' (c!y > O) ( 1 6)s{1 In sS fatIn the abo¥*e equations, dy is the plastic multiplier and,f' is the loading collapse yield surface, both to be definedin subsequent sections. The fourth-order elastic tensor isexpressed as follo¥vs:D *1 +=v (1--+ -lel- ( i 7)+ v)(1I- 2v)+*(b)Fig. 4. Relationsl]ip bctwee l specific volwre and naturai lognrit!Im of(a) nornrai stress to the generalized SMP and (b) suction¥¥'here:E (1 'v)(Lte)1: (18)l((s)in ¥vhich v is the Poisson's ratio, assumed as a constant, Eis the Young's modulus, e is the void ratio and l( is thecoefficient of compressibility for' the unloading-reloadin( -section of an isotropic consolidation test. Here thiscoefficient is supposed to be suction-dependent as supported by some aut.hors, to name but a fe¥v, BalmacedaVohn77etl'ic St/'ain IncrementsFor changes of stress state, the volumetric strain incre-ments are computed from the classical relationshipbet¥veen specific ¥'olume (1 +e) and natural logarithm ofmean stress, here substituted by the normal stress to thegeneralized SlvlP (Fig. 4(a)):de I '+e t/t'(s) dtN (24)(1991), Futai (1997) and Barrera ('_OO'_).In the original tij-clay model, the plastic strain incre-deP )'(s)-!c(s)dtN (25)ment tensor is further split into t¥vo components-one* I + e tNsatisfying the associared flo¥v rule and another related tothe increase in mean stress-as an attempt to express the¥vhere deinfluence of loadin_* path. For the sake of simplicity, suchstrain increments, respecti¥'ely^Similarly, from Fig, 4(b), the ¥'olumetric strain incre-a split ¥vas not considered herein.So far only strain increments associated to stresschange ¥ver'e obtained. To compute strain incrementsoriginated fr'om suction change, the follo¥ving equationsare su gested:c!c!= d * + c!Pstand for elastic and plastic volumetricments for chang:es of suction state are der'i¥'ed as:d = l(' cls (26)1 + e (s +p***,,)c/),< - ,(* c!s= 1" ( o + p.: , ) (27)' = l]*cls(plastic) (2 1 )c/and c!e= hPc!s¥vhere dc and dcr, denote elastic and plastic ¥'olumetricstrain increments, respecti¥*ely.¥vhere h* and hP are, respectively, the elastic and plasticsecond-order modulus tensors, ¥vhich vary vith suctionas defined belo¥v:h* = ---- 1J(* (22)3(1 + e)(s + p** ,)ISOTROPIC_ STRF,SS FRAMF,WORKThe mathematical structure of tii-unsat model underisotropic stress conditions is very akin to that of theonglnal Barcelona Basrc Model apart from three mainmodifications: (1) use of t , instead of p = (((Ti + (T2 + (73)/p ).* - /(*1 .h - 3(1 + e)(s+p=**m(23))So far coefficients i(* and ).* are, respectively, soil compressibility for elastic and virgin state of soil, both associ-ated to variations in suction; p* *'* is the atmospheric pres-sure ( = 100 kPa). A11 those coefficients of compressibility¥vill be geometrically outlined in the next section.3 -u*) as stress state variable; (2) use of a suctiondependent coefficient of compressibility for unloadin*'reloading conditions and (3) the collapse of soil due tosaturation compr'ises t¥vo cases that rely on how soilcompressibility at virgin state ().) varies vith suctionvariation. The first modification is a direct consequenceof tjj-frame¥vork assumed hitherto, whereas the second FLASTOPLASTIC ,IODEL FOR UNS TURATFD SOILSl'lll !617¥'ell-kno vn Loading C*ollapse (LC) yield f'unction isobtained independently of soll stiffness response ¥vithrespect to suction. Here, as In Alonso et al. (1990), thatequation defines a set of yleld ¥'alues (tNo) for each associ-(a)ated suction value and explains the apparent increase inpre-consolidation stress associated ¥vith suction increaseand the collapse phenoulenon obser¥*ed alongvettingpaths. The expression for LC" yield f'unction is given by:(tNR) =(!Nl) t¥,'c (30)t¥. 'o (;.(o} -{*)) !{;.(*) -(* ))in ¥vhich, tNo is the pre-consolidation stress for unsaturat-ed conditions; t c is the pre-consolidation stress forS;; osaturated conditions, and t¥.'R is a reference stress. Whatdistinguishes the derivation of CASE I from CASE 2 isl'/¥(t f{ Int! v L]basically t R. This parameter must be chosen so that thedifference bet¥veen N(O) and N(s), the reference specificvolumes at saturated and unsaturated states, respecti¥'ely,is the sarne for both cases. Details about ho¥¥' the aboveequation ¥vas derived ¥vill not be presented here since itl jr( )I !((ss¥Yellil g l(b)).(OTo delimit the elastic domain under isotropic1j.(s)condition, another concept inherlted from Alonso et al.s=0(1990) is that of a Suction Increase (SI) yield cur¥'e, whichsv(o) ::: Lfollo vs the same steps as demonstrated by Alonso et al.(1990) and Pinheiro (2004).Ois represented by the expression belolv:c o I I apses = so = constant (3 1 ):!''1'v(s)¥vhere sb may be interpreted as the maximum past suctionever experienced by the soil.stressIn this section, only a brief outline of tjj-unsat frameFrg. 5. Unsaturated soil responses: (a) CASE I and (b) CASE 2¥vork under isotropic stress-suction conditions ¥vaspresented. Emphasis ¥vas gi¥Jen to modifications performed to o¥'ercome some dra¥¥'backs inher'ited fromand third adjustments arise from experimentai observations (Balmaceda, 1991; Wheeler and Sivakumar, 1995;Futai, 1997; Barrera, 2000).BBM. In the follo¥ving section, attention is focused onsorne aspects related to three-dimensional conditions,lvhere the tjj-concept is connected ¥vith the traditionalThe t¥vo aforementioned cases of collapse response are:elastoplasticity theor'y.CASE 1, in which collapse al¥vays increases with netmean pressure (ori**inal BBM assumption), and C*ASE 2,in vhich soil collapse increases, reaches a maximumELASTOPLASTIC FRAMEWORKvalue, then decreases at hi_ :h net mean pressure (Fig. 5).The variation of compressibility ), with soil suction isgo¥'erned by the follo¥ving equation (Alonso et al., 1990):The main aspects to be described in this section reiateto standard concepts of elastoplasticity theory, such asyield and plastic potential functions, fio¥v rules, harden-;.(s) = ),(O)[(1 - r,) exp ( -fis) + /'il (28)where ;.(O) is the compressibility ), for saturated state; fiand rare fittin*' coefficients. The response of ), dependshighly on /';_; for r;. < 1, ). decreases with suction increase;whereas for /';> l, ), increases ¥vith suction increase.It is su*'gested a similar la¥v for commanding the varia-ing la¥vs, and stress-dilatancy relationship,Hinokio (200'_, 2004) is proposed. The relation is a nonlinear curve defined on the modified space, as follo vs:M*. - X"Y=tion of l( ¥vith suction chan*"e:l((s) = ,((O)[(1 - r ) exp ( -fis)/'*1 (29)¥'ith tjj-con-cepts extended to consider unsaturated states of soil.Initially, a generalization for unsaturated conditions ofthe stress-dilatancy relationship presented in Nakai andvhere X= ts l(tN + t s) and Y= c!e PI (32)/d8are, respecti¥'ely,¥vhere /((O) is the compressibility ,( for saturated state; /'*the stress ratio and plastic strain increment ratio; t¥.'s isis another fitting coefficient; and fi, for simplicity, isassumed to be the same as in Eq. (28).exactly the same as the stress variable due to suctionAn important characteristic of' those previousof the stress-dilatancy curve; and M> = corresponds to theadjustments is simplicity, since a unique equation for theeffect, i.e. (70; (x is a fitting exponent related to the shapeordinatevhere the plastic strain increment ratio is zero 1 1FARIAS ET AL618J 25(a)Data:lvlacari et al!( 2003)/Y T !,,I .OO!,j-unsato c1easuredo. 75o.50e eQE!:t]'3c!c (:' c:c!e(.>:: - *c･Q oFig. 6. Stress-diiatanc) relationship for tjfunsat model-3_o -2 5 -2_o - I .5(Fig. 6). This last parameter is determined under theData:partlcular situationlvlacari et al_ (2003 )vhere critical state is reached. In suchp + p,M*=X** l+ (33)X**The advantage of representing the stress-dilatancyeooegs> ;'..>' e e"5c'='s. .g75- .r.8B O.)Op8:.._ o{ ･･a.c o '-5g..;: oca!e-3.0 -2.5 -2 O - Ie..,obtained:( Y., il.)c!';:s co Q B A measured% *05I 25B B lvlthose critical ¥'alues of X and Y into Eq. (3'-) andrearranging the resulting expression, M* js eventuallyoo-o. 5( b)a case, X=X** and Y= Y**, and both variables may be¥vritten as functions of the friction angle at saturatedconditions (c.f. Nakai and Matsuoka, 1986). Substitutin*'-1.0- I _O-o 5c!e !'d e!'o.oo. 5relationship using modified stress-strain ¥'ariables is thatsoil response is uniquely captured regardless of therelati¥'e magnitude of the intermediate principal stressFig. 7. Stress-dilatanc) response under unsaturated conditions (a)tji-unsat mode and (b) BBMunder saturated states (Matsuoka and Nakai, 1974;Nakai and Matsuoka, 1983). It is interesting to note that,despite some considerable scattering, similar trend is alsoroughly observed for unsaturated states, as illustrates acompilation of TC (triaxial compression) and CTC(conventlonal TC) data gathered from tests performed byyield!r¥..lyieldplane SMacari et al. (2003) on unsaturated silty sand at differentmatric suction le¥'els (Fig. 7(a)). When the same data forstress ratio-dilatancy are plotted adopting the stress andstrain variables used in BBM (q/(p+p,) vs. d8. /d), acloud of points ¥vithout any tendency is obtainedS(Fig. 7(b)).Similarly to Alonso et al. (1990), t¥vo yield surfaces areFig. 8.Yield surfaces LC and SI at modified stress space tjjdefined. For convenience, the same acronyms are hereinemployed: LC, corresponding to load collapse yieldsurface and SI, corresponding to suction increase yieldplane (Fi**. 8). Ho¥vever, unlike BBM frame¥vork, thosestress states, i.e. ts=0, gives the expression for the LCyield surface function:yield surfaces, ¥vhich set the boundaries of elastic domainft(tN.,, ts, tNc,s) ts+t:.sIn t¥.'oTtNs(tN ,tstNs O) ** T ,=+of soil under unsaturated states, are represented in themodified stress space (t¥,', ts, s). For stress, or strain, or(35)suction paths that cross either LC or SI (at s=so) yieldsurfaces, permanent (plastic) strains are assumed tonormality condition (de P:dt = O), an ordinary differentialwhere tN.,c is the stress-type hardening parameter used todetermine the size of yield surface. The other terms ¥vereall previously introduced.The second y. ield surface is an extension of SI yieldequation can be deduced:curve (Eq. (31)) into the region ts>0 (non-isotropicoccur.From stress-dilatancy relationship (Eq. (3'-)) and(t¥= i-*)tN + tN. ,s (34)dt¥. ' t¥.-'M+*"'stsThe solution of that diff rentlal equatlon for theboundary condition expressed by t¥.'=t¥.'o at isotropicdomain) by means of a plane (or lvall) simply defined as,f*(s, so) s-s0=0, ¥vhich is the same expressionproposed by Alonso et al. (1990). The suction so ¥vaspreviously defined as the maximum past suction everexperienced by the soil. ELASTOPLASTIC MODEL FOR UNSATURATED SOILSThe plastic strain incrernents related to LC yield surface, at constant suction planes s, are calculated according to an associated flo¥v rule referred to lhe modified61().h¥'drostatic(yax i s1¥¥stress space:ag dy af' (36)/c!8 P = d y =at at,1:CrJ * *(-vhere dy is the plastic multiplier to be explicitly defined inthe Appendix and g is the plastic potential function,vhich coincides ¥vith the LC yield surface function J'*Generalized M-N(Eq. (35)).Regarding SI yield piane, the vector of plastic strainMohr-Coulombincrements induced by suction increase is defined as(d+P, O), in lvhich c/Extended D-Pstands for plastic strain incrementstriggered ¥vhen suction reaches ievels higher than athreshold, so (see Eq. (27)). Since this paper focusses onlyFig. 9.Failure criteria al conventional principal stress spaceon paths that touch L,C yield surface, the SI yield planevill never be directly activated but it ¥vill be affected indi-Data:rectly throu_2:h a coupled hardening la v as describedbelow.For each yield surface, L.C and Sl, a coupled strain-TC ! Macari and Hoyos (2001 )SS '¥.¥ ¥ '/j / "'v 50 kPatype hardening la¥v ¥vas conceived in order to relate theincrease (or decrease) of elastic domain to volumetricplastic deformation, de.P. Thus, t vo hardenin*' Ia¥vs,¥vhich command such interconnection, are considered inoco (:lOOkPaTE¥ _¥ A¥AA/ AQ (T("!Q Q (T : 200kPa' 'fthe follo ving:// ... li,; ;/!Ac!tNcI +d8 e p (3,7)tNC )' (O) - l( (s')dso i eso )' *::::1:; ./'/ .4r-;:':¥'1/SS ' -'i ''/i¥" '¥+- 100kPa!tlii¥. ¥ ¥ -h----I¥/TC' :,,:_･1: "t:::lj ･¥¥ic*Finally the failure criterion here employed is presentedSS ' ' '-- Generaiized M-NTEIto close this section. An expression similar to the oneoriginally proposed by Ohmaki (1979) and later used inthe context of unsaturated soils by Kato (1997) andMatsuoka et al. (200'_) is used here to generalizeExtended D-PFig. 10. Octahedral plane: Generalized iM-N and Exteutied D*PfailuFe criteriaMatsuoka-Nakai failure criterion. Based on the concepts;thus far introduced in order' to tackle unsaturated states,such extension is presented simply as:frictional anglevas regarded as bein*' suction-indepen-dent, a hypothesis perhaps valid only within a limitedtN. , + tNS= constantrange of stress-suction.here advocated, especially with respect to that describedThe proposed **eneralized failure criterion circumscribes Mohr-C*oulomb (M-C) failure criterion and iscircumscribed by the Extended Drucker-Prager (D-P)in Kato (1997), who proposed an extension ¥vhich alsofailure criterion in the conventional principal stress spaceleads to Eq. (39). Particularly, Kato (1997) conceived anew modified stress tensor based on a translated stress(( 1,(T2, (T3), as sketched in Fig. 9. The GeneralizedMatsuoka-Nakai (M-N) criterion coincides with M-C intensor ( = (1 + ael). In the opinion of the authors of thepresent paper, this leads to double countin_ : the suctioneffect in the denominator of Eq. (39). Here, on the otheraxisyrnmetric stress conditions (triaxial compression andtriaxial extension) and wit.h Extended D-P only in triaxialhand, this translated tensor is only applied to computecriteria, Generalized M-N has the advantage of generat-the direction cosines of SMP (al' a2, a3), i.e. the effect ofing a completely smooth surface; hence, it is moresuction acts indirectly in tN., and ts, therefore, avoidingappropriate from a computational standpoint.such inconvenience.The constant term on the right-hand side of Eq. (39) isa function, vhich dependents solely on the internalfrictional angle of soil under saturated conditions, asFigure 10 illustrates both Generalized M-N (solid lines)and Extended D-P (dashed lines) failure criteria togetherwit.h failure points obtained from experimental results ofassumed by Nakai and Matsuoka (1986). The internalseries of true triaxial tests on unsaturated samples of' siltyIt is ¥vorth to reemphasize the originality of the conceptcompression conditions. Cornpared to both failureMacari and Hoyos (2001). These authors performed a liFARIAS ET AL_620tota] due to due to( ) af'.D':af afiHtr a-f,strain stress suction: daddia(; ' atat ' at ic* I =; ds : 1+1dH Is the plastic module defined by:i¥'e decompos ition 'l+eof :>*train tensor 'H= - tNc______ ______ _____i_____r_ j() ((!" _'= E c!s" + ds!' : _b) Stress-like hardening parameter dt¥,'c:dtNc Hdy( tr af (43)i' , - d" _'at_l r-c!8 =d;'c*;j" :Gel eralized : __c'+t jl-iooke*s laColyd(rsistency cond itio 1 :d/" =0 ::> dl; D" :(c!e';+**c) Fourth-order elastoplastic rigidity tensor D*P (stress):Dep = D - (44)1' ( _,(D af! (afl .D'at1I I¥a(1'd) Second-order elastoplastic tensor h*P (suction):Hardening law:h'P D'P (h hP)-l Iaftaf D': (45)> dl ,,*c!a(4' )).(O) - l((s)X) icr*{'d8' }: ; (r*- -i* ds(4 1 )a[) as ats Dr!' :cr- - h'rdsSome of the partial derivatives in the above expresFrg 11. Numerical integraiion scheme of tjunsat constitutiverelationship for stress paths that only reach LC yield surfacesand under different stress paths (triaxial compression-TC, simple shear-SS and triaxial extension-TE)and diverse suction and octahedral net stress levels. InFi_"*.. 10, the inner, intermediate and outer curves correspond to suctions of 50, 100 and 200 kPa, respecti¥"ely.A more detailed description of these results is presentedat the end of the validation section.Another peculiarity of the generalization pr'oposedhere is that Generaiized lvl-N reduces to the orig:inalsions, as ¥vell as a more detailed explanation on ho¥v the4th order tensor D*P and the 2nd order elastoplastic tensorhep ¥vere obtained, are sho¥vn in the appendices in the endof this paper.MODEL VERSUS F.XPF.RIMF.N TTALRESULTS-VALIDATIONModel validation is a crucial step in order to check¥vhether a model properly describes the material behavioror not. In this paper, ¥'alidation is accomplished byreproducing stress-strain and suction-strain results of¥'on lvlises failure criterion as suction hypothetically tendsexperimental tests carried out on unsaturated samples ofdifferent types of soils. All the experimental data ¥veregathered from specialized geotechnical literature. Overall, tjj-unsat model requires 12 constituti¥'e parameters,to infinite values (t? snamely: t¥.=R, /c(O), ),(O), r , /';_, fi, ic*, ;,*, v, c, k*, and c .i¥,Iatsuoka-Nakai failure criterion as suction reaches nilvalue (tNS = O), i.e. ¥vhen the soil saturates; and reduces toco).Ho¥vever, the number of parameters to be used dependson the sort of pr'oblem, i.e. stress-suction state, yieldNUMERICAL INTEGRATION SCHF.MF,surface in¥'olved, etc. Besides that, initial stress-suctionrequires the de¥'elopment of algor'ithms in order tonumerically integrate their constitutive relationship.state (cr s) I and initial positions of LC and SI .¥'ield, '",'**surfaces must be specified.The first set of laboratorial test to be analyz,ed ¥ "asThese al,_,_crorithms or schemes ar'e iterative processes in¥vhich the stress, strain and suction states and the hardening parameter are updated for given stress, strain, and/orperformed by Barrera (200'_) on unsaturated samples oflow plasticity ciay in the Polytechnic Uni¥'ersity ofCatalonia (UPC), Barcelona, Spain. The a¥'erage contentsuction increments at each point corresponding to anof sand, silt, and clay are 39.4, 44.5, and 16.10/0, respec-experimental test. The diagram in Fig. I I briefly describesthe numerical integration scheme of tjj-unsat constitutivetively. Some other' engineering properties of that soilrelationship. Particularly, this scheme only refers to160/0 and G==2.71. A 38 x 76 mm conventional triaxialcell with controlled suction was used. The stress pathsIn general terms, the validation of constitutive modelsstress-suction paths that reach LC yield surface.Some of the mathematical expressions used in thatd), - -=( ) 8crvhere:a(Tfollo¥ved two phases-isotropic and shearing-bothunder constant matric suction of 800 kPa, as illustratedscheme are computed as follo¥vs:a) Plastic multipller dy:_1 !aft7 : D"c!. _-[afl :De:(h' + hp) -(CL,, according to USCS) are TvL= 3'_o/o, }t*p= 160/0, Ip=in Fi9:. 1'_.lJds} (40)Normally consolidated and induced overconsolidatedsoil samples ¥vere employed. Comparison bet¥veen simulation and experimental responses for the normally consolidated clay are presented in Fig. 13, ¥vhereas responsesfor the induced overconsolidated clay are presented in･, ELASTOPLASTiC hIODEL FOR UNSATURA'rED SOILS6213000q (kPa)qc)(1 :::; O.6252250'1c_ oo: "j ai lure!!! unSat750knl e as u redi ' -.' "+･. B'!o.,: *: 'B....;;-o.06* "800 kPaos pL' l0.06Fig. 12. Stress paths scheme driven along controiled suction triaxialiest performed by Barrera (2002)odata: Bar 'era (2002)t0.12L'{!3000cj (kPa)*hl,15 o._lJ-.0.24o 0.05c'o = O.629O i5o. 1o.0.25'( ,l 500tlf unSat750-- 11leaSUredFig. 14. Comparisons betlveen motiel a:nd expeFimental responses foroverconsotidatetl soil specimenoorable l.data: Barrera (2002)Parameters0,040.08¥_ icdel parameteFs foF different sets of experimental dat:gFutai (1997)Pereira (1996)t R (kPa)O/f (O)0.005O.0783000O.0072O.232O.0037O.005O 085Oi;_(O)oBarrera (2002)004/f6000;.so.1o.24O O OO I O l) O ' O ')lO.7r;O.833P (kPa i)20O OlO.007529'15'vO.3Sal 75O. 32.0O 5)t('r71f <,kFig. 13. Comparisons between model antl experimental responses forO.426SO O 25norma:ll) consolidatcd soil specimenexpression that basically modifies the hardeningFig. i4. The constitutive parameters used to simulatethose tests are sho¥vn in Table l. The pre-consolidationstress under saturated condition is 70 kPa. Figures 15 and16 illustrate the evolution of LC yield surface in bothdeviatoric (tN x ts) and isotropic (t xs) planes, at threestages of stress path: initial, final and at an intermediatestage. The dashed line represents the critical state line in aplane ¥vlth constant suction of 800 kPa.The stress-strain response was lvell described underboth situations. The proposed rnodel, however, ¥vasunable to represent the final dilatant soil behavior.parameter used here, i.e. Xds , , in which X depends on thestress ratio and the plastic volumetric strain and plasticshear strain increment ratio. According to the ¥'alue of X(either negative, positive, or null), de can be obtained.Nevertheless, it is important to note that an additionaiparameter is required. For further details, see alsoMatsuoka et al. (2002).The second set of experimental tests to be in¥'estigated¥vas carried out by Futai (1997). Those tests comprise of aseries of suction controlled oedometric tests performed innatural specimens of a residual soil from the State ofMor'e insight can be gained by plotting the evolution ofstress-dilatancy relationship as seen in Fig. 17. Someare lO, 16, and 740/0, r'espectively. Some other en_ :ineer-non-fitting data corresponding to the onset of soil dilativeing properties of that soil (CL, according to USCS) areresponse can be clearly identified. An alternative forovercoming this dra¥vback could be, for instance, to usethe hardening parameter proposed by Yao et al. (1999).2.74. According to Futai (1 997), a predetermined value ofsuction ¥vas initially imposed to the soil specimens andBased on experimental result.s of tr'iaxial tests on sandthen a vertical load ¥vas applied. After reaching theand clay, these authors formulated a phenomenologicaldesired level of vertical stress, the specimens ¥vere floodedMato Grosso, Brazil. The contents of sand, silt, and clayT4'= 500/0, wp= 260/0, Ip= 240/0, and G* betlveen '_.67 and FARIAS ET AL.69 2/1 500(kPa)!.data: Barrera (2002) I .OO!I 200!,j-unsat 0.7)-c900n a i600300c o Q e normal]v cons.A A A A overconsol.behaviorInrtial b ¥! ' (kPa)Ad s(-'o{-0.50- I .OOfi alinitia[Fig. 17. Stress-dilatancy relationst]ip for experimenta] resu]ts ofBarrera (2002)o.500200o (a)),. ( s )/+ (kPa)0.300Fig. 15. Evolution of LC yield surface at planes tN x ts and tN x s fornormall)' eonsoliclated soil specimeno.200o.008i 2000.0069000.005K(s)oooO )O i OO 1 50 200 2 Ocs (kPa):'. '¥¥Inl alo0,007/, (kPa)600o0.400-500 500 1500 2500 3500 4500 5500b'final/ ' (kPa)a bOO 500 1500 2500 3500 4500 5500250s (kPa)s (kPa)(b)200oo o o 11leasl,iFed15080d e i'- I .50 0.00 0.50s (kPa)400-A' '.._5Ae60300(/ e¥-500 500 I)OO ' OO )OO 4)OO ))OOi 500dilati¥'e0.50a80/[u UllSat1 oo60LCo50data: Futai (1 997)400initialofinal200/Y (kPa)-500 500 1500 2500 3500 4500 5500o50 1 OO 200150CT, (kPa)Fig. 18. Resuhs of model parameters calibration: (a) Variation of soi]compressibilrty lvitl] suction and (b) I.C )'ield curve at plane (1, xsFig. 16. Evolution of LC yield surface at planes t x ts and t¥, x,s foroverconsolidsted soi specirnenseem to be so significant.and then vertically reloaded. Two of those experimentaltests are simulated in the sequence. Figure 18 revealsFigures 19 and 20, on the other hand, illustrate asome results of model calibration: variation of soilcomparison bet¥ 'een model pr'ediction (solid line) andvolumetric soil response (dashed line) for the oedometriccompressibility ), and l( Ivith suction, and LC yield curveat plane (7. xs. Note that the compressibility ), increasesas suction increases; therefore, this soil is classified astests performed by Futai (1997). V,retting is indicated byan arrow in each figure. Observe that soil specimens didnot collapse under all vetting paths, as indicates f-** inCASE 2, under the proposed classification. Also, notethat the soil compressibility at unloading/reloading isFig. '-O(b), where only a negllgible deformation ¥vassuction-dependent, although such dependence does notthree-dimensionai stress-suc.tion space (p, q, s) arere*'istered. The stress-suction paths follolved along the ELASTOPLA TIC ivIODEL FOR UNSATURATED SOILS623O. 1 50lp. (J. s)),(s)D(1400 14) O)CJ (kPa)(a)oO. i 20ooo0,090(a) '+-; ---:. . -:.¥,. " ... ,'._ -,-- - p (kPa*B (325, 40. 120)'if_ ' C (320,35.0): '"'*"'1" (0.0600.010K(S)!A (1, O_ {20),' ';)_/E (1, 1, O)0.008oooo , 006s (kPa)o.004---- measured !/! unsatoFutai ( 1997)0.2400300c*(b)o o o 11leasuredotrj ullsato.4d (b)e400S (kPa)ett]n_..cr ¥ ,bo.3300s (kPa)data:clO. I200l OOoLC2000.5olOl1 OOO I OOOO1 OOl OOdata:(T, (kPa)Perelra ( 1 996)oFig, 19. Oedometric test O1: (a) Stress-suction path and (b) Model andexperimental response at plane (T, x 8,o2001 oo300!+ (kPa)Figo. 21. Results of model parameters calibration: (a) Variation of soil(P' c/' s)compressibility lvith suction and (b) LC yield curve at plane t. x e." 'I cl (kPa)F (1410, i50. 50) ', G (1425. 130. o)plotted in Figs. 19(a) and 20(a). A11 constituti¥'eparameter's employed to simulate the tests are reported inTable 1. Except for the initial part of' both curves (insidei(a)'_ _ --' -' -¥ :" -¥.p (kPa)__,_ .--¥'D (165. 20. Ioo) _.:;'i>iB (10. 5.200)-'(165. 20. 50)j'ii ' ='i_- I __ _" H(1.1.0)((..="- :',." "/ c (lo. l. Ioo)A ( I . o. 200)Figs. 19(b) and 20(b) supports that statement smces (kPa)meastu'edrnodel prediction and soil response are almost parallel.ti!ull S atodata :vd Futai ( 1 997)/e " .O. Io.0._o.3silty sand (SM-ML, according to USCS) de 'ived from a(b)o. 511 O I OO I OOOl OOOO(y, (kPa)Fig. 20. Oedometrie test O'*: (a) Stress-suction patl] and (b) Model andexperimental response at plane (T, x 8*consolidat.ion pressures are corr'ect.Model efficiency is further explored by isotropic tests atusing a triaxial cell. The soil corresponds to a residual' f--a_0.4However, these values of k difi r from those obtainedunder loading condition, but still inside the elasticregrme. Here it ¥vas assumed that the reported pre-constant net mean stress performed by Pereira (1996)¥¥'ettingI1the elastic domain), the soil behavior ¥vas fairly ¥velldescribed, especially the amount of collapse produced.The initial discrepancy is because the values of compressibility used in the simulations are those obtalned underunloading conditions. A glance at the unloading part ofgneiss of the State of Cear , Brazil. The contents of sand,silt, and clay are 4i.3, 43.2, and 15.50/0, respectively.Other engineering properties of this residual silty sand arevL=470/0, wp=300/0, Ip= 170/0, and G*='_.77. This sortof soil is often employed as a basic material for construction of dams in the northeast of Brazil. Generally, due toinappropriate compaction, that soil acquires a metastable structure, causing se¥'eral dams to fail during first 11FARI6,24o.80S ET AL.r,,, r ( kPa)¥vertinp = I O kPao.7524O(T,,.r = 50 kPa!!! Ul Sat- - BBM1'rr.YT r50 kPa l+-' '-. O.701 8O6' =a A3lleasVl'ed' e o o o.o 0.65>1 2Os :: I OOkPa' '-'e:1 OO kPa0.60oi c-er-e' ' e ' '200 kPacPa " ooe8 e /. -e//1.b- o o o6 Os = 50 kPao.55IOJl OOOl oos"(kPa)o240rig. 22. Collapse tcsts ilnder constant net mean s ress: Ex.'perimentaland sirnulation responses at plane s lction vs. void ratio(T,,,, = I OO kPas ;:: 200 kPasi 80;l 20lA : s: 100kPaI-1) d rostat i c**+axiSAAAs;:;50kPa6Oconst C:':orr' :::100 kPa((Ti '111/; ) : B rLcf ! = 100 kPaO240g! i ll :1'E :]D a5/'I::! *Al 80(T!t ::)O kPaO(cr; - t/II ) SS((7 Y11Y l!1' ) T E'6. ::: C' o- ThE!'2- e r B? _ e':Pb :BTCi 20':ss =200kPa' s ;;: I PO kPaQs L;-{e/ - L-f'..: vl. ' 'iiQ::- - ' - '; =O kPa6 O( f,,., = 200kParig. 23. Multi･stage drained true triaxial test under consiontcontrol!ed suction (aftcr Macari and Hoyos, 2001)o-o.l O -O OOO OO.05 oJ ()strainreservoir fillin _. Fig:ure '_1 sholvs some results of modelcalibration: variation of soil compressibility ;. and l( ¥vithFig. 24. True triax.'iai sheaF response from tirained TC tests for s = 50,100 and 200 kPa at cr**t =50, 100 anti 200 kPa, respectivel)suction, and LC ¥_'ield curve at plane tN xs. Similar toFutai's set of experimental data, this soil is also classifiedas CASE 2, since according to the proposed classifica-¥vas achieved. The final ¥'olumetric straintion, the compressibility ), increases as suction increases.¥vith absolute errors infer'ior to 20/0.Note again that the soil compressibility at unloading/reloading is suction-dependent, but conversely lc increases as suction increases.Pereira's isotropic tests consist of four Inundationtests, ¥vhere soil samples, initially submitted to a suctionof 370 kPa, ¥vere fully saturated (¥vith ¥vater) underdifferent levels of constant net mean stress, namely: '-O,50, 100 and ,_OO kPa. Those experimental results (dashedline) together ¥vith model simulation (solid line) aredepicted in Fig. '-'-. Only the ¥vetting process is describedvas pr'edictedTo close this section, a comparison betlveen theproposed model, BBM and experimental results of testsperformed by l¥,Iacari and Hoyos (2001) are presented.These authors published a series of drained true triaxialtests conducted on several identically prepared cubicalspecimens of recompacted silty sand to study the stressstrain-streng:th behavior of an unsaturated soil under'multi-axial stress states and suction-controlled condi-tions^ The soil vas retrieved from the PiedmontPro¥*ince, USA, a region predominantly composed byin a graph of ¥'oid ratio versus suction. All parametersemployed to simulate tii-unsat model are also summariz,edin Table 1. Those tests lvere performed under isotropicstress condition; therefore, fe¥ver parameters are neces-residual soils. The avera e contents of sand, silt, and clayare 58.4, 36.8, and 4.80/0, respectlvely.sary to run the model ¥vhen compared to the previouslished suction ¥vas kept constant throughout the testtests presented here that correspond to axisymmetric andthree-dimensional stress conditions. Once more, good(Fi_(,,_. 23). First the specimen ¥vas loaded under hydrostatic conditions to stress state point A ((T.*1= 50 kPa), thenagreement ¥vith soil mechanical behavior under fioodin_'*.monotonic shearing corresponding to either TC (TriaxialAccording to ilvlacari and Hoyos ( -OO1), each specimenfollo ved a multi-stage testing scheme ¥vhere a pre-estab-; ELASTOPLASTIC N,10DEL FOR UNSATURATED SOILS625r,,.! ( kPa)240(y,,,, = 50kPao A l measured} '1100 kP:8¥O'60o a ,s = 50kPaa1) 1**S ::: 50 kPaoo240240:= I oo kPae]l 8012060s = 50kPaO- s:cs aga :]A A A' 'l -A' a- tL_ .Al*'AAAA I OO kPa-A;:;;' - ' 'i +b.A' s := 50 kPagi - ' :a_ ?:r T' .. :,h'" r7" -'tQ'ra)s81' " s ::: 200 kPar.....s :::: 200 kPaa;' I ab kPa__9120:a o o '-'D.' a ;/o a's = 100kPa..._5 ' 5E: s' s ::' d ' s = 50 kPa* i;+60Sj': : e3l 80E r":ba:50kPa160n(T =1)OOkPa(y*,,, = 200kPao-o.-.240' g' 'l 20: : c.o240l 80eA A A A A .." t '. ' ' ". .'.'A*'CA A A A A '60a . gO,ee_oa . 4"T._,/C.CFs :: 200 kPa/ lrA IAook_P-ar_ ,i_ _ -i20;t&L'3(Tf"i ::: I OO kPal 80tl - ' s' 200kPadr il :'If1 :rk.,,_-L'}iiip' Q a;:; I OOkPa'__ .(T(,,,,- $1 :o Q G Q a 'e'.tjb e-o-Jo__a_ a a_ oo aQ60･--BBMo A Ea measuredS ::: 200 kPla'l: _1 P.q r . _!u -unsati 80t glt･ :'.sLJ(=)OkPa/i! unSat--- BBMi 80l 20r.,.! ( kPa)140ol O -O. 05O.OOO.05 O. I O-o.lO -O.05str'ainFig. 25. True triaxial shear response from drained SS tests for s= 50,100 and '*OO kPa at a<**t=50, 100 and 200 kPa, respectiveh.Compression), SS (Simple Shear), or TE (Triaxialic shearing was imposed to the specimen. The processwas repeated f'or the hydrostatic stress state at pointO. lOFig. 26. TrDe triaxial shear response from drained 'I=E tests for s= 50,100 and 200 kPa at a**1=50, 100 and '*OO kPa, respectivel)Table 2.Extension) stress paths ¥vas imposed, until the octahedr'alshear stress ( .**) reached an apparent peak value. At thispoint, the stresses are unloaded back to point A, and ane¥v hydrostatic stress path ¥vas followed until point B(cr..* = 100 kPa). Then, the same TC, SS, or TE monoton-o.05O OOstrainParameters for Macari and Ho .'os (2001) testsParame ersl¥*Iodel!, -unsattN = 36 kPa; K(O) = O.OI 1; ;_(O) = O.220;!' = i .O; f; = O.21 ; p= O.01789 kPa1;BBMp*= 36 kPa; /( = 0.01 1 ; ;_(O) = O.220;L Jc=27'; v=0.30; k*= l.3'_4; Oe=-'.Of= O.21 ; fi= 0.01789 kPac=27';l;*=0.30; k*= 1.324C (cr.** = 200 kPa).A series of 27 drained constant-suction tests ¥vereconducted, 9 for each stress path, i.e. TC. SS, and TE.Equally satisfactory responses vere achieved by bothThe experimental results (symbols) are shown inmodels along TC stress paths, in particular for (T ** equalFigs. 24-26, together' with simulations of tjj-unsat (solidto 100 and 200 kPa. Ho vever, for SS and TE stresspaths, ¥'ery different responses ¥vere obtained. Theline) and BBM (dashed line).Table 2 presents all parameters used in the simulationsfor both models. The parameters for BBM were allobtained from Macari et al. (2003). The parameters fortjj-unsat model are basically the same as those used inBBM, except for the additional parameter a ¥vhich wasobtained by best fit, and r , which is equal to 1.0 (novariation of the compressibility l( vith suction).*.proposed tjj-unsat model achieved much better agreementwith the experimental results than BBM. The main reasonis attributed to the failur'e criterion. BBM uses theperfect conical-shaped Extended Drticker-Prager failurecriterion, ¥vhereas tij-unsat employs the proposed gener-alization of Matsuoka-Nakai failure criterion, whichestablishes distinct values of shear strength depending on 攣626FARI、へS ET AL．the stress path on octahedral plane（5θθFig．10）． nlodel for ullsat麟raξed so目based on exIended SN’IP，Unsaturated Soils、P1・oc．ノ、∫’1n1．Co14。U1∼∫θ’1〃“θ18ゴ50’Zy（UNS、へ丁95），Paris， France（eds．byAionzo，EEandDelage，P、），Rotterdam，Baike−CONCI、US正ONS ma，2，739−744．9）Maatouk，A．，Leroue11，SandLaRochelle，P，（1995）：Yleldingand The maln負ndings of this work can be summarized as cr1“cal s［ate of a collaps猛ble u11sa“1ra｛ed silty soil，（7ゴo’θぐノ1’∼’（1∼♂（∼，foIIOWS： （1） Founded on simple adjllstments to BBM frame．work for isotropic stress cond圭tions and the generaliza− 45（3），465−477．10）Macari，E．J．a厳d｝｛oyos，L。R。（2001）＝Mecha臓icalbellaviourofa自 mSa田rated SOil Under mUlli−aXial StreSS SてateS，0θ0’θごh．刀θ5’，／、， ASTNi，24（1），玉4−22．tion for unsaturated cond圭tio勤s of concepts such as11）Macarl，E，J．，Hoyos，L．R、and Ard虚no，P．（2003）＝Co自s譲u［1vespat圭ally mob三lized p玉εしne，secon〔i−order modi負ed stress modelingofしmsaturaしedsoilbehavioru員deraxlsymmetr1cstresstensor∼ijandMatsuoka−Nakaifaihlrecriterlon，anew statesuslngas覧ress／suc【1onco臨o目edcぴbical〔es［ce琵，1ノ払・1．Plo∫一elastoplastic crit量cal state base（i model∼vas deve圭oped for（iescribing the mechanical behavior of soils． （2） The modi負cations to BBM framework forisotropic stress conditions、vere essentia1至y the use of amodi行ed mean stress IN instead ofρas stress vari＆blel theassumption of two cases of co至1＆pse response，wh量ch wasaccomplisLed by simpiy changlng botむ6tting parame輩ers1・ノand INR to apProprlate vahles，according to experimen−tal res慧lts；an（蓬the use of a suction−dependent coe伍cient ”c妙，19，玉一35、12） N−aIsuoka， H． a職d Nakai， τ． （1974）： S［ress−deforma【ion and streng由cllaracter1sticsofsoilunde口hree（ii圧erentprl職cゆal Stresses，P1噌oc．ノSC万，（232），59−70．13）Matsuoka，H．andNakai，τ．（1977）IStress・strainreiations厩psof soil based on tlle S難IP，Pヂo（〕．Sρθc’α1ひ・Se∫∫’0119，91171CSA4歪E， 王53−162．玉4）Matsuoka，H．andNakai，T，（1982）：Anewfa員urecriζer1onofso1ls lnthree−d1mensionalstress，Co1∼ゾ0⑳ηηα”oηα1∼ゴFα〃疋’1門θq〆 G’・α1π11αrル10’θがσZ∫，至UτA5｛，Delft，USA．蚕，253−263、15）Matsuoka，H，and Sm，D，A、（1992）l Ge陰era厩a振on of aof compress茎bility for unload圭ng−reloading cond玉tions， COnSti案面Ve laW frOm fr1CtiOnal ma【erialS tO COlleS1Ve ma【er1alSラ （3）Thegeneτalizatlon ofSMP forunsaturated 刈ゴv，λ4’〔ソ・01ηεぐ1r．Grα1π〃α1・con〔iitions was performed ia由e same way as previouslyma（ie by other authors；ho、vever，a different inteτpretεトtion of modlaed stress tensor 、vas herelu introduced，八／θ1eヂ1αな．Elsevier Sdence Publica一 ｛玉on，231−240．16） ｝〉latsuoka， H． and S麟n， D． A． （1995）： Ex［ension of spatiaIly mobilizedplane（SMP）tofrictionaiandcohesivemaτerialsand app1呈cation to ceme翁ted sands， So’Z∫ ‘7ηθF Fo∼イπ‘ノ‘7r’oη5， 35 （4），since the suαion effect was only accounted when calcl11aト 63−72．illg the diτection cosines of SMP、17）Matsuoka．H．，S駐n，D．A．，Kogane，A．，Nobしih1ko，E and （4） Tbe experimental results from true three−dimen−slonalラoedometric and lsotroplc tests gathered fromspeclalized geotecむnlca1至髭erature gave supPorε to tむetheoret玉cal framework、 T｝1e satisfactory agreementbe宅ween model and tests results員ighlights t｝1e app1量cab宝1一玉ty of the proposed formulat圭oR to real boundary va王uegeotechnlcal problems。 Ichihara，∼y、（2002）＝Stress−sξrai【1behav1our of unsaturated soil i陰 true毛r1axia【testS，Cα’∼、Gθo’（∼ch、／，，39，608−619．18）Nakai，丁．＆ndHi巖okio，養L（2002）：AnlsαroP1char（1eningmodel fornorma1！yandoverconsolfdatedsoilsw1thri」一co飛cep田nd s巨bloading surface concept，P1’o‘．／‘PS，Calgary，3−16．19〉Nakal，丁。aad｝｛inokio，M、（2004）：Asi照plemo（慰for鷺ormaHy a賞d overconsolidated so目s、、’i由un節ed materlal parameこers，∫o’Z5 α11‘1Fo∼’17ゴα”oη5，44（2），53−70．20）Naka1，丁．andMatsuoka，H．（1983）：Shearbe翁aviorsofsalldand clayundertbree−dlmens1onalstresscon踊oほ，So〃∫σ114Fα’11ゴα一ACKNOWLEDGEMENTS The authors ackno、vledge the 食nancia歪supPort pro−vided by 由e Brazilねn National Research ColmclI（CNPq）． ”o〃5，24（2），82−94、21）Nakal，T．andMatsuoka，H．（1986）：Ageneralizedelastoplas【ic cons｛itutivemodelforclayi簸由ree一（玉imensionalstresses．So1Z∫θノ1ゴ Fα’1∼面”017∫，26（3），81−98．22）Nakal，T．andM由ara，Y．（1984）＝Anewmecb舗calquanこiτyfor so賛s and its apPlica“o職to elastoplastic constitut茎ve models，So以∫ 01∼ごFα，11面∫’on5，24（2），82−94．REFERENCES23〉Ohmak玉，S．（1979）：SIreng縫1 and defor鵬a雛o【｝ charaαeristics of overcoIlsollda【edcohesivesoil．P1・o‘．3’ゴ∫11’．Co’∼∫、N濯〃71∠》θ∫ノ∼、 Gθ01ηθch。，Aac｝｝e自，465−474．i）Adams，13．、へ、and Wulfsohn，D（1998）l Critica1−state behaviour of anagrlcωturalso蕪，／．づ491q’c．五11913。Rε∫．，70〔4），345−354．2）Alo難so，B．E．，Ge麟s，A．and Josa，A，（1990）l A const1田tive modeI forpar毛lysaωratedsoils，Gσo’θc1∼吻∼’θ．40（3），405−430．3）、へxelsson，K．，Y薙，Y．and Runesson，K．（1989）＝Consti田葛ive properτiesalldmode騰ngofs11【ysoils，P”oc．12f1∼1CSA4班， Balkenla，R玉o Ja簸e玉ro，Brazi【，1，687−690，4）Balmaceda，A．（199玉）l Compaαedso簸s，A毛11eoreticai and experime陰tals田dy，Pノのrhε∫’∫，Barcelona，UPC（inSpan柚）．5）Barrera，NL （2002）：Experimen｛al study of hydro−mechanical behavior of collapsible so1ls，P110 7ア∼θ5’∫，Barcelo貸a，UPC （1旨24）P王録員eiro， 鍬工 （2004）： ’1ヌーunsat： a new elas！oP｝astic model for unsaturated so11s，zVσ∫’θrρ’∫5θ1・’θ’10／7，Brasilia；UnB，Brazli（in Portuguese）、25）Su簸，D．A， ，Ma【s柱oka，9．，Yao，Y．P．andlch註1ara，W．（2000）；An e！asto7plast1cmodelforu践sa覧uratedsoil1自tllree−dime醜onal stresses，So’Z∫θηゴFα’π面”oη∫，40（3），17−28．26）ToH，D．G、（！990）IAframeworkforunsaturatedso曲ebaviour． Gゴo’（∼（1∼η’（1μθ，40（｝），31−44．27）∼vang，Q．，Pufa届，D．E．and Fre｛員und，D、G，（2002）：A s田dy Qf cr1tlcalsta芝eo鷺anu鳶saturatedsiltysoi1，Cα’1．Gθo’θc11，ノ、，39， 213−2玉8． Spanish）．28）W短eder，S、、∫．andS1vakumar．V、（1995）：A陰elasto−Plas［icc面cal6） Fuτai，糞1．！yl、（玉997）：Analysis of oe（ionletric tests under controlled stateframeworkforunsaturatedsolls，Gゴαθ‘11∼瞭’ε，45（1），35−53． suc縫on1n collapsible soils，A（1α5rθ1”∠）’∬θr∫醒’o’1，Rio de Jaae1ro，29）Yao，Y， P．，Ma【suoka，H．，andSほn，D．A、（玉999）：Au顧ed elastoplasticmodelforclayandsandwiζht紅eSMPcriζerion，P’門oc・ COPPE（i“Pormguese）．7）Kato，S．（1997）IAcons虚u董ivemodelforunsa田ra｛edsoilsbasedon 8∼h 擁∼’∬ヂα1’α一八7（∼、t・Zθα1α11〔1 Co71∫ （フθ01刀θぐh。， Hobart （eds。 by the mo〔i1f㌔ed ISMP．Ploc 14’111CSル1FE，Hamburg．Balkema，互， Vitharana，N，andColman，R。）．AustralianGeomechan1csSociety， 69i−694． 2，997一王004．8）Ka【o，S．，Matsuoka，H、an（l Sun，五），A．〔1995），A cons戯uτlveゑ錨 ELASTOPLASTIC,IODEL FO R UNSATURAT ID SOILSAPPENDIX A1: DERIVATION OF ELASTOPLASTIC CONSTITLi TIVE TENSORSc!y aj't D :cl - afl D (h hP) af1aaD*P AND h*The total strain incremem tensor c/ _ consists of t¥vocomponents, namely, de as a result of change in net stresstensor (? and d as a result of change in matric suction s.c! = c!8 + d(AI )Those strain increment components can be expressed interms of elastic and plastic parts from the principle of'additive decomposition of strain incrernent.d* + dP) (A,3))] (A4)rule) and the elastic and plastic strain increment tensors¥vith respect to matric suction, (A4) can be re¥vritten asfollows:[ aj (h' + hP)ds<doat(AI 1)= De :d- hcpds (AI _')De '=D (-(Daft.D (A13)at' afl() :!*)aa '1- dy - (A5)The partial der'ivatives required to perform those pre¥'i-ous terms are expressed in the next appendix.APPENDIX A2: PARTIAL DERIVATIVESThe partial derivates herein presented ref'er only to LCyield surf'ace, since stress-suction-strain paths intersectingthe SI yield surface are not Involved in this study.At first, those partial derivatives referred to modifiedstress tensor'at ats at¥vhereaj"11(A 1 6)Mt¥' + t '{s tN'T T t¥' sa tNaj"tsc,-a ts[ M *( tN + t¥. 's)]"{(A17)a tNtion and hardenin*' Ia¥v.ata tsf* =f'*(ts, tN, tNc, s') =f*((r t s) (A6).' = - , Nc,atConsistency condition:vill be sho¥vn.af' atN_aj"+ aj" ats (A15)- atN atnet stress tensor and regarding both consistency condi-(A 1 8)::sa,, (t-t a) ts(A 1 9)Other necessary partial derivati¥'es are given belo¥v.aj't d(sr+ afl .dtNcdf t = :aj'Ea(r at :'c asc!s = O (A7)af l= ( tdtNc H dy tr afatatN,c(A8)af lat ,s¥vhere1+eH= - ),(O)-!c(s) tNCltN,o + t ,sat¥. 'aa j' t(A9)After handling some simple operations, the plasticmultiplier is defined asat atNcEventually, substituting Eq. (AIO) into Eq. (A5), the4th-order elastoplastic constitutive tensor Dep and '-ndorder tensor hcp can be explicitly expressed as f'ollows:In order to deterrnine d( , given a total strain incrementtensor d and a matr'ic suction increment ds, at first, theplastic multiplier dy must be defined. This can be accomplished by expressing the yield function f* in terms of theHardening la¥v:+aq *p 1__ aft e aJ'ISubstituting the expressions for the plastic strain increment tensor ¥vith respect to net stress (obtained from flo¥¥'da = D*: [dat(A I O)hep=Dcp (h'J h ) (bD s ' at (A14)The relationship between the net stress increment tensolcla and the elastic strain increment tensor d8* can beexpressed in ter'ms of the G*eneralized Hooke la v.c!cf D de*=D*:[d -deP-(d *+daflH tr(¥af )af .De: _aJ't( )=Rearranging (A2), it takes the follo¥ving form:- de P - (daa asc!s'here= (de* + d8 P) + (d * + dc P) (A_?)d8 * = d627),(O)-/((s) tNO l= - - --[[1-(A'_1)1*. ( ts ) IJ).(s)-/c(s) tNC tN0+t :s=11* --t; 'o + t¥. 's t , + t¥. 'sMt ,tNS(A'_2)The partial derivatives with respect to conventional netstress tensor are expressed as follo¥vs:aJ'Iaj't, atafl atsacratN ac ats a(1 FARIAS ET AL.69_sc) atslas¥vhereat,N = atN aljaa i=1 alj a(Tanda ts=3 ats alj--acT i=1 alj a(1(A24)Flnally. , the partial derivatives ¥vith respect to matricsuction are:as atN asats as atNo asaf'at¥. 'satN,sasa tsatNsa tsa (TOasat¥'SaSa (70asa= o(a (70d)bo + bl ao + b,(T¥vhereas as(A26)+ c3 (Ti !2c4(T4(A30)a tNO I asa tNOa t ,oalcasa/(as+atNOa)*a).as(A3 1 )a,(a)*atN atNs at¥.' acroa tNS as a ao as(A27)whereatN a 313 + 21._ (TO + Ij (Ta(To a( 0 I._ + 211 ao + 3(7= -fiK(O)(1 - f :) efi'(A32)= -fi),(O)(1 - r,) eF<(A33)asb) at lasas+ b4(T40)¥vhereat ,s a(70 =ka tN+ b3(7co + cl (TO + c. (Tacr(A, 5)a) atNslas(A29)wherea tsaf' af' atN + af' ats * af' atNOa ts(A28)as( )In t 'oa t¥, 'ot 'Oa)*).(s) - lc (s)tNRa tNO),(O) - ),(s)tNOal(), (O) - /((s)),(S) - K(S)(A34)(tNO )In -(A35)t¥' TRl | ||||
| ログイン | |||||
| タイトル | stress-Deformation Behavior under Anisotropic Drained Triaxial Consolidation of Cement-treated Soft Bangkok Clay | ||||
| 著者 | D. T. Bergado・C. Taechakumthorn・G. A. Lorenzo・H. M. Abuel-Naga | ||||
| 出版 | soils and Foundations | ||||
| ページ | 629〜637 | 発行 | 2006/10/15 | 文書ID | 20946 |
| 内容 | 表示 SOILS AND FOUNDATIONS¥'ol 46, No. 5, 629637, OcL. 2006,Japanese Geotechnical SocietySTRESS-DEFORMATION BEHAVIOR UNDER ANISOTROPIC DRAINED TRIAXIALCONSOLIDATION OF CEMENT'-TREATED SOFT BANGKOK CLAYD. T. BERGADoi , C. TAECHAKU*¥,ITHORNii), G. A. LoRENZOiii) and H. M. ABUEL-NAGAi )ABSTRACTIn this study the compression behavior of high vater content cement-treated soft Ban_g:kok clay is further in¥'estigated by conducting a constant stress ratio (CSR) test at various stress ratios (,7)･ The test utilized cement-treated clayspecimens lvith cement contents (A,+) of 100/0 and 150/0, each of vhich ¥vas in combination ¥vith 1000/0 and 1300/0 totalclay ¥vater contents. The test results confirmed that the ratio of after-curing void ratio to cement content (e*t/A,+) caneffectively characterize the compression behavior of cement-treated clay. The specimens with higher' values of e.*/A,yielded higher volumetric and shear strains at the same stress ratio. While those with lower values of e. /A,. resulted inlo¥ver shear strains, ¥vith consequent higher values of strain increment ratios (de lc!8=) both before and after tr'ansition-al yield points. Significantly, the e.*/A,, ratio has described the relationship of the compression yield loci of cementtreated clay at var'ious stress ratios and mixing conditions.Key words: anisotropic consolidation, compression, ground improvement, soil-cernent (IGC: D5/D6)prediction of the strains during drained loading.IN1'RODUCTIONThe stabilization of soft clay by deep mixing method(DlvlM) with cement admixtures has been applied for fewdecades in Asia as one of the suitable ground improvement t.echniques. Stabilization using cement has beenLABORATORY TESTThe Base C!ayThe base clay used in this study ¥ 'as taken from a siteextensively used because it leads to beneficial effects onthe strength, compressibility, plasticity, workability and¥vithin the campus of Asian Institute of Technologycornpactibility of problematic soft clay. Also theThe soil profile of the site consists of 2 m thickconsolidat.ion line in the (e, Iog p') plots are shifted tohigher stress levels (Uddin et al., 1997) ¥vith consequentclay underlain by about 6 m soft clay and about 5 rn stiffclay. Beyond the stiff clay the stratification consist ofalternating layers of stiff clay and dense sand with gravel(AIT), Ban*"kok located in the Central Plain of Thailand.tremendous increase of the apparent pr'econsolidationpressure (Balasubramaniam et al., 1999; Porbaha et al.,2000; Bergado and Lorenzo, 200'_; Horpibulsuk et al.,2003). In the deep mixing construction process, theveathereddo¥vn to 500 rn depth (Bergado et al., 1996). The soilsampling was carried out usin*' a Shelby tube samplerin conjunction with vash boring technique at 4 to 5 mdepth. The physical properties are summarized inmixing ¥vater content can be equal to or greater than theliquid limit of the base clay (Lorenzo and Bergado, 2004).The behavior of cement-treated soft Bangkok clay at highrnixin_ : vater content has been studied previously inTable 1. The undrained shear strength, S , as obtainedfrom unconfined compression (UC) tests, ranges from 16to 17 kPa.unconfined compression, one-dimensional consolidationand consolidated-undrained triaxial compression test,Method of Ceinent- Treated C!ay Preparationbut not in stress-deforrnat.ion behavior under anisotropicThe clay samples utilized in all Constant Stress Ratiodrained condition. In this study, both isotropic and(CSR) tests were remolded to water contents ranginganisotropic consolidation tests (i.e. constant stress ratio(CSR) test), ¥vere conducted. These tests aim to under'-from the liquid limit up to 1.3 times the liquid limit(1000/0 to 1300/0). In this study, f'or homogeneous andstand the relationships of strain ratio-stress ratio and theuniform mixing cement slurry was used ¥vithyield loci of cement-treated clay, ¥vhich are useful forcernent ratio (W/C) of 0.6. Type I Portland cement was*]Professor invater-he Geotechnical Engineering Program. School of' Civii Engineering, Asian Institute of Technology, Thailand (bergadoealt.ac.th).Formerly N . Eng. Graduate in the O eotechnical Engineering Program, ditto.Formerly D Eng- Gradua e in the Geotechnical Engincering Program, ditto.'+1 Research Fellolv, Depar ment of Civil Engineering, lvfonash University, AustraliaThe manuscript for this paper tvas received for revie v on February l, 2006; approved on ,July 5, 2006**),**l¥Vritten discussions on lhis paper should be submitted befoFe,1ay I , 2007o the Japanese Geotechnical Society, 4-38-2, Sengoku, Bunkyo-ku.Tokyo I 12-001 i, Japan Upon request the closing date ma_v be extended one month629 BERGADO ET AL630Ph¥. ica] properties of the base clay (Soft Bangl(ok Cla,.-)Table 1.Accordingly, the four series of tests corresponded tothe follo¥vin*' mixin*' condition: (i) 1000/0 total clay ¥vaterC_ haracteristic valuesPro pertiescontent with 100/0 cement content, (2) 1000/･ total clayLiquid limit. LL, ()l03¥vater content ¥vith 150/0 cement content, (3) 1300/0 totalPlasric limit, PL, (o/ )4360clay water content ¥vith 100/0 cement content and (4)Plasticity index, Pl, (9/e)76-84¥¥rater content, It', (o,/o)1300/0 totai clay ¥vater content ¥vith 150/0 cement content.O.62Liquidity index, LISpecin7en P/-eparatioll and TestingCJrain size ciistribution:Silt ( /o)6928Sand (O/e)Tota] unit ¥veigh , *, (kN_ /m3)14 30Clay (ollo)3Dr"v unit weigh , )'ti, (kNlms)7 . 73Initia] void ratio, e2.3Specifc gravity. G., .68Dark grayColorActiviryO.87Sensitivitv7 ,30After mixing, specimens ¥vere formed by pushing theclay-cement paste into 35.5 mm diameter by 71.0 mmheight PVC molds. This method of specimen preparationfacilitated removal of air bubbles. The molded paste ¥vasallo¥ved to protrude out from the other end of the mold topermit inspection for the occurrence of "honeycomb"structure. Pushingvas continued until the surface of theprotruding specimenvas uniform and smooth beforetrimming. The density of each specimen ¥vas monitoredto assure uniform density for a given set of mixin*' condi-utilized. The remolding clay ¥vater content (}v*) is here-tion. Finally, the mold together ¥vith the specimen ¥vas¥vaxed at both ends and placed in the humidity room, at ainafter defined as the ¥vater content of the remolded clayprior to the addition of cement slurry.temperature of 25'C and humidity of 970/0, to avoidPrior to the introduction of cement slurry, the baseclay ¥vith the required amount of additional ¥vater ¥vereAf'ter curin*' each specimen ¥¥'as removed from its moldfor Constant Stress Ratio (CSR) testing.placed inside a portable mechanical soil mixer andallo¥ved to mix together thoroughly. The amount of¥vater to be added to a ¥vet soil sample in order to get thedesired remolding ¥vater content ¥vas obtained using thefollo¥ving equation:A W,= TVT(1.v* - It* ) (1 )(1 + It*.)¥vhere: A W*+ =additional weight of ¥vater to be addedWT = total ¥veight of prepared original untreatedsoil samplev* = required remolding ¥vater contentw = natural ¥vater content of the soilThe remolded clay samples ¥vere mixed ¥vith slurry ofsi_ nificant loss of moisture during the 28 day curing time.In the CSR tests a back pressur'e of 400 kPa ¥vasapplied in order to obtain fully saturated specimens. Thecell pressure and back pressure ¥vere gradually increasedwith pressure increment of 25 kPa. During the application of pressure, the cell pressure ¥vas al¥vays maintained10 to 25 kPa higher than the back pressure. The backpressured specimens ¥vere allo¥ved to equilibrate for atleast 24 hours and the degree of saturation ¥vas checkedby measuring the pore pressure response under undrainedconditions. A Skempton B value of 0.98: 0.02 ¥vithinone minute ¥vas taken as the Index criterion of sufficientsaturation.The triaxial consolidation test ¥vas performedanisotropically by increasing both cell pressure andcement in order to obtain the cement contents of 100/0and 150/0 by using a mechanical mixer for approximatelypiston loads simultaneously so that the required stressratio ¥vas maintained constant. The consolidation path10 minutes until a homogeneous clay-¥vater-cementvas divided into increments such that the total increase inmixture ¥vas attained. Since the cement slurry has ¥¥'ater incell pressure is 50kPa in one day. Furthermore, theit, then the overall ¥vater content of the clay-¥vater-increase in cell pressure ¥vas applied in increments of10 kPa and, simultaneously, corresponding piston loadswere increased to maintain the specific constant stresscement paste just at the time of mixing ¥vill be the sum ofthe remolding lvater plus the lvater in the cement slurry.The overall ¥vater content is hereinafter called the tota!c!ay ),'ater colltent (C,,.), ¥vhich is defined as (Bergado andLorenzo, '-002; L,orenzo and Bergado, 2004a):Cw = }v=* + W/C (A,.) (2)ratio. Each increment was maintained for at least 3hours.After the cell pressure had been increased by a total of50 kPa, the load ¥vas maintained overnight (at least 10¥vhere: C, =total clay ¥vater content of the clay-water-hours) to ensure that 900/0 consolidation has beenattained as demonstrated in Fig. 1. This scheme ofcement paste (o/o) reckoned from the dryincremental loading is follo¥ved until the cell pressure ¥vasveight of soil onlyIt** = remo}ding ¥vater' content of the base clay (o/o)800 kPa. The axial deformation and ¥'olume change ¥verebefore mixlng the cement slurryW/C= ¥vater'-cement ratio by lveight of the slurrymonitored throughout the tests from displacementtransducer and the burette for measurements, respec-A,,, = desired cement content (o/o) is defined as thetively. The required loads to maintain the stress ratioconstant at each loading step can be calculated. For apercentage r'atio of the ¥veight of cement tostress ratio (,7) the relation bet¥veen deviator stress (q) andthe dry ¥veight of soilthe effective cell pressure (a ) is: ･f=.,IENT-TREATED SOFT BA*NGKOK CLAYcrTable 2.631Physicai properties of the cement ireated cia) specimensi{Totai clayCemenA** (O/comem,C*, (o, )rimel OO282S2828lO;130lOi151 OO13015After-curinCuring¥vatercomen ,unit ¥veight,'=(kN/m3)After-curinAfter-curin1'a er conlent,void ralio, e*,lIs' ()A14.91l4.992 . 2022279 87-81 .3522 Il14.08- 14. 1 32.s7-2.s9l05_6-l06.32S 8015 02l5 052 042 067214.29-14.372.63-2.649513.6717 591 6-72 967 1 -9696{e Qo sRESULTS AND DISCUSSIONS{Phys'ica! P/'operties of Celnent Tl'eated C!cly SpecimensThe physical properties of cement treated clay specio 0044mens are tabulated in Table 2. The total clay ¥vater_ Tl (llj P IN,'(PID-;{}contents of' 1000/0 and 1300/0 as ¥veH as cement content of100/0 and 150/0 ¥vere the main conditions set out during thekPit;specimen preparation. Accor'ding to the results in Table{)_, the after-curing unlt ¥veight increased and the initialvoid ratio decreased with increasing: cement content at agiven total clay ¥vater content. This result can be attri-iIO 20000 eoooO500001 oOOO;,** : I :,:}40eoobuted to the increasing amount of cementing productssoooobeing formed, ¥vhich eventually increased the amount ofsolids per unit ¥'olume. Furthermore, at given cement;Fig. 1. Experimental resLrlt from triaxial consolidation testdq 3ll_ da (3);So, the ratio of effective principal stresses ((7i/() can be(Ti 2fl3q(4)(T . 3 and- ,7-=il=･7p¥vhere: q = (Jj - (ring equation, proposed by Lorenzo and Ber*'ado (2004a)for cement treated soft Bangkok clay:e** (1 + co )G *y,,, _ I (5)Iratio, or in other ¥vords, any increase of cell pressuremust be accompanied by an increase of the deviator stress{equal to (3tl/(3 - I/)) times the cell pressure. Each series ofI.¥'olume of cement treated clay specimens. The afterand p = (Ti + 2cr .Any increase of (T must be accompanied by a corresponding increase in ai to maintain a constant stressi{content, the aforernentioned result can be attributed tothe subsequent increase of the volume of void per unitcuring void ratio, e.*, can be expressed using the follo¥v-obtained as follo¥vs:{content, the higher total clay ¥¥'ater content has resultedto lo¥ver after curing unit ¥veight and higher initial voidratio of' the cured treated specirnens. For a gi¥'en cementy*where ( )*=after-curing ¥vater content of the treated soilafter "t" curing time (in decimal); G**=after-curingmixing condition utilized stress ratios of 0.00, 0.25, 0.50,specific gravity of the treated soil (dimensionless); y*=after-curing unit ¥veight of the treated soil; and y+ =unitweight of water (kN/m3). The parameters w*, G**, and y*0.75, 1.00 and 2.00.can be measured in the laboratory. Lorenzo and Bergado('_004a) also proposed the empirical relationship of aftercuring void ratio, e.*, expressed as follo¥vs:1i{{[1 1 CIY GSo]iI 100{{eotiC1ocso!O 012A'I 0'012Log(t)+0.99) l-10011 OOC'ilOO j( Ah+10'0025AIY + 0.01 Log(t) + I '008(6){{.i.*{;¥vhere Gso is the specific gravity of the base clay=2.657(Lorenzo and Bergado, 2004a) and t is the curing time (indays) of t.he treated soil. The rest of the ter'ms have beendefined previously.Volutnetl'ic Def'Ol"lnation du/'ing Constant Stl'ess RatioTestsIn order to eliminate the effects of the differences of initial void ratio of the cernent treated soil specimens on therelationships of e versus log p', the compression curves1i i {BERGADO ET AL.632} Ii []+1 "i'e e e 'll,T] 1iHTJ'je+ i *c!ie'eO' h 'I} I] tdJL] i] t]e.,'eS'}-'/ctI] TX}X' I;:*"'l!'i] F I}t] t T s{ If},Il I{ ,{{] i} ] l*=*]{]¥. Iesn Errt:"cll¥. e n EffL･cl]he StTess (p'}Fig. 2. Voiumetric strain versus log p' relationships for C,,=1000/e Stress {pi)Fig. 4. Shear strain versus log p' relationships for C,, = 1000! and A= 100/0and A*, = 15 /othe greater the compressibility of cement treated specimens at the same total clay ¥vater content. Having lo¥veri) f] :!3c=1;F"li G e O C =1+ * i hJ -A c L=i 'l] f}t ]cement content has resulted to lesser amounts of" _i: el c-+' clL'I{""=1..cementing products as ¥vell as fewer pozzolanic reactions.h -!'i I'The effect of total clay ¥vater content and cementcontent on the volumetric yielding of cement treated clayspecimens is also sho¥vn in Fig. 3. The volumetric yielding; T} t] {]r .!r T7. -/'L!1 ,-1'f-rfis the stress point which separates the states of stress forwhich the volumetric deformation is regar'ded as smallwhen compared with those states of stress in lvhich thefr !I]l }T JI }$ ?1¥leen EtTect]h e Stress t )Frg. 3. Volumetric strain versus tog p' re ationships for ll=2.00volumetric deformation is r'e*･arded to as large. Thesevolumetric transition points can be estimated in a manner'identical to the Casagrande's method commonly used forthe estimation of the maximum past pressure of onedimensionai consolidation tests (Uddin and Buensuceso,200･_).were plotted in terms of volumetric strain and log ofThe data in Fig. 3 supports the previous finding ofmean normal stress (8,, vs log p') relationships. The 8,versus log p' relationships for the tests with 100010 totalclay ¥vater content and 150/0 cement content are presentedUddin (1995) that, for a given stress ratio (l7), the speci-in Fi**. )_. This figure reveals that the variations of stressratio has no significant effect on the 8versus log p'relationship.The relationships of volumetr'ic strain ¥vith mean normal stress (e,., Iog p') durin*' CSR tests sho¥vs that therelationships are similar regardless of stress ratio as seenmen ¥vith higher cement content can sustain highervolumetric yield stress. For the same cement content, thevolumetric yield stress tends to increase with decreasin*-total clay ¥vater content. These observed trends alsoconfirm the earlier findings of Bergado and L,orenzo(2002) on the one-dimensional compression of cementtreated soft Ban."kok clay at high ¥vater content.in Fig. 2. Like¥vise, the effect of the variations of stress ra-Sllea/' Straill Respollse,fronl Cor7stant Stress Ratio Teststio on the e , versus log p' relationship is small, especiallyThe typical relationship of shear strain lvith meanfor higher cement content and lo¥ver totai clay ¥¥'atercontent. Similar behavior was also found by Uddin andBuensuceso (2002).normal stress, 8* versus log p', durin*･ constant stressratio tests of cement-treated clay specimens ¥vith 1000/0total clay water content and 100/0 cement content issho¥vn in Fig. 4. It is evident that the higher the stressEffect of Tota! C!ay Water Contel7t and Cen7ent Colltel7ton Vohlmetric D forn7ationThe effect of total clay ¥vater content and cementcontent on the volumetric deformation cur¥'es of cementtreated clay specimens is sholvn in Fig. 3 corresponding tostress ratios (i7) of '_.OO. Fi**ur'e 3 demonstrates that athigher total clay vater content, Iarger volumetricdeformation were observed than at lo¥ver total clay watercontent for the same cement content. The results in Fi . 3simply demonstrated that, the lo¥ver the cement content,ratio, the _ reater is the shear strain incurred by thecement treated clay specimens at the same mean stress. Athigher cement content the influence of stress ratio onshear strain is significantly reduced and smaller than at10¥ver cement content.Effect of Tota! C!ay Water Conte/7t alrd Ce/7?e/7t Conteilton Shea/' Stl'ain ResponseIn order to study the effects of total clay lvater contentand cement content on the e* versus log p' relationships 肝633CEMENT−TREATED SOFT B、へNGKOK CL．へY1い叫 こロ タリ ヨs l 縦“判＝ ．z O e eい・、耳1・・ 轟G一一←一◇いr←一←一◇い・、 ’ぐヤヤマしミ リ ハ 1財o プ飼圃し”←一㊥ゆ〔・一 ［ゑ ｝c・㌔ ’・’…’ ！悼、 1播￥￥￥あ。卿i び『；） ＼、、儀キ き ざ プタ i 牙 1向【「 ＼＼ 、、、令 【IGユo i 芦 ず／『 、へ、、，、，、、、，1 ！著、← 、、 隔← 一 鴨 ＿ 、かq一一◆一一つ 魔、I I（冥｝O Pill iI雑Iil勘∫o INleanEfデ￠cu、￠SIrossiPI1卜s にRISI「05s R飢K）σ1｝Fig．5・ She謎r strain versus lo9ρ’re皿負tionships for∼1漏2．00Fig。7。S｛ressratio謎ndstrai“iacremen重ra載iorela載lonshipsforC、、篇 100％and．4、、＝董0％岡ユ1｝卜 1strains．The yiekl玉oci based on the characteristic of thestrain pa芝hs w呈11be discussed subsequerltly． The stress rat玉o and strai熱increment ratio re正ationshipsare useful ill the prediction of慮he strains during drεdRedload圭ng（Roscoe alld Pooroshasb，1963）．Consiclering thebi−linear characteris毛ics of the strain paths， t鼓e strainincrement I’at玉o during constant stress ratio tests has to becollsidered玉n two parts．The負rst one corresponds to thestate pr玉or to the transition points or inside y玉eld正oci玉nthe s￡rain paths ancl the other correspo亘ds to t熱e stateou o l O oユ o Ωミl o4 voh；lne伯cSlral【｝1ε、1afterthetransitionpointsoroutsideyieldloci．There玉ationships be芝ween strain 呈ncrement ratio and stressratio both inside and outside the yield loci are il玉ust！’ated野員9、6． B董一li臓ear rel段芝ionships of strain pa重hs for（コ、、篇1009もand・4、、＝ 10％i熱F三9．7．The figure s熱ows芝bat the strain increment rat重o，4ε、・／ゴε、，beforethetransltionpollltisgreaterthant勤ecorresponding values after the ￡ransition po量nt． 丁勤eof cemellt treate（i day，the test results at di圧erent totaIstrain increment ratio aud stress ratio relat圭ons負ips insideclaywatercontentandcementcoate厩areplottedast紅e bounclary are apPlicable for a11stress states corre−shown in Fig． 5． It is ev玉dent ia t｝1e agure that thesponding to the overcoasolidated state of tke cementv＆riationofshearstrainwi由stressratlolsgreatlyin一treated clay．Tむis overconso豆idatioll is evi（iently due to避uenced by the tota豆 clay water content and cementcementa左ion of hεしrdening ageat 、v圭th clay particlescon書α1t．The significant c勤ange in shear stra呈【1at higher（Balasubram＆nia買1e書＆1．，1999）．total clay water content a茎1d lower cement content can beobserved．Fur重her！noIle，for the s＆me stress ratio（η），atIower total clay water contellt and higher cemen毛content，higher distor重ional yield stress ls obtained，using the same F玉gure7furt紅er shows thα｛｝1玉9紅er stress rat重o renclersma正1er values of strain iacrement rat呈o，4ε，／4ε、，at bothinside and outs玉de芝he宅rallsit1on points。Therefore，at the屈gher stress ratio，重he compression behavior of cementmethod as th飢for volume毛ric yield s亡ress．treated clay specimens are goveme（i by d量stortion．TheS〃・αin Pα1hs σnol S1ヂθ55・Rα1io−S！1・αi17 111c1・θ1nθ1z∼ Rα∼iothe apP1圭cation of higher distortional stress（or（ievi＆torspeclmen tends to yield at lower mean yieid s芝ress due toRθ1α∼ioηShiρSstress）．However，at正ower stress ratio the value of strain The typical stra玉n paths fo110wed during the collstantillcrement ratio，4ε、ノ‘1ε、，tends to be higher both insidestress ratio tests is plotted in Fig．6 correspouding toand outs圭de the trans貢ion poiats，so the compressioa oflOO％total clεしy water content with IO％cemen重conteut．the specimen ls govemed by the volumetric beぬavior．As shown in the figure，the strain paths consist of twostraig勤t lines for any particu1αr stress ratio．τhe shearThus，at lower stress ratio，the cement treated clay tendsstrail1（ε，）versus volumetric strain（ε、）relationships fromto compress and fal1飢紅igher mean e狂ective stress．Moreover，Fig．7also includes｛he test results by Uddinthe constant stress rado tests in this study shows the（1995）todemo熱stratet熱ee任ectofmlxingwatel齢conte飢bi−1inear re董ationships forε葦1圭ser玉es of tests．The intersec一on straln increment ratio．The results show that as t勤e｛ion of tkese tYvo straigh重1重nes is a transition po圭n重andmixing water content decreases，the strain increment ratiorepresents ＆poiat which corresponds to the boundarydecreases。ξhat separates 豆arger shear strεしin fl畠om sma茎1er shear BERGADO ET AL.634lIT] T]12c-hl r [ h: :i :r': ii i h > ii: Ij! :::Ji: ::ll]: ci ¥ JF¥tl-: 1d1 -A i:- F -A T' :h¥¥ f'¥ ¥ IeFr -de¥")¥Ysi '"Lj::;JI'h+1I: :- lt}14', 12 1]- JiA t' ;:*R-SquaFed = O S2b lcll]X l]¥ ¥'' " A"¥"..:¥" "Q..,,* '..h L "t 1l [!' , " ,' .s- :i;ii B;'..,c-- _ 1;' - -S [TT} t'[] s 1' h* 1Slross Rs ]o {,{i 14eel AI,Fig. 8. E,ffect of vaiue of (e*>$/A,,) on stress ratto and strain incrementFig. 10. Re ationships of strain ivlcrement ratio at stress rati0=0.00vith e**t/A,.ratio re!ationsl]ipsl:!!eQ1 An TiC:; C:1] ::t>:J[] ',O O r_ i:i Jl <> , :":'i ' cet ' lLAL :rl':J:'iBT]x ,R-Squnred = O 97S2I :T 11 TO e O i'i T :c c c f'4t :i eel : l :: +] 1: )t ' ll: A A A flftI)ll 4T] 'zl 4 i} x *Stre . s R ttio fee}Fig. 9. F {ormalized plots of stress ratio and strain increment ratioA11Frg. Il. Relationships of dilatancy ratio at stress ratio = O.OO with e,,*/A ,,relationshipsNol-ina!ized P!ot and Effect of Mag/7itudes of AfterFrom Frg. 9, the unique line can be expressed by theCuring Voicl Ratio }vith Celnent Corlte/7t (e.,/A,,) ollSt,'ess Ratio (;7)-St/-ai,7 I/7c/'e,nellt Ratio (cls,,Id8.)follo¥ving empirical equation:Re!ation sll ipFrom the previous study of Lorenzo and Bergado(2004a,b), the ratio of after-curing void ratio to cementcontent (e**/A,,.) has been proven to be a fundamentalparameter that can effectively descr'ibe the combinedinfluences of total clay ¥vater content, cement content,curing time and curing pressure on the strength characteristics of cement treated clay. The strength is higher at10¥ver values of e.*/Aw ratio. This present study confi medthat the behavior of the strain increment ratio, dev/d8*, ofcement-treated clay can be described by the e */Aw ratio.Figure 8 indicates that cement treated clay at lo¥ver ¥*alueof the e**/A,,, ratio has higher strain increment ratio,de /ds=, compared to that ¥vith higher values of the e.*/A,,ratio at same stress ratio. Thus, the strain incrementratio, dev/de=, increases ¥vith decreasing e.*/A,., ratio.dstiiil = _0.1393n3+0.6879,71_ 1.169i,1+ I .O005 (7)c!e* " *(de /de)/(de /de ) ,, ooo¥vhere: (de/de;* ".*",*)- = < . = =,1 = stress ratio = qlp' .The empirical relationships of strain increment ratioinside yield locus at stress ratio equal to 0.00, (de lcl8,) at/7 =0.00, and e. /A,,, for cement-treated soft Ban_g:kok ispresented in Fig. 10, and the corresponding empiricalequation is given as follo¥vs:de,.( .= -O 1713 (Ae.,:)- +13.688* ) *t'/ = o oo., *idwhere: e.t = after cunn' vord ratroA,,, = cement content (in decimal).Moreover, from the relationship of strain incrementFurthermore, the str'ain increment ratios (de,./de,) bothratio (de /de*) ¥vith stress ratio (n), all curves have theinside and outside the yield loci can be related to the ratiosame trend as sho¥vn in Fi_,_". 8. Therefore, these curvescan be normalized to a unique line, as sholvn in Fig. 9, byusing the strain increment ratio at stress ratio equal toof (de /d *) at n=0.00 at outside yield locus di¥'ided byO.OO, (ds./de*) at n=0.00, as normalizing parameter'.bet¥veen the dilatancy ratio and e*t/A,(c!e /de*) at n = 0.00 at inside yield locus. The ratio ¥vill becalled heremafter "dilatanc} ratio" (ai). The relationshipis plotted inii CEMENT-TREATED SOFT BAN(3 KOK CLAYj c- 1" l' ) I e' :(- r::. I li - T r"A A A) L* i "i; ll//'"'//;;. "I;//"/[; [] [] C//;'1Z12;."'/ : '// tt; ____-1l{}fl.(} I[hTI [ [rIesn Efi'ectll e Stress ( 'lc'* i'{/[1 4*tiI;=; -ll.."/...'_ // //'/!, U X{,*! " ;l-' ' /{l f i;,, 17=;'*O O O C' Ii' '- T :: 11! cl':! - s[}f]i1 (*635},Tuu s¥. om sl:ze ¥. Iean Ef lect: e Stress (p')Fig. 12. 'Theyield lociofthetransitionpoiutsoftirebi-linear relation-Flg 13. N'ormalized yield lociships of strain path{{iI ,(.I*eFig. 11. The fitted empirical equation for the dilatancyratio and e.t/A,, can be expressed as:fi*ce= - 0.0046 i + 0.71 7 1 (9)(tR-Squared = O 9 q87cA *+I1[}{]{i¥*¥¥..here: ae= Diiatancy ratio = (de,¥¥c+¥･ St Ide* ) ,, = o oo,o 1**dede,1]d8s ) '1 = o oo,**s*d**tl{iAccording to Eqs. (6) to (8), the functions of stressratio (il)-strain increment ratio (de./dss) for cementtreated soft Bangkok clay both at inside yield locus andoutside yield locus can be predicted using the fundamental par'ameter', eol/Aw' vhich was recently proposed byt{ Iees *Fig. 14.*+Relationships of mean effective stress at ff= 0.00iLorenzo and Bergado (2004a).i,*,iYIELDING BEHAVIOR OF CEMENT TREATEDSOFT BANGKOK CLAYcement content and curing time on the yielding behaviorof cement-treated soft Bangkok clay.Norlna!ized P!ot of Yie!d LocusFigure l,3 shows the normalized plot of all the yield lociGenerally, graphical techniques are used to identify ayield point. The plot of the transition points of the bi-shown previously in Fig. 12. The mean effective yieldlinear relationships of strain path (e.g. Fi**. 6) determinesing parameter. The relationship of mean effective yieldstress at stress ratio equal to 0.00 is used as the normaliz-the yield loci as sho¥vn in Fi**. 12. The shapes of the yieldstress at stress ratio equal to 0.00 versus values of eol/A,,10ci obtained from the test are similar, includin** therelated result from previous study of soft Bangkok clayby Uddin (1995) at 800/0 total clay ¥vater content. It isis sho¥vn in Fig. 14. The fitted line in Fig. 13 can bedescribed by the follo¥ving empirical equation:evident in Fig. 12 that the location of the yield locus isp'o*m= - 0.0399q3norm- O.2,52q2no*maffected by the total clay water content and cement+ o. 3478q + 0.9996 (lO)content or dependent on ratio of after-curing void ratioto cement content (e.*/A,.).¥vhere: p'= normalize mean effecti¥'e stress = p' /no*** o ***Pat " = o oqno*m =normalize deviator stress=p o* ' x stressYie!d Locus versLis e , /A ,,.ratio (n)Figure 12 demonstrates that at lower values of e.*/A*,,the yield locus tends to position at higher stress levels.effective stress (p') at n=0.00 and eo /Aw for cement-This means stronger cement-treated clay at the lowertreated soft Bangkok (see Fig. 14) is obtained as follo¥vs:values of e.*/A,.. This relationship confirms the resultsfrom the study on the strength and one-dimensionalIn addition, the empirical relationships bet¥ 'een meanPat' oo0=0.490 (Aej:,:)2_31.903 (Ael,:) +733.179 (11)compression characteristics of cernent-treated soft Bang-kok clay (Lorenzo and Bergado, 2004a). Significantly,the e.*/A,r'atio pro¥'ides an effective basis for characteriz-ing the combined effects of total clay water content,f;{'i;¥vhere: e.1 = after-curing void ratioAw = cement content BE,RGADO ET AL.636CONCLIJSION,(c<>liTtr,(: ,From the results of Constant Stress Ratio (CSR) testand the subsequent analyses performed, the follo¥vin_"._conclusions can be dra¥vn:(1) From e,,-logp' and 8*-logp' relationships, the･j<>r-_ __ )IJ EI N=S[tt(S F :application of higher stress ratio caused greatereffect in shear straln but the effect on volumetricstrain is not significant. The compressibility andshear strain are affected by the e.*/A,, . The cementtreated clay specimens ¥vith lo¥ver values of e.*/A,,exhibit lolver compressibility and shear strains atthe same stress ratio.IQ I T1 TFrg 15, Predicted strain increment ratio-stress ratio relationship(2) The volumetric strain-shear strain paths sho¥vedbi-linear characteristics, corresponding to preyield (inside yield locus) and post-yield (outsideXI Iyield locus) conditions The strain increment}e ' e' [ 'ratlos (de,./d8,) of both at pre-yield and post-yieldf' ll l **conditions are affected by the stress ratio andtle.*/A,.. The higher the stress ratio, the lo¥ver' thet{ }p..."' _/"/' / _/' ll' _/ Ill* ll ///' lc-1'1i;;'l_ -/1/:/1''___li-* ***t H I I¥ !$ii:1I ,En C[i Jt S feS, 4 E 14 I*!] ]i)]Fig, 16 Predicted yield locusBy substitution of Eq. (lO) to Eq (9) for kno¥vn vaiueof e.*/A,,, the yield locus of cement treated soft Bangkokstrain increment ratio (d8./de,). Moreover, it isfound that at higher cement content and lo¥vertotal clay ¥vater content or lo¥ver value of (e.* /A,,,),higher values of strain increment ratio, (de/c!e,),at both inside and outside the yield locus ¥vereobtained.(3) The strain increment ratlo (c!8./d8,) ¥vere noTmaliz,ed b ., usin_g: strain increment ratio at =0.00,(d8.lcla*) at n = 0.00, as a normalizing parameter.The normalized data foilolv a unique function.Consequently, an empirical relationship of stressratio (n)-strain increment ratio (de /d8,) ¥vasobtained, ¥vhich is useful in settlement analysisusing the incremental stress-strain theory.clay can be predicted as sho¥vn in Figs. 15 and 16.(4) The shapes of the yield loci are similar for allMoreover, the initial void ratio can be calculated as afunction of total clay ¥vater content, cement content andconditions. The location of the yield locus can bedescribed by the value of (e**/A,.) for all proportions of total clay water content (Cw) and cementcuring time as ¥vell as the specific gravity of the base clay,as previously discussed by Lorenz,o and Bergado ('-004a).The plot of the str'ess ratio-strain increment ratiorelationships and the yield loci obtained from the resultsof CSR tests in this study. , confirms that the ratio ofafter-curing void ratio to cement content (e.*/A, ) isfundamental and sufficient to characteriz,e the strengthand compressibility of cement-treated soft Bangkok clayat hi_ ,_her ¥vater contents. Moreover, the normaliz,ingparameters such as the strain increment ratio at stressratio equal to 0.00, (d8 /de,) at ,7=0.00, and the yieldeffective mean stress ratio at stress ratio equal O.OO orisotropic condltion, (p') at n=0.00, have lllustratedexcellent relationship ¥vith the ratio of after-curing voidratio ¥vith cement content (e.*/A,.) as sho¥vn in Figs. lOand 14, respectively. Figure 1 1 has demonstrated that thedilatancy. ratio (ai) can be predicted by using only the r'atioof after-curin*' ¥'oid ratio to cement content (e.*/A,.).content (A, ). Therefore, e */A, has been confirmed to combine the influences of Cw and A*+ onthe yielding behavior of cement treated clay.(5) The yield locus ¥vere normaliz,ed by using the yieldmean effective stress at stress ratio equal to 0.00 orat isotropic condition as a normalizing par'ameter,and the normalized data follo¥vs a uniquerelationship. Consequently, an empirical relationship for predicting yield locus at a given ¥'alue of(e.*/A,.) has been proposed.(6) The plot ofthe stress ratio-strain increment ratiorelationships and the yield loci from the results ofthe constant stress ratio tests confirm that theratio of after-curing void ratio to cement content(e */Aw) is fundamental parameter and sufficientto characterize the strength and compressibility ofcement-treated soft Bangkok clay.Therefor'e, the stress ratio-strain incr'ement ratlo relation-ships and the yield locus of cement-tr'eated clay can beeasily predicted using the fundamental parameter e */A,..REFERENCF,Sl) Balastrbramaniam, A. S_LiT , D. GSharma A S SJL 濡奮葦CEN・IENT−TKE、へTED SOFT BANGKOK C王＿．へY KanlruzzaIIlaa，A、｝優、NI、，Uddin，K、and Bergado，D、T、（1999）： parameters of cemen［一ad【nixed clay−11ew apProacl｝， ノ、 Gθ01（ぞ（・ノr． Behavior of soft Ba【1gkok clayこrea芝ed w1t猶addi芝ives、1⊃roぐ，1／’h Gθoθ’∼yかoπ．Engrg、，ASC薮，130（10），三〇42・一1050． ．45’oηRθgCo’1∫SA／0五，Seou1，Korea，1H4．2）Bergado，D、T、andLorerlzo，G、A．（2002）lRecentdevelopme瓶sof 工eris工lcs of cemenトadmixed clay ill deep mixing，滅ル1α’θ1”、α、マ〃 ground1mprovemen｛in sofII Ba類gkok clay，P1’oc、＆v111ρ．五〇馳ゾθ’∼4 Engf9、，ASCE，18（2），1−14、 Tθcllno1、，SagaUniversity．Japan，17−26，3） Bergado， D、 T、， Anderson， L、 R、， 汽11ura， N、 and Balasubramaniam，A．S．（亘996）：50ゾf G”o正”∼4∫〃zρ”o、’θ〃∼θ1∼”n蓬637 五〇L∼’10ηゴα’∼ゴ0’hα五ノハゾ’｝on〃∼θ縦5，．ASCE Press、4）Bergado，D、T．，Lorellzo，G．A、，La1，Y P、a臓d Pun，A、（2003）：8）Lorenzo，G，A、alldBergado，D．T、（2004b）：F目ndamenζalcllarac一9） Porbaha，A．，Shibuya，S、and Kis｝1ida，τ，（2000）：S【ate−of一芝ile−a飛in deep mixing technoiogy、鎗art至Ill Geomaterial cilaracterizaτion， （｝1’o㍑ηゴ1〃1ρrovθ1ηθ’∼’／，，3，91−110．10）Roscoe，K、H、and Pooroosllasb，｝｛、B．（1963）l A出eoreΩcal and exper1mentalstudyofstrainsintriaxialcompressiomes｛soll Deep mixlng meこhod using cemenトadmixエure a篭higher wa【er normallyconsolida【edciays，Gθo’θぐ1マ〃ゆθ，13，12弓8 con【en芝asfoundat1onofPhexagollalwirere111forcedembankme撤，11）Uddln，K、（1995）：Streng由anddeforma｛ioncわaracteris：icsof Pノ’oc，2’∼ゴ∫∼π、Co厩甜v、50ゾ’So〃En9ヂg rθごh’∼01．，Maiaysia， 317−334．5） Horp1bu王suk， S、 and r㌧董iura， N、 （2001）： A new apProach for studylngbehaviorof−cememstabllizedcia》・s，Pヂoc、15’ノ∼∫CSMGE， Istanbul，Turkey，1759q762、6） ｝｛orpib娘1suk，S、，r〉liura，N、andNagaraj，T、S、（2003）：AssessnleΩ葛 cemen［￡reated Baηgkok clay，五），」E119．五）’∫∫θ1』∼α’10n，No．GT−94−1， Asia駐Institute of Tecbnology，Th＆琵and。玉2） Uddin，K、and Buensuceso，B．R，（2002）：L1meしreated c韮ay：Salienこ engineering Properこies and a concepωal mode1，50’15α1r4 酌姻面∼101∼5，42（5），79−89，王3）Uddin，K、，Balasubramaniam，A．S、and Bergado，D丁．（1997）l of s汀engtil development in ce【nenζ一admixed llig蚤1 water co員tent Engineering behavior of cemen［イreaエed sof［ Bangkok clay， clays with Abrams’Law as自basis，0εo’θご’∼1∼i（1μθ，53（4），439−444． Gθo’θc1∼、Eノ∼9∼8、／、，28（1），89−H9．7）Lorenzo，G，A、and Bergado，D．T．（2004a）：Fundamenこal | ||||
| ログイン | |||||
| タイトル | Fabric and Particle Shape Influence on K0 of Granular Materials | ||||
| 著者 | P. J. Guo・D. F. E. Stolle | ||||
| 出版 | soils and Foundations | ||||
| ページ | 639〜652 | 発行 | 2006/10/15 | 文書ID | 20947 |
| 内容 | 表示 I;T{SOILS Ai¥,D FOUNDATIONS¥;ol46,IN'o- 5,639-652. Oct 2006Japanese Geo echnical Socie }FABRIC AND PARTICLE SHAPE INFLUENCE ON Ko OF GRANULAR MATERIALSP. J. GUoi} and D. F. E. STOLLEii)ABSTRACTThis paper discusses the influence of f'abric and particle shape on Ko-values of cohesionless materials usingmicromechanical analysis and the results from a series of tests. Follo ving a simple analysis using Harr's pr'obabilistictheory that illustrates the dependency of' Ko on particle shape, a rigorous micromechanicai analysis is provided to takeinto account the efi ct of interparticle friction, particle shape and particle arrangement. The fabric effect is introduced¥'ia a joint density function of branch vectors. Both micromechanical analyses and experimental results sho¥v that theKo values are affected by fabric related to both the direction and the length of branch vectors. The effect of particleshape may be undermined if' one only considers the directional variation of the density of branch vectors (or contactnormals). The Ka values are sho¥vn to be also affected by the direction in lvhich deformation is restrained.Ke,_'vords: anisotropy, coefficient of earth pressure at r'est, f'abric, granular material, particle shape (IGC:critical state friction angleIN1'RODUC1'10ND6/E5)*.. Furthermore fcu a ¥¥all¥vith friction, the horizontal and the vertical stresses, (Tl'and (7The determination of geostatic stresses is very im-respectively, on the retaining wall are not theportant for the analysis and design of various geotechnical structures, including retaining lvalls, piles, tunnels,slopes, dams and excavations. Their estimation is crucialfor any numerical modelling of geotechnical engineeringprincipal stresses, ¥vhich is assumed in the application ofKb-values.problems involving non-liue tr soil beha¥'iour. In gener'al,mobilized angle of internal frictionFollo¥ving Terzaghi (19'_3) and Ro¥ve (1954), forsmooth lvalls, Ko rnay be determined in terms of thevertical stresses can be determined easily from depths,K0= I - sinunit ¥veight of soils and _"_,roundwater information. On thefrom empirical values of Ko, the coefficient of earthIn ¥vhichpressure at rest.failure. Bolton (1991) suggested rp*.b =¥*ertical ¥valls retaining) a normally consolidated granularfill. He found that when sufncient vertical settling of thefill occur's with the shear' strength within the granular fill0'95 smtion ratio (OCR) are needed to predict approximatevalues of Kb, ¥vhich can be evaluated by the equationproposed by Schmidt (1966)Kb** = Ko *(OCR)"* (4)(1)¥vhere Ko * is the coefficient of earth pressure at rest fornormally consolidated soils, with the exponent ln bein*"approximately gi¥'en by ln = sin ep. The experimental dataalso reveal that Jaky's equation appears to be valid forO I'Ko = I - sinat- 1 1 .5 ' for sand,the effective stress friction an*"le and the overconsolida-and the fr'ictional resistance on the ¥vall being fullydeveloped, the horizontal pressure on the wall can beexpressed as3,*b is less than the effective friction an*'1evhile Simpson (1992) assumed sin *.b=(sin ,)/ /2 L'ornormally consolidated clay.According to a revie¥v of laboratory data of over 170different soils (including both cohesive and cohesionlesssoils), Mayne and Kulha ¥'y (1982) concluded that onlyC onsiderable research has been carried out in the pastto pro¥'ide means for estimating Ko. Jaky (1944), forexample, studied earth pressure on unyielding, rough2m'b (,3)1 + sin m'bother hand, the horizontal stresses are usually estimated. )l-slnK0=;ah/cr¥( ;_ l+sm l+sinq'*.b:(2)iwith q, being the eff:ective stress friction angle measured incohesi¥'e soils and moderately valid for cohesionless soils.triaxial compression tests (Mitchell and Soga, 2005). ItA closer examination of the experimental data collectedby Mayne and Kulha¥vy (198)_) for normally consolidatedsand indicates that for dense sand in which >33', theshould be noted that Jaky's original ¥vork ¥vas fornormally consolidated soils, in ¥vhichis the same as theAssistant Professor, Departmem of C'ivil Engineering, Mc ,Ias er University, Canada (guopi'mcmaster ca).Professor, ditlo.The manuscripfor this paper ¥vas received for reYie¥v on November 14, 2005; approved on July 26, ,-006.¥¥rritten discussions on lhis paper should be submii ed before lvlay I , 2007 to the Japanese Geotechnical Society, 4-38Tokyo I2-001 1, Japan. Upon request the cfosing date may be ex'tended one month.639, ,Sengoku, Bunkyo-ku, GUO AND STOLLE640authors also observed, based on Ko-¥'alues measuredduring primary unloading, that n7=slnin Eq. (4)f) S! ..O 7lsl!'rpO()l ot e Denseappears to be ¥'alld only for the air-pluviated samples.0The discrepancies may be explained by differences in¥e/ I e' *+o eeeo o ¥.fJfabric that depends on sample preparation technique.lvlore recently, Chu and Cjan (2004) investigated theKo-values of loose sand by performing controlled strainpath triaxial compression tests. In order to achieve A'oconditions, the ratio between the volumetric strain andthe axial strain increments ¥vas controlled to be unity;i.e., de /de.=1, ¥vhich implied that the lateral strainincrement de*=0. The measured Ko-¥'alues, ¥vhich ¥veresignificantly affected by void ratio, ¥vere remarkablylo¥ver than that predicted by Jaky's equation. Moreover,the authors observed considerable difference in the Kovalues of samples prepared using wet-tamping and ¥vaterpluviatlon methods, ¥vhich again could be attributed torlll oee Q Q04e *¥¥¥J/ o le'jaJ[i3o/,D ::: 3OO(}O 4 fl 8O(1 eO 7sm ,j.)1r_r)the development of different internal structures related to-T)f+) ,ti ,iC}O i LiF elo:t 1e den t)rig. lSi)r leeilInfiuence of density on It'(]-values of cohesioniess soilsthe sample pr'eparation methods. Experimental data bylvlitchell and Soga (2005), Tsukamoto et al. (1998), as¥vell as Zlatovic and Ishihar'a (1997) show that sandspecimens prepared by wet-tamping tend to have moredilation than those prepared by lvater- or air-pluviationunder drained conditions for the same initial states. As aoverestimated by Eq. (2), as sho¥vn in Fig. 1(a).result, a specimen prepared by ¥vater pluviation has asmaller "nominal" Poisson's ratio, ¥vhich should lead toa smaller Ko-value. This "conclusion" contradicts theexperimental results of Okachi and Tatsuoka (1984). Ithas also been noted that the mobilized friction an le atMoreover, the difference between experimental A'r,-¥'aluescritical state, ho¥vever, is not sensitive to the initiai fabric,and Eq. (7-) ¥'aries ¥vith the relati¥'e density of soi] speci-since the induced fabric tends to erase the memory ofmens; that is, Eq. (2) overestimates Ko-¥'alues of loosesand and matches most experimental data of dense sand,initial fabric of soil specimens at large deformation One¥vould expect that loose sand specimens prepared usin_"..different methods should have the same effecti¥'e stresspredicated A'o-values from .Iaky's equation in the for'm ofEq. (2) are often smaller than experimental data onaverage, ¥vhile Ko-values of loose sands can easily beas sho¥vn in Fig. 1(b). In other ¥vords, in addition ro theinternal friction angle , a more accurate estimation of Komust take into account the effect of density or void ratio.Even though the friction angle and OCR are generallynnportant fol the evaluatron of A'o, other factors ha¥'ebeen found to ha¥'e significant influence on the Ko-valuesof granular soils as ¥vell. As pointed out by Mitchell andSoga (2005). Ko is state parameter that depends oncomposition, structure (or fabric), stress histor _', as ¥vellas loading directions. For example, Andra¥ves andfriction angle at failure but different Ko-values, o¥vin_".. tothe impact of fabric on deformation characteristics priorto failure.The possible influence of fabric on A'o-values has beenobserved from tests based on measurinshear ¥vavevelocity. According to Roesler (1979) and Stokoe et al.(1985), the shear ¥vave velocity in an elastic mediumdepends on the principal effective stresses actin>' in thedirections of the ¥vave propa*'ation and the particleEl-Sohby (1973) measured different Ko-¥'alues in triaxialKa consolidation tests ¥vhen either vertical or lateralstrains ¥vere restrained. The Ko-value measured at zerovertical strain ¥vas found to be smaller than that at nomotion. According to this findin*', it is possible to backcalculate the in-situ str'esses in different directions andlater'al strain, ¥vhich ¥vas attributed to the anisotropy ofthat the shear ¥vave ¥'elocities vary ¥vith fabric, one maythe specimens and the change of major principal stressargue that the back-calculated Ko-values should also befabric dependent^directions. Okachi and Tatsuoka (1984) measured Ko-hence estimate the Ko-¥'alue based on measured shear¥vave velocities (Fioravante et al., 1998). Holve¥'er, gi¥'envalues of Toyoura sand using a double cell Ko-triaxialBased on probabilistic theory, Harr (1977) demon-apparatus, in lvhich the zero lateral strain condition ¥vasstrated that the coefficient of lateral pressure in particu-achieved by continuously adjusting the cell pressure.They noted that the Ko-values of air-pluviated samplesare approximately 10 to 150/0 higher than correspondinglate medium depends on the transmission of contactforces through particles. For a homogeneous randomlvet-tamped specimens of the same void ratio ¥vhennormaliy consolidated. Ho¥vever, the relation betlveendistribution, Harr found that the coefficient of later'alpressure is uniquely determined by a stacking parameterthe peak friction angle and the ¥'oid ratio appeared to bethat is likely related to particle geometries and the distri-independent of the sample preparation methods. Thebution of contact normals.medium in which stress variations depend on the normall K+ "+P=Aztt*+f(641- .)(* ;r2 exp (5)crz(x,zlbz)=Pl_'7zv2 vz1/ / (;:_1'/: J:_( -i'T- ItVALUE OF GRANULAR ¥_ ,IATERIAL¥vith1' z' ; ( r+: t :+ :I, ;s'_I ;v. ftf hJ'(Ax)2 2 (Ax)2 (6)Az z A( 2)being the stacking parameter that describes the spatial ar-rangement of particles. When neglecting the body forceof the mat.erial, the lateral stress, ¥vhich is obtained fromthe equilibrium condition, is given asa]a(Tz I a2cTz+ v'7cr v(7z+v4 = v(7za. -'+F'ig. 2. Force transmission i l granular medium: (a) irregular particlesand (b) rectangular particles of the same size(7)An immediate observation is that ax= v(T at z=0, vhichimplies that Ko may be directly related to the stackin_cr,_parameter v. For a uniformly distributed pressure qacting on a strip ofHansson and Svensson (2001) carried out a series ofvidth 2a, the vertical stress at a pointis computed astests using a steel ring chamber to investigate the influencea J:: q fiTI exp(x- ) dof particle shape on the distribution of horizontal stresses'_vz2in unbound aggregates induced by a distributed verticalload. For aggre*･ates from the same source, ¥¥'hen subjected to a **i¥'en vertical pressure, the horizontal stresses inspecimens ¥vith flaky particles ¥ 'ere about 200/0 higherthan those with cubic par'ticles. As a result, the authorsconcluded that materials with flaky particles ¥vere likely(8)Introducing the transformation_x-t 1/T : 'd= -/' dt (9)It follows thatz= {J a)/Icr1 dtt' (10)q (1 a)/1r l2rlT_'1Texp - 2to be more unstable than the cubic ones, since largerhorizontal stresses tend to cause large horizontal defor-mation. This conclusion, however, is contrary to thefinchn*'s of Hobeda (1988), who argued that flakymaterial is more stable than cubic material.Given the curnulative-distribution function for a normally distributed random variable,= 1Jo/ (i:-Li)2W(z)Motivated by the above review, the objective of thisexp (1 1)paper is to explore the influence of fabric on Kb-values ofgranular materials. Starting ¥¥'ith Harr's probabilistictheory (Harr, 1977), ¥ve demonstr'ate that the coefficientEquation (lO) can be rewritt.en asof laterai pressure in particulate mediurn depends on(JZ = q { v/('¥;,rT)Similar to Eq. (7), the lateral stress due to the strip load is*･eometry and branch vectors, Ivhich describe thegrven as. a2(rz _(T'¥ = v(Tz + v2zax '. f(x+ a) expvaa) -(x[- a)2?J +-･vz2x[- (x_,- J}( 1 3 )(x a) expKo AND FORCE TRANSMISSION IN GRANULARMEDIUM: REVISIT OF HARR'S PROBABILISTICANALYSISHarr (1977), usin*･ the theory of probability, developedprocedures for estimating the distribution of stresses in aous, the distribution of vertical normal stress at a pointtreline as follo¥vsexp a'( ') xz=cr (O) va( 2aql¥/ t2)a'z(O) = 2qv/a z /2 v<;{=+*( 1 4)If a/z is large, ¥vhich corresponds to a uniformly dis-depends only on the porosity of the medium. When atributed surface load,point load P is applied normal to the surface at the originof coor'dinates (Fig. 2), the vertical normal stress at apoint (x, z) in the granular mass is postulated to be givenof the parameter v. AS a result, the stress components inEq. (14) are simplified asbyi'2v ' 2When x= O, one obtains the stresses at a point on the cen-semi-infinite granular medium subjected to normal surface tractions. Assuming that the medium is hornogene-iV/(izl ) i (12)particle shape, which affects the transmission of contactforces through particles. A more rigorous micromechanical analysis follo¥vs, in which the effects of particleconnectivity of particles, are taken into account. Tests onglass beads of various particle shapes are carried out toverify the theoretical Ko formulations.id u/(a/(zlf ))- 0.5 for a lirnited value(rz(0,4-)=q, CT (O z) v(T(O 4) (15) --GUO AND STOLLE6421!rA*nI2el hAA'vY :::(Ar)*/ I i I_'A:i*bt2 , h !aF g. 3. Parametcr v and particle arrangementIGiven that the deformation and stress distribution in thesoil mass are symmetr'icai ¥vith respect to the centreline,g. 4. Definition of (a) branch vector 8nd (b) contact normalthe Ko condition is automatically satisfied along theorientation distribution E(D, ¥vhich defines the portion ofbranch vectors vithin a range of I and l+ dl. Follo¥vin_centreline. According to Eq. (15), the coefficient of earthpressure at rest A'o is gi¥'en by the parameter v; i.e.vectors are statistically independent of their orientationsK0= v (16)R thenburg and Bathurst (1989), the lengths of branchand E(D can be expressed ascf *E(1) = I,(!")E(ln) ( 1 8)(T.¥vhich confirms that the lateral stress depends on the¥vhere /* is the leng:th of the branch ¥'ector I at a contactstacking parameter v. Referr'ing to Fi(,_. '_(a) and Eq. (6),point, m is a unit vector defining the orientation ofone obser¥'es that v determines the transmission ofis relatecl to particle geometr'y and the internal structure,branch vector l. L(!') and E(m) describe the directionaldependencies of the len*"th of branch ¥'ectors and theirorientation, respectively. Without loss of generality, forincluding the particle shape, the spatial arrangement andany direction that makes an angleconnecti¥'ity of particles in general. More specifically, foran ensemble of particles sho¥vn in Fig:. '_(b), Eq. (6) can bereference (e.g., the horiz,ontal axis), ¥ve assumecontact forces through particles, ¥vhich strictly speakin_cr._¥vith an axis ofI.(!') = ! [1 + ( ) cos '-( fi - fiL)1 ;expressed asE(m) =[1d,o cos _'(fi - fio)] ( 1 9)v = ' (ll :")2 _ 2 ('ri; I - x!) , _ I,/-, 2A･- ･-i- 1'Il[(,j+l)h] -(j/7)1 __ (1,' - (17)ij,_,f i) hlvhere ! is the a¥'erage length of branch vectors; ( ,o and a)define the degree of anisotropy associated ¥vith theorientation and the length of branch vectors, respectively; fio and fiL define the directions along ¥vhich the¥vhich indicates that the stackin..,_O parameter v tends tovary ¥vlth the particle shape. A closer examination ofFig. 3 reveals that v is also affected by the arrangement ofparticles in addition to particle siz,e. It can be sho¥vn thatin general O < v(AR)2/2 Ivith AR = I,//1 being the aspectbranch vectors have the maximum density and themaximum length, respecti¥'ely. PL can also be consideredas the preferential direction of the long particle axis foran ensemble of elongated particles. Substitutin_g: L(/') andE(ln) in Eq. (19) into Eq. (18) yie]dsratio of particles.Even though the above analysis based on Harr's!E(1)=- [1+(1,Lcos2(fi-fiL)][1+co cos'(fi)1 ('O)probability approach is some ¥'hat oversimplified gi¥'enthat the influence of inter-particle friction is not takenFor smallinto account in the evaluation of Ko, this analysis re¥'ealsals ¥vith ¥veak to medium anisotropy, Eq. ( -O) can bethat the internal structure and particle shape may haveinfluence on the value of Ko. The follo¥ving sectionexplores the dependency of A'o on fabric and particleshape via a more rigorous micromechanical analysis of27rsimplifies to1E(1)=- [1+(( )0+( ,Lcos '( ) cos '(fi fi)2frranular materials.+ ( ,L Sin 2(fi -fio) sin '_ L]¥vithMICROMF.CHANICAL ANALYSIS OF KoCOMPRESSIONBranc/1 Vectors anc! Tl7eil' Dist/'ibutionFor the general case of particles of arbitrary shape andgradation, the connectivity of an ensemble of particlescan be described using a graph of branch vectors I thatconnect the centres of gravity of any t¥vo contactingparticles, as sho¥vn in Fig. 4. For a granular ensemble, itis necessary to introduce a joint branch ¥,'ector length-,L and (1)O ¥'alues, ¥vhlch correspond to materi-(2 1 )L =fiL -fio bein*' the angle bet¥veen the directions ofthe densest and the longest branch ¥'ectors. V rhenelongated particles are deposited under gravity, thedirection of the densest branch vector is approximatelyperpendicuiar to the long axis of particles or the directionof longest branch vector's, yieldingL=,Tl.-. The jointbranch vector distribution function becomes1E(1)=2ri'll((D coL)JCOS '(fi)} (2-,)i ri+Ko VALUE OF GRANULAR N{ATERIALFor spherical particles of a single size, the length of abranch vector in any direction is the same as the d}ametelof the particle, indicating ( ) =0. Consequently, thedensity function E(/) simplifies to1E(/)=i643E(D!L :lc!VVF -(!')E(m)mV -mc/ V (28)It f'ollo vs that[1+co cos )(fi P)] (- 3)cr = N. Ji E(Df; Ic!V= N. Ji }/(!')E(ln)flnc!V ('_9)¥¥rhen the directional distribution of branch vectors islvith N* being the nurnber' of contacts per unit volurne andunif'orm in all directions (i.e., cT'Jo = O), for an ensemble of! the a¥*erage length of branch ¥'ectors. According to Ng(2001), the directional distributions of the branch vectorand the contact normal are statistically the same, ¥vhichnon-spherical particles, anlsotropy may de¥'elop o¥ving toparticle shape, ¥¥'hich induces directional variation ofbranch vector lengths such thatE(/) = 317r [1 - (1)L cos 2(fi -fio)] (-'4)yieldsJE(7=N.. L (/' )E(n) fnd V (30)¥vith n being a unit ¥'ector defining the direction of' theContact Forces anc! A vel'age St/'essesLet us consider an idealized, t¥vo-dimensional _O,_ranularcontact normal.When applying Eq. ('-6) to a specimen subjected toassembly, subjected to planar deformations, in ¥vhich theresistance to def'ormation comes only from in-plane contact forces. According to the micromechanics of grarrularbiaxial compression sho¥vn in Fig. 5, the contact forces atcontact m can be determined asf"')=cTll/I ("')! ( "' } (Fi 1nl("')+F1'_n2 );materials, given a representati¥'e elementary volume(REV), the rnicro-variables can be a¥*eraged and thenused to describe the macroscopic state and behaviour.For a cluster of rigid particles chosen in a REV ¥vithparticle connectivity represented by a graph of branch¥vhere !("'} is the br'anch vector length at contact ln, nl =¥'ectors I (as sho¥vn in Fig. 4), and assuming that the bodyplanes. When the fabric tensor Fjj is coaxial ¥vith theforces are negligible ¥vhen compared ¥vith interparticlestress tensor (Tij, the abo¥'e equation becomescontact forces, the average stress (7ij associated ¥vith theREV can be expressed in terms of contact forces, f,bet¥veen particles and local branch vectors, l, via (e.g.,Chang and Liao, 1990; Kr'uyt and Rothenburg, 2004)1 ",crjj=Vvith)l ) f (25)denoting a tensor-product operation and /7* bein_"_.F n2 ) (31)l (,,,]f{ '*=) cr22!("')(F_.jnl , l22(,,,)¥-sin e and n.=cos e are the directional cosines of thecontact normal, ¥vith e defining the orientation of contactf "') (TI IFI j l!("')n("'] f "') = ( 2f l!("')n "'1 (3_,)Given the inter'particle friction angle ep,,, sliding takesplace at contact ln ¥vhenJl =tan(e("')-ep!') (33),,, }f･*)Let us no¥v consider a Ko-consolidation test in lvhichthe number of contacts enclosed in V. Following Changthe vertical stress (;.･ is increased lvhile the lateral stressand Liao (1990) as ¥vell as Emeriault and Chang (1997), it(Tl! is adjusted to correspond to zero lateral deformation(i.e., el =0), which is achieved for the case in ¥ 'hich norelati¥'e sliding takes place bet¥veen any t¥vo particles onis assumed that one may extract the microscopic quantities from the macroscopic variables by invoking a socalled "localization" or "tracking" operation that isboundary A-A' in Fig. 5 . Without loss of generality,opposite to averaging. The contact forces bet¥veenimagine that a specimen of ¥veightless particles is put intopar'ticles can be expressed in terms of the average Cauchya mould that has a movable boundary. When applying astress, (rij, and the fabric tensor, F, as¥'ertical stress cT22, the specimen tends to deform unlessf = (TikFk'-'j l!J (26)¥vith1 '*=Fij = <l } l> - V]!j!j; Fij = I (27)lateral support or confinement is applied at the sametime. For a pair of particles on the boundary of thespecirnen, no lateral support is needed ¥vhen e("*),,because of inter-particle friction. In other ¥vords, ¥vhene("') ,, is valid at all contacts in the specimen, zerolateral strain is achieved vithout any lateral restraint,and F- I being the in¥'erse of F. Using the density functionindicating Kb= O. In the case of a("')> ep,,, (,,,)jl (or all) mustof branch ¥'ector given in Eq. (18), the fabric tensor Fmay be rewritten asbe applied in the lateral direction according to Eq. (33) tomaintain equilibrium of particles ¥vithout sliding. If theinternal structure or fabric is kno¥vn, one can calculateIThe concept of fs:o condi ion defmed as the absence of relative displacemen bet veen any two particles on he boundary A-A' in Fig. 5 and he Kocondition defined as zero average laterai strain vithin a represemarive elementary volume (RE¥r) are the same lvith regard to the a¥'erage meaning.This is because the average strain of a RE¥r can be calculated from the displacement uj on tlle boundaries S of the REV ¥'ia ejj= (1/2 r)is (uj,ij *i_ujnj)c!S, vhich implies that 8jl =0 Ivhen there is no relative displacement bet¥veen par icles on A-A'.i;{ GUO AND STOLLE644lfin ¥vhich the average of the f /.f... ratio is determined as fol-c T e( f'¥/ = 7z;-, Jf iNJ _/i aallcr:1 -_10¥vs:?tan (e- q;;')[1 + ( ) cos -' (e - eo)Ide',2 .;Jr In( (smnil)+co: ( -T b N･ ';') sm (q';' - 7-eo)Herein Simpson's three-point method is used to evaluatethe integral. For special cases of bedding plane beint:'(;horiz,ontal (e0= O) or verticai (e0= 'T/2), the above equation simplifies asAi { ep,il) co: ( - l[(f In) ;(sin,it') [cot lifi7rFig. 5. Biaxia! compression of a specimen( 4 )2 7TJ} !' (40)4tansmaccording to Eq. (29) or' (30) the stress components (TI I and(T22, ¥vhich yields the lateral pressure coefficient at rest asKO =llu cos 2eoJ)(7z4 2 I- -[u) [coti ¥'L(lc)E(m)flnlc/V_ !¥'1,(!c)E(n)f]nlc!V (34)(T22 i ¥'L(/c) E(m),f･_m2c/ Vi ¥'1,(!C) E(n) f._n2d VWhen the body force of a particle cannot be neglected,Eq. (34) is still applicable as long as the influence ofgravity is included in crll and cT22.in ¥vhich " + " and " - " correspond to e0=0 and Itl2,res pectively.In terms of the average length of branch vectors, giventhe joint branch vector length-orientation distributionE(D in E.q. (18), one hasj1 JI'< !i> = ni L (/ c) E(m)cl VThe ¥'alue of A'o can be determined alternati¥'ely bylr- Jousing the average contact forces <fl> and <./ > at A'n State.:x /7i[1 + (( ,0+(1)L cos 2 L) cos 2 (fi-fio)lc!fi (41)7zAccording to Eq. (32), one has<fl> = cfl iFI I I <!("')>; <f,_> = (722F._,_,1</ "')> (35)¥vhich ylelds for horizontal bedding plane<!1> i nl [1 + (( )o + (;( 'L cos 2which yields an alternate expression for A'o:A'o =,,ll - <fl><!2> !!._> F2l! (36)distribution of interparticle contact forces in all dlrections. It has been found that the <,fl>/<f._> ratio can beAccording to Eq. (36), the expressron of A/ becomesKo3calculated based on the micromechanics of granularmaterials vhen the directional ¥'ariation of normalcontact forces is given (see the Appendix for details),which, ho¥vever, requires other parameters to characterize the distribution of interparticle contact forces. In thefollowing sections, ¥ve ¥vill adopt a simplified approach toestimate the <fl>/<,f_.> ratio, ¥vith emphasis being placedL) cos 2 (fi-fio)]cJPll2[1 + (( )o + ( )L cos 2 L) cos 2(fi -fio)]clft3 + (( 'o + ( )L cos 2 L)(722 <f,..> <!i>FlllOne observes that the determination of Ko requires the¥rjth e0=0:(( )o + ( )L cos 2 L)F_.._1 {In(sm!!) T Aucoo}Jt 3 + (( '0+ a'L cos 2 L)Fll(43)¥vithAu = _(u) [cot[ ITu + 4 tan(4 ');isin luJ (44)on the infiuence of the shape and connectivity of parti-Referrin_g to the definition of fabric tensor in Eq. ('-8), itcles .can be shown that for horizontal bedding planesGiven that the ratio bet veen the components of con-F._21 Fli I -(( '0+d'L cos 2 L)/2 (45)tact forces ¥'aries according to Eq. (33) for any contactorientation, one can sho¥v that) << f > fmln <f._> ****: ･) (37)As a first-order' approximation, ¥ve assume for irregularpacking of particles that:, = )(L ff.=..; (3 8)Fli F..I + (( )o + ( )L cos 2 L)12and2 1 - ((1'0+( 'L cos '- L)/6A/0=JrI +(( )0+( 'L cos '- L)/6For materials with{In(sin;")+Aua 'a} (46)veak to medium anisotropy (say ( ,0and ( )L are approximately less than 0.3), since (( )0+("'Lcos 2 L)/6<< 1, one need keep only the linear terms of ( )Land ( ;o in Eq. (46). As a result, Eq. (46) is simplified asL r;rl+(O 6 "= +,i,,( i=]iK(, VALUE OF GRA{¥lTULARl i-(,V5in the vertical direction, as illustrated in Fig. 6(a). ¥VhenEq (50}assuming ( ,0=0 in Eq. (50), the Kb-value for isotropicO Eq (49]06o6 5decrease lvhen the contact normals are more concentrated==K,, x 1+(i = Iln(sin( =,)Os'lATERIALsoils is given asA -2 l-O == 6 [In(sin(o ) -?K = - iL In (sinv {ioi*.(Q =(jsoooFigure 6(b) re¥'eals that l 'hen ep,, varies in the range of 20oooV1'to 40', Eq. (51) is ver'y close to Jaky's equation gi¥'en by{alEqs. (1) and (2). As a result, one may argue that Jaky'sequation is applicable to materials with ¥veak to rnediumanisotropy. Equation (50) also indicates that a pre¥'iousO1OlO,,) (5 1)7z0 5L)0InterParl:icle iticti :*!1 a gle tp( * lloading history that makes the contact normals moreconcentr'ated in the vertical direction tends to decrease theKo-¥'alues in a subsequent reloading.K=Elongated ParticiesFor a natural deposit consisting of elongated particles,the long axes of particles tend to align in the horizontal- i In (sin (P)osKlj = O 95 - si¥'(Pdirection and the br'anch vectors in the vertical direction' "outnumber those in the horizontal direction, indicatin :v V6Ko ; { --'/'}ak¥ 's equation04q (I]fiL = O, fi0= rr/2 andn(p''¥*'"(bol'O 4 sin(p O 610 Il0Os4O 4FrictiOn angle (p ( ' }Fig. 6.) -=?coo ((1,L _3: J :o,,.Oj,KA,,coo;, ;ol'L = Tz /2. For this case, the J O expres-sion in Eq. (47) can be re¥ 'rltten asfz( ,a (Ko,,. i ) co-- , + A,, + .Koi,O,37r(5-7)This equation clearly sho¥vs that the values of' Ko increase¥vith ( )L but decrease vith ( )o. More specifically, for anensemble of elongated particles with a horizontal beddln_a._plane, the value of Ko tends to decrease ¥vhen the contactSimplified expressions for Ko2Ko 2 In (sm q',,) I -co0+( )Lcos 2 L _A,,()o (47)normals are more concentrated in rhe vertical direction.In the contrast. Ko may increase ¥vhen more particles ¥vithlarger aspect ratio ar'e aligned in the horizontal direction,According to the above analysis, in addition to thedegree of anisotropy, the Ko-values are affected by thedirections of the densest and the longest branch vectorsquantified by fio and fiL respectively. For ¥'ertical beddin_{_planes ¥vith ft0= O and fiL = 7z/2. Eq. (46) becomesK0=I + (( ,0 + (2,L cos 2 L)/6 .7r I - (( ,0+ ( ,L cos 2 L)/6 {In(sm ,,) -A;'d)of (48)¥vhich is indicated by an increased ( )L. This observation isqualitati¥'ely consistent ¥vith Eq. (17) based on Harr'sprobabilistic theory, ¥vhich provides only a conceptualmodel for a very special case in which the infiuence ofinterparticle friction and fabric is not appropriatelyaddressed.However, it should be noted that an increased aspectr'atio may simultaneously induce increase of the concen-tration of longer branch vectors in the horizontalSpecial Casesdirection (indicated by an increased ( ,L) and the densltySpherical Particlesof branch vectors in the ¥'ertical direction (indicated by anWhen particles are primarily round, the directionalIjand ( )o ha¥'e opposite influence on the value of Kb, whichThe expression of Ko for the case of horizontal beddingimplies that the Kb-values may decrease at some pointplane becomeswith an increase of the aspect ratio of particles and Komay have a maximum ¥'alue when particle shape changes.Figure 7 sholvs the variation of Kb-values with respectKb= - 2 1 -( ,0/6I7z I + co /6 [In(sm q,,,) + A,,( )o](49)to the fabric related to the particle shape and the densityof branch vectors at an interparticle friction angle of ,, =!{iwhich can be further simplified to2 1 -d)0/2K 7z I + ( )e/2 In (sin{Iincreased ( )o). According to Eq. (52), the increases of (1,Ldependency of branch vector length vanishes ¥vith d)L = O.30' for the case of horizontal bedding planes. When,,)(50)assuming a uniform distribution of the branch ¥'ector inThis equation indicates that the value of Ko tends toall directions (i.e., ( ,0=0), a variation of ( )L has smallinfluence on Kb, as sho¥vn in Fig. 7(a), but the anisotropy -GUO AND STOLLE6460.()/o 5f*r-fr*O')O,4rlrO^2Loadoi -coocells:)zio.3:o(a) CCi*2L::: OPnon-rotationalL,oadO. lO. I O.2 O.3O.4 O.5 0.6cell lKO = I - Silo 61 78 mmr ,((/' ¥o.5L,oadcell 2¥:()" : : ) ll )'1o.4¥ Dial aug:e)e )¥.*:)S ;h:!)- o. 1)Roller strip**7Fig. 8. IL'o tcst cello.2(b) 05L = Oll O 1 - l'O t a t i Q I a lO, l0. I O.2O 3 O.4O.5OKO = I - sin6Flg. 7. Depeudenc,' of Kl] on anisotrop)' associated to (a) branchvectorength and (b) the density of branch vectorsloads are then used to calculate the aver'age vertical andlateral stresses to determine the Ko coefficient^ Differentglass beads ¥vere mixed to_g:ether, yielding various particlearrangements and hence different distributions of branchvectors (or fabric). T¥vo types of surface textures ¥verechosen to study different le¥*els of Interparticle friction.Spherical and flattened particles of different sizes andaspect ratios, varying in a ran*'e of I .O to '_.8, ¥vere select-related to the density of branch vectors may haveconsiderable infiuence on the Ko-values, depending oninterparticle friction. As can be seen from Fig. 7(b), ¥vhena,L = O (i.e. , spherical particles), an increase of the branchvector density in the vertical dir'ection tends to reduce thevalue of Ko, Particularly for small interparticle friction.ed so that the influence of both the particle shape andpotential particle rotation could be identified. Table 1summarizes the characteristics of the glass beads used toform the A'o-test materials that are listed in Table 2.The _ :lass beads or glass bead mixtures lvere carefullyplaced into the test cell ¥vithout compaction or' vibration,¥vith the bulk unit ¥veight varying bet¥veen 15.0 and 16.4kN/m3. The Ko-¥'alues ¥¥*ere calculated as Kc = ai*/(7F,XPF.RIMENTAL STUDY¥vitha+, and (Th bein.' the applied vertical stress and theIn order to investigate the influence of particle shaperesulting horiz,ontal stress, respecti¥'ely. The initial stressand fabric on Ko-values, Ko compression tests werecarried out using a rigid mould made of aluminum, aso¥¥'ing to the ¥veight of the load platen and the self-¥veightsho¥vn in Fi**. 8. In order to reduce the friction bet¥veenthe ¥valis of the mould and the testing material, a layer ofof the tested material ¥vas considered as an initial"sitting" stress that is much smaller than the appliedvertical stresses during tests. Only Ko-values under lo vplaxiglass (6.5 mm thick), on ¥vhich dry lubricant ¥vas¥'ertical stress of (Tvapplied, Ivas put on the inner side of the mould. One sideof the mould could move freely on a roller strip and t¥voAccordin_9: to Fig. 9, ¥vhich presents the variation ofmeasured Ko-¥'alues ¥vith respect to the applied verticalstress (J for typical tests on Gl (# ) glass beads, Koapproaches a stable value ¥vhen (7.> 7 kPa.dial gauges were mounted to monitor any displacementof the plate. The vertical load vas applied on the specimen by loading ¥veights ¥vith t¥vo load cells measuring theresultin : Iateral forces. The measured ¥'ertical and lateral'-O kPa is in¥'esti_g:ated in this study.,* rK * ¥*ALUE OF GRANULARParticle shapeG' ', i "'*'"i"'t,'s (rouglsurface),647AveParticle sizemono-disperseS** (rougll surface) mono dlsperseG.RIALGlass beads used to form tcsied specimenslable l.i¥1aterial(AT*,,*･...a = 20.68 mma/b=2_17,b=9 58 mmaa= 33.30 mma/b = 2_8 1 ,b= I 16mmal/a. = I 13GO (gloss}'Ismoot}1 surface) mono dlspcrsec!=Gel (rougll surface) mono-dispersec!= 15 O m lG<Crushed limestoue, angularc!ns* = 7.5 mmSpeci flcas{)ecratio/a. =gravi ¥.*2.46.062.46105.0 mm2.502.46l .O2.75c!< l = 4.65 mmi¥Tote:} i lCharacterization of parriclese)ilT'able 2.Materials used in ll'(, testsComposition'Ia erialG glass beadsGj G2 '13Gl-G '*"';"""' ixture of(j"' O.i' t 'JG oecG1-( * ' {G"';,1' ./ ' =//"",i "t'*and G2, 'i'G !'rC 1 s l:3.15l¥,'1ixlure of G and G , illG :l,ZG = I ･ , )15.9ilvlix:ture ofG16.4and G,,1lc4:1,lC]1 = I : l15.0particle size c!< )=4.65 mm and the coefficient of unifbrmity C*= 2. I lo.4o o0.38angle (')15 7Crushed limestone, angular particles ¥vith lhe maximum size being 7.5 mm,limeslone 4Friction(kiN/m')l 5 .Olixture of G** and G ' inG :,tlG = I I ?-CrushedUnit ¥vei htmean13.3q'r = 36 iconcentration of longer branch vectors de¥'elops in thehorizontal direction, particularly for Gl and Gl-C}*2Q 6mixture. The bu･anch vectors (or contact normals) in thevertical direction, ho¥vever, usually outnumber those in.*o.36the horizontal direction. These are clearly sho¥vn in¥lFig. 1 1 , 1¥"hich presents the distribution of' both the lengtho.34and the orientation of branch vectors for Gl materials(mono-disperse) and G1-G2 mixture based on digitai0.32image analyses f'or biaxial cases. It should be noted ino. 3Fig. 1 1(a) the lengt.h of branch vector is normalized by itsoIO15maximum length that is equal to the maximum diameter,Applied ¥ ertical st 'ess av (kPa)Fig. 9. Variation of measured H'o*values against vertical stresses:Glparticles lvith horizontal bedding planeDo, of glass beadsA scrutiny of Fig. 11 reveals that, for Gl-G2 mixture,the addition of more flattened G2 particles into Gl resultsIn a substantral change in the distribution of' branchvectors. Statistically, the G1-G 2 mixture has se¥'eredirectional variation in the length of branch vectors,Influence oJ' Pa/'ticle ShapeFigure 10 sumrnarizes the experimental results for G!¥vhile no significant difference is observed in the distribu-" "..=' $ O)tion of branch vector direct.ions for both Gl and Gl-G2mixtures. Even though the experimental data are scattered, one can see that the Ko-value of Gi-G2 and Gl-G4mixtures are higher than that of G1 on the average. Themixture. In other ¥vords, the addition of G2 particles intomeasured a¥'erage Kb-value for *"lass beads Gl is 0.375,while those for G -G. and Gi-G4 mixtures are 0.407 and0.399, respecti¥'ely. Since particles tend to align themselves ¥vithin the horizontal plane under gravity and a-( )L for GI-G2 mixture. According to Eq. (5)-), anincrease in ( , ¥vith fixed ( ,0 induces an increased Kovalue, indicating Kb-12>Kb-i. This is consistent with theexper'irnental data in Fig. 10(a). Herein Ko-! and Kb-12 are¥vell-defined horizontal bedding plane is formed, aKo-values for GI and Gl-G2 mixture, respectively. For() glass beads and Gl-G2 (,=:,,j ,i;i..i'i.,;,,), G -G4 (-'-*=G: causes ( )L to increase significantly ¥vith coo notchanging much,vhich in turn results in a decrease of ( )o^J iGUO AND STOLLE64sK0_1= O 407 (GI +G, )elo 45OsJA i .* AeQA * e AQ p ee,jeQ ,QA eA eee_'04vo.35,"_Q Q e06o 4{),G eC G(a)O-60o3o 48 12N'umber o il 6 20 24-oo3060Branch vector orientation ( o )testsso 45604:s 41-v7o 35o-60-J)OOBr* nch vector orientatio03o 412N Tumber ofi6estsKol･ 0407(Gj G,)cc c ccco 45co.4cvc c(c)03o 48 i 6 20 24i2Nunlber oi tes svith rough surfacetexture: horizontal bedding planeGI-G4 (Fi*o, Il, Distribution of branch vectors for G] and Gl-G. mixture: (a)branch vector length and (b) branch vector orientationaddition to the par'ticle shape, the distribution of contactnormal has significant influence on Ko-¥'alues.The influence of interparticle friction is investigatednext by adding a small amount of spherical G3 ( ･.,V･)particles ¥vith smooth surface into Gl particles ¥vith amass ratio of n7G3:nlGl= 1:2.23. Referring to Table 2,Gl-G3 (･"'," ･' 'i･*"'.･,' O) and CJl-CJ (Fig. 10. Experimental K0'values of glass beads60( o )Influellce of Intelpartic!e FrictionK0-14 = O 399 (G : G4}o 350Q) mixtures consist ofboth Gl particles and some spherical particles, G3 (V･･'･'･" ) orG4 (c), ¥vhich have different surface textures. Ho¥¥'ever,the amount of spherical particles in CJ -G3 mixture is lessthan that in Gl-G4 mixture.Figure 12(a), which compares the measured Ko-¥'aluesof Gl-CJ3 ( O) mixture ¥vith those of Gl, clearly sho¥vse) mixture, ho¥vever, the mix of spherical G4Ko-13>Ko-1, which is partially attributed to particle shapeinfluences. The results are consistent ¥vith Fig. 10(b) for(c) particles ¥vith non-spherical Gi Particles at a mass ra-Gl-G4 ( s e) mixture. Chan*'es of interparticle frictiontio of G4:Gj = 1:1 yields more uniform distributions ofassociated ¥vith the CJl-Gboth the direction and the length of branch vectors, vitha larger decrease of ( ,o than a)L being observed. Accord-ute to lar*'e Ko-13 values. Figure 12(b) sho¥vs that the Ko-ing to Eq. (52), the variations of ( ,0 and (,L ha¥'e oppositecontributions to Ko-¥'alues, ¥vhich may increase ¥vhen ( )ois decreased more than ( )L. As such, one may expectKo-14>Ko-1 t,hat is confirmed by the experimental datapresented in Fig. 10(b). A close examination of testresults for Gj-G2 and Gl-CJ4 mixtures in Fi**. 10(c) sho¥vsthat Ko-i4 seems slightly smaller that Ko-i2. Ho¥ve¥'er, sincethe data points are scattered, Ko 12 and Ko-14 can be consid-ered to be the same statistically. Since the anisotropyinduced by particle shape in CJ1-G2 and Gl-G4 mixtures isquite different, Fi_ . lO(c) further confirms that, inmixture, ho¥vever, also contrib-vaiue of Gl-G3 mixture is higher than that of G1-G4mixture. Takin*' into account that Ko-14 A'o-1=0.024,Ko-13 Ko-] = 0.057 and the Gl-G3 mixture has less spher'lcal particles than G -G4, Fi**. 1'_ implies that interparticlefriction associated ¥vith the surface texture of particleshas a strong infiuence on Ko-values. As one might expect,smooth surface texture, indicating small interparticlefriction, increases the Ko-values.Figure 13 sho¥vs the influence of particle shape andinterparticle friction on Ko-values by comparing themeasured Ko-values of Gj-G4 ('S) and G3-G4 (oe)mixtures, ¥vhich were obt,ained by adding Gl and G3 ,'',',i649K{) VALUE OF GRAN. ULAR +¥,1ATERiALo. 5)o 45604jo 35so.3o 412iai gauge(b ) Roller strrp(a}16N ulnber o r testsFig. 14. PrepaFation of specimen witll different bcdding planeorientationso^ 5):mixture, o¥ving to the presence of flattened Gl particles,one expects ( )L_14 0 since the branch vectors in thehorizontal direction are long:er than those along: theo_45vertical face. Sirnilar to the discussion for Fig, iO(b),fiattened G] particles may reduce the concentration of'04contact normal in the ¥'ertical direction, yieldingo. 3 5( )o-i4<(1,0-34. E¥'entually, the joint effects of ( )causes Kb-34>Kb-14, ¥vhich is consistent03o 412Influence of Bedding P!ane Orientation16For an ensernble of elongated particles, the direction ofNumber of teslsthe densest branch vectors is generally perpendicular tothe bedding plane lvith the iongest branch vectors mostlyF'ig. 12. Influence of interparticle friction on Koparallel to the bedding plane, indicatingo 55)05Ko h¥lfi0= 7T/l - (( ,0( ,L)/6 1A,,aJo/In(sin ,,)(53)When expanding the above equation Into a series follo¥vin_g: Taylor's theorem and neglecting the nonlinear termso.4of ( ,0 and (1,L. Eq. (53) simplifieso 35Ko-. = I + 2( )o [[1 - 3A,,o 4Kb-i,i216Number oi' testsFig. 13.L ='_. Referring to Eqs. (47) and (48), the ratio of' the Kovalues for ¥'ertical and horizontal beddin** planes can beexpressed aso-, I=[+ (( )a ( ,L)/6 1 Ji - A,,( ,a/In(sm ep,,)o.45o.3and ( ,0vith Eq. (52).lnfiueuce of interpartic:e friction on 1(: spherical particles3Jl _In(sin ep,,)23 coL (54)It should be noted that this simplification is acceptabieonly for ¥veakly to medium anisotropic materials with ( ,Land ( ,0 both having values less than approximately 0.3.Dependin*' on the magnitude of anisotropy associatedI{,particles into spherical G4 particles with approximatelythe same mass ratio (mGl:nlG4= 1:1 for G1-G4 and n7G3:mG4=0.82:1.0 or 1:1.22 for G3-G4). One obser¥'es thatK0-34 is approximately 200/0 Iarger than Ko-14. Figure 13generally sho¥vs the same trend as Fig. iO(c), since G3 andGl particles have the same surface texture and hence thedifference bet¥veen K0-34 and Kb-i4 can be attributed toanisotropy related to variation of particle shapes. Morespecifically, the anisotropy of G3-G4 mixture is merely dueto the directional variation of contact normal, becauseG3-G4 consists of spherical particles of the same diameterand hence the branch vector len*'th is identical in alldirections, ¥vhich indicates ( ,L=0. However, for Gl-G4with the direction and the length of branch vectors. Ko-+for vertical bedding planes may be either larger or srnallerthan Kc-h for horizontal bedding planes. Arhen ( ,L ratherthan ( )o dominates the de*'ree of anisotr'opy. Kb-* will besrnaller than Ko-h, otherlvise Kb-* is larger than or close toKb-h .In order to verify Eq. (54), a series of testsvere carriedout to explore the variation of Kb ¥¥'ith bedding planeorientation. As illustrated in Fig. 14, the ri**id cell wasrotated by an angle¥vhen placing glass beads into thecell. When the cell is rotated to the vertical position, thebedding plane makes an angle 3 ¥vith the horizontalplane. Angles of a=60' and 90''ere chosen in thisstudy. Durin*Kb compression tests, ¥¥'hen the bedding { ,CJUO AND STOLLE650G I particlesG I - G2 ml¥ture8 :: oVO.4o6 = 60L)-900o 456e:/ 0.4: o.35KO = O.416Ae6 = OLK()_12 = O.407o.35(b)o. 1)5 10 15ol¥ ' LI5 lOo2015l¥;umber of tests1 ber of testsG4 particiesG1 - G3 ml¥tuleo 55o.Ko =0_453ooo.4･7 o.4oOoc o o ooocOO l¥0-13 = 0.432co^ 5"*'0.45c!c{' jjco.4c 6 :: 60V_90 O0.3o.3lO i56 =: o()(d)c 6 = 6OV_9000.3oo.35o 6=0O(c)o4Fio. 15.8jl)16l¥jumbe ' of tests1¥1lumber of testsplane angle'cInfiuence of bedding plane orientation on Ko values= O', no deformation is allo¥1*ed ¥vithin theo 3bedding plane, ¥vhile the restraint to deformation isperpendicular to the bedding plane ¥vhen=90'.Figure 15 compares the measured Ko-values of CJI and G4particles as lvell as CJl-G2, GI-G3 mixtures at =0', 60'and 90'. Even though the data are scattered, one observesthat the A'o-values of CJ particles at =60' and 90' aresmaller than those at =0', ¥vhlch is consistent ¥vithEq. (54) since the particle shape and (1,L dominate theanisotropy of Gl particle ensembles. For G4 particle ando.3¥lo 25o 2the other t¥vo glass bead mixtures, the influence of bedd-oin*' plane orientation on the Ka-¥'alues is very small,indicating that the contributions of ( )L and ( )o to Ko¥'alues are cancelled ¥vith each other.In order to obtain the influence of fabric on the Ko¥'alues of engineering soils, one set of tests lvere carriedout usin_1' 4¥.6t mber of testsFig, 16. Infitlence of bedding plane orientation on the K rvalues of alimestonelimestone ag_ :regates, ¥vith the particle shapesbeing irre*'ular and ¥'arying randomly. As a result, thelength of branch vectors may not ha¥'e a preferentialdirection and the anisotropy is primarily induced byCLOSING REMARKSThis paper discusses the infiuence of fabric and particlecontact normal distribution. The results in Fig. 16 sho l'shape on Ko-values of cohesionless materials via aA'a-.>A'o-i,, ¥vhich is qualitatively in a'leement wrthmicromechanical analysis and a series of experimentalstudy. The main findings stemming from the study in-Eq. (54).clude:1. In addition to interparticle friction, the internal 彫κけV．へLUE OF GR、へNUL、へR M、へ丁狂R玉、へL65！ structure，IIlcludiagtheparticlesぬapeandtねe 揮∼’ノ∼9αノー1鯉．41−（伽θ‘』」5姻4茄∼9”rθθ’5，25，355−358． sP＆tial arrarlgement of partlcles（or par￡icleI l l Kゼuyt，N、｝）、aIld Rothellb疑rg．L （2004）＝｝くineΣna雛c alld sta｛ic connectMty），a仔ectthe輪一val旦esofcohesio王｝less ass穏mptio里1s for QmQgご感zadou1n micromechanics of graaular 111aterials，A／8cノ∼α．A／α∼（∼ノ’、，36， 1157一三173、 materials、Jaky’sequation，whichdescribesthe dependencyofκ。onfrictiollangle，isaPplicableto12）Mayne，P．∼V、alldKulhawy，F，｝｛．（王982）：κり一〇CRrelat沁11sllipsin soils wit負weak to medium fabric．13）Mi1chell、」、K，alldSoga，K，（2005）：F禰伽ηθ∼∼’αZ50ゾ50〃 2． The relation between1＜o−va茎ues and particle shape isnαullique，sillce出evariationofparticleshape may c紅ange particle connectivity and l｝ence brancb vecエors，w圭1ich has Qpposite e貸ects or1ノ＜o一∼’alues． soll，／、Gθofθ（ソz王∼∼91．∂h『、，ASCE，108（GT6），851−872． β8ノ∼‘ハブ0ノ甲，3rd ed、，∼V員ey．14） Ngシ 丁 丁、 （2001）： 罫abric evolutiQn of ellipsoidal arrays with di脱rentpar｛iclesllal）es，ノど11grg、．》θ（ゾ∼，、蓋27（玉0）．994−999、15）Okachi．Y，andTa【suoka，F、（1984）：Somefaclorsa9セc［ingκ。一 valuesofsalldmeasuredinεriaxialcell，So’Z5α11ゴFα’nゴαω’15， 3． τhe∫（o−values may be di鐸ereat wllen the deforma− 24（3），52−68， tionllormahothebeddingPlanelsrestrai簸ed16） Roes！er，S．K、（正979）：Aniso【ropic sklear Inodulus due乳o stress rather than thαt隻n tlle bedcl呈ng Plane、Elongated or Hattenedparticlestend芝oreducethe人（）一values allisαroPy，／、080’θ（・ノ1、五ノ∼9．OA『、，、へSCE，105（GT7），87i−880．17）RQthellburg，L and Ba芝hurst，R、J，（1989）：Micromecllanicai 妻leaこures of grar｝ular asse窺1blies with planar elliptical pardcles， when restraint to deformation is norm＆I to the G40’θcノ∼1∼’σ∼’θ，42（1），79−95 bedd至ng Plane． ｝｛owever， the joillt efiセcts of18）Ro、、e，P、∼V、（1954）＝、へs〔ress−s乞ra1n由eoryξlor cohesionless soil particle shape alld particle connectivity illay result wkh apPiica【ions to ear【h I）ressure at I’esτ and moving 、va難s， ineiξheranincreaseordecreaseofκo−values．In closing，it卜as been shown that the fabric of granular G60’θc／2’∼’σ∼’θ，4（2），70−88、19） Schmidt，B、（1966）：Discussion of“Ear【無…）ressure at res〔relaζed【o s1ress his￡ory”，Cαn、（？θo’θc1∼、ノ、，3（4），239−242、materi＆ls has signi負callt e疲ect of theκb−values，which20） Si111pson，B、（王992）：Reta1温hlg sτruαures＝disPlacenlen芝alld design，nlay vary over a wide raage depending on the sh＆pe and Gゴαθch1瞭昭，42（4），541づ76、spatia重arrangement of par亘cles as well as the direct重on＆longwhich deforr【1atio蓋1is restrained．The orientation ofthe principal stresses relative to the beddillg p玉ane also2i） Stokoe，猛、｝一｛、，Lee，S、H，aηdKIlox，D，P、（1985）：S妻1earmoduii measurementsul1（ler篭ruetriax1als！1’esses，■1グvαノ∼（一θ5’ノ∼’加、41Yo∫ 7セ5’〃19801なε’1∼4θ’『C∫c1’c Con4’∼10〃5 （ed、by Kilos！a）， 166−185， ．へSCE，Nロew York、plays a role ill establisぬlng aノぐ（）一value for a co紅esionless22）τerzaghi，Kmaterial．These蝕dings demollstratethecllallenges23）Tsukamoto，Y、，lshiわara，民、andNa撒ka，丁，（1998）：Undrailledf＆cing tlle engineer∼、・ith respec老to identifying meallillgful deformatiollallds｛re照thcharac韮eristicsotsoilfromreclaimedK。一valuesforadvancedstressallalysis．（1943）」加oノーθ1’cα1So’！・、／θc1∼α1r’c∫，Wiley，NewYork、 deposi芝s in Kobe，5ρθ（』’α／／55ど’θoゾSo〃∫‘∼1∼ゴ」Foμηグσ’10’∼5，47−55、ユ4） Zla【ovic，S、and Ishi翁ara，K．（i997）＝Norrnalized behaviour ofl very loose aQI1−plastic soils：E貸壱cts of fabric，So’Z∫α1κノ1＝oえ’1∼（ノα’10’∼5，ACKNOV㌧1］LEDG￡MENTS Funding provided by t｝1e Natural Science andEnglneering Researcll Council of Canada is grateful玉yackllowledged． 37（4），47−56、AやPENDIX Referr玉ng to］巳q．（26），芝良e Ilormεtl component of thecontact force at a given contact point can be expressed asREFERENCES1）Andrawes，K、Z．and三1−Sdlby，M．A、（i973）：Facζors a飴ctl夏1gκG， ／、Gθo’θc1∼、五’∼9’、∠）A，、，．へSCE，99（S氏・17），527−539、2）Bolミon，M、D，（玉991）：Geotec員nicalstressanalysisforbridgeand ab撮men【desigΩ，Coη’ノ｝αぐfoノ覗θpo’F∫270，CrQwthome＝Transl）Qrt and Road Research Labora｛ory，3）C員ar19，C、S．and Liao，C、L、（重990）：Cons［itutive rela巨oll for a particulatemediumwith由ee貸ヒctofpar芝iclero［ation，1n’、／．So1∫43五、一1in許σi諏！1klli（A1）with n being出e contaαnormaL For an ellsemble ofcylindrical p＆rticles，the branch vectors are il1出e samedirections as出e contaαnorma正s11．Referring to thenoξion of t盤e average length of brε貰1cぬvector1，the ex−pression ofll in Eq．（A1）mαy be rewrittenαs／1、4σ吉11inj，σ1‘一σ…k碍（A2） S’1−1’ご∼μ1一θ5，26（4），437−455．4）Chu，J、andGan，C、L、（2004）：Eぜec【ofvoldra［ioonκoofloose sand，G40’θch〃’σ肥，54（4），285−288w油σ謹being the“τransformed stress”，Equation（A2）圭ndicates that∫i、can be alternat呈vely expressed as5）Emer1au1〔，F、鍛d Cねang，（二、S．（1997）l In【er！）a至』［i￠le forces and displacements in granular ma乳erials， Co〃∼ρ財’、 （フεo∼θch、， 20（3），五、＝くノ1、＞［1＋α、、cos2（β一β，）1（A3） 223−244．6）Fioravan芝e， V、， Jamiolkowski， 汽・1，． Lo Presti， D、 C「、 F、， 1〉lanfredil11， G． and Pedroni， S． （1998）： Assessment of 【he coe伍cien芝of韮he ear［h pressure at rest flronl s｝1ear wa、・e velocity measureme搬s，060！8ch11ゆθ，48（5），657−666，7）Ha陰sson，∫．and Svensson，P、（200圭）：Stress disτributiQn i取 unbound a99regate of road s芝ructure：h1貝uellce of surface roほ9h− nessandparticleshar）e，β”〃．五n9．Gθ01、だ1∼y、，60，223−226、8）Harr，M．E、（1977）：A／8chα’∼1（’50∫Pα’』∫’α’1α’θA／θ4’α♪湘 P”o加δ11∫5”c、4ρρ1−oαぐh，McGraw−Hil1，New York．9）HObeda，P、（1988）：Krossn諭gens be｛ydeise pas｛enkvalitet，sarskilIwhereβ，，de負nes tぬe orientation of the maximum normα1compoRent of contact forces，く囲、＞is the average normalcontact force，α耳達（ie且nes the magnltude of（11rectionalvariation of local norm＆I contacξforces．It should benoted由at由e maxlmum value ofプ1，colncides with thenlajor principal traasferred stressσ挙It cεm be shown thatthe contact force componentsプ1＆nclフらcan be related tothe normal and tangential coataαforces via med avseende pa koraform：en正1tteraturstudie，State臓s Vag−odl Tra盤kins撤u【，VTlnotatV68，LinkΦing、10）Jaky，」，（1944）：Thecoe餓c1eRtofearthpressurea甘est，ノ．So（b、ゐ徽凶、COSθ＋五si難θ一孟、（COSθ＋tanψメ、slnθ） GUO AND STOLLE652The <fl>/<j > can then be determined according to Eq.f* cos(e - ,,)cos(A4) (34) as;'f'_ tan(e -,,)f Sln(eCOS'f ;!t) e;!'i,(A5)o, other¥viSe/ll sin(e-< f >< f._>,,)[1 -an Sin 2(e- eo)][1 - c;' sin 2(O- go)]clei - Sinan T con3 - (COS -' ,u + Sinil;!)'l:/2cos(e _,,)[1_an sm 2(e e,,)][1 a) sln 2(e e )]del-an + (Dn(cos q'!'For the case of isotropic or ¥veakly anisotropic materialsIt follo vs that for isotropic materialsin ¥vhich, (a +co*,)/3<< I the above equation may be( :Koisosimplified to<f > = aI - +sin co,,(cos 2 ,, + cosq,;' f.,,) (A6)sini,)3<, f I >)< f._> (A7)1 - sin"o,,¥vhich has the same form as Eq. (2) and is very close toEq. (51). | ||||
| ログイン | |||||
| タイトル | Multi-scale Physicochemical Modeling of Soil-cementitious Material Interaction | ||||
| 著者 | Kenichiro Nakarai・Tetsuya Ishida・Koichi Maekawa | ||||
| 出版 | soils and Foundations | ||||
| ページ | 653〜663 | 発行 | 2006/10/15 | 文書ID | 20948 |
| 内容 | 表示 ,,,r;,SOILS AND FOUNDATIONSVol. 46,No),653-663, Oct2006Japanese Geotechnical SocielyMULTI-SCALE PHYSICOCHEMICAL MODELING OF SOIL-CEMENTITIOUSMATERIAL. INTERACTIONKENICH:IRO NAKARAli), TETSUYA IsHIDAii and KOICHI lvIAEKA¥vAiii)ABSTRACTA multi-phase physicochemical method for simulating the durability of cementitious composites is used to predictthe long-term degradation of underground concrete and cemented soil by calcium leaching. The objective is to developa unified approach that can be used for both cemented soils and concrete. This paper describes a computational modelbased on physicochemical thermodynamics that can calculate the voids of micron-to-millimeter scaie in soilfoundations as ¥*ell as the gel and capillary pores of nanometer-to-micron scale in cement paste. The proposed modelsho¥vs that the soil-str'ucture interaction of calcium-1eaching transport and underground ¥vater ad¥'ection are ¥'eryimportant ¥vhen assessing long-term durability of cementitious composites.Ke¥_' Ivords: cement, concrete, (durability), ground ¥vater, ieaching, (physico-chenrical pr'operty), soil impro¥'ement,(thermodynamics) (IGC: E1?_)any assessment of the long-term durability of under-INTRODUC.TIONSoil and cementitious composites are the primaryground concrete structures.Cemented soils are nehv kinds of engineering mater'ialsconstituents of ground and infrastructures. Assessing thelong-term serviceability of artificial cementitious compos-that can be used to improve the ground, make use ofsurplus soil, and enhance soil-structure performance.ites coupled with natural soil foundations requires aExamples of such materials are cemented soil and gravel(CSG) (Hirose et al., ,_OO1) and geosynthetic-reinforcedcement treated backfills (Watanabe et al., 7_002). Theunified physicochemical model, especially ¥vhen targetingintermediate materials such as cemented soils. In thispaper, state variables f'or pores in hardened cementhydrates (nanometer-to-micron in size) are integratedcemented soils generally have high ¥vater-to-cement ratiosand contain large voids, and so are thought to deteriorateinto thermodynamic state equilibrium equations thatmore quickly than ordinary concrete due to calciurnhave governing formulae for ¥'oids (micron-to-millimeterin size) in soil particles. The multi-phase multi-scaleconcrete models are extended to the geo-environment andleaching from cement hydrates.In Japan, cemented soils must be tested for hexavalentchromium leaching before they can be used, despite theirused to assess mid-and-long term changes and fluctuations in the material properties of coupled soils andlo¥v cement content per unit volume. Research to date hasstructures (Fig. 1).cemented soils, and there has been little investigation oftheir long-term durability. Particularly needed is a studyof the properties of cemented soils rhat have voids muchlarg)er than the pores in cement paste.The primary objective of this research is to apply thethermodynamic coupled analysis system (Maeka¥va et al.,mainly focused primarily on increasing the strength ofConcrete is bein..*a considered for use as a barriermaterial to solidify radioactive ¥vaste for geologicaldisposal. Because such waste contains materials ¥vith longhalf-lives, the bar 'ier must rernain stable for several tensof thousands of years, ¥vhich is far longer than the1999, '_003; Ishida and Maeka¥¥*a, 2000; Nakarai andlifetimes of convent.ionai infrastructures under normaluse. Ho ¥'ever, the per'formance of these materials overIshida, 2006) that was developed for concrete to foundations ¥vith larger voids in the soil particles. This wouldcreate a single numerical analysis rnethod for evaluatingthe material qualities and pore environments of cementedsoils, non-cemented soils, and concrete.such long periods is difficult to evaluate solely by experi-ments or accelerated tests. These laboratory-scalemethods must be firmly tied to theoretical approaches ifthey are to pro¥'ide reliable assessments of design andperformance. Soil foundations form part of the naturalbarrier, and their characteristics must be considered inl)ll,iii)Assistant Professor, Department of C'ivil Engineering, Gunma University, Japan (nakarai( ,ce.gunma-u.ac.jp).Associate Professor. Department of Civil Engineering, The University of 'Tokyo. Japan.Professor, ditto.The manuscript for his paper lvas received for revie v on February 6, 2006; arjproved on ,Ia}' 29, 2006.¥¥frilten discussions on this paper should be submitted before N"lay I , 2007 to the Japanese Geo echnical Society, 4-38-2, Sengoku, Bunkyo-ku,Tokyo I 12-001 1. Japan. Upon requesthe closing date may be extended one month.65.J" NAKARAI654ConcreteCemented soil Soi] foun dationSoil Porosityce ment hydrate= ; "? ' ;' ; ': ;' " 1' ;;i ? iET AL' ';'SS SVoid among soilE'*Fig. 1.Extended thermodynamic s,stem to soii materials:Size, shape, mix proportions, Equation c!initiel and boundary conditions O : Degree of treedom' 1i i';'7;'--<'-"'-' "f"=' ' 'Temperatufe pofe pressure, concentration of CL. CO-. O. and Ca:'+Tem pe ratu e"'' __::p ressurej Bi-madeil Porosity=hydrationlevel PoreH andConcentra ior!s ;; dis ributionof eachmoisture ; oforasitycam onent interlayerdistriutione & bound ic loridese t.> Gasnd dissoive ;{ 02 cor!centra on irig. 2.Gas and dissolvedi CO. eo centf tion iOverail sci]eme of DuCOM cheru0-physical coupled s)stemTHF.RMODYNAMIC MODELING OF CF,MF,r ITTF.DSOILTllel'moc!y/7an7ic A/7alytica! Systen7The process of cement hydration at an early age iscritical as it determines the long-term properties of acementitious mater'ial. lvlaeka¥va et ai. (1999) ha¥'edeveloped a computational method capable of simulatin_"._multi-scale chemo-physical events in concrete during thehardening stages (Fig. 2). The analytical method consistsof a hydration model incorporating the heat generationand ¥vater consumption properties of cement po¥vders, aover the ¥vide range bet¥veen nanometer and micronscales.Mu!ti-sca!e Pol-e Srructure Mode!A consistent method for analyz,ing natural geo-materials, cemented soils, and concrete must be able to take intoaccount the intrinsic characteristics of the soils. O_ ne keyissue is that the geometry of pores can ¥*ary greatly(Fig. 3). Sandy soils have a skeleton of partic]es, ¥vithlarge airspaces (¥'oids) dispersed throughout the material.In natural cemented soils, ¥vater' and cement cannot fillmicro-pore structure development model. Se¥'eral ¥*erifi-up the airspaces. The connecting pores define the soil'smechanical properties and permeability.In this study, the analytical method incorporates a ne vcations have pro¥'en that these models can simulatemicro-structural component representing the lar Oeearly-age development processes, such as heat generationand moisture profiles, for ar'bitrary mix proportions andairspaces in cemented and natural soils (Fig. 4). Thismeans the expansion of the multi-scale analytical systemenvironmental conditions. In addition, the analyticaiinto the large pores bet¥veen micron and millimetermethod can be used to assess the long-term durability ofrelnforced concrete, including the penetration of chloridescales. The inputs are the pore volume and the a¥'eragepore radius, ¥vhich are set according to the target mixproportion and the properties of the sand. It is assumedmoisture transport/equilibrium in micro pores, and aions and carbon dioxide, the corrosion of embeddedsteel, and calcium-ion leaching (Maekawa et al., ,_003;Ishida and ilvlaeka¥va, 2000; Nakarai and lshida, '_006).The target of this analytical method has been thecementitious material ha¥*ing the fine pores distributedthat the micro-spaces in the large airspaces of the soil areoccupied by ¥vater and do not provide space for cementhydr'ates to solidif.v. The existing model statisticallyexpresses the general pore structure of cemented soil 照SOIL＿CE氏1…三NTITIOUS！q。へTER1。A．L至NTER、へCTION655the pore struc芝ure becomes nner with cement hydr＆tionMix proportions（in volume）and coarser with calcium leacbiag．For thevoids betweensoil particles，a new characteristic value，β、d，is incorpo−1鴨ated to represent廿1e pea鼓pore rad重しls of the soil．丁捻e菖eometric shape of the voids is assumed to be collstantirrespective of hydratior1． In other words， β、d is aC（）nstaL“t．Un−ce囎nted Cemented Soil ＄oiIConcrete八4正’1∼i−5cα1θA40’甜ε’ノ9θT1−αn5po1’∼ノ》04θ1 The flux of liquid condensed waξer in cQn乞inuouspores，denoted byσ1，can be determined by l磁egrating diespec量ac月ux of l圭quid water over the ent圭re pore structureuslng a random pore size（iistribation model（Maekawaetal．，2003）．lndependent airspaceConnected voids 瓢ゴv）2▽P （3）amongsandpa吐icles、v豆1ere，φ is the毛otal poros圭ty（no【 inc正uding inter豆a｝・e1’fig．3・Mix群oport蚤on蹄dvoldi獄so銭m貸皇e劇spores）lm3／m31＆ndηis the viscosity Qf liquld wate1’［Pa−s］．In order to consider tl｝e圭nfiuence of the pore sizeLarge alrspace（micrO∼mmscale）cOo』2Cement paste matrixコ』0、1（nano∼microscale） η一11・exp（舞） （4）狐の℃Φomhe moisture transport，the viscosity oギ、vater in capll−laryαnd gel pores of且ner sizes is calculated as fo璽lows．01Newt一．owhere， ’70 is 芝he viscosity of 重iquid water under i（iealconditio董1s［Pa−sl and O。is the add玉tional G玉bbs energyrequired for the flux of l圭quid water under non−idea正瓜00condiξious［kcal／moll．Forthelarge−radius voids between01Pso1I p＆rtic正es，t紅e additiQn＆l G重bbs energy， G。，can beE−」1 1．OE−9 10E−7 10∈一5 ∼OE−3assumed to bezero，meaningthat the intrinsic vlscosityo￡ Pore raωus（m〉bu至k∼vater is used．Pore dlst将butionFl9・4・MuM−sc田e pore s【rudure modelLEACHING MODEL（Shimomura et aL，1997）．The distribution ofnanometer− Although long−term deterloration of re圭nforced con−crete is caused mai撮y by steel corrosion，mec執anlcaIto−millimeter scale pores is represented by the followingdamage to the concrete ltself ls mostly caused by cbemicalpore density function、 φ（1。）漏φ、dV、・d（1噂）＋φcpレ｛cp（1一）＋φ9［Vgl（1“）＋φlr （1）events tha毛distort the cement hydrate solids．Th圭s paperdescribes calclum leachlng from cement hydrates（Flg．5），、vhich is a common problem wit熱concrete ancl cementedw封ere，φ、d，φ。p，φgl，andφ1，aretheporositiesoft1｝evoidssoils，The leach玉rlg of cεし1cium fro111concrete is a problembetween the soll particles，c＆pillary pores in出e cementpaste，gel pores，an（i interlayer pores，respectively，［m3／for the extremely Iollg−term serviceability of a radioactivem31，μ、、d（1・），V。p（1），αnd殊（1・）are functlons th甑specify thesize distribu芝ion of the voids，capi1正ary pores，and gelpores，respectivdy，as given by芝he follo、v重ng e（luatiol1，which is based on the assump重ion that the Raleigぬ一Ritzwaste depos重亙ory，for wklch use the由ermody服micinteractlon of the geo−environment段nd the underground￠oncrete is a crucial factor．Cemented soil is sometimes inconξilluous contact with groundwater．In such cases，亡hee岱eαof leaching on long−term durabllity needs to bedistr圭bution is ＆PPlic＆ble to each pore i，including 重hestudied．Slnce cemented soils generally have high water一neYv正y def崖ned vo量ds between the so圭1partic玉es、重o−cement ratios and larger vo圭ds than concrete，they are Vi（1｝）躍1−exp（一βi1’）thoughttodeterioratemorerapidlythanconcrete。 4レうi（1’）＝βiノ璽exp（一Biノ呼）41nノ’ （2）ルfαε3Coπ5「εrvα∼io7z oゾ「卜Cヤα！cど乙μηwぬere，βi is a porosity distribution parεしme宅er μ／m】， Momentum，energy，and痴e mass How of mαterlalswhich represents the peak of porosity distr玉bution on amust satisfy the laws of conservation．The following masslogarithmicscale．Forcapillaryandgelpores，theparameters can be c段lculated from the material propertiesconserva芝ion Eq．（5）is applied i勲terms of the totalcalc重um ions 量n the pore solution a勲d the soli（1−phaseof theむydra｛es．In the cεしlculations，the varying micro−calcium in the system，in reference to the equation bystructures are童aken into accoun毛in suc鉦a manner thatG6rardet段L（2002）． 『657SOIしCEM娠NTITIOUS MATER三AL正NτER、へCTION 84、0 ユα 3．5￡30器α 25 Porosity Sma巽 PorosltyLarge Tortuosity Large Tortuosity Small＞8烈 20三 歪5δト 40Fig・6・ IorIuosi重y of pores00P亀1・s轟，、、、，鴨・／m弓405（lshida and Maekawa，2000；Maekawa e宜aL，2003），thenux of ca圭clum lons transported in a porous media takes（a）the following form（Fig．5）．婦（竃1・むピ・沁・）・▽C㎞＋φ・S・u・C㎞（7）Fig。7（a）。駁odelingof重or重uos塁Iyfo罫ceme蝋p段sIe4、0where， Ωa、、。 iS average tOrtUOS重ty， δ撫，。 iS averagecons毛riαivity，Z）i。，is重he di仔usion coef丑cient of a calciumion［m2／sl，▽T＝［∂／∂κ∂／∂y∂／∂婿is the Nabla operator，and uT圃ガ正バ凋is the velocity vector of a cα1cium lou重ransported by a solutiou fまow lm／s】．The capi11＆ry and − 〉ぺ切で⊂㎝gel pores in the cement pasεe and重he voids between theのsoil particles are trea毛ed as量on traasport pathways，段nd＞t勤e authors assume that no ions are trausported in thelnterlayer pores ln the cement paste （lshlda andMaekawa，2000；Maekaw＆et al．，2003）．Tbus，theporosity，φ，can be expressed bythe fo玉10wing equation．φ＝φcp＋φg汁φ、d（8）3．53．02．52、0のoコ1、5ト1．0to0001 0、2 0．3 0、405P・r・sity，Φvdlm3／m31 The丘rst term of Eq．（7）represents the compo【1ent of（b）di建usion driven by the conceutration gradient，whi里e t紅eseco【1d term is 童he component representing ＆dvect量onFig．7（b）。Modeling ofωrωosity for sanddriven by the flow of condensed liquid water ia the pore．The veloclty of t紅e calcium ions rela業ed to advection isassumed to reHect the bulk motion of the玉iquid water andto−cementratiosorleachedcementpaste．Forsoi玉is determined from the transport model for the liquidphase．The dlffusioa coe銀cient of the calcium lons isthe degree of compaction（Van Brakel et aL，1974），ThisexpIlessed by Einstein’s theorem belowl λ…。nmateri＆1s，由e value depends Iargely on the soil type aωwi正1be t紅e case for cemented soil，as weli．Here，it isassumed that重he tortuosity can be identi丘ed simply in D…。n；R・T・ （9）terms of the porosity of cement paste or soil particles．where，R ls the idea正gas consta煎 ［J／mol−K】，T isexpressed by the effective porosity，φpa，【，，as g量vell by z嘉、・戸absolute te組perature IK】，λi。，量s tぬe molar conductivi重y ofan ion ls鷺i2／mol】，zi。，圭s the ion va玉euce，and F is theThe重ortuosi重y of the pores in the cement paste，Ωpa，、。，isEq．（10）（Fig．7（a））シwhich is del’ived flrom the experimen−tal di狂usion coefaclent of c強10ride ions（Maekawa et al．，F＆radayconstantlc／moII．2003）．The重ortuosity of the voi（1s in tむe soil part圭cles， The transpo践properties of ions ln porous materia正s，Ω、、d，ls also assumed to be formulated in the same mamersucb as concrete and ceme貰1te（I and natural soi里s，depe薫1das the poros嚢y，φ、・d，as given by Eq．（11）（Fig，7（b）），withon their pore structures．III this s重udy，the pore struc芝urereferencetoVanBrakeletal．（1974），is computationally char＆cξerlzed by porosity，degree ofsaturation，tortuosity，and constrictivlty（A重kinson et aL， Ωpa，【ご際一L5tanh｛8。0（φp＆，【。一〇．25）｝＋251984）．Tortuosity is （ie且ned in terlns of porosity，εしnd φcp＋φglconstrictivity by the pQre radius玉n the proposed mu重ti−scale analytical system． φpa，、e； （王0） レpas【巳 Ω、d憲一1．5tanh｛4．O（φ、，d−0．15）｝＋2．5 （H） In this study，the tor重uosity factor，9，expresses theincreased length of the actua正 ion tl剛ansport pathwayaccordiag to the tortuosity of the pores （Fig。6）、It isξwhere，φp、、【。is伽e ef罫ective porosity tha亡is the sum of thegel and capillary pores acting as ion transport pathwayst紅ought to be higher for cement paste w圭th nne pores andper unlt volume of cement pas｛e lm3／m3】，and vp、、【，is thelow water−to−cement ratios，and lower for larger w謙er一unit volume of cement paste lm3／m31．For materials such NAKARAI658ET AL.li;S S# {1*s'+_{>1J ol;*== ;, 'l=" == = '5=: I _osc:o ;ol lc:oo =<'1 OoIFig. 8. Constrictivitl.' of pores-10 -9 8-675-4 - 3 2(r 5 k[m])iogoFig. 10^Mode!in"of constrictivit¥.05Pe k radius¥t:: 04al¥{: 03;)/ 1; J>o j-5 O 2.oFlo 9. E,ffcct of electrostatic FepulsionD- alprorninent¥-10-9as cemented soils that contain both pores in harcienedcement paste and ¥*oids bet¥veen soil particles, thelt =/r}ter8ctions areOOmacroscopic a¥'erage tortuosity is determined b¥_' simply/ llFine pore in which/-8/-lCh nge of porosity distributionwith ch nge of pe k radivs-65iog(r[rr]j)Fig, 11.Porosit,. distribution and peak radiusassigning ¥veights in proportion to the por'osities inpoi'e connectivity and the poreEq. (12).oQ*.* = -- " ".*t.' - c**i(c*..Lc l)Q,**i (i_,)c*p + cgj + c.dThe constrictivity is then formulated in order toexpress the effect of the pore connectivity and the electric6i=0.39)tanh 4(lo*(!P'k) 6 ,)040) (13)6i = O for r **k < ac*changes on the ¥valls of the micro-pores during masstransport (Fig. 8). Porosity and pore size distribution¥vere considered by Van Brakel and Heerijes (1974). Poredimensions are thoug:ht to be the main determinant ofconstrictivity (Atkinson et a]., 1984). Van Brakel et al.,'ail effect is expressed asconstrictivity. The constrictivity of the pores in a cementpaste and the voids of the soil particles are defined as afunction of the peak pore radius by Eq. (13) (Fig. 10).* -2'¥vhere, rP*"k is the peak pore radius [m] and ac** is an iondiameter parameter for calcium ions=0.6 x lO9 m. For(1974) and Peterson (1958) reported a significant range ofparameter ,'P"k, the peak radius of a capillary pore isg:iven in the case of hardened cement paste, ¥vhereas forconstrictivity, with a ¥'alue of about O.8 for ordinarythe ¥'oids bet¥veen soil particles, the peak radius of' theporous materials, ¥vhile Atkinson et al. (1984) r'eported a¥'alue of about O.OI for fine pores in cement paste. Poresvoids is used. These ¥*alues are determined from thein cement paste are distributed ¥videly over thenanometer-to-micron range, and pores of differentdimensions are mutuall _' connected in a random manner,The average rate of ion transport is thought to be lo¥ver infine pores due to the interactions bet¥veen the ions and thepore walls as ¥vell as to the smaller size. E.lectr'icalinteractions bet veen the ions and the pore ¥ +alls ha¥'einverse of the pore distribution parameters, B,p and B d,respectively. The peak pore radius, as a parameter in theRaleigh-Ritz distribution, does not directly express thefine pores in ¥vhlch interactions bet¥veen the ions and thepore ¥¥'alls are prominent, but it does determine the shapeof the pore size distribution (Fig. 11). In this study,constrictivity is modeled in this simplified manner as afirst approximation. In the future, a detailed study ofsmaller the por'e size, the greater the infiuence (Fig. 9). Instatistical processing for pore connectivity ¥vill benecessary. In addition, the ion concentration is ansoil voids lvhere the pore siz,e is much larger' than the ioninfluential parameter that also needs to be taken intoradius, the electricai interaction is relati¥'ely small.account (Sato et al., 1995). For materials such asConsequently, the absolute size of mutually connectedpores seems to be the dominant factor behind ion trans-cemented soil that contain both cement paste pores andport.In this stud.¥', the reduced mass transport caused by theis determined by simply assigning ¥veights in proportionbeen cited as a mechanism for' this (Sato et al., 1995); thesoil particle voids, the macroscopic a¥'erage constricti¥*ityto the porosities. rSOIL-CE IENTITIOUS ¥. , ATERIAL INTERACTIO ¥'Table l.659Mix. proportions for cemenl paste and cemented soilUni mass (kg/rn ) VoidsPorosit¥'¥Vater Cement Sand ("' at 7 days (', )l¥: o ¥¥* I C" ( ･ )612O 22O79 1706P50 50s50 5012231573,-26Cemented sandDeionized water Specl men'l2Cement pasteCondition of surface of specimen before immersion tcstsFig. 13.Deien zed w t8r, 4-SPeeime1 om O Imv; 5 x Ocrn *400:5Experiment and anal)sis for immersion test200coo3=, . = (c'P*c,.[)6 >p***=c*p + c l + c*d¥vhere,c.d8,,[ l cerTlented SandE3aoEAnalysisEx perimentFig, 121: 100( 1 4)(1):oCQQ)Jp,**t* is the constricti¥'ity of the pores in the cementOcement paste/ ;i/'_1' Ifl" ';/ i llltr '+' i _._'_ -,L..__--1o lo 20 30405a60Time (day)paste and 6.d is the constr'ictivity of the voids bet¥veen thesoil particles.Detel'ioration of Micl'olpol es by LeachingIt has been reported that the leaching of calcium leadsto a coarse pore structure in cement paste, which mayaccelerate calcium leaching. This study takes into accountthe incremental changes in the amount and size of thepores caused by the dissolution of calciurn hydroxide andC -S-H gel. The changes in the pore structure andFig. 14. Leached calcium from cement paste and cemented sand in theexperiments3EEOo::s600)400e'moisture re-distribution due to calcium leaching areJ::calculated by using the increased pore size and volurne inCQ(vthe existing thermodynamic coupled analysis systemQ)(Nakarai and Ishida, '_006).800// /i200>oSLeaching oj' Ca!ciuln from Cenlented SandIn order to cornpar'e calcium leaching from cementpaste with that. from cemented sand, cylindrical testcemented sand l,cem i'en:ANALYSIS OF CALCIUM LEACHING_l r/ i:sOFig. 15.1/____'/'"'-Ai_l't_ ast,,_,{ _ =* */*l.;o io 20 30 405060Time (day)Cumulative leached calcium in the experimentsspecimens of cement paste and cemented sand ¥vereprepared and subjected to an immersion test. The waterto-cement ratio ¥vas 500/0; the mix proportions are shownin Table I . The amount of calciurn ions leaching into thesolution lvas measured. The cylindrical specimens ¥verethat leached. The amount of calciurn that leached becamezero every 1 5 days ¥vhen the ¥vater was replaced. The totalamount of calcium that leached from the cemented sandwas larger than the amount that leached from the cement50 mm in diarneter and 100 mm in height. After sealedcuring for 7 days, the top and sides of the specimenpaste, in spite of the fact that, at initial immersion, thesurfaces (but not the bottom) ¥vere coated ¥vith rubber,and then immersed in deionized ¥vater at a liquid-t.o-solidsmaller volume of pores than did the cement pasteratio of I to 10 by volume (Fig. 12). The lvater ¥vas stirredat intervals of a few days and replaced every 15 days. Theconditions of the exposed surfaces before immersion aredescribed in Fig. 13. Large voids ¥ver'e visible in thecemented sand.Figure 14 sho¥vs the amount of calcium that leached, asdetermined frorn the chan*'e in the concentration in thewater. Figure 15 sholvs the cumulative amount of calciumcemented sand had smallel' quantities of cement and a(Table 1). The volume of pores is the sum of the volumeof voids bet¥veen the soil par'ticles (determined durin*'mixing) and t.he volume of gel and capillary pores in thecement paste at the age of seven days (as calculated in theanalysis) .A simple one-dimensionai analysis ¥vas carried out(Fig. 12). Input data such as mix proportions andenvironmental conditions ¥vere based on the experiments.While the porosity distributions in the cement paste over NAKARAI ET AL660/a)FF:s/Without advection1400 - - With advection /; / /cemented san/ r ::: I O 4m/cement300pe kz5a;o2001::e)coJ(Ipaste ¥' /--_ '##1 oo//"..¥''¥･ *H> Specimen(D"1u) 1010lu)e)'oQ)'ffl/// /j cemented sand1005l(Ur = I a rme)Water1015Q)*o 1000oCLO I O 20 30 40 50 60-O 05 O OO O 05-a loTime (day)Fig. 16. Leaehed calcium from cement paste and cemented sand in theo loDistance from surface(m)Fig. l?.Distribution of pore water pressure in the sensitivity anal) sisanal) sistime ¥vere calculated, the porosity of the ¥'oids among thesoil particles ¥vas a fixed value determined from the inputdata. In order to reproduce the conditions of the immersion test, an analysis of calcium ieaching, taking intoaccount the concentration gr'adient in the ¥vater aroundthe specimen and the decrease in the concentrationa)>oO>:O: =1 E-7! Cemented sand (r =10 m)'P==k(1)'-radient as ions leached into the ¥vater, vas carried out byQ,connecting the analytical elements representing the:Sdeioniz,ed water. To take into account the effects of threedimensional diffusion in ¥vater as vell as stirrin_"*, thediffusion coefficient of the calcium ions in the deionized¥vater ¥vas set to a value ten times larger than the value inOfree ¥vater. The analysis did not take into account thereplacement of the ¥vater.1 E-5 1 'S(1)1 E-1Cemented1 , sandp==*(ri ,:::::,=TIE-i3 Cement paste,=10 'm)- *i1 E-1 5 io.ooO 02 O 04 O.06 O.08o 10Distance from suriace(m)Fig, 18. ¥_ ioisture fiolv velocit) in sensitivity anall. sisFigure 16 sho¥vs the results of the ana]ysis. Thecalculated results for still ¥vater' ¥vithout advection ¥verecompared first. When the cemented sand ¥vas assumed tohave a fine pore structure comparable to that of thecement paste (peak pore radius: 10-' m), the amount ofcalcium that leached from the cemented sand ¥vas muchsmaller than the amount that leached from cement paste.This is because the ¥'olume of pores and the cementcontent per unit volume are both smaller. On the otherhand, in the analysis that considered the scale of theconnected large voids in the cemented sand (peak poreradius: 104 m), the amount of calcium that leached lvashigher due to the greater diffusion coefficient. Theseanalytical results demonstrate the absolute necessity oftaking into account the characteristics of the pore structure.Comparing the results of the analysis ¥vith those of theexperiment, ho¥ve¥'er, reveals that the amount of leachedcalcium ¥1*as underestimated. The reasons are thought tobe the effects of leached calcium from the sand grains andthe effect of advection due to stirring. In a preliminaryexperiment in vhich the same quantity of sand alone ¥vasimmersed for 15 days, about 80 mg calcium ¥vas leached.This means that sand in_"..redients can leach, but only to alimited extent. In order to maintain a constant concentration in the immersion solution, the solution ¥vas stirred.Because the pore structure of the cemented sand used inthis study ¥vas very coarse, this stirring may ha¥'e causedadvection ¥vithin the specimen, ¥vhich may have accelerated the leachin of ions.To look into this, a sensitivity analysis to determine theeffect of stirring ¥¥'as carried out by applying a smallpressure gradient to the inside of the test specimen in theout¥vard direction, as sho¥vn in Fig. 17. A ¥vater headdifference of O. I mm per 100 mm of depth ¥vas applied. Inthe cement paste and the cemented sand, ¥vhich ¥vasassumed to have fine pores, the ¥vater permeability ¥vasfound to be lolv and there vas practically no transport of¥vater (Fig. 18), so there lvould be no effect on the amountof calcium that leached (Fi**. 16). More specifically, underthe small pressure _9:radient used to simulate stirring, therevas practically no advection effect, and the transport ofions in the specimen lvas governed by diffusion alone. Itshould be noted that the cemented sand had high ¥vaterpermeability and sho¥ved significant transport of vater(Fig. 1 8), ¥vhich resulted in a sharp and high-level increasein the amount of calcium that leached (Fig. 16). Thisconfrms the need to carefully examine the experimentalconditions for their effects on advection, e¥'en though theeffects mav_ be minute. It is also vital to examine thedurability of cemented soil under ground¥vater fio¥v. Todate, no firm conclusions have been dra¥vn re_"*arding anyof these effects, aithough studies ¥vill continue. 「66圭SOIL−C薮！㌧「1薮NTITIOUS！〉1．へ丁嚴R王．へL五NTER、ACTION12A Concrete wltho磁soil Concrete 瓢a鼎，1、職，…騒翻．9 10驚B Concrete with soiIL ∈ ヨ醸 2 翻 ＼ 置 圃 O、8 Soil Concrete圏 麗 囲 rWith soil ’＼ほ ，” VVithout soiIIδ 06鳶50m＄urvey TargetoblectQ o40 0 2の0，5m黛Analysiselemen重s00Figほ9．Analys量s重arge傾ndeiements Concrete footing（WIC讐50％） 膣 Measurement 一……一一Analysis0，00 0，01 0、02 0．03 0、04 0．05 006Dintance至rom surface（m〉夏able2．Mixpropor亘ionsforconcre乳eFig，20， Disεribution of residu謡solid鱗帥ase calci臓篁n r＆〔io w／c Unltmass（kg／m3）No、 （％） WaIer Cement Sand GravdD55 55170309799 1104コ》 300∈∈ 25五θαchiηg oゾCα1ci‘’1η∫ン’01ηCθ〃1θ1π’∼io〃5Co1ηρ05i∫ε5in！o∼hθS乙〃γoμ1∼61i1∼g G11’oμ1∼‘13で 20σ躍 15 The effects of the surroundh199round on the Ieachingof calcium from concrete were analyzed by applying thesite structural survey proposed by Yokozek圭et＆L（2002）、墓to aηo正d underground concrete footing for a four−storiecl、⊇buildillg constructed ln1929．Concrete samples weretakena【4mbelowthegroundsurface＆ndatabout70cm⊆： 歪0、9E… 5Q一一Analysis without soil 1−Analysiswiths。“ rr ／碧 ／ξ i ／ 頚 ／ 頚 ／一H→ 〆〆〆 Soil l Concrete ＿＿＿一一’〆 蓼￡ 0ΦConcrete footing（WIC鷲50％）一5 一4 −3 −2 −1 0Dlntanceデroms麟ace（m）below the groundwater leve1（Fig．19）．The mix propoトtion of the concrete w＆s estimated from the compressiveFig．2LDis｛ribuほon of騒quid−phase c田cium ionstrengt｝1．Table2shows the results of an exanlination ofthe samples．The amount of calcium and silicon weremeasured using an energy dispersive X−ray an段lyzer Figure20shows the ratio of measure（玉and an＆至ytica至（EDX）．The remalning caicium ratio for the solid phasedlstributions of the remaining solid一凶ase calcium for thewas determined using two types of analyses：one analyslsunderground structul『e． Tbe ratio 玉s calculate（i bydlviding the amount of residual solid calcium by thefocused ou the concrete itself，while the o重her examinedthe interaction of the co烈crete with the surrounding so且found＆tion． In由eanalysisof重heconαe芝ealolle，thecoacentrationaverage amoullt of solid calcium in the non−leached p段rt。Figure21shows the dis書ributioll of Iiquid−phase calclum玉on concentrations in the ground and structure（analyzedof c＆1cium in the ground was taken as the boundaryva正ues）。The coup至ed analysis of the interaction of thecondition at the concrete’s free surfaces．The spec重且edconcrete with the surrounding so圭l foundation procluced avalue of1．3mmol／l was measured imhe groundwater in亡he v玉cinity of bui至ding．In童he＆nalys圭s of the interactiondegree of deterioratloa that was closer to the measuredresults tれau the one produced by the＆na正ysis of3ust雛1eof the concrete and the surrounding ground， the soiIconcrete（Fig．19）．As can be seen ln出e coupled an＆1ysis，elements were combined with芝he concrete elements．Inthe concentration of calcium in the ground increasedbecause of mass trαnsport from inside the structurecoasiderationoft虹edepthoflo録di伽slon，thethicknessofthesoileleme麗s∼∼7assetto5．Om．Slnce由erewereno（Fig．21）．The surroanding grouad mαkes the concent影a−datα on the details of the ground proper重ies， it wastion gradient small and reduces the rate of calciumassumed to be ordinary sandy gl齢ound without cemellt．Ieachin9． The m＆ss 宅ransport interaction is vlta至 forBaseci on the assumption，the porosity and peak poreratiollally assessing Iorlg−term calcium leaching and theradiuswerede肋edas35％andLO×10㎜4m，respec−subsequent deterloratlon of cementitious composites in atively．The effective di狂usion coe伍cient of a ca圭cium ion，foun（1ation．includ宝煎g tortuosity （Eq． （11）） and constric重ivity（Eq．（13）），as determlned from these set vαlues，w段s∠、θθぐh’ng wi1h G1’oμηグ／垂450’わillg C‘716iμ1η／011scalculated to be5．9×10覗m2／s in重he soil elements。 In orcler to analyze the ef董をct that ｛he sur1loundingMoisture traasport of the groundwater was Iloξa factorground had on leach宝ng Nvhen the ground was重reated as asince completely saturated states∼、・ere assumed lnanalysis．boundary co隻1dit玉on，a coupled ana至ys宝s of the surround−lng ground and the water environme虚was carried out i=NAKARAI662ET AL,labie 3. Mix proportions for cemented soilNo. ¥V/C _Unit mass (kg/m3) _ Voids; ¥¥rater Cement SandB I OO50l OO150 1000 40 O2 Ox 10'With soil (NO adsorption)EOEEE1,* +-5xi 06/ '.+t ,/ '¥,t/ With soil1 OxlOe:SCemented soil5 Oxl05O:{Cemented soil (W/C=year exposure)Opure water(Adsor ption)With WaterCQA With water...1/roo(/)o olo ooao'l,)o 03o 02Distance from exposure surface (m)BWith soil (without adsorption)Cemented soilJC. With soil (with adsorption)Cemented soilMO.Im-:sCQoooo/e)W'th so'l .(AdSorption)Withsoil¥¥(NoadSorption). =Wlth¥Water" 'i* *,,105O"20E:sC52 Oxl OScemented soil (Wlc::1 ye8r exposu ei5,Flg 22. Analysis elements30oEE 25102.0mDistribution of residllal solid-phase calciumFig. 24/-o 4-O 6-o 2OODistance from exposure surface (m)5 1 5xl06EEFig. 25.Distribution of liquid-phase calcium ionE I OxlO*:;taken into account, the cemented soil deteriorated to aC5coo 50xlO'1cio oOO5 1 O 1 5 20 25coCalcium ion in liquid (mmol/1)Frg 23. So!id-liquid equilibrium relations(Fig. '-)-). The subject of the analysis ¥vas cemented soil¥vith a water-to-cement ratio of 1000/0, c d of 400/0, and apeak pore radius of 106m. The mix proportions arelesser degree than in the case ¥vhere the specimen ¥vas incontact ¥vith ¥vater. This is because the ¥'olume of poresacting as ion path¥vays was reduced. When adsorptionwas taken into account, deterioration developed rapidly.This is because the pores in the ground maintained a lo¥vconcentration of free calcium ions due to the adsorptionof ions and the constantly high concentration gradient inthe cemented soil. These results agree ¥vith past results:cemented soil exposed to clay ground deteriorates fasterthan cemented soil immersed in fresh ¥vater (Ikegamiet al., 2004).listed in Table 3. After sealed-curin*' for seven days, thespecimens ¥ver'e exposed to deionized ¥vater and the'_round environment (with and without adsorption)(Fig. 22). The ground ¥vas saturated, non-cemented soil¥vith a ¥vater content of 600/0, a cvd of 600/0, and a peakCONCLUSIONSThe multi-scale computational system for concrete isextended to cemented soils and used to predict long-termpore radius of 106m. Adsorption was taken intofunctionality under moisture-rich conditions. Theaccount by adoptin_9: a simple linear equilibrium adsorp-micron-to-millimeter scale void structures of soils and thetion cur¥'e, as sho¥vn in Fig. 23. The amount of ionsadsorbed ¥vas determined according to examples takenfrom past research (Usui et al., 2005). Figure 23 alsonanometer-to-micron scale micro-pore structur'es ofcement hydrates ha¥'e been integrated into a singlesho¥vs the solid-liquid equilibriurn curve for the soundportion of the cemented soil at the age of one year.Figure 24 shows the distribution of solid-phase calciumremaining in the cemented soil one year after exposure,¥vhile Fi9:. '_5 sho¥vs the distribution of liquid-phasecalcium ion concentrations. When adsorption ¥vas notmulti-scale theorem. Focusing on the geometricalcharacteristics of pore structures, Iarge-scale voids of soilparticles, including cemented soils, were stochasticall"vmodeled and a thermodynamic theory for state equilibri-um ¥vas de¥'eloped. As for calcium leaching from bothcement paste in concrete and cemented soil, the absolutescale of the pores ¥vas extensively studied and experimen-j 663SOIL−CεへIENTIT五〇USき1．へTER1．へL玉NTER．へCT至ONtal正y ver至丘ed，as wαs t麺e ro王e of pores as ion pat瓦ways．The proposed computational scheme and sensitlvltyall＆lysesmakeitclearthaUhecouplillgofulldergroundconcrete、vith the surrounding foulldation is cruciεtl forrat玉on＆lly assessing the service life of structures ＆ndground e臓v玉ronments． T｝le advection of undergroundwaterwasαlsoquantiHedandrecognizedasαc面calfactor in determlning the extremely long−term service＆bil−ityOfSOil−StrUCtUreSyStemS． degradation process of cenlenししrea〔ed sQil．P”o（『■ノρ’z、CY、1〃∠三ノ∼9’召， Soc．，〔59−3）．1073避G74（lnJa1）anese）6）互shid＆，T、alld Maekawa．K，（2000）：All imegra【ed compu乞a［iol1εd systemfQrmass／ellergygelleraτlon，職1spor【，andmごchanicsQt 貸laterials and s芝rucしures，Co’∼cπ∼’θ五1ひ1一α1二、・q〆一／5C五、Jaぎ）an Socie芝y of C1vil EΩghleers，（36），129−144，71N至aekawa，K．，Chaube，R Palld Kisねi，丁・G999）＝ご、40‘ノθ〃i／1goゾ Co〃c’署∼8Pθノ∫o〃1∼α1∼cθ，E＆FN SPON．LoadQn，1999．8） 汽1aekawa，冠．，Ishida，Tξ逸nd Kfshi，T、（2003）：燕lui吃f−scaie nlode莚ng of co三1crete r）erformance−lntegra【ed maεe互’ial and s乞ructural mechal1玉cs，／．4‘1y．Co1κ7’θ’θτθごh’∼o！．．1（2），91−126，9） Nakarai， K．， Ish1da， T，a職d N玉aekawa， K，（2006）： へlocleling ofACKNOWLEDGMENTS The authors express the圭r sincere apPreciat玉on to I∼厘r．S．Nakaae and Mr．T．Usui for the experiments allddiscussions． This study was financial豆y supPorted byGra飢一in−Aid for Scienti且c Research（S）No．玉5106008，ancl YouPg Scieatists（B）No．16760358． ca1〔：1um leachlng fronl cen〕ent ｝1ydra｛es coupled wi【量1 登董icro−Po「e fQmla【ion，ノ、ぜ4‘1v、C「o’∼（一1烈θτθ（｝ノ∼1∼0／、，4（3）10）Pe芝erse【1，E，E．（1958）ID澄lusioni駿al）oreofvaryingcrossseαion， ．4、∫ C11、五、／、．4（3），343−345、11）SatQ，H、，Yui，M andYoshikawa、棄｛、（1995）l D滑uslonbehavior for Se and Zr in sodium−beΩ｛on1【e．P’『o（一，A／α’θヂ、Rθ5、Soご，Sダ1∼∼ρ．， 353，269−276．12）Shimomura，Tand Maekawa，K、（1997）：Anaiysis of由e drying sllrhlkage behavior Qfl coΩcre｛e us1ng nlicro nlechanical nlodel basedon〔hemicropores【ruct乳圭reof−collcre［e，瓶’9礁1∼θqブREFERENCES1）A【kinson，A．andNickersol1，A．K，（1984）：τiledi伽sionoflons τhroughwa［er−sa膿aζedceme蹴，ノ．A／α’81’、Sご’、，19，3068−3078、2）Bui1，M、，Rever芝ega！，E、and Oliver，，1、（1992）：A model ofエhe Coノ∼c・1祈fθRθ∫θαノ・ch、49，（181），303−322、13） Usui，T，，Isま1ida，丁，，Nakarai，K、andSak1窺1ura，T、（2005）：Calci貝窪｝ 1eaching ar｝田ysis co糠pied with bentoni￡e and surrouding soil，P’』o己 ノρ’∼、Co1∼（7−θre1’15’”￡f’θ．（27）（lnjapanese）．14）VaD Brakel，J、aΩd Heer芝jes，P、NI （1974）：、へnalysis ofd1αus玉oIl in auack of pure wa［er or under sa韮ura【ed l三me solutions on cement， macroporous media i員 【ernls of a porosi｛y． a 芝ortuosity and a 、へSTl〉I SτP 1123，227−241、 cons【rlc【1vi｛y faCtor，／ノπ．／、旋α’αノ∼4Mα∬T’『α1r5卿．蓋7，3） G6rard， B，， Le Be｝lego，C． and Bernard， 0、 （2002）＝Sim｛）h負ed modelingofcalciumleacぬingofconcretein、’ariousenviro臓me瓶s， A／θ！θ∼’αZ5α’∼ゴ3〃・召c’μ∼θ5，35，632−640． 豆093−1103、15）∼Va乞anabe，K，andτateya滋1a，氏1、（2002）：Shaking［abie｛es芝s on a Ilew type bridge abutmellt w琵h geogrid−reinfQrced cenlent treated4）Hirose，T、，Fulisawa，丁，，Nagayama，1、，Yos短da，H．andSasaki， T、（2001）：Designcrlteriafortrapezoid−shapedCSGdams，／ノ∼r、i6）YQkozeki，K、，Watanabe，K、，Furし【sawa，Y．，Daimon，M、，0τsuki， Co’η！ノ∼、ムαヂgθ0α〃1∫2001μ10rん∫hoρ，Dresdel1． N、aΩd Hlsada，M．（2002）：、へnalysisofoldstrucmresandaumerical5） Ikegami， ∼q．， Saτo． H、， 1chlba， T、， 0亡sロki， N．， Nis1琵da， 丁、 modelfordegradaεloηGfcoacreζebycalc紺m1onle霞cllil！9， τerashi，氏’LandOish1，K、「（2004）ISiml）li昌edpredictionmethodfor Co・1α’αθ乙め1”α1ヲ？1’∼’・・（40）・209−22匝・ back聞，P1｝oc、7’h1ノ∼’、Co’∼ゾ0θoεソ1∼’11．，Nice．L | ||||
| ログイン | |||||
| タイトル | Viscous Property of Loose Sand in Triaxial Compression, Extension and Cyclic Loading | ||||
| 著者 | Takashi Kiyota・Fumio Tatsuoka | ||||
| 出版 | soils and Foundations | ||||
| ページ | 665〜684 | 発行 | 2006/10/15 | 文書ID | 20949 |
| 内容 | 表示 ,SOiLS AND FOU*NDATIONS¥'ol_ 46, i¥'0, 5. 665684, Oct 2006Japanese Geotechnical Societ}VISCOUS PROPERTY OF LOOSE SAND IN 'TRIAXIAL COMPRESSION,EXTENSION AND C 'YCLIC LOADINGTAKASHI KIYOTAi) and FU ,{lO TATSUOKAii)ABSTRACTThe viscous property of sand under triaxial compression (TC), triaxial extension (TE) and cyclic triaxial loadin*'conditions ¥vas evaluated by using reconstituted loose samples of three types of' relatively fine uniform and relativelyangular sand (Silica No. 8, Toyoura and Hostun). The viscous property ¥vas quantified mainly by changing step¥visethe axial strain rate many times and partially by peT'forrning drained sustained loading, both during other¥visemonotonic loading (ML) at a constant strain rate. Such a peculiar feature of viscous property as that the viscous stressincrement decays ¥vith an increase in the irr'ever'sible strain dur'ing ML at a constant strain rate (i.e., the so-calledTESRA viscosity), ¥vhich has been observed vith Toyoura and Hostun sands in pre¥'ious studies, was obser¥'ed alsovith Silica No. 8 sand. The magnitude of ¥'iscous property is represented by the rate-sensitivity coef cient, fi, defined asthe slope of the !1 R/R - Iog {(i*)*r*** /(,;, i*)b*r.** } relation, ¥vhere A R is a sudden change in the principal stress ratio, R(T Icr. , caused by a step chan'e m the rrrevelsible shear straln rate from ( y i*) *f.** to ( p i*)*ft** at a given R value durin_',_other¥vise lvlL. The follolvin*" ¥¥'as found. The same definition for fi is relevant to drained TC and TE tests. In drainedcyclic triaxial loading, the fi value is obtained from the above-sho¥vn equation after re-defining the sign of A R andproportionally scaling the value of R. With the respective type of sand, the fi values under these different loadin :conditions are very similar. The effect of overconsolidation on the fi value is insignificant. Thevalues of these threetypes of sand are similar to each other and also to those of other ordinary types of sand and gra¥'el ha¥'ing lar*'elydifferent particle sizes. The decay rate of viscous stress increment ¥vith an increase in the irreversible shear strain, ¥vhichis another factor of the viscous pr'operty, is rather similar among the three types of sand, Ivhile the decay rate is slightlylo¥ver in ML TC than in ML TE. The effect of o¥'erconsolidation on the decay rate is insignificant,Ke .' words: cyclic triaxial test, Ioading rate effects, sand, triaxial compression, triaxial extension, viscous property(IGC: D61D7)Benedetto et al. (2005) in the torsional shear tests. On theother hand, the relationship among the ¥'iscous propertiesunder the TC, TE and triaxial cyclic loadin*' conditions isINTRODUC1'10NAccording to a number of previous studies that can befound in the literature (e.*'., Murayama et al., 1984;not ¥¥'ell understood. For this reason, it is not knownwhether the viscous property pararneters evaluated underMejia et al., 1988: Yamamuro and Lade, 199,3;the TC and PSC stress conditions can be applied to generai three-dimensional str'ess conditions.In vie¥v of the above, in the present study, the viscousproperties of reconstit.uted loose specimens of three typesMatsushita et al., 1999; Nakarnura et al., 1999; Lade andLiu, 1998, 2001; Howie et al., 2001; Di Benedetto et al.,2002; Tatsuoka et al., 2002; Ku¥vano and Jardine, 2002;Nabvir et al., 2001, 2003a, b; Pham Van Bang and DiBenedetto, 2003; Di Benedetto et al., 2005; Tatsuoka,of relatively fine uniform sands (Silica No. 8, Toyouraand Hostun), having relati¥'ely angular particles, ¥vereevaluated under the drained TC. TE and cyclic triaxialloading conditions at fixed confining pressure. It lvasattempted to find the relevant viscosity parameters thatcan be equally applied to those different loading conditions. The effects of isotropic-stress overconsolidation2004), sand exhibits significant creep deformation andstress relaxation in drained triaxial compression (TC)tests, plane strain compression (PSC) tests and torsionalshear tests. In these previous studies, essentially the sameviscous property was obser¥'ed with fully drained saturated sand (i.e., ¥vith negligible effects of delayed dissipationof excess pore water pressure) and air-dried sand. Thesewere also evaluated to a limited extent. It was also exam-previous studies vere performed mostly under TC orPSC stress conditions, except Nakamura et al. (1999),ined ¥vhether the stress-strain relation of Silica No. 8 sandPham Van Bang and Di Benedetto (2003) and Dihistories includin*' drained sustained loading can also befrom drained TC tests performed for various loadingi] Institute or Indus rial Science, University of 'Tokyo, Japan (kfyota@!iis.u- ok.vo.ac.jp).ii) Department of Civil Engineerin_ . Tokyo Uni¥,'ersity of Science. Ja )an (tatsuoka@ rs.noda tus.ac.jp).'The manuscript for this paper vas received for reviehv on August 2, 2005; approved on "lay 29, 2006Vritten discussions on tiris paper should be submitted befbre May I , 2007 o the ,Japanese Geotechnical Society, 4-38-2, Sengoku, Bunk_vo-ku,Tokyo 1 1'_-OOI , Japan Upon requesi the closing date may be extended one month.665 ilKIYOTA AND TATSUOKAG66fio¥v rule are modelled similarly as the con¥'entionalelasto-plastic theories. So, any elasto-plastic modeld8can be extended to a non-linear three-componentmodel by adding the (7' component appropriately.inviScid corriPonentrILLJP I (5i).The basic ¥'ariable for (7* is not "the general time t ",for ¥vhich it is not possible to define the origin in theobjective ¥vay (e.g.. Tatsuoka et al., '_OOO, 2001). Theviscous stress increment, c!(T', develops by either c!e '*or its rate, c!H y po-eiastic=*, or both and Is al¥vays proportional to.theinstantaneous (Trvalue; i.e , "d(T ¥vhen8"=r,,Iscomponent vjscous component( _iven as:Fig. 1. =0n-linear three-component model (Di Benetietto et al., 2002;Tatsuoka et al., 2002)[d(T '](=) = [cl { (T f (e i') ' g ( i*) }It.) (3)lvhere g (i*) is the viscosity function, ¥vhich is al¥vayssimulated by a non-linear three-component model (described below) using the parameters for the ¥'iscouszero or positive and given as follo¥vs for any strainproperty evaluated from the stress-strain behaviour uponstep changes in the strain r'ate applied durin_ other¥visemonotonic loading at a constant strain rate. Only loosespecimens ¥vere tested, because creep deformation can beobserved more clearly ¥vith looser specimens.ing):¥vhere IA BRIEF RF.VIF,¥V OF PRF.VIOUS STIJDIF.Sn7 are positive material constants. As explained in DiBenedetto et al. (2002) and Tatsuoka ('-004) and alsolater in this paper, these constants for a given type ofNon-!inear Three-con7ponel7t Mode!Although a number of elasto-viscoplastic constitutivemodels have been proposed for saturated clay little hasbeen proposed on the viscous property of sand (e._O.Yamamuro and L.ade, 1993; Di Pr'isco et al., 2000). DiBenedetto et al. (_7002,_005), Tatsuoka et al. (?_OO_ ),Komoto et al. (2003) and Tatsuoka (2004) sho¥ved thatthe viscous properties of a ¥vide ¥'ariet_v of geomaterials(i.e., clays, sands and gra¥'els) observed in dr'ained TC_and PSC_ tests can be described appropriately by the non-linear three-component model having the basic frame¥vork described belo v (Fi_"*. l).1. A given strain increment, de, consists of an elastic(i.e., rate-independent and reversible) component,d8*, and a rate-dependent and irreversible (i.e.,(si*) or stress ((Tr) path (¥vith or ¥¥'ithout cyclic load-[ f (I i'i)J_}J( :O) (4)",g, (b**) = c ' [ i - exp I8***I ,2. de* takes place only in component E,'; and c ,}' andgeomaterial ar'e determined based on the ratesensitivity coefficient, fi. The values of fi of threetypes of sand under various str'ess conditions andloading histories ¥vere evaluated in the present study,as explained later in this paper.Di Benedetto et al. ( _OO?_, 2005), Tatsuoka et al. (2002)and Tatsuoka (2004) sho¥ved that different formulationsof (7 are necessary for different geomaterial types thatexhibit different effects of recent history of ** on thecurrent (T ¥'alue. Firstly, a stress-strain model called thene¥v isotach" ¥vas pr'oposed to describe the ¥'iscousproperty of sedimentary soft rock (Hayano et al., ?_OOl)and some clay types (Tatsuoka et al., 1999c, '_OO'_), forwhich the current a during primary ML is obtained bydirectly integrating Eq. (3) ¥vith respect to 8*' as:inelastic or visco-plastic) component, de'*, ascJe=cl8*+de*' (1)i* i is the absolute value oflaFrom Eqsvhich is(8 ",i*) = a f(s i*) ' g.(i*) (5)(2) and (5), ¥ve ha¥'e:(T = (7 f (e i') ' { I + g, ( i')} (6)obtained by a h _'po-elastic model ha¥'ing a set ofe]astic modulus that are all a function of instantaneous stress state (and straln history ¥vhen relevant)The unique dependency of the current stress, (7, on the(e.g., Hoque and Tatsuoka, 1998, 2001; Tatsuoka etisotach property (Suklje, 1969). It is to be recalled that, inal., 1999a, b).Eq.3. A given effective stress, (T, consists of an inviscid(i.e., rate-independent) component, (Ti, and a viscous(i.e., rate-dependent) component, (T , as:(T = (7 { + (T ' (-?)4. (7is a unique function of irre¥+ersible strain, 8i*, inthe monotonic loading (lvlL) case along a fixed stresspath, in ¥vhich the irr'eversible strain rate, i*=aei'/instantaneous strain rate, , Ivas originally called the(6) (for the lvlL case), the current stress, (7, is a uniquefunction of instantaneous 'rreversible strain rate,**, andalso irreversible strain, 8i*. This difference in the strainor ", in the constitutive modellingrate parameter,results into largely different beha¥'iours, in particular¥vhen the strain rate chan_ es fast and during the stressrelaxation process, and the use of ei* in Eq. (6) is necessary to descrlbe realistically the stress-strain behaviour(Tatsuoka et al., 2000 and ,_OO1).at, is al¥vays positi¥*e irrespecti¥'e of the sign of stressrate, ( . The a f_ e i* relation, ¥vhich becomes hysteret-lc under cyclic loading conditions, and the relatedDecay of Viscous St/-essMatsushita et al. (1999), Tatsuoka et al. ()_OOO,200 1 ) ¥,1SCOSiTY OF SAND IN TRIAXIAL TES'TSr-i3('bC ; I :::r'li"I!rl'l1l;C}Cil )e '¥; 'lll5C ioe}i;h rlll')"CmlLn11dJ.' ' rl/asTiil:: ll-4(ll¥d" dJI n:rlT Ii r ;:lfiilif:';/:s iik i1:i J eiI'! "IIi C;{i"}!t}(C (}i tJJ(,l(,l-il I '- !f L - - "l(}ItCl l li 5t]n};: Inn:i - - }i f}' elic l ) inC '}iT f i Ifh( iTC (}fli: # P4 {f'7C i}fT{!eISilL:ar straln ' = , _ (..* {ob)Fig. 2. Rf]i5:T It :;'}2C*=l:=,[c!{( g,(t")}]{=}'(= =*)" }(8" r)a.*(7)H l" C ; 11J ::': , d : :L t T stl rlla/ H ' Fl:: I I C' }:iii:tl;:::::i: ::::::!'::i 4)cr = [d( ']L'fl'rll'lr' 1'1"r"!i" ))J:=1 ' ' : "'! '¥ i !l3ntch ; l ¥/ / ' L k it) fi Sa trir ued HL stv:1 s nd667t !1(]']lvhere o" is the current viscous stress (1vhen 8**=8*');[c!(r' J{*.*=) is the ¥'iscous stress increment that de¥'eloped inthe past (¥vhen e'*=r) and then has decayed until theplesent (¥¥hen e" 8") [c!{(T g,(8")}](rl is the ¥'iscousstress increment that cleveloped ¥vhen 8 *' =(Eq. (3)); andei* is the lrre¥*ersible strain aT the start of integration,¥'here (T =0. Tatsuoka et al. (2001, '_002) and DiBenedetto et al. (200'_) proposed the follo¥ving polverfunction based on experimental data:gd***1'(8 **relatlons from dralned PSC tests ((r 39' kPa) atdifferent constant i+s and a tes with step changes in i*, saturatedHostun sand (bach A) (iMatsu lita ct al., 1999: 'Tatsuoka ct a].,2000, 2001; Di Benedetto et al. 2002)T) = /'(t(8)¥vhere /'1 is a positive constant smaller than unity. Thepo¥ver form has a fundamental ad¥'antage in the integration of' Eq. (7) (Tatsuoka et al., 200'_).and Di Benedetto et al. (2002) reported that, ¥vith t¥vo fineuniform sands havin_g: relati¥'ely angular particles, Hostunand Toyour'a sands, the viscous stress increment, [d( ' l(*,,according to Eq. (3) decays ¥vith an increase in the strainVVhen /'1 = 1.0, Eq. (7) becomes totally differential,retur'ning to Eq. (5) (the ne¥v isotach model). The decayparameters r; of the tested sands ¥vere evaluated in thepresent study.Due to such decay feature as expressed by Eqs. (7) andduring the subsequent ML. This feature can be seen typically from Fig. 2, which sho¥v the test results obtained(8), the effects of irreversible strain rate,from a series of drained PSC tests at an effective horizontal stress, (Tl(' equal to 39'- kPa on saturated specimens ofthe (T' value during the subsequent loading become rran-air-pluviated RF Hostun sand (batch A).It may be seen that, in continuous ML of drained PSCTESRA model (i.e., temporary or transient effects ofat constanton the viscous stress component). Then, the value of (T'could become either positi¥'e or zero or negative depending on recent loading history e¥'en lvhen *' has ah ays. s that were different by a factor of up to 500(i.e., tests H30'_C through H307C;0=0.01250/0/min),the o¥'erall relationships bet¥veen the principal stressratio, R=(T(lcrl(' and the shear strain, y=8 -eh, fromthese six tests are essentially independent of the axialstrain rate,+. In the other test (HOSO1), the R vaiue sud-denly increases and decreases immediately after. in-creases and decreases step¥vise by a factor of 100. In thistest, as ML continues at a constantafter the respectivesudden change in R, the stress-strain cur¥'e exhibits amarked chan*'e in the tangent modulus and then tends to*'radually converge into the unique stress-strain curvethat is obtained by continuous ML at different s.The decay of the viscous stress increment, [d(T ](*), ¥vithstrain during the subsequent ML at a constant strain(i.e., irreversible strain acceleration),sient, or temporary. The ne v model is therefore called theirreversible strain rate and irreversible strain acceleratlonbeen kept positi¥'e.Rate-Sensitivity Coefficient fiDi Benedetto et al. ('_OO'_) and Tatsuoka et al. ('_002)proposed to express the magnitude of the viscous property of geomaterial as f'ollolvs.The sudden jump in R (at the fixed irreversible shearstrain) by a step¥vise change in the irreversible shear strainrate,*'= : - }f, from ( *')b*r.** to (' **)*f*** is defined asA R =A(( f lo' ). In the drained PSC tests and the drainedTC tests performed in the present study, the value of lo_,_"{( ) /( )b*r ,*} is nearly the same as log{( i,)*f*"/*f*** *** *** *follo¥ving a step change in the strain rate described above,¥vas also observed in other drained PSC tests on air-dried( i') .} The AR/R-loHostun sand (batch B) and saturated Toyoura sand (Di¥vhichBenedetto et al., 2002; Tatsuoka et al., 2002), in torsionalshear tests on air-dried Hostun sand (Di Benedetto et al.,2001) and in drained TC tests on ¥¥'ater-saturated and airdried Toyoura sand (lvlatsushita et al., 1999; Nawir et al.,2003a, b).*', and i s ratei'=a28i'/at2, on{(* *). .+ /() *f'**} relatrons*f* *f'rom these PSC tests are independent of the value of R atwas step vise changed ¥vhile they are highly linearalso as sho¥vn later in this paper. The slope of the relationis defined as the rate-sensiti¥'ity coefficient, fi.Matsushita et al. (1999) sho ved that the P value ofToyoura sand in ch'ained PSC and TC tests are nearly thesame. Na vir et al. (2003a) showed that the P ¥'alue ofWhen the viscous stress incr'ement, Ic!a'](=;, decays ¥vithToyoura sand is rather independent of density, confinin_"*,strain, the stress, a', is no longer a unique function ofand (6)) is unable to describe this peculiar feature ofpressure and vet condition (air-dried or saturated) indrained TC tests.Figure 3 summarises the fi values of several types ofviscous property. Di Benedetto et al. (200'_) and Tatsuokaet al. (2002) modified t.he ne¥v isotach model by introducing the decay function, gd*** (8**- ?), as follows:sand and *･ra¥'el, a crushed concrete aggregate and twokinds of compacted dried clay po¥vder, plotted againstthe mean diameter, D50. The fi value of Silica No. 8 sandinstantaneous e ' and**. The ne¥v isotach model (Eqs. (5) KIYOTA AND TATSUOKA66sI OOo locomp cted 'Hostun 's nd- comp ,cted***ei j(.t)FLJJinomori ei yPolrvder(Li et al 20D4)a 08ca,Silica Xo.S snnd= Drairied TCoven d edcrus ed concr8te80ggregate>pawder} Pharnvan 8ang et 31 (2003) []: J mL na R[versar d ,*: (Yasin et al 2003) /Q) , ,, *] ,.'o oo Nalr* r etO[II (Anh D n etal 20a4)Toyoura sand (fviatsushita et l 999: Modei chi 8 g avelATatsuoka et 81 2003: Hir8k wa. 2003: (Njri3 a '! 2003)i , 2a03a)IE-3 a al o 1 1 IoMean particle diamter, Dso (mm)Fig. 3. P-D<0 re]ations of various granular materials and compactedoven-dried clal.' powder (.see Table A1 in APPENDIX Al for thetest conditions)S'iiell ¥o.S sandMOstUn s ntV = I . 3RF Ilostun snnti:-Cl, o gin lchiba graveiClls nd No8 [] . ･'2005oSilica02 (Kjyota& Tatsuokaro) o u ['tl S llldD, = t} ri7? m {1>, 40{Deng & Ta suok 'c:e)6(t(Matsushit3 et al , 9s9: **Di Benedetto et l . 2aa2: *o,' a4 2a05] * '¥D, = O IS nIIT1t; = 1 64Aqil et l (2005) *C5a a6 oven-dried :alln cl y ,To}'our:1 snndl D*,= f).3i m 71L;.= 1 94oO OlOlParticle dia l eter ( m!l)Fig. 4. Gratn size distributions of tested sandsIt ¥vas confirmed, ho¥vever, that, ¥vith the fine uniformsands used in the present study, the fi vaiues evaluatedbased on axial strains locally measured and thoseplotted in Fig. 3 ¥vas obtained from one of the drained TCexternally measured are essentially the same (Na vir et al. ,tests described in the next section. The data obtainedunder other loading conditions in the present study are'_003a; Enomoto et al., 2006). The volume change of thereported later in this paper. The follo¥ving trends may beseen from Fig:. 3:amount of pore ¥vater expelled from and sucked into thespecimen by measuring the ¥vater height in a burette that1) ¥Vith Toyoura and Hostun sands, the fi values fromdrained TC and PSC tests are essentially the same.¥vas connected to the specimen ¥vith a lo¥v-capacity2) Except for a crushed concrete a gregate (Aqil et al..respective saturated specimen ¥vas obtained from thedifferential pressure transducer.The strains presented in this paper are logarithmicfrom 0.0013 mm to 7.8 mm. A noticeably higher fivalue of a crushed concrete aggregate would be dueones, obtained by integrating strain incr'ements definedbased on respective instantaneous specimen dimensions.Test Mate/'ia!s: The follo¥ving three types of relatively fine and uniform sand ha¥'ing relati¥'ely angularto such a special feature of the particles that stiff andparticles ¥vere used (Fig. 4): Silica No. 8 sand (a .Japanesestrong cores of gra¥rel particles are covered ¥vith arelatively ¥veak and crushable thin layer of mortar.Despite these important findings ¥vith respect tO theviscous property of geomaterial summariz,ed above, mostsand; Dj0=0.077 mm, U*=2.43, G*=2.655, e ,**= I .335and e i*=0.73), chosen to realize more contractive beha¥'iour than Toyoura and Hostun sands when loose because of a more angular particle shape (Kiyota et al.,of the available data were obtained by drained TC andPSC tests, but no systematic data from drained triaxial'_005); Toyoura sand (a Japanese sand; D50 = O. 1 8 mm, U*2005), the range of these fi values is ¥'ery small, beinessentially independent of D50 for a ¥'ery ¥vide rangeextension (TE) tests and drained cyclic triaxial tests canbe found in the literature. lvloreover, all the reconstitut.edspecimens of granular materials tested to evaluate theviscous property reported in the literature ¥vere normallyconsolidated ones, so effects of overconsolidation on thecoefficient fi are not kno¥vn.TEST PROCF.DURF,S= 1.64, G*=2.65, e***=0.99 and emi =0.62); and RFHostun sand (batch B) (a French sand; D50=0.3i mm,U.= 1 94 G =' 65 e =0 95 and e*i =0.55). Toyouraand Hostun sands are quartz-rich subangular sands,¥vhich ¥vere used by Di Benedetto et al. (2002) andTatsuoka et al. (2002) to study the viscous property ofsand. The test conditions are listed in Table 1.Specilllel7s: All the specimens ¥vere prepared by theair-pluviation method. To achieve the isotropic stressconditions at the top of the specimen ¥vhile ensuring freeAppa/'atuS.' An automated tr'iaxial apparatus ¥vasused. The specimens ¥vere 70 mm in diameter and 155 mmin height. To make the specimen deformation as uniformas possible, the top and bottom ends of specimen ¥vereaxial compression during specimen preparation, a collar¥vas set in advance at the top of the split mould andremoved immediately before applying an initial eff ctiveisotropic confining pressure (by partial vacuum) equalvell-lubricated by using a O.3 mm-thick latex rubber diskto 2 kPa to an air-dried specimen (Fukushima andsmeared ¥vith a silicone grease layer having an initialthickness of 0.05 mm (Tatsuoka et al., 1984). The deviator load ¥vas measured with a sensitive and lo¥v-compli-Tatsuoka, 1984). Then, the partial vacuum ¥vas increasedance load cell. As the axial strain ¥vas measuredexternally, the measured axial strains included anas eo in Table 1. The specimen ¥vas then made saturatedunkno¥vn amount of bedding error (Goto et al., 1991).to - )-O kPa ensuring the isotropic stress state at the topof specimen. The initial void ratio at this stage is denotedby supplying carbon dioxides and then de-aired waterfrom the bottom of the specimen and back-pressurized T¥,ISCOSITY OF SA.¥Dlable 1.TeslNoLoading history fmingpressure (kPa)14Toyourasandeo /e*O.927/0_906THO . 943 /O. 9 1 8(consiani slrain raie) 4003Vold ra ios*1,TC(conslant strain rate)1TRIAXIAL TESTSTCO.932/0 912TEO.945/0 922OCRl .OTC100O, 960 /o . 942407TE200O.954/0.9342.08CyclicO 939/0.916l_192/1. l9TC(constant strain rate)TE14SilicaTC(1vlth susiainedloading)o .o 1 95O.0200-o.o0125 - o ･) o.0254:i: O.O0125 - : : O ') O.OIS9O.O0125O.0125O. 1 25l 40190/1. l4004218o.25- O.OI 25Sustained loadinat c!= 300 kPa19O 125Sus ained loadinl 187/1. 130TC1.188/l .135TEl.190/1. 136drained creep for3 minutesO.O0125 - O.25 -l_180/ . 128l.181/1. 131l 7t,)al q=200 kPaO_0125O_OO 1 25 - O.25 O.0272- O O012_-O.25 O_0304l.lS9/1. 13420Cyclic21l.173/1. l2,-:!: O.O0125 - :!: 0.25 O_O'_23I.177/1. 145,,N. ole:2 o1 182/1.120162440l.187/1. 139(constant strain rate)23O OI 251.1S7/l i351 186/l12No SLegcndIniiial isotropic6l 5*)/ m i n ) fi- o,,o0125 - - o ･) o.0242O.94 1 /O 92613(O.OOI 25 - 0.25 O,.0200200llAxial strain ra eO.0125TClo669Triaxiai iest contiitions in the presentecl siuti,E cti¥=e cou'lalerialli¥'HostunsandTCO.918/0_893TE0.926/0 905O O0125 - 0.25 O.0214- O.O0125 - - O.25 0.0275Initial isotropicdrained creep for3 mir utesa) The period ofinitial drained creep immedia el_v before the s art of drained riaxial loading lvas 3 minutes in this test, Ivhile the period inthe other iests of Silica No. 8 sand ¥vas 180 minu es. This perlod 'as 3 minuies in all the iesLs on Toyoura and Hostun sands.b) Theaxial strain rateduring lvlL ¥¥'as equal o0.0125a. hnin, vhicll vas one tenth of O. 1250/6/minute in other similar ests Ncs. 14-16.c) Initial void rario (eo) and consolidated void raiio (e*).with pore pressure equal to 200 kPa.Loac!iilg Method.' With all these three sand types,for a range of overconsolidation ratio (OC*R) up todrained ML TC and TE tests ¥vith a number of stepa number of step changes in . ¥vas performed.All the triaxial tests were performed in an automatedlvay by using a precise gear system dri¥'en by a ser¥'o-changes in . were per'forrned. The follo¥ving other tests¥vere also performed:four. Moreo¥'er, one drained cyclic triaxial test ¥ 'itha) Silica No. 8 sand.' Effects of strain rate on themotor for axial loading together ¥vith an electricalstress-strain behaviour were evaluated by performingfour drained ML TC tests at constants that werepneumatic transducer for cell pressure control (Tatsuokaet al., 1994; Santucci de Magsitris et al., 1999). All thedifferent by a factor of up to 200. In four otherdrained TC tests, sustained loading tests ¥vereperformed during other¥vise ML at a constant ..specimens ¥vere subjected first to compression underMoreover, three drained cyclic triaxial tests with anurnber of" step changes in . ¥vere performed.b) Toyoura salld." The effects of isotropic-stress overconsolidation on the viscous property lvere evaluated400 kPa. The norrnally consolidated (NC) specimens¥vere then subjected to drained creep loading underisotropic stress conditions (hereafter called "isotropic-stress compression") at.=0.0250/0/min to¥vards (Th=isotropic stress conditions (hereafter called "isotropicstress drained creep loading") before the start of drained KIYOTA AND TATSUOKA67040J3540No 17- No lOa)z I O ,,I ( ,,e'O( 30*'*20Be3jle*10_)_, ,,* J OAc);s 2.0E,! I O20e..r)rained TC_.lO* f VN0.9:)_ 1,5=NoI= O Ol 25,,!lO. NO I O:=0 *. No {=:Af:'_ +0*'minlD,ained TC_,,.No 9:･ 1 5= 20 +.¥.o IS:, change from* O_OI 25 " min* +1 O. N'o I O:,*No i ! : = O **. No 12:s1 .oNo 9No I li 3 O, iO T To 18l O'-;,j .)_5lO ' E,,i ,!lo No 11 N09No lONo 12a)O r' to lO ,,20 +=103530>b) 7'1N* 9,5!s30No 18¥No lOll20)No i 1/xNO l?+/10> oooDrained TC.¥. =0.9:'o:No I S:o 4** O Oi25,f O.)･*･tnin'o {O:.* IO ,,. No il･=No 10No 12,lv i)/No I Ib) ¥l!l) 52015c;/N09 ',+.o lo>o= 20 ,).Drained TC.No 9:05. change hom I/IO ,* to 20 *=JNo I I :)6 8>,O 12 14 16o tnin_. I0L, ' No i 2:= E .= IC ;,*ooVertical strain. 8 ("/")40Pig. 5. a) R - 8*, and b) 8,*,: - c* re!ations from ML tests ((T; = 400 kPa)No lOc)with and without strain rate changes (Silica No. 8 sand)... e35triaxial loading at constant (Ti; for a per'iod of 3 minutes¥vith Toyoura and Hostun sands, ¥vhile it ¥vas 1 80 minutes¥vith Silica No. 8 sand, except 3 minutes in test 15. Assho¥vn later in this paper, the perlod of initial isotropicstress drained creep loading had significant effects on thesubsequent stress-str'ain behaviour of NC specimens.¥ lith o¥'erconsolidated specimens of Toyoura sand,, iO; . E E30lOge,:lOg6%- 2.5*!! O NOEg' )* 7_oe,I f I Oe )g /lOPnn {palpal st'sssst'sss :tio:tso' RTll 'i '2(j 8aftsi ()! I OJs- 1.5;t}RlOec-be :: RIo1 8!10*=400 kPa ¥vas follo¥ved by isotropic-stress unloading ate IOe' lOE _e'isotropic-stress drained creep loading for 3 minutes at crj;*= O 012* ;,,!iO. No 10:' lls;c:"'!e 'fgilrTeye･s b e yert csJ suasn'= - 0.0250/0 /min to¥vard (Tl( = 200 kPa (tests 5 and 7) or100 kPa (test 6). Then, the specimens ¥vere subjected toisotropic-stress drained creep loadlng for 3 minutes before the start of drained TC or TE Ioading.30))VISCOSITY IN DRAINED TC)The TESRA viscosity ¥vas obser¥'ed in drained TCtests on Silica No. 8 sand. Figures 5(a) and (b) sho¥v therelationships bet¥veen the principal stress ratio, R, andthe axial strain, e , and bet¥veen the volumetric strain,8 *1' and e from five dramed lvlL TC tests ((Tl; =400 kPa).In the first four tests, the axial strain rate,, ¥vas differ-ent but kept constant, equal to o/lO, o, 10 o and ,_O o,¥vhere 0= 0.01'_50/0/min. In test 18, . was changed step¥vise from ( )b*f ** to (lvlL at a constant)*f*** many times during other¥vise.. The nominal ratio ( .)L,*f***/()*r***ranged from 1/100 to 100.Figures 6(a) and (b) sho¥v the relationships bet¥veen R15lNo iO/,eo¥¥/ ¥20TESRA Viscosity of Si!ica IVo. 8 Sanclo Isd)lO05Drained TCe,No. lO:c,¥. To I S: , change from I !1 O *>ooo5lO= ,T= O 0135 , ;min.15o 2020lrre¥'ersible shear strain. 7 " (?/*)Fig. 6. a) and b) R- !" and c) antl d) 8:', - f" relarions from drainetiML TC tests at different constant strain rates and one test lvithstrain rate changes (Silica No. 8 sand, a; =400 kPa) VISCOSITY OF SAND IN TRIA¥lAL TESTShighly reliable due to unknolvn efi cts of beddin_",_ error.Table 2. Values of t} e parameters In Eq. (lO)To}oura HostunSilica No. 8E.( " Pa)';l6f 1140140#120*, 160to.50504loadlng is purel"v elastic.The elastic shear and ¥'olumetric strains at the end ofthe tests presented in Flg. 6, ¥vhere R is about 3.5, are== Hoque and Ta suoka (1998),, Based on externall} measured axial strains, including lhe BE effects(nat highly reliable)t) rrom the inliial slope of stress-strain curves from Lhe TC tests, usedLo obtain elastic strain incremen s in this studvand the ure elslble sheal straln y*'=ej*-ej:, and bet veen the irre¥*e 'sible volumetric strain, 8:,.1=8:So, E,t = 160 lvlPa ¥vas used so that the initial part ofstress-strain cur¥'e immediately af'ter the srart of TC2ej:,and y'* from these four ML tests presented in Fig. 5.Figures 6(c) and (d) compare the results from test 18 (¥vithstep changes in ,) and test 10 (at a constant , = o). Unfortunately, the ¥'olumetric strain in the slo¥vest lvlL test(test 9) is not reliable probably because of' slo¥v cell ¥vaterO.50/0 and O.'_50/,vhich are significantly smaller than thecorrespondlng irreversible stralns.As long as , is kept constant, any systematic efi cts ofstrain rate on the overall stress-strain relation are notnoticeable (Figs. 5 and 6). On the other hand, ¥*hen , (ory**) is Increased and decreased step¥vise, R exhibits a sud-den Increase and decrease by an amount that incr'eases¥vith an increase in R. These apparently contradictingtrends of behaviour could be explained in a unified lvay¥vhen based on the fact that, in test 18, as ML continuesat a constant , (or ,*') after a sudden change in R, thestress-strain cur¥'e tends to rejoin the one that is obtainedleakage through a latex rubber membrane into the specimen. So, the values of ej*', therefore the values of y*'by continuous ML at different constant , s (or ,'*s). Thistrend in beha¥*lour is indeed of' the TESRA viscosity.presented in Figs. 6(a) and (b) of test 9 Ivere obtained byCorresponding to such significant viscous effects asdescribed above, Silica No. 8 sand exhibited significantsubstltutin_('* the values of 8( rneasured in test 9 into thea¥*erage 8:, - 81: Ielatlon of the other thlee tests at hl'hel, s. This procedure ¥vas necessary also to evaluatechanges in the cross-sectional area of the specimen to obtain the axial stress in test 9.creep deformation. Fi**ures 7 and 8 sho¥¥' the results f'romtest No. 14 and t¥vo other similar tests ¥vith initialisotropic-str'ess drained creep loading for 180 minutes.A broken rectangle in Figs. 7(b) and 8(b) denot.es theThe respective irre¥'ersible strain component, de*'=d8range of strain in, respectively, Figs. 7(a) and 8(a). It may- c!8 *, ¥vas obtained from the ¥'alue of d8* obtained basedbe seen that the creep strain rate increases ¥vith anon the follo¥ving hypo-elastic model (Tatsuoka et al.,increase in the shear stress level and the axial strain rate1999a, b):during drained ML TC immediately before the start ofc!8= d(r( /E : (9a)d8 h = - c!8vhere c!8･ v:1* (9b)and d8 :* are the elastic axial (¥'ertical) and later-al (horizontal) strain increments; Eis the vertical elasticYoung's modulus; and v h is the elastic Poisson's ratiovhen axlally cornpressed at a constant (71(' Eand v ･i* arenot constant during the respective triaxial test at a constant (;i(, but they ar'e a function of instantaneous effectivevertical str'ess, (T(, as follo¥vs:E= E.o ' ((7 ' /(yo)"*' (1 Oa)rate at the start of' drained SL, is equal to the irreverslbleshear strain rate dur'ing ML imrnediately before the startof SL. It may be seen from these test results that the loading late effects due to the ¥'iscous property on the stressstrain behaviour are sig:nificant ¥vith Silica No. 8 sand.One of the complicated issues of the viscous propertyof sand is eft cts of loading history under isotropic stressstate (or more generally the ¥'olumetric creep under general stress conditions) on the viscous beha¥'iour during thesubsequent shearing. Figures 9(a) and (b) sho v the R - y *'and e:*-y** relations from t¥vo other drained ML TCis the constant; and vo is the ¥'alue of v ･1'tests at ( }{ =400 kPa in ¥vhich drained SL was performedat q= 200 kPa for '_4 hours. The specimens ¥¥'ere subjected to isotropic-stress drained creep loadin*' at ar; =400kPa for either 3 minutes or 180 rninutes before the startis equal to (a( /(Tl' )o, ¥ 'hich is the ¥'alue of (T( /of drained ML TC. Figures 9(c) and (d) sho¥v the timev l' = vo ' { ((T( l(Tl{) l(CT( /(TIOo }"'¥vhere E+0 is the value of Epresent case); mvhen (T( l(Tsustained loading (SL). Note that the initial shear strain( 10b)when (T( = (70 ( = 98 kPa in theat( ¥vhen the elastic property becomes isotropic (i.e. , E. =histories of shear and volurnetric strain incr'errlents, Zl yEh; the Young's modulus ¥vhen hor'izontally compressedand A8 *j, during drained SL at q=200 kPa. It may beat a constant (7O. The value of (cr(/crt{)o depends on thespecimen reconstitution rnethod. v0=0.2 and (cr( IcTIO0=seen that the creep strain i'ate is significant in both testsvhile the rate is aft:ected by the period of initial isotropic-1 .O Ivere assumed for these air-plu¥'iated specimens of fineabout 0.0010/0 at dift'erent effective stress states in severaistress drained creep loadin*" before the start of drainedML. This fact indicates that component P (Fig. 1) shouldha¥'e both the Cam-clay type yield locus, vhich developsby volumetr'ic yielding, and the stress ratio-t.ype yield10cus, ¥vhich develops by shear yielding (1.e., the doublehardening). This issue is discussed in detail by Kiyota ettriaxial tests. It seems ho¥vever that the Young'sal. (2005) and Siddiquee et al. (,_006).sand based on the pre¥'ious studies. The other elasticmodulus parameters are listed in Table '-, ¥vhich ¥vereevaluated by applying small unload/reload cycles ofdeviator stressvith a single axial strain amplitude of"modulus. E*, of Silica No. 8 sand obtained as above is not 、672KIYOTA AND TATSUOKA22 ））IsQtK）Plc−Slro3sdrai瞬creepbdbrこshearloaご旧glbri80mmじユo〉 ユ、oo−ごl l8↓18屈 】6召召一N・1415、置0125％nun No17・も、淵OO1250らmmNo】7 ＼、＼、煮』☆撚駕 16Noi4魏 14蕊員ぼ 1．2o l2黛lso！rOPIC甜cssdrai置10dcrccp昌。a麺t嘩＃ユ。・kPa＆3〔1・kPaへ篇川25・。min00 02 0謬 06 08 10 】2 14 16bご恥re shear lo3〔圭inq lb【i8（｝【11in㎜ 1．0 】0a）AxIais：minratelmmごdi飢e1｝b￠lbret縮S1巳rt〔｝fsロS面㍑dloadm里じ一00 0ユ 04 06 08 10 a）12 14 16 ［πeversibleshearstr貸1蓄1．ジ「〔％1 1rreversibleshearstrain．ジ「（％） 10 iOlsotropic−stressd繍￠dcro￠P↑篶lsαTopic−5t嚇dramedcr岬belbre3hoarloadinglbr180minbeR）re shoaτloading R｝r…SO n…in0．8…08訟06RζmgeofF19誘髪（｝6／鮎『縛つ釜04饗0290智鴬04202。／’ S：蕊翼ofsロ賦昌i訪od io＆dl窮匙No lじ00 し｝5 11） ！5 ユ0 25 3りb） 瞥 、 ＼ i φ〆一町 醐瞬” Sτユrτoゼ兜s竃amodloadln罫．NoN ∼ ∼ S脚fsu5庶dl。a占lnさN。ロ験1蝋贈．1きつ〔）0 冒 L ト ー 華o（｝ε磁ofsus幅総d【o認in閏NoI70005 …、0 15 ユ0 25b）3、0 1汀e・・ersiblesl職stra頭．γ匹「（％） ［πeversibleshearstτ且1…1、・「【τ（Ob、 贋06 ≧05ISQtrOPlc−stress dra加ed creep bじ薮》rごshear bad正ng lbr歪80min由ごs塾rt ofsus㎜gd loadi靱9Nol4 05−N・14華0】25％min 噸レ 蓉017＝を，＝00125％一min 跳04 03 003 e引oad［ng る02 q繍200kPa ．生 02 01 質OINol7／Iso柱opic−sビessd面nedcreepMqs “ じ1じ、 じ ㎜of瓢凶ごd 200A測st面ra｛e㎞m司ia監elybε飴re 答 醤014・Sus臨edio蕊面g、 壱04 馨 06l・adingatq一ユ00胱＆300贈a；邑、需㈱5％励c）be恥resh餓rloading偽rl80min 00c）三 一 一， 0．3 03送oぼopic−s注鄭dr血edα即be郵oresh㎝loa面9魚rl80鱒 No14二Sus臨ヒd lo＆dIng三 〇、2 飢q冨300kPa ヤっ 答奮葺釜 01 、Axja！sすぬTate㎞me伽芝elybelbre由e s㎜ofsus蜘ed load血9−No14＝量、鷲O l25％【ロ磁 。障二 一」）『oドノ 02 0 苓 1No l6＝Su5面nedめadlng 一 議q埠200kP＆ 芒 OI／lA：ぬalsα諭烈e痴mediatelybefbre山es甑ofsus腔血ed茎 oo bad加gatT200岬a＆300職も、鎚0125％「顧聴oτ㈱ic−s汀cssd面nedcre叩0 5 10 15 20 25d） Creep業繍e（卜ou6〉befo陀she撚b＆d加9最》r I80r田τ1 OOd）三o5 10 152025 Creeptime（hours）F負9．7．E琵ecIs・fsl・earstressleve1・n：a）Rvers・s7已【andb）ε瓢肇versusFig．8E疲ects・荊匙ia韮s｛ra蓋nra吐e・n＝a）Rversus点ndb）ε銭，lversus γi『rel飢i・ns，andtimehls吐・ries・fc）コンandd）コε、、，ldurlngsus輔 ン1「relaIlo盈s，a翻dtimehis重orlesofc）」γandd）」ε、。匪duri臓gSL ｛ai照ed loadi臓9（SL），drai臓ed ML TC重es｛s（S韮lica No・8s訓d，σ‘竺 400kP践）』 要673VISCOS亘τY OF S、へND至N TR王．へXI．へしTESTS0082、けPo口odoflso！rOPIc−s…ressdramedcrcePo 18 No 15．3IIliFlじ No16 i80駐U飛k006△SilicaN『o、8sand薗004i6目△1、灘』爵賢，，、、撃，編魯㊥ 002霧乞 0001、2一〇〇2翁⇒10一〇〇4△働（1．0 （｝2 〔｝、4 00 08 10 1コ14・N・18、TC，・CR司・σ義・轟4G・kPaβ瓢・・2721一〇〇6△ 1汀e・e酌lcshearstr｛湘．ジ「（％）a）ムN・19TE・CR菰1・、σ卜、・叫・・kP胆・3・4i一〇〇8 001 0、1 1 10 100＿ i o1之a芝ioof1irslle＆rs乳rai【篭ratesわelbreandalierasζepchallgePcrK）d ohSOtro｝）耳c−sττcss d職11ごd crccp No l53nlm− Nol6 180ξnin雛 08 予［「“ま蓄Cr／デbC【brcR二11聾巳ごof l・19．aコ0 06F量9ほ0、」RIR−1・9｛（プ『）3f、脅，／（プ『）憂，。r。，。｝relat韮・nsfr・m鼠drainedIC／o、 垂est（Fig．6）andadrainedTEIest（c，f．，Fig．17）Endof5u5【ユ1＝1￠dIQ“dm9，No聾5…i o4 En己of5幡臨監霞じ註 1Qadl織“ N臼 16愚 021璽㌦Sこユrτof5“駅ユInごd Io“dmg「No l5def玉ned in Fig．6（c）．The TE test data presented l！1Fig．10are exp豆ained later in this papeL h may be seen that t駐eS鵠r10f）us【βlnじdload：ξ燦 Nolbrelation呈s indepenclellt of t｝1e value of1∼ at which the三 〇〇strain rate was changed stepw呈seεしnd essentiα11y linear．05 1．0 ［5 2、0 25 300、0b） 1π￠・・ersibloshe餌漁in．ゾ「（％1脈ing the following equatlon to the TC test dat＆making出erelatlonpassthecoordlnate：∠R／R＝Oand（夕i「）、f、，，／ 墓 D5Pedω・fisoαopic・s臨5d面aedcr岬 ゴ 04 No15＝3m㎞No15（ンi「）bごf。「ピ撚至： 1 重㎜ No，16＝180m㎞∠、 讐e3 1装o、2 The Iineεしr re1＆tion presented ill Fig．10was obtained by！No16 琶 1こ o．1告・1・g・・（細一かln（総い1）whereδis出ecoe伍cientequαltoβ／1nlo．T｝1eβval組eofSilicaNo，8sandin出edrainedTCtestwasO，0272，whichis comparable wit勤tkose of other granular materiεし1s，ex−．へ；x1副sしra甘1rat￠㎜e（i』a【e【y before！he s㎜ofs邸励1edIGa磁ng飢q艦200kPa：￠、＝0125P“’血n 釜00c）蕊cept for c1−ushed concrete aggregate（c．f．，Fig．3）． Equ＆tion（13）can be I・ewrltten to由e lncreme慮＆1form：05‘1RR紹lnR；わ・ゴ（1nアi「）（12）On the other hand，、ve obtai茎1from Eq．（2）： 1∼蹴R f＋R V（13）As4R in Eq．（12）is de負ned at a行xed v＆lue ofジ（1．e．，the緒 l！value when the stl’ess jump starts），疑is e（1ua璽to4R’1騨A．滋al s汀ah1鳳t￠lmmedla【elybelbre偽es厭of4｛Rらg、（夕i「）｝．Tben，from Eqs．（12）and（13），we obtain：瓢臨。dl・adi騨q舅200kPa＝峡騨Oi25％掴Ωd）05 10 E5 20 25 CreePtime（醜ours）Fig、9． E庁ects of dura重ion of iso症ropic creep肇oading on＝段）石∼versus γi「容odb）εt㌔lversusγi『rel段重ions，9nd重imehlstoriesofc）」γ＆ndd） ∠ε、。lduri獄gSL，dralnedMLIC芝ests（SilicaNo，8sand，σ1警400 kPa） ゴ｛R f・9、（アi「）｝ ；わ・グ（lnアi「） （14a） R「十R vIn the case of isotach viscosity，for which R’徽R「・9、．（アi「），、ve obtain： 4｛1∼f・9、（シi「）｝ R f・｛1十9、（アi「）｝Rα∫ε一Sθn5i！ivi∫』y Co（がciε1πβ’11五）ノ’αinθゴTCSinceγi「iscoPst段ntand The viscous property of Silica No，8saucl in drainedEq．（14b），、ve obtain：τC was quanti丘ed as foHows． Figure IO shQws therelationshlpbetween∠RIRandlo9｛（ン1「）af，。，／（ア1「）b。f。，。｝from tesd8（presented in Fig．6（c）），where沼R and R are功・ゴ（1nアIT） （14b）therefore R f is constallt inご｛正n（1十9、（プ「）｝冨か4（ln夕i「）（重4c）工）espite t勤at Eq．（14c）isεしn apProxilnated solution of Eq． KIYOTA AND TATSUOKA674l lode! Simu!ation witll Si!ica No. 8 Salldi 20¥;Iscositv rBmelerslE,'* = O OOe(}6(Il 15It ¥vas examined lvhether the results of Silica No. 8t!minO.OI05) OF O 35 & TTsand, including the behaviour during drained creepbehaviour, can be simulated by the TESRA model usingO 035(b: l)ep O 35 & m= O 05e)_. )*=025&rT 003b =0the parameters for the viscous property determined basedon the P coefficient described above. According to theTESRA model, the ML stress-str'ain relation at any constant strain rate tends to converge to a unique r'eferenceI 10= 6 OI05iP05b *O(X)69stress-strain relation ¥vith an increase in y{*. It is particu- Rsnge oper ted in the -a) I oolarly the case as the stress state approaches the peak state.stlJd 'byN. awiret ai (2003)The reference stress-strain relation (i.e. , the R20E '= O OO006 P /mifollowing this principle. A typical one is presented in Fig.Toyou'a sand (b= O 00382 cx= O 23. m= O O4J Is12(a), ¥vhich ¥vas fitted to become the ultimate relationfor all the segmental R - yi* relations for different strainSilioa sand N 'o 8 (b= O O1 i 82) (x= O 23 m= O OSSiostuu sasd (b= O 00963) oL= O 23, m= O 044!IISl]Ica 5and NoO¥rates in a drained TC test in ¥vhich the axial strain ratevas changed step¥vise many times.The simulated R ( =R f+R ' ) - yi* relation is presented¥Hostun sand¥Toyoura sandl 05- y ** rela-tion) for the respective drained TC test ¥vas determined¥*iscosiiy parenleters ;in Fig. 12(a). The viscous component, R', ¥vas obtainedby directly integratin_g Eq. (16), ¥vhich is derived fromRan_2e operatedin the this studyl ooIE-5 IE-4 IE-3 O Ol OIne 'ersib e shear strain Fa e. d･/*'!d100lO(o/o!min)Eq. (7):= , 1(- )R･ =J: [dRFig. 11. Viscositl.' functions in a full-log plot for: a) Tol.'oura sand indrained TC ( 'alvir et al., 2003a) and b) the materials tested in theJ:= t= [c!{Rr g ( i')}1(.) gd .,(y=' ) (16)present studl_'(12) for the TESRA viscosity, Di Benedetto et al. (2002)and Tatsuoka et al. (2002) used Eq. (i4c) for both typesof viscosity (New Isotach and TESRA) for consistenc}'.By integrating Eq. (14c) ¥vith respect to ", ¥ve obtain:l +g ( i')=c,,'(j, ) (15)i*1b¥vhere cis a constant. The viscosity function (Eq. (4))should be defined to fit Eq. (15) for the range of'* of thedata from which Eq. (15) was derived. That is, Eq. (15) isvalid only for this range of*.Fi*･ure 1 1(a) sho¥vs the upper and lower bounds andavera'e relatronships betl een "I 0+*･, ( *)" and" (ona full'+-logarithmic plot) obtained from the plots forFigure 12(b) is a close-up of part of the ¥vhole stress-strainrelation. Figures 12(c) and (d) sho¥v the measured andsimulated stress-strain relations for another drained TCtest (test 14, Figs. 7 and 8), in ¥vhich one SL ¥vas per-formed at q=300kPa for 24hours. The modelparameters used to simulate the creep behaviour in Figs.12(c) and (d) ¥vere determined based on the fi coefficientobtained from the stress-strain behaviour associated ¥vithstep changes in the strain rate presented in Figs. I '_(a) and(b)It is also to be noted that the creep strain rate is controlled by not only the fi value (i.e., the ¥'iscosity function, g (i')), ¥vhich is independent of the density of sand,among others, but also the stiffness of the R r_ y** relaby trial and error. A relevant value was assumed fortion, ¥vhich is controlled by the density of sand.It may be seen from Figs. 1'_(a) throuc(;h (d) that all theviscous aspects of the shear stress-shear strain beha¥'iourof Silica No. 8 sand observed in these different tests are¥vell simulated by the TESRA model consistently usin._,_(Tparameter ai, ¥vhich represents the upper bound of g (")¥vhen ,i* becomes infinite. Figure 1 1(b) sho vs the averagethe same model parameters for the viscous property.On the other hand, the irreversible shear and volumet-relationships between "I.0+g ( **)" and y** (on a fulllogarithmic plot) from the drained TC tests on the threesand types tested in the present study. The relation for'ric strain relations, includin.++.O those during drained SL,Toyoura sand in drained TC obtained by Na¥ 'ir et al.(2003a). The respective relation has a linear part ¥vith aslope of b = P/In 10 that fits Eq. (15). A parameter j77 forthe average relation is equal to 0.05, ¥vhich was obtainedToyoura sand obtained from the present study(Fig. 11(b)) is ¥vithin the range presented in Fig. 11(a).With Silica No 8 sand, the experimentally obtained valueof b=fi/In 10 is equal to 0.0 _72/In l0=0.01 18, and ai=0.23 ¥vas assumed so that the log {1 +*･,,(j,i*)} -logi'relation becomes linear for the concerned range of strainwas not simulated in the present study. Ho¥vever, itssimulation by the same theor'etical frame¥vor'k as used tosimulate the shear stress-shear strain behaviour becomespossible by assuming that the irreversible volumetricstrain consists of the follo¥ving two components that de-velop in a delayed manner due to the ¥'iscous propertyduring SL, (Kiyota et al., 2005): 1) the component due toshear yielding, obtained from creep shear' strains basedrate. The other parameters necessary for the TESRAon the shear flow characteristics (i.e. , the relationship be-model simulation of Silica No. 8 sand are presented int¥veen the irreversible shear and volumetric strain increments) by shear yielding as observed during lvlL at a rela-Fig. 11(b). jviSCoSrrY OF SAND IN TRIAXIAL TESTS40,-5S ie 35TI Lrlti eI I O;I( = ¥ .L* E-*L - -eIUl(i 30e8 = e..J. t"' ¥,, E s 10 E'., iOO¥1)e merSlmul3t on: 20*/_Ol O ,l20675. .. -' /'s f' 3 *'rI O-* lReference s ress-str :n r F t OnlOlo R ;t :r :nce str ;s:0 ,,¥l}5traln rcratlonrE¥ptrl nemei O , ,V*.- 15!Dmfned TC'(ollours,;]al straln Fate before suslnlned !(x;d n1020lOa)DF2lned creep al q= 3eO Pa i'orminAxial str in rate from lilO to 1..-OG1Io,.= O O i25ooc)OV I * e(} mLn1015lOlrreversible shear strain_l* (o. )lrteh rsib]e shear strain. f" (9･t)O 6(,e,_- 05t:;* - ',1)j¥;lOE¥periment(,T 1.::: 04llO , gt iG1,.. . ･ ' ". SimulationReference stress-strain re ation･Ob);,oSin ula i0 lOg,,l; O,7;)E¥perinlen[ (eDrained TC.= O O 1vDrained creep nl q- 30.;'' Oiee'minkPa for4 I ovrs' ,ia! strain rate befbre sus ained leadin ,= O 1eirninAxi ;! strain rate frorn i!' lO , to 20 *,3 5 6oo8in"eversible shear strain. -/ * (a! )od)5 lO15C25Creep tin e (.hour)lodel of the TC test results of Silica N_ To. 8 sand, (Ti =400 kPa: a) vhole R-y*' relation b) a zoomed uprelation with many step changes in the axial strain rate, c) whole R " relation and d) time histor .' of y" during drained SLrio. 12. Similiation bv the 'TESRAtively fast shear strain rate, ¥vhich can be considered to berate-independent; and ･_) the component due to volumetric yielding, which is necessary as can be seen from thefact that the measured flow characteristics during drainedSL is noticeably different from the one during ML at aconstant strain rate (Figs. 7(b), 8(b) and 9(b)). Furtherstudies will be necessary to develop a relevant rnodel forrate-dependent volumetr'ic yielding.Effects of Isotropic-Stress Overconso!idationFigures 13, 14 and 15 show the R-y'* and 8{ 1 yi'relations from three drained TC tests on air-pluviatedthis trend in behaviour is due to effects of the ratedependent volumetric yielding discussed above.Figure 16 sho¥vs the relationships betlveen A R/R andlo' {( p i') /(p i') *f '} from these tests. The stress-strain* *f*** *relations from the drained TE tests on NC and OCToyoura sand of ¥vhich the data are presented in Fig. 16are shown in the next section. The rate-sensitivitycoefficients, P, obtained for the dlfferent ioadingconditions (TC, TE and triaxial cyclic) and different sandtypes, plotted in Figs. 10 and 16, are listed in Table 3. Theresults of the cyclic triaxial tests presented in Table 3 areexplained later in this paper.The following trends of behaviour rnay be seen fromToyour'a sand either normally consolidated (e.g., OCR =1 .O) or overconsolidated. The value of ( 1" during drainedthese figures and table:ML TC was equal to 400 kPa ¥vhen OCR = I .O; 200 kPal)The trends of viscous behaviour, including the decaymanner of viscous effects with an increase in y ', ofthe OC Toyoura sand specimens, are essentially the2)The rate-sensitivity coefficients, fi, of Toyoura sandwhen OCR=2; and 100kPa ¥1'hen OCR=4. In thesetests, the axial strain rate,*, was stepwise changed manytimes during otherwise ML at a constant . In Fig. 13,the result from a continuous ML test is also presented fora reference. It rnay be seen from Figs. 13(b), 14(b) and15(b) that the rate de:'*!/dyi' (positive for contraction)becomes larger with a decrease in the strain rate. Thistrend in behaviour may also be noted in Fig. 6(d) forSilica No. 8 sand. It may also be seen from these figuresthat this trend is stronger ¥vhen OCR= I . It is likely thatsame as the corresponding NC ones.¥vhen OCR=2 and 4 under the TC Ioading conditions are essentially the same as the NC ones. Theconfining pressure was different for the differentOCRs. However, the effects of confinin_9: pressure onthe fs value are negligible ¥vith Toyoura sand, according to Nawir et al. (2003a). lilKIYOTA AND TATSUOKA6764040No*¥ E<3 :OroYouT s ;Ide 3)e*a) 10E¥.30o 1:C ;a)e*E {o30Tc}1'ovr .s rxi5e .laEC 10l ( , = f I Oc:i,IO1'5, 52020DT ne TC. (; '= 400 kP .15¥. 'e l:= E.,= 0.0]15¥. =(, 3:from15Tlin.10lO04TO'Yours sOS!xTol ura-; ind,.¥*1'.**b) E ']oi, Ielo .= E lO= 02, ･ ; o 3l OE,iO: 06"JNo lt)S 04OCR* 4 ClE*= O Oll5 'h*miTt s ,*TQm . {O tO 20lOx¥o 6 DTainel:1 TC'. e '= 100 kP*.lO to 20 .,Vs,! I OOO,s) -02:'*rJ> =0.4t'); 02Dr sn ;ed TC. e *= 4LX) kJ*¥, e 1::,>t,:: OOo 2Fi(J.=E,* O0125 * rnirL'0.31,*rom4 6 8 iO2= 10o?,S -06146vithout strain rate ciranges (To .'oura sand, OCR = 1 ( : = 400 kPa)40¥. To 6. DFnt:.'d TC. o: .*=E ,* O Oi le u nlin_ E from100P:cToveur **>*arld4lrreYersible6 8 10i2 14shear strain. 7o 216 18 20(/ ). -ri* relations from a Ml. TC test with strainF g 15. R- '* and e'l,lrate changes (Tol. oura sand, OC_R=4, (;!1 = 100 1 Ps)o 06TOVOLib' lldIOcc. Ioo 0430l i' 4lOa 02,5,'o oo20-o 02v 1¥ ).Dr lincljTC cr '= 200 kPa OCR- 2 CI= O 0125-o 04im;J1. , fyom < ;1 O o OlO:'t'!-o os06TovouFs-sandb) E-'10R ¥OTC-OCR* cir,O kPa-= () {': r}C': ¥L) 4 rE-OCR= I r, c ,= 40 kP* r}{} 4L ;Q= r] r,1 e5TC-OCR* ･ ov ¥. O6 TC-OCR= 4 oA-o 08o ol04OCR= 4 O+10 [o 20o 08a)e'-O S8 20lrreversible shear stra in. f (9･ )13. R-yEr and 8:', '* relations from IML TC tests with ande 3b)>t'ei0¥. 07 TE-OC f =;*=c;. = 2r,rj kPa.o = iCO kP2. p= a O C}Oo. a = 2C)a kP10= O 0 5100Ratio oi iir shear strain rates beibTe and afier a step changeOEE, lO" 02E_Fio. 16 Relatlonshlps betl een,:: OO>1 R/R and log (v'.'F ,./ j,'.f"") for'Cand OC Toyoura sand specimens in drained TC and TElO *ce;;-O)¥oe,>. DT ncd TC. CT '* IeO kPe * O Oi25 o tnjTL EOCR= 2 OVISCOSITY IN DRAIl l'ED TRIAXIAL F.XTENSIONfrom E,= ' i O to 2O .Figures 17(a) and (b) sho v the relationships bet¥veen-O 4o 24lrreveTsible6 8 shearO strain.12 146 IS 20'!' ( 'o)R =(7f/a=cTl"I(T( and the absolute ¥'alue of yi*=e:1 e*h*,l y i* j , and bet¥veen e :f 1 and I y =* I from a parr of dramedtriaxial extension (TE) tests with and ¥vithout stepFig. 14. R- r" and L ::,i - ;"' relatrons from a ML TC test 11 tll stralnrate changes (Toyoura sand, OCR = 2, crt; = 200 kPa)changes in the strain rate on NC Ioose specimens of SilicaNo. 8 sand. The corresponding drained TC test data arepresented in Fig. 6.The decay parameter i'j (E.q. (8)) under TC, TE andFigures 18 and 19 sho v similar results for NC and OCcyclic triaxial loading conditions, Iisted in Table 3, are(OCR=2) specimens of Toyoura sand. The corre-discussed later' in this paper.spondin*' drained TC test data are presented in Figs. 13 rVISCOSl'TY OF SAIND IN TRIAXIAL TESTSYable 3.677List of the values of p and ,･1 for the difrerent test conditions3()[LoadinSandOCRiypet)* pep4,0Toyoura.oTECvclicTC02o,0242O5o_0254 o. ll ,o0.0189Drain i Tc¥. e.2:.h:0,4ii lO.=*- 400 kPO{ ll5, tk)mnxirL! 10 Io 20 .b)1-5o 0272lO2(}I2.010TEl¥:ro. 8fo.250.02la)1 52 o o.oi95 o_25TCroVe'eo,02l .OSilicai' u]o.3Ol0.0304xToYQur *se'Id* ;20O E :Ob) ¥. ) I .¥Ne;IieCyclicTCHostunTEloo.0223b)ioO .02 1 4o 25lOo.0275::15[';;'E io,Ola)Defined in }*** and averaged for respective loadirrg condit}ons_b)Dif ;cult to evalua e confidently-F: l,)S-05Dr incd TE Q.'= 4t}O kP02t,>=* E. * O(ll 2ShOOFT rLfronl s< *lO Io 2C, .N0.4-cL'4 6 8o40silie;¥;eNo 13ss:IdO 12 14 i6 IS20 1 1Absclu e value of irreversible shcar strain. ,(e.' )e' 3 5ea)130(rig. 18. a) R- i!"] and b) s;,*, - Iyi*i relations from iML TE tcstso ., .lwith and without strain ratc changes (Toyoura sand, OCR= 1)OE j ( ,'o , llr E, lONO93u _O15eDr:vned TENo 13 E = E*= -OOl**rru}l*ENo !91f )mlOt02C}Silica" 30IL *u;202(o S sanda)c {o+ *,5*/_140353Oe10:: ;iL",+Tc} ]u' "}-sendE ;leS'l( ;, E ioE+i I Ob)l5No i9. 10 ? 'o 13. 5¥+ o 7 DIl ine(iTE e,*= 200 kPl 0 .,-lOe: 2.0SE.,* e.OI 25?ntnOCR- 2 f).frQm E== 10to 2OQe:: 15;>. 2013: c =e 19:0,0O*= O.0125 e, from E10 to 20 ,.(C,= ! I OvS lO)i}'*'i from ML 'TE tcsts with andI O ,:Owithout strain ratc changes (Silica No. 8 sand* OCR= 1. (T ; =400:)kPa):) OO¥. *o 7. Draint:xl T5,= 0_Oi25 I jmlnoand 14. Fi**ures 20 and 21 show the results from a pair ofdrained TC and TE tests on NC Hostun sand. In thesedrained TE tests, (Tl( =400 kPaE :0le2 4 6 8 10 l' 4 16 IS 70 '1,*E, * lO15n n.Absoiute value of irreversible shcar strain, =1"F g 17 a) R l,,*'1; and b) c.*,To"our -s r]db)Drail L'd TE'S 05>:'=',ilo, l()vhen OCR= 1.0 and ,-OOkPa when OCR=2.0.(T '= 2(X) ki)a OCR= 2 efrom s*=*1 O Eo 2e *,2 4 6 8 10 12 146 IS20 1.Absolute value of irreversible shear strain* f (9., )Fig. 19. a) R- i}"'! and b) s::r"i relations from a ML TE testwith strain rate changes (To_voura sand, OCR=2, a ; =200 kPa)In the drained TE tests, R=(Tfl(T is equal to (Tr(/(T(while y*'= e: - e h' is negative. Other different test conditions bet¥veen the drained TE and TC tests are as follows:effecti¥'e confining pressure, p' = ((Tf + (7i + (T )/3 =((T( +2(TtO/3 is ((T +2a )/3, ¥ 'hich increases during1) Ovel'consolidation: In drained /1L TC, the meanML. In drained ML TE, p' Is (a +af)/3, ¥vhich '1KIYOTA AND TATSUOKA678o 084. o35elOzHostun-s Jldo 068ea I o ,30) 5hIOStliM Sallde);:!'E,!lO[].'o 04･ ii/ O 02S. ! lO*,ll OEa oO20-O 025N To 23. D,2Jned TC'. c. T'= 400 kP-O 04E,= O 0 25 9 irnirL E from E,,,*10 to 20 ,,oJ*J *-O OGI!/C!Test 3. TC-OCR= { O. c .= 400 kPil_ = O a 14CTest 4. TE-OCR= I (}. CF = 400 kPa. = a {) 75L¥=Hosturhsa'rd3.0O 08b)O ol10erO10100Ratio of iir shear strain rates before and after a step changee,flO: rr l:fr"! 20'e)ot*Fig. 22. Relarionslvips bet¥ een !fR/R and log (/:･fl"/, I'*F*'*.) for ¥_ 'CE, "I:sHostun sa:nd in TC and TE;> iO¥. 'o 23. DrainL:d TC. (;*'=E iOv>+,= O 0125 9s;TrirLfrom(}O kP2) Illherent Anisotropy: The direction of (7f is or-* *lO Io 20 **: OOthogonal to the direction of the beddin*" plane (i.e.,o l6 8 10 12 14 164gthe horizontal direction during specimen prepara-20tion) in TC tests ¥vhile it is in parallel in TE tests.I･reversible shear strain. T ("/*)'*Fig. 20. a) R- i *': and b) s.*,!iy"I rela:ttons from a ML TC testlvith strain rate changes (Hosiun sand, OC_R = 1, or= 400 1 Pa)40e 3)e30c'HosEun-sandEa) lOEl: 15oN. to 24. D Jlcd TIE, = O Oi25 9 jmjrLe400 kPthat, with the respective sand type (i.e., Silica No. 8, Toy-2 5oura and Hostun sands), the P values obtained based onthe R- I yi*1 relations from the corresponding drainedHOS u;1-sandb) E=]tcl o )//E iloTC and TE tests are similar (c.f., Table 3). These resultssuggest that the fi value evaluated by dr'ained TC tests,¥twhich is the most popular triaxial test method for sandt'and **ravel, can be applied ¥vithout si*･nificant modifications to other general triaxial loading conditions.It may be seen by rigorously examining Figs. 10, 16 andF:10o yc;>>c,/lel/ No 24. Ds ned T-OO22 that the ft value is slightly higher in the drained TEtests than in the drained TC tests under other¥vise thecF";;; 40() kP(Ef o.0125 9tJrnirL , from r !lo te 20 ,,:o2 4 6 8 102 14 16 i8Absolute value of irre¥*ersible shear strain,Fi('.- i yi* I relation is basically similar bet¥veen the respec-(Hostun sand). It may be seen from Fi_ s. lO, 16 and '_2* fil)m E!lO te 20 *:: *0.51 .O in the TC and TE tests, respectively.It may be seen fr'om Figs. 17 through 21 that the R = crf /viscous property in the drained TE tests is also of theTESRA type as in drained TC tests.The A RIR-log { i*). **,/( i') ,f"'} relations fr'omdralned ML TC and TE tests are summariz,ed in Fig:. 10(Silica No. 8 sand). Fig. 16 (Toyoura sand) and Fig. 22i _Ol:(Tf)/((Tf - (T ), is equal to 0.0 andences that can be seen are due likely to the factors listedabove (in particular term 2). It may also be seen that theg,j r I oO . E lOg'parameter, b = ((Tti¥'e pair of drained ML TC and TE tests. Some differ-IQe.20u. 53) Interllrediate Principa/ Stress: The Bishop'scr2S$ 2 Oft * ' txrQ**same test conditions. As mentioned earlier, the stressstate becomes more overconsolidated during dr'ained TE,unlike during ML drained TC. Ho¥vever, it is likely that20 22/ , (9/ )21. a) R- i '*1 antl b) c:* iy"i relations from a ML TEwith strain rate changes (Hostun sand, batch B; OCR= l)testdecreases during ML. Therefore, the stress conditionbecomes more overconsolidated in terms ofp' durin_",_drained ML TE.the effects of this factor are insignificant, as mentionedearlier. It seems, therefore, that the possible factors forthis difference include; a) inherent anisotropy; b) the intermediate principal stress; and c) the stress parameter tobe used to define the rate-sensitivity coefficient. Withrespect to the last term, the principal stress ratio, R = (Tf /(T , may not be relevant to define exactly the same viscosi- Fi=VISC OSITY OF SA ND IN 'IRIAXIAL 'TESIS679},*/ " Iff"/ f ll/ll///>' * l.l/ l!c:; 1,4J':*vS 07/,:*//ll f_;･t/ ' '::$O O1lri'l":']":"i':'1'**' -O 7ceJ:J J - ;C :Fig. 24.-2 l30eE o::25151 O t,lO;20b)Proportional rule to obtain viscous stress for h) ;teretic YF relation8s lO>c1 o:SiUca sand No SlO:sE lO/E Iea)1 OsvS 15" O.5t'lllOt:.> l.Ov'pe 05)>)10i¥. 'o 8. DrainedC> :lic, cr.E,,= O 0125v400kP*mil losl Ocs O_from **,*lO to 20e);: OO-lO_//.l_/* IS3Toyour sand3OOE=ONo 20.e{),Je' -l ODTaine(1 C> :lic.8,= 0,01 251g+ fromlrreversible shear strain. 'f ,*(o/ )cr'= 400 kPa'mirf+"I O to 20 ,J*-i 530Fig, 23. Effects of step changes in the strain rate on the normalizedSilica send ¥. 'o S:1 5stress･strain relation from cyclic triax'ial loading ('1'o . oura sand)ty parameter for the drained TC and TE Ioading conditions, as discussed in Tatsuoka (2006).It may also be seen from Figs. 17(b) through 21(b) that::15OE*e'! lOlarger with a decrease in the strain rate in drained TE testsc iol OE¥* 'o 20. DTnjned C'Yclic. e,*= 400 kP Le':O_ "E = O Oll ' *nxil3t)>VISCOSITY IN CYCLIC TRIAXIAL LOADINGTest Resu!tsFigure 23 sho¥¥'s the results from the following threedrained triaxial tests performed at ( = 400 kPa on looseE fromflOt020 *0.0-3J-Olrreversible shear strain. Jl,( 1.)Fig. 25. Effects of step changes in the strain rate on the normalizedToyoura sand:stress-strain reiation from c .'clic tria, ial loading (Silica No. 8 sand,Test 1.･ the specimen was loaded from the isotropicai = 400 kPa)stress state (point O in Fig. 24) to a maximum stresspoint in TC (point A in Fig. 24) by primary drained TCtraversing the TC and TE stress states:loading at.Y (positive) =R - I in TC,= o (=0.01250/0/min). Loading wasreversed at point A to¥vards the minimum stress pointin TE, followed by another load reversal to TC Ioading. Such load reversal ¥vas repeated. b*, ¥vas changedstep¥vise many times.Test 2: the specimen was subjected to primary drainedTC Ioading at aii = a = 400 kPa.Test 3: the specimen ¥'as subjected to primary drainedvhere R = (Tf lcr= cr( Icrh;Y (ne*'ative) = I -R in TE, where R = (T /a = (71',1(7( (17)Y= O at the isotropic stress state, ¥vhere R = I .Despite that it is subtle, Toyoura sand temporarilysho¥vs a slight rebound in the volumetric strain immediately after a change in the direction of loadin*" from TCto TE (Fig. 23). This trend of behaviour cannot bedrained triaxial tests on Silica No. 8 sand. In Figs. 23 andobserved in Fi**. 25 for Silica No. 8 sand. This may be dueat least partly to extra axial strain incrernents (negative)by bedding error at the top and bottom lubricated ends of25, the stress parameter, Y, defined by Eq. (17) isintroduced to achieve the continuity of stress whenspecimen, ¥vhich are larger with Toyoura sand, ¥vhich iscoarser than Silica No. 8 sand. Another possible reason isTE Ioadin*' at (71" = ( f =400 kPa.Fi**ure '-5 sho¥vs results fr'om one of three similar".i"*iol 0t::the rate d8 :r.1 / ! dy i* ! (positive for contraction) becomesas in drained TC tests.b)-*_,.* 20 * !KIYOTA AND TATSUOKA680stress conditions are repeatedly traversed:o 08o 06Toyoura sandR ' = R * .g, (a)i*) (18)where R f= = is the inviscid principal stress ratio componento.04( 00that is to be substituted into Eq. (1 8) to obtain the viscous-* o ooloading, Rf* js equal to R , and Eq. (18) becomes thestress ratio component, R '. During the primary TC or TE-o 02-o 04:that takes place upon a step change in'o 4. DTained TE.00242No S DTainedCyclicThe relationship bet¥veen the inviscid stress ratio, Y *, andSilica No 8 sand Ao 04fo 02ooothe h reversible shear strain, y ', for the test resultspresent.ed above is schematically depicted in Fig. 24. Forf ccthe Yt - y'* relation, referring to Eq. (17), ¥ve obtain:Yf (positive)=R f_ I in TC_;Yr (negative) = I - R r jn TE (_'O)-o 02Nishi et al. (2002) proposed the follo¥vin*' method to:A-o 04obtain the value of A R + (Eq. (19)). That is, "the in¥'iscide N'o IS Drained TC. P= O 0272 *;-o 06', A R A RA R =R A g ( y*') (19)wlrl-o oso 08;::c (viscosity, the follo¥ving equation, ¥vhich can be derived.from Eq. (18), is assumed to obtain a sudden change in Re ¥*=03.DTainedTC, =001CX) i-O 06o 06orl'Inal equatron R R g ( i*). For the TESRA typea-o 08O Olstress ratio R * at point (1) in Fig. 24, for example, isobtained by substituting Yf= *<(Yf)1 at point (1 ') IocatedA ¥. 'o 19. Draine ! TE. = O 0304¥* 'o 20.2 .22. DrEined CycUc. = O 0223 iAOilOOORatio of irr. shear stTain rates before and af er a step chan_ e.'*..'! *j"*** / hel=**along the primar'v_ TE Ioading branch" into Eq. (7-0). Thevalue of (Yi )1. is obtained by the follo¥ving proportionalrule:(Y ) - (Y )1-(Y )A .(Y ) (21)Frg '6 Companson of jR/R Iog L(/ ")*Ft,*/(y")b,f"'*} relationsfrom drained ML TC, ML TE and cyclic triaxial tests of loose!'- (Y )B_(Yf)Atriaxial tests of loose Toyoura sand (Fig. 23) and Silicawhere (Y )A and (Yf)B are the Yf values at kno¥vn pointsA and B. It is assumed that, ¥vhen unloaded from point A(under TC stress condition) to vards point C (under TEstress condition), the incremental stress-strain relationfrom poim B becomes the same as the one in the primaryTE. Ioadin_"*. ¥vith a shift in the strains. Note that, inFig. 24, the hysteresis loop is not closed, as seen fromFigs. '-3 and 25. For this reason, the proportional rule,Eq. (21), which is more general than the Masing's secondNo. 8 sand (the test presented in Fig. 25 and the other t¥vorule, is relevant (Tatsuoka et al., 2003).tests) ¥vith those from the drained ML TC and TE tests.Some data points, typica]1y point a, obtained from thecyclic triaxial tests deviate largely from those from theML TC and TE tests These data points are those immedi-When follo¥vin*" the proposal described abo¥'e, inFig. 24, the viscous stress component, R , immediatelyafter the start of unloading from point A becomes thesame as the value at the starting point O in the primaryTE Ioading for the same irreversible strain rate, asspecimens of a) Toyoura sand and b) Silica No. 8 sandthat the Toyoura sand specimens ar'e more dilative thanthe Silica No. 8 sand specimens, as seen by comparingFigs. 6(d) and 13(b).Figures 26(a) and (b) compare the ARIR-log{( i').f***/( i*)b,f "} relations from the drained cyclicately after load reversal vith a change in the sign of'*.The deviation tends to disappear as the loading continuesin the same direction.It is seen from the above that Eq. (5) (for the isotachtype), which is R =R*･g.( i*) in the present case, andEqs. (7) and (16) (for the TESRA viscosity) should bemodified to properly describe the viscous property underunloadin*' and reloading conditions, or generally undercyclic loading conditions, in ¥vhich the sign of irreversibleaxial or shear strain rate is changed repeatedly.obser¥'ed in the experiments. Moreover, the ¥'iscous stresscomponent, R ', at point B, ¥vhich is reached by unloading from point A , becomes the same as the value at pointB' during primary. TE Ioading, at ¥vhich R i (and thereforeYr) is the same as point B. Then, the viscous stress com-ponent, R', when unloading continues from point Bto¥vards point C becomes the same as the one for thesame values of Rf and i* during primar)' TE Ioading.Consequently, the viscous stress component can becomecontinuous ¥vhen the stress state returns from an unload-Modlfi cationsNishi et al. (2002) proposed the follo¥ving equation todescribe the isotach type viscous stress component undercvclic triaxial loadin conditions in which the TC and TEing (or reloading) branch to a primary loading branch.The same rule as described above is applied to other subsequent unloading and reloadin_9: branches.Figures 27(a) and (b) compare the relationships ,¥'1SCOSITY OF SAND IN TRIA¥lAL TESTSTo)L ur;O ri.SO 06sand 1makes point a deviate largely from the relation for the1liR=AR (negative). On the other hand, as (Y)1 isO 04a : 1O 02C:O (Tf)negative, and so is R*. Then, the stress ratio, lR-/R*,becomes positive, vhich makes point a located similarlyas the relation for the ML TC* and TE tests in Fig. '-7(a).-C) O-O.()4lvlL TC and TE tests in Fi :. '_6(a). As the value Y at pointa (i.e., (Y)1) is positlve (under TC stress conditions),)hl681=: = e No 3 Drained Tc p'==-O O(,:s'O4 Dri l)2( {] lnedTE P=00242 jos.Drainetic)clic'=(1'ois9It may be seen from Figs. 27(a) and (b) that the scallngrule (Eq. (21)) together vith the sign rule (Eq. ('-?-))appear to be relevant for the c_vclic triaxial loadin_",_conditlons traversing: the TC and TE stress conditions tobecome the same relation as the ML TC and TE ioading:*O OSO.OSconditions.One may consider that the ¥'iscous stress componentO 06during unloading or reloading is obtained only byproportionally scaling the total stress (cr = a r + (T ') and 8 i*O 04relation. In that case, the measured stress jump, A R, isO Olflscaled do¥¥'n by a factor of {(Y' )l-(Yf),A}/{(Yr)B_(Y')A} (smaller than unity) bef'ore being plotted inFig. '-7. This ¥vay of sc.aling makes the data morescattered than the plot presented in Fig:. 27. It seemsO OOC :-O Other'efore that the scaling of the viscous stress componentis not necessary.-O 04-O 06-O OSO1O O1iOlSUMMARY OF VISCOUS PROPERTY OF1 OORatio of irr. shear strain rates before and af'ter a s ep changeGRANULAR MATERIALF o '7 Compa:nson of J R /R*-log {(};i') /(1}i')E ,f< *fl relations*rl** ' '* '*from drained ML TC, ML I'E and c .'clic triaxial tcst of loosespecimens of a) Toyoura sand and b) Silica No. 8 sand'The follo¥ving facts can be reconfirmed from Table 3and Fig. 3:l) Thevalue is essentially independent of loadin_ ._method (PSC, TC, TE and cyclic triaxial).'_) These ft values of' the three different sand types arevery similar to each other.bet¥veen the stress ratio, AR-/R= <, and log ((y='),r* ,l3) These p values are comparable ¥vith those of otherf ,rl'-*"y(*Ib**i*) ,f,,,* } from the same data of ML TC and TE tests andcyclic triaxial tests presented in Figs. '-6(a) and (b). Thefollo¥ving tlvo stress parameters that are different fr'omt.hose in Flg. 26 are used in Fig. 27:1) AR-, Ivhich ha¥'e the same magnitude as AR (themeasured jump in R =(7f/a upon a step change inthe strain rate =A R ') and the same sign as A Y; i,e.,Fig. 3), except for' a relati¥'el}, high¥'alue of crushedconcrete ag regate.The parameter rl of the deca} functron gd .*,() *')(Eq. (8)) defined in terrns of },* for the respecti¥'e test con-dition ¥vas obtained by fitting Eq. (8) to the respective seg-change in the strain rate in all the lvlL TC and TE tests.'hen (Y)j >0 (TC stress conditions)The values of /･1 in each test ¥vere essentially independentAR=-AR= iYof th_e shear stress level ¥vhere the strain rate ¥vas step¥vise¥vhen (Y)1 <0 (TE stress conditions) (22a)2) R*, ¥vhich ha¥'e the same magnitude as the scaledstress ratio, for example, (R)i, at point (1 ') in Fig. 24and the same sign as (Y)1. (Eq. ('-3)): i.e.,chan_"*ed. The aver'age ¥'alue of' /'1 f'or each test conditionar'e listed in Table 3. It was not possible to confidentlye¥'aluate the values of rl dur'ing the unloading andreloading branches because of relatively small viscousstress components. It may be seen from Table 3 that thevalue of rl is similar among the three sand types. TheR* (positive) = (R)1, = (Y)1 + 1.0¥'alue of rl is slightly larger (i.e., a slightly slo¥ver rate ofvhen (Y)1. >0 (TC stress conditions)decay) in TC than in TE, Ivhile the efi cts of OCR are¥'er_v small.R* (negati¥'e)= - (R)1, = (Y)] - 1.0(2?_b)) ･ /, ** , + *i***For example at point a in FiO 23 (( + )b,,f*-=(,i')･ /( i')b,r.,'* 100 and A R is negatrve* * **ft**vhile R is positive. So, the r'atio A R/R is negative,po¥vder of' Fujinomori clay and kaolin (presented inmental R o /(7 i yi'j relation follo¥ving each stepAR-=AR=1]Ylvhen (Y)i, <0 (TE stress conditions)granular materials and compacted o¥'en-driedvhichCONCLUSIONSThe follo¥ving conciusions can be derived from the testdata and their analysis presented above: KIYOTA AND TATSUOKA6s21 . A fine uniform relatively angular sand, Silica No. 8sand, exhibited nearly the same stress-strain relationsin monotonic loadin_ : (ML) drained triaxial compres-RF,FF.RENCESl) Anh Dan> L. Q.. Tatsuoka, Fand Koseki, i. (2006): Viscoussion (TC) tests at constant strain rates that ¥veredifferent by a factor up to 200 under other vise theeffects on the stFess-strain characteristics of gravelly soil in cirainedsame test conditions. On the other hand, the de¥'iatorstress exhibited a significant jump ¥vhen the strainrate was changed step¥vise during other¥vise ML at aconstant strain rate, ¥vhile significant creep strainstook place during drained sustained loading at a constant deviator stress. These apparently contradictingtrends of loading rate effects can be explained in a unified ¥vay ¥vhen based on noticeable decay in a gi¥'enviscous stress increment ¥vith an increase in the irreversible shear strain (called the TESRA ¥'iscosity),2) Aqil. U.. Tatsuoka, F., Uchimura. T., Lohani. T. N. .. Tomiia, Y,and ¥1atsushima* K, (2005): Strength and cieformation characteris-as have been observed lvith To_voura and Hostunsands in the previous studies.2. With Silica No. 8, Toyoura and Hostun sands, the¥'iscous stress increment decays ¥vith an increase inthe strain (i.e., the TESRA type viscosity) in the lvlLtriaxial extension (TE) and cyclic triaxial loadingtests in the similar vay as the lvlL TC tests.3. The rate-sensit!¥'ity coefficients, fi, for the relation-ship bet¥veen the pr'incipal stress ratio, R=(Tflcr ,and the irreversible shear strain, y**, ¥vhich representsthe viscosity of a gi¥*en material, evaluated by the MLTE tests lvas very similar to the ¥*alue e¥'aluated bythe lvlL TC tests. lvloreo¥'er, in both TC and TE tests,the effects of overconsolidation on the fi ¥'alue ¥vereinsignificant. Furthermore, nearly the same P value¥ 'as obtained from cyclic triaxial tests ¥vhen relevant-ly scaling the stress parameter and redefining the signof the stress jump. These results suggest that therate-sensitivity coefficiem, fi, obtained by TC testscan be applied to general triaxial stress conditionswith minor modifications ¥vhen necessarv.4. The values of fi of the tested three types of sands aresimilar to each other, ¥vhile they are also similar tothose of other types of sand and gravel as ¥vell ascompacted oven-dried clay powder having largelyriaxial compression, Ceorec!1. re.st. J . AST*tif 29 (4), 330-340ics of recycled concrete aggrega e as a backfi]1 material, Soi!s anc!Fotinda!ions 45 (4), 53-723) Deng, j. and Tatsuoka. F (2004): Ageing and ¥*iscous effects on thedei'orma ion of clay in ID compression, Pr'oc. GeoF!'ontiel' 2005r_ongress. Geolns[inlte, ASCE, Austin. Texas. GSP 13g. SileCharacterization ar d'lodeling (edsby(ayne el al ).4) Di Benede o, H , Tatsuoka, F and Ishihara, h,l (2002): Timedependent deformation characteris ics of sand and their conslitutive modeling, Soils and Founclations, 42 (2)* 1-22.5) Di Benedetto. H., Tatsuoka. F.. Lo Presti. D , Sauzeat. C_ andGeoffro¥'. H, (2005): Time effects oTthe beha¥*iour or geomaterials,Keyncue lecture, Proc^ 3rc! Int. Synlp Defornla!!on C_ haracler!st!csof Geonlalerials. IS L_von 03 (eds. by Di Benedet o et al.), Balkema,Sept. 2003 2, 59-123.6) Di Prisco. C.. Imposimato. S^ And Vardoulakis, I_ (2000):,Iechanical modelling of drained creep triaxial les s on loose sand,Giolecllniclue, 50 (1), 73-827) Enomoto. T , Tatsuoka, F . Shishime, ,1., Ka¥vabe, S, and DiBenedetto, H (2006): V}scous properly of granular material indrained triaxia] compression. Proc. Geo!ech. Sy'mp Roma (to appear).8) Fukushima, S. and Ta suoka, F (1984): Strength and deformaLiolcharacteristics of satura ed sand at extFemely lo¥v pTessures, Soi!sanc! Founcla!ions, 24 (4), 30-4S.9) Golo. S.. Tatsuoka. F . Shibuya, S . Kirn, Y.-Sand Sato, T(1991): A simple gauge for local small strain measurements in thelabora orv, Soi!s anc! Founc!ations= 31 ( ), 169l80_IO) Hayano, K., ,Iatsumoto, ¥. I., Tatsuoka, F. and Koseki, J (2001):E¥'alualion of time-dependem deformation property of sedimemar) soft rock and its constituti¥'e modelling, Soils and Foundarions,41 (2). 21-38l l) Hiraka va. D^ (2003): Stl dv on residual deformation charac. eristicsof geosyntheric-reinforced soistFuctures, Dr. of Engineeringrllesis, University of Tok.¥'o (in Japanese).i2) Hoque. Eand Tatsuoka, F_ {1998): Aniso ropy in the elasticdeformation of ma erials, Soi!s ancl Foundations, 38 (i), 163-1 7913) Hoque, E and Tatsuoka, F^ (2004): Effects of stress ratio on small-slrain stiffness duriug lriaxial shearing, Gdo,echnique, 54 (7),429-439.14) Ho¥vie, J_ A.. Shozen. T_ and Vaid, Y. P. (2001): Effecof agein_",_different particle sizes (except for recycled crushedconcrete).on stiffness on loose Fraser Rover sand, Ac!vancec! Laborclrolt}'Stress-srrain Tes!in*" of Geomaterials (eds_ by Ta suoka et al.),5. The decay manner of viscous property ¥vith an15) Kiyota, T , Ta suoka, F. and Yamamuro, J. (2005): Drained andincrease in y** is similar' among the three differentundrained creep characteristics of loose saturated sa d anci theirrelation, Proc, GeoF]-on!ier 2005 Con*"ress. Ceolnstilu[e. ASCE,Ausiin, Texas, CJSP 138, Site Characterization and ¥= iodeling (edssand types. The decay rate in the ML TC tests isslightly smaller than in the lvlL TE tests. The effectsof overconsolidation history are ¥'ery small.ACKNOWLF,DC.F.MENTSPart of the experiment on Silica No. 8 sand and itsnumerical simulation ¥vas performedvith the help of lvlr.Alan Ezaoui, from the D partement G6nie Civil etB timent, Ecole Nationaie des Travaux Publics de l'Etat,France, when visiting the Universit_v of Tokyo. The helpof the staff of the CJeotechnica] Laboratory at theUniversity of Tokyo is greatly appreciated. Financialsupport from the IMinistry of Education, Culture andSport, Government of Japan is greatly ackno¥vledged.Balkema. 235243-by,1aynet al.).6) Komoto, N . Nishi, T . Li. J, Z,. and Tatsuoka. F (2003): Viscousstress-strain properties of undisturbed Pleistocene clay and itsconstitutive modelling, Proc. 3rd Int. S;*nl. Defonna!ion Characierislics of Ceomateria!s. IS Lyon 03 (eds. by Di Benedetto e al.),Balkema, September, 2003, 579-587,17) Ku¥vano, R. and , ardine, R. J (2002): Ort measu ing creepbeha¥'iour in granular materials through triaxial esting, CanGeotech. J., 39 (5), 061-l07418) Lade, P V_ ar d Liu, C_.-T. (1998): Experimentai sludy of drainedcreep beha¥'iour of sand, J. Engr*". * lech, ASCE, 124 (8), 9'_920.19) Lacie. P. V. and Liu, C_ -T. (2001): ¥. ,Iodeling creep beha¥'iour ofgranulaF materials, Con7puter Alerhoc!s anc! Adl'a,7ces fnGeomec!1anics (eds. bv Desai et al.), Balkema, 277-284,20) Li, J.-Z , Acosta- ,iartinez, H , Tatsuoka, F^ and Deng, J -L(2004): ¥riscous property of soft clay and itS modelling, Engineering VISCOS韮TY OF SAND正N TRI．へXIAL TESτS683 P’ヤα（漉θα1∼ゴPθ1プ01’〃∼θ∼κ・θoゾ5ψ0θρ051δ，P1｝oc、∫SO∫αんσ2004．351Taζsuoka，F、（2006）：五nelas芝ic delomlation characteris［ics ol 1−6 geonlateria1，Speci＆！Leculre，So1！S’1θ55−5〃て11刀8（∼1∼【1ylo1∵早、／（∼‘15ま’ヂ（∼一21）Ma正sushita，M、，TaIsuoka，F、，Koseki，」、，Cazacliu，β、，D1 η∼θ’π，イ、／0ゴθ1〃∼9α刀6！．41rαひ写Z5，P1’o（・、（9θo∫θ‘1r，εy〃1ρ、（eds，by Ling Benedet｛o，K．and Yasin，S，」、M、（1999）：τime effecζs oo【he pre−peak de妻ormadon properζies of sands，P1’oc、21∼ゴ／1∼∼、Co尺ズ ρ1捗搬’∼正！1｝θρ401’〃∼α∼’on Chα∼ααθ1一’5’ic5毎磁01∼副θ1”α15，∫S ro1｝ノno’99（eds、byJamiolkowskieta1、），βalkema，1，681−689、22）Mejla，C、A、，Vaid，Y、P．aKldNegし！ssey，D、（1988）：TlmedepelldeK1〔 et aL）．March16−17，2006，Roma，36） Tatsuoka． F．， N韮olenkamp， ヂ．， Tor§，T、，and Hillo，丁．（1984）＝ Behavior of lubrication layers of pla［ens in elemen｛｛es｛s，50〃5α1∼4 Fα’！1ゴα1’o∼∼5，24（1），IB−i28、37）Tatsuoka，F、，Sa芝o，丁 ，Park，C．一S、，Kim，Y．一S、，N・1し監kabi，」、N、and behaviourofsalld，P1’oc、11π、Co’アブRhθ010＆γα11グSo〃A1θchαノ1’ぐ5 Koha［a， Y、 （1994）： 汽leasuremen芝s of elastic properζies of （eds、by Keedwem，εlsevier Apl）11ed Science，312弓26、 geomaterialsilllabora［or｝’compressiomests，Gθαθご1∼．7θ甜、／、，23）Murayama，S、，Michih1ro．K、aPdSakagami，τ、（1984）：Creep characterisτics Qf sands，Soπ5α1κノ」Foε〃∼ゴαず’011∫24，（2），1−15、 ASTM．17（1），80−94、38）Ta〔suQka，F，Modoni，G、，J1ang，G、一L、，A君猶Dall，L、Q、，Fiora，24） Nakamura，Y，，Kuwano，」．and壬｛as翻imo乳o，S．（｝999）＝Smallslrain A、，八玉a｛sしKs員ita，NI、alld Koseki，」，（1999a）：Stress−s芝rain behaviour stlf責ness and creep ofτoyoura salld Ineasured by a ho賛ow cylinder a【sma！ls【raiRsofunboundgra且ularmaterialsandl￡s！aboraエory ＆P［）ara毛us，1二》roぐ、21∼‘ノ∫’1r．Co’1ゾニPヂθ一ノi【z〃‘”ぞ0（グb〃nα”01∼C1∼α1’αc一 老ests，Keyl10teLecture，P”oc、駒1甲ん∫hOρo∼』、／0ゴθ1〃n9α1∼4 ∼θノ’加（50∫Gθ01η醒θ廠Z∫，Tor1no，1999，Balkema（eds，by ．44v醐Cθゴτθ5”ノ19．砂U1めα’1∼ゴG1糊ε’1σノー」、愈πθ舶Z5，Ial1瞭y Janliolkowskiαal．），玉・i4玉一148，25｝Naw1r，9，，Kuwa蹴o，R，aad Tats襖oka，R（2001）：Eぼec￡s of s甘ess 21−22，1999．LjsbQa（eds、by Correia），Balkema，17−61．39）Tatsロoka，F．，∫ardille．R，J，，LQPres【i，D、，DiBenedel【o，｝｛、and paIh on the貝ow rule of sand in triaxial compression，〆蓋ゴγ、五αδ． Kodaka，丁「、（1999b）：C豹arac【er1sing ｛he preぜailure defor：11aζion Sr1で55−S〃w〃1 7’θ5’、 （3θ01刀α1θ1ゾαZ∫ （eds． by Ta芝suoka e【 ＆1、）． properdes of geoロ1aterlals，Thenle Lecture for【むe PlePary Sessioll Balkema，287−294、 No， 1， PI−oc． λ！∫「 ∫C Sル1F五， Ha且1burg， September 至997， 4，26） Nawir，棄｛．，Ta［s目oka，F、and Kuwa【10，R （2003a）＝Experiτnell芝ai 2129−2164、 evaluaτlonof由eviscousr）ropert1esofsandinshear，501Z5αノ1ゴ40） Taζsuoka， F．． San［ucci de N正ag1s乳ris． F，， 汽｛omoya， Y． and F加η面∼’oノ∼∫，43（6），B−31、 λ1a「uyanla，N，（1999c）：正so【ach beha、一iour of geonlalerials and註s27） Nawir，H、，Ta｛suoka，F ，and Kuwano，R、（2003b）：Viscous e鐸ects nlodeまi員9， ρroc． 2ノ∼ζノ ∫’∼’， ≦ミw1∼ρ． P’ぞ一∫α’1i’”8 ∠）（ヅ10〃1∼α∼’01r on ［he shear yielding charac【erisζics of saud， So’Z∫ α∼1グ Chα1ηαe’一Z5∫’c50ゾGθo〃∼α∼θ’｝’‘∼∠∫，1S roヂ’ノ∼099，Balkema，Rαter− ヂoμノ∼面”o’∼5，43（6），33−50、 dam，1，491−49928）Nishi，T、，KQmαo，N．and Tatsuok＆，F，（2002）：Simし瓢ialion of4至）Tatsuoka，F，，Sanしucci deMagisこris，F、、Hayano，K，，Momoya，Y， deformationduringcydicioadingofsoilbythegenerai！hree− andKosek1，J （2000）：Somenewaspec【sofτimee貸ec【son由e compo汽e撚modei，Pヂoc、37’1∼／ρ1∼、蜘’、Co厭、Gθαθご1∼、五ン’91召、， s【ress−s【ra1nbeha、’iourofst潰『geo猟aterials，KeynoteLec［ure，7hθ （Osaka〉JGS，（in Japanese）． Gθo’θd∼’∼’cεo∫κα1’‘1So〃∫一Soゾ’Rocん5，Pヂoc．21∼4／1∼r、Co’ゾκσ1’ゴ29）PbamVaΩBang，D、andDi Bellede【【o，脛、（2003）＝E昼ectofs［rain So〃5 α11（ノ 50ゾ’ 1∼oぐん5， Napoli， 1998 （eds． by 狂vangelis【a alld ra芝eo“由ebehav1ouroゼdrysand，P∼oc、3’マ4∫1π．⑤v1刀ρ． Picarelli），Balkema，2，重285−B刀、 P⑳1甲1刀α”o〃Chα1｝ααθ1｝’∫flc50ゾGθo’∼∼α！θ’ゴoZ5，∫5五3’oノ∼03（edsby42）Tatsuoka， F．， Uc騒imura、T、， Hayano， K、， Di BeaedetLo， 9．， Dl Benedetto eこa1、），Balkema，Sep韮、，1，363−373． Koseki，」、and S1ddiquee，M、S、A，（2001）1Time−dependent30）Samuccl de Maglstris，F「．，Kosekl，」、，Amaya，M．蕪amaya，S，． defOrmatiOn CbaraCter1SliCS Of S｛i貿 9eOmaξer1alS ln ea黛ineering Sato． T and τa｛suoka， F．（豆999）：A triaxial tesεing syslem to prac薮ce， ｛he Tわeme Lecture， Pノ’oぐ，2／1ゴ ／’∼∼、 Co1りく、 P1｝θ一ゾi‘7’々‘rθ evaiua【estress−strainbeilaviou罫ofsoils forwidera鷺geofls1rainand 0401’〃∼α！’01∼C11α1’ααθノ”5”C30ゾGθ0〃∼‘”θ1ゾαZ5，TOI−lno，1999（eds． s芝rain ra毛e，0θo’8c1∼、7を∫’、∫．，ASτNi，22（1），44−60． by Jamioikowsk1el al．），Baikema，2，三161−1262，31）Siddlquee，M．S、A、，Taエsuoka，罫、andτanaka，T．（2006）：FEM simuiaエionofζheviscouse窪ec【sonヒhestress−strainbellaviourof43）Tatsし…oka，F，，Isllihara，M、，Di Benedetto，H、and Kuwa鳥Q，R， sand in Plane strain coτnpression，So”5α’∼ゴFヒ）μ11ゴα’ioη∫，46（1）， geoma￡erialsand由eirsimulation，So〃5αηゴFα11∼面’ioノ∼5，42（2）， 99−108、 103−129、32）Suk垂je，L．（1969）：R1∼ε0109’cα1〆i5ρθα∫oゾ50’1A4θご1∼α’∼ic5，酵〆’1の呼一 （2002）：Time−depende凱shear deformation characteristics of44）丁撮suoka， F、， 氏lasuda， T． a鷺d S王ddiquee， L王． S、 A． （2003）： ∫1∼fe13c1θ1∼cθ，Londo“、 氏・lodell霊ng t！1e stress−strain behaviour of sand in cyc巨c plane stra1n33） Tatsuoka，F．（2001）：Impac｛s on geotecllnical engineering of several ioad1ng，Geo｛echnlcaland熱vironmenξa！Engineering，滅Gθαθc1∼、 reCent§ndingSfrOmlabOratOryStreSS−StraimeStSOngeOmateria1S， 五η、”1−oη五’∼grg，ASCE．茎29（6），June1，450−467． 2000Burmister Lecture at Columbia University，Gθo∫θぐ1∼1∼’c3、戸α45）Yamamuro，1、A、and Lade、P、V、（1993）：E貸をc【s of strain rate on 1∼oα4∫，Rα11万σcん∫α’1ゴ勲πh5微伽ノで5（eds．byCorrelaand 玉nsζabili【y of granu藍ar soi王s， Gθo’θc11， 7セs’、 ノ．， AST∼正， 16 （3）， Brandle），Balkema，69一王40、34） Tatsuoka，F．（2004）：E貸セc｛sofviscous proper盛esand ageingon直1e 304−313． stress−strainbehavioufofgeomaζerials．Pヂoc、G1−／σS駒1凹ん∫hoρ （eds、by Yamamuro and Koseki），ASCE Geo［echnical SPT，1｛0 air−dr1edmicacioussandinplanes【raincompressioΩ，P1’oぐ，／ρ’∼、46） Yasil1，S，∫．｝〉1．and Taしsuoka，F．（2003）；Viscous property of a雛 N竹∼、Coπゾニ（フθo’ε【ゾ1，だn9ヂ9，Ak1t＆．Jap＆nese Geo｛ec鼓nical Societ》・． 684KIYOTA AND TATSUOKAAPPENDIXA猟bleA玉。L量sIofβv幽esfromloadingleslsw謎hslepchangesinthes重mlnrate，presen｛edinFi9・3N瓶aIeriaiGrading propertiesOr1磁nalCrushedsandstone：Chiba grave！05亀）竺7、8mm，（molstPmユx漏39．6mm，compaαec玉）Uc竺1L2，De職s註yb∼VeI condltio鷺MoiSt（、私胤5％，S，謹77％）Dense，θ罵0．19（two Range ofε、Test me出od （％／m三n）Ref．βDra玉ned TC a覧 0．0006− 0．0335σ1沖490kPa α06％／miΩAnh Dan eτal．（2006）specimens）G、繍2．71Nlodel Chibagrave1A（air−driedcompaCted）Crushed saadstone：Ai卜dried050竺0、8mm，e筥0．584Dralned TC at O．008− 0，0244and O．556σ貞郡40kPa α00008％／min鍼玉rakawa（2003）（ρ灘L760uに漏2。1，and1。7709／cm3）0ロ葦轟x讐5．Omm，（3、漏2．74，θロ撚皿0．727，θn，iロ漏0．363Ir｛ostun sand（batch B；air−Pluviated）Quartz甲ric員Air−dr玉ed0、漏2．65，QuartZ−r1cllDi Beηede柱o et al・Alr−drledSaturatedθ￠罵0．72Dra玉賑ed TC aζ 0．006− 0．024P島am Van Bangand O。93σ‘竺80，200％ 0、6％／min400匙Paand D玉Benede鷺Oθコ0、658sub−angular，Pずα18mm，U3L64，Al卜driedG、謹2．65，（2003）Dra玉ned PSC at O，000108− 0。0219！Vlatsusl1髭a et al．σll筥400kPa 1。08％／min（1999〉τatsuoka e【al．θ、漏0．674Drained PSC at、0．004− 0，0207and o、673σ卜30 0．4％／mln ando．0226 （2004）and80kPaθnlax瀟0．99，θロ1111筥α62τ〉laISush髭a et a1、（1999）and（2002）θFn…＝1罵0．55ToyourasandDrained PSC at O．00025− 0．0219σ孟漏392kPa O．259も／mlnP5。漏0、31mm，u。讐L94，θ醗該x讐0．95，（a1r−pluvia【e（i）θ。讐0．698and O。700sub−a澱gular，Alr，dr1edθ、漏0。633−0。649Drained TC at O．00008− 0．0269H1rakawa（2003）σ孟罵40kPa O．008％／minS＆turatedθ讐0．658DrainedτC aI O．00108− 0呼0205σ≦罵200kPa LO77％／minSatura覧edθc讐0、605−0、925and a玉卜dr1edMa置susbitae【a1、（1999）Dral鷺ed TC at O。0008− 0。0242暮a、vir e芝 al．σ‘讐玉00− o．12％／m沁（2003a）Dralned TC at O．00125− 0。0272τbepresentstudy600kPaSHica sand0ず0．077mm，No、8U。識2，43，（alr−pluv玉ated）SaturaIedεC竺1，B5σll竺400kPa O．25％〆mlnθ、露2．655，θロ13×質L335，θ臨罵α73，Janlu隷a0∫。竺α16，river sandu。漏L99，（air−piuviated）FC筥7％，Alr−dr1edθo竺0．フ75Drained PSC a【 0、00125− 0．0273and O．821σ‘竺100 α125％／ml厳Yasln et a！、（2003）and400kPaG、瓢2．7，θm：Ex司．173，θ，，，in盤0．690C田shedconcretea黛黛re黛ateP50漏5ふ65，（w司．6．69， 1759／cmG、漏2石5，17、349も，（ρd）ほ、誌N需1．789／cm3F癖nomoriclay31MQist ρd漏L72・3FC讐王、2−2．玉％，0ず0．Oi7mm，Uc罵玉0，P1讐33，LL漏62％Drai資ed TC O、001− 0．0536Aq簸et al．（2005）σ孟＝20kPa O．1％／m1nnearly讐、t’。P己筥L69％A1r−driedθ。盟LO93Drained TC飢 0．002− 0．0444Lietal．（2003）σll漏77kPa α29も／m1n（脂竺4．29％，5，巳f漏8．09％）Air，driedθ。漏L202Drained TC at O．003− 0，0353σ孟漏80kPa Oβ％／mln（w轟r竺256％，S，．評4．68％）Kaoiin3卜05。望0、0013mm，AiトdrledPI罵4玉、6，い，ar讐03％，LL讐79．6動もS，、ユf漏0．5％）Ai卜dried（｝㌦讐α3％，θ。漏玉．38Dra呈nedτC at O．000046− 0．029σA漏王00kPa O．oo玉2？る／min（2005）θc漏L41Drai自ed TC a芒 0。000049− 0、030σ‘漏100kPa O．00B％〆ml鷺S，、ユf轟0，5％）1）Dengand TaτsuokaθC竺co践so玉idate謡vo玉d ratio．2）wユfandS「ほflmeas駄redaftereac蝕εesし3）Tlleβvalue a［ove鷺一dried state was inferred based o【｝［he respec【iveβ一S。relatiorL | ||||
| ログイン | |||||
| タイトル | Preliminary Report on the 17 February 2006 Leyte, Philippines Landslide | ||||
| 著者 | R. P. Orense・S. E. Sapuay | ||||
| 出版 | soils and Foundations | ||||
| ページ | 685〜693 | 発行 | 2006/10/15 | 文書ID | 20950 |
| 内容 | 表示 .SOILS AND FOUNDATIONS Vol. 46. No. 5. 6S_1"-693, Ocl 2006Japanese Geolechnical Societ)PRELIMINARY REPORT ON THE 17 FEBRUARY 2006 LEYTE,PHILIPPINES LANDSLIDEROLAiN'DO P. OREN'SEi) and S ¥, UEL E.S 4 pU Avii)ABSTRACTFollowing days of hea¥'y rainfall, a large-scale landslide occurred in Southern Leyte Province, Philippines, buryin_",_almost the entire village of' Guinsaugon and causing the death of more than 1000 people. The landslide, ¥vhich occurredalong the steep slope of Mt. Can-abag in the middle of the province, mobilized large amount of rocks and debris ¥vithestimated volume of about 101 5 million m3. This paper discusses the results of the damage investigation conducted inthe ar'ea after the disaster, Ivith emphasis on the general features of the landslide and on the hydro-geological aspects ofthe disaster. Based on the obser'vations made from the field in¥'estigation as ¥vell as additional information obtainedfrom ¥*arious sources, the main causes of the landslide are identified, and several sources of potential hazards arepointed out.Ke¥_' words: landslide, rainfall, site investigation, slope (IGC: B3 IC4)be caused by future disasters.IN'TRODUCTIONAt around 1 1 A.M. on 17 February 2006, a large-scalelandslide buried almost the entire village of Guinsaugon,OUTLINE OF 1'HE AFFECTED AREASt. Bernard tolvn in Southern Leyte, the PhilippinesGeo!o*"ica! alrd Topographica! Settil7gLeyte Island consists of t¥vo political regions: Leytefollo¥ving days of heavy rainfall. The landslide coveredaround 500 houses and a primary school building,and Southern Leyte provinces. The province of SouthernLeyte, Iocated about 675 km southeast of Manila (seeresulting in 139 deaths and 30 injuries ¥vhile 980 people¥vere reported missing, including '-48 school children(based on the report by NDCC (2006) as of 5 P.lvl. 28February 2006). The disaster displaced 3,264 people andFig. 1), is characterized by relati¥'ely flat land alon*' its18,862 people ¥vere affected. The total cost of damage toelevation of 948 m above rnean sea level. An activeinfrastructure and a*"riculture is estimated at USS2.2rnillion (OCHA, 2006).To investigate this disaster, the authors undertook anocular inspection at the site durin*" 12-14 March 2006,volcano, Mt. Cabalian (elev: 945 m), is located near thesoutheastern tip of the island, about 6 km to the east ofcoastal area and rugged mountainous interior region. Thehighest rnountain in the province is Mt. Nacolod ¥vith anSt. Bernard town. This volcano could be a possiblesource of the thick ¥'olcanic materials presently coveringSouther'n Leyte.about four ¥veeks after the disaster. This paper outlinesthe preliminary results of the reconnaissance works, vithemphasis on the hydro-geological causes of the disaster.The general features of the landslide, as ¥vell as the mainfactors lvhich triggered the disaster, are also discussed.It is to be noted that although detailed information areMost towns in the province are surrounded by steepnot yet a¥'ailable and further investigation is necessary tomountainous ran**e as high as 800 m. Guinsaugon villageis located at the foot. of the north¥vest-trending mountainous range. Young volcanic rocks co¥'er the top ofthese mountains. The steep slopes are often planted withcoconut trees, the area's main crop. Ho¥vever, because ofunderstand fully the mechanism involved, it is believedtheir shallow root system, coconut trees are kno¥vn not tothat a quick dissemination of the important findingsobtained will help other resear'chers perform morecontribute to soil stability.in-depth investi**ation on this landslide. Moreover, sincesimilar disasters may occur in other parts of the world,active fault system ¥¥"hich transects the whole PhilippineThe Philippine Fault Zone (PFZ), a 1,200 km-lon_"*.archipelago from the Luzon Island in the north toMindanao Island in the south, traverses throughSouthern Leyte Province, including the town of St.such as in Japan, understanding the mechanism andimpact of this landslide can also assist geo-scientists,engineers and planners in mitigating t.he damage that willBernard. The locations of major fault lines in the region*) Associate Professor, Department of Clvu Engineering, Yamaguchi Universit.v. Ube-shi. Japan (orenseC･yanlaguchi-u,,ac.jp)ii' president, Infra-tech s),stems Consultants, Pasig Cit)', Philippines (sesapuay( ･ yahoo .com) .The mar uscript for this paper ¥vas received for revie¥v on April 24 2006; approved on August 4, 2006¥vritten discussions on this paper shou d be submitted before *¥4ay I , 2007 to the Japanese Geotechnical Society, 4-38-2, Sengoku. Bunkyo-ku,Tok)'o I 12-001 l, Japan. Upon request the closing date may be ex ended one month.685f OREN+SE AND SAPU686Yare sho¥vn in Fig:. )_(a). On the other hand. Fig. 2(b) sho vsthe traces of t¥vo prominent structures in Southern L,eyteas obtained from satellite Ima_"._ery: the north-north¥vesttrending Philippine Fault Zone and a north vest-trendingf'jLUZON,structure oblique to the Philippine Fault. From the'L:--. ;? .Jfigure, it is apparent that the site of the Guinsaugon':Maniri ..j'-)'(1:trT1l¥(landslicie is locatecl at the inter'section of these t vo fal.lltsi(La*'may et al., ,_006)..c¥r+Guinsaugon,*' Il' L. r"."}' [ '.1PiThe Philippine Fault mo¥'es at a rate of approximatelySt. Bernard(Southern Leyie)!,f '_*'.' '" l!2 to 2.5 cm per year (Bar'r'ier et al., 1991 ). Because of this,j ,1 i ;/L' ffc I' !'l'f!'_'*+*sf ' :"" ,, j,'cSouthern Le .*te can be considered as a highly seismicarea. According to data from the Mines and GeosciencesBureau (lvIGB) Region 8, the pro¥'ince has experienced_ Ifr" *' !'!1;9.: ('t .'*"_r'r' V]SAYAS"'f r"""iI ' !j"-hIl')!'!! '' __.1'Jcstrong earthquakes in 1907, 1948 (M6.9) and 1984! '-':' t(lvl6.4). Because of the numerous faults presem in thearea, the underlying rocks are badly broken or fragmented, making them susceptible to ¥veathering and erosion.r"i J _-' 'j--i MINDAijtAOI""- 2 re'i'! f/ , j"L, ri/r' '.1 1.],*As a result, the underlying rocks are ¥¥'eathered and havechanged to clay, resulting in thick surface soil formationin the area.l.r: *'.* -_ I' !o loo 2ao kmPig. l. IMap of the Plli!ippines showing the locaiion of GuinsaugonPast Disasters in the RegionSouthern L,eyte's natural and **eologic features make itsusceptible to landsliding and flooding. On 5th Novembervillage199i, heavy rainfall due to the passage of a typhoon(b )( a)_ :'1?: ir': 'iit{1:' ; {L ;"IT ;i'- ;'f :" ":1i:1 :'i;: ;x/):;f_ i'till:"i -: {{P';'" $ ';;i -r! "'t:1 ' :/ rf;" ;t'ta : *;'sle l "'jS' i '::E';i' /ii'*l ';Ii;. ,t {; tL * /: t /!: *+ -_''(' 1 ;1 ; ::;;::;;] fxf' //j;:i! 1'i(":;::j;i i;/i:/:{;'ti/tl:;i:t;:: Ii;;:!;;:;::il;il:j?::{::; !'{ '---i*'1****' - *'*' =(;ij;;.i v;::;le;'L:; :5tji;:irs;S ?i;; '_S _'/;; ^;;'* :*' s*{ri'- =s_,*/' :i :';'_:'i/';;"<:f' 'S 't ';L ' ' - '#?; 1$ ';iJ; :_; ;f=:1T': 'eIft'l'i; f 4i; :ti'i* i' it- :"_'t:< :i' !';/''i;Ifi. ' 'i I' ';aJ' t i'=r S''-LEYTE ISLAND'$ :'1':!: ? ' s';i!' :" :;i;f' ..**''*i//_! //;:;; ;:l'-' $i'':'ti'"s"':;': {"'GuinS ugon='s': t;;1' "I" = 'J ;'i ;'* '9_:'*s..*'', ;"'**f"::;''.,_...S''* **.*** " * ** ": , """""/"..=_._･*. f.r"sf'l/""*: f"'!^ /;i;! '_' '' 'i;;_ ' *';::,,' ,.'" #""' /;'. .t':.; :: ;i: ; ;: ; fr'Ii_ = _ l{' _' F f: ;;_''s!i! (=' 'i " ':. . tabalian Bay{ :j;1 : i st'_' :s:r'l'{'o5i O km*Fig. 2. Relative !ocation of Guinsaugnn landslide and (a) distribution of faults and trenches in the islan(1 of Le)'te (from iv. Iines and GeosciencesBureau) and (b) estimated location of fauits in Southem Le)'te based on Jh ,RS-1 SAR mosaic (original data from Earth Remotc Sensing DataAnah.'sis Center and modified according to Lagma et al., 2006) .2006LEYTE LAiNDSLiDElOOD9002501 seO20012eOE1 sO80e Sa:10eeOe =503QO o80GE 700- eoo500c> 4ao300:687200c:oooJan Feb Mar Apr May J n Jul A:Jg Sep Oct Nov DecMontho1 fI f 1 1 2!1 O a,20I f21oI f31Fig. 3. Average and maximum monthly rainfall intensities from1980-2005 (based on PAGASA data)Fig. 4. Dai!y rainfall from Ol Januan.'-28 Februarl. 2006 recordednear the landslide sitc (based on PAGASA data)caused flooding in Ormoc City, Iocated in the ¥ "esternside of' Leyte Island. The levels of the t vo rnain riveraverage monthly rainfall durin_g: the typhoon seasonsystems, Anilao and Malbasag, rose and spilled intosetrlements lying alon_ : the riverbanks (Vitug, 1993).a erage drum' the "driest" month (i.e. May) is 91 mm.For the month of February, the average rainfall is 275lvloreover, flashflood s¥¥'ept do¥vn from the hill adjacentto population centers. As a result of this disaster, morethan 4,000 people ¥vere killed and o¥'er '_.OOO more ¥verereported missing. Illegal log:ging ¥vas considered as themm. Overall, the average annua:1 precipitation in Otikonbased on a¥'ailable data from 1980-2005 data is 2545 mm.Records of daily rainfall obtained at the Otikon stationindicate that bet¥veen 8-i6 February 2006, the area vasmain culprit of the disaster, with hills above the citystripped of vegetation necessary to prevent flooding anddrenched by 687.8 mm of rainfall, with the peak dailyerosion.During 17-20 December '-003, Iandslides and debrisFig. 4). It lvas at this time that the landslides occurred insuccession in the nearby Sogod tolvn, as discussed belo¥v.flo¥vs caused by heavy rainfall resulted in death of 207people, mostly in San Francisco to¥vn, Iocated in a smallBecause of concerns regarding possible fiooding andlandsliding, some residents of Guinsaugon left theirisland south of the Leyte mainland. The landslidechanged into debris flo v and deposited huge volume of'soil in the area, engulfing hundreds of houses and otherhomes and evacuated to safer places. After this, rainfallintensity some vhat subsided, vith an intensity of 32.4mm recorded the day prior to the landslide. As a result,civil engineering structures (Sakurai et al., 2004). Rainfallthe people lvho sought refuge came back to their homesrecords fr'om PAGASA (Philippine Atmosphericto resume normal daily activities.(No¥'ember-January) is about 350 mm, ¥vhile therainfall of 171.0mm occurring on 1'_ February (seeGeophysical and Astronomical Services Administration)As mentioned above, the average rainfall in the areaindicate that 699 mm of r'ain f'ell in Southern Leyte withinDecember. Moreover, detailed investigation conductedf'or the month of February is 275 mm, indicating that the9-day rainfall (frorn 8-16 February) prior to the landslideof 687.8 mm is rnore than 2.5 times the monthly average.In fact, the rainfall intensity registered for the wholeafter the disaster sho¥ved that the geolo_ ,_ic structure in themonth of Februar_¥' 2006 was 970.8mm, the highestarea played an important role in causing the disaster.monthly rainfall e¥'er recorded since 1980, including thetyphoon season (see Fig. 3). It is to be noted that severea 3-day period ¥vhen the disaster occurred, almost threetimes the a¥'erage rainfall in the area for the month ofFollo¥ving the 2003 Iandslides, go¥'ernment _･._eologistslisted 82.60/0 of the Southern Leyte province as prone torainfall in the area normally ran between November andgeologic hazards, such as landslides (DENR, 2006).Accordingly, regional geolo*'ists have planned in JanuaryJanuary. Such unusual climatic chan*'es are broughtabout by the appearance of La Niha phenomenon, which2006 to include the to¥vn of St. Bernard as among theareas to be sur'veyed during the year for the plannedgeohazard map, which up to no¥v has only been done forselected urbanized and urbanizing areas in the countryis associated lvith above-normal sea surface ternperaturesin the West Pacific and stronger t.rade vinds. This patterncan significantly enhance rainf'all across the West Pacificregion.(such as Metro Manila, Baguio, etc.). Unfortunately, thelandslide struck before the plan got under¥vay.DESCRIPTI0_¥' OF 'I=HE LA_NDSLIDERainfa!! CharacteristicsFeatu/'es of the Lanc!s!ideC.limate in Southern Leyte is characterized by theabsence of dry season with a ¥'ery pronounced maximurnrain period occurring in the rnonths of' November tofoot of Mt. Can-abag, the 800 m high mountain rangetraversing the interior portion of the Southern LeyteGuinsaugon village is a farming village located at theJanuary. Figure 3 shows the average and maximumPro¥'ince. Based on CY 2006 municipal survey, Guinsau-monthly rainfall intensities from 1980-2005 as recordedgon villa*'e had a population of 1,857 residents and 3,_1by PAGASA rainfall station in Otikon, Libagon to vnhouseholds (Ramos,(about 4 km from Guinsaugon). It can be noted that theoccurred on the eastern slope of the mountain range and_006). The massive landslide V..2006 LFYTE LAN'DSLIDE''e' /30L-aII oljSubrnarine slides,! isiopes atfailure sites 'i o subaerial siides, 1j JLj ooca+e*H/Li Assembiedby Sassa(1992) /) /(to ro)r o20; oooro)v1,/1ooa:c:e)o'CL 'L( ]oooooc(I2 iO>"ScoQ 'J oo'uJGlnsaugonslide a o e o e eeofo8105 10G 107 108 i09 iOio 1011 1012Volurne of Landslide (m3)Fig. 8. Relation betw'een falli b schung (or slope angle c*,.) andvolume of landsiide (based on original piot by To,vhata, 2000)689clebris, ¥¥'ith himself and his house riding on top of thefio ving mass of soils and rocks. Fortunately, he ¥ 'as res-cued do vnslope.Residents intervie ved mentioned t.hat after days ofhea¥'y rain, itvas a sunny dayvhen the landslideoccurred. This is consist.ent ¥vith the rainfall recordsvhich sho¥ ' that only '-.6 mm of rain fell on 17 February,,_006 (see Fig. 4). They heard a loud crash and felt theearth shake before ¥vater mixed ¥vith mud and bouldersfell from the mountain. This clearly points to the role ofantecedent rainfall in trig ering landslides. Water frompre¥'ious rainstorm may ha¥*e made its way from otherparts of the mountain range into the fragmented rocksoverlying mountainside. This allowed ¥vater to pressureto build up vithin the slope, creating a potentially dangerous condition.A report by the Presidential Inter-Agency C*omrnittee(2006) indicates that pre¥'ious events of landslides in thearea have occurred in the past, as extracted from topo-graphic maps and recent photographs. The reportclaimed that the presence of screes, or loose rock debrison the slopes of the mountain (no v covered ¥vith trees),are indications of old landslide events. Old debris flo¥vdeposits are also visible at the base of the mountain (seeFig. 5). Three generations ofvitnesses intervie¥ved at thesite claimed that they have not encountered landslides ofsuch large-scale in the past, indicating that the Guinsaugon landslide may ha¥'e a return period of more than 100years.F'ig. 9. The deposited field has numerous small lril s or hummocks:Inset sllows a 6 m ,vide and 2 m hia l hummockEarthcjuak e EffectThe Philippine Institute of Volcanology and Seismology (Phivolcs) reported that a small earthquake (M2.6)occurred at 10:36 A.lvl. on 17 February, '-006 ¥vith focalobtained for this slide is consistent ¥vith those observed inother subaerial siides, although the plot is some¥¥'hat indepth of 6.0km. The earthquake source is along theLeyte segment of the Philippine Fault System and anepicenter about 20 km from the landslide site (Phi¥'olcs,the lo¥ver limit.Some sur¥'ivors mentioned that durin*' the debris fio¥v,the surface of debris sho ved ¥vave-like pattern as itflolved further from the base. This would probablyexplain the hummocky nature of the deposited materials,as sho¥vn in Fig. 9. As the debris hardened and stabilized,the ¥vave patterns on the surface remained, producingsmall hills within the deposit. One hummock, shown inthe inset of Fig. 9, measures about 6 m ¥vide and ,_ mhigh. Some survivors claimed that the debris flo¥v lastedfor less than three minutes, an assessment which may bedifncult to comprehend in panic situations such as t.hiscase. Nevertheless, assuming that such accurate determination of' time period is possible and the stated du 'ationis correct, this would imply a debris flow velocity ofbetween 80-100 km/hr. This range is consistent ¥vith theestimates made by U.S. Army Corps of Engineers (C.ox,2006). It re*'istered an Intensity 11 based on PEIS(Phivolcs Earthquake Intensity Scaie) in Sogod to¥vn(equivalent to Intensity II-Ill of Rossi-Forel Scale).Similarly, the United States Geologic Survey recorded alvl4.3 earthquake at the same time, Ivith epicenter about4 km north of Guinsaugon and depth of 35 km (USGS,2006). Since both earthquakes occurred at the same time,there is reason to believe that they are one and the same,although the magnitude and locations ar'e different.Unfortunately, the actual rime of occurrence of thelandslide is uncertain. Immediately after the disaster,ne vspaper and television reports indicate that the slidehappened at around 10 A.M. (e.g., PDI, 2006; TimeAsia, '_006). The Presidential Inter-Agency Committee(2006) also indicated in their report that the landslide oc-2006) .curred at about 1000H. Several local people intervie¥vedduring the site visit, ho¥vever, mentioned that the land-It is interesting to note that some parts of the villa*'e¥vere transported as a whole by about 500 to 600 rn do¥vn-slide, accompanied by rumbiin*' noise from the mountain, occurred mid-morning sometime between 10 and 1 1slope. One survivor interviewed mentioned that he wassleeping in his house when the landslide occurred. HeA.M. Local officials of the province claimed that the di-claimed that his house¥'as s¥ 'ept away together'ith thesaster happened at lO:45 A.M., or 9 minutes af'ter theearthquake (C DRC, 2006; PHNO, 2006). Recently, there 'ORENSE AND SAPUAY690Fi**. 11. A large roek boulder at the front end of the debris fiolStCia yFig. 10. Large rock boulders which were transported a considerableSandGravel1 oodistance from the base of the slope:"rf 7Guinsaugon Soil =. +.e- 80is a gro¥ving consensus in the technical community thatthe earthquake happened before the landslide (Catane,2006) ./: .,);Q): 60IA ' ,>(:'a)Thus, considering that the actual time of occurrence ofthe landslide is uncertain, there is some debate on¥vhether it trig*"ered the slide or not. Intervie¥vs conducted¥vith local residents did not yield conclusive evidence.Some residents mentioned that they felt the earth movedbefore the landslide; others contended that they heard aloud noise and ¥vhen they looked at the source of thesound, they sa¥v the mountain crumbling do¥vn.Therefore, in order to ascertain the role of earthquakein the Guinsaugon landslide, it is necessary to establishthe actual time of occurrence of the landslide and todouble check the seismic parameters assigned to theu'CLS40e)oO-20/l:/;./, -Original Ground-1'Hr origjnal Ground-2: : Debris deposit (top)e Debris deposit (midd:e)Debris deposit (bottom)oO OOi O. 1 1 1 O I OOO O1Particle Size (m m)Fi･. i2. Grain size distribution of matcrials obtained at d fferentkocations in Guinsaugonearthquake, such as its magnitude and epicentrallocation. It is ¥vorthy to note that no other landslideswere generated along the trace of the Philippine FaultSystem in Southern Leyte at the same time as the 17February 2006 event.Gellera! Soi! Clla/'acte/'isticsdebris flo¥v (bottom), and the third some¥vhere in bet¥veen(middle).The _g:rain siz,e distribution cur¥'es of the five samplesare shown in Fig. 12. h may be noted that although theoriginal ground and the debris flo¥v deposits includedlarge cobbles and boulders as mentioned abo¥'e, thoseThe materials deposited at the valley floor consistedsizes lvere not represented in the grain size cur¥'es sho¥vnof sandstones, con_ lomerates (sedimentary rocks),mudstones, and breccias (produced by the mo¥'ement ofin the figure because of testin*･ Iimitation. It can be seenthat the original soil cover in the mountain slope has finesthe Philippine fault). Some of the rocks ¥vere huge, morethan 4 m in diameter, and they ¥vere scattered throughoutcontent of about 450/0, consistent lvith the materialsobserved in the slid mass. A view of the area ¥vhere thethe fan of the deposit as they traveled considerabledistance from the mountain source (see Fig. 10). Oneoriginal ground samples lvere obtained is sho¥vn inlarge boulder, measuring about 3.5 m in diameter, can bethe soil covering this par't of the slope.Fig. 13. The inset photo indicates the silty sand nature ofseen at the front end of the deposited debris (see Fig. 1 1).The materials obtained from the slid mass ¥vere veryApparently, this large boulder traveled a distance ofalmost 4 km, indicating the fluid-like behavior of themoving debris.much disturbed as a result of the debris fio¥v as well as theSoil samples lvere obtained at 5 different focations inrescue operations that followed after the disaster. Nevertheless, it can be observed that there is an increase in claycontent of the deposited debris, probably because of theeneral characteristics of the soilcrushing of rock masses dur'ing impact as the mountainin the re*'ion. T¥vo samples ¥vere obtained from theoriginal ground near the bottom ridge (see Fig. 5) northslope crumbled do¥vn. In addition, the falling debris mixed up ¥vith the alluvium comprising the rice field belo¥vof the failed slope. In addition, three samples ¥vere takenthe mountain. Moreover, the preferential grading of the¥vithin the debris flo¥v deposits-one near the base ofdebris is evldent.order to investi ate theslope (referred to as 'top'), another near the toe of the1 Tj.i; :_'*-='*!/"2006 LEYTF LANDSLIDE691; ,.,.##7* +*-''!r'"'i'+'*:*'^" #'. {'+' ;*;!. SS;-" "S i ;'"" ;i/;i-' i(*- S;s ""f ?**:!; - *** +*- ;*"** ** *;: *:* _ _:t+#s' i"' -'/ '!i-::{;t{' " " ' _*'*_'"; i''s-' !';' -:';-;iS **-- i:'i ;/ i; giji": i:" :i- ;:: ;:, ;;. __s' * L *l.'. ^"#'_'"' ''*#. _ ^' _ !:;;t i;:/( !j,;:; i.;;,t; ;;:" * f :'+'1i; i' ^ --* ;;:/';*i; f;:;i,:;!^*+ 'ri ?; ;i'' 'i" ;<!_!* *Fig. 13. Vicw of the ridge adjacent to t le failed slope where sample oforiginal ground was taken: Inset photo sho vs the detail of the sur-^;;s:; ,;'/'_"' x: #f *" -'"' '""}ir (;/'# ..- ..'""');:" .i;* ' '#'#*;" {")i" 1 :''''_*/; . - ". *"" ", -'*i''ii:;,? /'1 is; i li/:!" - i"' i; :;f;:i_* =' 'l*: . .;!' 's-- i'-ma n sea pi"S#'=;#;" ':':face soil in the slopeUnstab!e materiais on'; '' -i_;-' "'* *+i'- ':i!i :::_ *: ' **-*;:-; i' - S-' 'S_** i *'i_^ * * '- ;'"'- * ' +' s+#SS'+ ;:':;:= :i'i<' " +P ; i :*. * { ;tj*:;.'{･ s :ili:() .S }:;.'Li;iS i.;. .:;;'+ ;+ s1***' 't': t "': : ;r' i:t;;; ' ;:"/';."'" :':._ _ _!' .^-*_ _Fig. 15. One of the small river channels within the deposited debriscreated bl_ the damming of the Himbangan Rivervisit that the adjacent area ¥vas well-forested and there¥vas no evidence of deforestation at the site.The role of the earthquake prior to the landslidecannot be established until the actual time of occurrenceof the landslide is clarified. Ne¥'ertheless, it should bepointed out that a perturbation induced by an earthquake, ho¥vever small it is, could amplify in a topograph-ic condition such as in Guinsaugon and could triggermass movement in a fully saturated slope on the verge ofFig. 14. Photo sholving potential sources of instabilitics in the affectedfailure.areaCauSes oJ' the DisasterMost geologrc hazards such as landslides, are part of acomplex chain of cause and effect. The immediate cause isthe triggering mechanism, vhile other underlying factorsdefine the predisposition (proneness or susceptibility) toPossib!e Potentia! HazardsThe changes in the physical landscape in the affectedarea as a result of the landslide in Guinsaugon havebrought about the emergence of future hazards (see Fig.14). The steep slopes at the failure surface, accentuatedby numerous cracks, and the materials that rernain at thef'ailure. Based on the ocular inspection at the site, severalcro¥vn, are potential sources of future landslides.underlying factors can be identified clearly. Because thePhilippine fault line traverses the region, the volcanicrocks in the area are char'acterized by intense fract.uringand weathering, making them unstable and susceptible toLandslide scars adjacent to the failed slope are also indications of potential instabilities.mass movement. Moreover, such condition allo¥vedaccumulation of water in the loose saturated deposit, wasrain¥vater to seep into the r'ock fractures, further ¥veaken-also prevalent. There ¥vere also small river channelstraversing the deposited materials, especially near theing them. The steep terrains of the mountain surroundingthe valley rnake the slope susceptible to iandslide. Thetriggering mechanism, on the other hand, is the heavyDuring the site visit, it was noted that the depositedmat.erials were still saturated and soft. Ponding, orbase of the mountain (see Fig. 15). These river channelscame about as the deposited debris dammed therainfall in the area, made worse by the appearance of LaHimbangan River fio¥ving near the base of the mountain,Niia phenomenon. Intense rainfall softened the soilallo¥ving small tributaries to seek different flo¥v paths.Such conditions may trigger debris flo¥vs in the future.cover, vhich had already been made unstable by the faultline and the previous rainfall.Although initial reports blamed logging in the area asone of the causes, it is belie¥'ed that considering the size ofLANDSLIDES IN OTHER PARTS OF THEthe landslide and the magnitude of antecedent r'ainfall,PROVINCEdef'orestation did not play a significant role in triggeringOthe/' Slope Faiht/'esthe landslide. Moreover, it ¥vas observed during the sitePrior to the Guinsaugon iandslide event, a series of 1OREN+SE AND SAPUAY6 )2S':_:S! '?Agas"Agas " "F';irS!S!x',^'. ** ;j** *s･･ ,'" "* :,･･**_f. *i . **".eee ili;'io : jl: Sej so90di i ; c*sFig. 18. Slope fai ure and road collapse in Lepanto, St. Bermrd townBa y5osLepantoi S 'e ;$Pt F :f:a:Clay;St8ar dG Falre1 oot#"S ; f''caba fianBa y'lc!! s'"'oo- 80jolQ)Fig. 16. Map of Southern Le)te province sho l'ing loca:tions of otherlandslides visited during tl]e tiamage inspection: 60>4:)e)c:40O_c:e)(' 20- :::, as- Lep*"*'CLoO.OOI O. 1 1 OOO.O 1110Particie Size (mm)Pio, 19. Grain size distribution of materials obtained at otherlandslide sitcs in Sout!lern Lel.'teL,iloan buried 4 houses and blocked the only road goin_"._to the Pacific to¥vns. The occupants of the houses ha¥'eevacuated earlier. Another landslide occurred in L.epanto.'¥'illage, also in St. Bernard to¥vn, ¥vhere a portion of the･･･.*mountain collapsed and destroyed the adjoining roadFig, 17, Lands]ide and pavement collapse in the nearby Agas-agns,Sogoti town on 12 rebruar . 2006iandslides and mudslides brou*"ht about by days of heav_vrains occurred in other parts of Southern Leyte Province(see map sho¥vn on Fi_g. 16). O_ n 1'_ February '-006, just5 ciays before the Guinsaugon landslide, three major(see Fig, 1 8). This affected to some extent the transport of_g:oods and personnel to the Guinsaugon landslide site.Less than 2 km a¥vay, another landslide destroyed aportion of the coastal road, allo¥ving only one-1vaypassage of vehicles.Because of these landslides, the pro¥'incial governmentdeclared Southern L.eyte under state of calamity.landslides occurred in succession in Sogod to¥vn, Iocatedjust north¥vest of St. Bernard. One large landslideG/'ail7 Si e Distributionvhere surficial slopeSoil samples ¥vere also obtained at various affectedfailure as ¥vell as pavement collapse occurred. Thevolume of the mater'ia]s in¥'ol¥'ed in the flo¥v ¥vasareas to determine the g:eneral characteristics of the soilinvol¥*ed in the landslides. Aside from those samplecl inestimated at ?-0,000 m3. During the site vlsit a monthCJuinsaugon, t¥vo additional samples lvere obtainedafter the disaster, the roaddirectly at the base of the failed slopes: one sample inAgas-agas slide (see Fig. 17), and another one in Lepantooccurred in Agas-agas (see Fig. 17),vas still closed to traffic,causing inconvenience in accessing the Guinsaugonlandslide site. The t¥vo other landslides have volumesestimated at 15,000m3 and 7_,OOOm3, respectively. Thesliding masses of soil ¥vere deposited along the high¥vay,severely disrupting traffic in the area.In other parts of the pro¥'ince, at least four majorlandslides occurred, Ieaving 9 to¥vns isolated in thePacific and Panaon areas. A Iancislide in Hima_vangan,slide (see Fig. 18).The slide materials under¥vent generally lesserdisplacement compared to those of Guinsaugon, andtherefore, they can be considered as representati¥'e of thesurface soil co¥'er at the sites. Therain size distributioncurves of the t¥vo samples are sho¥vn in Fig. 19. It can beobserved that the t¥vo sets of samples are practically 2006 LEYTE LANDSLIDE-bimilar, ¥vith fines content bet¥veen 8085 /o. This is inag:reernent lvith the ¥'olcanic nature of' the soil in the area.The fines contents of' soils in these regions are much largerthan those in the Guinsaugon slope.CONCLUDli¥G REMARKSThe large-scale landslide in Southern Leyte, ¥vhichcaused the death of' more than I , 100 people, Ivas a cilsas-(. ) )Repol'! on !he Lalic!s!ic!e i,i St. Bel'!!arc!. Sol!ihern Le_vfe. Februar21. 2006, 54) Cox. S. H, (2006): L]'SACH FEST assists U_Sl ri[ es' Le}tesearch and rescue mission, rhe Pacific Collnect!on, Spri l2006,S-9.5) Departrnenl of Enh ironmenand ¥. 'a ural ResaurL: es, DENR (2006):Press Re/ea,se. 22 Pebruarv 20066) C] eagraphicai Sur e} InstituLe, (J S (l006); The position of thelandslide in Le Le island. Philippines as estimated from SpaceShu tle data, hLt ): ,! vhYIY.gsi go jp (in Japanese).ter ¥vaiting to happen. The intensity of the rainf'all prlor7) Heim, A. (1932): Lanc!s!ic!es anr! Hi!man Lil'e,s (Be!: s!iir; l!ncl*tfenichen !eben), (translaied b¥' Skerner, iN.), Bi-'Tech Pubiishers,to the disaster, coupled lvith the existence of ¥veak andf'ragmented rocks due to the presence of the Philippine8) Lagmay, A. N'I. A.. Ong, J. B. T , Ferl andez. D. F., Lal)us,Fault Zone and the steep slopes, ¥vere all in_a*redients f'or adisaster. Although governrnent geologists have already¥･;ancou¥'erl R.,RodolfQ. R. S . Tengonciang, A. P , Soria. J L . Baliaiall, E. G.,Quimba, Z. P , Liichanco. C. L.. PagLlican. E R . Remedio, A. RC., Loren2 o, G. R H.. Avila. F^ B. and Valdibia, ¥'. (2006):identified the area's geologic hazards as early as '-003,Pre!imina/'1' ( :*eo!ogica! Report on rhe Southern Le_,'!e L !nc!s!ir!e,measures to address the percei¥'ed hazards ¥vere nonexistent, or at least, not implemented. As pointed out,9) i¥'a;tional Disaster Coordinaiing Council, l¥TDCC (2006): Cfpc!a!epotential hazards still temain In the area and preventivemeasur'es should be implementecl as soon as possible tominimize damag:e from f'uture disasters.UP-Ateneo Team. 2006 Report, 9,A;o- 16 re Lanc!slic/e a! B!t*"_1'. Guinsaugon. Sl. Bel'ncll'c! Soluhel'nLeyte. http: ,f/¥ 'w v.ndrc go : ph^lO) orfice for the C oordination of Humanilarian Affairs, OCHAC2006): OCHA Sin!cltion Repori No. 8.･ The Phi!ippinesLands!ides, Ref.' OCHA /G VA-2006/9. February 24, 2006, 2.l I ) Philippine Daily Inquirer, PDI (2006): ST,'a!!olt'ec! b_1' !he Ecl, !h-33ACKNO¥VLEDGMEN J'SThe authorsvould like to ackno¥vledge the advice anclcomments pro¥'ided by Dr Sandra Catane and Dr. lvlarkZarco, both of the University of the Philippines. Thediscussions madevith Prof. Masayuki Hyodo ofYamaguchi Uni¥'ersity, as well as the assistance of Mr.Naotaka Kikka¥va, graduate student of' YamaguchiUni¥'ersity, are also appreciated. lvloreo¥'er, Mrs.Lourdes Tibig: of PAGASA assisted in securing: the rainfall data in Otikon. The funding for the site in¥'estigation¥vas provided thr'ough the Project S (InternationalStrategy) of the Faculty of Engineering, YamaguchiUniversity. The authors wish to express their deep gratitude f'or the assistance of the above-narned persons andor :anization.Dead. Hl!'1c!recj_s , liss!jlg in Le.1'1e * luds!ic!es. Februar} IS, 2006.i2) Philippine Headline N. ?e Ys Online. PHNO (.2006): Rains, minorearihquake blamed for landslide in Le.vte. February 7, 2006,http: ./,/ T v¥13) Philil)pi! ene¥ 'sliash org/2004 /02 /hl /hl I 03 ! 28 .hLm ^nstitu e or Volcanolog¥' and Seismology, Phivolcs(2006): Ear!hcluake Bu!!e!!n Afo2, http: /¥Y¥v¥v phlvolcs dost^gov.)h/Earthquake/LaiesrEQ/^14) Presidential In er-Agecy Commi tee (2006): T/1e ! 7 Februa,y 2006Bgl'. C; i!i,Isau*"on. Sot!!he/"n Le_1'te Lanc! !ic!e. Unpublisheci Report,¥. iarch 3. 2006. 30.15) Ramos. N . F. ¥,(2006): Le}te os calls for rescue, Scmtar !¥*eT 's.Februar) 22. 2006.6) Sakurai, ¥¥*., Kano. T , Tsuda, H., Hipolito. D l.. Alpasan, *¥1.T. and Damo. G_ C. R. (2004): The sedimem disasters thatoccurred in SOUtheFn Levle of the Philippines in December 2003. J.Jpn Soc. Fro,s!on Con[ro! Engineering, 57(4), 33-38 (in Japanese)17) Time Asia (2006): Slt'a!lol"ec! b_T' the E'ar[h-Deac!!_1' Lanc!s!ic!e hlthe Ph!!if;Pines C!ai,ns Hunclrec/s ofLil'es, February9, 2006^iS) To¥vhata, I. (2000): Lectul'e i¥ro!es in So!!D_1'namics. Department ofREFERENCESl) Barrier, R.. Huchon. P. and Aurelio, (_ (1991): Philippine fault: Akey for Philippine kinematics, Geo!o*'*'_ ', 19(1), 3235,2) C 'atane. S. (2006): Personal Communication.3) Citi2:ens' Disaster Response Cemer. CDRC (2006): A Pre!ilnincil:yCiYil Engineering. Uni 'ersity of Tok}'o.19) Unitecl S ates Geologic Survey, USGS (2C06): Pre!inlina!Lw Earihquake Repor!' ! fa**"nin!c!e 4.3 Le.vte. Phi!ippines, http: //neic usgs.gov/neis/bulletin/neicJgdn html^20) Vl ug, i¥, . D. (1993): PoLt'erfrorn !he Fores!. PhilipPine Center torInvesligalive Journalism Press,lanila. | ||||
| ログイン | |||||
| タイトル | Effects of Pore Fluid Compressibility on Liquefaction Resistance of Partially Saturated Sand | ||||
| 著者 | Mitsu Okamura・Yasumasa Soga | ||||
| 出版 | soils and Foundations | ||||
| ページ | 695〜700 | 発行 | 2006/10/15 | 文書ID | 20951 |
| 内容 | 表示 SOiLS AiND FOUNDATiONSVol.46 , ¥. ?o. 5.695700. Oc2006Japanese Geotechnical SacietyEFFECTS OF PORE FLUID COMPRESSIBILITY ON LIQUEFACTIONRESISTANCE OF PARTIALLY SATURATED SANDlvIITsU OKA iURAi) and YASUlvIASA SoGAii)ABSTRACTIt has been recognized that the soil resistance to liquefaction increases significantly as the degree of saturationdecr'eases. Ho vever, the effect of the degree of saturation reported in the literature ¥'aries videly bet veen researchers.In this study, infiuential factors of the liquefaction resistance of partially saturated sand are derived from theoreticalconsideration and effects of the factors are examined through a series of triaxial tests. It ¥vas confirmed that the degreeof saturation has a significant eff:ect on the liquefaction resistance. It also appeared that the liquefaction resistancedepends on the initial confining pressure and the initial pore pressure; the higher the confining pressure and the lo¥verthe initial pore pressure, the higher the liquef'action resistance of partially saturated sand. A unique relationshipbet¥veen liquefaction resistance ratios and the potentiai volumetric strain ¥vas found, ¥vhich enable to estimate theliquefaction resistance of partially saturated sand ¥vith the effects of the three factors taken into account.Ke _' words: confining pressure, degree of saturation, Iiquefaction, sand, triaxial test, voiumetric strain (IGC:D6)ReferenceINTRODUCTIONNatural soil deposits belo¥v the ground ¥vater table areeusually fully or nearly saturated with water (Tsukamotoet al., 2002). Recent investigarions re¥'ealed, ho vever,VAX)t,,that injection of' air in a soil could lo¥ver the degree ofGoto & Shamoto (20C} )Yoshimi et al ( 19 gq)Yasuda et al ( 199q)Ishihara et al ( OOI )A:/:saturation of the soil substantially (Tokimatsu et ai.,Hu mg et al (. 19c)c))AO;-1990; Okamura et al., 2003) and the unsaturated,xVcondition of the desaturated soil lasts for a long time,typically more than tens of years (Okarnura et al., 2006).This fact suggests that desaturation of soils could be an;,..''..v>v vefi ctive ¥vay to enhance the soil resistance to liquefactionin the fieid. It is, theref'ore, necessary to establish apractical method to estimate qualitatively the liquefac-l70tion resistance of partially saturated soils.80De lree olThe effect of degree of saturation on the liquefactionresistance has been studied through laboratory tests. Inthe early research works, degree of saturation of testedspecimens ¥vas mostly in the range close to 1000/0, because90saturation.ooIfoS･ ('/･)rig 1. Results of tests on the effect of degree of saturation ontiquefaction resistance (Liquefaction resistance is normalized ,viththat of full) saturatcd sand)the primary objective in those studies ¥vas to establish thestandard for the laboratory cyclic shear test to avoidundesirable unsaturated condition which resulted in1999; Yoshimi et al., 1989; Yasuda et al., 1999; Ishiharaoverestirnation of the liquefaction r'esistance (e.*'. Martinet al., '_OO1; Goto and Shamoto, 2002). Liquefactionresistances reported by any researchers consistentlyincreased with decreasing the degree of saturation.et al., 1978). Thereafter, partially saturated sands withdegree of saturation do vn to 700/0 were tested by severalresearchers. Figure I depict.s some recent test results inthe literature summarized in the form of t.he relationshipHo¥vever, the liquefaction resistance ratios ¥vere con-bet¥veen the degree of saturation and the liquefactionsiderably different for different sands tested at diff rentcondit.ions, indicating that the degree of saturation mayresistance of the partially saturated sand normalized ¥vithrespect to that of the fully saturated sand (Huang et al.,liquefaction resistances of partially saturated sands.i]ii)not be the only factor dominating the normalizedAssociate PrcfessoF, Gradua e School of Science and Engineering. Ehime University, Japan (okamura( ;,dpc.ehime-u.ac jp).Graduate Student, Kyoto University. Japan (formerly Ehime University)The manuscript f'or this paper ¥vas received for revie¥v on December 8, 2005; approved on May 29, ,-006,¥¥!ritten discussions on this paper should be slibmitted before May I , 2007 to the Japancse Geotechnicai Societ.v, 4-38-2. Sengoku,Tokyo 1 12-001 l, JapanUr)on request the closing date ma.¥' be extended one momh.695Bunkyo-ku, OKA ,IURA AN. D SOGA696As can be seen in Fig, i, existence of air in a soil8,. = Bw /A p (-? )significantly enhances the liquefaction resistance.Resear'chers have paid **reat attention to saturate speci-and ¥*olumetric strain of the fluid (¥vater and air mixture),mens completely for' Iaboratory tests and model groundse*f' is;for shaking table tests to avoid overratin_g soil resistancesto liquefaction. Replacement of air in the void of soils bycarbon dioxide follo¥ved by introducing deaired ¥vaterunder a ¥'acuum pressure is the typical technique that hasbeen developed. V,re, ho¥vever, often observe contradicto-ry phenomenon that a sand deposit in a small containeror a bottle, being almost filled vith ¥vater but containsvisible air bubbles in the deposit, can be easily liquefiedby shaking the container gently. This also alludesexistence of infiuential factors of the liquefactionresistance of a partially saturated sand other than thede9:ree of satur'ation.In this study, influential factors of liquefactionresistance of a par'tially saturated sand are derived fromtheoretical consideration and effects of the factors areexamined throug:h a series of triaxial tests. Results aresummarized in the form ¥vhich can be easily applied toevaluate liquefaction resistances of partially saturated= ApBfI -B.S,B,,S, ')e.f(¥vhere S* is degree of saturation of the soil mass and B*,Bw and Bf are bulk moduli of the air, the ¥vater and thefluid, respectively. Since B, is much higher than B., thesecond term in Eq. (3), S,/Bw' is negligible. IntroducingBoyle's lalv and assuming soil grains to be incompressible, ¥ve obtain the ¥'olumetrlc strain of the soil mass as;8' 4B. (1S)p0+Ap(1e Ap S,)-i+e_ e' 1+e(7*' Ie+e. (1 S,)p O'T (T.¥vhere po and e denote the absolute pressure of the fluidand the void ratio of the soil mass, respectively. Thehig:hest value of the ¥'olumetric strain for the soil isachie¥'ed ¥vhen the Ap attains its possible maximum ¥*aluewhich is equal to the effective confining str'ess, (7.'.. Thissands in situ.FACTORS AFFF.CTING L.IQUEFACTIONRF.SISTANCE OF UNSATIJRATED SANDExistence of air in the pore of a soil is considered toenhance the liquefaction resistance of the soil in t¥vo¥vays. The first mechanism is such that air in the poreplays a role of absorbing generated excess pore pressureshi :hest value of the volumetric strain is hereafter in thispaper termed as potential ¥'olumetric strain, e .TRIAXIAL TF.STIn this study, effects of the factors derived In thepreceding section ¥vere in¥'estigated through a series oftriaxial tests. Three testing parameters including theby reducin*" its volume. The bulk moduius of the poreinitial effecti¥'e confining pressure, cr , the back pressure,fiuid chan*'es significantly by the presence of air bubbles.po, and the degree of saturation, S,, ¥vere varied betweenThe bulk modulus and chan*'e in volume of the poretests ¥vhile the ¥'oid ratio of the specimens ¥vas keptfluid, that is air ¥vater' mixture, may be the factorsdominatin*' this mechanism. The second is the matricconstant throug:hout the test series.suction of unsaturated soils ¥vhich increases the effecti¥'eP/'eparatiol7 of Specil77enToyoura sand ¥vas used in tests conducted in this study.stress and thus the strength of soil mass (Bishop andBlight, 1963). The matric suction depends not only on thedegree of saturation but also on soil par'ticle siz,e. Formost liquefiable soils the matric suction is less signlficantcompared to the effecti¥'e stress of soils at the depth ofpractical concern, say several meters or deeper. For thefine sand used in tests in this study, for instance, thematric suction is at the highest 4 kPa if degree of saturation goes do¥vn to 700/0. In this study the first mechamsmis focused on. The effect of the matric suction is ne9:1ectedor the pressures of air and ¥vater in the pore are assumedto be the same Note that for liquefiable soils ¥vith higherfines contents, such as non-plastic silt and sand containing considerable amount of fines, the effect of the matricThe specific _g:ra¥'ity of the sand is 2.64 and the minimumand the maximum void ratios are e ,i =0.609 and e*** =O.973, respecti¥'ely. Triaxial specimens ¥vere eithersaturated or partiall}., saturated sand. Test specimens¥vere prepared as follo¥vs. Wet sand ¥vith a ¥vater contentof 50/0 ¥vas tamped to a relati¥'e density D,=40 /o in amold with internal dimensions of 50 mm in diameter andlOO mm In high. The sand ¥vas set in the triaxial cell anddeaired ¥vater ¥vas introduced from the pedestal for a¥vhile. Then the back pressure of 98 kPa ¥vas applied and¥'olume of ¥vater pushed into the specimen was measured.The measurement ¥vas continued for an hour since thevolume ¥vas observed to increase gradually probably duesuction could not be negli_"*.ible. Further investi*･ation isto dissolution of air in the pore ¥vater. Volume of air inneeded on this reg:ard.Consider a soil mass with the por'e filled ¥vith air andwater. For a small change in the pore pressure, Zlp, thevolumetric strains of the air and the ¥vater can be ¥vrittenthe specimen ¥vas estimated from Boyle's la v ¥vith themeasured volume of the ¥vater pushed into the specimen.The procedure of introduclng deaired ¥vater and the airby equations;s. = B* /A p ( I )volume estimation ¥vas repeated until the specimencontained predetermined volume of air. It should benot.ed that the adsorption path and the desorption path ofthe soil-water characteristic curves are generally different . L QUEPACTION R SISTANCE OF UN_ 'SATURATED SOILTable 1.Degree of'Triaxial test conditionsPoieniial volumeLricAbsolute backsaturation*, S. (o, )Effec ive confinin :pressure, (J*' (kPa)pressure, po (kPa)l OO49, 981 99Rerati¥*edeosity, D* (?･/o)69 T(97o o008449o-98 . 5)96(95O .OO 1 849s0.0030519 60.00 1 65o 00362199O 006019839 4390i 99O 0151297O OI 13199o 0300297o.0225199O . 045 l297o.033898(s9_0-92.0)8098(78 5-83.0)7098(70.0-72 o)Degree o1 99495 -96 . o).*o19 698strain,saturation in the parentheses was estimated from the measured volume of ¥vater pushed into the specimen by increasin lhe backpressure.(a) S.= I OO b, (r*' = 98 kP L pi) 199 kPa*^ 50v . ;>(b) Sr = 95.401!o'o.;'c :v; !b OS 1>oO-50: OS: 0,1.S Ol:: Ol<;-O Oi; Ox _O I<-O 2o^*e ;'1='V:/>(e'-O 2? 1001 100l'1-P0= 199 kPaOafo _ _50(r*' = 98 kPp^o) 501 v/ c)v2v>(o50'*'.1 -' OlO20Number of cyclesFig. 2.O10Numbcr of' cvcles20'I,pical rime ilistor) from tests on full) saturated and partiail) saturated specimensHo¥vever, the volume of the water pushed in and expelledfrom the specimen during increasin*' and decreasin*' theback pressure ¥vas essentially the same. This is probablydue to the matric suction of this particular sand beingvery lo v in the r'an_g:e of degree of saturation tested in thisTes'ting Pa/'alnetersThree testing parameters derived in the previoussectionver'e varied bet¥veen tests as sho¥vn in Table l. Itshould be noted that the back pressure, po, used through-out this paper is the absolute pressure instead of thestudy.ordinary used gauge pressure. The range of theFor the saturated specimen, deaired ¥vater ¥vas introduced until the Skempton's B value became 0.95 orparameters tested ¥vas ¥vide enough so that the range ofe covers that of possible field situation ¥vhich might behigher. The effective confining pressw'e was kept constantencountered in practice; the initial effective confinin_"*,to 10 kPa throughout the course of the preparation. Onpressur'e ¥vas varied betlveen 19.8 kPa and 196 kPa andcompletion of preparation, the initial effecti¥'e stress andthe ran*'e of S* ¥vas similar to that of the in-situ soilsthe back pressure ¥vere applied and the specimens ¥veredesaturated by the sand compaction pile installationsubjected to the cyclic shear stress ¥vith a frequency of'(Okarnura et al. , 2003, ,_006). The values of the potential¥'olumetric str'ain at the beginnin_ : of cyclic shearing, 8 ,O OI Hz under undrained condition.are also given in Table 1.It should be mentioned that the frequenc)' of shear OKAlvIURA AND SOGA698cycles in the tests being much lo¥ver' than those ofearthquake motions may allow air in the specimen tothe unsaturated sand indicated in Fi**. 2(b) is quite similarto those of the saturated sand except for the applied cyclicdissolve in pore water in accordance to generated excesspore pressure during cyclic shearin_g. According to theHenry's la¥v, a maximum of 3.8 cm3 in volume of air candissolve for the test condition shown in Table I ¥vhen thespecimen '*enerates a 1000/0 excess pore pressure ratio.stress amplitude being considerably higher.Effect of the FactorsHo¥vever, it ¥vas observed in preliminary tests thatback pressure on the liquefaction resist nce. Figure 3amount of air dissol¥'ed in the pore ¥vater in an hour afterdepicts the relationship betlveen cyclic stress ratios andthe number of cycles, N, to cause double amplitude axialstrain, DA, of 50/0 for cases ¥vith cr,'.=98 kPa and p0=199 kPa. As the degree of saturation decreases, the cyclicapplyin*" a back pressure of 98 kPa ¥vas ¥'ery limited,approximately 0.3 cm3 corresponding to an increase inS, of 0.30/0.This section discusses effects of the three factors, that isthe degree of saturation, the confinin*･ pressure and thestress ratio increased irrespective of the number of cycles.RF.SULTS AND DISCUSSIONSStress-strairl Re!atiol7s/1 ipFigure 2 shows t .,pical time histor'ies obtained fromtests on saturated and partially saturated (S*=95.40/0)specimens at the same confining pressure ((7 =98 kPa)and the back pr'essure (p0= 199 kPa). For the satur'atedspecimen, the excess pore pr'essure increased with thenumber of cycles. The axial strain started to increaseswiftly as soon as the excess pore pr'essure approached tothe initial eff cti¥'e confining pressure. This response istypical of a fully saturated loose sand. The response ofThe cyclic stress ratio almost doubled as the de*･ree ofsaturation decreased fr'om 1000/0 to 900/0, ¥vhile in therange of the degree of saturation lo¥ver than 90010 itincreased at a lower rate lvith decreasing the de*"r'ee ofsaturation. Hereafter, in this paper, the cyclic stress r'atioto cause DA=50/0 in 20 cycles is termed as the liquefaction resistance.Illustrated in Fi**. 4 are variations of the cyclic stressratio ¥vith number of cycles for tests in ¥vhich theconfining pressure ¥vas varied bet¥veen tests ¥vhile the0305:-VCr.'= 9S kPa_ pr' = 1 99 kPa)- 040251-:i. 03s 02:-e),, {"*)_ 02J:':):;)>,O lvoOO 70SO] 90O 96A 9SO 15,S'r = 100 'tc 100{5 10Nlumber of c) cles. .¥Oo]oOl litial ef'fective cont ning pressure. (T.' (kPa)Fig. 3. Effect of degree of saturation on the relationship betweenrig. 5. Revoiution ofcl. clic stress ratio and number of c . c]esvith an increase in initial05(a)96 o_p!' = 199 kPa04(b) S* =980. . p,; = 1 99 kPa*' 03' 02iquefaction resistanceeffective confinino* pressure05*rO i OOO' 03-¥ _rT0.4l l {L J r'a'r!6kPa'; dO*'':)rl Tb[;i:j:J6 t'a'.1:'i6kPa) R)>J Ol> OIt)o:'5 iri(,_* . 4.5 10Niumber ol"c¥ cles. AO i OOoOllONtlnrbeToi cycles A'h ,fiect of initia effeetive confining pressure on the relationship between cyclic stress ratio and number of c)cles50 1 OO 699LIQuEF、氏CTION RESISIANcE OF UNS、へTuR、へTED soIL050、5（ωσ，F濫98kl）a．、Sロ冴90％（b｝σ，「皿98kI）a、，∼、、皿70％。τ 04㍉ 0，4ビじ＾ 03＿ 03蓑02罫 02．2つ3，01．婁、O i00500550 100 5 10NUmberolcyclcs．．V50 5 10100NUmbeωfc》clcs．、NFig．6．E耀ec｛ofin漁lporepress巳reonIherelatio賎sh量pbeIweenc》’c置ics［ressra亘loandm鼠mberofc｝『cles（bl resultS t沁m pre、IOus stud｝（alresuksofしestil1禰ssヒud｝（ 」 A」、へbes毛巨t cしぼr㌧e1・9〆6500ε、‘・一10ノ塩 ○つ一○一 つムIo｝lour無sand，Dr篇40％0 98 98 70−100△ 49 98 96＿】00S識nd ∂f ，9r σ♂ μθ Re短re臓ceO Io》oura40％91−IGO9805（Hua口getab△ ro、oura60％90−1009805（Huangota1｝ ｝▽ To｝oura70％91−1009805（Huangetal、｝0 196 98 96−100ムTo・oura60％70−100980監Yoshimieml ｝」』・ 98 196 70−100002 004 ｝蕊 σC「（kPa）ρr’（kPalSr（％）、0＼i。9（6500ピ＋10）＋ Masa 85％94−iGO9867／196（、7asuda0．06（｝PotelltialvolUmetricstra紅1ε、0．02 004et ab006Potennal voiun潅etriC Straln ε玉Fig。7、Relat董onshipbetweenhypothe“calvolumeεricstralna臓dliquefacIionresis重旦nceofpar症ialb『s烈urateds謎騎dnormaiizedwithth撮offully s隷芝ur謎粟ed s＆nd（iegree of saturat玉on alld the back pressure were keptfactors o蹴 the liquefaction resistance discussed aboveconstant．The cyclic stress rat玉o of the partially saturatedqualitatlvely support the idea of the盒rst mechanismξhat，sand is apParent豆y depelldent on the玉nitia圭con行ning Pres−air in the pore plays a role of absorb玉ng generated excesssure．Li（luefactioll resistances are plotted aga圭nst in圭tiaIcoufin量ng pressures圭rl Fig．5．The liquefactionτesistancesofthepartiallysαξuratedsandincreasewi出theinl重i＆1con且鷺重ng Pressures， with the liquefac重ion res量s重ancesbeing higher for lower S，．The至i（1uefaction resistance ofpore pressures by reducing its vQlume．Thus，the liquefac−tion resistance ratio，which隻s the liquefεlction resistanceof a partially sa芝urated sand norma正ized with respect to重hat of the fu玉1y saturated sand，is plottecl against thepotential volumetric str＆in in Fig．7（a）．All the data llesthe partially saturated sand seems to＆pproach to that ofalong a unique cul−ve， conarm三ng that the poten丈ialfu1重ysaturatedsandasthecon且nlngPressuredecreasestovolumetric strain is the determini煎g factor oft難e e窃ect ofzero．hl other words，degree of saturation has a smallerdegree of saturation on th玉s speci負c sand at relativee圧ectontheliqueξactionresistanceofsandunderalowcon負nil19Pressure．Figure6illdicates effects of the backpressure on the cyclic stress ratio。The liquefactiondensity of40％．Data re重rieved from毛he1呈terature三s alsoshown in Fig．7（b）in the same manner．The d飢a plottedin this ngure was obtained from the tests on specimensresistance of the parξia11y saturated s＆n〔iεしpparently de−prepa罫ed using d星鉦ere正1t sand at di拝erent re正εしt圭ve densitypends on the back pressure，which圭s not重he case for satu−and subjected cyclic loadingεLt di郵erent con盒！1ing Pres−rated sand．王n oPPosition to tbe effect of the confiningsuresαs summarized in the figure．Despite重hese differe臓tpressure，the豆iquefaαion resistance decreases as the backconditions，＆H the（iata lies a董ong tぬe same curve as that inpreSSUre lnCreaSeS・Fig．7（a）．Thiscon且mst紅atthee鉦ectofthedegreeofsaturatioll on 正iquefact量on resist＆nce， which is arisen∠，iσμψぐ’ioll Rθ5i5∫α∼zぐθρ〆’∠）θ5ρ々’ノ’α∼θ61Sα11グfrom the丘rst mechanlsm，c＆n be es書imated using this Final至y，the effect of the potentiε芝1volu！netric s芝rain，curve．ε済，givenbyEq，（4）ontheliquefactionresistallcels Figure 7 and Eq． （4） 圭ndicate that the liquefactiondiscussed in this section．All the e仔ects of three inauelltialresistεmce of a soil under a very low confining Pressure is 700OK．へMUR、へ、へND SOG．へ3not th＆t sign韻cant for small scale models飢茎黛but forDel）由飲）蹴gro田1（iie、d ↓Ground、、atertable 謙G LIarger models and centrifuge models。In負eld conditions，providedthatlique負ablefoulldationsollisclesaturatedin一一一：at 蓋01ぬabove G Lsomeway with an 玉n重ention to enhance liquefac毛ion（θ＝06．7’；10kN！m㍉一（i華」L＿一20n1resistance，asigni員cante仔ectcallbeexpectedexceptforsolls at a s｝1allower depth．2 （li．［． 一5nl 1t was found that thereis aunique relationsh量p betweent熱e nonηalized I至quefaction resistance and the potentialG L −2厳1volumetric strain．The iiquefactlon resistance of partlallysaturated sand can be reasonably estlmated from that ofG L．一〇5n！fuHy saturated salld in conjunction with t｝1e potent圭al ＼、 ＼、ミ・⊇繋1、80 90100Degrceofsatura毛ion．5『，・（％）Fig．8．Vari段重沁鷺sofiiquef食ctionresislanceraIiowiII∬，a吐severaIvo墨umetric stra至n using the relationship obta量ned in th量sstudy．This relations麺p may be Iimited for soils with alow matric suction．Fllrther investigation is 勲eeded forthe Iiquefaction resistance of part三al豆y saturated such asnon−plastic silt and saad containing considerable amount dep｛hsof飴es．essentiaIly tbe same irrespective of the degree of satura−REFERENCEStion and t｝1e back pressuτe．This must be a reason why the1）Bishop，A．W．and Blig厩，G，￡．（1963）l Some aspeαs of e貿ectivesoil宝n a smaII scale model foτa shaking tab豆e test at1黛 stressinsaturatedan（玉partlysamra［edso澱s，Gθαθ（hn’σ∼’θ，韮3．envlronment can easily liquefy even if the model ground 177−197、2） GoIo， S． and Shalnoto， Y， （2002）： Estimatiorl metllod for t隔econtains considerable amount of alr bubbles（Okamura liquefaα玉on s【reΩ9こ110f unsa！urated sandy soil（part2），Proc37’1∼and Teraoka，2005）． ゆn、．へ7醒．Co1瑳Gθαθ‘1LEη918，，1987−1988． 丁熱e relationship indicated in Fig。7and Eq．（4）make itpossible to evaluate the liquefact量on resistance ratio for負eld cond嚢ions． Figure 8 dep圭cts variations of the至iquefact量on resistance rat圭o w茎t｝1 the above discussedt振ee factors for a fully submerged uniform sand deposltwithbuoyantunltweighげ薫10kN／m3，voidratioθ瓢0．6and water table being co圭ncided with the gτound璽evel（G．L，．）or at 10m above G．L。互t can be seen that tbeeffects of S，and the ef￡ectlve con負n圭ng Press11τe aτe moτe3）Huang，Y，，τsuc短ya，H．andlshihara，K。G999）IEs［imationof partial saturat1on elぞecτ o【1 1呈q疑efaction resistance of sand using P−wave velocity，P1ηぐ．／（フ55．wηρ．，113，431−434．4）Is賊1ara，K、，Tsuchiya，H．，Hロallg．Y．a自d Kamada，K．（2001）： RecentsεudiesonHquefactio睦res1stanceofsaad−e旋ctofsatura− tlon，Pro‘．4rlr／η’，Co’ゾ、Rθごθ’π．4ゴv‘71κθ111Gθo∼θ‘11．ε‘7π11σμαたθ E1191’9，αηゴSo’10、w1αη11c5，1−75） 釣iart玉a，G．R、，Fi自11，∼V．D．L、and See（玉，H、B，（1978）：E齪eCts of sys葛emcompllanceoniiquefactlontests，ノ．Gθαθ‘17．五η9’8．P’v．． ASCE．茎04（4），463−479．6）Okamura，M．，ls漁ara．M、andOshita，丁．（2003）＝Liq毛！efa面ollsigni負cant t勤an that of tke water table oτthe i勲itial pore resistance of san（i improved widl sand compaction p鉦es，So’Z∫αnゴpressu「e・ Fαぜn面”oη5，43（5），175−187、7）Okam球ra，M，andTeraoka，丁、（2005）：ShaklngIable芝ests［oinves一 芝igatesolldesatura“onasaliquefaαio自co蝋emleasure，Gθαθぐ1LCONCLUDING REMARKS Sρθぐ’α1P‘’か1’ごor’oη 145．．ASCE，282−293． Resistance to liquefaction of partia至1y saturated sand sa田rationan引1quefactionres1stancesofsandimprovedwithsandwas investigated through a series of triax量al tests in this compact1on piles，／．Gθo’θoh．（3θoθノ∼v’1’01L石11911g、，ASCE，B2（2），study． Three parameters obtained from theoreticalcons圭deration，that is the degree of saturation，the initia｝con§ningPτessuτeandtlleinitial貸uidpressurre，wereselected as testing par＆meters in the series of undrained8）Okamura，M．，lshlぬara，M、andτaR1縫ra，K．（2006）：Degreeof 258−264．9） Tokima｛sロ，K．，Yoshimi，Y、and Ari｝zumi，K．〔1990）：Evaluation of l1quefactionres1stanceofsandimprovedb》・deepvibra［ory compaαion．So’1∫αηゴFα〃1面’011∫，30（3），15M58．10）Tsukamoto，Y，Ishlbara，K．，Nakazawa，9、，Kamada，K．andCyCliC tτiaXial teStS． Huang，Y、（2002）：Reslsτance of par［iaHy samrated sa負d 〔Q It is co面rmed that the degree of saturationぬas liquefaction w註h refereace to longitudinal and s騒ear wave veloci−signific＆nt e任ect on tl｝e Iiquefact量on resistance of sand．T』e liquefaction resistance also depends oa the initialcon負ning pressure and the init三al pore pressure．The ef墨ectof the existence of air on the liquefaction resistance玉smore s玉gni員cant foτ soil under the higher confiningpressure and the Iower initial pore pressure。This factimplies that the e行ect of the degree of satllration of soil is ties，50’Z50η‘ノFoμη‘ノα”oη∫，42（6），93−104H）Yasuda，S．，Kobayashi，T，，Fukushima，Y。，Ko』ari，M alld Simazakl，T、（互999）：E霞ectofdegreeofsaturatlo蹟ontheHquefac− 60厳 s重rength of 蒼vlasa， Proご． 34’11 ノρノL 八竹f． Co∼7∫． （3θo’θ‘h． 五ηgrg．，207ロ072．12〉Yoslllml，Y．，Ta麟aka，K．and Toklmatsu，K．（1989）l Liquefac【io“ res1stanceofapartiallysaturatedsand，So’Z5α’1ゴだα〃∼伽’o／1∫， 29（3〉，豆57−162， | ||||
| ログイン | |||||
| タイトル | JGS NEWS | ||||
| 著者 | |||||
| 出版 | soils and Foundations | ||||
| ページ | I〜III | 発行 | 2006/10/15 | 文書ID | 20952 |
| 内容 | 表示 | ||||
| ログイン | |||||
- タイトル
- 表紙（Soils and Foundations）
- 著者
- 出版
- soils and Foundations
- ページ
- -〜-
- 発行
- 2006/10/15
- 文書ID
- 20937
- 内容
- ログイン
- タイトル
- Contents（Soils and Foundations）
- 著者
- 出版
- soils and Foundations
- ページ
- -〜-
- 発行
- 2006/10/15
- 文書ID
- 20938
- 内容
- ログイン
- タイトル
- Elasto-Plasticity of Unsaturated Soils: Laboratory Test Results on a Remoulded Silt
- 著者
- F. Geiser・L. Laloui・L. Vulliet
- 出版
- soils and Foundations
- ページ
- 545〜556
- 発行
- 2006/10/15
- 文書ID
- 20939
- 内容
- SOILS A.ND FOUNDATIONS ¥,'ol 46. N'a 5. 545-556. Oct 2006Japanese Geotechnlcal Societ}ELASTO-PLASTICITY OF UNSATURATED SOILS= LABORATORY TESTRESULTS ON A REMOULDED SILTFRAiN OISE GEISERi), LYESSE LALOUli} and LAURE 'T VVLLI Ti)ABSTRACTCurrent models of the elasto-plastic behaviour of unsaturated soils contain important underlying assumptions thathave not been tested due to a lack of adequate experimental data. To address this issue, the objectlve of this paper is topro¥'ide a comprehensive set of experimental data. An extensive experimental program has been performed on arernoulded unsaturated silt. To characterise its elasto-plastic behaviour, samples vere taken through various stresspaths, including wetting, dr_vin*' and compression. Experirnental results vere analysed to provide (1) evidence ofsuction-induced preconsolidation; (2) dependence of' cohesion and shear strength at failure on suction; (3) stiffness inrelation to suction and (4) uniqueness of the critical state line.Key words: deformation, Iaboratory tests, partially saturated soil, plasticity, shear strength, silts (IGC: D5/D6)behaviour of soils at a gi¥'en external loading pressureINTRODUCTION(e.g. Croney and Coleman, 1954; Blight, 1966; BiarezExperimental data showin_ : all aspects of the behaviourof a particular unsaturated soil are scarce. This is mainlyet al., 1988; Zerhouni, 1991; Fleureau et al., 1993). On afirst-time drying path the saturated sample is initially verydue to the many (well-knolvn) experimental difficultiescompressible and then, beyond a suction close to s*, itbecomes less compressible, sho¥ving a quasi-reversiblebeha¥'iour. These observations do not correspond ¥viththe assumptions made in the elasto-plastic frame¥vorkproposed by Alonso et al. in 1990 and extended by otherauthors (Wheeler and Sivakumar, 1995; Wheeler, 1996).and the time-consuming nature of testing unsaturatedsoils. Earlier research work studied the shear strength(Fredlund et al., 1978; Escario and Saez, 1986) andisotropic compression of unsaturated soil at differentinitial suction ¥'alues (Matyas and Radhakrishna, 1968)separately. More recently, significant progress has beening volume measurement by e.g. Alonso et al. (1990),In this videly-used model, it is assurned that the suctioneffect is similar to the effect of a mean effective stressunder isotropic loading conditions (i.e. with initial elasticbeha¥'iour follo¥ved by an elasto-plastic response).In this paper ¥ve contribute to a complete experimentalkno¥vledge of the stress-strain relationship of unsaturatedWheeler and Sivakumar (1995) both on compactedsoils by examing the behaviour of remoulded Sion silt.kaolin, C*ui and Delage (1996) on Jossigny silt, andfinally, Ma touk et al. (1995) on Trois-Rivieres silt.Samples ¥vere subjected to various stress paths including:(i) isotropic compression at controlled suction and (ii)drying-wetting by means of increasing and decreasing thesuction at a controlled external pressure. Both of these¥vere follo¥ved by shearing the sample to critical state.made in an attempt to better understand the link betlveenshear strength and volume change, and to characterise it¥vithin a single framework. In these ¥vorks the experimental results examined the stress-strain relationship, inciud-Ho¥vever, none of these ¥vorks addressed the relevance ofthe suction value, s*, at ¥vhich air enters into the pores ofsoils. If the suction applied to the soil is less than thisair-entry value, s*, the behaviour of the soil can accurate-As in previous research ¥ve assume the behaviour ofly be interpreted using the standard effective stressconcept (Fleureau and Indarto, 1993; Fleureau et al.,unsaturated soils can be fully described by two stress statevariables. It has been sho¥ 'n by Fredlund and Morgen-1995; Karube and Kawai, 2001; Kohgo et al., 1993).stern (1977) that the tot.al stress, the pore air pressure andVVhen the suction ¥'alue exceeds the air-entry value,the pore ¥vater pressure can be expressed in any t¥voho¥vever, t¥vo stress state variables may be necessary for aindependent stress combinations in order to characterisethe mechanical behaviour of unsaturated soils. Typically,the net stress and the matric suction are chosen as statevariables. In this paper, ho 'ever, the results are alsocomplete description of the soil. This dependency of thestress-strain relationship on suction is further examinedin this paper using experimental data obtained on Sionanalysed usmg the combmatron of the "saturated effective" stress and the matric suction. Such a combinationsilt .Other researches have examined the drying-1vettingi' Soil'Iechanics Laborator)*, S¥viss Federal institu e ofTechnoiog)*EN. c-EPFL, slvitzerland (1)'esse.lalouie epfl.ch).The manuscript for this paper ¥1'as recei¥'ed for revie v ort Januar}' l l, ,_005; approved on h'ta}, 29, 2006.¥vritten discussions on thls paper should be submitted before ¥. ,la ' I , 2007 to lhe Japanese Geotechnical societ ', 4-38-2, sel goku. Bunk}'o-ku,Tok.vo I 12-001 l, Japan. Upon request the closing da e may be exteuded or e month.545 GE SER ET AL.,)'*4(3"dlymq¥ ettm"' paths (Fig. i, A-H-H'). The sampleo¥vn ¥veight vas assumed to be negligible. The effectivepressure p' ¥vas kept constant and equal to zero. Thesamples (diameter 40 mm and height - 9 mm) ¥vere placedG FEon a saturated high air entry ceramic disc and subjectedI,AH' 45to a positive air pressure by increasing the cell pressure,p'iSH,,,1,'1,1c¥vhile the pore ¥vater' pressure u,, remained unchanged.In this ¥vay, the capillary suction s ¥vas equal to theimposed air pressure u*. For each suction le¥'el, at leastfour samples lvere prepared. ¥ rhen the variation of the¥vater content tends to be negligible, the hydraulicDFrg. 1. H¥. dro-mechanical stress pati]s foltowed in this stud .equilibrium is reached (usually after 200 to 1000 hours ondrying paths and took significantly longer on ¥vettingpaths). Two samples vere used to determine the ¥vatercontent and the other t¥vo samples ¥vere used for volumemeasurement. To determine the volume change, theallo vs continuity in the modelling of the saturated andunsatur'ated states,samples ¥vere removed from the pressure plate and placedfor four hours in petroleum in order to fill the air pores.Because petroleum is hydrophobic, it can be assumedMATF.RIAL PRF.PARATIONThe soil examined in the research reported her'e is asandy silt (USCS classification: CL-lvlL) from the regionof Sion (S¥vitz,erland). The density of solid particles isp,=2.794 Kg/m3. The index properties of the soil are:TvL=25.40/0, }t'l'=16.70/0, Jp=8.70/0. The grain sizethat this procedure causes no ¥vater volume change in thesample (preliminary obser¥'ations sho¥ved no significanttotal volume variation at this stage). The total ¥*olume¥vas then measured using a picnometer (L.agny, 1996;Geiser', 1999). Details on this technique as ¥vell as theaccuracy values are available in Peron et al. (2006).For the t/'icl.1"ia! tests, the samples (50 mm in diameter,care ¥vas taken in sample preparation to ensure the100 mm in height) ¥vere fir'st consolidated to a gi¥'enconfining pressure, p', (Fig. 1, A-B) under' saturatedreproducibility of the initial state. The sample preparation procedure consisted of mixing a kno¥ "n mass of drysoil lvith de-aired and demineralised vater to an initialone-dimensional loadin_*," history of the sampie, as theconfining pressure ¥vas al¥vays higher than the equivalent¥vater content lv=1.5 Tt'L. This ¥vater content ¥vasassumed large enough to produce a slurry that has nomean effecti¥'e stress applied during one-dimensionalloading. When the consolidation ¥vas completed, samplesinternal structure. To remove air bubbles trapped in thevas ¥'ibrated. It ¥vas then placed inside a¥vere subjected to drying path (B-C) at constant "saturated effecti¥'e pressure" p' by increasing u. ¥vhile maintain-hermetica]ly closed box for '_4 hours. The initial voiding constant total pressure, p, and u,.. Finally, ¥vhenratio eo at the slurry state varied bet¥veen 0.9 and 1. Forthe triaxial tests the samples lvere prepared in a mouldingequilibrium ¥vas reached (usually after one to threetube (K{) condition) subject to a vertical consolidation･ Path C-D: isotropic compression. This path ¥vasdistribution is 80/0 clay, 7,-o/o silt and 200/0 sand. Specialslurry, the soilstress of 100 kPa. This led to samples having initlal ¥'oidratios bet¥ *een 0.69 and O.76, and water content bet¥veen24.80/0 and 27.60/0.TF.STING PROGRAMMF, A¥. 'D PROC_F.DURF,SThe saturated beha¥*iour of the Sion silt ¥vas firstcharacterised. A total of 15 tests (on 89 samples) in thepressure plate apparatus and 44 saturated and 30 unsatu-conditions. This ¥vas assumed to erase the pre¥'ious¥veeks), samples ¥vere taken through various str'ess paths:obtained by increasing the confining pressure p ¥vhilekeeping both u^ and u,,, constant (thus allolving freeflo¥v of air and ¥vater). Pressure ¥vas applied in stepsand ¥vas maintained until equilibrium ¥vas achie¥'ed(usually after several days)^･ Path C--E: fully drained shearing (see Table i). Thispath l 'as achie¥'ed by increasing the deviatoric stressq = (71 - (T3 ¥vhile keeping both t/* and u,, constant. Thepaths (see Fig. 1). In the follo ving, a con7p/'ession patllrate of shearin*' varied from 0.0012 to O.O018 mm/mln(see next paragraph for details). For most tests, unloading-reloading ¥vas performed at an axial strain ofrepresents a path obtained by applying a total externalel = '-o/o .rated triax.'ial tests ¥vere performed using different stressstress (T] or cT3 (axial or lateral stress, respecti¥'ely) atconstant suction and a dryiilg-tt'etting path correspondsto a path obtained internally by modifying either u*, thepore air pressure or u,., the pore ¥vater pressure. We ¥villlater define the mean total pressure, p= (1 /3)((TI +2(T3),the mean eff cti¥'e pressure, p' =p - uw' and the mean netpressure, p>:< = p - u*.A pressure p!ate apparatu,s ¥vas used to study the･ Path C-F: constant ¥vater content shearing (seeTable '-). In this case the shearing vas carried out under¥vater-undrained conditions ¥vhile maintaining a constant pore air pressure u=,, thus alio¥ving air drainage.The pore ¥vater pressur'e u,, ¥vas measured during theshearing so that the suction ¥vas kno¥vn. The appropriate shear rate ¥vas 0.06 mm/min for these tests.･ Path C-G: constant mean effective pressure. This ELASTO-PLASTICiTY OF U*NSATURATED SOiLSlable l,eTUnsaturated drained shear testss = u* (r{A-B# B-C* C-D or C-G*=Tesilic]1 lp'(kPa) (kPa) (kPa)400NS-D 1 400450503I OOi¥'S-D-' 450NS-D3ler 500ei n:llTS*()("'O)(O. )o.801 o 6615 66619.583o.72 1 o.645 oo3NS-D4 600o.666003o.788 o.64NS-D5NS-D6NS-D7NS-D96005004004ao2006005003003o.7 o.65NS-D I l600600600NS-D 1 2NS*D 1 3100lOO1 OO33f_600600500502SO1 OO333S.* iei:1 '(-)lOOl OO547o.70 o.66r' = :l I .616.877l I .4niLlslcr49O 25O IlO.283O 1733o 334802o 724o.74o 33o.25O_755 O 62O_712 0.67O.712 O 6320 46.6, 7o.08o 4714. l620291* see paths in Fig. 1_Table 2. Unsaturated constant water content shear tests (path A-B-C-measured using pressure-volume controllers. Very fe¥vF' in Fig. 1)ex'perimental data exist in the literature for this method.((T ),i!*Test A-B and C-E B-C and C-E l"j *'al (sla!)ejnil(-)(kPa) (Ol'a)*n tUNS-U1 1200O O 74 23 O30 O.735 2 1 . I O. 15200(kPa)NS-U2 200U2NS-U3300300NS-U4 300NS-U5 300U51000NS-U6 300NS-U7 300NS-U8 30060 O 71 20.8 O.3O 0. 7 1 22 OlOO O.718 18.6 O 33200 O 738 lO.6 O.66280 O 712 8.2 O_93O O.748 20.5 Ol OO O.7 1 2 1 7_6 O. 1200O 743 O.2280 O 712 7 6 O.289*3consisted of increasing the deviatoric stress vhilekeeping both the mean effective pressure and the suction constant.Cell pressure, air pressure andOur tests have shown that temperature and atmosphericpressure changes, as ¥ 'ell as air leaks, considerablyinfluence the results. An impro¥'ed configuration isintroduced here by usin_ : a rnixed ¥ *ater and air controller: the air ¥'olume is limited t.o that present inconnection tubes only. With this modification, thevolurne change of the sample can be satisfactorilymeasured. Ho¥ve¥'er, undetectable air leaks are stillpossible. The precision of such an improved system isestimated atO.?_･_ cm3 representing O. 1 IC/o of a conven-tional sample volume of 200 cm3.For the results presented in the follo¥ving, all triaxialcells l 'ere also calibrated to deduce the sample volumechange from the cell volume change (follo¥ving Head,1986), to allo¥ " a rough doubie check. For some tests,only the ¥vater volume changes A V,. and the initial andfinal degrees of' saturation (S* * ** and S* n , respectively)were determined. The value of tS*"*¥vas estimated fromthe hydric path results using the Tv-S* cur've and S* fwas'ater pressure ¥veremeasured using GDS pressure controllers. Suction to thesample ¥vas applied or measured using the axis-translation technique (f'or details see Fredlund and Rahardjo,1993), usin_g: high air-entry ceramic disc ¥vith air-entryvalues of 100, 300, 500 and 1500 kPa.measured at the end of the test. The volumetric changesVolulne ChangesMeasurement of volume changes in triaxial tests isindicates that the complete equalisation of' pore waterpressure throughout the sample is possible if the timeessentialrequired to fail the sample is set to:could then bevritten as A V=A V,. /S*.Shea/ RateThe shear rate for the drained unsaturated tests (pathC-E) was determined in accordance ¥vith the classicalGibson and Henkel method (1954). This approachvhen analysing the mechanical behaviour of asoil. In the case of a saturated test, volurne change is onlydue to vater exchange and can easily be measured ¥vith aburette or a pressure-volume controller. In the case ofunsaturated samples, however, sample voiume change istf= H21(llc.(1 - Ur)) (1)¥vheret : tirne required for' the sample to fail,H : half height of the sample (5055 mm),n: numerical factor depending upon the extent andrelated to both ¥ 'ater and air volurne changes and cannotbe measured so readily (Laloui et al., 2006). The air-¥vatervolume method has been used in this ¥vork for the volumelocation of the drainage boundary. For our tests since thechange measurement. In this approach, the volumetricwater drainage ¥vas only performed at the bottom of thechange of' the sample is obtained by simply adding the airsample via the high air value ceramic, ll = 0.7 ,and water ¥'olume changes. Both ¥'olume changes areUf: average degree of dissipation of t.he induced pore GEISER ET AL.,)'*48¥vater pressure at failure. CeneraHy O.95 is assumed to besuf lcient to find the soil intrinsic charac eristic uncierdrained conditions,c*: consolic.iation coefficient, calculated usin_"*. Head's(see Figs. )-(ci) and 2(e)). Note that, no hysteresis ispresent for the oven-dried samples. This result confirmsthat there is a behavioural difference bet¥veen o¥*en-driedrelationship (1986):cnature of the beha¥*iour that occurs, ¥vhen the samples are¥vetted after ha¥*in : been cirieci at a suction of 300 kPa= T9*)(2H)2/r,)o (2)t,)o corresponds to the time at ¥vhich the soil reaches 900/)of its consolidation for a :iven load. This ¥vas cleterminedfrom the isotropic consolidation path (C-D) at differentvalues of suction. By proceeding in this fashion, thee¥'olution of the soil permeability vith suction, thepermeability of the high air entry disc and the drainageboundary ¥vere already taken into account.samples and samples subjected to high suctions (¥vhereconsiderable hysteresis lvould be expected).Figure '-(b) sho¥vs the suction consolidation plane. Thescatter of the data is quite important, as an error of ,_01on t,he volume measur'ement implies an error of about 5010on the void ratio value. Starting: from initial void ratio of0.9-1.0 for s=0 (not sho¥vn in this logarithmic plane),the void ratio reduces to about O.7 for suction ¥'alues oflOOkPa. Due to the data scatter, the compressibilityFor example, for a consolidation stress of 400kPa,¥vith a high air entry disc of 500 kPa and a suction oflOOkPa yields: r90=72000s, T,;t)=0.848 and ,_H=110mm c, =0.14,5 mm2/s. According ro Eq. (1), t*"= (1 101index cannot be determined. Note that fitting a straightline through the triangle mar'ks (¥vetting path) yields aslope of around O.017. This ¥'alue can be compared lviththe unloading sarurated compressibility from isotropic,-)2/0.75 ･ O. 1425 ･ (1 - O.95) = 56608 Is * 1 57/1 . Assumin_ ,_compression (/t-* O.004 to O.OI 1).The shrinkage curve (Fig. '-(a)) confirms the obser¥*ations of other authors (Biarez, et al., 1988; Fleureau andthat failure occurs for an axial strain of almost 100/0, ashear rate of l.2 um/min has to be set. In the tests, therate ¥'aried bet¥veen I .'_ and I .8 /Imlmin depending on thepermeability of the high air entry ¥'alue ceramic and onthe applied stress and suction level These values are inIndatro, 1993).Vhen the ¥vater content decreases, thevoicl ratio first follows a line close to the saturation curve(i.e, e= ()'</y,.) It.') and then c.lecreases slight]y.agreement ¥vith those used by Ho and Fredlund (198,_)and later bv_ Delage et al. (1987).Isotl'opic Col77pressiol7 Tests ol7 U/7saturatec! Sclnlp!es(Path C-D)RESULTS AND INTERPRF.TATIONDlying- 'Vetting Bellavioul' (Pat/7s A -H-H' )Figure '_ sho¥vs the characterisation of silt in relation topaths A-H-H', performed under zero net pressure p=i=.The simultaneous measurement of vater contents andIsotropic compression tests lvere conducted by increasing the pressure in steps at pre-selected ¥*alues of suctionbet¥veen O and ?_80 kPa (Fig. 3(a)). Only ¥vater volumetricstrains 8., (defined as the variation of the water ¥*olumeA Vw over the initial total volume V , 8,,, =A V,, / VO) ¥vererecorded in this first series. All samples ¥vere preconsoli-¥'olume changes anci their representation, as suggested byBiarez et al, (1988), gi¥'es the complete state of the soil.dated under saturated conditions to an effecti¥*e meanpressure of 300 kPa and then dried to a given le¥'el ofThis representation includes: (a) the shrinkage curvesho¥ving the void ratio e as a function of ¥vater content It',suction (O, 100, 200 and 7_80 kPa) ¥vhile keeping p' (saturated effecti¥'e pressure), at 300 kPa, before starting the(b) the consolidation plane sho¥ving e as a function ofisotropic compression (path ABCD, Fig. 1). Thesuction (logarithmic scale), (c) the degree of saturation S*(logarithmic scale), and (e) the usual retention curvesho¥ving }t' as a function of the suction (logarithmicesrimated yield points (in a p' Iogarithmic representation)are identified by a change in slope. For the case of s= 100kPa, no clear yield point is detectable. Plotting the yieldpressure in terms of both p* (net pressure) and p' versusscale).suction allo ¥'s the examination of the variation of .vielciThree different symbols are represented: (i) the circlescorrespond to dryin_"* of the samples, ¥vith a slurry at anlocus (Fig. 3(b)). Up to the suction corresponding to theair-entry ¥'alue, one ¥vould expect the yield cur¥'e to beinitial ¥vater content of I .51'vL, (ii) the triangles representsamples first dried to a gi¥'en suction of 300 kPa and then¥*etted by decreasing the suction, (iii) the crosses cor-¥'ertical in the s-p' plot (because beha¥*iour under saturated conditions is governed solel_v by p-u, ) and inclined at45' from the vertical in the s p=i= plot (p= =p'-s). There isrespond to samples first dried in the o¥'en at 105'C anda simple mapping bet veen the tlvo curves separated bythen ¥vetted by decreasin_a* the suction.the magnitucie of suction applied.Isotropic consolidation tests gi¥'e information on theas a function of w, (d) S* as a function of suctlonFi ure 2 demonstrates that this soil remains almostsaturated on a drying path belo¥v the air-entry suction, s*,vhich is approximately 50 kPa (see Fi :. '_(c) and )_(d)).Further increasing: the suction led to a sig:nificant reduc-tion in S*, though such reduction rapers off above a suction value of 400 kPa (Fig. 2(d)). Note that the relation-variation of the compressibility ¥vith suction. ),' is definedas the elasto-plastic slope in the In (p') versus e plane and).=:< as the corresponding compressibility in a In (p*)versus e plane. The ¥'alues are summarised in Fig. 4 forthe Sion silt and also for other soils frorrl the literature:ship bet¥veen ¥¥*ater content and degree of saturation is theJossigny silt (Vicol, 1990), Trois-Rivi res silt (l¥,Iaatouksame in all three cases (Fi . ?(c)).et al., 1995), kaolin (¥¥rheeler and Sivakumar, 1995 andThe experimental results also re¥*eal the hystereticSivakumar, 1 993), Steerbeek silt (Leclercq and rlELASTO-PLASTICITY OF UNSATURATED SOILS5- C).1i(b)a(L)d' O 8 :08CQLoA A:,_>Al06402030A : i-Aia06o1011_(c)1 041 ooo1 oo¥ (d)Air entry(/)coCQ0505 -CQ(1)o(D(:)a)(DOo40102030Water content, w [o/o]oo1o1 oo I oao I oooo40(e)30 - ¥¥Drying path (w jt = I .5 wL)p ( jw jtWetting ath= dried)^ Wetting path(initia[ly dried at 300 kPa)c:(D- 20c:ooL(D(Is 10 -:a1i O I oooo1 oo1 oooSuction, s [kPa]Pig. 2.Behaviour of the Sion silt uDder drying 2lnd wetting paths (pressure plate)Velbrugge, 1985), kaolln (Matyas and Radhakrishna,1968). For se¥'eral of the soils sho¥¥'n in Fig. 4(b) an initialconfining pressure of (7 =600 kPa and at different suction levels (s=0, 50, 100, '_OO and 280 kPa). The initialincrease of ),* at low suction value is noticed, follo¥ved byrnodulus and the maximum deviatoric stress tend toa reduction.gradually increase ¥vith increasing suction. In saturatedsoils, suction and p' (under isotropic loading conditions)D/'ained Shear Tests (Pat/Is C-E)Figure 5 sho¥vs the stress and strain data for triaxialdrained shear tests at a constant "saturated effective"have sirnilar' effects on the volume cham e and shearstrength (Laloui et al., 2005). Each sample sholved a peakde¥'iatoric stress ¥vhich ¥vas then follo¥ved by a gradual CJEISER ET AL55 oo06*(a)[> (oe(aj/e )/>.C:_CL'U)o/ /E 02o:5O-HCsat (s=0kPa)H HCNSI (s = 100 kPa)3e)400300600l 'I/'"Ii '/.... .-r..---/ "-- e'lHCNS3 (s = 280 kPa)4/d :..-"-'"'3-HCNS2 (s = 200 kPa)'(S/B . !/ ;' ' _ '*CLE>/2'e)5/O800 Iooo2CO 600800400oSaturated eftective mean pressure, p' [kPa]Suction, s [kPa]03300(b)p'>' 02._:(u)(,)e)oo 10a :sHF Kaolin (Wheeler et al ')E- Steerbeek silt ',/ r' - ¥-y- Kaolin (Matyas et al )/ >;"U)i(/EO O.1 Rl __1___"_'l eO(Ds o:Cli:'¥(b)"{3-' Jossigny silt*$- Trois-R'v'eTes silt*(p*CL 200 -- S'on silt_' :: : ' **s-::L A_'o600500400preconsolidation pressure [kPaJFig. 3. Unsaturatcti isotropic tests: (a) experimental resu!ts and)･ielding points and (b) evolution of the preconsolidution pressurewith suctionreduction to¥vards critical state. Visual obser¥'ation of thesamples has sho¥vn that the decreasing stress after thepeak coincides ¥vith the development of shear bands. Thetest at s= '_80 kPa (corresponding to S,* 300/0) PresentedO200 600400Suction, s [kPa]800Fig. 4. Conlpressibilit _' as a function of sucrion in (a) a saturatedeffective stress approach and (b) a net mean stress approach fordiffercnt soilspressure (T3: '-OO, 300 and 1000 kPa. The rele¥'ant stressstrain relationships are sho¥vn in Fig. 7.Shear bands appear before the peak in deviatoric stresswhen the ratio between the initial suction s and ((7 )i i* isa dlfferent behaviour, in ¥vhich shear bands started tolarge (typically, for Sion siit, ¥vhen the ratio s/((T )i i, isdevelop early in the test and the stren_._"th could not bemobilized.Figure 5(b) illustrates the ¥'olumetric strain, in ¥vhichthe samples sho¥ved compression ¥vhich lvas follo¥ved byover 0.45). For ratios do¥vn to O.3, Iocalisation can stillappear, but this occurs after the peak. For ratios smallerthan 0.3 (Fig. 7(c)), no significant suction-induced effectsdilation as the shearing progressed. The amount ofnegligible in comparison to the compression effects.The relationship bet¥veen 81 and uw (and s), representeddilation increased ¥vith increasing suction.Drained shear tests at the constant net confinin9:pressure of (T =400 kPa and at different suction levels(s=0, 50, 100 and 200 kPa) are plotted in Fig. 6. As inthe previous tests, the initial modulus and the maximumde¥'iatoric stress gradually increase ¥vith suction^ Thiscan be observed implying that the drying effects arein Fig. 7, mainly shows that the built up pore-¥vaterpressure is smaller for unsaturated than for saturatedsamples, as the fluid in the unsaturated case is a mixtureof air and ¥vater and thus is more compressible.behaviour is similar to that observed in saturatedE!astic Behaviourcondition for tests performed under increasing confiningpressure. Ho¥vever, in this case even for a large value ofaxial strain, q never reaches a unique residual value.In order to describe the elastic behaviour of Sion silt,an unloadin*' path was usually performed at about 20/0 ofaxial strain during the shearing tests. T¥vo different "elas-tic" moduli are defined: (i) the secant modulus E* definedCor7st(?/7t ,Vater Coi7tent Shear Tests (Paths C-F)In this series of tests, samples ¥vere consolidated tothree different ¥*alues of saturated effecti¥*e confinementas the slope in the el - q graph at a given axial strain 8i of0.50/0 and (ii) the unloading modulus E defined as theaverage slope in the 81-q plane durin*' unloading. lELASTO-PLASTICiTY OF UNSATURATED SOILS1 5001 60a(a)CQCUi- 1200- r-u)u)a)/ ¥ _-r *.lu)4Lc'):- ll'l' } -u)(D(13 = 600 kPa (s = 50 kPa)(13= 600 kPa (s= 100 kPa)400 ･*?-' - ( 3 = 600 kPa (s = 200 kPa)C-i -･cF3 = 600 kPa (s = 280 kPa)ooo"::oas 500' Satvrated (s = O kPa)H ' NSD2 (s = 50 kPa)- NSD3ter (s = 100 kPa)-- NSD5 (s = 200 kPa)'5; - k!･;(1)a1 5 255 10e-* -- - ' __ll+---( 3 = 600 kPa (s = O)o 'oICOO " /-i-co 800oas//CT"/CLD_551o205 Io 15OAxial strain, 81 [o/o]2aAxia[ strain, 81 [o/,]-1o(b)'** "- O>KOOes--s::- '1"c(Q*co++oCQ2Oe) 3E*C::(b)r;$> 1u)¥¥*oot2¥.eL- ______( ----t. ; ---- ...¥ ___-(3r-"- Ie- -'L¥ " x 14¥E4>'_"> / "$ _¥ *¥6¥(1)+'(1;55 10 20 25ric strain 8*10oAxiai strain, 81 [o/o]Fig. 5. Drained shearing tests at an effective confining pressure (T of600 kPa and at different suction levels (s=0, 50, 100, 200 and 280kPa): Ax'iat strain 81 versus (a) deviatoric stress q and (b) volumet-¥ *¥¥e8i5o(',,¥*75x-20Axial strain, 81 [o/o]Frg. 6. Drained shearing tests at a net confining pressure a3* of 400kPa and at different suction levels (s=0, 50, 100 and 200 kPa):Axial strain 51 versu s (a) tlevialoric stress r/ and (b) ,vater volumetric strain 8***Figure 8 sho¥¥'s these rnoduli as a function of suction atcase is represented by the critical state line at saturationels of "saturated effectrve" , p' , and net mean(CSL), as the peak strength and the strength at criticalstress, p*. As ¥vould be expected, suction increases thestate are close for normally consolidated tests on saturat-stiffenin*' of the soil at a gi¥'en confinin*" stress a or cT .ed samples. Lines are plotted through the peak stren*'thpoints determined at the same suction level. The presentdata on the Sion silt sho¥v that intercept a (a rneasure ofdifferent leSimilar observations ¥vere made by Fleureau (1992), Cui(1993) and Lagny (1996).cohesion) increases ¥vith suction, Ivhile the slope (/1p**k)Peak Strengthremains almost constant.Peak strength qp**k obtained from constant ¥vater content tests are plotted as function of suction in Fig. 9. Itcp**can be seen that qp**k increases with suction for lolv valuesof effecti¥'e confining pressure ((7 i i* = 200 kPa) but slight-figure is based on a surnmary proposed by Delage andGraham (1995), the data on Al-Agoza clay (Mashhourly decreases for high values of effective confining pressureet al., 1995) and our o 'n resu[ts. No clear trend can beobser¥'ed for the variation of the friction angle cp*.k. Forthe silts, it appears that cp**k decreases ¥vith suction,particula '1y for Trois-Rivi res silt, which is a relativelycollapsible soil. In comparison, Sion silt is not collapsibleand cp**k is almost constant. The cohesion as a functionof suction (Fig. 11(b)) is similar for all the soils (exceptTrois-Rivieres silt), Ieading to some simplifications in themodelling of shear strength of unsaturated soils.When the peak shear strength points are plotted, in a(cr3i*it=1000 kPa). (T j*,j*=300 kPa represents an inter-mediate state. In Fig. 9(b), the results are scaled bydividing qp*"k by the effective confining pressure. Notethat a rnaximum value of qp*<*klcr i it = '3' I is found close toa suction value equivalent to the air-entry ¥'alue (s*=50kPa).The points representing the peak deviatoric stress versus the corresponding net mean pressure p* are plotted inFig. 10 for tests on unsaturated samples. The saturatedFigure 1 1(a) sho¥vs, as a comparison, the f'riction angleas a function of suction for diff;erent soils. This 552GEISER ET ALLo(¥,o(1CQorQcLo!': iOLlsa ao-aLr- aeoo::;C')'l',(c¥{c¥lc¥1I il:a,CL0c')(!)u)cco r¥eou):) :):)Lr)(!);c:OCe,* ;-t!) ;'O:;CLU)cl)(1):)Z fzzf･ , .. ,,{=0C:CQu)-OT-75o><<"･:1-tr)¥a__. _.: -faaooo oo l!)ao 'oaalr)C tc:]ar ' A-* 'aLoooc:)oa ooLooc,Lr)C ( J-- Lr)c¥Lr)c¥::)V)z:)(1)Z(1)Zr)[ed ] "n 'eJnsseJd-ieseN¥ eJOdLr)c¥oc:[E?d ] S 'UO!;onS([ed ] b 'SSeJ;S O!JOle!Aear):)OCQCLO,( 'o_:x 'xocoao c lCu)u)Q)F(:),- oOLc J2(Qc:0f-tOro¥o1'Q, ;LOa::CLCl)"'C:;(1)cl'as' :oo oCLoU)CQt[:')c!)f', ,:: ,d<_ (:) _I **_ t=_ oo o a o oUDtf)C[ 3d ] b SSeJ;S OVOIE;lAea [8d ] s uol ons,[ d ] n 'eJnsse.Jd-Je; /V¥ eJOdac¥11 ro_o_:J-ooll !1 -- Lr) __ r)(o:):)oco(O:) z z",,)Z if 'a)Q,- tr)Lr)o- a) !- 0Q):;s-::' :e e- o 'l::a<C. .='ooo o o oce o [edC ] S a'uo!}onSoc¥Ct[ed ] b sseJ;S OiJO elAea!***[ed ] n 'eJnsseJd-Je e,V¥ ejOdFig. 7.Constant watcr content shearing tcsts: (a) (cT ) n t = 200 kPa, (b) ((T!) =300 kPa and (c) ((T ) = 1000 kPa' ni* n 553EL．ASTO−PLASTICITY OF UNS．ATURAT狂D SOILS2500200UnめadingmodulusE s司80kPa ！㊥ ノ㌔ ！■，o 20GO” ！／150住而首儀襲国φ田σ筆00SecantmodulusE（ε＝05％）、 き で U甲｝辱』一P＿…／1一⑦；＝＝＝醐88臨“・D”■響’”餅コ℃o稠18撃：； ゆ・埴． 一＠一一σ『載600kPa50 ’㎜壕 ・・直1｝6岬甲・◆ 一一●一一σ｝＝400kPa 匪3言1 一・慨一σ’＝500kPaののΦ s瓢200kPa ノ’ ’／1500・一 ㊧ん τ1灘13 ノろ』 畔 ル／ ／諺のQ 1…1 ！髪＼C＄Lats＝。kPao ノ彰 S雷5ひ55kPa讐ノニ☆言講避c口）Φo rトP☆＝400kPa。a／00 50o250 300100 150 200Suction，slkPalFiσ8．2000500 1000 1500Net rnean pressure，P★［kPaIE盟9stic mod面as a function ofsucIion for Sion si賑Fig．10． Pe貸k s重reほgIh for di『ferent suαions in theρ牝17p鳳ane（individり 副valuesofsuctionaregive賎inFig、12）2500（a〉團 60「一 ↑・2000圏囹3iRit＝200kPa十σ鵬 3init襯300kPa”毎一げα． 1500一邑 焉 の 攣 Madridciayedsand層一「緬幅Guadalix cIay『冨・唖J。sslgnysilt （a） 1 ×．一50一Φ1⑳に．・一。一掌rois−Rivi合res sllt、 、・一・響・一AトA9Qza ciay“Sionsilt㌧骨σ甲 3init 篇屡OOO kPaσ億1000＝｝ 、o 、8ε 1一印ゆ砥500革 爾鯉、◎塞30K00 50100 150 200250 300、 卜 』 甲 ■騨 』ゾ ド 2010Suction，s lkPa】500 10001500Suction，s lkPal35500（b）（b） ｝・3 400− 1 三の 2．5−0◆髭3・・∋ 1b 闘 雷蕊 ・ 。’國 ユσ 2翻O 、 ，の 一 ，’。1・・1〆§20叶②！メ樗⑧1，5一一◆1 諺ソ0 50歪OG 150 200250 300Suction，s lkPa】 0齢一0500 10001500Suction，＄【kPa】Fig。9．Pe段kdeviatorics亘ressasaf照cIionofsuction（cons重anIwater con｛en韮重esIS）K9．11．罪「riαlonangle（幻andcohesion（b）a重peakstreP9芝hversus suc額o臓（netmeanstressinterpre雌io臓）グー（1p1＆ne（Fig．12），the slope connecting them，ηp，、k，canQnce more be assumed to be coast＆nt。The cohesion alsoC1・i！iごα1S！α！（∼increases（a1豆thepoints wit紅s〉O ares圭芝uated on or＆bove While signlncαnt rese＆rch e貸brts have addressed thethe cSL line at s鱗o）．Qu＆n重itatively the effect is 正essre1εttionship between s難ear strength＆nd suc宅ion，only apronounced重han in theρ＊一（1plane．few have exam量ned｛he e9奄ct of suction o11critical sta重e（e、g。Tol119901Wheeler and Sivakumar，1995；Maatouket al．，1995）．The tests on saturaξed samp正es are p至otted in GEISER ET AL.554Fig. 13 for the Sion silt: the Critical State Line (CSL,) hasa slope of M= I .3 ¥ 'ith a correlation coefficient r of O.99.A11 the points corresponding to unsaturated samples(solid dots) are close to the CSL, Iine. The scattering of theexperimental points is similar to that observed in saturated conditions. This ¥ 'ould mean that the critical state isuniquely defined in a p' interpretation for the consideredle¥'els of suction. Taibi (1994) has obtained similar resultsfor unsaturated soils,Figure 14 sho¥vs the critical state points in a p* interpretation, ¥vhere a unique line can no longer descrlbe theCSL. The results seem to be similar to those described byMaatouk et al. (1995), ¥vith a decreasing slope M and anincreasing cohesion ¥vith suction, respectively.25001 23Yie!c!ing13(Q20ao -s = O kPa1500 --100 eO_x200 n"' =CTa,(1)3iour. Fe¥v experimental r'esults are available in theliterature for the determination of yield locus in the case50 50e)c,,o laoo oCQ>e)OThe kno¥vledge of the shape of the yield locus and its¥'ariation ¥vith suction is an important aspect of beha¥'-i aoof unsaturated soils (Zakaria et al., 1995; Cui andDela>"e, 1996; Geiser et al., 1998). The procedure used todetermine the yield surface is as follo¥vs. The samples arefirst loaded isotropically ¥vith a consolidation pressurep = 400, respectively 600 kPa. They are then unloaded todiff rent values of confining pressures prior to shearin*".1 OO7127 .83 )soo -o55o I ooo50D5002000Saturated effective mean stress, p' [kPa]The defined yield limit then corresponds to the highestvalue of the mean effective stress (400, respectively 600kPa) and a specific ¥'oid ratio. The unloadin*' steps movedthe stress state inside this yield surface. Since the stressPeak strength for different stlctions in the p'-q planeFig. 12.250030ao: Norma]ly consolid drained (s=0 kPa): Normaily consol undrained (s=0 kPa)Overconsolidated drained (s=0 kPa)25aoCUe Unsaturaied samples (s>0 kPa)-cr 2aooe) 15aoe>e)C 50a -e' 501 OO71 l'CSL at s = O kPa1 oo,^ep'" e e 83500*e551s = 100 kPa4ooooooO1 50aCritical state line for saturated anti unsoturated statesFig. 14.300225ol1 oooOO _O 1_'vv _O 210¥*tl-o 350}Oo 2 4 i;0 (yo 108Fig. 15.50020aoCritical state line for different suctions in the p *q planeO20CQCL ( 15cr500Net mean pressure, p [kPa]Effective mean stTess, p' [kPa]ril:F. 13.i oo100oaoO*23ioo. p;'oOtQ>e)CUOM=1 32aoe ' i'v)u)oo 10ao -15ao -u)e)M=13c,)13cl)eci2aoofCLicyCri 'oal State Line at s=0 kP lCL-o 41 oo, =i150200p (kPa)ldentification of the yielti point in the case of a triaxial tcst[illlll FLAS'TO-PLASTI(,TY OF UNSATURATED SOILS6co5ao- - s = O kPc p* =40akP40a -cr300 -_}D06p ¥D08scocL! ( 200 -s=iOOkPacr 40a' s = 280 kPaDO1cTD02D018pDOIO100 rD019¥*7; 300 ool i 200-NSD13l(O l'a100 -D09/NSD4>¥¥¥ ¥NSDi iNCNS12,7 __O200400Saturated effective rnean stress, p' [kPa]1*1l.bo400200NSD9e)o014p¥oNSD{;, A s=200kPacl)- D012pi) ¥ ¥lD¥017oo 6 ¥¥rNSDi2¥u)l D07DO 5pv;C4CSL at s = O kPa;¥:CSL at s = O kP500 e s=50kPao p' = 600 kPafOoo600p' [kPa], dsP800Fig. 17. Yield points under unsaturated conditions in an saturatedeffective stress representation for a saturated preconsolidationpressure of 600 kPaFig. 16. Stress paths, yield points and plastic strain vector incrementsunder sa$urated conditionspoint ¥vas ¥vithin the yield surface, initial strains due to apaths, it ¥vas found that the behaviour is different interms of volume variation ¥vhen the suction increasesabove the air entry value. Isotropic compression tests atshear stress ¥vould be mainly elastic, until the stress pointconstant suction revealed that the preconsolidationreached the yield surface, and after that it becarne plastic.pressure increases ¥vith the suction in the "effectivestress" approach. This increase is not as pronouncedrather limited in the net stress approach. Frorn thetriaxial shear test, an increase of stiffness and peakstrength ¥vith suction at constant mean effective or netThe combination of pre-yield and post-yield linearitypermits bilinear extrapolation techniques for identifyingthe yield point (Graham et al., 1982). Yield points aredetermined from a stress-strain criterion by using variousprocedures, all consisting of identifying a change of slopepressures is only sholvn for lo¥v confining stress. Suctionin the stress-strain planes (Fig. 15).Figure 16 sho¥vs the yield points in saturated conditionsappears to ha¥'e an effect similar to that of mechanicaloverconsolidation vhen representing the results in therepresented in the p'-q plane, together with the plasticeffective stress plane. Softening appears post-peak for thestrain increments at the onset of yielding. In this figure,cases of high suction or lolv net mean pressure. In thethe yield locus corresponding to t¥ 'o consolidationpressures are dra vn by interpolation. The behaviourp'-q plane, the critical state line is shol 'n to be independ-vould clearly be represented by a non-associated flo¥vent of suction (in the studied range of stress and suction);this is not the case in the p*-q plane. Finally, it is sho¥vnthat the yield locus increased ¥vith suction.rule.Figure 17 sho¥vs the effect of suction on the yield sur-face at a saturated preconsolidation pressure pof 600kPa. Although a complete determination of the yieldlocus is not possible based on so felv points (includingdata points for isotropic loading q= O), the general trendof suction hardening is clearly visible (see continuouslines). The effect of suction can be seen as a result of asuction-induced preconsolidation. Similar results wereobtained for compacted unsatur'ated soils (Zakaria et al.,1995; Cui and Delage, 1996). Similar r'esults are observedin a p* representatlon (Geiser, 1999).CONCLUSIONSA remoulded silt has been subjected to various loadingpaths, and the interpretation of the r'esulting datacontribute to our understanding of the behaviour of'unsaturated soils,The drying-¥vetting tests confirmed the hystereticnature of the behaviour. Under more general loadingACKNOWLEDGEME_NTSThis ¥vork ¥vas funded by the Swiss NSF, grantGruaz'_1-42360.94. The authors gratefully thank lvlr. G.for his help in performing the laboratory testing.REFERENCESl) Alonso, E. E., Gens, A. and Josa, A. (1990): A consriiu ive modelfor partially sa urated soils, Gdotecllnique, 40(3), 405-430,2) Biarez, J_. Fleureau, ,J. N'I., Zerhouni, N,1. I. and Soepandji, B. S,(1988): Variarions de volumes des sols argileux lors de cycles dedrainage-humidification. Revue F,'an a!se c!e Gdotechilique, 41,637 13) Blight, G_ E(1966): Strength characteristics of dessicated cla_¥*s,ASCE J. Soil N'Iech. Fourld. Engrg. Div., 92, 19-37.4) Croney, D. and (,*oieman, J. D. (1954): Soil structure in relarion tosoil suc ion, J, Soi! Science, 5, 75-84.5) C ui, Y. J (1993): Etude du comportement d'un limon compactnon satur et de sa modelisation dans un cadre elasto-plastique,PhD Thesis, Ecole nationale des Poms et Chauss6es, Paris 556GEISER ET、AL、6）Cui，Y．，LandDelage，P，（1996）IY1eidingandplasτlcbehaviourof a鷺unsa【urated co【npacτed silt，（360∼εc／7’∼i（1”〔∼，46（2），291−311．7）Delage，P、and Graham，J．（1995）＝Mec｝1anlcal behaviour of 五’1913．，19（3），2H−24L25）Kohgo，Y。，Naka！lo，M、andMiyazak1，τ，（玉993）二Theore庶aI aspec【sofcons【imtive1nodel1ngforunsaIし星rateδso1ls，50’Z∫αnゴ unsaturated so澱s：Undersζanding t鮭e behav1our of unsaturated soils Fo朋ゴα1’01∼∫，33（4），49−63． requires concep田al models，Pro‘。1n∫．Co11∫ U1∼，∫碗’”α’ωSo礁，26）Lagny，C．（1996）＝Comporteme賊 mεca自ique des sols 且ns sous Par1s，1223−1256． fortesco離a醸esαfortespressionsn6gat1ves，P1のr1∼θ5’∫．狂cole8）Deiage，P．，Suraj de S1lva，G．P．R．and de Laure，狂．（三987）：Un Cenτrale Parls、 nouvei apPare“甘iaxiai pour les sols【10n sat柱r（｝sラP／10ご．9∼1r E∼〃「ト．27）Laloui，L．and Nuth，！〉i、（2005）：Anin［roduc“on toIhecoほsti篭utive Co1ザ5M圧，Dublin，1，26−28． modeHingofuns＆turaτedsoils，REOC‘Eε〃’，ノ．C’v’1だ119’11θθ1”’119ノ．9〉 Escario，V．and Saez，J．（1986）：The shear s芝rengt為of par雛y satu− 9（5−6），651−670、28）Laloui，L，，P6ron，｝｛．，Gelser，F、，Rifa’1，A．andVu騰eξ，L（2006）： ra｛edsolls，Gゴo’θc／11殉肥，36（3），453−456．10） F玉eureau，」．r〉1，（1992）＝Conヒr玉butioa a1ラ（箕ude eτa la mod（｝蕪sat玉on 、へdvances ln volume measllremen芝 in u：｝satura吃ed 毛riaxial tes！s， des materiaux polyPllasiques，ノノ‘7わ’〃∼‘π’0117γ∼θ5’∫，Ecole Ce【貰rale So’Z5αη（ノFoε〃∼4α”017∫，46（3），34玉一350． Paris．29）Leclercq，J．a員dVerbmgge，J．C．（1985）：Prop説t6sg60m6can1queslI）Fleureau，、L M．and lndaゴto（1993）l Comporteme郎du疑mQn de Jossignyremanl6sQumlsaunepressioninterstitiellen6ga［ive，…2〉 Fleureau，、1、NI．，K鮭eirbek−Saoud，S．，Soemi芒ro，R，andτa玉bi，S。 （1993）： Bellav玉or of c！ayed so甜s on dry1ng−wetting Pa芭hs， Cαη．豆3） F玉eureau，J．KI．，K｝｝eirbek−Saoud and Taibi，S、（1995）＝Exper霊men− talaspectsandmodelllngoω1ebe無avlourofso1isw1由anegative14） Fredlu職d， D． G． a簸d レlorgerlsτern， N． R． （三977）＝ Stress s［ate variablesfo田nsaturatedsoils，擁5C五一G万，447−465． Variatio頁ofしmsa田ratedsollshearstrengthparameterswi出suc− t1on，P1’oご，1’π，Con∫Uη5ρ’”昭’θゴSo’Z5，Par1s，1487−1493． cぬaracIeristlcsofpartiallysa田raτedsolls，04αθぐh17ゆθ，茎8（4）， 432−448．三5）Fredh鵬d，D．G．arld Rahard30，H．（1993）l So’1A4e‘hρ11’c5弄011 U1∼5θ∼ど〃窟θαF So〃5，Jolm WiIey and Sons．（1978）： Thesllearstreng由ofu職samratedsoils，Cθπ．0θαθぐ11．ノ．，15，andLaloul，L．（2006〉：A鷺improvedvolume measurementindetermi漁gsoilwaterre【entioncし星rve，0θ01θc1∼．33）Peron，H，，｝｛uecke1，T， 琵5’．／，，20（1），34）Sivakumar，V．（1993）＝Ac蹴icalsta【eframeworkforuIlsaturated soils，PhZ）7γ1θ5’∫，Un玉versi【y of Shef盗eld． 313−321．i7）Gelser，F．（玉999）：Comporteme猷繭can即ed’unllmonnon6ωde exp6rimentale et mod61isatio厳co“s虚田i、・e，PhOSwissFederaIlns【iτuteofτechnology，Lausan鷺e．F，，Laloul，L a賎d Vulllet，L （1998）：Yield1ng of a18）Ge1ser， 45（3），465−477．32）M飢yas，E、L．and Radhakrishna，H．S．（1968）：Vo1ロme change pressure，Pヂoc、∫1π、Coη∫Uη，∫α1ま〃門α∼θゴ50’Z∫，Paris，57−62， τ11θ5’∫， cr玉嫉ca王sτa葛e of a co賛apsible unsaturated si1［y soil．Gゴo∫θc／111’‘7∼’θ，31） 汽4ashhour，1〉L 親1．，lbrah1mラ汽’1．L aRd EトEmanラ魏L 氏・L （1995）： Gθ01θ‘1∼、／、，30，287−296、 saエur61 so1，Facu116des Scie昆ces Agro…10m1ques Gembloぴx、30）Maa芝ouk，A．，Leroue員，S．and la Rochelle，P．（1995）：Yielding and Rεv置’θだノ「ロ’∼9傭θゴθGゴαθchlliσ‘’θ，62，59−66．16）Fred1闘d，D．G．，Morge“stem，N．R．and W1dger，R、A， des sols【10【｝satur6s、Compteイe【玉dus dロCo玉loqし【e su「Ie t「avail du35） Soii∼loisτure Equ圭pmen覧Corporat1oほ（1985）：Coτnmercial pub11ca一 【io職s，P．O．Box30025，Sanτa Barbara，CA，USA、36）Taib1，S．（1994）：Comportementm6caniqueed1》・draul1quedessols parI1e！lemerlt satur6sラPhZ）71hε∫’∫，Ecole Centrale Paris． remoulded sandy s玉1【ln saturaτed and u昆saζurated sIates， P’・00 211ゴ37）To註，D．G．（玉990）：Aframeworkfor糖nsaturatedsoilbehaviour， ∫’π．Co／4．Un5θ’∼！1’θ’留So1Z∫， 1，Beijing，54−59． Gだo’（∼ch171（1∼’θ，40（1），31−44・F、， Lalo虚， L・and Vu1韮et， L・（2000）：On the volume38）Vicol，T、（1990）l Comportemem bydraulique et m6canique d’un 加unsaturated仁r1axial teSt，U’15α’∼〃’α’θ4So〃5、ブoノ貯 measureme数t limonnonsatur6．ApPllcatio自alamod611s煎on，P1∼07hθ5Z5，Ecole19〉 Geiser， ．451α（eds． by Rahardjo，ToH and Leo119），Balkema，669−674．20） Gibson，R． E。andHe臓kei，D．，L（1954）＝ln創uenceofdurationof ξesτs a【COnStant rate Of Stra1n On meaSUred drained Sτren9由． Na“onale des Ponts et Cl玉a越ss6es，Paris．39） V▽lleeier，S。」．（1996）：王nc1駄sionofspec1員cwatervolume、vid擁n an elasto−plasticmodelforunsaτurate〔isoi1，Cσ11．Gθo’θごh．ノ、，33， G40’θch吻∼擢，4（1），6−15． 42−57．2玉）Gra恥am，」、，Pinkney，R，B．，Lew，K．V，a鷺d Tra玉nor，P．G、S、 （1982）；Curve踊ngandlaboratorydata，Cαη．Gθo’θ‘17．ノ，，19，40〉 、Vheeler，S．」、andS1vakumar，V．（1995）：An e！asto−plas【1ccri篭ical 201−205．41） Zakar玉a，L、Vhee玉er，S。J．andAnderson，∼V．F．（玉995）：Yieldingof22）Head，K．H．（1986）lA4α17置’θ10ゾ50〃五αウoノ“θ’01アrε5r∫11g，Pentec｝藁 u簸sa芝ura葛ed compacted kaoli員．Pヂ Press． 223−228、23）Ho，D，Y．FandFredlund，D「G、（1982），Amu1τistagetr1axialtes〔 forunsaヒuraIedsolls，0θ01ech、ル5’．ノ．，5（1），18−25．42｝Zerllouni，M．L（199玉）：R61edelapressionl瓢ers面ellen6gative dans le comporξeme蹴des sols−ApPllcaほon aux ro臓es。ρ1の24） Karube，D．and Kawa1，K、（200玉）＝The role of pore water玉自tile 7「hθ5Z5，Ecoie Centrale Par玉s。 mecha虚cal b曲aviorofunsatura［ed soi蓋s，Gθo’θご1r，Gθ0109． state framework for unsa［urated soi1，Gごo’θcノ〃1’（1∼！θ，45（1），35−53．o‘、 Uη∫01∼〃η’θゴSo’Z∫，Paris，
- ログイン
- タイトル
- seepage Failure Mechanism of The Gouhou Rockfill Dam during Reservoir Water Infiltration
- 著者
- L. M. Zhang・Q. Chen
- 出版
- soils and Foundations
- ページ
- 557〜568
- 発行
- 2006/10/15
- 文書ID
- 20940
- 内容
- SOILS AND FOUND¥TiONS¥*ol46, N'o )* 557-56s, Oct. 2006Japanese C; eotechnical Socie }SEEPAGE FAILURE MECHANISM OF THE GOUHOU ROCKFILLDURING RESERVOIR WATER INFILTRATIONL. M. ZHANGi) and QUNDAMCHEN ii)ABSTRAC.TThe catastrophic failure of the 71-m high Gouhou concrete-f'aced rockfill dam in Qinghai Pro¥'ince, China, hasdra¥vn many studies. This paper aims at providing ne¥v understanding on the modes and process of this failure, whichcould be applicable to similar dam failures. The geometrical and hydraulic criteria for internal erosion in rockfillmaterials are assessed. Unsaturated-saturated seepage theory is used to analyze the Gouhou dam since the rockfillmaterials of the dam ¥vere unsaturated before reser¥'oir ¥vater infiltration. The ¥vater infiltration is simulated by severalcases of transient seepage analyses. According to the study, a perched-water table formed in the dam ¥vhen thereservoir lvater infiltrated into the rockfill from the top of the concrete face. The perched water spread nearlyhorizontally along stratifications in the rockfill and exited from the downstream slope at a hi**h elevation as observedbef'ore the breach of the dam. The hydraulic gradient of the perched ¥vater table ¥'as the highest near the wetting front,vhich might pro¥'ide necessary hydr'aulic conditions to trigger internal erosion and piping failure. Based on thegeometrical conditions of the rockfill materials and the hydraulic conditions in the dam, the susceptibility of internalerosion is e¥'aluated and the possible modes and process of seepage failure of the dam are described.Ke _'vords: intemal erosion, piping, rockfill dam, seepage analysis unsaturated soils, water infiltration, vetting front(IGC: D6/E6/E7)the Gouhou dam since the rockfill materials of the damI_r JTRODUCTION¥vere at an unsaturated condition bef'ore reservoir fillin9:On 27 August 1993, a catastrophic failure of the 71-mThe lvater infiltration process and associated hydraulicconditions ar'e simulated by several cases of transientseepage analyses. Based on the geometrical conditions ofthe rockfill materials and the hydraulic conditions in thedam, the susceptibility of internal erosion is evaluatedand the possible modes and process of the seepage failureof the dam are described.high Gouhou rockfill dam occurred in Gonghe County,Qinghai Pro¥'ince, China during the first high reservoirle¥'el operation of the dam. The dam is one of manyrockfill dams that failed due to seepage problems duringreservoir fillin_ :. According to the statistics (Fell et al.,1992; ICOLD, 199) ; Foster et al., ,_002), other thanovertopping, internal erosion and piping are the primarycauses of failures and major hazards in embankmentdams. Many dam failures due to erosion have beenreported, e.g., Teton and Fontenelle dams (USCOLD,1988). Panshet dam (Singh and Varshney, 1995), andGEOMETRICAL AND HYDRAULIC CRITERIA FORSEEPAGE EROSIONSchuler (1995) summar'ized sever'al criteria f'or internalerosion and suggested tlvo steps to assess the susceptibility of internal erosion. First, geometrical conditions forseveral European dams (Charles, 1998).Although many studies on internal erosion of damsha¥'e been carried out (e.g., Charles, 1998), the processinvolved in internal erosion is still not vell understood.internal erosion should be checked according t.o ge-The objective of this paper is to provide ne¥v understanding on the modes and process of dam failures thatSecond, hydraulic conditions should be assessed according to hydraulic criteria for a critical seepage force tocause the inner erosion of movable grains.Many geometrical criteria can be used for the assessment of internal erosion of soils. Some criteria are basedon filter rules. A ¥vell-kno¥vn filter criterion, DI5F/ornetrical criteria for particle motion in the soil skeleton.may occur during reservoir filling such as the failure ofthe C}*ouhou dam. The geometrical and hydraulic criteriafor internal erosion in rockfill materials are assessed.Unsaturated-saturated seepage theory is used to analyze*] Associate Professor, Departmenof Civil Errgineering, The Hong Kong Universit} of Science and Technology, Hong Kong (cezhangl@"ust.hk).**)Associate Professor, S a e Key Laboratory of Hydraulics and i¥,Iountain Ri¥'er Engineering, C ollege of Hydraulic and HydroeiectricEngineering, Sichuan University. C'hina (cqfqe sina.com).The manuscrlpt for this paper ¥vas received for revielv on September _1", 2005; approved on July 26, 2006.¥Vritten discussions on this paper should be submitted before May I , 2007 to the Japanese Ceo echnical Society, 4-38-2, Sengoku, Bunkyo-ku,Tokyo I 12-001 l, Japan. Upon request the closing date may be extended one momh.oO7 ZHANG AND558C_HEN0870P otection pebblTO,P r pet war'3282.0_! Norrna!wat er:eyel_3 7 *Ol;7T 3 ..*-;3281=0Water stopConorete faceAl'=3267 '$¥CoRcrete face:･ '¥･¥TT 3260 Ol/. 7.(5:) ¥' fO ,;;3240.pl ¥ I ll'S Ciose-up view A- 3220 OI *3214.20*rT 32 o a-+ 321 2 20Gr nod )riteCurtain groutinFig. 1.Riverbed GraveiMaximum cross-section of the Gouhou dam (after Gouhou Dam Faihlre Investigation Team, 1996): A l unitsD85B4, ¥vas proposed by Terzaghi and Peck (1948) usingthe filter material diameter D15F (the diameter of filterparticles at ¥¥'hich 150/0 by ¥veight are finer) and the baseinmetersbased on numerous seepage stability tests of soilsconvex shaped grain-size distributions:O. 76(DIoglos)D90+ (b!;I << )D90, 15･ IoglO(b,:)1 86vith+ I (2)material diameter Ds5B (the diameter of base particles atwhich 850/0 by ¥veight are finer). Although the criterion¥vas developed for uniform soils, it is often used in prac-¥vhere D90, Dls, and D60 are the particle diameters attice for graded soils as ¥vell. Sherard et al. (1984) defined a¥vhich 900/0, 150/0 and 600/0 by ¥veight are finer, respec-nar'ro¥v boundary Dl5F/D85B=9 between erosion failureand filtration success using these t¥vo parameters.Tomlinson and Vaid (,_OOO) also concluded that a soil-tively.filter system ¥vith Dl5F /DSSB < 8 ¥vould not fail based on angations by the United Sates Bureau of Rec]amationexperimental study. of piping erosion. Several other(Mantei, 1985) for the sand ., surface soils at Calamusdam sho¥ved that the up¥vard seepage resulted in tinygeometrical criteria define internal erosion using moreparameters, such as D95B, and D75B (the diameters of thebase particles at ¥vhich 950/0 and 750/0, respectively, byweight are finer) (e.*".. Honjo and Veneziano, 1989).Vaughan and Soares (1982) presented an experimentalHydraulic criteria for internal erosion are usually indicated by a critical hydraulic gr'adient. Labor'atory investi-pipes at hydraulic gradients as lo¥v as 0.23. Skempton andBrogan (1994) gauged critical gradient values of 0.2 toO.34 for up vard flo¥v conditions. Den Adel et al. (1988)measured critical gradient ¥'alues of 0.16 to 0.17 for arelationship between the permeability of a filter and thesize of particles that pass through the filter. A boundaryfor stable filtration (i.e., for the filter to retain thesmallest particles that ¥vould be ¥vashed a¥vay durin_',_steady flow of fines driven by horizontal water fio¥vs.erosion) was expressed as k = 6.7 x 10-6 ! '2, in ¥vhich k isthe coefficient of permeability and 6 is the size of theThe Gouhou dam ¥vas a concrete-faced rockfill dam 71m high Detalls of design, construction, operation, andparticle that ¥vould just pass the filter.failure of the dam have been reported by the GouhouAnother category of geometrical criteria is proposed toassess vhether the physical nature of a soil allo¥vs themotion of its finer particles ¥vithin its o vn pore space.Dam Failure In¥'estigation Team (1996). The rockfill ¥vasdirectly founded on a sandy gravel of approximately 10 mSherard (1979) divided hetero_ eneous embankmentmaterials into t¥vo parts, a coarse fraction and a finefraction represented by DssFi * and Dl5c.****, respecti¥'ely.FAILURE OF THF. GOUHOU DAMthick. The dam crest ¥vas 265 m long, 7 m ¥vide at anelevation of 3281.00 m. The design, normal and check¥vater levels lvere all 3278.00 m and the correspondingreservoir volume was 3.1 million m3. The upstream andThe DI*c.**>*IDs5Fi** ratio of the embankment materialsshould be less than 4 to 5 to be stable. Kenney and Lau(1985) developed a technique ¥ 'ith ¥vhich a *"rain-sizeThe maximum cross-section of the dam is sho¥vn indistribution curve can be interpret,ed as the ratlo of thethe cushion material supporting the concrete face and itspercentage increment H corresponding to the gradationbet¥veen a diameter D and its fourfold 4D to F, themaximum design particle diameter ¥vas 100 mm. Zone IIpercentage finer than D. Internal erosion is not likely todo¥vnstream slopes ¥vere 1:1.61 and 1:1 .50, respectively.Fig. I . The rockfill ¥vas divided into 4 zones. Zone I ¥vaslvas a transition z,one ¥vith the maximum design particlediameter bein 400 mm. Zones 111 and IV ver'e the main1.3 (1)rockfill ¥vith the maximum design particle diametersbeing 600 mm and 800 mm, respectively.Reservoir filling began in September 1989 before thedam was completed. ¥Vhen the construction of the damBurenkova (1993) pr'oposed an empirlcal cnterlon¥vas completed in October' 1990, the reservoir ¥vater leveloccur ¥vhenHF SEEPAGE FAILURElvIECH AN I S559l¥vas as hlgh as 3'-74. 10 m (,3.90 m below the normal ¥vaterlevel) and seepage fio¥v ¥vas obser¥'ed at both the do¥vnstream slope at elevation 3'_'_3.00 m and the riverbed. Theseepage flo¥v disappeared in 1991 and 19921vhen the¥vater levels lvere only bet¥veen 3260.70 rn and 3262.60 m,¥vhich indicated that there ¥vas leakage in the dam aboveselevation ,326,_.60 m, but no leakage belo¥v elevation3,_67_.60 m.' i ;Startin*' from 14 July 1993, the reservoir lvater level-c.ts** .'rose continuously from 3261.00m to 3277.00m. Thevater le¥'el reached 3277.00 m at noon 27 August 1993.According to measurements of the traces of ¥vater level,the highest vater le¥elas 3'77 30 m, Ivhich ¥vas O.70 mlo ver than the normal ¥vater level. In¥'estigations afterthe dam failure re¥'ealed that water had flo¥ved into thedam frorn the joint bet¥veen the bottorn platform of theparapet vail and the concrete face since noon, 27 August.The ele¥'ation of the bottom of the parapet vail ¥vas{a) Govhouock !i dam 3fter breach13277.00 m, ¥vhich ¥vas 0.30m lower than the designedelevation 3277.30 m due to settlement of the dam. At"about 20:OO hours the same day, t¥vo children in Gouhouvillage witnessed water seeping out from the do¥vnstreamslope of the dam at a high ele¥'ation of 3260.00 m (seeFig. l). At ?_1:OO hours, the reservoir management staffheard loud noises and salv protection pebbles rollingdo¥vn from the upper portion of the do¥vnstream slopemixing ¥vith ¥vater flo¥vs and mist. One hour fortyminutes later, the dam breached at '_'_:40 hours. Aphotograph of the remnant of the dam is sho vn inFig. 2(a). The middle part of the darn breached. The(b) Close-up of the defeotive connection betweenthe pa apet wall and the concrete faceFig. 2. Photos of the Goulrou dam after failure (after Gouhou DamF'ailure Investigation Tcam, 1996)breach ¥vas trapezoidal. The top ¥vidth of the breach ¥vasi38m. The bottom of the breach ¥vas 28 m wide atele¥'ation 3'_50.00 m.particles during construction. Chen and Zhao (1996)Many studies have been carried out after the disastrousfailure in order to find the causes of the failure. AccordIn*' to the findings of the Gouhou Dam Failure Investigation Team (1996), there ¥vere se¥'eral structural problemsanalyzed the stability of the darn slope and conductedsteady-state seepage analyses using a saturated-onlyanalysis method. The dam vas considered to be uniformwith the dam. First, the ¥vater stops at joints of' concrete-Chen and Zhang (2006) conducted a three-dimensionalface panels did not function properly, especially at theupper part of the concrete face. Second, the connectionbetween the concrete parapet ¥vall and the concrete face¥vas not maintained pr'oper'ly in a segment along the damaxis (see Fig. 2(b)), ¥vhich left a concentrated flo¥vchannel frorn the reservoir to the rockfill. Third, theconcrete face ¥vas separated from the transition materialseveral rneters belo¥v the parapet ¥vall. Finally, theanalysis of ¥vater infiltration into the Gouhou dam usin_a,_embankment materials ¥vere evident.ly stratified o¥ving tosegregation of rockfill particles during construction,especially near the crest of the dam. These structuralimperfections created leakage channels. The resultedinternal erosion by seepage ¥vas considered as a directcause that triggered the dam failure.Liu and Miao (1996) conducted permeability tests andseepage stability tests ¥1'ith the darn rockfill materialstaken from the remnant of the breached darn using a300 mm-diameter permeability cell. Liu et al. (1998)conducted a model test to study the failure mechanism ofthe dam. The model rockfill was stratified with fine andcoarse layers to simulate the segregation of the rockfilland the'hole concrete face ¥vas assumed ineffective.saturated-unsaturated seepage theory. The three-dimensional characteristics of seepage through the dam bound-ed by step abutments ¥vere studied. The geometricalconditions of the rockfill materials and the hydraulicconditions in the dam, as lvell as the modes and mechanisms of seepage f'ailure of the dam associated with theprocess of ¥vater infiltration into the originally unsaturat-ed rockfill, however, have not been sufficient.1y studied.These will be the focus of study in this paper.CONCEPTUAL I? ITFILTRATION MODEL ANDMATERIAL PROPERTIESGove/'ning Equations jbr Seepage through UnsaturatedSatu/'atec! Soi!sSeepage flo¥v in unsaturated soils, as seepage in saturat-ed soils, is governed by Darcy's law and the continuityequation. The governing equation for water flow throughunsaturated-saturated soils can be obtained by introducin_ Darcy's la¥v into the continuity equation. In the ZHANG AND CHEN5601 oo10{)90908080.' 70> .' 70e)c; 60r:a:cl'; 60o 50c 50c:e,e,CLc:Q;40e,o*302040302010oooco10a iOolaiooe1 aoGrain size (mm)Fi(;. 3. GFain-size distribution curves of the materia!s in the 4 zones(Based on data from Gouhou Dam Faiiure Investio*ation Team*1996)study, total stress changes and deformation of the soilskeleton are not considered. Taking the total hydr'aulichead ll as the unkno¥vn and the soil as a transverselyanisotropic material, the governing differential equationfor t¥vo-dimensional flow throug:h an unsaturated soil isas follo¥vs (Fredlund and Rahardjo, 1993):a:¥' (¥k.) +aay (k)OOGrain size (mm):!ae,a/7 (3)y** aVl at¥vhere y, is the unit wei{)ht of water; e,,, is the volumetricwater content; V/ is soil suction; t is time; k* and kv are thecoefficients of permeability In the x- and y-direction,respectively and are functions of the soil suction.Sin7p!rfied Profi!es for A na!ysisThe Gouhou dam as sho¥vn in Fig. I is a z,oned rockfilldam. According to results of an in¥'estigation of theremnant of the dam after failure (Gouhou Dam FailureInvestigation Team, 1996), the maximum grain sizes ofthe materials in zones I, II, 111, and IV ¥vere approximately 100, 400, 600 and 800 mm, respectively. Se¥'eral **rain-size distribution curves of these materiais are sho¥vn inFig. 3. Except for the mater'ial in zone I, the grain-sizedistribution curves of the materials in other 3 zones donot differ considerably. As large boulders ¥vere fe v at theborro¥v site, the dam ¥vas in fact not e¥'identl _, zoned.Ho¥vever, the field investigation revealed that the rockfilllvas seriously segregated durin_g: construction due to the¥videly-graded nature of the materials and insuf cientquality control. Therefor'e the grain-size distributions ofthe rockfill materials are highly scattered. Figure 4 sho¥vsFig. 4. Grain-size distribution curves of the finest, medium, andcoarsest rockfi i materials (Based on data f rom Gouhotl DamFailure Investigation Team, 1996)Considering the fact that horizontal sand¥viches ofcoarse layers and fine layers ¥vere present in the dam butthe dam lvas not e¥*idently zoned, four cases of transient¥vater infiltratlon analyses (i.e., Cases I, II, 111 and IV)are performed in this study to simulate possible conditions of the Gouhou dam. The simplified profile for CasesI-III is sho¥vn in Fig. 5(a). Case I invol¥'es a uniformrockfill dam ¥vith the concrete face not effective aboveelevation 3260.00 m. The g:rain-size distribution of thefinest rockfill (see Fig. 4) is taken as the material for zone1 in this case. The riverbed gravel (zone 3) is the same inall four cases. Cases 11 and 111 both include a sandwichlayer (zone 2) of 10 m thick between elevations 3260.00and 3270.00 m. The grain-siz,e distribution (see Fig. 4) ofthe medlum rockfill is taken as the material for zone I inthese two cases. The sandwich layer is the finest rockfill inCase 11 but the coarsest rockfill in Case 111 (see Fig. 4).Case IV represents a fully stratified dam and the simplified simulation profile is sho¥vn in Fig. 5(b). The lvholedam is divided into 7 Iayers, sand¥viched aiternately bylayers of the coarsest rockfill and the finest rockfill. Allthe rockfill materials are assumed isotropic in the seepagesimulation. The simulation cases and the correspondingzoning and materials are summarized in Table 1.M:ateria! P/-opertiesFour materials, that is, the finest, medium, and coarsest rockfill and the riverbed gravel, are involved in theseepage analyses (see Table 1). The index properties ofthese materials are listed in Table 2 and the grain-sizedistributions of these materials have been plotted inthe grain-size distributions of the finest, medium, andcoarsest rockfill samples obtained from the field duringFi**. 4.construction and after failure. The segregation resulted intic curve and the permeability function, need to besandwiches of coarse layers and fine layers in the dam.The coarse layers ¥vere about 0.3 to O.4 m thick each anddefined to solve the partial differential equation (Eq. (3))for the transient seepage analysis. The soil-¥vater charac-extended from the upstream to the downstream. Theteristic cur¥'e is a relationship between the volumetricsaturated coefficients of permeability of the coarse layers¥vater content and the soil suction in the soil. Aswere as high as 0.02 to O.44 m/s, ¥vhich ¥vere 13 ordersof magnitude greater than those of the fine layers.experimental data ¥vere lacking, the cur¥'e in this paper¥vas estimated from the g:rain-size distributions and indexT¥vo soil property functions, the soil-¥vater characteris- SEEPAGE FAILUREly561¥. IECH NIS 11 Zero ux80!ee'Av )o )60B^fAl+328i oo/ one '- 3270_oo;e .- // Zone 2 (Sandwich)e,v 604,1 eB:260.00^(o );(¥ :" ･-4a1 eto $¥>d.Zane I (Uniform rock jl)Tota head H=10 rrl20cInitial water tab e I O¥TnZone 3 (Riverbed gravel)o322a oa, .32i o ooZero fux boundaryoi ao i sc502acx250(a) Cases 1-Ill801 yl Zero ux boundary)o ^s: ¥ " /+ - -3281 Oa:e60 _BA(: /f _ . >¥¥- ･' e e8;?)O/c 1 e_3_ 273_,0_o_3265 oos SS .B40Totai head H=10 m20 _3220 OO/321 O aooZe.lo_ilux boundary50 1 OOoFig. 5.Table 1.X1 50 200 250(b) Case IVSimpiified prof'lles and bounda , conditions for transient seepage analysis of tho four casesSimulation cases and their corresponding zoning and materi･-alslable 2.Index propertics of the four materials used in seepage ana!}-sisCaseI (Hon ogeneous)ZoninlIII (Coarse sandlvich layer)Finest rockfill3Same as zone lRiverbed ravell*¥1edium rockfill,II (Fine sandrvich iayer)i¥,Ialerial2Finest rockfill3Rh･erbed1lvledium rockfillravelN+1aterialFinest rockfillSpecificInitial waterg:ra¥'it¥.'contentG,Tt' ( , )Coarsest rockfili2 682.682 68Riverbed2.71N"ledium rockfillravelSaluratedcoe cient ofPorosit yperrneabi ityn (7･ )k._,t ( x lO 5 mls)5O.,-12.,)O 21l I .63* )O.2 l12 *3O 27:).23 l74Coarsest rockfill3IV (S ratifted dam)RiverbedravelThe 2nd, 4th, 6lh layers Coarsest rockfiHThe rest laversRiverbed g:ravelFoundation. Fincst rockfillmated soil- ¥'ater characteristic curves and permeabilityfunctions for the soils considered are sho¥¥'n in Fig. 6.Initia! Conditions alrd Boundaly ColrditionsThe initial ground ¥vater table is set at the base of thedam and the 10 m-thick riverbed is submerged. Abo¥'e theproperties of the soil (Fredlund et al., 2002). Thepermeability functlon is a relationship bet¥veen theinitial ¥vater table, the initial soil suction increases linear-coefficient of permeability and the soil suction. In thispaper, the permeability functions for the materials ¥vere14.2kPa, ¥.vhich is the suction in the rockfill thatcorresponds to the average compaction ¥vater content ofestimated using the Fredlund et al. (1994) predictionmethod. The caiculations vere assisted by a prograrnSoilVision (SoilVision Systems Ltd., ,_OOl). The esti-3.50/0 during construction.ly ¥vith the elevation. The maximum suction is 1lmited toThe boundary conditions for the seepage analyses aresholvn in Fig:. 5. It is assumed that the concrete face is ZHANG AND CHEN562impervious belo¥v elevation 3260.00 m in C_ases 1-III andbelo¥v elevation 3265.00 in Case IV, but is ineffbcti¥'eabove these specified ele¥'ations because of the defecti¥'econnection bet¥veen the parapet ¥vall and the concretedefined as a rising: ¥vater le¥'el from elevation 3277.00 m atthe base of the parapet ¥vall to the maximum ¥vater levelof 3'_77.30 m ¥vithin the first day and a constant ¥vaterlevel of 3277.30 m after¥vards. A zero fiux boundar'y isface and the separation bet veen the concrete face and thetr'ansition zone. Therefore, the boundary condition of theapplied along the dam crest. The do¥vnstream slope isupstream slope surface of the dam is divided into t vois less than the elevation head and other¥vise a freeparts: a zero flux condition belo¥¥' elevation 3'_60.00 m inoutflo¥v boundary. The bottom of the r'iverbed is definedas a zero flux boundary due to the lo¥v permeability of thebedrock beneath it.Cases IIII or 3265.00m in Case IV and a total headcondition above the elevations. The latter condition isdefined as a zero fiux boundary condition if the total headANALYSIS OF WATER INFll,TRATION INTO THF,o 30ROCKFILLo 25e,oThe transient infiltration analyses ¥ 'ere carried outusing the finite element progr'am SVFlux (SoilVision020Systems Ltd., 2003) together ¥vith a partial diff renceq,equation solver FlexPDE (PDE Solutions Inc., '_003).The program SVFlux can be used to analyz,e both steady0.1Sq,E O Ostate and transient flo¥vs throug:h saturated and unsatu->orated soils.o 05Case I-Umforll7 DanlO OO1 E-02 1 E O{1 E+00 1 E+01 1 E 02 1 E+03 1 E+04 1 E+05 i E 0eMatrie suetio:( ) Soii-water e(kPa)r oteristio curvesA uniform rockfill dam is studied in this case considering that there is no evident difference among the materialzones. The finest material in Fig:. 4 is considered in thetransient seepage analysis for easy convergence. The1 E )2process of ¥vater infiltration, as indicated by the pore-¥vater pressure contours obtained by the analysis, isshown in Fig. 7. The contours ¥vith zero pore-¥vatereS:.._ I E-OSs)pressur'e represent the transient vetting fronts. Waterfio vs into the dam from the upper part of the upstreamce,8 1 E-08slope where the concrete face is ineffective. The vettingfront advances do¥vn¥vards ¥vith time. Before the ¥vettingJatee)1 E- ie'front reaches the initial ground ¥vater table in the1 E-14E-02 1 E-O11E+00 1 E+0I E+02 1 E+03 1 E+041E+051E+06MatFic suetion (kPa)(b) Pemleability funotionsrig. 6. Esrimated soil-watcr characteristic cilrves and per leabilityfunctions for the four soilsriverbed, the rockfill is divided into t¥vo z,ones by¥¥'erting front. One is the saturated z,one ¥vithin¥¥'etting front; the pore ¥vater pressures ¥vithin itpositi¥'e. The other is the unsaturated zone outsidethethearethe¥vettmg front the pore ¥vater pressures ¥vithin it arenegative. The maximum pore- "ater pressure occurs atthe upstream slope face at elevation 3260.00 m. The3277 30 m2i6a() t = 2 days( ) t = 5 days3277 30 mo;7¥"a *{ j';;;'1: !;;;1{;; o0/;(o) t = 8 daysFig. 7.(d) i = 18aysPore-water pressure contours (in l{Pa) during ihe infiltration proecss, Case I SEEPAGE FAILURE56'olvIECHANIS*¥Ipore- vater pressures decrease gradually f'rom thevater table, a fio¥v channel forms and the veloclty atmax'imum at the slope surface to zero at the vettingfront. The rnaximum negati¥'e pore pressure outside thepoint C* in the flo¥v channel increases abruptly. Also thevelocity at the dam toe increases ¥vlth time graduaHy. Att= 13 days, the velocity at point C increases substantiallyperched-1vater table depends on the limit imposed on themaximum initial soil suction in the dam.again because the previousl"v unsaturated zone near theAfter 5 days, the bottorn of the ¥vetting front joins theupstream face is completely saturated and the infiltrationground ¥vater table in the riverbed (Fig. 7(b)) and alvater can only fio¥v do¥vnstrearn. After '-O days, the¥'elocities at the t¥vo points approach constant vaiues,vhich indicate that the flolv field nearly arri¥*es at aseepa_ :e channel from the upper portion of the upstreamslope to the rlverbed f'orms in the dam (Fig. 7(c)). Afterl 8 days, the ¥vater pressures increase monotonically fromthe phreatic surface to the bottom of the dam and thesteady-state condition.T¥vo additional analyses ¥vere also conducted assumin_"*.flo v nearly reaches the steady-state condition (Fig. 7(d)).that k* is t¥vo times k! and four times k , respecti¥*ely. TheThe evolution process of the seepage flow sho vs that theperched ¥vater table does not exit from high ele¥'ations atthe do vnstream slope but flows do vmvards to joint theinitial g:round ¥vater table. If the reservoir vater levelpersists, then the steady-state fio¥v condition ¥vill bereached and ¥vater exits frorn the do vnstrearn slope toeand the riverbed. This is not the seepa*'e pattern observedflo v patterns obtained ¥vere all sirnilar to those in Fig. 7except that the rates of ¥vetting front development werefaster. The 2 to 4 times increase in k* did not change thedo¥vn¥vard flo¥v pattern in the uniform darn.Cclses II-IV-Effect OJ StranficationTo include the effect of material stratification in theon the site.dam, a horizontal sand¥vich layer located bet¥veenThe changes in flo¥v ¥'elocity at the dam toe 'rand pointC on the base (see Fig. 5) ¥vith time are shown in Fig. 8.The velocities at the darn toe and point C are nearly zeroelevations ,3 _60.00 rn and 3270.00 m as sho¥vn in Fig. 5(a)is considered. The sand¥vich layer f'or Case 11 is the finestbefore the wetting front merges lvith the ground watersaturated coefficients of permeabillty of the fine sand¥vichand the coarse sand vich are O. 19 and 19.9 times, respec-table in the riverbed at t= 5 days as sho¥vn in Fig. 7(b).Once the ¥vetting front merges lvith the initial ground2 OE-05and for Case 111 the coar'sest. In Cases 11 and 111, thetively, of the coefficient of permeability of the mediurnrockfill, as shown in Table '-.The pore- vater pressure contours during the infiltration process in Case 11 vith the finer sand¥vich layer are1 eE-osshown in Fig. 9. There are t¥¥*o dominant flo¥ * directions.One is the down¥vard flo¥v to the riverbed and the other is1 205the horizontal fio¥v along the inter'face betlveen theuniform rockfill and the finer sandwich. Cornpared with_oa, 8{} -06the results of Case I, nevertheless, the horizontal flo¥v ino>this case with a finer sandlvich is much more pronounced.4Frgure 10 shows the pore-¥vater pressure contoursE*aduring the infiltration process in Case 111 ¥vith the coarserO OE+005 10o1520Tirne t (day)Fig. 8. Changes in fiolv velocity at the tlam toe r and point C* on thebase lvith time, Case I3277 03 m(a) t = O I dayssandl¥'ich layer. In Fig. lO, the do vn¥vard flo v plumediminishes and there is only one dominant fio¥v direction,i.e., the horizontal direction along the interface betweenthe coarser sand vich and the uniform rockfill. Thehorizontal fiow to the do¥vnstream slope surface is much3277 09 m(b) t = O 3 days255a(o) t = O 5 daysFig. 9.(d) t = O 8 daysPore-water pressure contours (in kPa) during the infiltration process, Case 11vith a finer sandwich la)'er ZHA iG36=iA¥. DCHEiN7327! al5 m.(1_¥t¥SOJiil!; 50.¥L/50o50(b) t = O 15 days(a) t = D G5 d ys3277 090 rn_.7 3277 D4S m.T7 3277 135 m*--li i i 50 ¥¥¥*':,(/¥50 .+.o¥(d) f = O 45 days(c) t = a 3 daysFig. lO. Pore-water pressure contours (in kPa) tiuring the infiltration process, Case HI Ivith a coarser sandwich la)er1and the finer rockfill belol ' (Fig. 10) can be explained bythe transfer condition in the seepage theory (Craig, 1997).04l _ -- -''1 2 -04oE*a4¥Vhen ¥vater flo¥vs across a boundary between t¥vodissimilar soils, the direction of fio¥v ¥vill chan_ e to¥varclsthe normal direction of the boundary as ¥vater' flo¥vs fromF 8 aE-05a soil ¥vith higher permeability ro a soil ¥vith lowerio 6CE*OSe,>- =--- __ __ _ i4 O -a5-*2 oE*a5permeability and vice ¥'ersa. The flo¥v direction dependslargely on conditions at the ¥vetting front where soil isinitially unsaturated. As can be seen from Fig. 6(b), acoarser soil ¥vill ha¥'e a smaller coefficient of permeabilityo a *eaOO I 0Tllrne t ( ay)O 4 O 503Fig. Il. Changes in f ow velocit at point D on tiownstream siope andthe (iam toe T with time, Case 111faster than the vertical fio¥v to the riverbed. After 0.15days (3 6 hrs), the ¥vetting front reaches the surface of the¥¥*hen the soil is desaturated. Ther'efore, ¥vhen ¥vater fio¥vsfrom the finer sand¥vich do vn into the rockfill, thedi 'ection of the flo v ¥vill turn more to¥vards the ¥*erticaldirection as sho¥vn in Fig. 9. Con¥'ersely ¥vhen ¥vater flo¥vsfrom the coarse sand¥vich do¥vn into the rockfill, the fio¥vdirection ¥vill turn more to¥vards the horizontai directionas sho¥vn in Fig. 10. The lateral spread of fluids at theintei'face of t¥vo media ¥vas also observed in centrifugemodeling of the mobility of dense non-aqueous phasedo vnstream slope at e]e¥*ation 3260.00 m as sho¥vn inFig. lO(b). Ho¥vever, the ¥vetting front has not reachedliquids in saturated soils (Pantazidou et al., ,_OOO).A stratified rockfill dam (Case IV in Fig. 5), ¥vhich hasthe ri¥*erbed after O.45 days (10.8 hrs). This reproduces7 alternating coarse and fine layers, is analyzed toqualitatively the phenomenon obser¥*ed at the Gouhourepresent better the effect of se*'re_"*,ation of rockfill duringdam ¥vhere the perched-¥vater first flolved out from thedo¥vnstream slope near elevation 3260.00 m and eventual-construction. In this case, the finest and the coarsestrockfill material are used for the alternating layers assho¥vn in Fig. 5(b). Figure 12 sho¥vs the pore-¥vaterpressure contours during the infiltration process in CaseIV. At first, the infiltration ¥vater spreads along theinterface bet¥veen the second coarse layer and the thirdl.¥' Ieci to the catastrophic failure of the dam.The changes in the ¥'elocity at point D on the do¥vnstream slope and the dam toe T (see Fig. 5) Ivith time inCase 111 are sho¥vn in Flg. 1 1 . The ¥*elocity at point D is¥+ery small before the ¥vetting front arrives at the do¥vnstream slope at r=0.15 days as sho ,'n in Fig. 10(b). The¥'elocity at the exit point D increases abruptly at t= O. 15days, ¥vhich Indicates that the lvetting front arri¥*es at thefine layer in the horizontal direction. The horizontal flo¥vto¥vards the do¥vnstream slope surface is faster than the¥'ertical flolv to¥vards the riverbed. After I day, the¥vettin front almost reaches the surface of thedo¥vnstrearn slope and a flo¥v channel forms from theupstr'eam slope to the do¥vnstream slope. Ho¥vever, thedo¥vnstrearn slope at elevation 3265.00 m as shown inFig. 12(b) ¥vhile the do¥vn¥vard mo¥'ement of seepagevelocity at the dam toe keeps at a lo¥v value ancl does notlvater is still limited. Therefore, this case also reproduceschange much during the infiltrarion process, vhichthe phenomenon observed at the Gouhou dam lvhere theperched- vater first exited from the do vnstream slopeindicates that the fio¥v through the toe is not likely tocause seepage failure.The dominant horiz,ontal seepage fio¥vs along theinterface bet¥veen the rockfill and the finer sand vich(Fig. 9) and t.he interface bet¥veen the coarse sand¥vichnear ele¥*ation 3260.00 m. SEEP GE FAILURE565¥iECHANIS¥. I(aj t = a 5 days(b) t= I a d3y3277 30 m7 3277 30 m5050(c) t = 1 5 d ysFig. 12.(d) t = 2 4 d ysPore*wateF pressure contours (in kPa) during the inflltration process, Case IV (stratified darn)1POSSIBLE FAILURE MECHANISMS OF THE DAMThe infiltration analyses descr'ibed in the previoussections sholv that the seepage ¥vater can indeed flolvthrough the dam and exit from the do¥¥'nstream slope at ahigh elevation (see Figs. 10 and 1'_), as observed in thefield. The possibility of seepage failure of' the dam thendepends on ¥vhether or not the geometrlcai and hydraulicconditions for internal erosion failure are met.C:)1:)- F'n:est-o-. Med'urr!08･-t - Coarsests:cH+F=1O--- - H/F:::i 3c:e) 0 5Q,S:)o a4c:SStable 'u)CQ 02c')Geolnetl'icct! Conditions foi' Seepage Fai!ureIn or'der to assess the susceptibility of internal erosion,the geometrical conditions f'or internal erosion should be:r:aevaluated first. T¥vo g:eometrical criteria mentionedearlier for assessing the possibility of int.ernal erosionproposed by Kenney and Lau (1985) and Burenkova(i993) are used in this study because these criteria aresuitable for soils ¥vith smooth gradations (Schuler, 1995).In a smooth gradation, the soil is neither gap-graded norcomposed of' t¥vo distincti_¥* diftbrent size fractions. TheUnstab eo 0204Oc81F mass fraction smaile than DFig. 13. Relaiionship between H and F corresponding io variousdiamcters D or ti]e ihree orain-size distriblrtions accordin" toKennev and Lau (1985)fore, the three rockfill-materials are all likely to suffergrain-size distributions of the three rockfill-materialsfrom internal erosion if' necessary hydraulic conditionsadopted m the translent seepage anal ses (i.e., theare present and the seepage exit is not lvell protected.grain-size distributions of the finest, medium and coarsestrockfill in Fig. 4) are smooth distributions. According toHyc!rau!ic Conclitions f'ol' Seepage Fai!ul'ethe method of Kenney and Lau (1985), the F¥'alue used inthis criterion should be less than O.'_ because the uniformity coefficients U* of the rockfill materials are largerthan 3.0 and the rockfill materials are videly graded. Thevalues of H and F corresponding to various diametersD for the three g:rain-size distributions are calculated andThe hydraullc gradients in the dam during the reser¥'oir- vater infiltration process are obtained by the ti'ansient seepage analyses. Figure 14(a) sholvs the horizontalhydraulic gradients along the do¥vnstream slope surface(see Flg. 5) for the four simulation cases at times t= 18are also plotted in Fig. 13. Within the F ¥'alues bet¥veendays (Case I, vater exits from the slope toe), t= 0.8 days(Case II, the per'ched ¥vater is about to mel"ge ¥vith theground ¥vater table), t=0.1 5 days (Case 111, the perchedO and 0.2, some H/F values of all the three rockfill-¥vater just reaches the dolvnstream slope), and t='-.4materials are less t.han the criticai value of' I .3. Therefore,days (Case I¥r, the perched ¥vater is about to arrive at thethe three rockfill-materials are susceptible to internal erosion.elevation 3230.00 m are greater than 0.5, but the mode ofpresented in Fig. 13. The lines F+H= I and H/F= 1.3The geometrical criterion (see Eq. (2)) of Burenkovado¥vnstrearn slope). In Case I, the gradients belolvperchedvater movements in this case is not the one(199,3) is another criterion recommended by Schuleroccurred in the field. In Case II, the perched ¥vater does(1995) for soils ¥vith smooth gradations. The parametersin Burenko¥*a's criterion for the three rockfill-materialsare calculated and listed in Table 3. All values of D901D6anot reach the do¥vnstream slope surface; therefore, thehydraulic gradients along the A-A section are very small.for the three rockfill-materials exceed the respectiveare ..*areater than 1.0. The maximum h.vdraulic gradients,¥ 'hich are 1.04 and 1.35, respecti¥'ely, both occur at thevalues of 1.86 Ioglo(D9(}/D15) + I in the criterion. There-In Cases 111 and IV, the _",_radients near the ¥vetting f'ront Z,HANCJ AND566Tabie 3.c!l¥,iaterialCalculated parametcrs in Burenkova's criterion for the three rockfill-materiais(mm) c! o (mm) dl= (mm)Finest rockfi l20.2N,Iedlum rockfill50.0Coarsest rockfill240.03l22.044 O-e- Ca5e l'1(Ll: ;l 'c;n H:6.52,6 8,2.821 .65.45?_.65sO 8 days3260,aco>Q)3250&i4 965 465^05hydraulic gradient values near the ¥vetting front and insome regions of the dam are greater' than the allo¥vablegradient in the four cases. Particularly in Cases 111 andIV, failure may initiate in the sand¥vich at the do¥vnstream slope ¥vhere the hydraulic gradients are as high asO.9 and 1.49.ec:. 62l0.1'_-0.32. According to Fig. 14(b), the horizontalCase iV t::2 4 d ys32TOFl S6 l*(d {)/c! *)According to results of permeability tests by L,iu andlvliao (1996), the allowable hydraulic gradient of thecoarse rockfill to prevent seepage erosion ¥vas onlyH}- case lii' t=0 15 days'O.76 lg(c!,;o/cl <) + 1O 6s 18 d ysI - Case li'c!,;)/d6]O.I_ "32903280CHEN@ Wetting front3240Process of Fai!tlreAccording to the transient seepage analyses, stratifications of coarser and finer layers are a trigger that acceler-32303220OO-o 5051015Horizontal hydrau!ic gradient(a) Section A-A in Fig 56-e-Case i t=18 days- - Case li, t=0 82 121:)H: Case !ii, t=0possible failure process of the dam can no¥v be illustratedin Fig. 15. First, the rockfill materiais are susceptible tointernal erosion according to the geometrical criteria of5 days-h Case iV, t=2 4 days08Kenney and Lau (1985) and Burenko¥'a (1993). At noon27 August 1993, the reser¥'oir ¥vater level exceeded thebottom platform of the parapet ¥vall. Water flo¥ved Intothe dam throu*'h the channel bet¥veen the parapet ¥valll:'>J:c:04oNo:C Oslope at a high elevation and indeed creates the hydraulicconditions for seepage failure^ If the rockfill of the damwere perfectly uniform, the dominant seepage fio¥v ¥vouldbe do¥vn¥vards to¥vards the r'iverbed.Based on the aforementioned extensi¥'e analyses, theaysQ)vates the perched ¥vater to spread along the horizontaldirection. The perched ¥vater exits from the do¥vnstreamO 102030 SO 6a40Distance from upstream sur ace (m)( ) Sectian B-B in Fig 5Fig. 14. Horizontal hydratllic gradients along tlre dolvnstream slopesurfaee (Section A-A) and the horizonta:1 section B-Band the concrete face and filled the gap bet¥veen therockfill and the concrete face (see Fi**s. 2(b) and 5).Driven by *'ra¥'ity, ¥vater infiltrated into the rockfill andwould have ad¥'anced nearly horiz,ontally from theupstream slope to the do¥vnstream slope along stratifications formed during construction (see Figs. 10 and 12). Aiarge unsaturated zone lvould still be present belo¥v theperched ¥vater. The propagation of the ¥vetting front¥vould be associated ¥vith a hydraulic gradient (seeinterface between the coarse layer and the fine layer.The horizontal hydraulic gradients along B-B section atelevation 3265.00 m (the middle section of the sand¥vichin Fig. 5(a) for Cases l-III and the interface bet¥veen thecoarse layer and the fine layer in Fig. 5(b) for Case IV) atthe same times as in Fig. 14(a) are sho¥vn in Fig. 14(b). Inall the four cases, the hydraulic gradients are large nearthe ¥'etting front, reaching O.72, 0.31, 0.9 and 1.49 inFig. 14(b)) that exceeded the criticai gradient for internalCases I, II, 111 and IV, respectively. In Cases I and II, thezone vould then fall and roll down along the slope¥vettin_ : fronts do not reach the do¥vnstream slope surfaceand seepage failure at the sand¥vich elevation is not likely.together ¥vith ¥vater and mist. Finally, after a large part ofIn Cases 111 and IV, the maximum hydraulic gradients arebreached as ¥vas observed in the field.both located at the do¥vnstream slope sur'face, i.e. the exitof the infiltration ¥¥'ater.erosion. Once the ¥vettlng front reached the do¥vnstreamslope surface, the fine particles in the rockfill would belost gradually under the action of the seepa*'e force. Apiping channel would form progressively across the dam.The fio¥v rate ¥vould then incr'ease significantly, ¥vhich¥vould cause ¥vashout of the rockfill at the do¥vnstreamslope. Large slope protection pebbies above the erodedthe downstream slope ¥vas ¥vashed a¥vay, the dam iSEEPACE FAILURE IECHANIS 1A3277.30 ,(m ¥e ¥;･."." "(1 ) . '"T 326i .OC m l,4567l* + (6)(2)¥. :¥- -F ;:,- - +j: _ (5):;(4)Concrete face;= .-¥rT 3260,00 m(3)(2) Water infiltration into rockfill(4) Progressive development of piping(5) Washout of slope and falling of pebbles(3) Initiation of internal erosion(6) Dam breach(1 ) Water level risingFig. 15.Postulated seepage failure process based on rational anal)sesACKNOWLEDGEME_NTSCONCLUSIONSThe f'ollo¥vin*' conclusions can be dra¥vn based on thene¥v understanding obtained from the analysis of ¥vaterinfiltration into the Gouhou rockfill dam, the fio¥v patterns and hydraulic gradients in the dam, as vell as thegeometrical characteristics of the rockfill materials:(1) Based on the *'eometrical criteria of Kenney and Lau(1985) and Burenko¥'a (1993), the rockfill materialsof the Gouhou dam ar'e susceptible to internal erosion if necessary hydraulic conditions are present.( _) A perched-water table formed in the dam ¥vhen thereservoir ¥vate, infiltrated into the rockfill from thetop of the concrete face. The vettin*' f'ront advancedThe described ¥vork is substantiall), supported by agrant from the NSFCIRGC Joint Research Schemebet¥veen the National Natural Science Foundation ofChina and the Hong Kong Research Grants Council(Project No. N-HKUST61 1 /0,3). The authors ¥vould alsolike to thank Prof. D. G. Fredlund for his ¥'aluablecomments on this lvork. The permission from Prof. Z. Y.Chen of' China Institute of ¥Vater Conservancy andHydropo ver Research. Beijing, to use the t¥vo photos inFig. 2 is also gratefully ackno¥vledged.¥vith time and divided the dam into t vo zones: aREFERENCESsaturated zone inside the ¥vetting f'ront and an unsaturated zone outside the ¥vetting front.l) Burenkova, V V(3) If the rockfill of the dam ¥vere perfectly uniform(Case 1), the dominant infiltration plume vouldmove do¥vn¥vards to join the ri¥'erbed and ¥vould notexit from the do¥vnstream slope surface at highele¥'ations.(4) The dam ¥'as in fact stratified due to segre*"ation ofsoil particles during construction. Stratifications inthe dam, ¥vhether' fine or coarse layers, could causethe horizontal spreading of infiltration plumes toaccelerate (Cases II, 111, and IV), In particular, t.heperched ¥vater ¥vould spread nearly horizontallyalong the interface betlveen a coarser sandrvichmaterial and the finer rockfill mater'ial belolv. Assuch, the perched ¥vater ¥vould fiolv through therockfill and exit from the dolvnstream slope at ahi*･h elevation as observed before the breach of theGouhou dam. The lateral spreading can beexplained by the theory of seepage across the interface of t vo dissimilar rnedia.(1993): Assessment of suffbsion in non-cohesionand graded soils . Filters iil Geotec'llnica! ailc! H_vc!rau!ic En*"ineering(eds. by Brauns. J., Heibaum, ¥. ,and Schuier, U_), A. ABalke-ma, Ro erdaln, Netherlands, 357-360.2) Charles, j. A. (199S): Internal erosion in European embankmentdams-progress report of ¥vorkinroup on inlernal erosion Inembankmem dams. Danl Sc{fer_v (ed. by Berga, L^), A. A. Balkema,Rotterdam, Netherlands, 2, Ij 67l576.3) Chen, Q and Zhang, L. h,i. (2006): Three-dimensional anaiysis of¥vater infiltration into the Gouhou rockfill dam using: saturatedunsaturated seepage theory. Can Georech. J., 43(5), 449-461.4) Chen, Z. Y. and Zhao, Y_ Z. (1996): Slope stability anaiysis of theGouhou dam-deterministic model. Goi!hou Conc'rete*Fclcec!Rockfi!l Dam-Desi*"n. Construction. Opera!ion, and Faihu'e (ed.by China National Flood and Drought Pre¥'ention Ofi ce), ¥¥*aterC*onservancy and Hydropower Press, Beijing, 55-60.5) Craig, R. F. (1997): Soi! Afechanics, 6 h ed., E & FN Spon, London.6) den Adel. H,. Bakker, K J. and Breteler, M K_ (1988): Internalstabili "v of minestone. ProcIn!. S_1'mp !Vfode!!ing Soi!-rilaterStructure In!erac!ions (eds. by Kolkman, P. A , Lindenberg. J. andPilarczyk. K. ¥V.), A. A. Balkema. Rotierdam. Netherlands,225-23 1 .7) Fell, R., , 'Iac(J*regor. P, and Stapledon, D (1992): Geotechniccll¥'ith a hydraulicEn*"ineering of Enlbankment Danls. A. A. Baikema, Rotterdam,Netherlands*'radient that is higher than the critical ¥'alue needed8) Fos er, *¥,1., Fell, R and Spannagle, i¥,1. (2000): The s atis ics of(5) The wetting front lvas associatedto cause internal erosion. When the wetting frontembankmem dam failures and accidems, C(In. Ceotechreached the do¥vnstream slope surface, pipingl OOO- I 024 .failure would be triggered since the geornetricalconditions of the rockfillerosion.vere susceptible to internalJ., 37(5),9) Fredlund, D. G. and Rahardjo, H. (1993): Soi! IVlecllanics forUlisatiira!ecl Soi!s, John ¥¥rjley & Sons, inc_, Ne¥v YorklO) Fredlund, D. G., Xing. Aand Huang, S. (1994): Predicting hepermeabili y func ion of unsatura ed soils using soii*water charac- 568Z｝｛、へNG．へND C騒EN11） Fredlund，NI，D、，∼Vilson，G、∼y、and Fred1し【nd，D G．（2002）＝Use20）PDESoluεlonhlc、（2003）∫1avPOど3R師θ1で11cd癒〃7∼’θ1，Antloch， Callfomla，USA、 of こhe grain，size dis［ribution for estlmatio鳶 of 芝he so藍一、vater21） Schuler，U．（1995）：How ［o deal、、Fith ［he probiem of suαuslon， cllaraCterisdccurve，Cαノ1、（｝θαθch．／，，39（5），lio3−m7． Rθ5θα1でhα’1ゴ五）（∼vθ！oρ11∼θ1∼’〃1’hθF’θ1ゴ（∼ズ五）α〃15，SNCLD，Crans− ［eristiccurve，Cσ11．Gεo’θぐ11．ノ．，31（4），533−546．12）GouhouDamFailure…nvestigationTeam（19％）1Technicaldetails Nlo爲tana，Sw髭zerian（玉，1−15， of dle Go曲ou dam，Gα！11α！Cα∼c1’αθヂαcθ41∼ocんガ〃0α1η一22）Sherard，、ヌ．L．（197∼））：S1nklloles1n dams ofcoarse，broad玉y grained ρε∫’91∼， Co11∫11一∼’ぐ1’011， 0Zフθ’日α”011， θ11ご ノ『θ〃∼〃ぞ （ed． by Chhla soils，ηα11∫θα’0115Qブ／3’1∼∫ノπ．Coη9，加rg8加1η∫，1飢emaIioIlal Na｛ional Flood and DrQught Preve【1tion Of資ce），∼Vater Conservan− CommlssiononLargeDams，Paris，France，2，25−35． cy and｝畷ydrQpower Press，Beijing，111−245，23）Sllerard，」，L，，Dほnn1gan，L、P，andTalbα，，」13）Ho頃o，Y．andVeΩez1ano，D．（1989）l Improved熱ltercr紅er1on for cohesiolllessso1ls，ノ 0θ01θc11、五11913．，H5（1），75−94．14）1COLD（1995）：Dam fa1沁resl stat1stic analysis，β正’〃α”∼99，∫1r1θノR（玉984）：Baslc l》roper［ies of sa【｝d and gravel良lters，．1．Gθo∫θごh、ど1191宮．，110（6）， 684−700．− no’10ηα1Coノη1η’5∫10η011加19θDσ〃∼∫，1皿ema【io良aICommlsslon on Large Dams，Par1s．15）Keほney，T．C，and Lau，D．（1985）l I厭emal s【abi比y ofgranωar 51Iers，Cαη．0θo’θc11，／、，22（2），215−225．16）Liu．，LandMiao，L．L（1996）＝蔦xperlmen｛alstudyofseepageand24）Singh， B． and Varshney， R、 S、 （玉995）＝ Eng’1∼θθ1””1g ／10r ∬1η加1∼ん1ηθ’π0αη15，A．A．Ralkema，Brook丘eld，USA，25） Skempζon，A，、V．and Brogan，J，｝〉i σ994）：ExperimeaIs on p1pl【｝9 insandygravels，G80’θc／1吻z’θ，44（3），449−460．26） Soi1V1sioa Systen｝s Ltd．（2001）：So〃VZ5’011 U5∈∼r’∫（3∼”ゴθ Vθ1510η 3．0，Saskatoon，Canada・ seepages〔abilityofGouhourock翻maIer1als，Gα’hα’Co11α門θ1θ一27）SoiiVisionSystemsL【d．（2003）：3Vノマ∼！xU∫θ1・1∫イ、伽π’013．12， 汽α‘θ‘1Roご勺5〃ρα’n−0θ5191∼，Coノ∼，∫’ノw‘’10’r，OPθ’“α110’1，θノ1げノ『α〃”1で 5館’”αθ4／U’∼、∫副〃一α’θび月11”θE！θ1ηθ1π2五）／3P5θθpαgθご》o礁〃11g， （ed．byChlnaNa柔1onalFlooda“dDroughtPreve【1tiα10伍ce）， Saskatoon，Saska芝chewan，Canada． ∼Vater Conservancy a琵d Hydropower Press，Be1jing，18−25．17）Liu，」．，Dlng，L。Q．．M玉ao，L．」、and Yan9，K．｝｛、（1998）：Mo〔墨eI28）τerzag厩，K．and Peck，R，（1948〉＝So〃A（1θc11αηic5”∼Eng’ηθα1ng P1’αα’ぐθ，John Wiley and Sons，Inc、，New York． s｛面yonfail肝emechan1smso琶heGoullourock611dam，C／71η．ノ、29）τomh簸son，S．S．and Va1d，Y．P。（2000）＝Seepage forces an（玉 ∫ノ』｝，4”，ノ『η9’9．，（王D，69−75． confin玉ng Pressure effects on piping erosion， Cα11， （フθ01θc11、 ，1．，18）Ma肌el，C，L．（1985）：Seepageco蹴rol forembanKmentdamsUSBR prac【iceラ SθθP‘∼9θ αノ7ゴ五，＆7ん‘19‘∼ノ》o〃1 ∠ ‘7171∫ ‘∼114 ／11∼ρo‘〃1ゴ〃1θ1r15 （eds。 by Volpe， R。 L． arld Ke鰻y， ∼V． E．）， ASCE， New York， 37（王），1−B．30｝ USCOLD（1988）：Lesso自s fronl dan11ncidents，USA−II，Prepared by τhe subcomn貰圭uee of Dam hlddents a貧cl Acc1dents of tbe Cen〔rifuge s田dy of DNAPL transport in granしElar media，ノ． Commi貰ee on工）am Safe［y of由e U．S．Com搬iRee oΩLarge Dams （USCOLD），American Socie［y of C1vll Engineers，New York・31）Vaughan，P．R．andSoares，H．F．（三982）：Desig頁of負iters forclay Gθo’θごh「Gθoθ17v〃’011，E∼7918。，韮26（2），105−ll5「 coresof（玉ams，／．（｝θo’εc1∼、どノ1grg，0’v、，108（1），17−31． 299−305、19）PanIazidoロ，M．，Abu−Hassane1n．Z。S、alld Riemer，M、F、（2000）：
- ログイン
- タイトル
- The Role of Nature of Particles on The Behaviour of Rockfill Materials
- 著者
- A. Varadarajan・K. G. Sharma・S. M. Abbas・A. K. Dhawan
- 出版
- soils and Foundations
- ページ
- 569〜584
- 発行
- 2006/10/15
- 文書ID
- 20941
- 内容
- SOILS AND FOU¥_*DATIONS ¥;ol46, NTo, ),569584, Oct. 2006Japanese GeoLechnical Sociel)THE ROLE OF NATURE OF PARTICLES ON THE BEHAVIOUR OFROCKFILL MATERIALSA. ¥rARADARAJANTi), K. G. SHAR IAii), S. M. ABB sii!) and A. K. DHA ¥*A 'iY)ABSTRACTThe nature of' the particles of se¥'en allu¥'ial rockfill materials and three quarried rockfill materiais are expressed interms of uncompacted void content and unconfined compressive strength of each of the rockfill materials. Drainedtria.¥'ial tests are conducted on modeled rockfill materials. The beha¥'iour of' the r'ockfill materials is related to theunconrpacted void content and unconfined compressive strength of the rockfill materials. A predlction procedure isproposed to determine the angle of shearing resistance of the rockfill materials using uncornpacted void content andunconfined compressive strength of these materials.Key words: rockfill materials, triaxial tests, uncompacted void content, unconfined compressi¥'e strength (IGC: D3/D6)particles as the basis. This procedure assumes implicitlyINTRODUCTIONthat all the factors affecting: the stren9:th of the rockfillmaterial can be related to the size of the part.icle. But, it isRockfill dams are constructed using materials mostlyobtained by blasting rocks in quarries. These materialsconsist of angular to subangular particles. Rockfill damsare also constructed ¥vith materials collected frornkno¥vn that the factors such as shape, surface roughnessand strength of the particles also affect the strength of' thematerials are a¥'ailable in the riverbeds of the tributariesrockfiH materials. This paper deals ¥vith laboratory testing of rockfill materiais collected from ten project sitesand correlation of the behaviour of these materials*ithof the major ri¥'ers, Ganges and Indus in India. These¥'arious characteristics of the particles.ri¥'erbed in some cases. Large quantities of thesealluvial rockfill materials consist of rounded andsubrounded particles as a result of impact, rolling andREVIEWsliding action in the ri¥*erbed. Rockfill materials consistof particles as large as 1200 mm. It is known that theParticles of' rockfill materials are primarily derivedfrorn quarries b), blasting rock or collected from riverbeds. The characteristics of the particles are expressed byinterparticle contact stresses increase ¥vith the size of theparticles ¥vhen they are subjected to loading in anengineering structure such as rockfill dam The lalgethe mineralogy, size, shape and surf'ace texture. Themineralogy depends on the parent rock from ¥vhich thecontact stresses cause breakage of particles. The natureof particles such as shape and roughness also affect thebreakage of particles. The behaviour of rockfill materialsparticle is deri¥'ed. The size is defined by the size of thesquare hole in a screen of a sieve in GeotechnicalEngmeering. The rockfill particles are mostly equidimen-are affected by the breakage of particles besides all otherfactors that aft ct the behaviour of' granular rnaterialsconsisting of smaller sized particles.sional. The degree of roundness of the particles is qualita-tively described as angular, subangular, subrounded,rounded and well rounded (Lambe and Whitman, 1969).As the sizes of the rockfill materials are large, somekind of rnodeling technique is often used to reduce theSurf'ace texture of the particle refers to minor features ofsize of particles so that the samples prepared ¥vith smallersize particles can be tested. The material parameters froma surface of a particle, independent of size, shape, ort.he tests are used to get the parameters f'or large sizeprototype particles by extrapolation usin_ : the size of thetexture are dull, polished, smooth or rough, striated,frosted, etched or pitted (Lambe and Whitman, 1969).*) Head, Dept, of Ci¥'il Engineering. Dr.de2:ree of' roundness. Sorne terms used to describe surface,1.G, R_ Educational and Research Instituie (Deemed University). Chennai 600095, Tamil Nadu, India(formerly Dogra Chair Professor. IIT Delhi).*=} Professor and Head. Dept of C*i¥'il Engineering, Indian Insritute of 'Technolog), Hauz Khas, Nelv DelhiIOOi6, India (kgsharma@civil.iltd_ernet_in).**=} Reader, Dept. of Civil Engineering, Jarnia N,Iillia Islamia, Jarnia Nagar, iNew Delhi I 10025, India**u Director. CSivIRS, Hauz Khas, tNe¥v Delhi 1 100i6, India.The manuscript for this paper ¥vas received for revie¥v on November 1, 2004; approved on N,Iay 29, 2006¥Vritten discussions onhis paper should be submitted before ¥. ,Iay I ,*007 to the Japanese Geo echnical Socie v, 4-38-2. Sengoku. Bunkyo-ku,Tokyo I 12-001 l, Japan_ Upon request the closing date may be extended one month.56C)_ VARADARAJAN ET AL.570Youd (1973) used the ratio of minimum radius of theR mJlt Sa lrDam Slte !r 1" ' 111' lr"rlparticle edges to the inscribed radius of the entire particle_¥;.:TT 1'/tr:tf ; ';' !x'r'r'14 t"; /"_ +1;: s '; !_ !;tl"(ol Dsrl' Siteto depict the roundness of the particle. Over the yearsrseveral tests have been evolved for measuring coarseag*'regate quaiity in High¥vay Engineering in terms ofYes[erm Y:ImuF n Can' ] Sito f'/"'/rl :1 _ r ' T $ : P:lrbati Dsn] Siteparticle shape, angularity and sur'face texture. Standardised tests include percentage of fractured par'ticles(ASTM D5821-1995), fiat and/or elongated particles inr J' ^' th :: 'fl;1:: j;i /d;;-if /'h /i' r) ;･j::;I'; ';:/:;;; '/ti/'_i iare*'ates and it is similar to the uncompacted voids testfor fine aggregates (ASTM C1252-1998). This test is moreobjective and less labour intensive and less time consum-'"' ';( 4' 'trlli " s "; t s;- ;:7: F Ft1"I 1 " .,/ ! '; '_ I:sij l: rJ4*; !Q'; ;uYiEl/TGhri D:lrn Sit::i ,;r'-l; fxr!coarse aggregates (ASTM D4791-1999), and index ofparticle shape and texture (ASTM D3398-2000). Alhrich(1996) proposed an uncompacted voids test for coarse' * =1' __'r"$-4 : ;/ r _ v'cL/f' '- x'! T; s' { '" ""/r'$1 't' :¥:"J'f ' ;s; . , _ 'i/ i' ;'1 ' 'T;";' l ;fecki ]n l iaterialsl * r)'tuarTTied(T r Rockl" u la e isBoth T} es orl ockfln ¥' Ialerinls'P "" ";1;) , lling (Hossain et al., '_OOO).Rockfill materials contain particles of large size and itis dif cult to test them. Therefore, the siz,e of the rockfill!' + ^-! ti';'fss i _'::L:'::'::'1 :.':;::,:/:i:::'Si2;;;i;r/':''{ ';)"_ ir';) t'J:mater'ials is reduced using modeling technique. Four!!"modeling techniques are used to reduce the siz,e of the; 'I_"AFrockfill materials viz. the scalping technique (Z.eller and2 ;f' 'Li" ' 'l '! J;{:? .::;H"i i ] _ltl' J#:llF ""; I -": ; rl';,. I -11 R:/rWullimann, 1957), parallel gradation technique (Lo¥ve,1964), generation of quadratic _ rain size distributioncurve (Fumagalli, 1969), and replacement technique(Frost, 1973). The parallel gradation technique ¥vas)f! " l'uriln D:] siteFig. 1. Location of the project sites on the mapconsidered the most appropriate out of these four tech-the prediction of the angle of shearing resistance forniques (Ramamurthy and Gupta, 1986).Rockfill materials have been tested using lar_"*e scaletriaxial testing equipment. Specimen diameter in thesetests ranged from 15.2 mm to 500 mm, the maximum sizeprototype rockfill materials using the character'istics ofthe particles.of the particles ran>'ed from 3.8 to 100 mm and themaximum confining pressure ranged from 0.69 to 13.8MPa (Hall and Gordon, 1963; Marsal, 1967; Fumagalli,ROCKFII,L MATERIALS1969; lvlarachi et al., 197,_; Thiers and Donovan, 1981;sites in India. The locations of the projects are sho vn inAnsari and Chandra, 1986; Venkatachalam, 1993;Fig. I . Six of the sites are located in the states of Punjab,Varadarajan et al., 2003). These researchers conductedtests on a wide ran*'e of rockfill materials. They haveconcluded that (i) the stress-strain behaviour of theUttranchal, Uttar Pradesh and Har'yana in the northernpart of India. One site is in West Bengal state in theeastern part of India. Seven alluvial and three quarriedrockfill materials ¥vere chosen for the study. A briefrockfill material is nonlinear, inelastic and stressdependent, (ii) an increase in confinin_pressure causesincrease in the ¥'alue of peak deviatoric stress, axial strainand volumetric strain at failure, and (iii) an increase inthe size of the particles results in an increase in volumetricstrain at the same confining pressure. They found that thebehaviour of the rockfill materials depends on mineralcomposition, particle siz,e, shape, gradation, and relativedensity of the rockfill materials.The material parameters for the large prototype siz,erockfill materials were obtained from the materialparameters of the modeled rockfill materiais usin_ *Rockfill materials ¥vere collected from seven projectdescription of the location and the rocks are presented inTables 1(a) and 1(b). The alluvial rockfill materials ¥verefrom the beds of the tributaries of the t¥vo major riversGanges and Indus. Representative rockfill materials ¥verecollected from the project sites. The grain size distribution cur¥'es of all the materials are sho¥vn in Fi :. '_. Themaximum particle size ran_9:es from 200 to 1200 mm. A¥vide ran_"*e of gradation characteristics is observed int.hese materials.The photographs of typical allu¥'ial and quarriedrockfill materials are sho¥vn in Fi_"._s. 3 and 4. Strikingextrapolation techniques ¥vith the maximum particle sizeof the rockfill materials as the basis (Venkatachalam,differences in composition and nature of particles are1993; Var'adar'ajan et al., 2003).each alluvial rockfill material consists of roundedSCOPF,particles ¥vith rounded and smooth surfaces of ¥'ar'iousrock types, each quarried rockfill material consists ofparticles ¥vith angular and rough surfaces of same rockThe scope of the in¥'estigation lvas to determine thecharacteristics of the particles of the rockfill materialsfrom various project sites, to conduct triaxial tests onmodeled rockfill materials and to propose a procedure forobserved in the tlvo types of rockfill materials. Whereastype. THE ROLE OF NATURE OF ROCKF LL iATERiALS571lOO-h Rs!80e,-hsr tisnl ( 3 2O rurF] l/_bah ie sr { OO ru/}/-- r- Puru! ia {ianl ( I L0V rTlnl l/¥VYC (SE] (25 mnl mo eled)L////VYC (SE] (SO nna mo eled)- - YYC (SE) (5C mrl mo s]ed)e)//- ･ Psrbatl d2;n (700 mm}, , 40///-- - h oi d2m (600 mnl}60eeJ:t S-i -Tehr: dsm (2:S rllnl'-1 - VYC (SE) (2L}O n]m'--c- ¥YVC ( BS) (250 rnm)/20oO,llO1lOOOlOOMaximum Particle Size (mm)Fig. 2.'Table 1(a).SNo.l.A luvial rockfill materials usedProject nameTehri DamGrain size distribution curve for the rockfill materialsLocationName of the rocksOld DobataQuar zite, phyllite,borro¥v area,sandstone, graniteDistrict 'TehriTehri DamS. NoNew DobataQuartzite, phylliie,borro¥v area,District Tehrishaie, IirnestoneProject namel . Kol DamQuarried rockfill materials usedLocatiorlKol, District Bilaspur,Name of the rockLirnestoneHimachai Pradesh Stale2Garhl"al,Uttaranchal State, *Table 1(b).Purulia Dam Purulia, ¥Vesi BengalHornblande-Siate = quartz-schist3. Parbali Dam Kartah quarry, Sainj, QuartziteDis rict Ku lu, HimachalPradesh StateGarh¥val,Uttaranchal S ate3*Kol DamKol, DistrictQuartzite, Iirnestone,Bilaspur,shale, sandstoneHimachal PradeshThe nature of the particles primarily refer to size,shape, sur'face texture and mineralogical composition ofState4RanjiSagarDam)+Shah NeharShahpur Kandi,Quartzite, jasper,the particles. The sizes of the particles and their distribu-Districtshale, con_"..lomerate,Gurdaspur,Punjab Stateclaystoue, sands one,tion in a rockfill material are determined by sieveAt running:,¥,Iicaceousdistance (RD)7410, nearsandstone,rlts of chartTerrace, DistrictKangra, HimachalHosain et al. (,_OOO), has been adopted herein for rockfillquartz tePradesh Statematerials. The test apparatus proposed by Alhrich (1996)was fabricated and is shown in Fig. 5(a). With thisVesternFoundation ofYamunabridge, DistrictCanalYamuna Nagar,Quartzite, marbel,limestoneHaryana Staie7Foundation of siltYamunaejector site,CanalDistrict YamunaphylliteNagar, HaryanaStateapparatus, material vith maximum particles size of 19.0mm can be tested. The apparatus and the test procedureare briefiy described in the follo¥ving.Quartzite, Iimestone,shale, sandstone,Vesternanalysis.The shape, surface texture and gradation of fineaggregates are quantitatively expressed by a singleproperty kno¥vn as Uncompacted Void Content (UVC)(ASTM C1252-1998). The sarne concept, ¥vhich has beenextended to coarse aggregates by Alhrich (1996) andSansarpur6.NATURE OF PARTICLESThe apparatus consists of a top and a bottom cylinder.The bottom cylinder called cylindrical measure, is oneside open on the top. The top cylinder which functions asa funnel, is fitted lvith a conical cylinder at the bottom.The opening at the bottom is provided ¥¥'ith a lid ¥vhichcan be opened suddenly to pour the material in thecylindrical measure (Fig. 5(b)).The upper cylinder is filled freely with 5 kg of rockfillmaterial after striking off the excess material. The bottomlid is suddenly opened to allow the material to freely fall VARADARAJAN ET AL.57_v'=":}j{ist.,!;* :."*. ,(-"'* ";S i'*.: .{(a)Frg 3. A]luvial rockfi 1 matcrials obtained from bridge sitc. ¥VesternYumuna CanalFig. 5(a).Apparatus useti to determine Uncompacted Void CoutentH4Jl ;n m!s*d.=}I60i'F'I +l a2 mm1 smm!L*- H I=+Fig. 4. Quarried rockfill materials obtained from Ko] Dam Site(b)in the cylindrical measure. The material collected is¥vei hed after le¥*elinFig. 5(b).l,ine diagram of UVC apparatusthe surface. The IJVC is calculatedas :UVC = V-F/G x 100 (1)V¥vhere,V=Volume of the material collected in the cylinch･icalmeasure in ml,F=Net ¥vei**ht of the material collected in cylindricalmeasure in gm,G = Specific gravity of the materialthe maximum particle size. Also the value of UVC_ forRanjit Sagar material is less than that for Puruliamaterial for the same maximum part.icle siz,e. Lo¥¥'ervalue of UVC indicates more material (particles) per unitvolume (i.e. higher density) (Eq. (1)).A material having different average particle sizes but¥vith same uniformity coefficient (i.e. parallel gradation)and shape and surface texture ¥1*ill attain lo¥ver void ratio¥vith larger a¥'erage particle size, provided the compactionTo study the effect of size, three modeled rockfillmaterials ¥vith maximum sizes of 19.00, 9.50 and 4.75mm ¥vere prepared from each rockfill material usingeffort is same (Lambe and Whitman, 1969). The decreaseparallel gradation technique (L.o¥ve, 1964). The ¥'alues ofRanjit Sagar and Purulia rockfill materials are ¥vellgraded ¥vith uniformity coefficient 131 and 15 respectively. But, for the same maximum particle size. Puruliarockfill material sho¥vs higher value of UVC than RanjitUVC for each materialvere determined. Semi log plotsbetween the maximum particle sizes of the modeledmaterials and UVC ¥ver'e plotted. Typical plots for t¥vorockfill materials from Ranjit Sagar dam site and Puruliadam site are sho¥vn in Fig. 6. The plots are found to belinear and may be used to determine t.he value of UVC forlar_ :er particle sizes as sho¥vn in Fig. 6. In Fig. 6, it isobserved that the value of UVC decreases with increase inin the UVC value ¥vith increase in particle siz,e obser¥'ed inthis study (Fig. 6) also confirms this finding.Sagar rockfill material (Fi_ :. 6). This may be attributed tothe fact that the particles of Purulia rockfill material ¥vithangular and rough surfaces attain lo¥ver density (higherUVC) than the particles of Ranjit Sagar rockfill material¥vith rounded and relati¥'ely smooth surfaces. Therefore, r=THE ROLE OF NATURE OF ROCKFILL ivIATERIALS573ss40sou30's>120>< ioe)::: ** :3sos'lOv>- :es:o:4lMaximum Particle Size (mm)10o :o 40 eo so 1:o i40 160 Iselo{)UCS (Fig. 6. T)pical plot of uncompacted void content vs max'imumparticle sizePa)Fig. 7. Variation of UVC with UCS for aiiuvial and qilarricd rockfilimateriaisthe ¥'alue of UVC may also be used for comparing theshape and surface characteristics of the particles bet¥veent¥vo rockfill mater'ials having similar gradation curves.2.5 k**) is loaded in a drum of 700 rnm diameter andThus, the value of UVC may be used to quantitatively500 mm length alongrepresent size asof particles.1 i cast h･on balls. The drum is rotated about its axisymmetric axis on the vertical plane at a speed of 30 to 33 rpmupto 500 re¥'olutions. The aggregate is then taken out andvell as shape and surface characteristicsIndividual particle strength is one of the factors thatafi ct the shear strength of **ranular materials and therockfill materials in particular as the particle is subjectedto hi**h interparticle stresses durin*' shearing. In thisstudy, the strength of the particle is represented by thevith abrasive charge consisting ofsieved through 1.7 mm Indian Standard (IS) sieve. TheLos An*'eles Abrasion value, expressed in percentage, iscalculated f'rorn the ratio of the material passed through1 .7 mm IS sieve of total weight of the materiai taken. TheUnconfined Compressive Strength (UCS) of the rockLos Angeles Abrasion value (LAV) for alluvial rockfillfrom ¥vhich the particle is derived. The UCS value formaterials are also plotted in Fig. 7. It is remarkable tonote that the nature of' variation of LAV of the alluvialmaterials ¥vith respect to UCS is similar to that of UVC.each rockfill material is determined as f'ollolvs.Blocks of representative rock vere collected from theproject sites. At least five cylindrical specimens of sizes38.1 mm in diameter and 76.2 mm in length ¥ 'ere coredfrom the rock. Each specimen lvas tested in a compression testing machine with a constant stress rate of O.) tol .O MPa/s till failure (ASTM D _938-95). The failure loadas expressed in stress is the UCS of the specirnen. Anavera*"e of' UCS values of the five specimens is taken asthe UC.S value of the rock.Three modeled rockfill materials with rnaximum particle sizes 25, 50 and 80 mm were obtained using parallelThe LAV of quarried materials also shovved similarbehaviour (not sho vn in figure).It is noted in Fig. 7 that there is scatter of points andthere is no specific trend for ¥'arious alluvial rockfillmaterials in the plot between UCS and UVC/LAV. Thevalue of UVC for an alluvial rockfill material isdependent on the roundness and the smoothness besidesthe size of the particles. Incr'eased roundness and smooth-ness ¥vill result in reduction in the UVC value for therockfill material consisting of sarne sized particles. Thegradation technique (Lo¥ve, 1969) for each rockfillmaterial. Typical gradation curves for the modeleddegree of roundness and smoothness may not be same formaterials of a rockfill material are shomaterials considered in this study are derived from therocks of Himalayas and are the product of the riverbed'n in Fig. 2. Thesemodeled materials ¥vere used later in triaxial tests. Theall the alluvial rockfill materials. The alluvial rockfillvalues of UVC for these maximum particle sizes wereobtained by extrapolation from the UVC values alreadyaction during ¥ "ater fio¥v in the tributaries of the majordetermined for smaller maximum particle sizes.The values of UVC vere plotted against the values ofUCS for all the modeled rockfill materials as shown incarry broken rock pieces of various sizes producedFig. 7. As observed ear'lier, it is found that the ¥'alues ofUVC decreases with increase in particle size and the valueof UVC is high for quarried rockfill material as comparedto the value of UVC for alluvial rockfill rnaterial for thesame maximum particle size.An abrasion test ¥vas also conducted on the rockfillparticles to determine Los Angeles Abrasion Value (IS:2386: Part 4: 1963). In this test an aggregate of 5 kg¥veight (20l2.5 mm size, 2.5 kg and 12.5-10mm size,rivers Indus and Ganges (Fig. 1). These snow-fed riversprimarily by glaciation and ¥veathering of rocks/boulders. The impact, rolling and sliding actions of the rockpieces in the ri¥'erbed during ¥vater fio¥v cause roundnessand smoothness to the rock pieces. The riverbed-actionson the rock pieces depend essentially on the ¥'elocity of¥vater fio¥v and the nature of the riverbed. As theseactions are not same for all the rivers, the roundness andsmoothness of the rock particles are different for eachrockfill material and this is reflected in the scatter of thepoints in the plots bet veen UCS and UVC/LAVobserved in Fig. 7 for various alluvial rockfill materials. ¥rARADARAJAN ET AL.574OTable 2. Details of drained triaxial testsgQu eSNo.ilvlaleria]s from .Maximum Confining pressure,particle (rl (¥. ,{Pa)size CJP:ston, ****(mm)HYd rc JiLC ch(sTr,berdreEnog ?lRanjit Sagar Dam Site = 25, 50, SO 0.35. O.70 1 10 1 40)80Tehri Dam Si 25,e 50,O_352.O 704,-hYdQvilc oii too {(both borro¥v areas) I .056, I .4083SeQling ctornps¥Vestem Yamuna C_anal 25, 50, 80 O.2, 0.4, O 6, O 8ond outerm e m brenes(both sites)4+Shah Nehar Si e 25, 50, SO ; 0.2, O.4, O^6, O 8)Kol Dam Si e 25, 50, 80 O.3> O 6, O.9, l.2orik38 1 cm c x 81.,3 cm height)(both ma erials)6.Puru ia Dam Site 25, 50, 80 O.3, O 6, O.9, l^27^Parbati Dam Site 20. 40. 80 O.3, 0.6. O.9, l._)See:]na clernp5Tabte 3. Details of the triaxial cel!ParticularsApplied byCapacityFrorn Wetero ,vrrette ferC_onfining pressureAir- va er pressure s.vstem 3 lv{Pa9erv o I rmeesVr nci*Yo t umeFechQnQeAxial loadSpecimen sizeH .'draulic pressure unitiQtereipressure875 7 kNLen_ .*th = 813 mm, Diameter = 38 1 mmFig. 8. Trislxia] test setupIn Fig. 7, it is noted that bet¥veen the t¥vo rockfillmaterials from Tehri dam site (points corresponding toUCS ¥'alues 106.47 and 136.96 MPa) the mater'ial ¥vithhigher UCS sho¥vs lo¥ver UVC/LAV though they belon'_to the same area and might have been subjected to similarriverbed action. As such, it appears that the effect ofriverbed action on the material ¥vith higher UCS is moregiven by Abbas ('-003). A brief description of theexperimental procedure is presented in the following.The quantity of various sizes of rockfill materialsrequired to achieve the gradation of the modeled rockfillmaterial for preparing the specimen at specified relati¥'edensity ¥vas determined by weight. The sample ¥vasthan the one ¥vith lo¥ver UCS for comparable riveTbedprepared using a split mould. The sample ¥vas prepared infive layer's in the split mould by compacting each layer byaction. Therefore, it is probable that there is a generala ¥'ibrator. The sample ¥vas saturated by allo¥ving ¥vater totrend, as sho vn by a¥'erage linear lines in Fig. 7, that aspass through the base of the triaxial cell, and using a topdrainage sy. stem for removing air voids. The sample ¥vassubjected to the required consolidation pressure and thensheared by applying axial loading ¥vith a rate of loadingUCS increases UVC decreases provided the riverbedaction is similar for all the alluvial rockfill materials.TRIAXIAL TESTSConsolidated drained triaxial tests ¥vere conducted onthe modeled rockfill materials. A dry density corresponding to 870/0 of relative density ¥vas adopted forof I mm/min. Readings of vertical displacement, volumechange, and axial loads were recorded at periodic intervals.testing. The confining pressure ranges for the tests ¥vereF,XPERIMF.NTAL RESULTSchosen depending upon the dam/abutment hei*･ht in eachSti'ess-St/'ail7- Vohune Change Re!ationsllipsproject. Details of the tests are presented in Table '-.Large size triaxial testing facility at the Central Soil andMaterials Research Station, Ne¥v Delhi, India, a Government of India Research Station ¥1'hich pro¥'ides laboratory and field testing services for most of the river valleyprojects in the country, ¥vas used for testing. Specimensize of 381 mm in diameter by 813 mm in length ¥vas usedfor testin*'. Details of the triaxial cell used for thespecimen size is sho¥vn in Fig. 8. Details of the equipmentused are g:iven in Table 3.The complete details of the experimental procedur'e areStress-strain-volume change relationships of themodeled alluvial rockfill materials are sho¥vn in Figs. 9 to15. It is observed that, in general, axial strain at failureincreases ¥vith increase in confinin*" pressure andmaximum particle size. Volume change r'esponse sho¥vscompresslon for three of the alluvial rockfill materialsfrom Tehri dam site (Old Dobata), Kol dam site, andRanjit Sagar dam site. The ¥'olume compression increases¥vith confining pressure and maximum particie size inthese materials. Three of the remaining alluvial rockfillmaterials from Shah Nehar site, and Western Yamuna THE ROLE OF NATURE OF ROCKFiLL IATER ALS757566:,--"Iw'i} : Inl d::::^*:))r:4:e,4')/.'e,Cl).ox-X'x E Eh9'5rF'; E. '-,S-E(1 3. ! 3r(f 71.s 'te 1>e,> *,e,:x_{4r/ .x -l.Ar-r Jef}_ J:A:r A-A1A.a. ' ef e- e- ' h o:.o -o *e *o -o1l?'OO15l_:)*Ax'ial Strain ((Vo)Axiai Strain (o/o)(i) Stress-Strain Behaviour(i) Stress-Strain BehaviourOOes -0.4e:: -O.4(,), -08c,. ,_e.**- 11)_ _0.8o>>- I .6-1.215Axial Strain (olo)(ii) Volume Change BehaviourFig.9. Stress-strain-volume chan"e behaviour of aliuvial rockfi lmaterial obtained from old dobata borrow area, 'Tehri Dam Site15Axial Strain (olo)(ii) Volume Change BehaviourFig. lO. Stress-strain*volume chan"e behaviour of alluvial rockfiiimaterial obtained from new dobata borrolv aFea. T=ehri Dam SiteCanal (Bridge site and Silt Ejector site) sho¥v volumecompression initially and some dilation latter duringbreakage factor, Bg. The value of B* is calculated byshearing. The dilation nearly vanishes ¥vith increase insie¥'ing the sample using a set of sieves (80 to 0.075 mm)confining pressure and maximum particle size. The netvolumetric strain is compressive in all the cases. Therockfill material from Tehri dam site (Ne¥v Dobata)sho¥vs mixed trend in the volume change behaviour.before and after testin*'. The percentage of particlesretained in each sieve is determined at both stages. Dueto breakage of particles, the percentage of particlesretained in large size of sieves will decrease and theStress-strain-volume change relationships of the threepercentage of particles retained in small size sieves ¥villincrease. The surn of decreases will be equal to the sum ofquarried rockfill materials are sho¥vn in Figs. 16 to 18. Inthese materials also, axial strain at failure increases ¥¥'ithconfining pressur'e as ¥vell as maximum particle size. Allthe quarried materials sho¥v compression in the initialincreases in the percentage retained. The decrease (orincrease) is the value of the breakage factor B_* (Marsal,1967).part of shearing and dilation in the later part of shearing.The relationships bet¥veen UCS and B* for all theThe dilation in volumetric strain decreases considerablymodeled rockfill materials ¥vith the maximurn particle size¥vith increase in confining pressure and the maximumof 50 mm for three confining pressures, 0.4, 0.6 and0.8 MPa are sho¥vn in Fig. 19. It is observed that theparticie size.Efi ct oj' UVC and UCS on B/'eakage Factol'Breakage of particles ¥vas obser¥'ed during triaxialtests. The breakage is expressed quantitatively by thebreakage increases ¥vith increase in confining pressure,(T3 for both alluvial and quarried rockfill materials. Theincrease in confining pressure causes an increase incontact stresses leading to an increase in particle break- lVARADARA JAN HT AL.57G93.0)-.5,,*:62.Ov')' c'):,e;(/)(/,Oi^**;,*.:,O3.l.O>e,e):0.5O0.01215Axial Strain (o/o)Axiai Strain (o/o)(i) Stress-Strain Behaviour(i) Stress-Strain BehaviourOO): -*s -O.4-1,(,e, -0,8. ,,, _7_S -1.'>>-1 .6-315{5Axial Strain (o/o)Axial Strain (olo)(ii) Volume Change Behaviour(ii) Volume Change BehaviourPi*. 11. Stress*strain-volume chan*e behaviour of alhlvia rockfilimaterial obtained from Ranjit Sagnr Dam Siteage.In Fi**. 19 it is also noted that the quarried rockfillmaterials ¥vith higher UVC ¥'alues (Fig. 7) sholv higher B*Fi(p.12. Stress-strain*volume chan"e behaviour ofaliuviai rockfi ln{atertal obtajned from Shah Nehar S tein density (Fi_ . 6). Increase in density causes increase ininterparticle contact stresses leading to increased particlevalues than the alluvial rockfill materials. The higherUVC ¥'alues in the quarried rockfill materials are due tobreaka_ e. Similar effects of size of the particles andconfining pressure on breakage factor ¥vere obser¥'ed byMarsal (1965), Vesic and Clou*'h (1968), lvlarachi et al.an_9:ular and rough particles as obser¥*ed earlier and as a(1969), Venkatachalam (1993) and Varadarajan et al.consequence they undergo higher breakage than the(2003 ) .allu¥'ial rockfill materials.The rate of increase of Bg ¥ 'ith (T3 is sho¥vn in Fig. '-Ofor the same materials. It is found that the quarriedrockfill materials ha¥'in** particles of angular and roughsurface sho¥v hi_"*,her rate of breakage than the alluvia]rockfill materials ha¥'in*' particles of rounded and smoothsurface.The effect of maximum particle size on B* is sho¥vn inFi . ,_1 for the samples tested at the same (73 equal to 0.8MPa. It is observed that the breakag:e increases ¥vith theincrease in the maximum particle size for both t.¥'pes ofrockfill materials. Vith the increase in the size of theparticles, the ¥'alue of UVC decreases indicating increaseAs the breakage factor is related to the UVC, thescatter of points observed in Figs. 19 and 21 is attributedto the scatter of the points in the relationship bet¥veenUCS and UVC in Fig. 7 for the alluvial rockfill materials.Also, the avera_",_e lines indicated in these figurescorrespond to the average lines sho¥vn in the relationshipbet¥veen UCS and UVC in Fi_"._. 7.Effect of UVC ancl UCS ol7 Vohnnerric Stl'air7The effects of the maximum particle size and theconfining pressure on the volumetric strain at failur'e aresho¥vn in Figs. 2,_ and 23 for the t¥vo types of rockfillmaterials. It is observed that volumetric strain at failure 「577THE ROLE OF N．へTURE OF ROCKFILL M、へTERi、へLS3。03．5 ③③φ⇔φ⇔ φゆ3．0姦菱 2，5Φ舜轟 2．5筐峯 ヂ 囲魁鼠し 4φ竃2．0 ゆ訂一一講ぞ｝萌’弩1．5 繧礁鴇誰2・or一『 『一「 ゴ㎜旧㎜ 一蝉一 一溌韮．3．乞溺 ム齢ム 一一燃匿艶一 盒合 ．憲1．o4〉㊤’鐸㊤ 1。Oo1 β鋤O Gミー92MPユ00ム噺司4MP＆臓G汗o尊MPユ o．5X σこ訓）SMP，乞 ：5mmd一吋、一一 憩ロtIud隅、0。5 s臼mmd。n、、o．o0．000E5亘0，，1015Axial Strain（（％）Axi3置Straln（％）（i）Stress−S辻ギainBeh謎、1iour（i）Stress−Strahl Be垂1av量OUr （1．0 oOσ汗02MPユ△侮累り4MPa× o罫口硫初く・MP翁）一〇．5 oo￠㎜×G轡OSMP．一⑧σこ塁G鉢陸】aAσfooMPa駕 一（1．12−o．2 ムムa＆こ一1．o口σザ〔｝oMPax σゼ1）8MPa 25mmd、諏需鳳 50m期d『』レ、、）一 sommd，二4．5一 Sl与mmd＝、一 一 一goユ5mmd．．，りO G；一Q2MPa△鰍甥u4MPa一一 5「｝mmd一、、麗σr編GOMP＆⇔σぜi2MP註の o田警厨躍一2．oφ亀⇔％軸⑳⑧￠￠＞＞ 一2，5 一〇．3051015Axi21Sむ’ain（％）（童産）Vo翌ume Change Behavio騒roさ1（1ま5Axla嚢Str段藍n（％》）（li）VolumeChangeBellaviourFig．13。Stress勒sIrain騨vo加mecha鰍gebeh賃viourof謎量1賎via汁oc酬l ma亀eri賃lob芝ained舞om擁dgeSitegWesこer羅YamunaCanalf「19・玉4・S｛ress・s症rain【・d礪echangebella、Plourof“賎uvi田rock韮銭increases with maximum partlcle size and the con行ningfailure envelopes for e＆c紅 maximum p＆rticle size of m“乳er亘ε監量ob載ai無ed from SilεKjedor Si症e，、、▼es重er鳳Yε毫π田na Canalpressure for bo宅h the niaterials．These負ndings on volu−rock徹l material passed througll the origin as shown inmetriC Strain at failUre are，in general，Simllar tO thOSethe Fig．24 for the tyP呈cal rockfill mate1’重als．From t熱enoted for breakage factor．τhat is，lower the UVC，angle of t熱e s玉ope，αofthe fa玉lure envelope，the angle ofhigher is the breakage factor leading to higher volumetricShearingreSiSξanCe，φWaSCalCUlatedaSφ一Sia㎜1（taηα）str段in at failure．As noted in the previous sectlon，the（Lambe and Whitman，玉969）for ea曲rock薮H material．scatter iR the points in the relationship be重、veen UCS andB、in Figs．19and2玉宝s related to the scatter of points in雌∼α（ゾPαπic1εShσP召011φtherela￡ionships between UCS alldUVC in Fig．7for由ealluvlα1materials．Therefore，由e scatter of points ThevariationofφwithUCS圭sshownin｝7ig．25forthethτeesizesofmodeled＆lluvlalan（lquarriedrock創Iobserved in Figs．22an（123is a豆so due to the sca賛er ofmε粍erials．hisobservedthatξhevaluesofφforquarriedmaterialsarehlgher山anthoseforalluvialmaterials．ThepointsinFig．7．quarried rock創l materials wi由higher value of UVC！41191θoゾ’Shθαノ●加g Rθ5Z5’‘7n6θφ From the stress−strain cur、ノes the values of（σ1一σ3）atfailure for each con負ning Pressure，σ3，were determinedand with these values the plots ofρ（；（σ1十σ3）／2）vs（1（襯（σ1一σ3）／2）weremade foreach rock長II maξerlal as shownin Fig．24for typical alluvia1（01d Dobata，Tehrl Dam）＆nd quarried （Paruliε1 Dam） rockfi11 materials． 丁王1e（F玉g．7） are 豆ooser than the aHuvial rockfill ma【el’ials．Therefore，a looser quarried rock負ll material wouldprovide lower interlocking resistεしnce during shear圭ngthan an alluvial rock行11m飢erial．However，the natureof par盤cle shape and surface texture also εし9奄ct theinterlockingreslstanceduringshearing．瓢ghervalueofUVC for quarried materi＆I also iadicates more angular l¥,ARADARAJAN ET ALOi S3.s:,3 * ()4'--::¥j:.;'cL' 2.f)e,.'C!), ! 5.Oe3;･l .O>e)'pQO . 50.0o15OAxial Strain (( ())5 1 o15Ax. ial Strain (olo)(i) StressStrain Behaviour(i) Stress-Strain BehaviourO.O1¥- -O.s- I .Oi.,eso-c -1._:)(1e,t,= -2.0, _l>-, .515>,Axial Strain (94,)(ii) Volulne Change Behaviourrig. 15. Stress-s,rain-volt me cl]ange behaviour of alluvial rockfillmaterial obtained from Kol Dam SiteAx ial Strain (olo)(ii) Volume Change BehaviourFig. 16. Stress-strain*voltlme change behaviour of quarriedinateria! obtajned from K*ol Dam Sitcrockfil!and rougher particles than the allu¥*ial rockfili material asalready noted in Fig. 7. Due to this, quarried rockfillmaterial ¥vould provide higher interlocking resistancedurin9: shearing: than the alluvial rockfill material,et al. (2003) have sho¥vn that the c value increases ¥viththe increase in maximum particle size for alluvial rockfillFurthermore, in the case of quarried rockfill materials the(2003) have reported decrease in the c value ¥vith increasein maximum particle size for quarried rockfill materials.As sho¥vn in Fig. 7, the ¥'alue of U¥rC decreases ¥vith theincrease in maximum particle siz:e for both allu¥'ial anddilatancy caused by the angular and rough particlesduring shearing as sho¥vn by the ¥'olume change behaviour in Figs, 16, 17 and 18 Ieads to higher shearingresistance. Considering the net eff'ects of density andnature of the particles for the t¥vo types of rockfillmaterials, it is e¥*ident that the eff ct of shape and surfacetexture of particle is more dominant than the effect of thedensit.v of the rockfill material leading to higher angles ofshearing resistance for the quarr'ied rockfill materialsthan those for the allu¥'ial rockfill materials.E.fi;ect of Partic!e Size oil cIn Flg. 25, it is observed that the c value decreases ¥viththe maximum particle size for quarried rockfill materialand it increases lvith the maximum particle for allu¥'ialrockfill material. Venkatachalam (1993) and ¥raradarajanmaterials. Marachi et al. (1969) and Varadarajan et al.quarried rockfill materials. A Iarger sized rockfill material1 'ith lo¥ver value of UVC_ ¥vould be denser and ¥vouldexhibit higher interlocking resistance during shearing.It is observed from Fi_g:. 21 that larger siz,ed rockfillmaterials ¥vith lo¥ver UVC value also undergo higherbreakage during shearing. The effect of breakage is torecluce the resistance during shearing. Therefor'e, the neteffect of denseness and breakage on shearin_"_ resistance¥vill decide the nature of change of c ¥vith respect to t,heincrease in the maximum particle siz,e. It is noted that therate of averag:e increase in breaka e factor ¥vith incr'easein confining pressure is higher for quarried rockfillmaterials than that for alluvial rockfill materials THE ROLE OF NATURE OF ROCKFILL hIATERIALS:)579:)O cr ;$03 lPsA (;;06 lPaa l;:;[ o .Ipe I t eX o;:: 1 2 IP(tll44J- o mrn d:::;X:3X)(.-3]XC1ealIS1s:'C,,1X'--' SO mm d:? i' Xr¥le. ･i: 1'X5 rTIFTI d:?11 I?,e,k(le,AC:1oo246 8ltl'OeeeOc:olO4 6 8oAxial Strain (o/*)lOAx'iai Strain (olo)(i) Stress-Strain Behaviour(i) Stress-Strain BehaviourQ.Oo.oeeee c:o::l'-0.5s: -1.0Cl)vcs,.e, _lOO cJ1=0i .rpae, _2.0A (T =06 {Pa as * O, ¥.1Pa::X c>-1.5= 1 2 iPa*･*mnl d***.- sO n]I l d 's'>- SO mrn d=: '-3.0lOlOAxial Strain (ol*)Axial Strain (o/o)(ii) Volume Change Behaviour(ii) Volume Change BehaviourFig. 17. Stress-strain-volume ciranoe bel]aviour of quarried rockfillFio. 18. Stress-strain*volume cl]anoe behaviour of quarried rockfiilmaterial obtained from Parbati Dam Sitema eriat o ]tained frorn Purulia Dam Site(Fig. 20). Therefore, the effect of breakage on the shearing resistance of quarried rockfill materlal is higher thanthat for' alluvial rockfill material. Therefore, the effect of15¥*"-¥breakage on the c value appears to be more dominant inS lOthe case of quarried rockfill materials than that in the caseOof alluvial rockfill rnaterials. Therefore, the valuedecreases with the increase in the maximum particlefor quarried rockfill mater'ials ¥vhereas the valueincreases with the increase in the maximum particleof csizeof csizefor allu¥'ial rockfill materials as sho¥vn in Figs. 25 and 26.- -Allullai (O 6 ¥. rpn)A- O.lL*-rried tQ 8 1Pa)Llnear (A]luFi**. 27. It is significant to note that the value of c as ¥vellas the average r'ate of increase in the value of c. IPa))L--･-･ ･ ･---*¥'>-- Bl 1raeEr (Ailt 1 n! (O S ;¥. rpa )i !.:)=__--1..,_ :_ !:'1,:$J:*'- 0e:tI t",* 'e]i;,, -_;__ e*o･_-o 75 Ioo 125The avera*'e rate of change of c ¥'alues ¥vith respect tomaxirnum particle size has been plotted ¥vith UCS valuesfor both types of the rockfill materials as sho¥ 'n inal (O 4- - 1_Inear {Ailullsl {O e ¥. Ipa))r]Jo IEffect of UCS on cA!lu l; i (O 4 1Pn}'*- A[lu la! (O S ¥. IPa}e QL:err;ed (rJ 4 , Ipn]-B O, arr:ed (O 6 ¥. IPa]Fig. 19. Variation of B,150l 75UCS (MPa)vith UCS for the twoty pes of rockfillmaterials¥'ithrespect to maximum particle size increase with theand 21 on the average, the value of' UVC decreasesincrease in the UCS value for alluvial rockfill materials assho¥vn in Fi**s. 26 and 27. As already observed in Fi**s. 7(denseness increases) ¥vith the increase in the UCS valueand the breakage factor increases ¥vith the increase in the i580 ¥*ARADARAJAN ET ALs2.5¥-¥12.0t)'*.*** 6A: l･S$es,e J:i5s>b<- - * }Iu"isl t25l.OHil. 5_nrn)A! it*11; i i s ) mrn)!ll '1 { I s{) mm)¥-O.:'_* - -e-QL;: rr:edt:5m:1 )cSH - ( ts3rr eti ( s j nlmO.o r'='****'i QO 1 2060140**l OOl 60l :)_:)-OUCS (MPa)UCS (MPa)Fig. 23. Variation of voiumctric strain at failure witl] UCS at threerig. 20. varlation of average ratc of change of B,, wiul rospecto a*ma¥. imum particle sizeswith UCS123-- 1022^s:8ee64ot)*2p ( , IPa)o5 o7:):)-l OOl 2550rig. 24. p-q diagram for t)'picarig^ 21. variation of B,, 1 'ith UC_S for the tlvomaterialsalluvia] and quarrled rockfillmatcrialsUCS (MPa)l. pGS of rockfillje 'I r =' !,..___"__ -- ,,- -'=itil**' t= l*i=*=1)**'* **+ r)<' *=:* *h== )**};**1 I **=*J(* * -! *=*f= : +*'* } i***hr *'- .f'li :'i*:****- ;*=*1**}"'s ; _ * ? *=* +t* IY**'t h=i: !== 2.04: },;t*c**'*I*<:' '-=. 'H - !* *' ** r *='*-s- !'**h*1* i)*=n +*=*'1.:).:)-i{***ki i:'f, 1,0s(( ss Q.5eS O.oj1 rF-o.520oi ]7 1i l" m m i':]rtio]e size {n'm)loo(] 50 l_･ O 200UC_S (l rpa)Fig. 22. Variation of volt nretric strain at fai!ureconfining pressuresrig. 25. Variation of c-value with nraximum particle sizevith UCS ai threeUCS ¥'alue for the alluvial rockfill materials (Figs. 19 and_1). As discussed in the previous section, the effect ofincrease in denseness (lo¥ver UVC value) is to increase theshearin : resistance during shearin due to hi9:her interlocking, but the effect of increase in denseness is also todecrease the shearing resistance due to the damage causedb_¥' high breakage of particles. It appears that the effect ofdenseness in increasing the shearing resistance duringshearing is more domlnant than the effect of breakage ofparticles in decreasin_cT._ shearing resistance. As a result, thec value as ¥vell as the rate of increase in c value ¥vithrespect to the maximum particle siz,e increases ¥vith theUCS value. ¥Vith regard to quarried rockfill materials, ithas not been possible to arrive at any conclusion on theeffect of UCS due to limited data.PREDICTION OF c FOR PROTOTYPE ROCKFILLMATF.RIAl,Shear strength of geologic materials has been expressed THE ROLOF NATURE OF ROCKFILL ¥1ATERIALS5Sl5 Orockfill materials from the triaxial test results. The value45of (x' ¥vas found to be nearly constant and ¥vas equal to0.937.e,e,The parameter B' has been expressed as a function ofthe baslc characteristics of the rockfill materials that;b4 Qe,3 :)-affect their behaviour. These characteristics includee,particle size, nature of particle shape ancl surface, particle30strength, gradation and relati¥'e density, In this study, theparticle size, the nature of particle shape and surface and2050 Ioo 150O2 (] (}UCS (rvlPa)gradation are expressecl in terms of UVC and the particlestrength Is represented by the UCS of' the representativerock f'rom ¥vhich the particles are cierived. Accordingly,the value of' B' is expressed as:B' = Cl P '=rrg 26, Variation of c-vaiue witi] UCS of thrce max'inlL m particlesizeswhere CI' C , pl and pC2(UVC) " (4)are constants,P normalized UCS value. In this study the UCS isnormalized ¥vith UCS ¥'alue of' Ranjit Sagar rock-(].20fill rnaterial ¥vhich is the highest ¥'alue. Any otheri¥*alue could ha¥*e also been usecl for normaliza-O.15tion,UVC uncompacted void content expressed as fraction.1 O.1(]The relative densit.v has not been included in the abo¥'e<:,relationship (Eq. (4)) as all the modeled rockfill materialsvere tested vith the same relative density.eJ0.05<The ¥'alues of the constants C!, C , pl and p¥veredetermined as follolvs.().ooo50 Ioo 150The value B' ¥vas determined using Eq. (4) at four200UC*S (tvrpa)Fig. 27. Variation of average rate of change of c-valuc witl] respect toconfining pressure with UCSconfining pressures for each modeled rockfill material.The avera :e of f'our values¥'as calculated. This ¥*alue ¥ 'asused in Eq. ( -) along ¥vith the ¥*alues of' P and UVC ofthat material. Thus three equations ¥vere formed for thethree modeled materials for each rockfill material.T¥venty one of such equations ¥vere f'ormed for se¥'enas a f'unctional relationship bet¥veen shear strength andnormal stress or principal stresses by various researchersallu¥'ial rockfill materials and nine equations lvere f'ormedfollo¥ving Mohr-Coulomb failure criterion (deMello,constants Cl, C , pl and pl ¥vere foLmd using least squaresfitting method for alluvial and quarried r'ockfill materialsseparately. With these constants, the relationships for theprediction of the B' value ¥vere found to be:1977; Yoshinaka and Yamabe, 1981; Franklin andDusseault, 1989; Ramamurthy, '-OO1). Herein, the following relationship is proposed for the rockfill materialstested under triaxial condition("(71 (7 =B cTl+2cr (_.)P* Pafor the three quarrled rockfill materials. The fourB' = 0.85016PO I - 2 14964(UVC) (5)for alluvial rockfill materials and,B' = O.58072Po iwhere, B' is a non-dimensional parameter based on indexproperties of the rockfill materials, c ' is non-dimensionalparameter, CTI and cr3 are the major and minor principalstresses and p* is atmospheric pressure expressed in thesarne unit as the principal stresses.The parameter, a' can be determined by conducting atleast t¥vo triaxial tests with two different confiningpressures as:log ((Ti-(73)iae' log= (al- CT3)j - I (3)((71+2(73)iO.59167(UVC) (6)for quarried rockfill materials.The validity of' these Eqs. (5) and (6) ¥vas ¥'erified asfollo¥vs:Using the Eqs. (5) and (6), the value of B' ¥vas predicted f'or each modeled rockfill material. The values of al atfailurevere then predicted using Eq. (2) for the fourconfining pressures, (T3 used in the triaxial tests. F=romthese vaiues of crl and (T3 at failure, the ¥'alue of c ¥vascalculated. The ¥'alues of c predicted for all the modeledrockfill materials have been compared ¥vith the observedvalues from the tests in Figs. '-8 and 29. It has been((Ti + '-CT3)i- l¥vhere subscripts i and j+ I indicate tlvo triaxial tests.The values of' ( '¥'ere determined for all the rnodeledobserved that the error bet¥veen the predicted andobserved c-¥'alue is in the range of -8 to + 1'_(olo). Assuch the predlction may be considered satisfactory. Using ¥IARADARAJAN ET AL.5s24550c Tehri Dam ( Old Dobaie)Tehri Dam (N+el¥'Dobata)c Koi D ulll puru]ia DamA P arbat i DamA Kol D mX Ranjit Sa_ ar Damc Sl]ab Nellar45ooVestern Yamuna Canal (Brid*._,e Site)+ ¥ *estern Yamtlna Canal {Silt Ejecto te),o pancheshlr. ¥.epalXes>*i-*e, 40X.,1iddie Siang,+e +cc';>42eyc ie,35coAAoB4AooAoAe,39304030:,:, o4239Obs e]'¥ed 4hVal ue4:,.-Obs e r¥ed c･Val ueFig. 28. Comparison of observed and predicted c-values for alluvia]Fig. 29. Comparison of observed and predicted c-values for quarriedrockfill materialsrockfill materiaisTable 4.Comparison of c-values of prototype rockfill materialsc-values basedc-vahles based onDifferenceon po ver la liu c-¥'alues(degree)index properties(degree)51 441 9Tehri Dam(New Dobata)46 , i39 7- 6.5- i 4 07Kol Dam41 .636.35.3- 12.74Ranjit Sagar Dam63 34 1-7- 17 6Shah Nehar43 ,240.52 7- 6 25¥Ves ern Yamuna Canal50 343 .4- 6 9- 13.7245.843.5- 2.3- 5 .02Kol Dam38.8473,59 . 02Purulia Dam37l3 8 ,, 8l4.58Parbati Dam40.440.0h,laterial siteTehri DamDifference(o,6)(degree)- 1 8.68(O d Doba a)AHuvial- 2780(Bridge Sile)¥¥restern Ya nuna Canal(Silt Ejector Si e)QuarriedEqs. (5) and (6), the values of c ¥vere predicted for analluvial obtained from Panchesh¥var Hydro-electric37- o 99The value of c for prototype siz,e rockfill material ¥vasdetermined ¥vith the Eq. ('-) using B' values as calculatedPo¥ver Project, Nepal and a quarried rockfill materialfrom Eqs. (5) and (6) for the corresponding values ofobtained from Middle Siang Hydro-electric Po¥verUVC of the prototype size. The values of c predicted fora prototype size of 300 mm for all the rockfill materialsare presented in Table 4. For comparison, the values ofc vere predicted for all the rockfill materials using thecommonly used extrapolation technique using po¥ver la¥v(Varadarajan et al.. 2003). Significant differences arenoted bet¥veen the predicted c ¥'alues by the t¥vo procedures. It is believed that the c ¥'alues predicted by theprocedure used in the present study is realistic as itincludes most of the basic characteristics of the rockfillProject, Arunachal Pradesh (materials not included forthe determination of constants in Eqs. (5) and (6)) andare sho¥vn in Figs. '-8 and 29. The predictions appearquite satisfactory.As more data are a¥'ailable ¥vith time, constants in Eqs.(5) and (6) may be further refined. Equations (5) and (6)can then be used ¥vith confidence to predict the angle ofshearing resistance of rockfill materials for the design ofdams . TRE ROLE OF N．へTURE OF ROCKHLL M．へTERI．へLSma芝eriaiwhereasthecommonextrapo1＆tionprocedureused collsiders ollly the maximum particle size of由erock負llmateriaL58316／1NcGE−35／99from出eMlnistryofwαterResources，ResearcllandDevelopmentDlvisiol1，Govemmentofln（iia．The assistaace provided by various project aut熱oトitlesisgratefullyacknowledged．CO翼CLUSIONS The c紅aracteristics of particles from seven alluviaIrockfill nlaterials aud three quarried rock且11 買1aterialshave been quautltatively expressed by ullcompacted voidcontent and uncon負ned compressive strength of the rockparticles．王）ecre＆se in the ullcompacted void content withdle maxinユum par￡icle size and average（iecrease圭n theuncompacted void content with uncon負ned compressivestrength of the particles are observed．Angularαnd roughsurfaced pεtrticles ofquarried rock負互1materials are foundto hεtve higher uncompacted void co陰tent than宜he roundREFERENCES D 、へbbas， S、 釣「1、 （2003）：Test三ng and n｝odeling the bel｝avioしlr of riverbed and quarried rock自11nla乳e藝als，Pノ∼五） Tノ∼θ5’5，RT Delh1， New Delhi，王ndia．2》．へ組rich，R、C、（1996）：Inf沁enceofaggregatepropert1eso【1perform− ance Qf heavy−du｛y hQt−mix asphal【 pave道1ellts， 71’α’∼∫po1マα1’o∼7 1∼θ5θα’℃h1∼θco1｝イ1547，Transl）ortatioll Research Board，Nationai Researcll Cou疏c11，Washingτoll D、C3》．Ansa嫉，K、S、andCilandra，S、（1986）：｝穫owoughtolletodeternli【｝e so貢parameters to be used ia【he clesign of ear〔妻1aad rock撮l dam？， Pヂoぐ，／’1伽nGθo’θ‘一11，Co／1∫．，NewDelhi，2，1−6、4）ASTM C l252（1998）：S礁∼ゴαヂゴT25’A／θ∼hoゴ．五〇r Uノ∼co11∼ρααθ4and smoo由 surfaced particles of alluvial rock負ll 歓「o’ゴCo’∼‘θ1∼ωゾF加ε、4ggrθ9αθ妨／ノ漁ε1κ’θゴαvp‘’1『’1ぐ1θ51即θ，materialS． S‘〃プ汝c（∼7εY1‘”｝θ，αノ14（フ’”α4’1∼9ノ，．へST｝〉正S［andard、 From the drai貧ed tri＆xial tests on山e mQdeled rock負llIIlaterials of alluvial and qua…』ried rockfil塁Rlaterials，thefOllOwingCOnCIUSiOnS＆redraWa． i） The axial stra玉n，volumetric str3in and breakage5）．へSTM D 2938 （！995）：S’α11ゴα1『4 Tθ5’Mθ∫ノ∼04∫oノ『U1∼co1｛！『’∼e4 Co〃∼ρ∼（ぞ55’yθ 511ぞ∼19∫h ￠ブ1∼∼’θご’ 1∼oごん Co∼ぞ 5ρ（∼c1〃1θn5， ．へSτ！∼・1 Standard6）ASTM D3398（2000）＝∫襯伽・ゴτε5’Mθrhoゴ、戸01・／ノ1ゴαq〆 。499∼θ9α1θρθ∼’1’（ゾθ5ノ∼oρθ【∼’∼oF7ε』Yπ〃｝θ，、へSτ）》I Standard． factor increase wit益 col1負aing Pressure and7）ASTMD479i（1999｝：S∼α1∼ゴαノゼTθ5’A／θ’1∼oゴ∫01’F1α’Pα1一”（b1θ5， maximumparticlesize。 li）丁負e average rate ofbreak＆ge factor witll 五101∼9α副Pα航ゾθ5，01。F1醒αノz‘1五ノo刀9α’θ‘1PαノYic1θ∫加Co鷹θ cQn食n呈ng Pressure is higher for（lual−r圭ed rockf｝ll materiahhan that for a11uvial rock最11material． iii） The angles of shearing resistance for quarried rocknl至nlaterials are higher than those for a重luvi− al rock負ll materials with compar＆ble unconaned compressive stl’eng書h of rock particles． lv）Theangleofshearingresistanceforalluvi＆l ！1gg’ぞgα18，AST｝〉I Standard．8）ASTM D5821（1995）13’α1r‘1α1’ゴ7’θ5’、・》θ11∼04∫01・0θ’θ1・〃1加〃∼g〃∼θ Pθ’｝c8∼∼1α9（∼ oゾ」F1て∼c1ど’1署‘ノ ραノ7’c1θ5 111 Coα1写（∼。499ノ“‘∼9‘r∫θ， ．へST∼㌧I Standard，9） de卸1ello，V．F、B．（！977）：Re負ectio【｝ondes1gndecisionsof i）rac巨cal significance ｛o embankrllen［ dan】s， 17’1∼ Rα’1ん’1∼θ 五θc’μ∼θ， Gθo’εc／11瞭’θ，27（3），281−354．10）Franklin，」．A、andDusseaしElt，M、B、（王989）IRo欲五1∼911∼θθ∼”1∼8． McGraw−Hiil Publ三slliug Company，New York，237−269、11）Fro黛，R、」、（1973）：So〃1θ7θ∬’〃g五』vρθ∼・’θncθ5α1∼4Cノ∼αrθc1θ1へi∫”cs rock行ll materiαls lncreases with the maximum oゾβα’1ゴ8ヂー（31甲αvθ！F1〃∫11∼五απh∠）α〃1∫，刈STど∼イ1，SτP523＝207， particle size and opPosite trend is noted for quar−ま2） Fumaga目i，E．（1969）：Tests o騒 collesiollless materials for rockfill ried rock且ll materials． v） The angles of shearing resistance as we圭l as the rate of 圭11crease in angle of resistance ㍉v疑h maxlmum particle size incre＆se with the increase dams，／．3MF五，ASCE，95（SM1），313−332、王3） Hali，E，B and Gordon，B．B、（1963）：τr1ax1a1毛esting usiag large scale high r）ressure eq糠ゆment，〆iS7込／，STP36王，315−328、14）Hossain，氏・L S、，Parker，F．aud Kandha1，P、S、（2000）：Compar1son aΩdevaluatiolloftesζsfQrcoarseaggregate，湘S7M／、τθ5’，Evα1、， in the ullcon行ned conlpressive strengtぬ of t紅e JTEVA，28（2），77−87、 rockparticlesforallu、・ialrock且llmateri＆1s．15） 至S 2386： Part 4 （1963）： A／θ’hoゴ5 0Lブ 71θ5’ノ10r 、4gg1’θgα’ε∫ノlo〆 vi） The behaviour of rock行ll m＆terials，in general， 買玉ay be exp圭a玉ned呈n tel’ms of the uncompacte（i Conぐ〆αα Aグθc1∼σ刀1cα1 P1臼oρθ1’”ε5， Bureau of Indian Stalldard， India、16） L【ambe，丁 ∼V、alld∼V11貢man，R，V，（1969）：So11A／θぐ1∼α’11c5，3rd ed、， void content and ullcol1且ned conlpressive 、V疑ey EasterΩLtd．，New Delhi、 strength of the rock particle．17）Lowe， 」 ， （1964）： Shear strerlgt暴 of coarse embankment dam vii）Arelationshiphasbeendevelopedtopredictthe an黛le of s紅ear圭ng resista！1ce of mo（1eled rockhl正 m飢erials using the uncompacted vold coatent of materiais，P”of．8〃∼∫1∼∼．Co’∼9．五αrgθ五）α1115，3，745−761．18）Maracili，N、D．，GlanC、K、，Seed擁、B、andDuncan，J．養L（1969）： S〃’θ∼1g！11α’∼406∫01’〃1α”oηCソ1α照αθだZ5”c50ゾ9Roc姻”A1α∫（∼がαな， RePort No、TE69（5），C1vil Engineering Depar【nlent，University of 由e rock負ll materlals and ullcon伽ed compressive Ca墨ifornia，Berkeley，US、へ、 strength of the rock particles．It is believed that19）Marac撤，N、D．，Chal1，C，K．andSeed，R．B，（1972）：Eva！職io自of thls method is superior to the existing method properties of rock自ll materla垂s， 、ノ． 5A4F五， ASCE， 98 （S｝》11）． based on maximum size of particlesαnd may be used to predict theαngle of s封earing resistance of 95d玉4．20）Marsa1，R．」、（1965）l Discuss1on，Pノ・o（・、，6’h ICSAグ■E，3，310−316．，So〃21）Marsal，R．J、（1967）：Largescaleこestingofrock良Uma芝erials，ノ prototype size rockhll materials．It鼓as potential A4θc1∼、α’∼4Fα∼ノ∼ゴ五）’v．，ASC狂，93（2），27−43、 to beused fortheprediction oft紅e ang至eofshear−22）Ramam穏rこhy， T、 （200D： Sllear strength response of some geologicalmaterialsi田rlaxlalcompression，1n1．ノ．RocんMθご1∼、 iPg resistance for the des呈gn of rockfi至l dams． A伽’∼∼gSc、，38，683−697、23）Ramamurthy，T．and Gur）芝a，K，K （1986）：Response r）aper to熱owACKNOWLEDGEMEMST｝1e researc至l work∼vas pαrtly supPorted by Gr＆nt No． ougllt one【o determine soil parameters【o be used in the design of ear樋1and rock丘駐dams，P”oc，∫（｝C，2，15一三9．24） τねiers，G、R、and DQnovan，T．D、（1981）：Field densi｛y grada￡ion 58婆V、へR、へD、へR、へ」．へN ET．へL， 51∼eθrS〃マθ119’hρブεo’／，〆当S7ン》，STP740（eds、byR。N、Yo臼gandE ma芝eria！stmde湘ghsIresses，／、＆》π，滋SCE，94（SM3），661−688．28）Yosh1naka，R、a自dYamabe，τ、（i981）＝Astゴengthcri毛eriopofrocks C．To、mse自d），American Society of Tes［ing and Nlaterials， a厳（irockmasses，P／90ぐ．1’π．＄L”71ρ．馳αんRoぐた，Tokyo、 315−325．29｝You（i，丁、L．（1973）：Factorscomro目ingmaximし三ma臓dminimLml25）Varadarajan，A．，Sl｝arma，KG ，Venkatachalam．K、alldGし騨a， AK，（2003）：Tesii睦ga竃1dmodelhlgIworocknIlmaterials，ノ． deロsities ofsa！lds，Sρθc’α1τθclr111cσノP置’δ！’ぐσ’1011No．523， 0θo∼θclr。Gθoθ’1v．￡1∼91召．，ASCE，129（3），206−21830）Zeller，JandWulllma…1n，R．（1957）汀hesbearstre丘9dloftheshell26）Venkatachalam．K．σ993）：Prediction of mechallical behaviour of IllateriaIs for tbe GQ−Sche除e【｝alp Dam． SwiIzerlaad， PIPoc． 4 rock鼓11nlater1ais，Ph．0． r／1θ515，i1，τ Delh1， ∫CSA’1Fε．London，2．399−404、 and柔rlaxiai【est玉11gofiarge−sizerock角ll forlittlebluerundam，乙αZ）．27）Vesic，A Bandqough．G W、（1968）：Eehaviourofgranular 月1ηθ’ソcθη∫oぐ紐γ〆ひ1厚々5”ngo∫．、如θ1ソαな．98−122．
- ログイン
- タイトル
- An Investigation of Diffuse Failure Modes in Undrained Triaxial Tests on Loose Sand
- 著者
- J. Desrues・I.-O. Georgopoulos
- 出版
- soils and Foundations
- ページ
- 585〜594
- 発行
- 2006/10/15
- 文書ID
- 20942
- 内容
- rSOILS Ai¥'D FOUi¥TDATIOi¥TS Val 46. No^ISI )94 Oci '006Japanese Geo echnicai Societ}AN INVESTIGATION OF DIFFUSE FAILURE MODES IN UNDRAINEDTRIAXIAL TESTS ON LOOSE SANDJACQUES DESRUEsi) and loAN'i¥1'Is-OREsT s GFORGOPOULOsii)ABSTRACTIn this paper ve present an experimental study perf'ormed as an attempt to exhibit non-localized, diffuse failuredef'ormation modes in sand specimens submitted to test conditions leadlng to unstable failure. In particular, we areinterested in diffuse modes ¥vhich may appear in common triaxial compression tests on undralned loose sand specimens. A special series of triax'ial compression tests are repor'ted. These tests resemble the comman triaxial compressiontests but are modified in such a ¥vay that after the peak in the stress-strain curve, test control is changed from straincontrol to stress-control. More precisel_¥', a special kind of load-control is used, based on an original device ¥vhichallo¥vs to recover displacement-controi after a dynamic step in the post-peak regirne. It is sho¥vn that the control usedallo¥ "s f'or the obser¥*ation of the failure modes occurring in the unstable branch of the test.Kev lvords: difiuse failure, dynarnic instability, Iocalization, shear band, stress-strain controlled triaxial compressiontests (IGC.:D6/F6)Chambon ('-OOO) and others- have sho¥vn that shearINTRODUCTIONbanding can be predicted solely on the basis of the con-A proper description and understanding of failure institutive la¥v that describe the beha¥'iour of the material.g:eomaterials is a rnajor concern in natural hazardmitig:ation. Localized failure is kno¥vn to control aOn the other hand, other theoretical investigations-Dar¥'e et al. (2000), Nova (1994)- suggest that insome loading conditions, Ioss of stability can occur fornumber of catastrophic ruptures obsel'¥'ed in the field(among other references, "Failure" by Scott (i987), buteft ctive stress states far bef'ore the plastic failure stressthere are cases in ¥vhich rupture seems to concern all or alar*'e part of the volume of the material involved in thecondition or the shear banding: bif'urcation criterlon ismet, and lead to diffuse rather than localized failure.problem. In the laboratory, a number of experimentalGajo ('-OOO, 2004) in¥'estigated theoretically and experimentally the onset of the instability in saturated,loose sand samples and analyzed the infiuence of loadingsystem compliance on the instability under stress-con-studies, e.g. Vardoulakis et al. (1978, 1985), Drescher(198,_), Han (1991), di Prisco ('-OOO), Desrues et al. (1985,1989, 2004), Tatsuoka et al. (1986, 1990), Yoshidatrolled conditions. The tests ¥vere performed undeldrained conditions rather than undrained, but special(1994), Kato et al. ('_OO1), Arthur et al. (1977, 1982),Finno et al. (1995, 1996) and others, have shown thatstrain localization is obser¥'ed in a large range of testbands ar'e likely to occur even in lvell refined tests,including: slenderness reduction and careful end lubrication (Desrues, 1996, ,_004). In loose sand and elevatedmean effective stress, Iocalization can be delayed sig-loading paths ¥vere follo¥ved, starting from an anisotropicstate of stress (cl, p') with q de¥'iatoric stress and p' meaneffective stress. The loading paths in¥'ol¥'ed imposed increase of the pore pressure in order to reduce p' at constant cl, or other stress path control in¥'olving a decreaseof'p' as an intermediate phase in the test. These tests leadto catastrophic failure, or limited failure ¥vith a dynamicnificantly but it remains the final deformation mode(Desrues, 1989). Shear bands are observed also in un-strain jump, depending on the deviatoric loading systern(dead loads or pneumatic piston). This study shares somedrained tests, in vhich the deformation is constrained topoints vith the one discussed in the present paper, but thelatter ¥vas concerned more ¥vith the question of diffuse orlocalized failure. Vaid and Si¥'athayalan (2000) in a veryconditions for geomaterials. In dense sand specimenstested under lo¥ ' to moderate mean effective stress, shearan isochoric deformation mode due to the pore fluidtrapped in the specimen (Han, 1991), (Mokni, 1999).Theoretical studies in the frame vork of BifurcationTheory-Rice (1976), Vardoulakis (1995), Desrues andChambon (1989), Chambon et al. (2000), Desrues anddetailed study of the fundamental factors that affect theobserved liquefaction susceptibility of saturated sands,discuss among other factors the effect of loading tech-*' Direcleur de Recherche, CNRS-Universit6 de Grenoble. FrancePhD Student, Naiional Technicai University of Athens, Greece (IGeorgopoulosC,mechan ntua.gr)^The manuscript for this paper ¥vas received tor revie¥v on November 12, 2004; appro¥'ed on July 26, 2006_¥Vritten discussious on this paper shou d be submiited beforeTokyo I 12-001 1 , JapanUpon reques,Ia.v I , 2007 to the Japanese Geotechnical Society, 4-38-2, Sengoku, Bunk_vo-ku,the closing date may be ex ended one month.585 DFSRUES AND GEORGOPOULOS58(,+'r '//';/ 'rii:-" : "(d)i (e) r$1 s :'t'¥- ;Irt;[i.(e)iL 'x::tl'(a)(oF g. 1, General synopsis of the triaxia] installationniques on the apparatus-specimen interactions in monotonic liquefaction tests. The techniques studied includestrain-controlled, dead ¥veight, pneumatic piston andFig. 2.General vielv of the triaxial installationpneumatic piston plus a volume booster. Ho¥ve¥'er, no experimental information is gi¥'en about localiz,ed or non-localized nature of the deformation process during thebe adjusted in the range 0.0001-5.9999 mm/min. Theunstable deformation phase, neither in CJajo (2000, '_004)nor in Vaid and Si¥'athayalan ('_OOO). In fact, deforma-axial load is measured by a load celllring (c), Ivhosecapacity is - 30 kN. An L,¥IDT is used for measuring thetion modes can hardly be characterized experimentallysince they are supposed to occur along unstable loadingaxial deformation of the specimen and it is placed on thebranches for ¥vhich the brutal acceleration of the deformation process does not allolv to obser¥'e the transientdeformation modes of the specimen.top of the cell. The cell pressure is controlled by amechanical valve and the pore pressure by a mercury potsystem (e), ¥vhich allo¥vs at the same time for volumechange measurements during the drained phases of theIn the follo¥ving ¥ *e present a simple, prospecti¥'e,tests (consolidation). Both the cell pressure and the poreexperimental study performed as an attempt to observepressure are measured by pressure gauges. A11 themeasurements are recorded using a data acquisitioneither localized or non-10calized, diffuse failure deforma-tion modes in sand specimens submitted to tests conditions typically leading to unstable failure. A special testsystem under computer control (f).In order to achieve the special test control describeddevice is used to let the system jump into the dynamicmode after load peak, but only for a short whlle. Afterthat, displacement control is restored, allo¥ving for acharacterization of the kinematics the specimen under-above in section I , a slight modification ¥vas made to the¥¥'ent during the unstable, quasi instantaneous part of themainly stems from the necessity to be able to control thepath.stress and not the strain in a triaxial test, after the peak intriaxial apparatus. The modification consists of theinstallation of a spring bet¥veen the piston of the cell andthe load cell/ring. The purpose of such a modificationthe stress-strain cur¥'e in the softenln_"._ region. TheF,XPERIMENTAL SF,T-UPIn the follo¥ving, a short description of the triaxialapparatus used is given and the special device developeddescribed system consists of an elastic spring of A'* stiffness, vhich has a metal box on one of its ends. The metalbox is connected to the one end of the spring via a boltis described. Further information and details on theand a nut. The bolt is scre¥ved at one end of a piston. Thespring itself can freely slide along the piston, ¥vhich goesprocedure of triaxial testing for soils can be found in soilthrough the spring. What can prevent the spring frommechanics handbooks, e.g. Bishop and Henkel (1957), ormore recently Bardet (1997), Head (1992).sliding is a nut at the one end of the piston. A metal box isThe triaxial apparatus used is a basic strain-controlledaxisymmetric triaxial apparatus. Figures I and 2 sho¥v thethrough the spring up to the load cell/ring. At the sametime the box ¥vith the nut serves as a re ulator for themain features of the installation. It is made of t¥¥'opre-stress le¥'el of the elastic spring. This means that, bykeeping the other end of the spring fixed (i.e. scre¥ved atindependent components, namely (a) a loading frame50 kN in capacity, manufactured by Wykeham Farrance,including a frame and a motorized scre¥v jack controllin_"_.the displacement of the bottom platen of the system and(b) a home-made triaxial cell. The displacement rate canused to transfer the axial forces fr'om the specimenthe load cell) and by scre¥ving the nut at the other end,one can compress the spring at a desired level. This ¥villlatei' on prove out to be useful. Figure 3 shows a typica]vie¥v of the described system. A photo of this system is U+¥,DRAINED TRIAXIAL TESTS ON LOOSE SANDESpeeirn ro+ e+)/""I_*. t st5587--xSp ngFig. 5.Schematics of the specimen-spring s,stemr･.'IT¥+** *_'*/ o.esD_*oQ 4INSTABILITY CO_NDITION FOR 1'HE SPECIMENSPRI_NG SYSTEMe.;Let us consider the systern specimen-spring described*//*'i ;J: 2lE.l I ' '//"/*.s*.__J:; Ii 1; S s e242s.: 1' i[ ,j ¥'¥,. : r¥'in Fig.denotedpcnnt Adepends,o, . . .) = f'( xA, . . .)* '* : 2,*+r! * : o *r'*. oe1;2_Z--ee¥--'¥.f '; /' 'The force applied by the specirnen on polnt A isFs */A, and the force applied by the spring ondenoted as Fsp,;A. The response of the specimenthe history of xA, including the present state:Fs ./A = f (xA - . ( I )i ¥ "'-_'-',- ; f: / i'oi5.asrson+_..')4 .::j/with xo = O.The response of the sprlng is linear, ¥vith a constant stiffness K,:= - K,(xA - _¥"B)Frg. 3. Side vielv of ihe spring system.Assuming that the mass of the system is concentrated atpoint A, the fundamental equation of dynarnics reads:F ' F nls **iA+ sp,iA=.(3)Usm' Eqs. (1) and (2) in (3):f (xA, . . .) - K*( XA - xB) = lni!.Let us consider a given state ¥ *hich has been reachedfollo¥ving a quasistatic loading path. Up to this state, theacceleration A is zero.f(x ) K(x xB)=0 (4)The system becomes unstable as soon as a small perturbation of the system does not lead to small oscil}ations(which in practice ¥vill decay due to imperfections likefrictionai and/or ¥'iscous eft cts), but to increasing dis-placement (either oscillating or monotonous) from therest position x. . Addin*' a small incrementai displacementu* to x* in Eq. (3) ¥ve *'et:J'(x. , + uA,. . .) -K*(XA + uA -xB) = n7( iA T tiA) = miiA (5)Frg. 4. Metal box, nut, eiastie spring and load cel!Substracting Eq. (4) from (5) gives:f(x. +LlA,...)-j'(xA,...)-K*ualso gi¥'en in Fig. 4.The device works in the following way: as long as theload transmitted to the spring-box system is lower thanthe pre-stress level, nothing happens to the spring: thesystem behaves as a rigid block. As soon as the axial loadexceeds the pre-stress level, the sprin (' starts to compress,i.e, it stores additional elastic energy. When the instabil-ity condition for the sprin a-specimen system is reached-nlu (6)The expansion of f(xA + uA,. . .) is a difficult task, as soonas non-elastic behavior is considered, due to the strongnon-1inearity of the constitutive equation. The study ofthe stabillty of an equilibrlum state can be restricted tothe beginnin*' of the rno¥'ement after a perturbation ofthe equilibrium, ¥vith a discussion of the different cases¥vith respect to loading and unloading.this condition is discussed in detaii in section 3, the sys-As illustrated in Fig. 6, in the general case (not elastic),tem jumps into a dynamic mode and the spring releasesthe energy stored by stretching back. Ho¥vever, the boxthe specimen has t¥vo possible responses. Depending onthe sign of the incremental stretch undergone, ¥vithrespect to the state, ¥¥'e have loading for continueddeformation process, and unloading for reverse deforrna-does not allow more energy release than the amountstored after the pre-stress level ¥vas over passed. So thedynamic part of the test is limited in ter'ms of specimendeformation, depending on the pre-stress level.tion.Considering that the present equilibrium state is a DESRUES AND GEORGOPOULOS588, +*,oAxFspe!AthenAe /T7; i:(,A)/"" ' Be /r ･ TT 7(A A)/"'!=A+Band using Eq. (8) for t=0 ¥ve get:A + B = t/ok l03din9/r- ' -peak._On the other hand, using It=0 for t O l eselastic. / Io{din*' ¥¥^kunioadin9e.kt' = /･i -[Ae'=/T- ;TTrBe ;:,i (K= A1 },"""I. elsstie= 1 /Y [A Bl Ok Unloading5ticelastic'/*-(XA-Xo)then A -B=0These conditions on A and B can be met with A = B=u0/2, then we have from Eq. (8):Fig. 6. Force-stretch characteristics of the specimen, vith loadingunioading branches in pre-peak and post-peak regimeu=.uo[ei /77;TT7;;7(A A )/"'tTe (9)compression state, the initial phase of later mo¥'ementIt is time no¥v to discuss the respective values of thetangent stlffness of the specimen K* and the stiffness ofthe spring K*. If the specimen exhibits a characteristicioad-stretch response ¥vlth a peak follo¥ved by a decrease¥vill be either loading, Ivhich corr'esponds to negative uA,or unloading, ¥vhich corresponds to positive uA. Depending on the sign of uA, the load increment corresponding toa small incremental displacement uA ¥vill read:f(xA + uA) -f (x. ) = - K:u,uA<,O Ioadingu, >0 unloadinf(x, +LlA)-f(xA)= -A'**uvith A': the tangent stiffness of the specimen for loadingand K:' the tangent stiffness of the specimen for unload-/Tx-xiTT';;(A -K,)/"'!]in the load like in Fig. 6, then one has to distinguish prepeak from post-peak states, and in both of them loadin_'_.from unloading (in the sense defined above).Before Peak: u<0 Ioadmg Ke=K:>. O (a)u>0 unloadin a A'* K**>0 (b)After Peak' u<0 Ioading K K <0 (c)u>0 unloading A'. K**>0 (d)mg.The equation for tlA (denoted u for concision) durin_"._the initial phase of the movement is then:mu J- ( KK*)u = O (7)¥vith A'*=K: or K:' dependin_g: on the sign of u.In cases (a), (b), (d), ¥ve have K*A',> O. Then the squareroot / ,T 77; is real and the general solution Eq. (9)of the differential equation involves only imaginary expo-nents. We have:u = uo cos (l¥/･ t)Classically the solution of this differential equation islooked for in the form:u = e ""'then ii= - O)2u and Eq. (7) becomes:(A' +K co2)u=0and for non-z,ero u:¥vhich is an oscillatin_g: movement, indicating that perturbations do not _g:row. The equilibrium is stable. Ho¥ve¥'er,in case (c), K:+K* can be negative if: K:<, -A'* ¥vhichmeans that the tangent stiffness of the specimen is nega-tive, Ivith a modulus higher than the stiffness of thesprin c'. ThenK K co2=0The t¥vo roots of the equation (possibly complex) are:/K* + K*co = +_ ,'/" ln/Y /r.T T l. /llK: A',!l/¥ //71/ I - n7-" """ - l. --and Eq. (9) becomes:u = uo /2 [e'rr T7 ? t + e'/K;-K, !"' tJ( I O)u=Ae"!{K.+f() ,,,t Be '/?rTT7 ,(,( A) ,,,, (8)in ¥vhich the second term gro¥vs exponentially ¥vith time,¥vhile the first decays exponentially. Neglecting the firstone ¥ve have:L,et us assume that the initial conditions (arbitrary pertur-u=uo/- e'/ A']. A "'i (11)and the general solution of the Eq. (7) is:bation applied) are: for t=0, u=uo and tt=0. For t=0¥ve have:e'/{A:.-A),,,r e "(A 'i)"'!/ =1We can conclude that a sufficient condition for instabilityof the system is:K..< -K* (1_7) fUNDRAINED TRIAXIAL TESTS ON LOOSE SAND589is, up to a certain level, and by keeping the other end ofthe spring firmly scre¥ved at the load cell. By this setout,Consolidated undrained tr axi21 oompression test (Hostun Sss]¥ve predefine the initial pre-stress level force of the sprin'_.This means, in other¥'ords, that the spr'in*' Ivill be pre-stressed up to a certain point f'rom the very first beginningof the test, ¥vhich ¥vill allolv us later on to investigatevarious cases of difitlse modes of' failure.Let us no¥v follo¥v ¥vhat happens if the spring is pre-<compressed. In the beginning of the undrained triaxialcompression test and up to the point ¥vhere the axial loadAxjal deformitiorl 'is less than the pre-stress f'orce level, the spring ¥vill not be,Tlmjadditionaily compressed.Fig. 7. Specimen's force-displacement curve for loose Hostun sand S:sUp to no¥v, the test itself resembles the comrnonundrained triaxial compresslon test. As soon as the axialforce is passed, this means that ¥ve have exceeded theSpring Stlffness' Se!ectionOne major point that is ¥vorth mentioning is the selec-tion of the elastic spring. The main purpose of thisexperimental investigation is to be able to be st.ress-con-pre-stress force level, the spring ¥vill start get compressedfrom its initiai state.At the peak in the load-displacement cur¥'e, K*=0 andthe instability condition K,< -K is not met immediatelytr'olled af'ter the peak, in the stress-strain curve of the soil(and cannot have been met before). After passing thespecimen, in a strain-controlled test. In order to achievethis, ¥ve ha¥'e to choose a spring ¥vith stiffness matchingEq. (1 '_), ¥vhich can be reformulated as: K* < - K keepingpeak in the stress-strain cur¥'e, K* becomes negati¥'e, ¥vithin mind that K* is the slope of the load-displacementcurve of the specimen in its softening branch, i.e.essentially a negative quantity, vhile the rigidity of thespring K; is essentially a positi¥'e one. This value of K* isassumed to go¥'em the post-peak behavior of the specimen considered as a ¥vhole, in its softening branch, aslong as the test remains non-dynamic (negligibleacceleration, Iow strain rate). Indeed, ¥vhatever thedeformation of the specimen is, diffuse or localized, itspost-peak axial force-displacernent characteristics can becharacterized by a K* value for' the specimen consideredas a structure. We discuss the behavior of the systemspring-specimen vith r'espect to the rat.io of Kand K .an increasing absolute value llK*:1. If the spring has beenproper'ly selected (proper stiffness K*), Iater or sooner thecondition will be met. Then the system specimen-sprin_ ,_vill start accelerating. The axial load continues todecrease and the spring to extend. However, ¥vhen theinitial pre-stress force is reached on this load-decreasin_",_branch, the system of the metal box-bolt-nut pre¥'ents thespring from fully extending to its original length. Fromthis point, the specimen will not r'eceive any more energyfrom the spring. Depending on the conditions, the systemmay or may not return to a strain-controlled behavior.Indeed, although a part of the potential (elastic) energytransrnitted to the system during the dynamic jump hasbeen dissipated in plastic deformation, another part hasbeen conver'ted to kinetic energy. This part has to beTo determine the relevant stiffness, we performed adissipated by plastic deformation also, before thestrain-controlled undr'ained triaxial compression tests onloose Hostun S28 sand. The steepest (negative) post-peakmovement stops. Thus, depending on the pre-load level,the specimen may be completely destroyed in the subse-inclination of the curve in the axial force-deformationquent rnovement, or recover some ri*･idity after thedynamic step-accelerating then decelerating phases.In the belo¥v experimental analysis, an attempt toexplore the various modes of failure is given, and thediagram ¥vas found to be K*= - 1.782 kN/mm (seeFig. 7). Thus, in order to fulfill inequality 12 sooner orlater after the peak, the stiffness of the elastic springvhich ¥vas selected, ¥vas smaller than K* (K,= 0.257 kN/rnm) .effect of the pre-stress force level to the failure mode isdiscussed.The smaller the stiffness of the spring, the sooner ¥villcome the dynamic jump after the peak. Ideal load control(dead load) is equivalent to a spring ¥vith vanishin_g:EXPERIMENTAL RESULTSstiffness. In this case the instability ¥vould occur just atTesting P/'ogi'canpeak load, but practical difficulties ¥vould result frornA series of five undrained triaxial compression tests¥vas performed in order to investigate the aforementionedextrernely lar_ :e -¥'irtually infinite indeed- deformat.ionof the spring.P/'e-st/'es's Level Se!ectionBy using the aforementioned system of the metal boxbolt-nut at the one end of the spring, we can control theelastic energy that ¥vill be given to the specimen in thesoftening region. This is easily accornplished by scre¥vingthe nut at the one end of the sprin_g:, where t.he metal boxdiffuse modes of failure. Loose specimens prepared bymoist tamping technique (50/0 Ivater content) fromHostun sand S28 were subjected to undrained triaxialcompression. According to previous ¥vork done by Hanand Vardoulakis (1991), the preparation of sand specimens vith the moist tarnping technique inevitable leads toa stratificarion of the sand specimen. X-ray tomographieshave clearly shown the existence of such layers inside the DFSRUES AND GEORCOPOULOS590Table l. U ldrained triax. ial compression tests in Hostun sand S2sDeformatioF}Void Relal 've SaturarionNo. Porosit}degreeratio denstest e [ -] n [ I Dr [CUSPROI053CUSPR02 1 .OS9C_ USPR03 1 . i 22CUSPR04 1 . 1 2 lCUSPR05 1 .40O 513O.52iO.529O.528O^533_ _ rate.t¥'] S. [ . ]- 4.999 499- 25_o- 24. 5599,699,699 7[mm/min]2.02 OVar'ious ratesl .OTable 2.No testUntirained triaxial conlpressionh,10bilized frictionangle ctests inPre -stressC_USPROlC_USPR02)_3 5040016_2e850CUSPR03CUSPR049 3e9.7e16.308 S o.t)C_USPR059 8 o,/o96 'ble¥*elHostun sand S'sTolalliquefaclionNOYESNONONOlOspecimen. It is quite possible that the tested specimenspossess some degree of orthotropy, but according to theresults obtained from biaxial tests this stratification doesnot seem to infiuence the geometric characteristics offailure modes in a significant manner. lvforeover, accord-ing to Han and Vardoulakis (1991), the observed shearband thickness does not seem to be related to the thickness of the layers. The ratio of height to diameter of thespecimen ¥vas kept constant for all tests (H/D= l, D=100.0 mm). Enlarged lubricated end platens ¥vere usedboth in top cap and pedestal. The application of the axialload lvas achieved through a loading r'am, ¥vhich cameinto contact with the top cap of the specimen through asphere, in order to avoid the de¥'elopment of bendin_"._moments to the specimen. Elastic membranes of 0.40 mmof direct observation. The specimen ¥vas obser¥'ed andphotographed through the pressure cell during the test,but the last observation and photo*"raph was done aftercell removing. In case of ¥vell-developed shear band(s)reachin*' the outer boundary, the lines of the grid ¥vouldhave been distorted in the ¥vell-kno¥vn figure illustratedby biaxial tests available in the literature (e.g. Desrueset al., 198_ , 1989, 2004; Vardoulakis et al., 1978, 1985;Tatsuoka et al., 1986, 1990). This of course is not enoughto guarantee that no localization took place inside thespecimen, since inner localized deformation modes mayexist, as sho¥¥'n by Desrues et al. (1996) using X-raytomography, and confirmed later by Alshibly et al.(2003) .R esu!tsthickness and 100.00 mm in diameter ¥vere used. AnAs already mentioned a series of five undrained triaxialestimate of the minimum and maximum ¥'oid r'atio for theHostun S2s sand has been previously given b_v Combecompression tests on loose Hostun sand S2s ¥vere performed in order to verify the modes of failure In the(1998) (e f*'=0 689 e = I 036). The "rain solid densitysoftening re*'ion. The effect of the pre-stress force level ofp* is '-.65 gr/cm3. The ¥'alues of porosity n and void r'atiothe spring to the total loss of the specimens' resistance iscritically investigated. For this reason, fi¥'e sand specimens ¥vere tested in undrained triaxial compression test,each one at a different pre-stress force level of axial force. , ",** . >e in Table I of the five specimens are calculated after theisotropic consolidation. A11 specimens ¥vere fully saturated (degree of saturation S,=99.4 99.70/0) and ¥vereisotropically consolidated up to p' =800 kPa, under aback pressure equal to u = 50 kPa. The confining pressure¥¥'as kept constant during the test, equal to (7.= 850 kPa.Table I summariz,es the five undrained triaxial compression tests. As far as strain rates are concerned, it shouldbe stressed that, as soon as the pre-stress le¥'el selected isreached, the spring starts takin*' a part of the overalldeformation rate imposed to the specimen-spring system;consequently the strain rate is reduced at this point, andthe strain rate reduction lvith respect to the overall defor-of the spring system. In this ¥vay we are able to controlthe ener*'y given to the sand specimen after the peak inthe softening: reg:ion.Table 2 summarizes the results of the triaxial tests. InTable 2 the first column is the No. of the test. The secondcolumn is the mobilized friction angle c in degrees, ¥vhilethe third sho¥vs the ratio in percenta*'e of the pre-stressforce level of the spring to the maximum axial forcemeasured durin_g: the test. If this percentage is equal tozero, this means that the spring is not at all pre-stressed,mation rate is depending on the currem tangent stiffnessof the specimen. Consequently, since the stiffness of thespecimen is monotonously decreasing along the test, thewhile a value of 1000/0 or more means that the springstrain rate reduction is maximum lvhen the pre-stresslevel is first reached, and decreases continuously fromthe spring. Finally, in the last column, ¥ve indicate¥ 'hether or not the sand specimen lost completely itsthis point. The reduction vanishes at the peak stress, andbecomes negative as the axial load start decreasing; i.e^the strain rate increases after the peak, due to the exten-resistance, meanin_ :, ¥¥*hether itsion of the sprin_._". h is easy to sho¥v that the strain rateremained soiid after the dynamic deforuation phase,becomes infinite when the criterion for a dynamic jump ismet. As far as strain field monitoring is concerned, onlyjump. Only one test, namely CUSPR-02, ¥vas completelyactually does not compress itself during the test, as theaxial force can not go beyond the pre-stress force level of¥'as fully liquefied or not.Figure 8 presents the shape of the five specimens in t,hefinal state. In four among the five tests, the specimensretainin*' the geometry of the final state after the dynamicdirect naked-eye observation and photography of thedestroyed by the deformation under¥vent during theouter surface of the cylindrical specimen ¥1*as performed.jump. The experimental pro*"ram ¥vas conducted in theHo¥vever, a grid vas dra¥vn on the membrane beforefollo¥ving lvay: first confirm that the over-pre-stressedspecimen preparation, in order to improve the efficiencyspring does not play any role (test CUSPR-Ol). Then･l r. ;U 'DRA NED TRIAXIAL TESTSOiNLOOSE SAND591Canso!idated Undrained Triaxiai CorTlpression Test (H0Stun Sia)sOl[:3'*o'iflff]¥.r2 0¥J: evs ?ol-h evs Fe2-x-eus R 03* evs pR (>4-{r- evspn e52ee/' -' '1 ;D,:ruspR-031 OO/5e,oo o I D O e20eee o eosAxia*= I,o O oo 025o ol 5strain sl [**#'*:i'"'** *F'ia. 9. Deviatoric stress versus axial slrain response for all fivespecimensConso idated Undra ned Tr axiai Cofnpres$ion Test {Hostun Sis)Fig. 8. Final configuration of the difrerent specimens: The specimenwithout label on tl]e photograph is tes CUSPR-024, [;*"o* -j3 e¥'alidate the ef iciency of the spring in promoting a jumpin the dynamic regime as soon as the theoretical conditionin Eq. (12) is met (test CUSPR-02) Then find empiricallythe threshold in the pre-stress force to apply to the springbefore testing, in order to avoid the complete destruction2se rlimit the amount of energy relaxed by the spring in thespecimen after the start of the dynamic jump. The finalshape of the specimens in the tests CUSPR-03, CUSPR04 and CUSPR-05, illustrated in Fi_"_.. 8, sho¥v that thiscondition could be met ¥vith pre-stress force above 88010CVSFR G102-; -cvspR03 'e- euspp' e45'=_I ; F :･ "' ': )_ ehll:1't 4 ETlo'4i'2 ' j; ; ,2 ! :' f : J.._l/'lIso - :l't'Ieo i + ,' I'o 1o ilt/1/ : i::-cuspp'e5 '2 ) tl'1 L{1 9s s't}/ :;e-- -- -of the specimen after the dynamic jump. In fact, asexplained in section '_, pre-stressing the spring allo¥vs to=- ---- cvsp_-so1!ee2$4 es 07Msan erteetivo prQs5t,ro p'Fio. lO. Deviatoric stress versusspecimensmean*eekPajeffective stress for all fiYeof the peak load of the tes . This exact value is notconsidered of particular significance. Indeed, both thepeak bef'ore the jump seem to be controlled by thevariability of the specimen preparation and the uncertain-responsible for the ¥'ariability of these features.ty on the exact behaviour of the spring-box system nearIn the same way, q versus p' curves sho ¥'n in Fig. 10indicate that, except in test CUSPROl, all the tests jumpthe pre-stress load, due to imperfections in the rather sirn-ple mounting of the experimental device, are responsibleof not really well controlled experimental response of thesystem as the axial load approaches the pre-stressed loadof the spring. Ho vever, the objective of the set of tests isfulfilled ¥vith the demonstration of the possibility (i) totri_ :ger a dynamic jump in the post-peak part of the testand (ii) to control it to recover a def'ormed but still solidconfigui'ation of the specimen after the jump.pre-stress level. In fact, the imperfections in the tests areat some point after the peak, directly to the near-liquefiedstate ¥vith ¥'anishing de¥'iatoric stress and near-vanishingmean effective stress. The scatter in the curves is large,and it can be seen that the initial stage of the deviatoricloading, represented here by the gray triangle, is veryconfused. This is attributed to the fact that the isotropicIn the follo¥ving, the stress-strain response of thecompression of the ¥'ery loose sand deposit obtained bymoist tamping is unstable and induces large fluctuationsin the undrained pore pressure at the beginning of thedifferent tests are discussed in detail. Figure 9 presents thedeviatoric loading. Even at larger de¥'iatoric stress ievel,deviatoric stress versus axial strain curves for the fi¥'ee.g. test CUSPR03 and CUSPR05 sho¥v sudden decreasestests. As mentioned above, due to the extra mechanicallinks introduced in the loading system by the springof the mean efi ctive stress p', not leading to the specimen collapse ho¥vever since the deviatoric stress startsincreasing again after a ¥vhile.Hence, all t.he tests did lead to more or less completeliquefaction. Figure 1 1 shows that in all the cases, poredevice, some scatter appears in the cur¥'es. Ho¥ve¥'er, aslong as the peak in the stress-strain curve is not reached,all curves are limited betlveen t¥vo straight lines, as in theFig. 9. Past the peak, the curves diverge each fromothers. In test CUSPRO1, a progressive decay of themobilised de¥'iatoric stress with increasing axial strain isobserved. In all other tests, a brutal drop occurs. Thisdrop corresponds to the spring suddenly uncompressing.Ho vever, neither the peak load nor the delay after thepr'essur'e becornes almost equal to the cell pressure,indicating near complete loss of mechanical strength ofthe material of the specimen. In this figure, the porepressure is plotted against strain of the specimen, ¥vhichallo¥vs to see the different phases of the test. In only onetest (CUSPR-O'_), the loss of mechanical strength is 1DESRUES AN TD592GEORGOPOULOSConsafidated Undr ined Triaxia Compression Test (Hostun S2a)DISCUSSIONlesc- .- ?･ -QeThe above ¥vork ¥vas performed in order to in¥'estigate, r r-f- tl :-Fthe modes of failure in geomaterials in undrainec.i' 7ce-Eee-see-s see- aD,c-br,/::compression tests on very loose specimens of Hostun S xsand. No strain localiz,ation could be observed in any of"_ _ _ _ev$1- - c ;E: p. 02{xevs i:2c lY -- r'clseTe- -- evsFco *ss= eL;c3ses- s 0 ;;oe r.",e e o o o ois o c20 o eico e2so oe5Axial 5S･ain sl -]Fio*. 11. Evolution of specimen's pore pressure ngainst total axialdeformationthe five specimens tested, so tlley are consic!e/'ed 1lavin*(ullcle/1gaone dlffuse nlodes offai!Lli'e. It should ne¥'ertheless be mentioned that in triaxial tests on loose, contract-ing sand specimens, it is usually difficult to decide1¥'hether a mode of failure is diffused or localized. Usin :X-Ray Computed Tomography on sand specimens testec.iin drained conditions, Desrues et al. (1996) have sholvnthat complex strain localization patterns can be hidden tothe naked eye observation of the outer membrane of thespecimens. Thus a more extensive triaxial program istotal since the pore pressure reaches the cell pressure.needed so as to ¥'erify and in¥'estigate the deformation ofHo¥vever, the difference bet¥veen the recorded cellthe specimen around the q peak. Whether or not shearbands occur in tests in loose specimens, drained orpressure and pore pressure may not be the most rele¥'antcriterion to decide bet¥veen total and near-liquefaction;indeed, ¥vhen approaching liquefaction, the differencebecomes small vith respect to both pressures so it may beaffected by small instrumental discrepancies like e.g. zerodrift of the pressure cells. For example, in a preliminarypublication (Ser¥'ant, 2004), test CUSPR-03 ¥vas quotedas totally liquefied, but re-evaluating the data for thedifferent tests, the authors consider that the most relevantundrained, in biaxial or a.¥'is.vmmetric triaxial or even Intrue triaxial tests, has been addressed by quite a fe¥vauthors in the past, ¥vith contradictory results in fact.Lade et al. (1988) concluded that instabilitycharacterlzed by a runoff of stress-carrying capacity ofthe specimen-can occur in saturated loose sand prior toattaining the failure stress state, ¥vithout formation ofshear bands. Chu et al. (1993), perfomling tests vithliquefaction in the present case is more the final shape ofstrain-path testing i,e. controlling the ¥*oiumetric versusaxial strain increment in axisymmetric tria.¥'ial tests reportthe specimens.runa¥vay instability occurring in an number of cases andIn fact, the essential difference bet¥veen the differentcases is shown in Fig. 8 ¥vhich presents the shape of thefive specimens in the final state. In four arnong the fiveindicate that in a!! il7stabi!ity tests, fOl･n7ation of sheai-indicator of tota! Iiquefaction ¥vith respect to /7ear-tests, the specimens remained solid after the unstabledeformation phase, retaining the geometry of the finalstate ¥vhen the testing machine ¥vas stopped. Onl.v onetest, namely CUSPR-02, ¥ 'as totally destroyed by theba/7ds c/id llot occu/'. Han and Vardoulakis (1991) sho¥vthat in undrained displacement-controlled biaxial tests onloose sand specimens no loca!ization tt*as obse/-ved, vhilefor load controlled tests and for large strains the c!efornlatiol7 Ioca!izes inside !he /'apid!_}, c! fol'n7ing zol7e. Katoet al., in a study of undrained shear characteristics ofdeformation under¥vent during the dynamic jump, andsaturated sand under anisotl opic compression, usingcould not even be dismounted from the testing cell. Thisis ¥vhat happens In common load-controlled tests alon'_sands from contractive to dilati¥'e, r'eport that at 300laa;(:'ia! strain, though shear bands It'as not obsei'vec! illunstable loading paths: nothing can be said about theactual deformation process during the initiation of thesa/77p!es, tllere seenl to be non-hoi710gelleities ill tl7e straincatastrophic fio¥v, because the only observable state issa/7lp!e. As for axisymmetric triaxial tests, De Gennaro etal. ('_004), in a study of the infiuence of loading path oncompletel"¥' distorted.c!istribution due nlain! y to ,fl'iction at botll enc!s of tl7eV rhat can be said from the observations illustrated bythe undrained behavior of a medium loose sand, reportphotographs presented in Fi**. 8 is that the specimensundrained triaxial compression and extension tests, bothCUSPR-Ol, CUSPR-03, CUSPR-04, and CUSPR-05strain-controlled and load-controlled, vithout anyapparent necking or strain localization. Conversely,lvlokni and Desrues (1999), in undrained displacememseem to ha¥*e undergone a diffuse mode of plastic defor-mation during the dynamic step, ¥vithout any obviousstrain localizations (shear bands or localized zones).Nothing can be said from the photograph of specimenCUSPR-02, but there is no reason ¥vhy the behaviour ofcontrolled biaxial tests, did obser¥*e localization in loosethese specimen lvould have been different in the initialand very loose sand, occurring lvhen the stress sTatereaches the line of maximum mobilized friction determined from drained tests on the same sand. Finno er al.sta*'e of the dynamic failure. Indeed the difference in thefinal shape bet¥veen this test and the others is that the(1996) in displacement-controlled undrained biaxial testson loose sand observed localization also; they state thatamount of energy delivered by the spring in test CUSPR-t/7e stl'ess state tvllen t/1e !ocedi atioll begins is vely closeO'_ ¥vas larger, due to the lo¥v pre-stress force used in thisto, yet precedes that col'/'esponcling to !17e /7la; :'inlum/770bi/ized friction. In the early stages of the tests, theyspecific case.described non persistent shear bands. Finally, for load- 593UNDR．へ亙N狂D TR更．へXI．へL T狂STS ON LOOS狂S．へNDcolltrolledulldraiaed【es｛，tllePresents葛udycollcludes芝〇三1011−localizedfai沁rlewl｝且eHanalldVa1’doulakls（1991）reportedlocalizatiorloccurrillgadargestraia。Fromthesedi働rellts芝udiesandprobablyafewo出ernotcltedlluhis brief ove王』、4ew，it apPearls thanloαgreeme飢lsAC藝《残▼OWL猛》G覧餌’狸鋸τIS 丁姦e audlors would韮ike to acknowledge the EU project五）θ9ノ＾σ‘／σ1io’∼ α114 11∼5F！αわ11々i（95「 ill G（∼011∼α∼θ々σZ5 w々ノ1、！4ρρ1’ω1io11’o H砿σ1’ごA4’／1g鷹ノ01∼（DIGA）iR the frame．work ofτhe Humaa Pαe厳ial P1’ogram，Research Train−foundon出epresenceorabsenceofstrainlocalizado王1in由etestsdesqlibedi王1volvingloosesandspeclmells． ingNetworks（｝｛PRN−CT−2002−00220）。However，it should be Roted that the st旦dies re至）ortiRg noloca至ization（lnduding t韮1e present one）were pel』formedwithout any specia1 π1easurlng efモort ξo char＆cterizes芝rain負eld taking place、vitl≧ia由e specimens；the state−ment of absence of evidence of locε盛izatio自was foundedon simple，direct naked−eye observation of the outersurfaceofthespecimens．Conversely，漁esmdiesco11−cluding to由e preseace of shear bands ln tl康e speclmenswere using advanced measurlng methods，Ilke X−ray pho一こograplまy（｝｛an and V＆rdou1＆kis）or stereophotogram−111etry（で〉lo裟ni arld Desrues，Fillno et al．）．Consequendy，鼠EF￡R配銅〒c氾s里）．組shibli，K、A、，Badste，S，N、andS【ure，S、F、（2003）＝S正rainlocali− z撮ion iasand：Pla【1esζrai【｝versus【rlaxialcompressloll，ノ．G（∼01θc！r， 五ηg’2、，、へSC狂．129（6），483−494、2）、へrthし【r，」、R．F、a【1d DunsζaΩ，丁、（1982）：Rupturelayersiagrar1目la重・ media，／U7．4AICo／1／1∠）4、Fα〃、θノー‘〃∼、．、1θ‘1’α，（eds、byVem僕eer． P、．A and Luger，H、」、），Baikeala，453−459、3）．へrしhur，J，R．F、、Dunstan．τ、，．へ1一．氏lli，Q、．へ，J，L、and．へssa磁，．へ． （1977）l Plasζic delomlatiQII and faHure in gral湘lar media， ααθc111∼蜘θ，27，53−74．4）Bardet，J P、（1997｝：εApθ1『’〃∼θ1∼’α1So’1・、1θごノ1‘’ノ∼’（5．Prelltice Hall、the conclusioas dτawn from the la貰er can be conside王・ed5）Bishop，、へ、W、and｝｛enkel，D、」．（1957）：7ノ尼A／θα5ど’1うθ111θnでoゾ∫α1tohavestl’ongerlfoundations． P1’oρθノー1嬬’11’hθ7ノ”α．v’α1rθ5∼．狂dward．叛moldL［d、6）C無ambon，R、，CrQchepeyre，S、a正1d Desmes，∫、（2000）l Loca巨za− doncri｛erialQrllQI1巨薯1earcons［i｛utiveequatioΩsQfgeoma芝erials．CONTCLUSION ∠、1θぐhCo1∼，ヂノ”ぐ’，．、如．，5，61−82、 A！1experimel宜al smdy was pelqformed，uslllg an origi一 soils under Stra1n∫〕a［h【eStin9、ノ、G〔∼01θぐh、オシ∼9ノ習、，．叛S（二⊃E，玉19（5）．王1alsimplemechanicaldevice，Ioilwestigatethemodesoffailure along unstable Ioading Paths III ulldr＆illed室ri＆xialcomやressiOmests． Tllecollcep芝ofasprll19−boxdeviceprove（hobesuc−cessfuhn t｝lat lt aUowed for recordillg specinlen deforrrla−tionevenalongullstable，dynamlcalp袖s．lndeed，wewereable芝operfor簸1actualuustable（leformationincre−Inents呈n the unload圭n黛bral・1ch of芝he箸est in undrεtinedllquefyhlgspecimel主s，stillkeepirlgtllepossibilitytoobserve tlle k呈nemat玉cs of the specinlen during theseinCrements． As far as the kirlema亘cs chal’acterizatio鶏is concemed，a烈且vesandspeclmensapParentlyu茱1derwentdi仔usemodes of failure and no s甘aln localizatioa、vas observedwlthnakedeye．ltshouldneverthelessbementionedth飢量n a t婁i＆xial test it is usua墨ly di伍cult to dec玉de whether amode of fallure is digused or localized．One ofthe malordenc猛ofthe triaxial test，＆s far as the characte1’izatioII ofthe mode ofdeformatioll is concemed，is the fact that theobservat玉on of the specimen during and afterξhe test isllmited to its o臓er boundary．Previous studies，uslngadvanced full岨eld meαsurillg teclmiques1汰e X−raytomography（Desrues et aL，1996），11ave shown thatフ）Chu，」、．Lo，S、一C、R、alldLee，1，K．（i993）：lnsこab11iこyof『grallu1＆r 874−8928）Combe，A．｛、（19981：Coml）or〔eIIlemdusabled『90stuI∬二sau triaxiaiax1sym6【rique．ComparaisonaveclesabledラHos硫mRF． ノ∼αρρo／Y‘！θ51α9θ，Universi【y Joseph FOur1er、9｝Darve．F andLaouafa，F、（2000）；Insしabllldesi【｝graaularmaterlais alld ap【）蕪cadoll tQ landslides．．、∫θch、Coノ∼，」Frlc’、、、／σ1、．5，627−652．10）DeGe【marQ，V、，Canou．、1、．Dupla，J．CalldBenahmed，N． （2004）：hl自ueace ot IQadiIlg Path QΩtlle ulldra1lled bellaviour of a mediumloosesallcl，c研、Gθorθc／1．／．．41，166−180、I D Desrues、」．and ChambQn，R （1989）：She訊r ba【圭d analysis for grall目lar nlateriais＝ ほ｝e ques［ion oゼ incl’enlenτal Ilon lilleari［y． ／ノ∼9θ’1’8三〃㌧鍾1℃1∼’y．，59，187週96、12） ￡）esrues、J，and ChamboI1．R、（2000）：Shear band allaiysis alld shear modulicalibration，／’1！、ノ、501’455∼η’（・1、．39，13−14，3757−3776、13） Desl’ues，」、and Hanlnlad，∼V （里989）＝Shear bancling del）endellcy oll nlean s芝ress level ill sand，P1＾o（一、21∼4／1π、耳Fo16た31∼oρ01r五〇cα1Z5‘∼一 ”o〃 αノ1‘ノ θヴセ〃ヤα！”01∼， Gdallsk、 57−68 （eds、 by Dembicki， E，， Gudehus，G and Sikora，Z、），Techn、U【11v，Gdansk、i4） Desrues，」、and V199ia【li．G、（2004）：Strain localiza【ion ill salld：an overvlew Qf the exぎ）erinlenこal resu1芝s ob【ailled in Grellob！e 目si自g SleI’eOPhoしogran㌶11elry，1η’、ノ．八「疋！〃∼ ’i1∼α’．A4θ’1∼、Gε01ηθ（・ノ∼‘7n’（5， 28（4）．279−321、15）Desrues，J，Lanier．」、andSωtz，P（1985）：Localizationofthe deforma［ionimestsollsalldsampie、E’∼91gFノ’αc1、．、／θ（レノ∼、，21， 909−921、16）Desrues J，Ch＆mboほ，R、，Mok【雀i，M aIld Mazerolle，F．（1996）： Void rat1o evok耗ioII i籍side shear baIlds in tri＆xial sal1〔I specinlensstrainlocalizationcallremal曲iddentothe！1akedeyein studiedbycomPu芝edtQmograplly，0σ01θぐ1r1瞭昭，46（3）、529−546、17）diPriscQC、．正mposimato．S．andVar（loulakis，1、（2000）：Medlal1レsu由test conditions，An interesting directio王l to extend cal n｝odeling Qf drailled creep triaxia1【es【s on loQse sand，Gゴo∼θぐ1∼一山isstudyistoperformblaxialcompressio厭ests，w良erethe霧10des of fai互ure are easier c紅ar＆cterized．Such testscou豆d be，for exaτnple，performed in the biaxia韮apPara− ノ瞭’θ，50（1），73−82、18） Drescher ．へ．aΩd Vardoulakis． 1 （1982｝：Geonle【ric soften1ng ia triaxiahes50ngranu！armaterial，040∼θ（’ノ11r1σ肥，32（4），291−303、重9｝ Drescher， ！X、， Vardoulakis， 1． alld ｝逼an， C、 （1990）： 、へ bi−axialtus proposed and designed by Varclo艮lakls and Drescher apparamsforこestlngsoils，Gθo’θ‘・1r、τθ5∼、ノ、，GTJODJ，13．（1990）orinthebiaxialapPara宅usdeveloped＆nddeslgned 226−234、by Desrues（1985）．Both of由em allow for free shearbandformation，wbilethesecondoneinadditlQnallowsforfulレ負eldillcrementalstralnmeasuremeatmonitorlngcluring tlle test．20痔inno，RJ，，Harr臨，W，W、Mooney，M、、へ．a【1dViggialli，G、 （1996）＝Strai員locεdiza［IQn a【1d undrained s芝eady state of sa臼d5，ノ． 0θ01θ（・ノ∼．五1rg／3、，ASCε．122（6｝，462−473、2i）Gajo，A（2004）＝Thein飾enceofs》一stemcomplianceollcollapseot tr1axial sa【1d sarnples，Cα’1，（3θo’θぐ11、ノ、，41，257−273、22｝Gajo，A，Pif1をr，L．and De Polo，F （2000）；．へ11alysis Qヂcerta1…｝賑、一 凋594DESRUES．へNDGBORGOPOULOS factors a貿ect玉ng t蝕e unstabie beha、・iour of saturated loose sand，32）Servant，G．D、F．，Darve，F，，Desrues，，LandGeorgopoulos，LO． Mεc11．Co1了， （2004）＝D縦use modes of failure ln geomaterials，p401・1ησ∫’oηE1一’α。Mθ’．，5，21シ237． C12α’・ααθ1・’5”‘50ゾPGθ01norθパ（7Z5（eds．by Di Benede艮o，Swe【s and23）Hlaa，C．a簸d Vardoulak1s， 1， （玉991）：Plane−s［rain compress叢Qn experlmentsonwaτer−sa芝ura［ed鋤e−gra1ne（isand，0σo’θc／111ゆ’θ， Ze琵linger）． 41（1），49−78．33）Tatsuoka，F，，Sakamoto，M．，Kawamura，τ、andFukushima，S．24）Harr1s，W、W．，Viggia廊，G。，MooΩey，Mi A、 and F魚no，R．」L （1995）：UseofstereoP！10togrammetryこoanab・ze由edevebpmen【 （肇986）：Stre【㌃gth and deforma｛ion characterist1cs of sand玉n plane of shear bands in sand，（3ε01θoh．τε5∼．ノ．，GTJODJ，18（4）， Fo∼’1∼4σ！’0115，26（1），65−84・ strain compression at extremely low pressures．SoiZ∫α’∼ゴ 405−420、34）Ta覧suoka，F．，Nakamura，丁．，Hua鷺9，GCand鉛鷺i，K．（1990）：25）Head，K、H（1992）＝A如1∼∼σ10∫50’1加ひ01’σ∼o’ツrθ∫’〃19，3跡ective StrengthanisotropyandshearbanddirectlQn1nplanestraln［estof Stress■eSts，、Joぬn∼V蔵ey a員αSo陰s，｝｛玉目，R． sand，Soiz∫σn‘ノFo∼〃rゴα’10η・∫，30（i），35−54．26）Kato，S。，lshihara，K．a職dTQwhata，1．（2001）IUn（玉ra1nedshear characterist1csofsatuτatedsa鷺du員deranlsotropicconso照a芒lon， a霞ec竃ing鮭quefactlon susceptibil玉ty of sands，Cα1∼．0θo’8c1L／1，37， So’なσ1∼4だα〃1ゴσ1’oη∫，41（1）ラレ1L 592−606．35）Vald，Y，P．and S1va出ayalan，S、（2000）：Fu艮damental faαors granular malerlals with non assoc1ated gow，／．だη913．∫》θぐ13F36）Vardoulakis，La職dGraf，B、（1985）＝CallbraIio臓ofcons伽t1ve modelsforgra臓ularmateriais賢slngdatafromb1ax1alexperlments， ASCE，韮14（12），2173−219L28）Mok頭，M andDesrues，」、（1999）＝Sζrai自10calizationmeasure−37）Vardoulakis，璽．a簸dSulem，J．（1995）：βψ〃でσ∫’oη瀦’1ψ5Z5’1127）Lade，P．V，Ne夏son，R．B、and ko，Y．NL（玉988）：1昆stab員ity of， ments1n undra玉ned plane＿strain b1ax三al｛esこs on Hostun RF sand， ！、4eぐノ∼。Co1∼、ノ『’”01、ルノα’．，4，419−441． G60’θごh11ゆθ，35（3），299−317， Gθo’nθc11απ’c5，Blackie．38）vardoulakis，L，Goldsc姓eider，M．andGudehus，Q』G（1978）l29）Nova，R，（韮994）：Corltrollabilityofζheincreme猷airesponseofsQil Fornla芝ion of shear ban（重s玉n sand bo〔玉les as a bifurcation prob蓋em， specimons subjec［ed εo arb貢rary load玉ng ρrogram蹟es，ノ・・、グθぐh． ／〃．／．劫〃ア1．〆4ηθノ．ノ、4θ’1∼、（沁o〃1θ‘／7．，2，99一玉28． βθ加v。ル1α’、，5（2），193−201，30）Rice，．L R．（1976）l The localiza【lon of plast1c deformatio目，39）Yos短da，τ。，τalsuoka，E，S1ddlque，M、S．A．and Kamegal，Y、 （玉994）：S無ear band1ng l鷺sand observed1n plane strain compres− 7＝ノ1θo’で”‘01α11（ゴ〆置ρ∫ン〃θびA4θ‘1’α11’c5（ed．by Koiter，、V．丁．）．Nortb− sion，ゐo‘θ〃ξ醒’011‘71∼ゴ81舜〃℃θ”o’1771θ01二γ，弄019So’1∫αη4Rocκ∫ Ho駐and Publisl1頭g Company，207−220， （eds，by Cha瓢bon，R。，Des田es，J．Vardou蓋akis，L），Balkema，3玉）Sco［t，R。F．（198フ）：Falkire，（％αθごh1∼iσμθ，37，423−466、 三65−179．
- ログイン
- タイトル
- A Practical Numerical Model for Seepage Behavior of Unsaturated Soil
- 著者
- Kazunari Sako・Ryosuke Kitamura
- 出版
- soils and Foundations
- ページ
- 595〜604
- 発行
- 2006/10/15
- 文書ID
- 20943
- 内容
- r}SOILS AND FOUi¥DATIOi¥'S Vol46. N'o. 5, 595-604, Ocl. 2006Japanese C; eotechnical Societ}A PRACTICAL NUMERICAL MODEL FOR SEEPAGE BEHAVIOROF UNSATURATED SOILKAZUNARI SAKoi) and RYOSUKE KITA IURAii)ABSTRACTIt is irnportant to estimate the seepage proper'ties of unsaturated soils lvhen performing an unsaturated-saturatedseepage analysis, ¥vhlch is used to clarify the slope failure mechanism and predict the occurrence time of slope failuredue to rainfall. Kitamura et al. (1998) proposed a numerical model to quantitatively estimating the seepage propertiesof unsaturated soils. And they ha¥'e compared numerical results vith laboratory soil tests in order to examine thevalidity of the numerical model. Consequently, it has been found that the numerical model must be impro¥'edmoreover. In this paper a practical numerical model for seepage behavior of unsaturated soil is proposed to improvethe previous model proposed by Kitamura et al. (1998). Firstly, the basic theories of the previous model are explained.Calculation results are compared ¥vith those obtained from the laboratory soil tests in order to examine the validity ofthe previous model. Then, ve perfor'm sorne improvernents of the previous model based on hydro-mechanicalproperties, and propose a ne¥v parameter, named "parallel translation index ( Ipt)" ' From the results ¥ve showed thatthe relationship between the ne¥v parameter and the uniformity coefficient (U*), expressed by logarithm is linearrelation. Therefore, the reasonable seepage pr'operties of soils can be computed from the impro¥'ed nurrrerical modelusing only the popular soil parameters.Ke,_' ,vords: grain size distriction, soil-¥ 'ater characteristic curve, uniformity coefficient, unsaturated soil, void sizedistribution (IGC.: E7)seepage behavior of unsaturated soil is p 'oposed for theINTRODUCTIONimpro¥'ement of the previous model by Kitamura et al.(1998). First, the basic theories of the previous model areSoils located above the ground ¥¥'ater table are generally in an unsaturated condition. For' such soils, changes innegative pore-¥vater pressure have significant influence onmechanical properties, e.g, the coefficient of permeabil-re¥'ie¥ved. Secondly, calculation results are compar'ed¥vith those obtained from the laboratory soil tests in orderto examine the validity of the previous model. Then, ¥veperform some irnpro¥'ements in the previous model basedity, the shear strength, the compression index etc.on hydro-mechanical properties, and propose a ne¥vparameter, ¥vhich is named "parallel translauon mdexTherefore such changes may result in many geotechnicalproblems (e,g, mounding belo¥v ¥vaste retention pound,slope f'ailures, ground movements involving expansi¥'e(Ip,)".soils, and collapsing soils etc.) (Fredlund and Rahardjo,1993).THE NUMERICAL MODEL FOR SEEPAGEBEHAVIOR OF UNSATURATE SOILThe seepage proper'ties of unsaturated soils (i.e. thesoil-water characteristic curve (SWCC), and the relationships between degree of saturation ( S*), and unsaturatedsaturated permeability coefficient (k)) play key roles inUnsaturated soil is composed of three phases, viz. thesolid phase (soil particles), the liquid phase (pore-1vater)and the *'as phase (pore-air). Figure 1(a) shows a soilunsaturated-satur'ated seepage analysis. van-Genuchten(1980) pr'oposed numerical methods for obtaining theelement ¥vith a f'e¥v soil particles. This soil-mass situationseepage properties. He has proposed a close-formcan be modeled as shown in Fig, 1(b), ¥vhere voids filledequation for the hydraulic properties of unsaturated soil.with ¥¥'ater and air are represented as a pipe with adiameter (D), and an inclination angel (6). The soilKitamura et al. (1998) have proposed a numer'ical modelfor seepage behavior of pore-¥vater in unsaturated soilbased on some mechanical and probabilistic considera-particles are represented as the other impermeable partsof the model minus the space occupied pipe. Figure 2sho¥vs cross section of the element in Fig. 1(b). Thetions on the scale of soil particle size.In this paper a practical numerical modei of thevolume of' the element ( V*), and that of the pipe ( Vp), are*' Ritsumeikan Universi y, shlga, Japan (kaz-sako( ;+fc_ritsurnei.ac.jp).= Kagoshima Universil)', Kagoshima. Japan.=,The manuscript for this paper vas received for revie¥v on December 13. 2004; approved on June 7, 2006,¥Vritten discussions on tlris paper should be submi ted before i¥,Iay I . 2007 to the Japanese Geotechnical Socie y, 4-38-2, Sen_(',*oku, Bunkyo-ku,Tokyo 1 12-001 l. Japan. Upon requesl the closing date may be extended one month.595 SAKO AND596KITA *lLJRAThe shape of voids in soil is complex because the shapeand siz,e of soil particles are random, and the structureof their assembly is irregular. Therefore, D and e areregarded as random variables. Consequently, probabilitydensity functions for D(Pd(D)) and e(p*(e)), can beintroduced to esrimate the void slze distribution in a soilmass.First, Pd(D) is described. It is kno¥vn from the grainsiz,e analysis that the grain size distributions are approxi-mately expressed by the lognormal distribution. Thedistribution of void in a soil mass ¥vas measured by the(a)mercury intrusion proximity apparatus (Sato et al.,199'_); Yamaguchi et al., 1993). From these experimentalresults it ¥vas found that the ¥'oid size distributlon couldD!,be expressed by the lognormal distribution. Therefore,the use of the lognormal distribution can give Pd(D) asf ollo¥vs:- 'J(]n D - )., )P (D) i l Jr', 'D exp 2 : (3)j¥' In/1. 2: (4)(5): =!In +(1lcr,)2jI ,1(b)Fig, l. ¥_ iodeling of parric]es and voiti in soil mass: (a) a containerlvit!1 a few soil particles and (b) Pipe and the other impermeabieparts¥vhere, ).* =mean value of the lognormal distribution+ = standard deviation of the lognormaldistributionDD,,!1*= mean ¥'alue of D(7* = standard deviation of D.s in etan O/!+ and ( , are obtained from correlation of the grainsize distribution lvith the void size distribution. The siz,eof D is related to that of soil par'ticles because the size ofvoids is related to that of soil particles. The void siz,edistribution can be correlated ¥vith theSLDDlrain size distribu-tion based on the follo¥ving three assumptions.(1) The height of container in Fig. 1(b) (Di,) is set toDlo' It ¥vas found from the previous research ¥vork(Akai, 1969) that Dlo is one of factors that infiuencethe permeability coefficient:Dj* = Dlo (6)f)(2) !1, is expressed by the follolving equation:Fig. 2.Cross section of ihe container shownin Fi('^ l(b)represented by the follo¥ving equations respecti¥'ely:D , DhV*=D sine' tane Dh (1)D) D !'Vp (= -/T _, sin e (2)¥vhere. V..=volume of the container in Fig. 1(b)V0=¥*olume of the pipe in Fig. l(b)D= diameter' of the pipee=inclination angle of the pipeDh= height of the element in Fig. 1(b).fl= Di, ' P** (7)¥¥hele P,,= parameter used to fit the void ratio obtainedfrom calculation ¥vith that of experiment.(3) The coefficient of va 'iation ofthe void siz,e distribution is equal to that of the grain size distribution. Unoet al. (1998) have studied measurement methods ofvoid size distribution for sandy soil It has beendescribed in their paper that the void size distributionfor drying process of the SWCC is parallel to the grainsize distribution. Therefore, this result is applied torelate the void siz,e distribution ¥vith the g:rain sizedistribution:= * (7, (8)u* ,u* NU ,1ERICAL JvlODEL FOR ¥*OIDSvhere,Using Pd(D) and P*(O), voic.i ratio (e), volumetric= coefficient of var'iation,lvater content (TV,), suction (s*,), and unsaturated-saturated permeability coefficient (k), are deri¥'ed based onu* = mean value of the grain size,cr*= standard devlation of the grain size.The above three assumptions give 1, and (7.. Thus, Pd(D)can be computed by using the data of grain size distributlon.Next, P*(e) is described. A relationship bet¥veen acontact angle of adjacent soil particles (fi) and e issome mechanical and probabllistic consideration on thesoil partlcle size (Kitamura et al., 1998).Since the vold ratio is defined as the ratio of the ¥"olumeof voids to the ¥'olume of soil particles, It is expressed asfollo¥vs:=J -. ldefined in Fig:. 3. The distribution of e is related to that of'fi (i.e. the conjugate relation). Oda (197,_) has measuredthe contact angle at a contact point of adjacent particlesby optical microscope and sho¥vn the fr'equency distribu-tion of contact angle. Kitamura (1985) assumed a pentagon shape sho vn in Fig. 4 as P*(e) based on these results.p*(e) can be expressed as:217r-'Tr/2:i c'i- i'efr 12 ' fto ,_Equation (10) Indicates the expected ¥'alue, Ivhich ¥vasderived based on the probability theory, and the integration inter¥'al is expressed from O to f_. Ho¥vever, in thecalculation, the function is integrated from ()., -4Lj,) toInitially the ¥'oid ratio Is computecl from Eq. (10) ¥vhere, 7t( <e<0-)p (e) - 2/Jr --? 'cl,.__ V,-V Pd(D) P(e)c!ec!D()., + 4c , ).0+ '7z59 //!, is gi¥'en by Dlo. The calculation result is compared,? ( ITo e(9), )viththe ¥'alue obtained from the laboratory soil test. In orderto ag:ree ¥vith the actual void ratio obtained from thelaboratory soil test, iterati¥'e method is used by applyin_"._where, .= Iolvest height of' P*(e).j* is determined to be O. 159 ¥vhen the ratio of the mini-mum height to the maximum height of P*(a) is 1:3.*=O. 159 is used in the numerical experiment.change in P*, in Eq. (7). Finally, P*, in Eq. (7) is determined, and Pd(D) (i.e. ¥'oid size distribution) is obtainedfor a void ratio obtained from the laboratory soll test.The volumetric lvater content is defined as the ratio ofthe volume of the pore- vater to the total volume of soiland it is expressed as follolvs:I f'i '/2 VpI /e(c!)J j V.--V Pd(D) P (O)dec!D1+e 1+e o *'(11)¥vhere, e= ¥*oid ratio (Eq. (lO))e(c!) = ratio of' the ¥*olume of' the pore-¥vater to thevolume of the soil (In saturated condition,e(d) is equai to e.)c/=maximum diameter of pipes filled lvith¥vater.The suction is defined as the diff rence bet veen poreair pressure (u*1)' and pore-1vater pressure (u,.), (i.e. u* -u,,) Fl(rure ) sho¥ s a capillar) phenomenon. ForceFig. 3. Relationsl]ip between conta:ct angle of adjacent soil particles,P, and inclination angle, eequilibrium in the vertical direction can be expressed bythe follo ving equation:p,( e )P( j ' )*Co!p- :,l･_o(a), : ;!-- 7L12ofT;-,(b)Fig. 4. Distribution of contact angle, P, and inclination angle. O: (a) Probabilit)･ densit) function of contact angle, P(fl) and (b) Probabilit)density function of inclinarion angle, P*(O) 1 i59sSAKO AND KITA ･1URAD4 . sin e'A l! ' JzO-P 128 ･ /1 ' Dh ( 1 7)On the other hand, flux of water through the soilelement in Fig. 1(a) per unit time (Qe) is also expressed bythe follo¥ving equation in ¥vhich Darcy's lo¥v is applied:, Dh' tanO (18)Qe=k"i'A=k'i'D Dsinewhere. A =cross section area of the container inFig. l(b)7=average hydraulic gradient of soil mass inFig. 1(a).The average hydraulic gradient of the soil mass inFig. l(a) can be expressed as follo ¥'s:7= 4 ! / y,. ( 1 9)Capillary phenomenonFig. 5.DhQ. is equal to Qp. Combining Eqs. (17), (18), and (19)Jr ' d 'JZTs' COS (x= - ' d 2 . /1c ' ylv(12)4gives the follo¥ving equation:k-= y,. ' D i ' 7z ' sin e (_.O)D , D!*[ l¥vhere, T==surface tension128･/1 sin e ' ran e( = contact angle of meniscus at a contact pointof soil particlesSince D and e are random variables, the unsaturated-h* = pressure headsaturated permeability coefficient is expressed as follo vs:y*+ = unit ¥veight of lvater.Rearranging Eq. (12) gi¥'es /1c as sho¥vn in Eq. (13):/7 4 T coscyw ^ dk=J 'lj**/2_. -(13)o -.,!2y . 'D3 ' Tz ' sin e[[ D , D ' IJ1'_8 ･/J 'sin eT tan e('_1)The suction in the nearby meniscus is equal to the ¥vaterpressure that corresponds to pressure head. So, suction isexpressed as follo¥vs:s = y,, h 4' T='cos ce (14)dThe unsaturated-saturated permeability coefficient ¥villNUMERICAl. PROCEDIJREThe numerical procedure for the above model isdescr'ibed as follo¥vs;1) Dj,, P･ and a. are obtained from the grain siz,edistribution by using Eqs. (6), (7) and (8) in lvhich P,= isbe described by the follolvin_9::set to I .O. 2) ).Flux of laminar flolv in the pipe per unit time (Qp), isand (T into Eqs. (4) and (5). Then. Pd(D) can be comput-expressed using the Poisseuille la¥v as follo¥vs:ed from Eq. (3). 3) P*(e) is obtained from Eq. (9). 4)= )( 2･1･Op!;;;･D 4 (15)fz¥vhere, /! =viscous coefficient of ¥vateri = hydraulic gradient,In Fig. 1(b), i for the laminar' fio¥v in the pipe is definedas follo¥vs:._ Aul),,, (16)l Dh Isin eand. can be calculated by substituting !!,Using Pd(D) and P*(e), e can be calculated fromEq. (10). Follo¥vin_2: that, this calculatlon result is compared ¥vith the labor'atory soil test result. 5) The value ofP** is changed, and then the procedure from 1) to 4) isrepeated until the ¥'alue of e is corresponds to theexperimental result. 6) The saturated volumetric ¥vatercontent (W.***) is given by 'V.,**=e/(1 +e). 7) The valueof W. from O.O to W *** is substituted into Eq. (1 1), andthen d, ¥vhich corresponds to each value, can be obtained.8) Substituting d, ¥vhich correspond to arbitrary volumetric ¥vater content, into Eqs. (14) and (21) ¥vill result in s¥vhere, Au=difference of pore-¥vater pressur'e bet¥veenthe top and the bottom of the container inFig. 1(b).Substituting Eq. (16) into Eq. (15) gives the follo¥vin_"._equation:and k.NUMF,RICAI. EXPF.RIMENTTable I sho¥vs values used for the numerical experiment. The input parameters include T,, /!, e, the density NUivIERICALTable l,¥. *10DELFOR VOIDS599Values used for 2 numerical experimentSampleShirasuDenslty of soil particle (g/cm;)2.62873_4S x 10 ;Surface tensioll (Nlrn) ( ¥!ater temperaiure is 15'C)138x lO ;Coef cient of viscosity (Pa's) (¥ 'a er temperature is 15'C)Lo¥vest height of probabilhy density function of e, (*O. 1 59¥roid ratiol.71Grain size dislrlbutionPercentage finer by ¥veight (9/0) Grain size (mm))_if;t}Percemage finer by weiglGrain size (mm)( !.)I37.9o_05291*+135 3o 037632.7o,023930 lO 0139lO0.019 OO98 29.5095,84.75l91 22.00i=86 1o.8501.-27.4o 009974.40.4,_5l24.so 007063,0o.2501.(20.9o 003646 oO 106It/14.4O O0154 1 .4o 075of soil particle (p*) and the grain size distribution. Theseparameters are obtained from simple soil tests andcrcommon scientific tables.The values of the input parameters are obtained fr'omsoil tests on Shirasu and applied in the numerical experi-fail ¥vith heavy rainf'all.Figure 6 sholvs the grain sizesize distribution that have beenthe parameters expressed in Tableshow the grain size distributionThe dash line represents the approximate gr'ain sizedistribution due to the 18 dots, and this is expressed bythe lognormal distribution. The solid line is the void sizedistribution, and it is given as the cumulative distributionC:str i but i enstr I'' 0Ca i cu i aii c,[r*oe9080ejO70,/(U4:oe)c6050404Jdistribution and the voidcalculat.ed by the use ofI . In Fig. 6, the 18 dotsobtained from soil tests.soornent. Shirasu is defined as a non-cemented part ofpyroclastic flo¥v deposits and one of the famous volcanicproducts. Shirasu particles are porous and their density isless than that of the usual sandy soils. Therefore Shirasuground is easily eroded and Shirasu slopes often easilyIZe L r[cQ30::::3,:)2010o1 o 71 O s I 0 50-4Gra n s zeFig. 6.1 0 3 1 0 2{ ODiameter of the1{Ol1 Oop I pe(n1 02)Grain size distribution and void size distributionfunction based on P (D) as sho¥vn in Eq. (3). The voidbecause it has been assumed that the coefficient ofthe soil test results, the values of k computed by themodel appear to have been overestimated.In the numerical experiment, it is regarded that allvariation of the void size distribution is equal to that ofthe grain size distr'ibution. The seepa*'e pr'operties (i.e.pore-¥vater included in the soil mass contributes to generate the suction and the flo¥v ¥vater lvhich relates to thethe SWCC and the r'elationship between S* and k) ofper'meability coefficient. Ho¥vever, part of pore-watercontained in voids probably does contribute to the actualseepage behavior. Taking account of the hydro-mechani-size distribution (i,e, the solid line in Fig. 6) is parallel tothe grain size distribution (i.e, the dash line in Fi**. 6)Shirasu as sho vn in Table i are calculated using Pd(D).Figure 7 shows the SWC*C obtained from the numericalexperiment and ¥vater retention test on Shirasu. It isfound from Fig. 7 that the suction values calculated bythe proposed model are smaller than that obtained fromsoil test at the same degree of saturation. Figure 8 sho¥vsthe relationship between S*, and k. In comparison ¥vith--cal properties, ¥ve ¥vill rnodif'y the proposed model in thenext section. 1 iSAKO A¥.(]*oaD KITA*¥,IURA1 ooSoil p ulicie90 -A i i'C8 cLi a L on8070 -C(60ei._-i: $ "=50 --O:40 -+J30 -cl)20 -10Absorbed ¥vaterFree ¥ 'ateroo20 30 40 50 60 70 80 90 10010Fig. 9.Conceptl!al statcs of pore1'atcr and air in unsaturated soilDegree of saturation, S. (";)Fig. 7.Soil*water charactcristic eurveimprove the previous model.In the previous model, it is assumeci that all pore-¥vater'included in the soil mass contributes to g:enerate thesuction and the flo¥v ¥vater estimated by the permeabilitycoefncient. Using the parameters of the proposed numerical model, the ¥'olume of all pore-¥vater included in the1 02C-q)¥(1)::S;(1)･ ;+J101 i.100 =08 c ; at'onsoil mass (V,.) is e,x'pressed as follo¥vs:1 O 11 0 2j J::.iV,, = Vp Pd ( D ) P( (e )clec!D (22)( S *1 O 3CU *cl?a1 0 5On the other hand, part of the pore-¥vater contained inQ)L{-1 O 6voids probabl"v actually contributes to the seepage behav-CQO1 0 7ior as mentioned above. Therefore, c! In Eqs. (14) andL+J:SCJQ);Lh+,Q,LO,>(Q,Jc,) "-::)-OCQQ,Q,t) -{ 0 4(21) is reduced to obtain the reasonable value of SLI and k-.10 8The volume of the por'e- ¥'ater that contributes to thesuction (V,.,u) is expressed by the follo ving equation:10 9 " - -10 1a10-11= I 'rlI "*="-V,, ,u V1012o10 20 30 40 50 60 70 80 90 100Degree of saturation, S. ("t)Pd ( D ) Pc (e )d ec/D (23)*o '--,l¥vhere, V,.su=volume of the pore-¥vater contributlng tothe suction (V ,sL < V,.),d,i =maximum diameter of pjpes filled ¥vithFig. 8. Relationship between the de,*,_ ree ofsaturation andtlns tt ratcd-saiuratcd permeabilii, coefi cientvater that contFibutes to suction (c! u<, cl).And, the volume of the pore-¥vater that contributes to thepermeability coefFicient (V,.k) is as follo¥vs:IMPROVEMF.NT OF PREVIOUS iviODF.LFigure 9 sho¥vs a conceptual picture of soi} particles,pore-¥¥'ater and pore-air in unsaturated state. Pore-¥vat.eris divided into absorbed vater and free ¥vater. Free ¥vateris further subdivided into static and dynamic free ¥vater.Static free vater probably contributes to the suction asmeniscus ¥vater. Dynamic free ¥ ;ater probably contributes to the permeability coefficient as fio¥v ¥vater. InV,.k=j l:: (24)(iVp Pd ( D ) Pc (e )c!edDO 2¥vhere, V,.k=¥'olume of the pore-¥vater that contr'ibutesto the permeability coefficient (V,.k < V,.),c/k=maximum diameter of pipes filled ¥vithhvater that contributes to the permeabil;tycoefncient (c!k < d).conformity ¥vith the above-mentioned concept, an im-When d**, and c/k are used instead of d in Eq. (14) andprovement of the proposed numerical model is discussed.Eq. (21), respecti¥'ely, the following equations areobtained as the modified model:In this section an improvement in the ¥'old siz,e distribt, -tion is performed for static and dynamic free ¥vater. Inthis paper, ¥ve notice he ¥'oici size distribution, and i¥]fL'N'IERICTable 2.L N･IODELThe paFameter used io calculate ihe void size distribution¥,'oid size dis rlbuiionTest resultsDegree of,1aximum diameter ofSuclionsaturaLion pipes filled lvi h waterlaximum diameier of pipes filled wi hCumula ive percentages¥ 'aleror Yoid size distributlonhacontributes tohe suciions,, (kPa)c! (mm)92 so 988_07 x lOi3.00 >< lO92 5967.66 X lO !l 50X lOI96.2S. ((l601FOR ¥,OIDS)c!,u (mm)(?･ )i96.3384.54*92.S4 x lO16 oo x l0 292 44S2 . l4.912 28 x 10 !5_99x lO l91.36S19.Sl8_3.00 x 10 i84 243.749 20_1 .98 x lO ;71 26I x lO2.24 x lO :1 OOd 1ir ibL]t7Cc n r ;[ itt tJczi'llOO -90 =go lc60,)50C:,:)OoL 50( );'hth; r.:jsir o vel Od8 1_404J'O:e) 40>(1,+JcT: 3060=¥ I'Y11'70c:J:K} '*c cLi 8t en {b' J /F804J:* ･ 8= i80 i2020 '___/ ____. _ _______ _ ___10 /"I"ljJooO1 0 7 1 O e I O s I 0 4 1 0 3 { 0 2 1 O 1Diamete30:#;o lo 20 30 40OO { OI { 02of the piPe ( lll)Degree of5060safu rat i on70s.80go1 oo(*+.)Fi*. 10. Void size distributionFig. 11. Soil-water characteristic curve (aftcr tl]e improvement of thenumerical model)s'** =4 ･ T* ' cos Oi (_,5)cl * **=Jo'J"'I -"),,..D3'7z'sinek -- --*' P[ ( DD Df*-) J' P. (a )d edD1_'8･// sin e tan e(, 6)cl and c/***, ¥vhich correspond to the experimental resultssolid line. Therefore, 6 of the dash line is equal to that of'the solid line. The dash line is derived by a change in ), inEq. (3) under the constant coefficient of ¥'ariation.The result that vas obtained using the modified voidsize distribution of the dash line in Fig. 10 is sho¥vn inFrg 11. In this figure, it can be seen that the resultscomputed by the use of the improved ¥'oid size distr'ibu-Because the results for the cases ¥vhere S* is 90.70/0 andtion is in good agreement ¥vith the soil test results.94.70/0 in Fig. 7 probably have an influence of the airentry value, Table 2 does not include the calculationestimate d*** ¥vas applied to calculate dk, and the result isresults for these cases.Fig:u 'e 10 sho¥vs void size distributions. The solid linesho¥vn in Fig:. 12. Here it can be seen that the calculationresult agrees ¥vell ¥vith the soil test result. Ho vever, sincein this figure represents the void size distribution that isthere is only one saturated permeabiiity test result, thecalculated in the case sho¥¥'n in Table 1. The circularpoints sho¥v the distribution of d and the triangular¥'alidity of k cannot f'ully be examined. So, it is necessarypoints sho v that of d, . It is assumed that the cumulativepercentages of void size distribution of c!s are equal tothose of c!. The dash line in Fig:. 10 sho¥vs the void sizetests in the near future.distribution contributing to suction. The curve that*-_lognormal distribution. The dash line is parallel to therespectively. And these results are shown in Table 2.in Fig. 7 are calculated by the use of Eqs. (11) and (･- _ ),1approximates to the trian*'ular points ¥vas fitted usin_",_Therefore, the sarne improvement method used toto carr'y out many unsatur'ated saturated permeabilityThe proposed practical numerical model aims tocalculate the S¥ rCC and the relationship bet¥veen S* andk by the use of the parameters obtained fr'om some soil 瀦602SAKO AND KITAMURAtests．newparameteriscalle（i‘‘paralle至translationin（iex（1P【）”． As in the above−mentioned explanatlon，the void size ∼Ve 芝ake the case， 、vhich is shown in F圭9． 11 fordistribut圭on contr量buted to suction（i．e．the dash line ininstance，andcalculαte／pt．Figure13shows由eprocedureF圭9．10）is parallel to the void s茎ze distribution（i．e．theforobtalning1P、．ltisfolmdfromFig。13thatthemeanvalue of the void size distribut量on，which coτresponds tosolid line in Fig．10）．And由ey have由e same coef五cientof variation．The diEerence in each void size distribution50％of the cumulative percentage，contrlbuted to suction（the dash line）is equivalent to31。9％dlameter of the voldis expressed by the di牙er』ence among those mean values．Estimating由e d湿erence ln each mean value ofvoid size sizedistrlbution（thesolidline）（tbeallow①）．Thevaluedistr疑）ution gives a new parameter，which is proposed inofthepercentageisne∼、11yde負nedas／P、．lnthiscase，／P、isset to31．9（to aIlow②）．The same method ls also used inorder to improve the previous model ln this paper．Thethe relationship between S，andた．102 Table3shows the populaτsoil parameters an（i IP［forlol l o ①繍儲篇繍篇C窪lcじi飢…α官byてh3preViousmodei1001 の祠’避1α2レ㊦10−3巳． ゑ申」 ①Zき」賦r馴こ脚OaiC乳li就瑠緯暮し、＝…駈ぽfro轟・εO愛夢＝5 蝶」一瀦−CaiculatiGn（byτhθi窩1proved蹟ode1） ＼ 籠 o 10”11でΦ蛍噂の ol・胴一 ①10090、lo冒4忌・“5 0』 o聾邸一の・一￠一＝：）・一 』 邸 Φ 鰭 』 ① 血 “一τ㎜…㎜…｝ヲ7 ！』10樽6①10−7制10需8obO邸篇①①10−9706050Ω．①＞10寵10邸10”11コ匠03io−12 0一≦て，餌宅 下3〕 2銭r80lO−5蓬一 ＞，Z5 d i str i bUt l cn contr I鶉し美tεj to SuCt lOn 穆 臼厨“昌竃一℃｝①嚇曹”−磨一’10i d40一一』蕊』．諸翌30、農／．2010璽0 20 30 40 50 60 70 80 90 望000Degreeofsaturation，5（％）1σ7 iO幕6 10葡5 10廊4 10冒3 1σ2 10−I loo lol 102 ！F Diameter of the pipe （㎜）F童9，12、 Re嚢段霊量onship be琶ween tbe degree of s段重ura“on aηd the u願s飢腿ra霊e6印sat毛照｛edperme段bili重ycoe餓cienI（af吐er！heimpro、一e・Fl9，13。VoidsizedisIribu重lonIha“わeprocedareforo漁ining吐he me煎ofdlenu贈rlc田modeり P徽lieltr段臓sl頗onindex，1PIjsadded重oTable3・ V段hies o郵Ihe some general parame｛ers費nd蕪1e p段rallel｛r3nslation index Ciassif㌔cation ofSample ρ、 geomaterlals for θ｝ （9／cm3）eng玉臓ee【ing purposes ／Pl ／P軍o［1） （abOUt perm1abi1琵yu￠（about suct1o員）（cm） coe鰍ient）玉Shirasu SV−G2，52三、93至．49×10隔326，3415．12Shirasu SV−G2．551．267，88×豆0』高50、1529。3B．63Shirasu SV−G2，51豆、371、05×10湘335、4022。37．54S厩rasu2。621，691，95x10−494．豆739。05S｝擁rasu SV−G2，441．245、85x玉0葡459．7528．19．5Sh三rasu SV−G2．421，276．97x豆0即嵩55．9228、88，1S｝玉玉rasu SV−G2．63夏、7夏2，06×10㎝485．8331．9Ω．0S｝1叢【aSu SV−G2．541．754．08x10−459．0137、411，6Sh玉rasu SVG2461、46叢、41×10皿333．4718、32、681、42玉，86×10−56789SVVS3．618．82、710Shlrasu11Shirasu SV−G2、491．294．12XIO而482，8932．67、812Sむ1rasu SV−G2．581、577，24×10−448．2129．36「313S量1圭rasu SVG2、5444．8521．814Si11rasu豆5Sl1玉rasu1、501。44x10楠3VS2 72玉．662「89×玉〇一6sv2．581、142。73x玉0−4260．53457．1553．7846．017，06，656．2夏8。846．01玉6銘 NU ,IERICAL lvIODEL FOR ¥,OIDSpermeabilit"¥' coefncient, respectively. From these figures,it could be seen that the influence of' the void ratio on the¥'alue of lp* is small; ther'efore, the proposed rnodel can be15 samples. It is found from Table 3 that lp= is related tohe uniformity coefficient. The relatlonship bet¥veen U*and lp, about suction is sho vn in Fig. 14. The horizontalaxis is U* and is expressed ¥vith logarithm. On the otherhand, the vertical axis sholvs lpt' These t¥vo parametershave a linear relation as shown in Flg. 15.The relationship betlveen U* and 1 '* about permeabilityalso applied to the soil samples, which have the samegrain size distr'ibution and the different value of voidratio, in order to estimate lp* by using the ¥'alue of U*.coefficient is sho vn in Fig. 15. The horizontal axis is U*CONCLUSIONSand is expressed by logarithm. On the other hand, theIn this paper, the practical numer'ical model forvertical axis sho¥vs lp*. Fi_･._ure 1 5 also sho¥vs that these t voseepage beha¥'ior of unsaturated soil lvas proposed inorder to improve the numerical model. Firstly, the basictheories of the previous model vere re¥'ie¥ved. Thenumericai r'esults ¥vere compared ¥vith those obtainedfrom the laboratory soil tests in or'der to examine thepararneters ha¥'e a linear relation.From Figs. 14 and 15, it vas found that lpt can be deter-mined from the grain size distribution curve. Therefore,the S¥ fCC and the relationship bet¥veen S* and k can becomputed from the proposed practical numerical model¥'alidity of the previous model. It ¥vas found from theseresults that the suction values calculated by the previousmodel ¥vere smaller than those obtained f'rom soil test atthe same degree of saturation. In addition, it vas alsodetermined that the values of k calculated by the pre¥'ioususin_-' only some popular' physical and soil parameters assho¥vn in Table 1.Next, the applicability of l , to samples, ¥vhich aremade by the soil lvith the same grain size distribution andhave different value of void ratio, is examined. Table 4sho¥vs the ¥'alues of some general parameters and l forrnodel ¥vere overestimated in comparisonvith the soil testShirasu and Toyoura sand. These parameters areresults. Therefore, improvements of the previous modelrepresented in Figs. 16 and 17. These Figures sho¥v therelationship bet¥veen e and lp* about the suction and the¥vere needed to estimate the r'easonable seepage propertiesof soils.1 oo1 oo909080:¥70><Q)><8070 -a:)c:lc:c:60co60c:o50+-50+Jc:CQ40(,,('oz:cco30+Je)+'･ ,*+ '+' -20e)*** "++:Q3020*CQ10C40'(Q: ,*; !}10 -c:*..,"*oo1 OO{10Un i f orm i t yFig. 14. Relationship between the parallel translation index and theuniformit, coefficient about suction'Table 4.Classification oengineering purposesShirasu2 .4534)15. Relationship between the paralle! translation index and theuniformity coeffieient about permeabilit) coefficientID I o(cm)UfToyoura sandI p*(about suction)(aboutpermeabi itycoefiicien )30.9o.531.80.41 .3730.8o.5o 7420 61 .817 5l 4J .5 llcoefficient u.Values of lp* ,vith difference in void ratioSample = geomaterials for= P* e(g/cm3),Fi,,.ooo1 OOUniformity coefficient, l/.L=_603l .472 64o 803_16 x lO i1 37 x lO:ll.36l .62 SAKO AND KITAlvIURA60450from the Ministry of Eclucation, Sports, Science andTechnology, .Japan.i Te c} Jr sanri_,*¥1;40Shi asuNOTATIONxQ)c!::;:30 -c!k:to peFmeabi it_v coefficiemc:oc!u 'J(Ec:CQD:hc:diameter of pipeheight of the element in Fig. l(b)pressure headIP :parallel lranslarion indexD,,:+Ja,10p,(e):CQP ( D ) :cCLP,< :O 608 1 1 4 1 6O1.2su 'r<:V'V.:V k:)c:-* ;o8Sh"3 s f "_iasuJCQ(D:cT+Je)V -u'I"( :(x:7fi:3:6cc:c::othe soil elemeut in Fig_ l(a) per unitflu¥.' of laminar flo¥v in the pipe per unh timesuctionsurface ensionvolume of the container in Fig. l(b)¥'olume of the pipe in Fig. l(b)¥'olume of all pore-¥vater included in soil mass¥'o ume of pore-wa erhat contributeso permeabiliivcoefricient9cl)hrouglrimeV '10parameter in order o fit the void ralio obtained fromflux of ¥¥'atero_eO_p:Fig, 16. Relationship between tlre parallel translation inclex and thevoid ratio about suctionprobabi]ity density funclions for eprobabilit_v density functions for Dcalcula ion lvith that obtained from experimentVoid ratio, e:maximum diameter of pipes filied ¥vith ¥vaier lhat contributesto suction20 -(,,><maximum diameter of pipes fi]led ¥vith ¥vatermaximum diameter of pipes filled with ¥vater that comribmesvolume of pore-¥va er contributing to suction¥'oiumetric ¥vater contentcomact angle of meniscus at a co tact poincontact angle of adjacent soil parliclescoefncient OF Yariarionof soil particleslo¥vest height of P*(e)4/'* :standaFd deviation of l0 nor nal dis rlbutioninclination angle of pipemean value of lo :normal ciislribution3u<:mean ¥'alue ofu* :mean vaiue of D5cy:e:(J,:2(T* :rain sizestandard deviation of rain sizestanciard devialion of DcCQ1CLO.6 1 1.4 1 6O1 28Void ratio, eREFF,RF,NCESl ) Akai, K(1 969): Eve,1!s on Seepage, Soi! ,Vfechanics (ed_ by hJogami,T.), Gihodo, 99l02 (in Japanese).2) Frediund, D. G. and Rahardjo, H, (1993): Soi! fVechanics forFig. 17. Relationship bet veen the parallel translation index' and thevoid ratio about permeabilrty c08ff]cientWe performed the improvement of the previous modelbased on the hydro-mechanical properties, and proposedlp* Then, it ¥vas sholvn that the relation bet¥veen lp* andU* expressed by logarithm lvas a linear relation. Conse-quently, reasonable seepage properties of soils could becalculated from the proposed practical numerical modelusing only. some popular physical and soil parameters assholvn in Table I . Therefore it can be concluded that theproposed practical numerical model can contribute tomany geotechnical problems.U]Is(Ituratec! Soi!.s, ohn ¥¥?iley & Sons, 39.3) Kilamura, R. (1985): A h,1arko¥' model of particulate material lvithan isotropic fabrics, Proc. In! Con f. 1¥runl * fe!h. Engr'g^, rheor.App!. (!¥TU! ,JETAS.)"), 455-4644) Kiiamura, R., Fukuhara, S., Uemura, K , Kisanuki, J. arl;d Sevama,¥. ,1. (1998): A oumerical model for seepage through unsaturated soil,So!! and Founc!a!ions, 38 (4), 261-26_5) Oda, ¥.,1. (1972): Ini ial fabrics and their relations to mechanic.alproperties of granular malerial, Soi!s anc/ Founc!ca!on.s, 12 (1).17366) Sato, K., Soba> T , Ku¥vayama, T, and Uno, T. (1992): hlercuryintrusion echnique for macro pore measurement of particulate soil,Proc JSCF, (430/Ill-18), 39-142 (in Japanese).7) Uno, T^= Kamiva, K. and Tanaka, K. (1998): The distribution ofsand ¥*oid diameter by air in rusion method and moisture characleTistic cur¥'e method, Proc. JSCE, (603/lll-44), 35-44 (in Japanese)8) Yan-Genuchten, h,l Th. (1980): A closed-form equation for predictirrg the hydraulic conducrivit)' of unsa uraled soil, Soi! Sci. A,11. ,J.,ACKNOWl,F.DGEMF.NTThis research ¥vork vas supported by the Grant-in-Aidfor Scientific Research (No. 1'_79)_009, No. 13450196)44 (5), 892898.9) Yamaguchi, H^, Hashizume, Y and lkenaga, H (1992): C_hange inpore size distribulion or peat In shear processes, Soi!s anc!Fou,1c!ation.s, 32 (4), -16
- ログイン
- タイトル
- Uplift Capacity of Pile Groups Embedded in Sands: Predictions and Performance
- 著者
- K. Shanker・P. K. Basudhar・N. R. Patra
- 出版
- soils and Foundations
- ページ
- 605〜612
- 発行
- 2006/10/15
- 文書ID
- 20944
- 内容
- rSOILS AND FOUii¥]'DATIONS¥*ol46,NO), 605-6 1 2 ,Oct 2006Japanese Geotechnical Soclel}UPLIFT CAPACITY OF PILE GROUPS EMBEDDED IN SANDS:PREDICTIONS AND PERFORMANCEK. SHA TKERi), P. K. BASUDHARii) and N. R. PATRAiii)ABSTRACTThe paper pertains to the development of a simple semi-empirical method of analysis for predicting the upliftcapacity of pile groups embedded in sand assuming an irrverted truncated rectangular pyramidal f'ailure surface.Various pile and soil parameters such as length, diameter of the pile, group configuration, spacing of the piles and thesoil properties such as density, angle of' internai friction and the pile-soil interface f'riction angle ha¥'ing direct influenceon the uplift capacity of the pile group are incorporated in the analysis. The predicted values of uplift capacity of pilegroups ¥vith different configuration and length to embedment ratio are then compared ¥vith model test results carriedout as a part of the present investigation and also ¥vith the values reported in literature. The predictions are found to bein good agreement ¥vith the measured values validating the de¥'eloped method of analysis.iKewords limrtmg equilibrium, model test, pile,pile _",_roup,sand, uplift (IGC.: E4)embedment length, number of piles in a group and spac-INTRODUC.TI0_NPrediction of uplift capacity of' single piles anding of piles in a group. Madha¥* (1987) studied the interaction betlveen t¥vo identical piles in tension using bound-especially of pile groups is one of the most interestin_ ._ary integral technique. The reduction in individual pileareas of research in geotechnical engineers. Some of thestudies conducted on the behavior of single piles undercapacity due to the existence of another pile is quantifieduplift loads are due to So¥ 'a (1970), Vesic (1970),and it is found to depend on the spacing and length toRao and Venkatesh (1985), Chattopadhyay and Pisediameter ratio of piles.It is evident from the literature as cited abo¥'e that mostof the available studies are limited to single piles onl_v.But increasing use of **roup of piles to resist and sustain(1986), and Ramasamy et al. (2004). These studies areuplift loads requires accurate assessment of upliftvery helpful in understanding the behavior of piles undertensile loads and predicting the value of uplift capacity ofsin*'1e piles. But, Iiterature on such studies on the upliftcapacity of pile *'roups embedded in sand are scanty (Daset al., 1976; Siddamal, 1989; Chattopadhyay, 1994; Patr'aresistance for safe and economical design of' pile founda-and Pise, '-003). The theories to predict the upliftshape, spacing, embedment length to diameter ratio oflv:1eyerhof' (1973), Das and Seeley (1975), Isrnael andKlym (1979), Das (1983). Levacher and Sieffert (1984),tions. As such, there is a need to develop methods topr'edict the uplift capacity of pile groups and such ananalysis is presented in this study. The uplift resistance ofpile groups depends on several ¥'ariables like group size,capacity of piles ¥vere developed mostly by extending theanalysis of horizontal plate anchors under uplift loadspiles, soil type and its density and soil-pile friction an*'1e.Considering some of the above parameters a simplifiedanalysis based on limiting equilibrium is proposed toassuming development of failure surfaces starting fromthe edges of the anchor. Based on experimental observation and test data, lvleyerhof and Adams (1968) proposedpredict the uplift resistance of the group of piles. Labora-a general theory of uplift resistance for a strip footing intory rnodel tests on group of piles were conducted inmedium dense sand under axial uplift loads at differentsoils with the assumption that soil mass having approxi-pile spacing and lvith varying embedment length tomately truncated pyramidal shape is lifted up and forshallo¥v footing the failure surface extends up to theground surface. The theory ¥vas further' modified todiameter ratio. The predicted values of uplift capacitywere compared ¥vith the model test results so obtainedand vith other published experimental data to check thevalidity of the developed method of analysis.analyze circular footings and square and rectan*"ular pilegroups. Das et al. (1976) and Chattopadyay (1994)concluded that the efficiency of a pile group variesi:li tvithResearch Scholar, Ci¥'il Engineering Depar ment, Indian Institu e of Technology Kanpur, Kanpur 208016, India.Professor, di to, (pkbde=iitk.ac.in).Asst. Professor, ditto.'The manuscript for this paper ¥vas received for review on July 25, 2005; approved on ivlay 29, 2006.Vritten discussions on his paper should be submitted before " ay I , 2007 o the Japanese Geolechnical Society, 4-38-2, Seugoku, Bunkyo-ku,Tokyo I i2-001 l, Japan Upon request the closirrg date may be extended one month.605 lSHANKER ET AL.606¥vedge and its fr'ee body diagram are sholvn in Fig. 1.*,J ''UI*iThe mobilized shear resistance AT along: the fai]urefL__J'l)yrsurface of length zl L, at limiting condition is,A T=A R tan c (1)"" lL_illiL'p!IAZI"+tII]I'!'!!!'- r!v "I*::lli T TTWhere AR=Normal force acting on the failure of the¥vedge' Q?i r& ;iQ1";:rTT7TrFl;r'fl I1: I [ f'Pil :- Il _ LLll_Lz/'1 eLL----zlAR IOcose+KAQsine (2)( I,-AQ=yV rherezlZ ll (3)- Z-.)Following Chattopadhyay and Pise (1986) the coefficientof lateral earth pr'essure within the ¥vedge is taken as,tan 6Fig. 1. Free body diagram of lvedgeSTATF,MF,NT OF THF, PROBLEMK (1 sin c) tan c (4)Substituting Eq. (3) and Eq. (4) into Eq. (2) ¥ve get,Zi R = y (1, - Z(cos- e+A'zi.Z)sine ( )sin e) AZFigure I sho¥vs a typical general pile group (a 2 x '_ piiegroup is sho¥vn here) of diameter d and length L embedded in soil. The plan dimensions of the pile group are aSubstituting Eq. (5) into Eq. (1), ¥ve get(and b. The friction angle of the soil is c and the pile-soilinterface friction angle is 6. The object is to determine the)AT=y AZI, - Z(cos e Ksln e)AZtanc (6)ultimate uplift capacity of the pile group.Considerin*' the vertical equilibrium of the ¥vedge andANALYSISIn studying the per'formance of piles ¥vith enlargedbase, Dickin and Leun'* (1990) critically discussed thevarious possible types of slip surfaces namely the verticalslip surface model, inverted truncated cone or pyramidalmodel, curved slip surface model considered by severalassuming that the *eight of the pile group of the lengthA Z is equal to the total weight of the soil correspondln_"..to the volume occupied by each pile in the group for thelength IZ.( p + A P) - P+ q(a + 2x)(b + '_x)- (q + Aq )(a + _x + 2A x)(b + 2x+ 2ZI x)investigators in estimating the pile capacity. It is observedthat the analysis is relatively simpler if the slip surface isassumed to be linear making: an an2:le ¥vith the verticalthat depends on the factors like friction angle and angle-A W- 2(a+ b + 4x+ 2A x)ll Tsin e = O (7)Substituting Eq. (6) into Eq. (7) and on simplificationgetof dilatancy (V/), which is a function of the relativec/. '= 2q(a + ' ,)dZdensity of the soil. From literature it is found that forsingle piles this angle has been assumed to be equal to anyc!Z dZ+ 2(a + b + 4x) )'(L - Z) M (8)(Vermeer and Sutjiadi, 1985), c/2 (Clemence andVeesaert, 1977), c (Murray and Geddes, 1987) or a funcBased on the above discussion, in the present analysisan expression for the uplift capacity of pile group isderived based on the assumption that under limitin_"..condition, soil mass around the pile group fails as aninverted truncated pyramidal solid body havin*" similarcross section as that of the pile group extending up to theground surface passin*' through the tip of the pile at anangle fi from the vertical.Derivatiol7In the limiting equilibrium condition, ultimate capacityof the pile is attained ¥vhen the mobilized shear strengthalong t,he failure surface and the vei*･hts of the soil andpiles balance the applied forces. A ¥vedge of thickness A Zat a height Z above the tip of the pile is consider'ed; the'_q(b + '_x)+ (a + 2x)(b + ?_x) dq + d Wone of the follo¥ving namely the dilatancy angle (V/)tion of c (Sutherland et al., 198,_).ve¥vhere M=(cos e+Ksin e) tan cReferrin*' to Fig. I the follo¥ving relations are obtained,c!x cote x=ZcotedZdq= yq y(I-Z) c!"' ' ' ' ･ -This on substitution into Eq. (8) yields,dPdZ- = 2q(a + 2Z cot e) cot 0+ '_q(b + '_Z cot e) cot e+ (a+ 2Z cot g)(h + 2z cot e)( - }')+d W+ _'(a + b + 4Z cot e ) y( L - Z) I I (9)dZs- UPLIFT C APACITY OF PILE G ROUPS60T1dW c!Z=(a+'x)(b 'x)y (lO)here3Setting q=y(L-Z) and Kl=a+b and substitutingEq. (10) into Eq. (9) the Eq. (9) can further be simplifiedto a form as gi¥'en belo¥vdPdZ=2yLKI cot e + 8yLZ cot I e- 2yZA'I cot e- 8yZ2 cot I e + '_KI yLM '_KI yZM+ 8,yZLK cot e- 8),MZ2 cot e(11)that on integration yields an expi'ession for the grossultimate uplift capacity as,89PLegends= 2yL2A'I cot 6+ 4y cot 2 eL3 - yKl cot eL2L3- 8y cot2 e 3 + ,_Kl yL2M-K yML2L34yMcot eL 8yMcot e 3 (1_')P.=K}'(cot e+M)L * 43 y cot 6(cot 6+M)L3 (13)The net uplift capacity of pile group is,P*** = yL2(CI K! + c2L) - ,V,. (14)V,rhere, Cl and C2 are the dimensionless constants equalto (cot e M) and4- cot e (cot e+M) respectively.3n ylrd2W,._,_, is the self ¥vei**ht of the pile group = 4¥*ire rope11)Aluminum strip6 Pile capiodel Pile7.,Pulle)8.4¥* {agnelic base plale9 Dead 1 i htDizrlFig. 2,･fodel lankau eEx.'perimental set*upinfiuence of the piles and loading there on is reported tobe in the range of 3-8 pile diameters (Kishida, 196,3).Model piles ¥vere prepared from mild steel rod of7_O mm x 20 mm cross section. The length of embedmentof pile, L in sand bed ¥vas 400 mm, 600 mm and 800 mmresulting L/d as 20, 30 and 40 respectively. The pile-soilinterface friction angle ( ) Ivas f'ound to be 26' from thedirect shear test. Pile caps ¥vere prepared for '_ x 1, 3 x 1,2 x '_, 3 x 2 and 3 x 3 pile groups (at 3d, 4d and 6d spac-ing) using 12 mm thick mild steel plate. As most of theWhere, n is the number of piles in a group.For L/d> ?-O the failure surface is assumed tangentialto the pile surface up to 0.3L from the tip of the pile.Hence Eq. (1 1) is integrated bet¥veen the limits O to 0.7Land added to the skin friction developed in the remaininglength.It is to be noted that the pile group capacity will be theminimum of the values predicted by considering grouppreviously studied model test were conducted for L/dratio ranging from 12 to '_Ovith only a fe¥v tests conduct-ed ¥vith higher L/d values, in the present study the samehas been taken on higher side i.e 20, 30 and 40. With theaddition of data ¥vith hi**her L/cl ratio the data bankrepresented short, intermediate and long piles. The spacing ran*"ing from 3d to 6d is generally adopted in design.As such, the same 1¥*as chosen representing piles ¥vithaction or the capacity of an individual pile multiplied bythe number of piles in the group. Hovvever, it. is obser¥'edcloser' to large spacin*".that only for spacin*' beyond 6d piles in a group actsindividually. The present paper is concerned vith the*'roup action only that is consistent with experimentalsand bed (made by rainfall technique) composed ofresults. In recommending the capacity that is to bemum and minimum dry densities of the sand ¥vere foundadopted in design one must consider' ¥vhich one of theto be 16.2 and 14.74 kN/m3 respectively. Sand ¥vasabove two mechanisms *'ives the minimum value andadopt the same.The above predictive model is validated by experimen-poured uniforrnly into the tank throu*'h the slot hopperkeepin*' the height of fall of 300 mm. By using abo¥'etechnique medium dense bed ¥vas prepared ¥vith a dry unittal studies made on model piles, ¥vhich are as follows.¥veight (y) of 15.8kN/nf, corresponding to relativeThe model piles were embedded in horno*'eneous dryuniformly graded Ennore sand having uniformitycoefficient of I .71 and specific gravity of ･_.69. The maxi-density (D,) of 54.30/0 and angle of shearing resistanceEXPERIMENTAL DETAILSTests on model pile groups ¥vere conducted in a steeltank (size 990 mmx975 mm x 970 mm). The tank ¥vassufficiently large enough to take care of the effect of theedges of the tank on the test results as the zone of(c) of 38'.Piles were subjected to tensile loading through a pulleyarrangement ¥vith a fiexible wire whose one end ¥vasattached ¥vith the pile cap and the other end lvith aloadin*' pan over which dead loads are gradually placed insta*'es. A schematic dia*'ram of the complete experimen- 60sSHANKER ET AL.tal set-up ¥vith the loading system and pile in place andready for test is sho¥vn in Fig. '-. T¥vo dial gauges ¥vithmagnetic base ha¥'ing sensitivity of O.OI mm ¥vere used tomeasure the displacement placing them on the pile cap at180' apart and equidistant fr'om load axis.RF.SUL,TS AND DISCUSSIONSeries of tests ¥vere conducted in medium dense soil tostudy the effect of pile spacing (s), Iength to diameterratio (Llc!) and number of piles in a group (ll) on theuplift capacity of model pile groups. The load ¥'ersusdisplacement curves lvere plotted for all the pile groupsand some of them presented in Figs. 3(a), 3(b) and 3(c).The load-displacement curves sho¥v similar beha¥'ior fordifferent spacing and length to diameter ratio. By usingthe double tangent method the gross ultimate uplift load¥vas found. The net ultimate uplift load of a pile group(* )Pig. 3(a). Upiift load versus displacement curves (3 x I pile group with4d spacing)¥vas re¥vorked by subtracting the corresponding self¥veight of piles and cap.Variations of group efficiency ¥vith respect to pilespacing for different pile groups ¥vith I,/d ratio being: ?_O,30 and 40 are presented in Figs. 4(a), 4(b) and 4(c)respectively. From these figures it is obser¥'ed that there isa definite trend of Increase in the gr'oup efficiency ¥vith theincrease of pile spacing. From Fig. 4(b) for a 3 x 3 pilegroup the efficiency is increasing from 490/0 to 600/0 as thespacing changing from 3d to 6d. Similar trend has beenobser¥'ed for other pile groups. Further, it is observedthat the group efficiency is ciecreasing ¥vith the incr'easingnumber of piles in a group. For any given spacing themaximum efficiency has been observed for 2 x I pilegroup and minimum efficiency for 3 x 3 pile group. From(b)ri"_* . 3(b). Upiift foad vers s dispiacement curves (3 x 2 pile group with3d spacing)Figs. 5(a) and 5(b) it is obser'ved that the group efficiencyis significantly affected bv_ Iength to diameter ratio of thepile group. For any gi¥'en pile group and spacing thegroup efficiency is decreasing as the length to diameterratio of the pile group increasing. From Fig. 5(a), for a3 x I pile group at 3d spacing as the L/c! ratio increasesfrom '_O to 40 the reduction in the group efficiency isaround 140/0.The theoretical ¥'alues of the net uplift capacities fordifferent group of piles considered for experimentalstudies ¥vere estimated from Eq. (14). Different trialvalues of fi, the angle that the slip surface makes ¥vith thevertical ¥vere taken to estimate the theoretical pile groupcapacity and compared the same ¥¥'ith experimental(c)observations. It vas obser¥'ed that an angle equal to c14gi¥'es values that are in good agreement ¥vith experimentalFig. 3(c). Uplift load versus displacement curves (3 >< 3 pile group lvitl]results. The same is adopted for further predictions. A4d spacing)comparison of the predicted and measured values assho¥vn in Figs. 6(a), 6(b) and 6(c) demonstrates a closeagreement as most of the data points lie very close to theideal line. A quantitative comparati¥'e study ¥vasconducted to estimate the deviation of the predicteduplift capacity from the measured one. It ¥vas observedthat for 890/0 of the data (40 out of 45) the deviation ¥vas¥¥'ithin 300/0 and for 550/0 of the data (26 out of 45) theerror ¥vas even less than 100/0. Thus the absolute relativeerrors bet¥veen the predicted and measured values lie ingeneral in a range lvhich may be considered to be ¥vell¥vithin the range of experimental error and errorsinherent to the models. Ho¥vever, for the sake of spaceand brevity these computations are not presented here.While doing the model testing, an attempt ¥vas made tocheck the validity of the assumption of plane fai]ure UPLIFT CAPACIT " OF PILE GROUPS1iOO -･-6a9O1¥l); o')>C'i:,¥l- -8C -jL)(!'(1;Ov3¥S [)ac ing ( s/d )8064e)e;60 -l::r SO-,, ,,:;S(j)4a2a 3a 40406L'd*as8tioSpadng (s/d)(a)(a)Fig. 5(a).Variation of group efflciencyvith L/cl ratio, 3 x I pile groupVariarion of group efiiciency witi] pile spacing, Llc!= 20Fig. 4(a).oO -____ _G.J_r_o_Llp_hl7-eiaox Ixo:h-l118aVc:ov3xq,O8c;; -'60e;SOQ,oC:sO404020a2 3 4620 3C 40soud r8'*iaSpacing (s/d)(b)(b)Variation of group efficieuc, wil 1Fig. 4(b).le spacing, L/d=30Fig. 5(b).Variation of group efrrcienc, wiih L/d ratio, s/d=6lvere further checked ¥vith the experimental data reportedby various investigators as follolvs.leoG roLlp size8a -vefficiency of pile groups of size 2 x I , 3 x I , 4 x I , 2 x '_, 3x '_, 3 x 3. Rough wooden piles of diameter 12.7 mm andLlc!= 24 were used as model piles. lvledium condition ofsand ha¥'ing y = 15. 10 kN/m3, c = 31 ' and D*= 21 /o ¥vas3 :1eo --e'3¥3ceDas et al. (1976) reported net uplift capacity in terms of3¥11¥,ve)x l40used as the soil media. Pile-soil interface friction angle 620234S8rSp cing ( _!d)(c)Flg. 4(c).Variation of group efficienc) with pile spacing, L/d=40¥vas taken as 19.3' (Das, 1983). The measured values of'the net uplift capacity of pile groups lvere indirectlye¥'aluated from the reported efficiency diagram. Themeasured values of the net uplift capacities for differentgroups and the corresponding predicted uplift capacitiesusing Eq. (14) are plotted in Fig. 7. Most of the data lievery close to the ideal llne. The percentage of error in thepredicted values from the measured one is found to beless than 300/0 for 830/0 of' the total data (10 data pointssurface by introducing wet soft tissue papers at differentlevels in the soil strata. Ho¥vever, the adopted techniquedid notvork and the verification of the assumptionre*'arding the slip surface could not be made.out of 1'_ data points).Siddarnal (1989) reported axial uplift test results onmodel mild steel pile groups of size 2 x I and ,_ x 2 having,After comparing the predictions made by using theL/d=20 and 40. The spacing of 2, 4 and 6 times the pilepresent method vith the experimental data obtained fromthe present investigation, the correctness of the modeldiarneter for 2 x I pile groups and ,- and 4 pile diameterfor 2 x 2 pile groups vere used. The dlameter of the pile 1*i!."SHANKER ET AL.610120 -80a *7aolcat-60Gz 80z- 5CalC40aA +,:: 60'; 300CL 40!20a201 ooaoa 100 2aO 3aa 4aO 500 6aa 7CO 8aaa 20 40Me sLsred Pnu (N)60 80 1 oO 1 20Measured Pnu (N)(a)*- 2xl 2dx 2x2 2 5dComparison vith present model test resuiis, I./d= 20Fig. 6(a).- 3x 1 2do 3x2 2d1 200Fig. 7.-4=2xl 3d--x- 2x2 4d･ 2xi 4d+ 2x2 6d= :4d- - 3xl 6d- 3x2,4d3x2 6d,3xComparison with Das et al. (1976) model test resultsOOoZ8aoO*e)l 1'6aov1Q,_ r;- o-'lLF '400+1400DA 2i200e I-Iooo>< >K-o' 800200 *e)lcieal line6001oQ;CLO 2ao 40a eOO 8ao laao 1200400" easvred Pn (N)200( b)aoComparison lvith present model tcst results, L,/d=30Fig. 6(b).200 400 600 8co loao i200 14aoMe sLJrBd Pnv (N)-.= Lld=20 2xl 2d* L/d=20 2x I ,6d2aoo-L/d=40 2x I ,4d+ L/d=20 2x2 2d3 L/d=40,2x2 ,2dc}- ud=2a 2x 4dB ud=40,2x ,2d-4 ud=4a 2xl 6d-S: L/d=2a.2x2,4d-e L!d=40 2x2 4d1 500Fig. 8.zCLeColnparisonvith Siddamal ( 983) model test resultsoaO¥vas 20 mm. Dry sand havin*' y= 16.1 kN/m3, c=40.5'v::e,and= 23' ¥vas used as the foundation medium. Figure 8sho¥vs the comparison bet¥veen the predicted values ofuplift resistance by the present theory ¥vith the measuredc500ovalues of uplift test results. It is seen that the predictedO 500 150a 20ao1 OOOvalues are in reasonable agreement ¥vlth the experimentalMe sured Pnu (N)values with 700/0 of the data having error, Iess than 300/0.2x I-x,6ds 2xl.3d A 2xl 4d -x3xl.3d- 3xl,4d +-3xl,6d2x2,3d- - 2x2,4d-4 2x2.6d {;- 3x2,3d - 3x2.4d3x3,3d c - 3x3,4d :E- 3x3,6d3x2,6dChattopadhyay (1994) repor'ted limited uplift test resultsfor model pile groups of size '_ x I and '_ x2 and I,/d=15.78, 23.68 and 31.57. Aluminium tubes of outer diameter 19 mm ¥vere used as piles. The groups ¥vere tested(c)Fig. 6(c).Comparison with present model tcst resu ts, I,Id=40for spacing 2.3d, 4d, 5d and 6d. Coarse to medium sand¥vith D60=0.95 mm, Dl0=48 mm, C = I .98, c=40' and6=25' (,-13c) and unit lveight of y= 17.00 kN/m3 ¥vereused. From the load dlsplacement diagrams, the nets UPLIFT C APACITY OF PILE GROUPS61130a50a40az:_ 2003aa:,Q,5,2aaI aoC1 aaOOa 3ao 400 Sao1 OOr, easured Pn1 OO 2aao2002xl ,Lld=23 68-- 2xlX4 5dH - 2x - 3d2x- ,8d-h, 2xi L/d=31 57 ･ 2x2,L/d= 5 78a 2x2,Lld=2368 E 2x2,Lfd=31 573x ,6d-- 2x2 3d-+- 3xl 4- 5d-4 2xl Ud=15 78 -Fig. 9. Compariso}1 wrth Chattopadya)' (1994) model test resultsuplift capacity of pile and pile *"roups ¥vere measured.The theoretical and measured net uplift capacities areplotted in Fig. 9 sho¥ving the predictions to be in closeproximity to the ideal line ¥vith 670/0 of the data (4 out of6) having error, Iess than 300/0.Patra and Pise (2003) conducted model test on pilegroups of' size 2 x 1, 3 x 1, '_ >< '_, 3 x 2 using dry Ennoresand as f'oundation medium. The specific gravity anduniformity coefficient of the sand ¥vere '_.64 and 1.6respectively. The unit weight of' the sand during testin_',_¥vas 16.4 kN/rn3 (D, = 800/0). The corresponding angle ofshearing resistance c = 37'. Aluminum alloy tubes of 19mm outer diarneter, 0.81 mm wall thickness were used asmodel piles. To increase the ¥vall friction of pile, fineEnnore sand was **lued around the pile by adhesive. Thelengths to diameter ratios of piles were 12 and 38. Thepile-soil interface friction angiebetween smooth androu*'h surfaces of piles and sand ¥vas evaluated from thedir'ect shear test results and reported as 20' and 31'respectively. The theoretical and measured net upliftcapacity of rough pile groups for L/d ratio of 12 areplotted for comparison in Fig. 10. lvlost of the data (9 outof 12 i.e 750/0) is very close to the ideal line ¥vith error, Iessthan 300/0. Thus, it is seen that the semi-empirical modeldeveloped presently acquits itself quite ¥vell in predictinthe values of uplift capacity of pile groups that are inclose agreement ¥vith measured values.3aoMeasured Pnu' (N)(N}2x2 6dFig. lO.-4- 3xl 3d2x2 4 5d3x2 3d - - 3x2 4 5d -O 3x2 6dComparison wrth Patra and Pise (2003) model tcst resultsconsidered to be permissible in such predictions.However, the predictive model needs to be verified ¥vithfield tests and for spacing beyond 6d.NOTATIONThe follo¥ving symbols are used in this paper.a and b=plan dimensions of the pile groupC1 and C2= dimensionless constan sD* = relative densityc!= pile diarne erK= Iateral earth pressure coefficienL = embedded length of pileLlc!= ratio of embedded length io diame er of pileP** = ultima e uplift capacity of pileP *= net ullimate uplift capacity of pile1 'V=¥veight of the elementai strip'; . = self lveight ofhe pile groupA Z= thickness of ¥vedge elememe= angle of failure surface ¥vith horizoulalfi= angle of failure surface ¥vith ver icalc =angle of internal friction of the soil= pile-soil interface friccion an".__le)'= unitveight of the soilREFERENCES1) C hauopadyay. B_ (, . (1994): Uplift capacity of pile groups, Proc.!3th ICSIVIFE, Ne¥v Dethi, India, S39-5422) Chattopad),ay. B. C and Pise, P. J. (1986): Uplift capacit)' of pilesin sand, J. Geotech. E,1gr*". Div , ASC E, 112 (9), 888904.3) C*lemence. S. P, and Veesaert, C. J. (1977): Dynamic pullovtresistance of anchors in sand, Proc. IntS_1'nlp- Soi! Stl'ucrure Inter-action, Roorkee, India, 389397.CONCLUSIONSBased on the studies reported in the previous sections itcan be concluded that the pr'oposed model has excellentpotential in predicting the uplift capacity of pile groupsembedded in sand. The error mar*'in between the predict-ed values and the experimentally observed values ingeneral is ¥vell ¥vithin 300/0 (which may attribute to eitherexperimental error or error' due to the model) and may be4) Das. B. M. (1983): A procedure for estimation of uplift capaciiy ofrou_ :h piles, Soils ailc! Fbunc!a!iolis, 23 (3), 122126.5) Das, B, h,l and Seele.v, G R. ( 975): Uplift capacity of buriedmodel piles in sand. J. Geo!ech. Eng. Dil' . ASC'E, 101 (G TIO),l0911094.6) Das. B. i¥,1., Seelev, G. R. and Smith, E. J. (1976): Upllft capacilof group piles in sand, J. Geotech. Eng Dil' , ASCH, 102 (GT3)282-286.7) Dicking. E. A. and Leung. C. F_ (1990): Perfofrnance of piles ¥vithenlarged bases subjected to uplifl forces, Can Ceotec'h J., 27 (5), 612SH、へNK蕪R狂丁、へL． 546−556．16）Ramasamy，G、，Dey，B．and Indrawn，E．（2004）l Studies on skin8） Isη1ael，N、F．and Kiym，T、、V、（1979）＝Up！ift and be＆rillg capacity frlCt1oniロpileSunde口ensileandcompressiveload，∫’∼伽1∼ of shor［plers1【1san（三，ノ、Gθo’θ‘h，五ン∼9’8．0’V．，ASC三．105（GT5）， Gθo’ech，、／、，．34（2），276−289． 579−594．17）Rao，K．S．and Venkatesh，K H．（互985）：UI）11f【behavlor of short9）Kishida，｝4。（1963）：Stress dis【rlbほtion by model piles in sand，So’1∫ αηゴFo』〃τ‘1‘πノ0／15，4（1），1−23，10）Levadler，D．R、and Sie圧er【，，」、G，（1984）：Tes董onmodeherlslon piies i自u賢iform sand，So’Z∫απ4Fo”114α1’0113ラ25（4〉，1−7・18）S1ddama1，U，V、（1989）：Be！1aviQrofpilegroupsunderupli田oads， ル4、7セ‘1∼、771θ∫’∫，1至丁，民11aragpur，lndia。 P1】e5，、ノ．0θ01θch。￡η813．D疵，ASCE，玉10σ2），1735−1748，i9） Sowa，V．A．（1970）＝Pulling capacity of co員creτe cast in−s1しu boredmMadav，M「R、（1987）：班clencyofpilegroupsimellsion，Cθn． piles，Cα1∼・（7θo’θ‘1∼．ノ、，7，482−493・ Gθo’θc11、ノ．，24，149−153．20）Sutherland，H B、，Raalay．τ．、V、and Fa（H，M．0，（i982）：Up11ft12）Meyerhof，G．G．（1973）IUpll負resisζa員ceofincli簸eda良chorsa頁（1 capacity of embedded anchors in sand，Proc．31ゴ∫n’．Co1ゾβθ1∼θ、・、 piles，P’qoc、8’1r∫CSハ4FE，Nloscow，2，167−172． α岱1ro1でS”・zκ’∼’1巴∫，Cambridge，MA，2，451−463。i3），〉茎eyerhof，G、G．and Adams，、L L （1968｝：丁藍e ulti【nate upli負21）Vermeer，P．A、a巖d Su頃ad1，W、（1985）：τ11e up鮭食res1s〔ance of capacityoffoundations，Cα’LGθo∫θc／L．∫．，5（4），225−244。 shal正ow embedcled andユors，P1’oc。 1111置∫CεA4ノ『E，San Fra旨dsco，14）Murray，三．，1，andGeddes，JD．（1987）：Upllfτofancllorpla【esin CA，3，1635一1638．22）Veslc，A。S．（1970）＝Testso郎nstrumen！edplles，ogeecheerivers1［e， sa賑d，ノ、Gθo’θc11、五17g’8．，ASCE，113，202−215．15）Patra，N、R．a駐d Plse，P J、（2003）：Up蕪fξcapaciτ｝・ofpile groロps in ／．、∫o’1∠、4θ（r1∼．roε’ηθ「．Eηg’8、0’v．，ASCB，96（S鼓12），561−584． sand，E！θ‘’〆011．．／．（｝θo’θch．E’∼91習．，8，Bundle．B．鑑
- ログイン
- タイトル
- An Elastoplastic Model for Unsaturated Soils under General Three-dimensional Conditions
- 著者
- M. M. Farias・M. Pinheiro・M. P. Cordao Neto
- 出版
- soils and Foundations
- ページ
- 613〜628
- 発行
- 2006/10/15
- 文書ID
- 20945
- 内容
- rSOILS AND FOU*¥DATIONS Vol, 46.N'o ), 6 1 3-628 . Ocl. '*006J2',panese Geolechnical SocieL}AN ELASTOPLASTIC MODEL FOR UNSATURATED SOILS UNDERGENE.RAL THREE-DIMENSIONAL CONDITIONSM. M. FARL ¥si) M. PINHEIRoii} and M. P. CORDAO NETOiii)ABS'I'RACTEngineering problems concerned either directly or indirectly ¥vith unsaturated soils ar'e more and more common,ranging f'rom aspects related to seepage to those related to shear stl ength and volume change. A fe¥v constitutivemodels have been conceived to describe and quantify these problems all of them ¥vith some ad¥*antages and ch"a vbacksRegarding mechanical behavior, the so-called Barcelona Basic Model (BBM) has achieved ¥vide acceptance ingeotechnical engineering, basically due to its simple mathernaticai formulation and good description of phenomenaassociated ¥vith unsaturated soils, especialiy collapse. Another concept that has emerged as a po verful frame¥vork totackle three-dimensional states in granular materiais is that of a modified stress tensor, such as tjj. In this paper bothBBlvl isotropic structure and tjj concepts are combined to pr'opose a ne¥v elastoplastic model for unsaturated solls,called tjj-unsat. Modifications and generalizations for unsaturated states are introduced to accommodate thoseframelvorks and o¥'ercome some inherited ch･a vbacks. At the end of' this lvork, experimental data gathered fromspecialized geotechnical literature is used to support the theoretical framework. The satisf'actory agreernent bet veensirnulations and tests results emphasizes the applicability of the proposed formulation to real boundary valuegeotechnical problems.Ke¥.' "ords: collapse phenomenon, constitutive la vs, elastoplasticity, tjj concepts, unsaturated soils (IGC:D6/EO/E 1 3 /E 1 4)DO/D,3/D5/hand, the keystone of tjj-unsat three-dimensional stressINTRODUCTIONframe¥vork is related to the concept of SpatiallyMobilized Plane (SMP) and concepts associated to thatThis paper presents an alternati¥'e constitutive modelfor describing the mechanical behavior of soils, particularly at unsaturated states. The model, named tjj-unsat, isbased on the classical theory of plasticity, inasmuch as itplane, such as the modified stress tensor tjj andMatsuoka-Nakai f'ailure criterion. In order to grasp themeanin*' of these concepts, Iet a soil sample be submittedto three dift rent principal stresses until complete soiluses concepts such as yield and plastic potentialfunctions, flo¥v rules, hardening la¥vs. It is also foundedfailure is achie¥'ed. If three Mohr circles and theiron the critical state theory, vhose legitimization forunsaturated states has been extensi¥'ely supported bymany authors, to name but a fe v, Alonso et al. (1990),respective failure envelopes are plotted for each pair of"principal stresses (al-(T2), (al-(T3) and ((T2-a3), thenthree planes of mobllized shear strength can be defined.Axelsson et al. (1989), Toll (1990), lvla touk et al. (1995),The SMP will simply represent a composition of theseWheeler and Sivakumar (1995), Adams and Wulfsohnmobilized planes. In other ¥vords, SlvlP ¥vill represent the(1998) and Wang et al. (2002).The model adopts t¥vo ¥vell-established frarne vorks:one for Isotropic stress-suction conditions and anotherone for true three-dirnensional stress conditions. For theplane ¥vhere soil particles are considered most mobilizedon the a¥'erage in a 3D stress space (lvlatsuoka and Nakai,former, the isotropic frame¥vork of Barcelona BasicModel (BBM) is assumed. This model, vhich became abenchmark in literature for unsaturated soils, vasinduced by stress state (Nakal and Mihara, 1984).1977). The modified stress tensor tjj is regarded as arnechanical quantity able to account for the anisotropyFinally, Matsuoka-Nakai is a purely frictional failurecriterion based on the stress invariants related to theSMP. In a simple manner, it takes into consideration thedeveloped by Alonso et al. (1990) in order to reproduceseveral characteristics of the mechanical behavior ofinfluence of intermediate stress on soil strenth.Modifications to BBM f'rame vork ¥vere performedunsaturated soils. It offers a simple guideline to representand quantify soil collapse due to saturation. On the other¥vith the aim to o¥'ercome some dra¥vbacks associated to*' Professor, Dept. ofCivil and Environmental Engineering, University of Brasilia, Brasilia. DF, 70910900. Brazil (rnunizC ."S unb br),PhD Student, Dept, of Civil Engineering, Universitv of C*algar}', Calgary, AB, T2N IN4, Canadaiii] phD. Dept_of C'ivil and Environmental Engineering, Universlt}' of Brasilia, Brasilia, DF, 70910900, BrazilThe manuscript for this paper ¥vas recei¥'ed for revie v on November 2, 2005; ap )roved on June 13, 2006¥¥･'ritten discussions on thls )aper should be submitted before lvla ' l , 2007 to the Japanese Geotechnical Societ y, 4-38-2, Sengoktl, Bunkyo-ku,Tok)'o I 12-001 1 , Japan. Upon request the closing date ma)' be extended one month**]613 FARIAS ET AL.614r:.. '//" '/ipl' !)hI(cr )ipnff'h 3r-¥¥¥3!,(TO O Y(],,,,hA¥¥¥ '¥.･ cr5'¥- nr r (. l + (Ti] ): :]･:¥<'=i'::!=7/ ¥'i 'j.:.:=aGene 'aliz,ed! SMSMP(T, (Tj (TFig. 1. Mobi ized planes due to stress state, natural cohesion and soilsuction(. +. )Cthe description and estimation of soil collapse; ¥vhereasgeneralization of SMP, modified stress tensor tjj andlvlatsuoka-Nakai failure criterion vere proposed in orderto encompass unsaturated states of soil.In this paper, the stress tensor a is regarded to as thenet stress ((1=c total u*1), ¥vhere (Tto *1 stands for totalIII ((T, )Fil:r. 2. Generaiized SMP in the tl]ree-dimensionai principal stressspacestress tensor and I is the second order unit tensor(Kronecker's delta). The term suction refers to matricsuction (s=u -u, ), ¥vhere ua and uw are pore air andpore ¥vater pressures, respecti¥'ely.and the generalized SMP turns into the original SMP. Onthe other hand, for hypothetically high values of suction,the soil tends to an isotropic stress state, and as a conse-quence, the generaliz,ed SMP tends to the octahedralGF.NF.RALIZF.D SPATIALLY MOBll,IZF.D PLANF,plane.From Figs. I and 2, it can be shown that theThe concept of Spatially lvlobilized Plane (SMP)generaiiz,ed SlvlP intercepts the axis I, 11 and 111, (¥vhichaddressed in this paper is a generaliz,ation of t.hatcorrespond to the principal stresses (71' (T2, and cT3,originall.v conceived by lvlatsuoka and Nakai (1974) forcohesionless saturated soils-see aiso ¥vorks of Matsuokar'espectively) at points proportional to the square root ofthe principai stresses shifted by cTa The direction cosinesof the normal to this plane can be ¥¥'ritten as:and Nakai (1977, 1982) and Nakai and Matsuoka (1983).This generalization is established upon the extensiondj=lproposed by Ohmaki (1979) and Matsuoka and SunI 2(199'_, 1995), ¥vhich accounted for the effect of naturalcohesion of soil. Lat,er, other authors, based on theinterpretation of soil suction as a sort of apparentcohesion, developed constitutive models for unsaturatedsoils using SMP concepts (Kato et al., 1995; Kato, 1997;Matsuoka et ai., 2002).The idea herein suggested only accounts for theapparent cohesion due to soil suction. It can be readilyfigured out through Fig. 1, ¥vhich illustrates three Mohrcircles and their respecti¥'e failure envelopes shifted by cro./ - (-')(i= 1, 2, 3)iwherei are the principal values of the tensor stress(=(1+(701), and I._ and 13 are, respectively, the secondand third invariants of 6. For' clarity, the three stressinvariants are expressed as follows:I 1 = tr ( ) = I! + 3(70I. = - [tr (- 2)2 - tr ( 2)1 = J._ + 211 (TO + (TI 3 = det ( ) = I_.. + I._cro + Il (T(3)+ (7This shift-term can be concei¥'ed as a Cauchy stress actin_ :isotropically on the soil structure. In a general form, (70can be expressed as follo¥vs:(TO = k*s ( I )¥vhere k* is a soil parameter and s is the soil suction. Thesuction effect vas assumed in accordance lvith Alonsoet al. (1990). This linear relationship is simple andadequate from a practical engineering standpoint. Otherauthors, namely, Sun et al. (2000), proposed a morein ¥vhich ll' I._, and I..･, are, respectively, the first, secondand third invariants of the ori_defined in the previous section.inal stress tensor a, asGENERALIZF,D MEC_HANICAL QUANTITY tijAn immediate outcome of above extension is also thegeneralization of the concept of tensor' t, a mechanicalquantity that reflects the induced anisotropy of granulareffect.materials under saturated states (Nakai and Mihara,1984). In a general form and under unsaturated condi-It is important to note that the infiuence of a truecohesion could be easily incorporated by adding the termtion, it can be ¥vritten as a function of the second-ordertensors (1 and a (Pinheiro, '_004):sophisticated non-linear equation for expressin*' such an(c'cot c) to the right-hand side of Eq. (1); ¥vhere c standsfor true cohesion, and c stands for internal frictionalangle of the soil under saturated condition.Particularly ¥vhen the soil is fully saturated (70 ¥'anishes,t = aa (4)where a is a tensor computed from direction cosines ofthe normal to the generalized SMP. This dimensionless 7 ..,ELASTOPLASTIC< IODEL FOR UNSATURATED SOILS615invariants depend on (7a, i,e. they are infiuenced by the!state of soil suction as ¥vell.Gener'alizedASMP31 + 71, (TO + Il (tabo + bl ao + b2(TtD .ts co + cl (TO + c2 crB(9)tN = I, + 211 aa + 3crt a+ b3(7+ c3 (T+ b4(r5' !/2c4 (r40( I O)¥vhere the coefficients bi and ci (i=0, 1,...,4) areex'pressed as follolvs:bo = Il I. 13 - 91cbl = 11 1h+ ,_1= 31 j I1･. - 1) 1_.1*911 13 - 61!b3 = '_1 "IFrg. 3. Generaiized SMP and modified stress invariantsb4 = 21) II I_. - 913- 61._c0=1cl = 41! I,symmetric tensor is obtained through reverse transformation from its eigenvalues a as sho¥vn belo¥v:a = QaQ Tc. = 41(5)c3 = I '_Ilc4 = 9vhere the components of tensor a are g)iven by:[o did' O o] oa=OOd *In Eq. (5), Q is the orthogonal transformation rnatrix,numerically determined from the eigen¥'ectors of stresstensor (1 using, for instance, Jacobi rotation procedure.The definition of modified stress tensor t is the same asthe original one used by Nakai and lviihara (1984); there-fore the same terminology is adopted here. The onlydifference for unsaturated conditions is the cohesiveeffect produced by suction (s), 1¥'hich is incorporated intothe tensor(=a+(701) with (To(=k,s) and this affectsonly the direction of the generalized SMP, via the valuesof dj in Eq. (2). Under saturated conditions, this effect¥'anishes and the generalized Spatially Mobilized Planeand therefore the modified stress tensor t coincide ¥viththe original concepts.The modified stress invariants tN., and ts, respectively,normal and shear stresses acting on the generalized SMP,as for tjj-clay model (Nakai and Matsuoka, 1986) are+ 61.It can be easily verified by simple inspection that forcohesionless soils under saturated condition, i.e. (r0=0,Eqs. (9) and (10) reduce to those used in tj -clay model.Finally, just to emphasize, a different concept ofgeneralized SMP is advocated in this ¥vork in contrast¥vith Kato (1997) and Matsuoka et al. ('_OO'_). Theseauthors conceived a new modified stress tensor based on atranslated stress tensor(= (1 :- (rol). Here, ho¥ve¥'er, thistranslated tensor is not directly used to define themodified stress tensor t, but is only applied to calculatethe direction cosines of SMP (al, a2, a3), i.e. the effect ofsuction acts indirectly at t by adjusting the SMP direction.STRAIN INCREMENTsStl'ain Increlnents on the Gene/'a!i< -ec! SMPThe strain increments c/8N., and des, nor'mal and shearstrains on the generalized SMP, respectively, are thestrain invar'iants in the modified str'ess space t. In *'eneralterms, they can be expressed as follo¥vs:d8N = c!8:a (1 1)defined as:t , = t:a (6)d&s = il deD Il (1 2)tD = t - t ,a (8)where de is the total strain incrernent tensor and deD is the¥vhere ll･[i = /T denotes the norm of a tensor and tDstands for the deviatoric stress tensor related to thegeneralized SMP. Together with modified stress invariants, those strain increments play an important role onmodified stress space t (Fig. 3).The modified stress invariants on the orig:inal SMP canthe stress-dilatancy relationship to be delineated in thets = lltD Il (7)also be redefined as functions of the conventional stressinvariants II' I._ and 13 (Nakai and Matsuoka, 1986); thesame can be stated for the generalization introduced here.Ho 'ever, in that case, those extended modified stressc!8D = ci8 - dea ( 1 3)deviatoric strain increment tensor referred to thesequence.Strain Increlnent 'rensorsBased on concepts of the classic theory of Plasticity,the total strain increment tensor is split into t¥vo 1 !ET AL.compouents, according to the additive decompositionl' ::: Ierule:!c/8 = c!e* + c!sP ( 1 4)! t) Ill !T*¥vhere c!8* denotes the elastic strain, ¥vhich can bel '"'*1:'!..: '/, (s)(a)obtained from the generalized Hooke's la¥v; ¥vhereas cl8denotes the plastic strain determined according to anassociated fio¥v rule referred to t-space.c/8* = (D*) - I :c/a ( 1 5)' ::: i + (::)deP = c!y af ' (c!y > O) ( 1 6)s{1 In sS fatIn the abo¥*e equations, dy is the plastic multiplier and,f' is the loading collapse yield surface, both to be definedin subsequent sections. The fourth-order elastic tensor isexpressed as follo¥vs:D *1 +=v (1--+ -lel- ( i 7)+ v)(1I- 2v)+*(b)Fig. 4. Relationsl]ip bctwee l specific volwre and naturai lognrit!Im of(a) nornrai stress to the generalized SMP and (b) suction¥¥'here:E (1 'v)(Lte)1: (18)l((s)in ¥vhich v is the Poisson's ratio, assumed as a constant, Eis the Young's modulus, e is the void ratio and l( is thecoefficient of compressibility for' the unloading-reloadin( -section of an isotropic consolidation test. Here thiscoefficient is supposed to be suction-dependent as supported by some aut.hors, to name but a fe¥v, BalmacedaVohn77etl'ic St/'ain IncrementsFor changes of stress state, the volumetric strain incre-ments are computed from the classical relationshipbet¥veen specific ¥'olume (1 +e) and natural logarithm ofmean stress, here substituted by the normal stress to thegeneralized SlvlP (Fig. 4(a)):de I '+e t/t'(s) dtN (24)(1991), Futai (1997) and Barrera ('_OO'_).In the original tij-clay model, the plastic strain incre-deP )'(s)-!c(s)dtN (25)ment tensor is further split into t¥vo components-one* I + e tNsatisfying the associared flo¥v rule and another related tothe increase in mean stress-as an attempt to express the¥vhere deinfluence of loadin_* path. For the sake of simplicity, suchstrain increments, respecti¥'ely^Similarly, from Fig, 4(b), the ¥'olumetric strain incre-a split ¥vas not considered herein.So far only strain increments associated to stresschange ¥ver'e obtained. To compute strain incrementsoriginated fr'om suction change, the follo¥ving equationsare su gested:c!c!= d * + c!Pstand for elastic and plastic volumetricments for chang:es of suction state are der'i¥'ed as:d = l(' cls (26)1 + e (s +p***,,)c/),< - ,(* c!s= 1" ( o + p.: , ) (27)' = l]*cls(plastic) (2 1 )c/and c!e= hPc!s¥vhere dc and dcr, denote elastic and plastic ¥'olumetricstrain increments, respecti¥*ely.¥vhere h* and hP are, respectively, the elastic and plasticsecond-order modulus tensors, ¥vhich vary vith suctionas defined belo¥v:h* = ---- 1J(* (22)3(1 + e)(s + p** ,)ISOTROPIC_ STRF,SS FRAMF,WORKThe mathematical structure of tii-unsat model underisotropic stress conditions is very akin to that of theonglnal Barcelona Basrc Model apart from three mainmodifications: (1) use of t , instead of p = (((Ti + (T2 + (73)/p ).* - /(*1 .h - 3(1 + e)(s+p=**m(23))So far coefficients i(* and ).* are, respectively, soil compressibility for elastic and virgin state of soil, both associ-ated to variations in suction; p* *'* is the atmospheric pres-sure ( = 100 kPa). A11 those coefficients of compressibility¥vill be geometrically outlined in the next section.3 -u*) as stress state variable; (2) use of a suctiondependent coefficient of compressibility for unloadin*'reloading conditions and (3) the collapse of soil due tosaturation compr'ises t¥vo cases that rely on how soilcompressibility at virgin state ().) varies vith suctionvariation. The first modification is a direct consequenceof tjj-frame¥vork assumed hitherto, whereas the second FLASTOPLASTIC ,IODEL FOR UNS TURATFD SOILSl'lll !617¥'ell-kno vn Loading C*ollapse (LC) yield f'unction isobtained independently of soll stiffness response ¥vithrespect to suction. Here, as In Alonso et al. (1990), thatequation defines a set of yleld ¥'alues (tNo) for each associ-(a)ated suction value and explains the apparent increase inpre-consolidation stress associated ¥vith suction increaseand the collapse phenoulenon obser¥*ed alongvettingpaths. The expression for LC" yield f'unction is given by:(tNR) =(!Nl) t¥,'c (30)t¥. 'o (;.(o} -{*)) !{;.(*) -(* ))in ¥vhich, tNo is the pre-consolidation stress for unsaturat-ed conditions; t c is the pre-consolidation stress forS;; osaturated conditions, and t¥.'R is a reference stress. Whatdistinguishes the derivation of CASE I from CASE 2 isl'/¥(t f{ Int! v L]basically t R. This parameter must be chosen so that thedifference bet¥veen N(O) and N(s), the reference specificvolumes at saturated and unsaturated states, respecti¥'ely,is the sarne for both cases. Details about ho¥¥' the aboveequation ¥vas derived ¥vill not be presented here since itl jr( )I !((ss¥Yellil g l(b)).(OTo delimit the elastic domain under isotropic1j.(s)condition, another concept inherlted from Alonso et al.s=0(1990) is that of a Suction Increase (SI) yield cur¥'e, whichsv(o) ::: Lfollo vs the same steps as demonstrated by Alonso et al.(1990) and Pinheiro (2004).Ois represented by the expression belolv:c o I I apses = so = constant (3 1 ):!''1'v(s)¥vhere sb may be interpreted as the maximum past suctionever experienced by the soil.stressIn this section, only a brief outline of tjj-unsat frameFrg. 5. Unsaturated soil responses: (a) CASE I and (b) CASE 2¥vork under isotropic stress-suction conditions ¥vaspresented. Emphasis ¥vas gi¥Jen to modifications performed to o¥'ercome some dra¥¥'backs inher'ited fromand third adjustments arise from experimentai observations (Balmaceda, 1991; Wheeler and Sivakumar, 1995;Futai, 1997; Barrera, 2000).BBM. In the follo¥ving section, attention is focused onsorne aspects related to three-dimensional conditions,lvhere the tjj-concept is connected ¥vith the traditionalThe t¥vo aforementioned cases of collapse response are:elastoplasticity theor'y.CASE 1, in which collapse al¥vays increases with netmean pressure (ori**inal BBM assumption), and C*ASE 2,in vhich soil collapse increases, reaches a maximumELASTOPLASTIC FRAMEWORKvalue, then decreases at hi_ :h net mean pressure (Fig. 5).The variation of compressibility ), with soil suction isgo¥'erned by the follo¥ving equation (Alonso et al., 1990):The main aspects to be described in this section reiateto standard concepts of elastoplasticity theory, such asyield and plastic potential functions, fio¥v rules, harden-;.(s) = ),(O)[(1 - r,) exp ( -fis) + /'il (28)where ;.(O) is the compressibility ), for saturated state; fiand rare fittin*' coefficients. The response of ), dependshighly on /';_; for r;. < 1, ). decreases with suction increase;whereas for /';> l, ), increases ¥vith suction increase.It is su*'gested a similar la¥v for commanding the varia-ing la¥vs, and stress-dilatancy relationship,Hinokio (200'_, 2004) is proposed. The relation is a nonlinear curve defined on the modified space, as follo vs:M*. - X"Y=tion of l( ¥vith suction chan*"e:l((s) = ,((O)[(1 - r ) exp ( -fis)/'*1 (29)¥'ith tjj-con-cepts extended to consider unsaturated states of soil.Initially, a generalization for unsaturated conditions ofthe stress-dilatancy relationship presented in Nakai andvhere X= ts l(tN + t s) and Y= c!e PI (32)/d8are, respecti¥'ely,¥vhere /((O) is the compressibility ,( for saturated state; /'*the stress ratio and plastic strain increment ratio; t¥.'s isis another fitting coefficient; and fi, for simplicity, isassumed to be the same as in Eq. (28).exactly the same as the stress variable due to suctionAn important characteristic of' those previousof the stress-dilatancy curve; and M> = corresponds to theadjustments is simplicity, since a unique equation for theeffect, i.e. (70; (x is a fitting exponent related to the shapeordinatevhere the plastic strain increment ratio is zero 1 1FARIAS ET AL618J 25(a)Data:lvlacari et al!( 2003)/Y T !,,I .OO!,j-unsato c1easuredo. 75o.50e eQE!:t]'3c!c (:' c:c!e(.>:: - *c･Q oFig. 6. Stress-diiatanc) relationship for tjfunsat model-3_o -2 5 -2_o - I .5(Fig. 6). This last parameter is determined under theData:partlcular situationlvlacari et al_ (2003 )vhere critical state is reached. In suchp + p,M*=X** l+ (33)X**The advantage of representing the stress-dilatancyeooegs> ;'..>' e e"5c'='s. .g75- .r.8B O.)Op8:.._ o{ ･･a.c o '-5g..;: oca!e-3.0 -2.5 -2 O - Ie..,obtained:( Y., il.)c!';:s co Q B A measured% *05I 25B B lvlthose critical ¥'alues of X and Y into Eq. (3'-) andrearranging the resulting expression, M* js eventuallyoo-o. 5( b)a case, X=X** and Y= Y**, and both variables may be¥vritten as functions of the friction angle at saturatedconditions (c.f. Nakai and Matsuoka, 1986). Substitutin*'-1.0- I _O-o 5c!e !'d e!'o.oo. 5relationship using modified stress-strain ¥'ariables is thatsoil response is uniquely captured regardless of therelati¥'e magnitude of the intermediate principal stressFig. 7. Stress-dilatanc) response under unsaturated conditions (a)tji-unsat mode and (b) BBMunder saturated states (Matsuoka and Nakai, 1974;Nakai and Matsuoka, 1983). It is interesting to note that,despite some considerable scattering, similar trend is alsoroughly observed for unsaturated states, as illustrates acompilation of TC (triaxial compression) and CTC(conventlonal TC) data gathered from tests performed byyield!r¥..lyieldplane SMacari et al. (2003) on unsaturated silty sand at differentmatric suction le¥'els (Fig. 7(a)). When the same data forstress ratio-dilatancy are plotted adopting the stress andstrain variables used in BBM (q/(p+p,) vs. d8. /d), acloud of points ¥vithout any tendency is obtainedS(Fig. 7(b)).Similarly to Alonso et al. (1990), t¥vo yield surfaces areFig. 8.Yield surfaces LC and SI at modified stress space tjjdefined. For convenience, the same acronyms are hereinemployed: LC, corresponding to load collapse yieldsurface and SI, corresponding to suction increase yieldplane (Fi**. 8). Ho¥vever, unlike BBM frame¥vork, thosestress states, i.e. ts=0, gives the expression for the LCyield surface function:yield surfaces, ¥vhich set the boundaries of elastic domainft(tN.,, ts, tNc,s) ts+t:.sIn t¥.'oTtNs(tN ,tstNs O) ** T ,=+of soil under unsaturated states, are represented in themodified stress space (t¥,', ts, s). For stress, or strain, or(35)suction paths that cross either LC or SI (at s=so) yieldsurfaces, permanent (plastic) strains are assumed tonormality condition (de P:dt = O), an ordinary differentialwhere tN.,c is the stress-type hardening parameter used todetermine the size of yield surface. The other terms ¥vereall previously introduced.The second y. ield surface is an extension of SI yieldequation can be deduced:curve (Eq. (31)) into the region ts>0 (non-isotropicoccur.From stress-dilatancy relationship (Eq. (3'-)) and(t¥= i-*)tN + tN. ,s (34)dt¥. ' t¥.-'M+*"'stsThe solution of that diff rentlal equatlon for theboundary condition expressed by t¥.'=t¥.'o at isotropicdomain) by means of a plane (or lvall) simply defined as,f*(s, so) s-s0=0, ¥vhich is the same expressionproposed by Alonso et al. (1990). The suction so ¥vaspreviously defined as the maximum past suction everexperienced by the soil. ELASTOPLASTIC MODEL FOR UNSATURATED SOILSThe plastic strain incrernents related to LC yield surface, at constant suction planes s, are calculated according to an associated flo¥v rule referred to lhe modified61().h¥'drostatic(yax i s1¥¥stress space:ag dy af' (36)/c!8 P = d y =at at,1:CrJ * *(-vhere dy is the plastic multiplier to be explicitly defined inthe Appendix and g is the plastic potential function,vhich coincides ¥vith the LC yield surface function J'*Generalized M-N(Eq. (35)).Regarding SI yield piane, the vector of plastic strainMohr-Coulombincrements induced by suction increase is defined as(d+P, O), in lvhich c/Extended D-Pstands for plastic strain incrementstriggered ¥vhen suction reaches ievels higher than athreshold, so (see Eq. (27)). Since this paper focusses onlyFig. 9.Failure criteria al conventional principal stress spaceon paths that touch L,C yield surface, the SI yield planevill never be directly activated but it ¥vill be affected indi-Data:rectly throu_2:h a coupled hardening la v as describedbelow.For each yield surface, L.C and Sl, a coupled strain-TC ! Macari and Hoyos (2001 )SS '¥.¥ ¥ '/j / "'v 50 kPatype hardening la¥v ¥vas conceived in order to relate theincrease (or decrease) of elastic domain to volumetricplastic deformation, de.P. Thus, t vo hardenin*' Ia¥vs,¥vhich command such interconnection, are considered inoco (:lOOkPaTE¥ _¥ A¥AA/ AQ (T("!Q Q (T : 200kPa' 'fthe follo ving:// ... li,; ;/!Ac!tNcI +d8 e p (3,7)tNC )' (O) - l( (s')dso i eso )' *::::1:; ./'/ .4r-;:':¥'1/SS ' -'i ''/i¥" '¥+- 100kPa!tlii¥. ¥ ¥ -h----I¥/TC' :,,:_･1: "t:::lj ･¥¥ic*Finally the failure criterion here employed is presentedSS ' ' '-- Generaiized M-NTEIto close this section. An expression similar to the oneoriginally proposed by Ohmaki (1979) and later used inthe context of unsaturated soils by Kato (1997) andMatsuoka et al. (200'_) is used here to generalizeExtended D-PFig. 10. Octahedral plane: Generalized iM-N and Exteutied D*PfailuFe criteriaMatsuoka-Nakai failure criterion. Based on the concepts;thus far introduced in order' to tackle unsaturated states,such extension is presented simply as:frictional anglevas regarded as bein*' suction-indepen-dent, a hypothesis perhaps valid only within a limitedtN. , + tNS= constantrange of stress-suction.here advocated, especially with respect to that describedThe proposed **eneralized failure criterion circumscribes Mohr-C*oulomb (M-C) failure criterion and iscircumscribed by the Extended Drucker-Prager (D-P)in Kato (1997), who proposed an extension ¥vhich alsofailure criterion in the conventional principal stress spaceleads to Eq. (39). Particularly, Kato (1997) conceived anew modified stress tensor based on a translated stress(( 1,(T2, (T3), as sketched in Fig. 9. The GeneralizedMatsuoka-Nakai (M-N) criterion coincides with M-C intensor ( = (1 + ael). In the opinion of the authors of thepresent paper, this leads to double countin_ : the suctioneffect in the denominator of Eq. (39). Here, on the otheraxisyrnmetric stress conditions (triaxial compression andtriaxial extension) and wit.h Extended D-P only in triaxialhand, this translated tensor is only applied to computecriteria, Generalized M-N has the advantage of generat-the direction cosines of SMP (al' a2, a3), i.e. the effect ofing a completely smooth surface; hence, it is moresuction acts indirectly in tN., and ts, therefore, avoidingappropriate from a computational standpoint.such inconvenience.The constant term on the right-hand side of Eq. (39) isa function, vhich dependents solely on the internalfrictional angle of soil under saturated conditions, asFigure 10 illustrates both Generalized M-N (solid lines)and Extended D-P (dashed lines) failure criteria togetherwit.h failure points obtained from experimental results ofassumed by Nakai and Matsuoka (1986). The internalseries of true triaxial tests on unsaturated samples of' siltyIt is ¥vorth to reemphasize the originality of the conceptcompression conditions. Cornpared to both failureMacari and Hoyos (2001). These authors performed a liFARIAS ET AL_620tota] due to due to( ) af'.D':af afiHtr a-f,strain stress suction: daddia(; ' atat ' at ic* I =; ds : 1+1dH Is the plastic module defined by:i¥'e decompos ition 'l+eof :>*train tensor 'H= - tNc______ ______ _____i_____r_ j() ((!" _'= E c!s" + ds!' : _b) Stress-like hardening parameter dt¥,'c:dtNc Hdy( tr af (43)i' , - d" _'at_l r-c!8 =d;'c*;j" :Gel eralized : __c'+t jl-iooke*s laColyd(rsistency cond itio 1 :d/" =0 ::> dl; D" :(c!e';+**c) Fourth-order elastoplastic rigidity tensor D*P (stress):Dep = D - (44)1' ( _,(D af! (afl .D'at1I I¥a(1'd) Second-order elastoplastic tensor h*P (suction):Hardening law:h'P D'P (h hP)-l Iaftaf D': (45)> dl ,,*c!a(4' )).(O) - l((s)X) icr*{'d8' }: ; (r*- -i* ds(4 1 )a[) as ats Dr!' :cr- - h'rdsSome of the partial derivatives in the above expresFrg 11. Numerical integraiion scheme of tjunsat constitutiverelationship for stress paths that only reach LC yield surfacesand under different stress paths (triaxial compression-TC, simple shear-SS and triaxial extension-TE)and diverse suction and octahedral net stress levels. InFi_"*.. 10, the inner, intermediate and outer curves correspond to suctions of 50, 100 and 200 kPa, respecti¥"ely.A more detailed description of these results is presentedat the end of the validation section.Another peculiarity of the generalization pr'oposedhere is that Generaiized lvl-N reduces to the orig:inalsions, as ¥vell as a more detailed explanation on ho¥v the4th order tensor D*P and the 2nd order elastoplastic tensorhep ¥vere obtained, are sho¥vn in the appendices in the endof this paper.MODEL VERSUS F.XPF.RIMF.N TTALRESULTS-VALIDATIONModel validation is a crucial step in order to check¥vhether a model properly describes the material behavioror not. In this paper, ¥'alidation is accomplished byreproducing stress-strain and suction-strain results of¥'on lvlises failure criterion as suction hypothetically tendsexperimental tests carried out on unsaturated samples ofdifferent types of soils. All the experimental data ¥veregathered from specialized geotechnical literature. Overall, tjj-unsat model requires 12 constituti¥'e parameters,to infinite values (t? snamely: t¥.=R, /c(O), ),(O), r , /';_, fi, ic*, ;,*, v, c, k*, and c .i¥,Iatsuoka-Nakai failure criterion as suction reaches nilvalue (tNS = O), i.e. ¥vhen the soil saturates; and reduces toco).Ho¥vever, the number of parameters to be used dependson the sort of pr'oblem, i.e. stress-suction state, yieldNUMERICAL INTEGRATION SCHF.MF,surface in¥'olved, etc. Besides that, initial stress-suctionrequires the de¥'elopment of algor'ithms in order tonumerically integrate their constitutive relationship.state (cr s) I and initial positions of LC and SI .¥'ield, '",'**surfaces must be specified.The first set of laboratorial test to be analyz,ed ¥ "asThese al,_,_crorithms or schemes ar'e iterative processes in¥vhich the stress, strain and suction states and the hardening parameter are updated for given stress, strain, and/orperformed by Barrera (200'_) on unsaturated samples oflow plasticity ciay in the Polytechnic Uni¥'ersity ofCatalonia (UPC), Barcelona, Spain. The a¥'erage contentsuction increments at each point corresponding to anof sand, silt, and clay are 39.4, 44.5, and 16.10/0, respec-experimental test. The diagram in Fig. I I briefly describesthe numerical integration scheme of tjj-unsat constitutivetively. Some other' engineering properties of that soilrelationship. Particularly, this scheme only refers to160/0 and G==2.71. A 38 x 76 mm conventional triaxialcell with controlled suction was used. The stress pathsIn general terms, the validation of constitutive modelsstress-suction paths that reach LC yield surface.Some of the mathematical expressions used in thatd), - -=( ) 8crvhere:a(Tfollo¥ved two phases-isotropic and shearing-bothunder constant matric suction of 800 kPa, as illustratedscheme are computed as follo¥vs:a) Plastic multipller dy:_1 !aft7 : D"c!. _-[afl :De:(h' + hp) -(CL,, according to USCS) are TvL= 3'_o/o, }t*p= 160/0, Ip=in Fi9:. 1'_.lJds} (40)Normally consolidated and induced overconsolidatedsoil samples ¥vere employed. Comparison bet¥veen simulation and experimental responses for the normally consolidated clay are presented in Fig. 13, ¥vhereas responsesfor the induced overconsolidated clay are presented in･, ELASTOPLASTiC hIODEL FOR UNSATURA'rED SOILS6213000q (kPa)qc)(1 :::; O.6252250'1c_ oo: "j ai lure!!! unSat750knl e as u redi ' -.' "+･. B'!o.,: *: 'B....;;-o.06* "800 kPaos pL' l0.06Fig. 12. Stress paths scheme driven along controiled suction triaxialiest performed by Barrera (2002)odata: Bar 'era (2002)t0.12L'{!3000cj (kPa)*hl,15 o._lJ-.0.24o 0.05c'o = O.629O i5o. 1o.0.25'( ,l 500tlf unSat750-- 11leaSUredFig. 14. Comparisons betlveen motiel a:nd expeFimental responses foroverconsotidatetl soil specimenoorable l.data: Barrera (2002)Parameters0,040.08¥_ icdel parameteFs foF different sets of experimental dat:gFutai (1997)Pereira (1996)t R (kPa)O/f (O)0.005O.0783000O.0072O.232O.0037O.005O 085Oi;_(O)oBarrera (2002)004/f6000;.so.1o.24O O OO I O l) O ' O ')lO.7r;O.833P (kPa i)20O OlO.007529'15'vO.3Sal 75O. 32.0O 5)t('r71f <,kFig. 13. Comparisons between model antl experimental responses forO.426SO O 25norma:ll) consolidatcd soil specimenexpression that basically modifies the hardeningFig. i4. The constitutive parameters used to simulatethose tests are sho¥vn in Table l. The pre-consolidationstress under saturated condition is 70 kPa. Figures 15 and16 illustrate the evolution of LC yield surface in bothdeviatoric (tN x ts) and isotropic (t xs) planes, at threestages of stress path: initial, final and at an intermediatestage. The dashed line represents the critical state line in aplane ¥vlth constant suction of 800 kPa.The stress-strain response was lvell described underboth situations. The proposed rnodel, however, ¥vasunable to represent the final dilatant soil behavior.parameter used here, i.e. Xds , , in which X depends on thestress ratio and the plastic volumetric strain and plasticshear strain increment ratio. According to the ¥'alue of X(either negative, positive, or null), de can be obtained.Nevertheless, it is important to note that an additionaiparameter is required. For further details, see alsoMatsuoka et al. (2002).The second set of experimental tests to be in¥'estigated¥vas carried out by Futai (1997). Those tests comprise of aseries of suction controlled oedometric tests performed innatural specimens of a residual soil from the State ofMor'e insight can be gained by plotting the evolution ofstress-dilatancy relationship as seen in Fig. 17. Someare lO, 16, and 740/0, r'espectively. Some other en_ :ineer-non-fitting data corresponding to the onset of soil dilativeing properties of that soil (CL, according to USCS) areresponse can be clearly identified. An alternative forovercoming this dra¥vback could be, for instance, to usethe hardening parameter proposed by Yao et al. (1999).2.74. According to Futai (1 997), a predetermined value ofsuction ¥vas initially imposed to the soil specimens andBased on experimental result.s of tr'iaxial tests on sandthen a vertical load ¥vas applied. After reaching theand clay, these authors formulated a phenomenologicaldesired level of vertical stress, the specimens ¥vere floodedMato Grosso, Brazil. The contents of sand, silt, and clayT4'= 500/0, wp= 260/0, Ip= 240/0, and G* betlveen '_.67 and FARIAS ET AL.69 2/1 500(kPa)!.data: Barrera (2002) I .OO!I 200!,j-unsat 0.7)-c900n a i600300c o Q e normal]v cons.A A A A overconsol.behaviorInrtial b ¥! ' (kPa)Ad s(-'o{-0.50- I .OOfi alinitia[Fig. 17. Stress-dilatancy relationst]ip for experimenta] resu]ts ofBarrera (2002)o.500200o (a)),. ( s )/+ (kPa)0.300Fig. 15. Evolution of LC yield surface at planes tN x ts and tN x s fornormall)' eonsoliclated soil specimeno.200o.008i 2000.0069000.005K(s)oooO )O i OO 1 50 200 2 Ocs (kPa):'. '¥¥Inl alo0,007/, (kPa)600o0.400-500 500 1500 2500 3500 4500 5500b'final/ ' (kPa)a bOO 500 1500 2500 3500 4500 5500250s (kPa)s (kPa)(b)200oo o o 11leasl,iFed15080d e i'- I .50 0.00 0.50s (kPa)400-A' '.._5Ae60300(/ e¥-500 500 I)OO ' OO )OO 4)OO ))OOi 500dilati¥'e0.50a80/[u UllSat1 oo60LCo50data: Futai (1 997)400initialofinal200/Y (kPa)-500 500 1500 2500 3500 4500 5500o50 1 OO 200150CT, (kPa)Fig. 18. Resuhs of model parameters calibration: (a) Variation of soi]compressibilrty lvitl] suction and (b) I.C )'ield curve at plane (1, xsFig. 16. Evolution of LC yield surface at planes t x ts and t¥, x,s foroverconsolidsted soi specirnenseem to be so significant.and then vertically reloaded. Two of those experimentaltests are simulated in the sequence. Figure 18 revealsFigures 19 and 20, on the other hand, illustrate asome results of model calibration: variation of soilcomparison bet¥ 'een model pr'ediction (solid line) andvolumetric soil response (dashed line) for the oedometriccompressibility ), and l( Ivith suction, and LC yield curveat plane (7. xs. Note that the compressibility ), increasesas suction increases; therefore, this soil is classified astests performed by Futai (1997). V,retting is indicated byan arrow in each figure. Observe that soil specimens didnot collapse under all vetting paths, as indicates f-** inCASE 2, under the proposed classification. Also, notethat the soil compressibility at unloading/reloading isFig. '-O(b), where only a negllgible deformation ¥vassuction-dependent, although such dependence does notthree-dimensionai stress-suc.tion space (p, q, s) arere*'istered. The stress-suction paths follolved along the ELASTOPLA TIC ivIODEL FOR UNSATURATED SOILS623O. 1 50lp. (J. s)),(s)D(1400 14) O)CJ (kPa)(a)oO. i 20ooo0,090(a) '+-; ---:. . -:.¥,. " ... ,'._ -,-- - p (kPa*B (325, 40. 120)'if_ ' C (320,35.0): '"'*"'1" (0.0600.010K(S)!A (1, O_ {20),' ';)_/E (1, 1, O)0.008oooo , 006s (kPa)o.004---- measured !/! unsatoFutai ( 1997)0.2400300c*(b)o o o 11leasuredotrj ullsato.4d (b)e400S (kPa)ett]n_..cr ¥ ,bo.3300s (kPa)data:clO. I200l OOoLC2000.5olOl1 OOO I OOOO1 OOl OOdata:(T, (kPa)Perelra ( 1 996)oFig, 19. Oedometric test O1: (a) Stress-suction path and (b) Model andexperimental response at plane (T, x 8,o2001 oo300!+ (kPa)Figo. 21. Results of model parameters calibration: (a) Variation of soil(P' c/' s)compressibility lvith suction and (b) LC yield curve at plane t. x e." 'I cl (kPa)F (1410, i50. 50) ', G (1425. 130. o)plotted in Figs. 19(a) and 20(a). A11 constituti¥'eparameter's employed to simulate the tests are reported inTable 1. Except for the initial part of' both curves (insidei(a)'_ _ --' -' -¥ :" -¥.p (kPa)__,_ .--¥'D (165. 20. Ioo) _.:;'i>iB (10. 5.200)-'(165. 20. 50)j'ii ' ='i_- I __ _" H(1.1.0)((..="- :',." "/ c (lo. l. Ioo)A ( I . o. 200)Figs. 19(b) and 20(b) supports that statement smces (kPa)meastu'edrnodel prediction and soil response are almost parallel.ti!ull S atodata :vd Futai ( 1 997)/e " .O. Io.0._o.3silty sand (SM-ML, according to USCS) de 'ived from a(b)o. 511 O I OO I OOOl OOOO(y, (kPa)Fig. 20. Oedometrie test O'*: (a) Stress-suction patl] and (b) Model andexperimental response at plane (T, x 8*consolidat.ion pressures are corr'ect.Model efficiency is further explored by isotropic tests atusing a triaxial cell. The soil corresponds to a residual' f--a_0.4However, these values of k difi r from those obtainedunder loading condition, but still inside the elasticregrme. Here it ¥vas assumed that the reported pre-constant net mean stress performed by Pereira (1996)¥¥'ettingI1the elastic domain), the soil behavior ¥vas fairly ¥velldescribed, especially the amount of collapse produced.The initial discrepancy is because the values of compressibility used in the simulations are those obtalned underunloading conditions. A glance at the unloading part ofgneiss of the State of Cear , Brazil. The contents of sand,silt, and clay are 4i.3, 43.2, and 15.50/0, respectively.Other engineering properties of this residual silty sand arevL=470/0, wp=300/0, Ip= 170/0, and G*='_.77. This sortof soil is often employed as a basic material for construction of dams in the northeast of Brazil. Generally, due toinappropriate compaction, that soil acquires a metastable structure, causing se¥'eral dams to fail during first 11FARI6,24o.80S ET AL.r,,, r ( kPa)¥vertinp = I O kPao.7524O(T,,.r = 50 kPa!!! Ul Sat- - BBM1'rr.YT r50 kPa l+-' '-. O.701 8O6' =a A3lleasVl'ed' e o o o.o 0.65>1 2Os :: I OOkPa' '-'e:1 OO kPa0.60oi c-er-e' ' e ' '200 kPacPa " ooe8 e /. -e//1.b- o o o6 Os = 50 kPao.55IOJl OOOl oos"(kPa)o240rig. 22. Collapse tcsts ilnder constant net mean s ress: Ex.'perimentaland sirnulation responses at plane s lction vs. void ratio(T,,,, = I OO kPas ;:: 200 kPasi 80;l 20lA : s: 100kPaI-1) d rostat i c**+axiSAAAs;:;50kPa6Oconst C:':orr' :::100 kPa((Ti '111/; ) : B rLcf ! = 100 kPaO240g! i ll :1'E :]D a5/'I::! *Al 80(T!t ::)O kPaO(cr; - t/II ) SS((7 Y11Y l!1' ) T E'6. ::: C' o- ThE!'2- e r B? _ e':Pb :BTCi 20':ss =200kPa' s ;;: I PO kPaQs L;-{e/ - L-f'..: vl. ' 'iiQ::- - ' - '; =O kPa6 O( f,,., = 200kParig. 23. Multi･stage drained true triaxial test under consiontcontrol!ed suction (aftcr Macari and Hoyos, 2001)o-o.l O -O OOO OO.05 oJ ()strainreservoir fillin _. Fig:ure '_1 sholvs some results of modelcalibration: variation of soil compressibility ;. and l( ¥vithFig. 24. True triax.'iai sheaF response from tirained TC tests for s = 50,100 and 200 kPa at cr**t =50, 100 anti 200 kPa, respectivel)suction, and LC ¥_'ield curve at plane tN xs. Similar toFutai's set of experimental data, this soil is also classifiedas CASE 2, since according to the proposed classifica-¥vas achieved. The final ¥'olumetric straintion, the compressibility ), increases as suction increases.¥vith absolute errors infer'ior to 20/0.Note again that the soil compressibility at unloading/reloading is suction-dependent, but conversely lc increases as suction increases.Pereira's isotropic tests consist of four Inundationtests, ¥vhere soil samples, initially submitted to a suctionof 370 kPa, ¥vere fully saturated (¥vith ¥vater) underdifferent levels of constant net mean stress, namely: '-O,50, 100 and ,_OO kPa. Those experimental results (dashedline) together ¥vith model simulation (solid line) aredepicted in Fig. '-'-. Only the ¥vetting process is describedvas pr'edictedTo close this section, a comparison betlveen theproposed model, BBM and experimental results of testsperformed by l¥,Iacari and Hoyos (2001) are presented.These authors published a series of drained true triaxialtests conducted on several identically prepared cubicalspecimens of recompacted silty sand to study the stressstrain-streng:th behavior of an unsaturated soil under'multi-axial stress states and suction-controlled condi-tions^ The soil vas retrieved from the PiedmontPro¥*ince, USA, a region predominantly composed byin a graph of ¥'oid ratio versus suction. All parametersemployed to simulate tii-unsat model are also summariz,edin Table 1. Those tests lvere performed under isotropicstress condition; therefore, fe¥ver parameters are neces-residual soils. The avera e contents of sand, silt, and clayare 58.4, 36.8, and 4.80/0, respectlvely.sary to run the model ¥vhen compared to the previouslished suction ¥vas kept constant throughout the testtests presented here that correspond to axisymmetric andthree-dimensional stress conditions. Once more, good(Fi_(,,_. 23). First the specimen ¥vas loaded under hydrostatic conditions to stress state point A ((T.*1= 50 kPa), thenagreement ¥vith soil mechanical behavior under fioodin_'*.monotonic shearing corresponding to either TC (TriaxialAccording to ilvlacari and Hoyos ( -OO1), each specimenfollo ved a multi-stage testing scheme ¥vhere a pre-estab-; ELASTOPLASTIC N,10DEL FOR UNSATURATED SOILS625r,,.! ( kPa)240(y,,,, = 50kPao A l measured} '1100 kP:8¥O'60o a ,s = 50kPaa1) 1**S ::: 50 kPaoo240240:= I oo kPae]l 8012060s = 50kPaO- s:cs aga :]A A A' 'l -A' a- tL_ .Al*'AAAA I OO kPa-A;:;;' - ' 'i +b.A' s := 50 kPagi - ' :a_ ?:r T' .. :,h'" r7" -'tQ'ra)s81' " s ::: 200 kPar.....s :::: 200 kPaa;' I ab kPa__9120:a o o '-'D.' a ;/o a's = 100kPa..._5 ' 5E: s' s ::' d ' s = 50 kPa* i;+60Sj': : e3l 80E r":ba:50kPa160n(T =1)OOkPa(y*,,, = 200kPao-o.-.240' g' 'l 20: : c.o240l 80eA A A A A .." t '. ' ' ". .'.'A*'CA A A A A '60a . gO,ee_oa . 4"T._,/C.CFs :: 200 kPa/ lrA IAook_P-ar_ ,i_ _ -i20;t&L'3(Tf"i ::: I OO kPal 80tl - ' s' 200kPadr il :'If1 :rk.,,_-L'}iiip' Q a;:; I OOkPa'__ .(T(,,,,- $1 :o Q G Q a 'e'.tjb e-o-Jo__a_ a a_ oo aQ60･--BBMo A Ea measuredS ::: 200 kPla'l: _1 P.q r . _!u -unsati 80t glt･ :'.sLJ(=)OkPa/i! unSat--- BBMi 80l 20r.,.! ( kPa)140ol O -O. 05O.OOO.05 O. I O-o.lO -O.05str'ainFig. 25. True triaxial shear response from drained SS tests for s= 50,100 and '*OO kPa at a<**t=50, 100 and 200 kPa, respectiveh.Compression), SS (Simple Shear), or TE (Triaxialic shearing was imposed to the specimen. The processwas repeated f'or the hydrostatic stress state at pointO. lOFig. 26. TrDe triaxial shear response from drained 'I=E tests for s= 50,100 and 200 kPa at a**1=50, 100 and '*OO kPa, respectivel)Table 2.Extension) stress paths ¥vas imposed, until the octahedr'alshear stress ( .**) reached an apparent peak value. At thispoint, the stresses are unloaded back to point A, and ane¥v hydrostatic stress path ¥vas followed until point B(cr..* = 100 kPa). Then, the same TC, SS, or TE monoton-o.05O OOstrainParameters for Macari and Ho .'os (2001) testsParame ersl¥*Iodel!, -unsattN = 36 kPa; K(O) = O.OI 1; ;_(O) = O.220;!' = i .O; f; = O.21 ; p= O.01789 kPa1;BBMp*= 36 kPa; /( = 0.01 1 ; ;_(O) = O.220;L Jc=27'; v=0.30; k*= l.3'_4; Oe=-'.Of= O.21 ; fi= 0.01789 kPac=27';l;*=0.30; k*= 1.324C (cr.** = 200 kPa).A series of 27 drained constant-suction tests ¥vereconducted, 9 for each stress path, i.e. TC. SS, and TE.Equally satisfactory responses vere achieved by bothThe experimental results (symbols) are shown inmodels along TC stress paths, in particular for (T ** equalFigs. 24-26, together' with simulations of tjj-unsat (solidto 100 and 200 kPa. Ho vever, for SS and TE stresspaths, ¥'ery different responses ¥vere obtained. Theline) and BBM (dashed line).Table 2 presents all parameters used in the simulationsfor both models. The parameters for BBM were allobtained from Macari et al. (2003). The parameters fortjj-unsat model are basically the same as those used inBBM, except for the additional parameter a ¥vhich wasobtained by best fit, and r , which is equal to 1.0 (novariation of the compressibility l( vith suction).*.proposed tjj-unsat model achieved much better agreementwith the experimental results than BBM. The main reasonis attributed to the failur'e criterion. BBM uses theperfect conical-shaped Extended Drticker-Prager failurecriterion, ¥vhereas tij-unsat employs the proposed gener-alization of Matsuoka-Nakai failure criterion, whichestablishes distinct values of shear strength depending on 攣626FARI、へS ET AL．the stress path on octahedral plane（5θθFig．10）． nlodel for ullsat麟raξed so目based on exIended SN’IP，Unsaturated Soils、P1・oc．ノ、∫’1n1．Co14。U1∼∫θ’1〃“θ18ゴ50’Zy（UNS、へ丁95），Paris， France（eds．byAionzo，EEandDelage，P、），Rotterdam，Baike−CONCI、US正ONS ma，2，739−744．9）Maatouk，A．，Leroue11，SandLaRochelle，P，（1995）：Yleldingand The maln負ndings of this work can be summarized as cr1“cal s［ate of a collaps猛ble u11sa“1ra｛ed silty soil，（7ゴo’θぐノ1’∼’（1∼♂（∼，foIIOWS： （1） Founded on simple adjllstments to BBM frame．work for isotropic stress cond圭tions and the generaliza− 45（3），465−477．10）Macari，E．J．a厳d｝｛oyos，L。R。（2001）＝Mecha臓icalbellaviourofa自 mSa田rated SOil Under mUlli−aXial StreSS SてateS，0θ0’θごh．刀θ5’，／、， ASTNi，24（1），玉4−22．tion for unsaturated cond圭tio勤s of concepts such as11）Macarl，E，J．，Hoyos，L．R、and Ard虚no，P．（2003）＝Co自s譲u［1vespat圭ally mob三lized p玉εしne，secon〔i−order modi負ed stress modelingofしmsaturaしedsoilbehavioru員deraxlsymmetr1cstresstensor∼ijandMatsuoka−Nakaifaihlrecriterlon，anew statesuslngas覧ress／suc【1onco臨o目edcぴbical〔es［ce琵，1ノ払・1．Plo∫一elastoplastic crit量cal state base（i model∼vas deve圭oped for（iescribing the mechanical behavior of soils． （2） The modi負cations to BBM framework forisotropic stress conditions、vere essentia1至y the use of amodi行ed mean stress IN instead ofρas stress vari＆blel theassumption of two cases of co至1＆pse response，wh量ch wasaccomplisLed by simpiy changlng botむ6tting parame輩ers1・ノand INR to apProprlate vahles，according to experimen−tal res慧lts；an（蓬the use of a suction−dependent coe伍cient ”c妙，19，玉一35、12） N−aIsuoka， H． a職d Nakai， τ． （1974）： S［ress−deforma【ion and streng由cllaracter1sticsofsoilunde口hree（ii圧erentprl職cゆal Stresses，P1噌oc．ノSC万，（232），59−70．13）Matsuoka，H．andNakai，τ．（1977）IStress・strainreiations厩psof soil based on tlle S難IP，Pヂo（〕．Sρθc’α1ひ・Se∫∫’0119，91171CSA4歪E， 王53−162．玉4）Matsuoka，H．andNakai，T，（1982）：Anewfa員urecriζer1onofso1ls lnthree−d1mensionalstress，Co1∼ゾ0⑳ηηα”oηα1∼ゴFα〃疋’1門θq〆 G’・α1π11αrル10’θがσZ∫，至UτA5｛，Delft，USA．蚕，253−263、15）Matsuoka，H，and Sm，D，A、（1992）l Ge陰era厩a振on of aof compress茎bility for unload圭ng−reloading cond玉tions， COnSti案面Ve laW frOm fr1CtiOnal ma【erialS tO COlleS1Ve ma【er1alSラ （3）Thegeneτalizatlon ofSMP forunsaturated 刈ゴv，λ4’〔ソ・01ηεぐ1r．Grα1π〃α1・con〔iitions was performed ia由e same way as previouslyma（ie by other authors；ho、vever，a different inteτpretεトtion of modlaed stress tensor 、vas herelu introduced，八／θ1eヂ1αな．Elsevier Sdence Publica一 ｛玉on，231−240．16） ｝〉latsuoka， H． and S麟n， D． A． （1995）： Ex［ension of spatiaIly mobilizedplane（SMP）tofrictionaiandcohesivemaτerialsand app1呈cation to ceme翁ted sands， So’Z∫ ‘7ηθF Fo∼イπ‘ノ‘7r’oη5， 35 （4），since the suαion effect was only accounted when calcl11aト 63−72．illg the diτection cosines of SMP、17）Matsuoka．H．，S駐n，D．A．，Kogane，A．，Nobしih1ko，E and （4） Tbe experimental results from true three−dimen−slonalラoedometric and lsotroplc tests gathered fromspeclalized geotecむnlca1至髭erature gave supPorε to tむetheoret玉cal framework、 T｝1e satisfactory agreementbe宅ween model and tests results員ighlights t｝1e app1量cab宝1一玉ty of the proposed formulat圭oR to real boundary va王uegeotechnlcal problems。 Ichihara，∼y、（2002）＝Stress−sξrai【1behav1our of unsaturated soil i陰 true毛r1axia【testS，Cα’∼、Gθo’（∼ch、／，，39，608−619．18）Nakai，丁．＆ndHi巖okio，養L（2002）：AnlsαroP1char（1eningmodel fornorma1！yandoverconsolfdatedsoilsw1thri」一co飛cep田nd s巨bloading surface concept，P1’o‘．／‘PS，Calgary，3−16．19〉Nakal，丁。aad｝｛inokio，M、（2004）：Asi照plemo（慰for鷺ormaHy a賞d overconsolidated so目s、、’i由un節ed materlal parameこers，∫o’Z5 α11‘1Fo∼’17ゴα”oη5，44（2），53−70．20）Naka1，丁．andMatsuoka，H．（1983）：Shearbe翁aviorsofsalldand clayundertbree−dlmens1onalstresscon踊oほ，So〃∫σ114Fα’11ゴα一ACKNOWLEDGEMENTS The authors ackno、vledge the 食nancia歪supPort pro−vided by 由e Brazilねn National Research ColmclI（CNPq）． ”o〃5，24（2），82−94、21）Nakal，T．andMatsuoka，H．（1986）：Ageneralizedelastoplas【ic cons｛itutivemodelforclayi簸由ree一（玉imensionalstresses．So1Z∫θノ1ゴ Fα’1∼面”017∫，26（3），81−98．22）Nakal，T．andM由ara，Y．（1984）＝Anewmecb舗calquanこiτyfor so賛s and its apPlica“o職to elastoplastic constitut茎ve models，So以∫ 01∼ごFα，11面∫’on5，24（2），82−94．REFERENCES23〉Ohmak玉，S．（1979）：SIreng縫1 and defor鵬a雛o【｝ charaαeristics of overcoIlsollda【edcohesivesoil．P1・o‘．3’ゴ∫11’．Co’∼∫、N濯〃71∠》θ∫ノ∼、 Gθ01ηθch。，Aac｝｝e自，465−474．i）Adams，13．、へ、and Wulfsohn，D（1998）l Critica1−state behaviour of anagrlcωturalso蕪，／．づ491q’c．五11913。Rε∫．，70〔4），345−354．2）Alo難so，B．E．，Ge麟s，A．and Josa，A，（1990）l A const1田tive modeI forpar毛lysaωratedsoils，Gσo’θc1∼吻∼’θ．40（3），405−430．3）、へxelsson，K．，Y薙，Y．and Runesson，K．（1989）＝Consti田葛ive properτiesalldmode騰ngofs11【ysoils，P”oc．12f1∼1CSA4班， Balkenla，R玉o Ja簸e玉ro，Brazi【，1，687−690，4）Balmaceda，A．（199玉）l Compaαedso簸s，A毛11eoreticai and experime陰tals田dy，Pノのrhε∫’∫，Barcelona，UPC（inSpan柚）．5）Barrera，NL （2002）：Experimen｛al study of hydro−mechanical behavior of collapsible so1ls，P110 7ア∼θ5’∫，Barcelo貸a，UPC （1旨24）P王録員eiro， 鍬工 （2004）： ’1ヌーunsat： a new elas！oP｝astic model for unsaturated so11s，zVσ∫’θrρ’∫5θ1・’θ’10／7，Brasilia；UnB，Brazli（in Portuguese）、25）Su簸，D．A， ，Ma【s柱oka，9．，Yao，Y．P．andlch註1ara，W．（2000）；An e！asto7plast1cmodelforu践sa覧uratedsoil1自tllree−dime醜onal stresses，So’Z∫θηゴFα’π面”oη∫，40（3），17−28．26）ToH，D．G、（！990）IAframeworkforunsaturatedso曲ebaviour． Gゴo’（∼（1∼η’（1μθ，40（｝），31−44．27）∼vang，Q．，Pufa届，D．E．and Fre｛員und，D、G，（2002）：A s田dy Qf cr1tlcalsta芝eo鷺anu鳶saturatedsiltysoi1，Cα’1．Gθo’θc11，ノ、，39， 213−2玉8． Spanish）．28）W短eder，S、、∫．andS1vakumar．V、（1995）：A陰elasto−Plas［icc面cal6） Fuτai，糞1．！yl、（玉997）：Analysis of oe（ionletric tests under controlled stateframeworkforunsaturatedsolls，Gゴαθ‘11∼瞭’ε，45（1），35−53． suc縫on1n collapsible soils，A（1α5rθ1”∠）’∬θr∫醒’o’1，Rio de Jaae1ro，29）Yao，Y， P．，Ma【suoka，H．，andSほn，D．A、（玉999）：Au顧ed elastoplasticmodelforclayandsandwiζht紅eSMPcriζerion，P’門oc・ COPPE（i“Pormguese）．7）Kato，S．（1997）IAcons虚u董ivemodelforunsa田ra｛edsoilsbasedon 8∼h 擁∼’∬ヂα1’α一八7（∼、t・Zθα1α11〔1 Co71∫ （フθ01刀θぐh。， Hobart （eds。 by the mo〔i1f㌔ed ISMP．Ploc 14’111CSル1FE，Hamburg．Balkema，互， Vitharana，N，andColman，R。）．AustralianGeomechan1csSociety， 69i−694． 2，997一王004．8）Ka【o，S．，Matsuoka，H、an（l Sun，五），A．〔1995），A cons戯uτlveゑ錨 ELASTOPLASTIC,IODEL FO R UNSATURAT ID SOILSAPPENDIX A1: DERIVATION OF ELASTOPLASTIC CONSTITLi TIVE TENSORSc!y aj't D :cl - afl D (h hP) af1aaD*P AND h*The total strain incremem tensor c/ _ consists of t¥vocomponents, namely, de as a result of change in net stresstensor (? and d as a result of change in matric suction s.c! = c!8 + d(AI )Those strain increment components can be expressed interms of elastic and plastic parts from the principle of'additive decomposition of strain incrernent.d* + dP) (A,3))] (A4)rule) and the elastic and plastic strain increment tensors¥vith respect to matric suction, (A4) can be re¥vritten asfollows:[ aj (h' + hP)ds<doat(AI 1)= De :d- hcpds (AI _')De '=D (-(Daft.D (A13)at' afl() :!*)aa '1- dy - (A5)The partial der'ivatives required to perform those pre¥'i-ous terms are expressed in the next appendix.APPENDIX A2: PARTIAL DERIVATIVESThe partial derivates herein presented ref'er only to LCyield surf'ace, since stress-suction-strain paths intersectingthe SI yield surface are not Involved in this study.At first, those partial derivatives referred to modifiedstress tensor'at ats at¥vhereaj"11(A 1 6)Mt¥' + t '{s tN'T T t¥' sa tNaj"tsc,-a ts[ M *( tN + t¥. 's)]"{(A17)a tNtion and hardenin*' Ia¥v.ata tsf* =f'*(ts, tN, tNc, s') =f*((r t s) (A6).' = - , Nc,atConsistency condition:vill be sho¥vn.af' atN_aj"+ aj" ats (A15)- atN atnet stress tensor and regarding both consistency condi-(A 1 8)::sa,, (t-t a) ts(A 1 9)Other necessary partial derivati¥'es are given belo¥v.aj't d(sr+ afl .dtNcdf t = :aj'Ea(r at :'c asc!s = O (A7)af l= ( tdtNc H dy tr afatatN,c(A8)af lat ,s¥vhere1+eH= - ),(O)-!c(s) tNCltN,o + t ,sat¥. 'aa j' t(A9)After handling some simple operations, the plasticmultiplier is defined asat atNcEventually, substituting Eq. (AIO) into Eq. (A5), the4th-order elastoplastic constitutive tensor Dep and '-ndorder tensor hcp can be explicitly expressed as f'ollows:In order to deterrnine d( , given a total strain incrementtensor d and a matr'ic suction increment ds, at first, theplastic multiplier dy must be defined. This can be accomplished by expressing the yield function f* in terms of theHardening la¥v:+aq *p 1__ aft e aJ'ISubstituting the expressions for the plastic strain increment tensor ¥vith respect to net stress (obtained from flo¥¥'da = D*: [dat(A I O)hep=Dcp (h'J h ) (bD s ' at (A14)The relationship between the net stress increment tensolcla and the elastic strain increment tensor d8* can beexpressed in ter'ms of the G*eneralized Hooke la v.c!cf D de*=D*:[d -deP-(d *+daflH tr(¥af )af .De: _aJ't( )=Rearranging (A2), it takes the follo¥ving form:- de P - (daa asc!s'here= (de* + d8 P) + (d * + dc P) (A_?)d8 * = d627),(O)-/((s) tNO l= - - --[[1-(A'_1)1*. ( ts ) IJ).(s)-/c(s) tNC tN0+t :s=11* --t; 'o + t¥. 's t , + t¥. 'sMt ,tNS(A'_2)The partial derivatives with respect to conventional netstress tensor are expressed as follo¥vs:aJ'Iaj't, atafl atsacratN ac ats a(1 FARIAS ET AL.69_sc) atslas¥vhereat,N = atN aljaa i=1 alj a(Tanda ts=3 ats alj--acT i=1 alj a(1(A24)Flnally. , the partial derivatives ¥vith respect to matricsuction are:as atN asats as atNo asaf'at¥. 'satN,sasa tsatNsa tsa (TOasat¥'SaSa (70asa= o(a (70d)bo + bl ao + b,(T¥vhereas as(A26)+ c3 (Ti !2c4(T4(A30)a tNO I asa tNOa t ,oalcasa/(as+atNOa)*a).as(A3 1 )a,(a)*atN atNs at¥.' acroa tNS as a ao as(A27)whereatN a 313 + 21._ (TO + Ij (Ta(To a( 0 I._ + 211 ao + 3(7= -fiK(O)(1 - f :) efi'(A32)= -fi),(O)(1 - r,) eF<(A33)asb) at lasas+ b4(T40)¥vhereat ,s a(70 =ka tN+ b3(7co + cl (TO + c. (Tacr(A, 5)a) atNslas(A29)wherea tsaf' af' atN + af' ats * af' atNOa ts(A28)as( )In t 'oa t¥, 'ot 'Oa)*).(s) - lc (s)tNRa tNO),(O) - ),(s)tNOal(), (O) - /((s)),(S) - K(S)(A34)(tNO )In -(A35)t¥' TRl
- ログイン
- タイトル
- stress-Deformation Behavior under Anisotropic Drained Triaxial Consolidation of Cement-treated Soft Bangkok Clay
- 著者
- D. T. Bergado・C. Taechakumthorn・G. A. Lorenzo・H. M. Abuel-Naga
- 出版
- soils and Foundations
- ページ
- 629〜637
- 発行
- 2006/10/15
- 文書ID
- 20946
- 内容
- SOILS AND FOUNDATIONS¥'ol 46, No. 5, 629637, OcL. 2006,Japanese Geotechnical SocietySTRESS-DEFORMATION BEHAVIOR UNDER ANISOTROPIC DRAINED TRIAXIALCONSOLIDATION OF CEMENT'-TREATED SOFT BANGKOK CLAYD. T. BERGADoi , C. TAECHAKU*¥,ITHORNii), G. A. LoRENZOiii) and H. M. ABUEL-NAGAi )ABSTRACTIn this study the compression behavior of high vater content cement-treated soft Ban_g:kok clay is further in¥'estigated by conducting a constant stress ratio (CSR) test at various stress ratios (,7)･ The test utilized cement-treated clayspecimens lvith cement contents (A,+) of 100/0 and 150/0, each of vhich ¥vas in combination ¥vith 1000/0 and 1300/0 totalclay ¥vater contents. The test results confirmed that the ratio of after-curing void ratio to cement content (e*t/A,+) caneffectively characterize the compression behavior of cement-treated clay. The specimens with higher' values of e.*/A,yielded higher volumetric and shear strains at the same stress ratio. While those with lower values of e. /A,. resulted inlo¥ver shear strains, ¥vith consequent higher values of strain increment ratios (de lc!8=) both before and after tr'ansition-al yield points. Significantly, the e.*/A,, ratio has described the relationship of the compression yield loci of cementtreated clay at var'ious stress ratios and mixing conditions.Key words: anisotropic consolidation, compression, ground improvement, soil-cernent (IGC: D5/D6)prediction of the strains during drained loading.IN1'RODUCTIONThe stabilization of soft clay by deep mixing method(DlvlM) with cement admixtures has been applied for fewdecades in Asia as one of the suitable ground improvement t.echniques. Stabilization using cement has beenLABORATORY TESTThe Base C!ayThe base clay used in this study ¥ 'as taken from a siteextensively used because it leads to beneficial effects onthe strength, compressibility, plasticity, workability and¥vithin the campus of Asian Institute of Technologycornpactibility of problematic soft clay. Also theThe soil profile of the site consists of 2 m thickconsolidat.ion line in the (e, Iog p') plots are shifted tohigher stress levels (Uddin et al., 1997) ¥vith consequentclay underlain by about 6 m soft clay and about 5 rn stiffclay. Beyond the stiff clay the stratification consist ofalternating layers of stiff clay and dense sand with gravel(AIT), Ban*"kok located in the Central Plain of Thailand.tremendous increase of the apparent pr'econsolidationpressure (Balasubramaniam et al., 1999; Porbaha et al.,2000; Bergado and Lorenzo, 200'_; Horpibulsuk et al.,2003). In the deep mixing construction process, theveathereddo¥vn to 500 rn depth (Bergado et al., 1996). The soilsampling was carried out usin*' a Shelby tube samplerin conjunction with vash boring technique at 4 to 5 mdepth. The physical properties are summarized inmixing ¥vater content can be equal to or greater than theliquid limit of the base clay (Lorenzo and Bergado, 2004).The behavior of cement-treated soft Bangkok clay at highrnixin_ : vater content has been studied previously inTable 1. The undrained shear strength, S , as obtainedfrom unconfined compression (UC) tests, ranges from 16to 17 kPa.unconfined compression, one-dimensional consolidationand consolidated-undrained triaxial compression test,Method of Ceinent- Treated C!ay Preparationbut not in stress-deforrnat.ion behavior under anisotropicThe clay samples utilized in all Constant Stress Ratiodrained condition. In this study, both isotropic and(CSR) tests were remolded to water contents ranginganisotropic consolidation tests (i.e. constant stress ratio(CSR) test), ¥vere conducted. These tests aim to under'-from the liquid limit up to 1.3 times the liquid limit(1000/0 to 1300/0). In this study, f'or homogeneous andstand the relationships of strain ratio-stress ratio and theuniform mixing cement slurry was used ¥vithyield loci of cement-treated clay, ¥vhich are useful forcernent ratio (W/C) of 0.6. Type I Portland cement was*]Professor invater-he Geotechnical Engineering Program. School of' Civii Engineering, Asian Institute of Technology, Thailand (bergadoealt.ac.th).Formerly N . Eng. Graduate in the O eotechnical Engineering Program, ditto.Formerly D Eng- Gradua e in the Geotechnical Engincering Program, ditto.'+1 Research Fellolv, Depar ment of Civil Engineering, lvfonash University, AustraliaThe manuscript for this paper tvas received for revie v on February l, 2006; approved on ,July 5, 2006**),**l¥Vritten discussions on lhis paper should be submitted befoFe,1ay I , 2007o the Japanese Geotechnical Society, 4-38-2, Sengoku, Bunkyo-ku.Tokyo I 12-001 i, Japan Upon request the closing date ma_v be extended one month629 BERGADO ET AL630Ph¥. ica] properties of the base clay (Soft Bangl(ok Cla,.-)Table 1.Accordingly, the four series of tests corresponded tothe follo¥vin*' mixin*' condition: (i) 1000/0 total clay ¥vaterC_ haracteristic valuesPro pertiescontent with 100/0 cement content, (2) 1000/･ total clayLiquid limit. LL, ()l03¥vater content ¥vith 150/0 cement content, (3) 1300/0 totalPlasric limit, PL, (o/ )4360clay water content ¥vith 100/0 cement content and (4)Plasticity index, Pl, (9/e)76-84¥¥rater content, It', (o,/o)1300/0 totai clay ¥vater content ¥vith 150/0 cement content.O.62Liquidity index, LISpecin7en P/-eparatioll and TestingCJrain size ciistribution:Silt ( /o)6928Sand (O/e)Tota] unit ¥veigh , *, (kN_ /m3)14 30Clay (ollo)3Dr"v unit weigh , )'ti, (kNlms)7 . 73Initia] void ratio, e2.3Specifc gravity. G., .68Dark grayColorActiviryO.87Sensitivitv7 ,30After mixing, specimens ¥vere formed by pushing theclay-cement paste into 35.5 mm diameter by 71.0 mmheight PVC molds. This method of specimen preparationfacilitated removal of air bubbles. The molded paste ¥vasallo¥ved to protrude out from the other end of the mold topermit inspection for the occurrence of "honeycomb"structure. Pushingvas continued until the surface of theprotruding specimenvas uniform and smooth beforetrimming. The density of each specimen ¥vas monitoredto assure uniform density for a given set of mixin*' condi-utilized. The remolding clay ¥vater content (}v*) is here-tion. Finally, the mold together ¥vith the specimen ¥vas¥vaxed at both ends and placed in the humidity room, at ainafter defined as the ¥vater content of the remolded clayprior to the addition of cement slurry.temperature of 25'C and humidity of 970/0, to avoidPrior to the introduction of cement slurry, the baseclay ¥vith the required amount of additional ¥vater ¥vereAf'ter curin*' each specimen ¥¥'as removed from its moldfor Constant Stress Ratio (CSR) testing.placed inside a portable mechanical soil mixer andallo¥ved to mix together thoroughly. The amount of¥vater to be added to a ¥vet soil sample in order to get thedesired remolding ¥vater content ¥vas obtained using thefollo¥ving equation:A W,= TVT(1.v* - It* ) (1 )(1 + It*.)¥vhere: A W*+ =additional weight of ¥vater to be addedWT = total ¥veight of prepared original untreatedsoil samplev* = required remolding ¥vater contentw = natural ¥vater content of the soilThe remolded clay samples ¥vere mixed ¥vith slurry ofsi_ nificant loss of moisture during the 28 day curing time.In the CSR tests a back pressur'e of 400 kPa ¥vasapplied in order to obtain fully saturated specimens. Thecell pressure and back pressure ¥vere gradually increasedwith pressure increment of 25 kPa. During the application of pressure, the cell pressure ¥vas al¥vays maintained10 to 25 kPa higher than the back pressure. The backpressured specimens ¥vere allo¥ved to equilibrate for atleast 24 hours and the degree of saturation ¥vas checkedby measuring the pore pressure response under undrainedconditions. A Skempton B value of 0.98: 0.02 ¥vithinone minute ¥vas taken as the Index criterion of sufficientsaturation.The triaxial consolidation test ¥vas performedanisotropically by increasing both cell pressure andcement in order to obtain the cement contents of 100/0and 150/0 by using a mechanical mixer for approximatelypiston loads simultaneously so that the required stressratio ¥vas maintained constant. The consolidation path10 minutes until a homogeneous clay-¥vater-cementvas divided into increments such that the total increase inmixture ¥vas attained. Since the cement slurry has ¥¥'ater incell pressure is 50kPa in one day. Furthermore, theit, then the overall ¥vater content of the clay-¥vater-increase in cell pressure ¥vas applied in increments of10 kPa and, simultaneously, corresponding piston loadswere increased to maintain the specific constant stresscement paste just at the time of mixing ¥vill be the sum ofthe remolding lvater plus the lvater in the cement slurry.The overall ¥vater content is hereinafter called the tota!c!ay ),'ater colltent (C,,.), ¥vhich is defined as (Bergado andLorenzo, '-002; L,orenzo and Bergado, 2004a):Cw = }v=* + W/C (A,.) (2)ratio. Each increment was maintained for at least 3hours.After the cell pressure had been increased by a total of50 kPa, the load ¥vas maintained overnight (at least 10¥vhere: C, =total clay ¥vater content of the clay-water-hours) to ensure that 900/0 consolidation has beenattained as demonstrated in Fig. 1. This scheme ofcement paste (o/o) reckoned from the dryincremental loading is follo¥ved until the cell pressure ¥vasveight of soil onlyIt** = remo}ding ¥vater' content of the base clay (o/o)800 kPa. The axial deformation and ¥'olume change ¥verebefore mixlng the cement slurryW/C= ¥vater'-cement ratio by lveight of the slurrymonitored throughout the tests from displacementtransducer and the burette for measurements, respec-A,,, = desired cement content (o/o) is defined as thetively. The required loads to maintain the stress ratioconstant at each loading step can be calculated. For apercentage r'atio of the ¥veight of cement tostress ratio (,7) the relation bet¥veen deviator stress (q) andthe dry ¥veight of soilthe effective cell pressure (a ) is: ･f=.,IENT-TREATED SOFT BA*NGKOK CLAYcrTable 2.631Physicai properties of the cement ireated cia) specimensi{Totai clayCemenA** (O/comem,C*, (o, )rimel OO282S2828lO;130lOi151 OO13015After-curinCuring¥vatercomen ,unit ¥veight,'=(kN/m3)After-curinAfter-curin1'a er conlent,void ralio, e*,lIs' ()A14.91l4.992 . 2022279 87-81 .3522 Il14.08- 14. 1 32.s7-2.s9l05_6-l06.32S 8015 02l5 052 042 067214.29-14.372.63-2.649513.6717 591 6-72 967 1 -9696{e Qo sRESULTS AND DISCUSSIONS{Phys'ica! P/'operties of Celnent Tl'eated C!cly SpecimensThe physical properties of cement treated clay specio 0044mens are tabulated in Table 2. The total clay ¥vater_ Tl (llj P IN,'(PID-;{}contents of' 1000/0 and 1300/0 as ¥veH as cement content of100/0 and 150/0 ¥vere the main conditions set out during thekPit;specimen preparation. Accor'ding to the results in Table{)_, the after-curing unlt ¥veight increased and the initialvoid ratio decreased with increasing: cement content at agiven total clay ¥vater content. This result can be attri-iIO 20000 eoooO500001 oOOO;,** : I :,:}40eoobuted to the increasing amount of cementing productssoooobeing formed, ¥vhich eventually increased the amount ofsolids per unit ¥'olume. Furthermore, at given cement;Fig. 1. Experimental resLrlt from triaxial consolidation testdq 3ll_ da (3);So, the ratio of effective principal stresses ((7i/() can be(Ti 2fl3q(4)(T . 3 and- ,7-=il=･7p¥vhere: q = (Jj - (ring equation, proposed by Lorenzo and Ber*'ado (2004a)for cement treated soft Bangkok clay:e** (1 + co )G *y,,, _ I (5)Iratio, or in other ¥vords, any increase of cell pressuremust be accompanied by an increase of the deviator stress{equal to (3tl/(3 - I/)) times the cell pressure. Each series ofI.¥'olume of cement treated clay specimens. The afterand p = (Ti + 2cr .Any increase of (T must be accompanied by a corresponding increase in ai to maintain a constant stressi{content, the aforernentioned result can be attributed tothe subsequent increase of the volume of void per unitcuring void ratio, e.*, can be expressed using the follo¥v-obtained as follo¥vs:{content, the higher total clay ¥¥'ater content has resultedto lo¥ver after curing unit ¥veight and higher initial voidratio of' the cured treated specirnens. For a gi¥'en cementy*where ( )*=after-curing ¥vater content of the treated soilafter "t" curing time (in decimal); G**=after-curingmixing condition utilized stress ratios of 0.00, 0.25, 0.50,specific gravity of the treated soil (dimensionless); y*=after-curing unit ¥veight of the treated soil; and y+ =unitweight of water (kN/m3). The parameters w*, G**, and y*0.75, 1.00 and 2.00.can be measured in the laboratory. Lorenzo and Bergado('_004a) also proposed the empirical relationship of aftercuring void ratio, e.*, expressed as follo¥vs:1i{{[1 1 CIY GSo]iI 100{{eotiC1ocso!O 012A'I 0'012Log(t)+0.99) l-10011 OOC'ilOO j( Ah+10'0025AIY + 0.01 Log(t) + I '008(6){{.i.*{;¥vhere Gso is the specific gravity of the base clay=2.657(Lorenzo and Bergado, 2004a) and t is the curing time (indays) of t.he treated soil. The rest of the ter'ms have beendefined previously.Volutnetl'ic Def'Ol"lnation du/'ing Constant Stl'ess RatioTestsIn order to eliminate the effects of the differences of initial void ratio of the cernent treated soil specimens on therelationships of e versus log p', the compression curves1i i {BERGADO ET AL.632} Ii []+1 "i'e e e 'll,T] 1iHTJ'je+ i *c!ie'eO' h 'I} I] tdJL] i] t]e.,'eS'}-'/ctI] TX}X' I;:*"'l!'i] F I}t] t T s{ If},Il I{ ,{{] i} ] l*=*]{]¥. Iesn Errt:"cll¥. e n EffL･cl]he StTess (p'}Fig. 2. Voiumetric strain versus log p' relationships for C,,=1000/e Stress {pi)Fig. 4. Shear strain versus log p' relationships for C,, = 1000! and A= 100/0and A*, = 15 /othe greater the compressibility of cement treated specimens at the same total clay ¥vater content. Having lo¥veri) f] :!3c=1;F"li G e O C =1+ * i hJ -A c L=i 'l] f}t ]cement content has resulted to lesser amounts of" _i: el c-+' clL'I{""=1..cementing products as ¥vell as fewer pozzolanic reactions.h -!'i I'The effect of total clay ¥vater content and cementcontent on the volumetric yielding of cement treated clayspecimens is also sho¥vn in Fig. 3. The volumetric yielding; T} t] {]r .!r T7. -/'L!1 ,-1'f-rfis the stress point which separates the states of stress forwhich the volumetric deformation is regar'ded as smallwhen compared with those states of stress in lvhich thefr !I]l }T JI }$ ?1¥leen EtTect]h e Stress t )Frg. 3. Volumetric strain versus tog p' re ationships for ll=2.00volumetric deformation is r'e*･arded to as large. Thesevolumetric transition points can be estimated in a manner'identical to the Casagrande's method commonly used forthe estimation of the maximum past pressure of onedimensionai consolidation tests (Uddin and Buensuceso,200･_).were plotted in terms of volumetric strain and log ofThe data in Fig. 3 supports the previous finding ofmean normal stress (8,, vs log p') relationships. The 8,versus log p' relationships for the tests with 100010 totalclay ¥vater content and 150/0 cement content are presentedUddin (1995) that, for a given stress ratio (l7), the speci-in Fi**. )_. This figure reveals that the variations of stressratio has no significant effect on the 8versus log p'relationship.The relationships of volumetr'ic strain ¥vith mean normal stress (e,., Iog p') durin*' CSR tests sho¥vs that therelationships are similar regardless of stress ratio as seenmen ¥vith higher cement content can sustain highervolumetric yield stress. For the same cement content, thevolumetric yield stress tends to increase with decreasin*-total clay ¥vater content. These observed trends alsoconfirm the earlier findings of Bergado and L,orenzo(2002) on the one-dimensional compression of cementtreated soft Ban."kok clay at high ¥vater content.in Fig. 2. Like¥vise, the effect of the variations of stress ra-Sllea/' Straill Respollse,fronl Cor7stant Stress Ratio Teststio on the e , versus log p' relationship is small, especiallyThe typical relationship of shear strain lvith meanfor higher cement content and lo¥ver totai clay ¥¥'atercontent. Similar behavior was also found by Uddin andBuensuceso (2002).normal stress, 8* versus log p', durin*･ constant stressratio tests of cement-treated clay specimens ¥vith 1000/0total clay water content and 100/0 cement content issho¥vn in Fig. 4. It is evident that the higher the stressEffect of Tota! C!ay Water Contel7t and Cen7ent Colltel7ton Vohlmetric D forn7ationThe effect of total clay ¥vater content and cementcontent on the volumetric deformation cur¥'es of cementtreated clay specimens is sholvn in Fig. 3 corresponding tostress ratios (i7) of '_.OO. Fi**ur'e 3 demonstrates that athigher total clay vater content, Iarger volumetricdeformation were observed than at lo¥ver total clay watercontent for the same cement content. The results in Fi . 3simply demonstrated that, the lo¥ver the cement content,ratio, the _ reater is the shear strain incurred by thecement treated clay specimens at the same mean stress. Athigher cement content the influence of stress ratio onshear strain is significantly reduced and smaller than at10¥ver cement content.Effect of Tota! C!ay Water Conte/7t alrd Ce/7?e/7t Conteilton Shea/' Stl'ain ResponseIn order to study the effects of total clay lvater contentand cement content on the e* versus log p' relationships 肝633CEMENT−TREATED SOFT B、へNGKOK CL．へY1い叫 こロ タリ ヨs l 縦“判＝ ．z O e eい・、耳1・・ 轟G一一←一◇いr←一←一◇い・、 ’ぐヤヤマしミ リ ハ 1財o プ飼圃し”←一㊥ゆ〔・一 ［ゑ ｝c・㌔ ’・’…’ ！悼、 1播￥￥￥あ。卿i び『；） ＼、、儀キ き ざ プタ i 牙 1向【「 ＼＼ 、、、令 【IGユo i 芦 ず／『 、へ、、，、，、、、，1 ！著、← 、、 隔← 一 鴨 ＿ 、かq一一◆一一つ 魔、I I（冥｝O Pill iI雑Iil勘∫o INleanEfデ￠cu、￠SIrossiPI1卜s にRISI「05s R飢K）σ1｝Fig．5・ She謎r strain versus lo9ρ’re皿負tionships for∼1漏2．00Fig。7。S｛ressratio謎ndstrai“iacremen重ra載iorela載lonshipsforC、、篇 100％and．4、、＝董0％岡ユ1｝卜 1strains．The yiekl玉oci based on the characteristic of thestrain pa芝hs w呈11be discussed subsequerltly． The stress rat玉o and strai熱increment ratio re正ationshipsare useful ill the prediction of慮he strains during drεdRedload圭ng（Roscoe alld Pooroshasb，1963）．Consiclering thebi−linear characteris毛ics of the strain paths， t鼓e strainincrement I’at玉o during constant stress ratio tests has to becollsidered玉n two parts．The負rst one corresponds to thestate pr玉or to the transition points or inside y玉eld正oci玉nthe s￡rain paths ancl the other correspo亘ds to t熱e stateou o l O oユ o Ωミl o4 voh；lne伯cSlral【｝1ε、1afterthetransitionpointsoroutsideyieldloci．There玉ationships be芝ween strain 呈ncrement ratio and stressratio both inside and outside the yield loci are il玉ust！’ated野員9、6． B董一li臓ear rel段芝ionships of strain pa重hs for（コ、、篇1009もand・4、、＝ 10％i熱F三9．7．The figure s熱ows芝bat the strain increment rat重o，4ε、・／ゴε、，beforethetransltionpollltisgreaterthant勤ecorresponding values after the ￡ransition po量nt． 丁勤eof cemellt treate（i day，the test results at di圧erent totaIstrain increment ratio aud stress ratio relat圭ons負ips insideclaywatercontentandcementcoate厩areplottedast紅e bounclary are apPlicable for a11stress states corre−shown in Fig． 5． It is ev玉dent ia t｝1e agure that thesponding to the overcoasolidated state of tke cementv＆riationofshearstrainwi由stressratlolsgreatlyin一treated clay．Tむis overconso豆idatioll is evi（iently due to避uenced by the tota豆 clay water content and cementcementa左ion of hεしrdening ageat 、v圭th clay particlescon書α1t．The significant c勤ange in shear stra呈【1at higher（Balasubram＆nia買1e書＆1．，1999）．total clay water content a茎1d lower cement content can beobserved．Fur重her！noIle，for the s＆me stress ratio（η），atIower total clay water contellt and higher cemen毛content，higher distor重ional yield stress ls obtained，using the same F玉gure7furt紅er shows thα｛｝1玉9紅er stress rat重o renclersma正1er values of strain iacrement rat呈o，4ε，／4ε、，at bothinside and outs玉de芝he宅rallsit1on points。Therefore，at the屈gher stress ratio，重he compression behavior of cementmethod as th飢for volume毛ric yield s亡ress．treated clay specimens are goveme（i by d量stortion．TheS〃・αin Pα1hs σnol S1ヂθ55・Rα1io−S！1・αi17 111c1・θ1nθ1z∼ Rα∼iothe apP1圭cation of higher distortional stress（or（ievi＆torspeclmen tends to yield at lower mean yieid s芝ress due toRθ1α∼ioηShiρSstress）．However，at正ower stress ratio the value of strain The typical stra玉n paths fo110wed during the collstantillcrement ratio，4ε、ノ‘1ε、，tends to be higher both insidestress ratio tests is plotted in Fig．6 correspouding toand outs圭de the trans貢ion poiats，so the compressioa oflOO％total clεしy water content with IO％cemen重conteut．the specimen ls govemed by the volumetric beぬavior．As shown in the figure，the strain paths consist of twostraig勤t lines for any particu1αr stress ratio．τhe shearThus，at lower stress ratio，the cement treated clay tendsstrail1（ε，）versus volumetric strain（ε、）relationships fromto compress and fal1飢紅igher mean e狂ective stress．Moreover，Fig．7also includes｛he test results by Uddinthe constant stress rado tests in this study shows the（1995）todemo熱stratet熱ee任ectofmlxingwatel齢conte飢bi−1inear re董ationships forε葦1圭ser玉es of tests．The intersec一on straln increment ratio．The results show that as t勤e｛ion of tkese tYvo straigh重1重nes is a transition po圭n重andmixing water content decreases，the strain increment ratiorepresents ＆poiat which corresponds to the boundarydecreases。ξhat separates 豆arger shear strεしin fl畠om sma茎1er shear BERGADO ET AL.634lIT] T]12c-hl r [ h: :i :r': ii i h > ii: Ij! :::Ji: ::ll]: ci ¥ JF¥tl-: 1d1 -A i:- F -A T' :h¥¥ f'¥ ¥ IeFr -de¥")¥Ysi '"Lj::;JI'h+1I: :- lt}14', 12 1]- JiA t' ;:*R-SquaFed = O S2b lcll]X l]¥ ¥'' " A"¥"..:¥" "Q..,,* '..h L "t 1l [!' , " ,' .s- :i;ii B;'..,c-- _ 1;' - -S [TT} t'[] s 1' h* 1Slross Rs ]o {,{i 14eel AI,Fig. 8. E,ffect of vaiue of (e*>$/A,,) on stress ratto and strain incrementFig. 10. Re ationships of strain ivlcrement ratio at stress rati0=0.00vith e**t/A,.ratio re!ationsl]ipsl:!!eQ1 An TiC:; C:1] ::t>:J[] ',O O r_ i:i Jl <> , :":'i ' cet ' lLAL :rl':J:'iBT]x ,R-Squnred = O 97S2I :T 11 TO e O i'i T :c c c f'4t :i eel : l :: +] 1: )t ' ll: A A A flftI)ll 4T] 'zl 4 i} x *Stre . s R ttio fee}Fig. 9. F {ormalized plots of stress ratio and strain increment ratioA11Frg. Il. Relationships of dilatancy ratio at stress ratio = O.OO with e,,*/A ,,relationshipsNol-ina!ized P!ot and Effect of Mag/7itudes of AfterFrom Frg. 9, the unique line can be expressed by theCuring Voicl Ratio }vith Celnent Corlte/7t (e.,/A,,) ollSt,'ess Ratio (;7)-St/-ai,7 I/7c/'e,nellt Ratio (cls,,Id8.)follo¥ving empirical equation:Re!ation sll ipFrom the previous study of Lorenzo and Bergado(2004a,b), the ratio of after-curing void ratio to cementcontent (e**/A,,.) has been proven to be a fundamentalparameter that can effectively descr'ibe the combinedinfluences of total clay ¥vater content, cement content,curing time and curing pressure on the strength characteristics of cement treated clay. The strength is higher at10¥ver values of e.*/Aw ratio. This present study confi medthat the behavior of the strain increment ratio, dev/d8*, ofcement-treated clay can be described by the e */Aw ratio.Figure 8 indicates that cement treated clay at lo¥ver ¥*alueof the e**/A,,, ratio has higher strain increment ratio,de /ds=, compared to that ¥vith higher values of the e.*/A,,ratio at same stress ratio. Thus, the strain incrementratio, dev/de=, increases ¥vith decreasing e.*/A,., ratio.dstiiil = _0.1393n3+0.6879,71_ 1.169i,1+ I .O005 (7)c!e* " *(de /de)/(de /de ) ,, ooo¥vhere: (de/de;* ".*",*)- = < . = =,1 = stress ratio = qlp' .The empirical relationships of strain increment ratioinside yield locus at stress ratio equal to 0.00, (de lcl8,) at/7 =0.00, and e. /A,,, for cement-treated soft Ban_g:kok ispresented in Fig. 10, and the corresponding empiricalequation is given as follo¥vs:de,.( .= -O 1713 (Ae.,:)- +13.688* ) *t'/ = o oo., *idwhere: e.t = after cunn' vord ratroA,,, = cement content (in decimal).Moreover, from the relationship of strain incrementFurthermore, the str'ain increment ratios (de,./de,) bothratio (de /de*) ¥vith stress ratio (n), all curves have theinside and outside the yield loci can be related to the ratiosame trend as sho¥vn in Fi_,_". 8. Therefore, these curvescan be normalized to a unique line, as sholvn in Fig. 9, byusing the strain increment ratio at stress ratio equal toof (de /d *) at n=0.00 at outside yield locus di¥'ided byO.OO, (ds./de*) at n=0.00, as normalizing parameter'.bet¥veen the dilatancy ratio and e*t/A,(c!e /de*) at n = 0.00 at inside yield locus. The ratio ¥vill becalled heremafter "dilatanc} ratio" (ai). The relationshipis plotted inii CEMENT-TREATED SOFT BAN(3 KOK CLAYj c- 1" l' ) I e' :(- r::. I li - T r"A A A) L* i "i; ll//'"'//;;. "I;//"/[; [] [] C//;'1Z12;."'/ : '// tt; ____-1l{}fl.(} I[hTI [ [rIesn Efi'ectll e Stress ( 'lc'* i'{/[1 4*tiI;=; -ll.."/...'_ // //'/!, U X{,*! " ;l-' ' /{l f i;,, 17=;'*O O O C' Ii' '- T :: 11! cl':! - s[}f]i1 (*635},Tuu s¥. om sl:ze ¥. Iean Ef lect: e Stress (p')Fig. 12. 'Theyield lociofthetransitionpoiutsoftirebi-linear relation-Flg 13. N'ormalized yield lociships of strain path{{iI ,(.I*eFig. 11. The fitted empirical equation for the dilatancyratio and e.t/A,, can be expressed as:fi*ce= - 0.0046 i + 0.71 7 1 (9)(tR-Squared = O 9 q87cA *+I1[}{]{i¥*¥¥..here: ae= Diiatancy ratio = (de,¥¥c+¥･ St Ide* ) ,, = o oo,o 1**dede,1]d8s ) '1 = o oo,**s*d**tl{iAccording to Eqs. (6) to (8), the functions of stressratio (il)-strain increment ratio (de./dss) for cementtreated soft Bangkok clay both at inside yield locus andoutside yield locus can be predicted using the fundamental par'ameter', eol/Aw' vhich was recently proposed byt{ Iees *Fig. 14.*+Relationships of mean effective stress at ff= 0.00iLorenzo and Bergado (2004a).i,*,iYIELDING BEHAVIOR OF CEMENT TREATEDSOFT BANGKOK CLAYcement content and curing time on the yielding behaviorof cement-treated soft Bangkok clay.Norlna!ized P!ot of Yie!d LocusFigure l,3 shows the normalized plot of all the yield lociGenerally, graphical techniques are used to identify ayield point. The plot of the transition points of the bi-shown previously in Fig. 12. The mean effective yieldlinear relationships of strain path (e.g. Fi**. 6) determinesing parameter. The relationship of mean effective yieldstress at stress ratio equal to 0.00 is used as the normaliz-the yield loci as sho¥vn in Fi**. 12. The shapes of the yieldstress at stress ratio equal to 0.00 versus values of eol/A,,10ci obtained from the test are similar, includin** therelated result from previous study of soft Bangkok clayby Uddin (1995) at 800/0 total clay ¥vater content. It isis sho¥vn in Fig. 14. The fitted line in Fig. 13 can bedescribed by the follo¥ving empirical equation:evident in Fig. 12 that the location of the yield locus isp'o*m= - 0.0399q3norm- O.2,52q2no*maffected by the total clay water content and cement+ o. 3478q + 0.9996 (lO)content or dependent on ratio of after-curing void ratioto cement content (e.*/A,.).¥vhere: p'= normalize mean effecti¥'e stress = p' /no*** o ***Pat " = o oqno*m =normalize deviator stress=p o* ' x stressYie!d Locus versLis e , /A ,,.ratio (n)Figure 12 demonstrates that at lower values of e.*/A*,,the yield locus tends to position at higher stress levels.effective stress (p') at n=0.00 and eo /Aw for cement-This means stronger cement-treated clay at the lowertreated soft Bangkok (see Fig. 14) is obtained as follo¥vs:values of e.*/A,.. This relationship confirms the resultsfrom the study on the strength and one-dimensionalIn addition, the empirical relationships bet¥ 'een meanPat' oo0=0.490 (Aej:,:)2_31.903 (Ael,:) +733.179 (11)compression characteristics of cernent-treated soft Bang-kok clay (Lorenzo and Bergado, 2004a). Significantly,the e.*/A,r'atio pro¥'ides an effective basis for characteriz-ing the combined effects of total clay water content,f;{'i;¥vhere: e.1 = after-curing void ratioAw = cement content BE,RGADO ET AL.636CONCLIJSION,(c<>liTtr,(: ,From the results of Constant Stress Ratio (CSR) testand the subsequent analyses performed, the follo¥vin_"._conclusions can be dra¥vn:(1) From e,,-logp' and 8*-logp' relationships, the･j<>r-_ __ )IJ EI N=S[tt(S F :application of higher stress ratio caused greatereffect in shear straln but the effect on volumetricstrain is not significant. The compressibility andshear strain are affected by the e.*/A,, . The cementtreated clay specimens ¥vith lo¥ver values of e.*/A,,exhibit lolver compressibility and shear strains atthe same stress ratio.IQ I T1 TFrg 15, Predicted strain increment ratio-stress ratio relationship(2) The volumetric strain-shear strain paths sho¥vedbi-linear characteristics, corresponding to preyield (inside yield locus) and post-yield (outsideXI Iyield locus) conditions The strain increment}e ' e' [ 'ratlos (de,./d8,) of both at pre-yield and post-yieldf' ll l **conditions are affected by the stress ratio andtle.*/A,.. The higher the stress ratio, the lo¥ver' thet{ }p..."' _/"/' / _/' ll' _/ Ill* ll ///' lc-1'1i;;'l_ -/1/:/1''___li-* ***t H I I¥ !$ii:1I ,En C[i Jt S feS, 4 E 14 I*!] ]i)]Fig, 16 Predicted yield locusBy substitution of Eq. (lO) to Eq (9) for kno¥vn vaiueof e.*/A,,, the yield locus of cement treated soft Bangkokstrain increment ratio (d8./de,). Moreover, it isfound that at higher cement content and lo¥vertotal clay ¥vater content or lo¥ver value of (e.* /A,,,),higher values of strain increment ratio, (de/c!e,),at both inside and outside the yield locus ¥vereobtained.(3) The strain increment ratlo (c!8./d8,) ¥vere noTmaliz,ed b ., usin_g: strain increment ratio at =0.00,(d8.lcla*) at n = 0.00, as a normalizing parameter.The normalized data foilolv a unique function.Consequently, an empirical relationship of stressratio (n)-strain increment ratio (de /d8,) ¥vasobtained, ¥vhich is useful in settlement analysisusing the incremental stress-strain theory.clay can be predicted as sho¥vn in Figs. 15 and 16.(4) The shapes of the yield loci are similar for allMoreover, the initial void ratio can be calculated as afunction of total clay ¥vater content, cement content andconditions. The location of the yield locus can bedescribed by the value of (e**/A,.) for all proportions of total clay water content (Cw) and cementcuring time as ¥vell as the specific gravity of the base clay,as previously discussed by Lorenz,o and Bergado ('-004a).The plot of the str'ess ratio-strain increment ratiorelationships and the yield loci obtained from the resultsof CSR tests in this study. , confirms that the ratio ofafter-curing void ratio to cement content (e.*/A, ) isfundamental and sufficient to characteriz,e the strengthand compressibility of cement-treated soft Bangkok clayat hi_ ,_her ¥vater contents. Moreover, the normaliz,ingparameters such as the strain increment ratio at stressratio equal to 0.00, (d8 /de,) at ,7=0.00, and the yieldeffective mean stress ratio at stress ratio equal O.OO orisotropic condltion, (p') at n=0.00, have lllustratedexcellent relationship ¥vith the ratio of after-curing voidratio ¥vith cement content (e.*/A,.) as sho¥vn in Figs. lOand 14, respectively. Figure 1 1 has demonstrated that thedilatancy. ratio (ai) can be predicted by using only the r'atioof after-curin*' ¥'oid ratio to cement content (e.*/A,.).content (A, ). Therefore, e */A, has been confirmed to combine the influences of Cw and A*+ onthe yielding behavior of cement treated clay.(5) The yield locus ¥vere normaliz,ed by using the yieldmean effective stress at stress ratio equal to 0.00 orat isotropic condition as a normalizing par'ameter,and the normalized data follo¥vs a uniquerelationship. Consequently, an empirical relationship for predicting yield locus at a given ¥'alue of(e.*/A,.) has been proposed.(6) The plot ofthe stress ratio-strain increment ratiorelationships and the yield loci from the results ofthe constant stress ratio tests confirm that theratio of after-curing void ratio to cement content(e */Aw) is fundamental parameter and sufficientto characterize the strength and compressibility ofcement-treated soft Bangkok clay.Therefor'e, the stress ratio-strain incr'ement ratlo relation-ships and the yield locus of cement-tr'eated clay can beeasily predicted using the fundamental parameter e */A,..REFERENCF,Sl) Balastrbramaniam, A. S_LiT , D. GSharma A S SJL 濡奮葦CEN・IENT−TKE、へTED SOFT BANGKOK C王＿．へY KanlruzzaIIlaa，A、｝優、NI、，Uddin，K、and Bergado，D、T、（1999）： parameters of cemen［一ad【nixed clay−11ew apProacl｝， ノ、 Gθ01（ぞ（・ノr． Behavior of soft Ba【1gkok clayこrea芝ed w1t猶addi芝ives、1⊃roぐ，1／’h Gθoθ’∼yかoπ．Engrg、，ASC薮，130（10），三〇42・一1050． ．45’oηRθgCo’1∫SA／0五，Seou1，Korea，1H4．2）Bergado，D、T、andLorerlzo，G、A．（2002）lRecentdevelopme瓶sof 工eris工lcs of cemenトadmixed clay ill deep mixing，滅ル1α’θ1”、α、マ〃 ground1mprovemen｛in sofII Ba類gkok clay，P1’oc、＆v111ρ．五〇馳ゾθ’∼4 Engf9、，ASCE，18（2），1−14、 Tθcllno1、，SagaUniversity．Japan，17−26，3） Bergado， D、 T、， Anderson， L、 R、， 汽11ura， N、 and Balasubramaniam，A．S．（亘996）：50ゾf G”o正”∼4∫〃zρ”o、’θ〃∼θ1∼”n蓬637 五〇L∼’10ηゴα’∼ゴ0’hα五ノハゾ’｝on〃∼θ縦5，．ASCE Press、4）Bergado，D、T．，Lorellzo，G．A、，La1，Y P、a臓d Pun，A、（2003）：8）Lorenzo，G，A、alldBergado，D．T、（2004b）：F目ndamenζalcllarac一9） Porbaha，A．，Shibuya，S、and Kis｝1ida，τ，（2000）：S【ate−of一芝ile−a飛in deep mixing technoiogy、鎗art至Ill Geomaterial cilaracterizaτion， （｝1’o㍑ηゴ1〃1ρrovθ1ηθ’∼’／，，3，91−110．10）Roscoe，K、H、and Pooroosllasb，｝｛、B．（1963）l A出eoreΩcal and exper1mentalstudyofstrainsintriaxialcompressiomes｛soll Deep mixlng meこhod using cemenトadmixエure a篭higher wa【er normallyconsolida【edciays，Gθo’θぐ1マ〃ゆθ，13，12弓8 con【en芝asfoundat1onofPhexagollalwirere111forcedembankme撤，11）Uddln，K、（1995）：Streng由anddeforma｛ioncわaracteris：icsof Pノ’oc，2’∼ゴ∫∼π、Co厩甜v、50ゾ’So〃En9ヂg rθごh’∼01．，Maiaysia， 317−334．5） Horp1bu王suk， S、 and r㌧董iura， N、 （2001）： A new apProach for studylngbehaviorof−cememstabllizedcia》・s，Pヂoc、15’ノ∼∫CSMGE， Istanbul，Turkey，1759q762、6） ｝｛orpib娘1suk，S、，r〉liura，N、andNagaraj，T、S、（2003）：AssessnleΩ葛 cemen［￡reated Baηgkok clay，五），」E119．五）’∫∫θ1』∼α’10n，No．GT−94−1， Asia駐Institute of Tecbnology，Th＆琵and。玉2） Uddin，K、and Buensuceso，B．R，（2002）：L1meしreated c韮ay：Salienこ engineering Properこies and a concepωal mode1，50’15α1r4 酌姻面∼101∼5，42（5），79−89，王3）Uddin，K、，Balasubramaniam，A．S、and Bergado，D丁．（1997）l of s汀engtil development in ce【nenζ一admixed llig蚤1 water co員tent Engineering behavior of cemen［イreaエed sof［ Bangkok clay， clays with Abrams’Law as自basis，0εo’θご’∼1∼i（1μθ，53（4），439−444． Gθo’θc1∼、Eノ∼9∼8、／、，28（1），89−H9．7）Lorenzo，G，A、and Bergado，D．T．（2004a）：Fundamenこal
- ログイン
- タイトル
- Fabric and Particle Shape Influence on K0 of Granular Materials
- 著者
- P. J. Guo・D. F. E. Stolle
- 出版
- soils and Foundations
- ページ
- 639〜652
- 発行
- 2006/10/15
- 文書ID
- 20947
- 内容
- I;T{SOILS Ai¥,D FOUNDATIONS¥;ol46,IN'o- 5,639-652. Oct 2006Japanese Geo echnical Socie }FABRIC AND PARTICLE SHAPE INFLUENCE ON Ko OF GRANULAR MATERIALSP. J. GUoi} and D. F. E. STOLLEii)ABSTRACTThis paper discusses the influence of f'abric and particle shape on Ko-values of cohesionless materials usingmicromechanical analysis and the results from a series of tests. Follo ving a simple analysis using Harr's pr'obabilistictheory that illustrates the dependency of' Ko on particle shape, a rigorous micromechanicai analysis is provided to takeinto account the efi ct of interparticle friction, particle shape and particle arrangement. The fabric effect is introduced¥'ia a joint density function of branch vectors. Both micromechanical analyses and experimental results sho¥v that theKo values are affected by fabric related to both the direction and the length of branch vectors. The effect of particleshape may be undermined if' one only considers the directional variation of the density of branch vectors (or contactnormals). The Ka values are sho¥vn to be also affected by the direction in lvhich deformation is restrained.Ke,_'vords: anisotropy, coefficient of earth pressure at r'est, f'abric, granular material, particle shape (IGC:critical state friction angleIN1'RODUC1'10ND6/E5)*.. Furthermore fcu a ¥¥all¥vith friction, the horizontal and the vertical stresses, (Tl'and (7The determination of geostatic stresses is very im-respectively, on the retaining wall are not theportant for the analysis and design of various geotechnical structures, including retaining lvalls, piles, tunnels,slopes, dams and excavations. Their estimation is crucialfor any numerical modelling of geotechnical engineeringprincipal stresses, ¥vhich is assumed in the application ofKb-values.problems involving non-liue tr soil beha¥'iour. In gener'al,mobilized angle of internal frictionFollo¥ving Terzaghi (19'_3) and Ro¥ve (1954), forsmooth lvalls, Ko rnay be determined in terms of thevertical stresses can be determined easily from depths,K0= I - sinunit ¥veight of soils and _"_,roundwater information. On thefrom empirical values of Ko, the coefficient of earthIn ¥vhichpressure at rest.failure. Bolton (1991) suggested rp*.b =¥*ertical ¥valls retaining) a normally consolidated granularfill. He found that when sufncient vertical settling of thefill occur's with the shear' strength within the granular fill0'95 smtion ratio (OCR) are needed to predict approximatevalues of Kb, ¥vhich can be evaluated by the equationproposed by Schmidt (1966)Kb** = Ko *(OCR)"* (4)(1)¥vhere Ko * is the coefficient of earth pressure at rest fornormally consolidated soils, with the exponent ln bein*"approximately gi¥'en by ln = sin ep. The experimental dataalso reveal that Jaky's equation appears to be valid forO I'Ko = I - sinat- 1 1 .5 ' for sand,the effective stress friction an*"le and the overconsolida-and the fr'ictional resistance on the ¥vall being fullydeveloped, the horizontal pressure on the wall can beexpressed as3,*b is less than the effective friction an*'1evhile Simpson (1992) assumed sin *.b=(sin ,)/ /2 L'ornormally consolidated clay.According to a revie¥v of laboratory data of over 170different soils (including both cohesive and cohesionlesssoils), Mayne and Kulha ¥'y (1982) concluded that onlyC onsiderable research has been carried out in the pastto pro¥'ide means for estimating Ko. Jaky (1944), forexample, studied earth pressure on unyielding, rough2m'b (,3)1 + sin m'bother hand, the horizontal stresses are usually estimated. )l-slnK0=;ah/cr¥( ;_ l+sm l+sinq'*.b:(2)iwith q, being the eff:ective stress friction angle measured incohesi¥'e soils and moderately valid for cohesionless soils.triaxial compression tests (Mitchell and Soga, 2005). ItA closer examination of the experimental data collectedby Mayne and Kulha¥vy (198)_) for normally consolidatedsand indicates that for dense sand in which >33', theshould be noted that Jaky's original ¥vork ¥vas fornormally consolidated soils, in ¥vhichis the same as theAssistant Professor, Departmem of C'ivil Engineering, Mc ,Ias er University, Canada (guopi'mcmaster ca).Professor, ditlo.The manuscripfor this paper ¥vas received for reYie¥v on November 14, 2005; approved on July 26, ,-006.¥¥rritten discussions on lhis paper should be submii ed before lvlay I , 2007 to the Japanese Geotechnical Society, 4-38Tokyo I2-001 1, Japan. Upon request the cfosing date may be ex'tended one month.639, ,Sengoku, Bunkyo-ku, GUO AND STOLLE640authors also observed, based on Ko-¥'alues measuredduring primary unloading, that n7=slnin Eq. (4)f) S! ..O 7lsl!'rpO()l ot e Denseappears to be ¥'alld only for the air-pluviated samples.0The discrepancies may be explained by differences in¥e/ I e' *+o eeeo o ¥.fJfabric that depends on sample preparation technique.lvlore recently, Chu and Cjan (2004) investigated theKo-values of loose sand by performing controlled strainpath triaxial compression tests. In order to achieve A'oconditions, the ratio between the volumetric strain andthe axial strain increments ¥vas controlled to be unity;i.e., de /de.=1, ¥vhich implied that the lateral strainincrement de*=0. The measured Ko-¥'alues, ¥vhich ¥veresignificantly affected by void ratio, ¥vere remarkablylo¥ver than that predicted by Jaky's equation. Moreover,the authors observed considerable difference in the Kovalues of samples prepared using wet-tamping and ¥vaterpluviatlon methods, ¥vhich again could be attributed torlll oee Q Q04e *¥¥¥J/ o le'jaJ[i3o/,D ::: 3OO(}O 4 fl 8O(1 eO 7sm ,j.)1r_r)the development of different internal structures related to-T)f+) ,ti ,iC}O i LiF elo:t 1e den t)rig. lSi)r leeilInfiuence of density on It'(]-values of cohesioniess soilsthe sample pr'eparation methods. Experimental data bylvlitchell and Soga (2005), Tsukamoto et al. (1998), as¥vell as Zlatovic and Ishihar'a (1997) show that sandspecimens prepared by wet-tamping tend to have moredilation than those prepared by lvater- or air-pluviationunder drained conditions for the same initial states. As aoverestimated by Eq. (2), as sho¥vn in Fig. 1(a).result, a specimen prepared by ¥vater pluviation has asmaller "nominal" Poisson's ratio, ¥vhich should lead toa smaller Ko-value. This "conclusion" contradicts theexperimental results of Okachi and Tatsuoka (1984). Ithas also been noted that the mobilized friction an le atMoreover, the difference between experimental A'r,-¥'aluescritical state, ho¥vever, is not sensitive to the initiai fabric,and Eq. (7-) ¥'aries ¥vith the relati¥'e density of soi] speci-since the induced fabric tends to erase the memory ofmens; that is, Eq. (2) overestimates Ko-¥'alues of loosesand and matches most experimental data of dense sand,initial fabric of soil specimens at large deformation One¥vould expect that loose sand specimens prepared usin_"..different methods should have the same effecti¥'e stresspredicated A'o-values from .Iaky's equation in the for'm ofEq. (2) are often smaller than experimental data onaverage, ¥vhile Ko-values of loose sands can easily beas sho¥vn in Fig. 1(b). In other ¥vords, in addition ro theinternal friction angle , a more accurate estimation of Komust take into account the effect of density or void ratio.Even though the friction angle and OCR are generallynnportant fol the evaluatron of A'o, other factors ha¥'ebeen found to ha¥'e significant influence on the Ko-valuesof granular soils as ¥vell. As pointed out by Mitchell andSoga (2005). Ko is state parameter that depends oncomposition, structure (or fabric), stress histor _', as ¥vellas loading directions. For example, Andra¥ves andfriction angle at failure but different Ko-values, o¥vin_".. tothe impact of fabric on deformation characteristics priorto failure.The possible influence of fabric on A'o-values has beenobserved from tests based on measurinshear ¥vavevelocity. According to Roesler (1979) and Stokoe et al.(1985), the shear ¥vave velocity in an elastic mediumdepends on the principal effective stresses actin>' in thedirections of the ¥vave propa*'ation and the particleEl-Sohby (1973) measured different Ko-¥'alues in triaxialKa consolidation tests ¥vhen either vertical or lateralstrains ¥vere restrained. The Ko-value measured at zerovertical strain ¥vas found to be smaller than that at nomotion. According to this findin*', it is possible to backcalculate the in-situ str'esses in different directions andlater'al strain, ¥vhich ¥vas attributed to the anisotropy ofthat the shear ¥vave ¥'elocities vary ¥vith fabric, one maythe specimens and the change of major principal stressargue that the back-calculated Ko-values should also befabric dependent^directions. Okachi and Tatsuoka (1984) measured Ko-hence estimate the Ko-¥'alue based on measured shear¥vave velocities (Fioravante et al., 1998). Holve¥'er, gi¥'envalues of Toyoura sand using a double cell Ko-triaxialBased on probabilistic theory, Harr (1977) demon-apparatus, in lvhich the zero lateral strain condition ¥vasstrated that the coefficient of lateral pressure in particu-achieved by continuously adjusting the cell pressure.They noted that the Ko-values of air-pluviated samplesare approximately 10 to 150/0 higher than correspondinglate medium depends on the transmission of contactforces through particles. For a homogeneous randomlvet-tamped specimens of the same void ratio ¥vhennormaliy consolidated. Ho¥vever, the relation betlveendistribution, Harr found that the coefficient of later'alpressure is uniquely determined by a stacking parameterthe peak friction angle and the ¥'oid ratio appeared to bethat is likely related to particle geometries and the distri-independent of the sample preparation methods. Thebution of contact normals.medium in which stress variations depend on the normall K+ "+P=Aztt*+f(641- .)(* ;r2 exp (5)crz(x,zlbz)=Pl_'7zv2 vz1/ / (;:_1'/: J:_( -i'T- ItVALUE OF GRANULAR ¥_ ,IATERIAL¥vith1' z' ; ( r+: t :+ :I, ;s'_I ;v. ftf hJ'(Ax)2 2 (Ax)2 (6)Az z A( 2)being the stacking parameter that describes the spatial ar-rangement of particles. When neglecting the body forceof the mat.erial, the lateral stress, ¥vhich is obtained fromthe equilibrium condition, is given asa]a(Tz I a2cTz+ v'7cr v(7z+v4 = v(7za. -'+F'ig. 2. Force transmission i l granular medium: (a) irregular particlesand (b) rectangular particles of the same size(7)An immediate observation is that ax= v(T at z=0, vhichimplies that Ko may be directly related to the stackin_cr,_parameter v. For a uniformly distributed pressure qacting on a strip ofHansson and Svensson (2001) carried out a series ofvidth 2a, the vertical stress at a pointis computed astests using a steel ring chamber to investigate the influencea J:: q fiTI exp(x- ) dof particle shape on the distribution of horizontal stresses'_vz2in unbound aggregates induced by a distributed verticalload. For aggre*･ates from the same source, ¥¥'hen subjected to a **i¥'en vertical pressure, the horizontal stresses inspecimens ¥vith flaky particles ¥ 'ere about 200/0 higherthan those with cubic par'ticles. As a result, the authorsconcluded that materials with flaky particles ¥vere likely(8)Introducing the transformation_x-t 1/T : 'd= -/' dt (9)It follows thatz= {J a)/Icr1 dtt' (10)q (1 a)/1r l2rlT_'1Texp - 2to be more unstable than the cubic ones, since largerhorizontal stresses tend to cause large horizontal defor-mation. This conclusion, however, is contrary to thefinchn*'s of Hobeda (1988), who argued that flakymaterial is more stable than cubic material.Given the curnulative-distribution function for a normally distributed random variable,= 1Jo/ (i:-Li)2W(z)Motivated by the above review, the objective of thisexp (1 1)paper is to explore the influence of fabric on Kb-values ofgranular materials. Starting ¥¥'ith Harr's probabilistictheory (Harr, 1977), ¥ve demonstr'ate that the coefficientEquation (lO) can be rewritt.en asof laterai pressure in particulate mediurn depends on(JZ = q { v/('¥;,rT)Similar to Eq. (7), the lateral stress due to the strip load is*･eometry and branch vectors, Ivhich describe thegrven as. a2(rz _(T'¥ = v(Tz + v2zax '. f(x+ a) expvaa) -(x[- a)2?J +-･vz2x[- (x_,- J}( 1 3 )(x a) expKo AND FORCE TRANSMISSION IN GRANULARMEDIUM: REVISIT OF HARR'S PROBABILISTICANALYSISHarr (1977), usin*･ the theory of probability, developedprocedures for estimating the distribution of stresses in aous, the distribution of vertical normal stress at a pointtreline as follo¥vsexp a'( ') xz=cr (O) va( 2aql¥/ t2)a'z(O) = 2qv/a z /2 v<;{=+*( 1 4)If a/z is large, ¥vhich corresponds to a uniformly dis-depends only on the porosity of the medium. When atributed surface load,point load P is applied normal to the surface at the originof coor'dinates (Fig. 2), the vertical normal stress at apoint (x, z) in the granular mass is postulated to be givenof the parameter v. AS a result, the stress components inEq. (14) are simplified asbyi'2v ' 2When x= O, one obtains the stresses at a point on the cen-semi-infinite granular medium subjected to normal surface tractions. Assuming that the medium is hornogene-iV/(izl ) i (12)particle shape, which affects the transmission of contactforces through particles. A more rigorous micromechanical analysis follo¥vs, in which the effects of particleconnectivity of particles, are taken into account. Tests onglass beads of various particle shapes are carried out toverify the theoretical Ko formulations.id u/(a/(zlf ))- 0.5 for a lirnited value(rz(0,4-)=q, CT (O z) v(T(O 4) (15) --GUO AND STOLLE6421!rA*nI2el hAA'vY :::(Ar)*/ I i I_'A:i*bt2 , h !aF g. 3. Parametcr v and particle arrangementIGiven that the deformation and stress distribution in thesoil mass are symmetr'icai ¥vith respect to the centreline,g. 4. Definition of (a) branch vector 8nd (b) contact normalthe Ko condition is automatically satisfied along theorientation distribution E(D, ¥vhich defines the portion ofbranch vectors vithin a range of I and l+ dl. Follo¥vin_centreline. According to Eq. (15), the coefficient of earthpressure at rest A'o is gi¥'en by the parameter v; i.e.vectors are statistically independent of their orientationsK0= v (16)R thenburg and Bathurst (1989), the lengths of branchand E(D can be expressed ascf *E(1) = I,(!")E(ln) ( 1 8)(T.¥vhich confirms that the lateral stress depends on the¥vhere /* is the leng:th of the branch ¥'ector I at a contactstacking parameter v. Referr'ing to Fi(,_. '_(a) and Eq. (6),point, m is a unit vector defining the orientation ofone obser¥'es that v determines the transmission ofis relatecl to particle geometr'y and the internal structure,branch vector l. L(!') and E(m) describe the directionaldependencies of the len*"th of branch ¥'ectors and theirorientation, respectively. Without loss of generality, forincluding the particle shape, the spatial arrangement andany direction that makes an angleconnecti¥'ity of particles in general. More specifically, foran ensemble of particles sho¥vn in Fig:. '_(b), Eq. (6) can bereference (e.g., the horiz,ontal axis), ¥ve assumecontact forces through particles, ¥vhich strictly speakin_cr._¥vith an axis ofI.(!') = ! [1 + ( ) cos '-( fi - fiL)1 ;expressed asE(m) =[1d,o cos _'(fi - fio)] ( 1 9)v = ' (ll :")2 _ 2 ('ri; I - x!) , _ I,/-, 2A･- ･-i- 1'Il[(,j+l)h] -(j/7)1 __ (1,' - (17)ij,_,f i) hlvhere ! is the a¥'erage length of branch vectors; ( ,o and a)define the degree of anisotropy associated ¥vith theorientation and the length of branch vectors, respectively; fio and fiL define the directions along ¥vhich the¥vhich indicates that the stackin..,_O parameter v tends tovary ¥vlth the particle shape. A closer examination ofFig. 3 reveals that v is also affected by the arrangement ofparticles in addition to particle siz,e. It can be sho¥vn thatin general O < v(AR)2/2 Ivith AR = I,//1 being the aspectbranch vectors have the maximum density and themaximum length, respecti¥'ely. PL can also be consideredas the preferential direction of the long particle axis foran ensemble of elongated particles. Substitutin_g: L(/') andE(ln) in Eq. (19) into Eq. (18) yie]dsratio of particles.Even though the above analysis based on Harr's!E(1)=- [1+(1,Lcos2(fi-fiL)][1+co cos'(fi)1 ('O)probability approach is some ¥'hat oversimplified gi¥'enthat the influence of inter-particle friction is not takenFor smallinto account in the evaluation of Ko, this analysis re¥'ealsals ¥vith ¥veak to medium anisotropy, Eq. ( -O) can bethat the internal structure and particle shape may haveinfluence on the value of Ko. The follo¥ving sectionexplores the dependency of A'o on fabric and particleshape via a more rigorous micromechanical analysis of27rsimplifies to1E(1)=- [1+(( )0+( ,Lcos '( ) cos '(fi fi)2frranular materials.+ ( ,L Sin 2(fi -fio) sin '_ L]¥vithMICROMF.CHANICAL ANALYSIS OF KoCOMPRESSIONBranc/1 Vectors anc! Tl7eil' Dist/'ibutionFor the general case of particles of arbitrary shape andgradation, the connectivity of an ensemble of particlescan be described using a graph of branch vectors I thatconnect the centres of gravity of any t¥vo contactingparticles, as sho¥vn in Fig. 4. For a granular ensemble, itis necessary to introduce a joint branch ¥,'ector length-,L and (1)O ¥'alues, ¥vhlch correspond to materi-(2 1 )L =fiL -fio bein*' the angle bet¥veen the directions ofthe densest and the longest branch ¥'ectors. V rhenelongated particles are deposited under gravity, thedirection of the densest branch vector is approximatelyperpendicuiar to the long axis of particles or the directionof longest branch vector's, yieldingL=,Tl.-. The jointbranch vector distribution function becomes1E(1)=2ri'll((D coL)JCOS '(fi)} (2-,)i ri+Ko VALUE OF GRANULAR N{ATERIALFor spherical particles of a single size, the length of abranch vector in any direction is the same as the d}ametelof the particle, indicating ( ) =0. Consequently, thedensity function E(/) simplifies to1E(/)=i643E(D!L :lc!VVF -(!')E(m)mV -mc/ V (28)It f'ollo vs that[1+co cos )(fi P)] (- 3)cr = N. Ji E(Df; Ic!V= N. Ji }/(!')E(ln)flnc!V ('_9)¥¥rhen the directional distribution of branch vectors islvith N* being the nurnber' of contacts per unit volurne andunif'orm in all directions (i.e., cT'Jo = O), for an ensemble of! the a¥*erage length of branch ¥'ectors. According to Ng(2001), the directional distributions of the branch vectorand the contact normal are statistically the same, ¥vhichnon-spherical particles, anlsotropy may de¥'elop o¥ving toparticle shape, ¥¥'hich induces directional variation ofbranch vector lengths such thatE(/) = 317r [1 - (1)L cos 2(fi -fio)] (-'4)yieldsJE(7=N.. L (/' )E(n) fnd V (30)¥vith n being a unit ¥'ector defining the direction of' theContact Forces anc! A vel'age St/'essesLet us consider an idealized, t¥vo-dimensional _O,_ranularcontact normal.When applying Eq. ('-6) to a specimen subjected toassembly, subjected to planar deformations, in ¥vhich theresistance to def'ormation comes only from in-plane contact forces. According to the micromechanics of grarrularbiaxial compression sho¥vn in Fig. 5, the contact forces atcontact m can be determined asf"')=cTll/I ("')! ( "' } (Fi 1nl("')+F1'_n2 );materials, given a representati¥'e elementary volume(REV), the rnicro-variables can be a¥*eraged and thenused to describe the macroscopic state and behaviour.For a cluster of rigid particles chosen in a REV ¥vithparticle connectivity represented by a graph of branch¥vhere !("'} is the br'anch vector length at contact ln, nl =¥'ectors I (as sho¥vn in Fig. 4), and assuming that the bodyplanes. When the fabric tensor Fjj is coaxial ¥vith theforces are negligible ¥vhen compared ¥vith interparticlestress tensor (Tij, the abo¥'e equation becomescontact forces, the average stress (7ij associated ¥vith theREV can be expressed in terms of contact forces, f,bet¥veen particles and local branch vectors, l, via (e.g.,Chang and Liao, 1990; Kr'uyt and Rothenburg, 2004)1 ",crjj=Vvith)l ) f (25)denoting a tensor-product operation and /7* bein_"_.F n2 ) (31)l (,,,]f{ '*=) cr22!("')(F_.jnl , l22(,,,)¥-sin e and n.=cos e are the directional cosines of thecontact normal, ¥vith e defining the orientation of contactf "') (TI IFI j l!("')n("'] f "') = ( 2f l!("')n "'1 (3_,)Given the inter'particle friction angle ep,,, sliding takesplace at contact ln ¥vhenJl =tan(e("')-ep!') (33),,, }f･*)Let us no¥v consider a Ko-consolidation test in lvhichthe number of contacts enclosed in V. Following Changthe vertical stress (;.･ is increased lvhile the lateral stressand Liao (1990) as ¥vell as Emeriault and Chang (1997), it(Tl! is adjusted to correspond to zero lateral deformation(i.e., el =0), which is achieved for the case in ¥ 'hich norelati¥'e sliding takes place bet¥veen any t¥vo particles onis assumed that one may extract the microscopic quantities from the macroscopic variables by invoking a socalled "localization" or "tracking" operation that isboundary A-A' in Fig. 5 . Without loss of generality,opposite to averaging. The contact forces bet¥veenimagine that a specimen of ¥veightless particles is put intopar'ticles can be expressed in terms of the average Cauchya mould that has a movable boundary. When applying astress, (rij, and the fabric tensor, F, as¥'ertical stress cT22, the specimen tends to deform unlessf = (TikFk'-'j l!J (26)¥vith1 '*=Fij = <l } l> - V]!j!j; Fij = I (27)lateral support or confinement is applied at the sametime. For a pair of particles on the boundary of thespecirnen, no lateral support is needed ¥vhen e("*),,because of inter-particle friction. In other ¥vords, ¥vhene("') ,, is valid at all contacts in the specimen, zerolateral strain is achieved vithout any lateral restraint,and F- I being the in¥'erse of F. Using the density functionindicating Kb= O. In the case of a("')> ep,,, (,,,)jl (or all) mustof branch ¥'ector given in Eq. (18), the fabric tensor Fmay be rewritten asbe applied in the lateral direction according to Eq. (33) tomaintain equilibrium of particles ¥vithout sliding. If theinternal structure or fabric is kno¥vn, one can calculateIThe concept of fs:o condi ion defmed as the absence of relative displacemen bet veen any two particles on he boundary A-A' in Fig. 5 and he Kocondition defined as zero average laterai strain vithin a represemarive elementary volume (RE¥r) are the same lvith regard to the a¥'erage meaning.This is because the average strain of a RE¥r can be calculated from the displacement uj on tlle boundaries S of the REV ¥'ia ejj= (1/2 r)is (uj,ij *i_ujnj)c!S, vhich implies that 8jl =0 Ivhen there is no relative displacement bet¥veen par icles on A-A'.i;{ GUO AND STOLLE644lfin ¥vhich the average of the f /.f... ratio is determined as fol-c T e( f'¥/ = 7z;-, Jf iNJ _/i aallcr:1 -_10¥vs:?tan (e- q;;')[1 + ( ) cos -' (e - eo)Ide',2 .;Jr In( (smnil)+co: ( -T b N･ ';') sm (q';' - 7-eo)Herein Simpson's three-point method is used to evaluatethe integral. For special cases of bedding plane beint:'(;horiz,ontal (e0= O) or verticai (e0= 'T/2), the above equation simplifies asAi { ep,il) co: ( - l[(f In) ;(sin,it') [cot lifi7rFig. 5. Biaxia! compression of a specimen( 4 )2 7TJ} !' (40)4tansmaccording to Eq. (29) or' (30) the stress components (TI I and(T22, ¥vhich yields the lateral pressure coefficient at rest asKO =llu cos 2eoJ)(7z4 2 I- -[u) [coti ¥'L(lc)E(m)flnlc/V_ !¥'1,(!c)E(n)f]nlc!V (34)(T22 i ¥'L(/c) E(m),f･_m2c/ Vi ¥'1,(!C) E(n) f._n2d VWhen the body force of a particle cannot be neglected,Eq. (34) is still applicable as long as the influence ofgravity is included in crll and cT22.in ¥vhich " + " and " - " correspond to e0=0 and Itl2,res pectively.In terms of the average length of branch vectors, giventhe joint branch vector length-orientation distributionE(D in E.q. (18), one hasj1 JI'< !i> = ni L (/ c) E(m)cl VThe ¥'alue of A'o can be determined alternati¥'ely bylr- Jousing the average contact forces <fl> and <./ > at A'n State.:x /7i[1 + (( ,0+(1)L cos 2 L) cos 2 (fi-fio)lc!fi (41)7zAccording to Eq. (32), one has<fl> = cfl iFI I I <!("')>; <f,_> = (722F._,_,1</ "')> (35)¥vhich ylelds for horizontal bedding plane<!1> i nl [1 + (( )o + (;( 'L cos 2which yields an alternate expression for A'o:A'o =,,ll - <fl><!2> !!._> F2l! (36)distribution of interparticle contact forces in all dlrections. It has been found that the <,fl>/<f._> ratio can beAccording to Eq. (36), the expressron of A/ becomesKo3calculated based on the micromechanics of granularmaterials vhen the directional ¥'ariation of normalcontact forces is given (see the Appendix for details),which, ho¥vever, requires other parameters to characterize the distribution of interparticle contact forces. In thefollowing sections, ¥ve ¥vill adopt a simplified approach toestimate the <fl>/<,f_.> ratio, ¥vith emphasis being placedL) cos 2 (fi-fio)]cJPll2[1 + (( )o + ( )L cos 2 L) cos 2(fi -fio)]clft3 + (( 'o + ( )L cos 2 L)(722 <f,..> <!i>FlllOne observes that the determination of Ko requires the¥rjth e0=0:(( )o + ( )L cos 2 L)F_.._1 {In(sm!!) T Aucoo}Jt 3 + (( '0+ a'L cos 2 L)Fll(43)¥vithAu = _(u) [cot[ ITu + 4 tan(4 ');isin luJ (44)on the infiuence of the shape and connectivity of parti-Referrin_g to the definition of fabric tensor in Eq. ('-8), itcles .can be shown that for horizontal bedding planesGiven that the ratio bet veen the components of con-F._21 Fli I -(( '0+d'L cos 2 L)/2 (45)tact forces ¥'aries according to Eq. (33) for any contactorientation, one can sho¥v that) << f > fmln <f._> ****: ･) (37)As a first-order' approximation, ¥ve assume for irregularpacking of particles that:, = )(L ff.=..; (3 8)Fli F..I + (( )o + ( )L cos 2 L)12and2 1 - ((1'0+( 'L cos '- L)/6A/0=JrI +(( )0+( 'L cos '- L)/6For materials with{In(sin;")+Aua 'a} (46)veak to medium anisotropy (say ( ,0and ( )L are approximately less than 0.3), since (( )0+("'Lcos 2 L)/6<< 1, one need keep only the linear terms of ( )Land ( ;o in Eq. (46). As a result, Eq. (46) is simplified asL r;rl+(O 6 "= +,i,,( i=]iK(, VALUE OF GRA{¥lTULARl i-(,V5in the vertical direction, as illustrated in Fig. 6(a). ¥VhenEq (50}assuming ( ,0=0 in Eq. (50), the Kb-value for isotropicO Eq (49]06o6 5decrease lvhen the contact normals are more concentrated==K,, x 1+(i = Iln(sin( =,)Os'lATERIALsoils is given asA -2 l-O == 6 [In(sin(o ) -?K = - iL In (sinv {ioi*.(Q =(jsoooFigure 6(b) re¥'eals that l 'hen ep,, varies in the range of 20oooV1'to 40', Eq. (51) is ver'y close to Jaky's equation gi¥'en by{alEqs. (1) and (2). As a result, one may argue that Jaky'sequation is applicable to materials with ¥veak to rnediumanisotropy. Equation (50) also indicates that a pre¥'iousO1OlO,,) (5 1)7z0 5L)0InterParl:icle iticti :*!1 a gle tp( * lloading history that makes the contact normals moreconcentr'ated in the vertical direction tends to decrease theKo-¥'alues in a subsequent reloading.K=Elongated ParticiesFor a natural deposit consisting of elongated particles,the long axes of particles tend to align in the horizontal- i In (sin (P)osKlj = O 95 - si¥'(Pdirection and the br'anch vectors in the vertical direction' "outnumber those in the horizontal direction, indicatin :v V6Ko ; { --'/'}ak¥ 's equation04q (I]fiL = O, fi0= rr/2 andn(p''¥*'"(bol'O 4 sin(p O 610 Il0Os4O 4FrictiOn angle (p ( ' }Fig. 6.) -=?coo ((1,L _3: J :o,,.Oj,KA,,coo;, ;ol'L = Tz /2. For this case, the J O expres-sion in Eq. (47) can be re¥ 'rltten asfz( ,a (Ko,,. i ) co-- , + A,, + .Koi,O,37r(5-7)This equation clearly sho¥vs that the values of' Ko increase¥vith ( )L but decrease vith ( )o. More specifically, for anensemble of elongated particles with a horizontal beddln_a._plane, the value of Ko tends to decrease ¥vhen the contactSimplified expressions for Ko2Ko 2 In (sm q',,) I -co0+( )Lcos 2 L _A,,()o (47)normals are more concentrated in rhe vertical direction.In the contrast. Ko may increase ¥vhen more particles ¥vithlarger aspect ratio ar'e aligned in the horizontal direction,According to the above analysis, in addition to thedegree of anisotropy, the Ko-values are affected by thedirections of the densest and the longest branch vectorsquantified by fio and fiL respectively. For ¥'ertical beddin_{_planes ¥vith ft0= O and fiL = 7z/2. Eq. (46) becomesK0=I + (( ,0 + (2,L cos 2 L)/6 .7r I - (( ,0+ ( ,L cos 2 L)/6 {In(sm ,,) -A;'d)of (48)¥vhich is indicated by an increased ( )L. This observation isqualitati¥'ely consistent ¥vith Eq. (17) based on Harr'sprobabilistic theory, ¥vhich provides only a conceptualmodel for a very special case in which the infiuence ofinterparticle friction and fabric is not appropriatelyaddressed.However, it should be noted that an increased aspectr'atio may simultaneously induce increase of the concen-tration of longer branch vectors in the horizontalSpecial Casesdirection (indicated by an increased ( ,L) and the densltySpherical Particlesof branch vectors in the ¥'ertical direction (indicated by anWhen particles are primarily round, the directionalIjand ( )o ha¥'e opposite influence on the value of Kb, whichThe expression of Ko for the case of horizontal beddingimplies that the Kb-values may decrease at some pointplane becomeswith an increase of the aspect ratio of particles and Komay have a maximum ¥'alue when particle shape changes.Figure 7 sholvs the variation of Kb-values with respectKb= - 2 1 -( ,0/6I7z I + co /6 [In(sm q,,,) + A,,( )o](49)to the fabric related to the particle shape and the densityof branch vectors at an interparticle friction angle of ,, =!{iwhich can be further simplified to2 1 -d)0/2K 7z I + ( )e/2 In (sin{Iincreased ( )o). According to Eq. (52), the increases of (1,Ldependency of branch vector length vanishes ¥vith d)L = O.30' for the case of horizontal bedding planes. When,,)(50)assuming a uniform distribution of the branch ¥'ector inThis equation indicates that the value of Ko tends toall directions (i.e., ( ,0=0), a variation of ( )L has smallinfluence on Kb, as sho¥vn in Fig. 7(a), but the anisotropy -GUO AND STOLLE6460.()/o 5f*r-fr*O')O,4rlrO^2Loadoi -coocells:)zio.3:o(a) CCi*2L::: OPnon-rotationalL,oadO. lO. I O.2 O.3O.4 O.5 0.6cell lKO = I - Silo 61 78 mmr ,((/' ¥o.5L,oadcell 2¥:()" : : ) ll )'1o.4¥ Dial aug:e)e )¥.*:)S ;h:!)- o. 1)Roller strip**7Fig. 8. IL'o tcst cello.2(b) 05L = Oll O 1 - l'O t a t i Q I a lO, l0. I O.2O 3 O.4O.5OKO = I - sin6Flg. 7. Depeudenc,' of Kl] on anisotrop)' associated to (a) branchvectorength and (b) the density of branch vectorsloads are then used to calculate the aver'age vertical andlateral stresses to determine the Ko coefficient^ Differentglass beads ¥vere mixed to_g:ether, yielding various particlearrangements and hence different distributions of branchvectors (or fabric). T¥vo types of surface textures ¥verechosen to study different le¥*els of Interparticle friction.Spherical and flattened particles of different sizes andaspect ratios, varying in a ran*'e of I .O to '_.8, ¥vere select-related to the density of branch vectors may haveconsiderable infiuence on the Ko-values, depending oninterparticle friction. As can be seen from Fig. 7(b), ¥vhena,L = O (i.e. , spherical particles), an increase of the branchvector density in the vertical dir'ection tends to reduce thevalue of Ko, Particularly for small interparticle friction.ed so that the influence of both the particle shape andpotential particle rotation could be identified. Table 1summarizes the characteristics of the glass beads used toform the A'o-test materials that are listed in Table 2.The _ :lass beads or glass bead mixtures lvere carefullyplaced into the test cell ¥vithout compaction or' vibration,¥vith the bulk unit ¥veight varying bet¥veen 15.0 and 16.4kN/m3. The Ko-¥'alues ¥¥*ere calculated as Kc = ai*/(7F,XPF.RIMENTAL STUDY¥vitha+, and (Th bein.' the applied vertical stress and theIn order to investigate the influence of particle shaperesulting horiz,ontal stress, respecti¥'ely. The initial stressand fabric on Ko-values, Ko compression tests werecarried out using a rigid mould made of aluminum, aso¥¥'ing to the ¥veight of the load platen and the self-¥veightsho¥vn in Fi**. 8. In order to reduce the friction bet¥veenthe ¥valis of the mould and the testing material, a layer ofof the tested material ¥vas considered as an initial"sitting" stress that is much smaller than the appliedvertical stresses during tests. Only Ko-values under lo vplaxiglass (6.5 mm thick), on ¥vhich dry lubricant ¥vas¥'ertical stress of (Tvapplied, Ivas put on the inner side of the mould. One sideof the mould could move freely on a roller strip and t¥voAccordin_9: to Fig. 9, ¥vhich presents the variation ofmeasured Ko-¥'alues ¥vith respect to the applied verticalstress (J for typical tests on Gl (# ) glass beads, Koapproaches a stable value ¥vhen (7.> 7 kPa.dial gauges were mounted to monitor any displacementof the plate. The vertical load vas applied on the specimen by loading ¥veights ¥vith t¥vo load cells measuring theresultin : Iateral forces. The measured ¥'ertical and lateral'-O kPa is in¥'esti_g:ated in this study.,* rK * ¥*ALUE OF GRANULARParticle shapeG' ', i "'*'"i"'t,'s (rouglsurface),647AveParticle sizemono-disperseS** (rougll surface) mono dlsperseG.RIALGlass beads used to form tcsied specimenslable l.i¥1aterial(AT*,,*･...a = 20.68 mma/b=2_17,b=9 58 mmaa= 33.30 mma/b = 2_8 1 ,b= I 16mmal/a. = I 13GO (gloss}'Ismoot}1 surface) mono dlspcrsec!=Gel (rougll surface) mono-dispersec!= 15 O m lG<Crushed limestoue, angularc!ns* = 7.5 mmSpeci flcas{)ecratio/a. =gravi ¥.*2.46.062.46105.0 mm2.502.46l .O2.75c!< l = 4.65 mmi¥Tote:} i lCharacterization of parriclese)ilT'able 2.Materials used in ll'(, testsComposition'Ia erialG glass beadsGj G2 '13Gl-G '*"';"""' ixture of(j"' O.i' t 'JG oecG1-( * ' {G"';,1' ./ ' =//"",i "t'*and G2, 'i'G !'rC 1 s l:3.15l¥,'1ixlure of G and G , illG :l,ZG = I ･ , )15.9ilvlix:ture ofG16.4and G,,1lc4:1,lC]1 = I : l15.0particle size c!< )=4.65 mm and the coefficient of unifbrmity C*= 2. I lo.4o o0.38angle (')15 7Crushed limestone, angular particles ¥vith lhe maximum size being 7.5 mm,limeslone 4Friction(kiN/m')l 5 .Olixture of G** and G ' inG :,tlG = I I ?-CrushedUnit ¥vei htmean13.3q'r = 36 iconcentration of longer branch vectors de¥'elops in thehorizontal direction, particularly for Gl and Gl-C}*2Q 6mixture. The bu･anch vectors (or contact normals) in thevertical direction, ho¥vever, usually outnumber those in.*o.36the horizontal direction. These are clearly sho¥vn in¥lFig. 1 1 , 1¥"hich presents the distribution of' both the lengtho.34and the orientation of branch vectors for Gl materials(mono-disperse) and G1-G2 mixture based on digitai0.32image analyses f'or biaxial cases. It should be noted ino. 3Fig. 1 1(a) the lengt.h of branch vector is normalized by itsoIO15maximum length that is equal to the maximum diameter,Applied ¥ ertical st 'ess av (kPa)Fig. 9. Variation of measured H'o*values against vertical stresses:Glparticles lvith horizontal bedding planeDo, of glass beadsA scrutiny of Fig. 11 reveals that, for Gl-G2 mixture,the addition of more flattened G2 particles into Gl resultsIn a substantral change in the distribution of' branchvectors. Statistically, the G1-G 2 mixture has se¥'eredirectional variation in the length of branch vectors,Influence oJ' Pa/'ticle ShapeFigure 10 sumrnarizes the experimental results for G!¥vhile no significant difference is observed in the distribu-" "..=' $ O)tion of branch vector direct.ions for both Gl and Gl-G2mixtures. Even though the experimental data are scattered, one can see that the Ko-value of Gi-G2 and Gl-G4mixtures are higher than that of G1 on the average. Themixture. In other ¥vords, the addition of G2 particles intomeasured a¥'erage Kb-value for *"lass beads Gl is 0.375,while those for G -G. and Gi-G4 mixtures are 0.407 and0.399, respecti¥'ely. Since particles tend to align themselves ¥vithin the horizontal plane under gravity and a-( )L for GI-G2 mixture. According to Eq. (5)-), anincrease in ( , ¥vith fixed ( ,0 induces an increased Kovalue, indicating Kb-12>Kb-i. This is consistent with theexper'irnental data in Fig. 10(a). Herein Ko-! and Kb-12 are¥vell-defined horizontal bedding plane is formed, aKo-values for GI and Gl-G2 mixture, respectively. For() glass beads and Gl-G2 (,=:,,j ,i;i..i'i.,;,,), G -G4 (-'-*=G: causes ( )L to increase significantly ¥vith coo notchanging much,vhich in turn results in a decrease of ( )o^J iGUO AND STOLLE64sK0_1= O 407 (GI +G, )elo 45OsJA i .* AeQA * e AQ p ee,jeQ ,QA eA eee_'04vo.35,"_Q Q e06o 4{),G eC G(a)O-60o3o 48 12N'umber o il 6 20 24-oo3060Branch vector orientation ( o )testsso 45604:s 41-v7o 35o-60-J)OOBr* nch vector orientatio03o 412N Tumber ofi6estsKol･ 0407(Gj G,)cc c ccco 45co.4cvc c(c)03o 48 i 6 20 24i2Nunlber oi tes svith rough surfacetexture: horizontal bedding planeGI-G4 (Fi*o, Il, Distribution of branch vectors for G] and Gl-G. mixture: (a)branch vector length and (b) branch vector orientationaddition to the par'ticle shape, the distribution of contactnormal has significant influence on Ko-¥'alues.The influence of interparticle friction is investigatednext by adding a small amount of spherical G3 ( ･.,V･)particles ¥vith smooth surface into Gl particles ¥vith amass ratio of n7G3:nlGl= 1:2.23. Referring to Table 2,Gl-G3 (･"'," ･' 'i･*"'.･,' O) and CJl-CJ (Fig. 10. Experimental K0'values of glass beads60( o )Influellce of Intelpartic!e FrictionK0-14 = O 399 (G : G4}o 350Q) mixtures consist ofboth Gl particles and some spherical particles, G3 (V･･'･'･" ) orG4 (c), ¥vhich have different surface textures. Ho¥¥'ever,the amount of spherical particles in CJ -G3 mixture is lessthan that in Gl-G4 mixture.Figure 12(a), which compares the measured Ko-¥'aluesof Gl-CJ3 ( O) mixture ¥vith those of Gl, clearly sho¥vse) mixture, ho¥vever, the mix of spherical G4Ko-13>Ko-1, which is partially attributed to particle shapeinfluences. The results are consistent ¥vith Fig. 10(b) for(c) particles ¥vith non-spherical Gi Particles at a mass ra-Gl-G4 ( s e) mixture. Chan*'es of interparticle frictiontio of G4:Gj = 1:1 yields more uniform distributions ofassociated ¥vith the CJl-Gboth the direction and the length of branch vectors, vitha larger decrease of ( ,o than a)L being observed. Accord-ute to lar*'e Ko-13 values. Figure 12(b) sho¥vs that the Ko-ing to Eq. (52), the variations of ( ,0 and (,L ha¥'e oppositecontributions to Ko-¥'alues, ¥vhich may increase ¥vhen ( )ois decreased more than ( )L. As such, one may expectKo-14>Ko-1 t,hat is confirmed by the experimental datapresented in Fig. 10(b). A close examination of testresults for Gj-G2 and Gl-CJ4 mixtures in Fi**. 10(c) sho¥vsthat Ko-i4 seems slightly smaller that Ko-i2. Ho¥ve¥'er, sincethe data points are scattered, Ko 12 and Ko-14 can be consid-ered to be the same statistically. Since the anisotropyinduced by particle shape in CJ1-G2 and Gl-G4 mixtures isquite different, Fi_ . lO(c) further confirms that, inmixture, ho¥vever, also contrib-vaiue of Gl-G3 mixture is higher than that of G1-G4mixture. Takin*' into account that Ko-14 A'o-1=0.024,Ko-13 Ko-] = 0.057 and the Gl-G3 mixture has less spher'lcal particles than G -G4, Fi**. 1'_ implies that interparticlefriction associated ¥vith the surface texture of particleshas a strong infiuence on Ko-values. As one might expect,smooth surface texture, indicating small interparticlefriction, increases the Ko-values.Figure 13 sho¥vs the influence of particle shape andinterparticle friction on Ko-values by comparing themeasured Ko-values of Gj-G4 ('S) and G3-G4 (oe)mixtures, ¥vhich were obt,ained by adding Gl and G3 ,'',',i649K{) VALUE OF GRAN. ULAR +¥,1ATERiALo. 5)o 45604jo 35so.3o 412iai gauge(b ) Roller strrp(a}16N ulnber o r testsFig. 14. PrepaFation of specimen witll different bcdding planeorientationso^ 5):mixture, o¥ving to the presence of flattened Gl particles,one expects ( )L_14 0 since the branch vectors in thehorizontal direction are long:er than those along: theo_45vertical face. Sirnilar to the discussion for Fig, iO(b),fiattened G] particles may reduce the concentration of'04contact normal in the ¥'ertical direction, yieldingo. 3 5( )o-i4<(1,0-34. E¥'entually, the joint effects of ( )causes Kb-34>Kb-14, ¥vhich is consistent03o 412Influence of Bedding P!ane Orientation16For an ensernble of elongated particles, the direction ofNumber of teslsthe densest branch vectors is generally perpendicular tothe bedding plane lvith the iongest branch vectors mostlyF'ig. 12. Influence of interparticle friction on Koparallel to the bedding plane, indicatingo 55)05Ko h¥lfi0= 7T/l - (( ,0( ,L)/6 1A,,aJo/In(sin ,,)(53)When expanding the above equation Into a series follo¥vin_g: Taylor's theorem and neglecting the nonlinear termso.4of ( ,0 and (1,L. Eq. (53) simplifieso 35Ko-. = I + 2( )o [[1 - 3A,,o 4Kb-i,i216Number oi' testsFig. 13.L ='_. Referring to Eqs. (47) and (48), the ratio of' the Kovalues for ¥'ertical and horizontal beddin** planes can beexpressed aso-, I=[+ (( )a ( ,L)/6 1 Ji - A,,( ,a/In(sm ep,,)o.45o.3and ( ,0vith Eq. (52).lnfiueuce of interpartic:e friction on 1(: spherical particles3Jl _In(sin ep,,)23 coL (54)It should be noted that this simplification is acceptabieonly for ¥veakly to medium anisotropic materials with ( ,Land ( ,0 both having values less than approximately 0.3.Dependin*' on the magnitude of anisotropy associatedI{,particles into spherical G4 particles with approximatelythe same mass ratio (mGl:nlG4= 1:1 for G1-G4 and n7G3:mG4=0.82:1.0 or 1:1.22 for G3-G4). One obser¥'es thatK0-34 is approximately 200/0 Iarger than Ko-14. Figure 13generally sho¥vs the same trend as Fig. iO(c), since G3 andGl particles have the same surface texture and hence thedifference bet¥veen K0-34 and Kb-i4 can be attributed toanisotropy related to variation of particle shapes. Morespecifically, the anisotropy of G3-G4 mixture is merely dueto the directional variation of contact normal, becauseG3-G4 consists of spherical particles of the same diameterand hence the branch vector len*'th is identical in alldirections, ¥vhich indicates ( ,L=0. However, for Gl-G4with the direction and the length of branch vectors. Ko-+for vertical bedding planes may be either larger or srnallerthan Kc-h for horizontal bedding planes. Arhen ( ,L ratherthan ( )o dominates the de*'ree of anisotr'opy. Kb-* will besrnaller than Ko-h, otherlvise Kb-* is larger than or close toKb-h .In order to verify Eq. (54), a series of testsvere carriedout to explore the variation of Kb ¥¥'ith bedding planeorientation. As illustrated in Fig. 14, the ri**id cell wasrotated by an angle¥vhen placing glass beads into thecell. When the cell is rotated to the vertical position, thebedding plane makes an angle 3 ¥vith the horizontalplane. Angles of a=60' and 90''ere chosen in thisstudy. Durin*Kb compression tests, ¥¥'hen the bedding { ,CJUO AND STOLLE650G I particlesG I - G2 ml¥ture8 :: oVO.4o6 = 60L)-900o 456e:/ 0.4: o.35KO = O.416Ae6 = OLK()_12 = O.407o.35(b)o. 1)5 10 15ol¥ ' LI5 lOo2015l¥;umber of tests1 ber of testsG4 particiesG1 - G3 ml¥tuleo 55o.Ko =0_453ooo.4･7 o.4oOoc o o ooocOO l¥0-13 = 0.432co^ 5"*'0.45c!c{' jjco.4c 6 :: 60V_90 O0.3o.3lO i56 =: o()(d)c 6 = 6OV_9000.3oo.35o 6=0O(c)o4Fio. 15.8jl)16l¥jumbe ' of tests1¥1lumber of testsplane angle'cInfiuence of bedding plane orientation on Ko values= O', no deformation is allo¥1*ed ¥vithin theo 3bedding plane, ¥vhile the restraint to deformation isperpendicular to the bedding plane ¥vhen=90'.Figure 15 compares the measured Ko-values of CJI and G4particles as lvell as CJl-G2, GI-G3 mixtures at =0', 60'and 90'. Even though the data are scattered, one observesthat the A'o-values of CJ particles at =60' and 90' aresmaller than those at =0', ¥vhlch is consistent ¥vithEq. (54) since the particle shape and (1,L dominate theanisotropy of Gl particle ensembles. For G4 particle ando.3¥lo 25o 2the other t¥vo glass bead mixtures, the influence of bedd-oin*' plane orientation on the Ka-¥'alues is very small,indicating that the contributions of ( )L and ( )o to Ko¥'alues are cancelled ¥vith each other.In order to obtain the influence of fabric on the Ko¥'alues of engineering soils, one set of tests lvere carriedout usin_1' 4¥.6t mber of testsFig, 16. Infitlence of bedding plane orientation on the K rvalues of alimestonelimestone ag_ :regates, ¥vith the particle shapesbeing irre*'ular and ¥'arying randomly. As a result, thelength of branch vectors may not ha¥'e a preferentialdirection and the anisotropy is primarily induced byCLOSING REMARKSThis paper discusses the infiuence of fabric and particlecontact normal distribution. The results in Fig. 16 sho l'shape on Ko-values of cohesionless materials via aA'a-.>A'o-i,, ¥vhich is qualitatively in a'leement wrthmicromechanical analysis and a series of experimentalstudy. The main findings stemming from the study in-Eq. (54).clude:1. In addition to interparticle friction, the internal 彫κけV．へLUE OF GR、へNUL、へR M、へ丁狂R玉、へL65！ structure，IIlcludiagtheparticlesぬapeandtねe 揮∼’ノ∼9αノー1鯉．41−（伽θ‘』」5姻4茄∼9”rθθ’5，25，355−358． sP＆tial arrarlgement of partlcles（or par￡icleI l l Kゼuyt，N、｝）、aIld Rothellb疑rg．L （2004）＝｝くineΣna雛c alld sta｛ic connectMty），a仔ectthe輪一val旦esofcohesio王｝less ass穏mptio里1s for QmQgご感zadou1n micromechanics of graaular 111aterials，A／8cノ∼α．A／α∼（∼ノ’、，36， 1157一三173、 materials、Jaky’sequation，whichdescribesthe dependencyofκ。onfrictiollangle，isaPplicableto12）Mayne，P．∼V、alldKulhawy，F，｝｛．（王982）：κり一〇CRrelat沁11sllipsin soils wit負weak to medium fabric．13）Mi1chell、」、K，alldSoga，K，（2005）：F禰伽ηθ∼∼’αZ50ゾ50〃 2． The relation between1＜o−va茎ues and particle shape isnαullique，sillce出evariationofparticleshape may c紅ange particle connectivity and l｝ence brancb vecエors，w圭1ich has Qpposite e貸ects or1ノ＜o一∼’alues． soll，／、Gθofθ（ソz王∼∼91．∂h『、，ASCE，108（GT6），851−872． β8ノ∼‘ハブ0ノ甲，3rd ed、，∼V員ey．14） Ngシ 丁 丁、 （2001）： 罫abric evolutiQn of ellipsoidal arrays with di脱rentpar｛iclesllal）es，ノど11grg、．》θ（ゾ∼，、蓋27（玉0）．994−999、15）Okachi．Y，andTa【suoka，F、（1984）：Somefaclorsa9セc［ingκ。一 valuesofsalldmeasuredinεriaxialcell，So’Z5α11ゴFα’nゴαω’15， 3． τhe∫（o−values may be di鐸ereat wllen the deforma− 24（3），52−68， tionllormahothebeddingPlanelsrestrai簸ed16） Roes！er，S．K、（正979）：Aniso【ropic sklear Inodulus due乳o stress rather than thαt隻n tlle bedcl呈ng Plane、Elongated or Hattenedparticlestend芝oreducethe人（）一values allisαroPy，／、080’θ（・ノ1、五ノ∼9．OA『、，、へSCE，105（GT7），87i−880．17）RQthellburg，L and Ba芝hurst，R、J，（1989）：Micromecllanicai 妻leaこures of grar｝ular asse窺1blies with planar elliptical pardcles， when restraint to deformation is norm＆I to the G40’θcノ∼1∼’σ∼’θ，42（1），79−95 bedd至ng Plane． ｝｛owever， the joillt efiセcts of18）Ro、、e，P、∼V、（1954）＝、へs〔ress−s乞ra1n由eoryξlor cohesionless soil particle shape alld particle connectivity illay result wkh apPiica【ions to ear【h I）ressure at I’esτ and moving 、va難s， ineiξheranincreaseordecreaseofκo−values．In closing，it卜as been shown that the fabric of granular G60’θc／2’∼’σ∼’θ，4（2），70−88、19） Schmidt，B、（1966）：Discussion of“Ear【無…）ressure at res〔relaζed【o s1ress his￡ory”，Cαn、（？θo’θc1∼、ノ、，3（4），239−242、materi＆ls has signi負callt e疲ect of theκb−values，which20） Si111pson，B、（王992）：Reta1温hlg sτruαures＝disPlacenlen芝alld design，nlay vary over a wide raage depending on the sh＆pe and Gゴαθch1瞭昭，42（4），541づ76、spatia重arrangement of par亘cles as well as the direct重on＆longwhich deforr【1atio蓋1is restrained．The orientation ofthe principal stresses relative to the beddillg p玉ane also2i） Stokoe，猛、｝一｛、，Lee，S、H，aηdKIlox，D，P、（1985）：S妻1earmoduii measurementsul1（ler篭ruetriax1als！1’esses，■1グvαノ∼（一θ5’ノ∼’加、41Yo∫ 7セ5’〃19801なε’1∼4θ’『C∫c1’c Con4’∼10〃5 （ed、by Kilos！a）， 166−185， ．へSCE，Nロew York、plays a role ill establisぬlng aノぐ（）一value for a co紅esionless22）τerzaghi，Kmaterial．These蝕dings demollstratethecllallenges23）Tsukamoto，Y、，lshiわara，民、andNa撒ka，丁，（1998）：Undrailledf＆cing tlle engineer∼、・ith respec老to identifying meallillgful deformatiollallds｛re照thcharac韮eristicsotsoilfromreclaimedK。一valuesforadvancedstressallalysis．（1943）」加oノーθ1’cα1So’！・、／θc1∼α1r’c∫，Wiley，NewYork、 deposi芝s in Kobe，5ρθ（』’α／／55ど’θoゾSo〃∫‘∼1∼ゴ」Foμηグσ’10’∼5，47−55、ユ4） Zla【ovic，S、and Ishi翁ara，K．（i997）＝Norrnalized behaviour ofl very loose aQI1−plastic soils：E貸壱cts of fabric，So’Z∫α1κノ1＝oえ’1∼（ノα’10’∼5，ACKNOV㌧1］LEDG￡MENTS Funding provided by t｝1e Natural Science andEnglneering Researcll Council of Canada is grateful玉yackllowledged． 37（4），47−56、AやPENDIX Referr玉ng to］巳q．（26），芝良e Ilormεtl component of thecontact force at a given contact point can be expressed asREFERENCES1）Andrawes，K、Z．and三1−Sdlby，M．A、（i973）：Facζors a飴ctl夏1gκG， ／、Gθo’θc1∼、五’∼9’、∠）A，、，．へSCE，99（S氏・17），527−539、2）Bolミon，M、D，（玉991）：Geotec員nicalstressanalysisforbridgeand ab撮men【desigΩ，Coη’ノ｝αぐfoノ覗θpo’F∫270，CrQwthome＝Transl）Qrt and Road Research Labora｛ory，3）C員ar19，C、S．and Liao，C、L、（重990）：Cons［itutive rela巨oll for a particulatemediumwith由ee貸ヒctofpar芝iclero［ation，1n’、／．So1∫43五、一1in許σi諏！1klli（A1）with n being出e contaαnormaL For an ellsemble ofcylindrical p＆rticles，the branch vectors are il1出e samedirections as出e contaαnorma正s11．Referring to thenoξion of t盤e average length of brε貰1cぬvector1，the ex−pression ofll in Eq．（A1）mαy be rewrittenαs／1、4σ吉11inj，σ1‘一σ…k碍（A2） S’1−1’ご∼μ1一θ5，26（4），437−455．4）Chu，J、andGan，C、L、（2004）：Eぜec【ofvoldra［ioonκoofloose sand，G40’θch〃’σ肥，54（4），285−288w油σ謹being the“τransformed stress”，Equation（A2）圭ndicates that∫i、can be alternat呈vely expressed as5）Emer1au1〔，F、鍛d Cねang，（二、S．（1997）l In【er！）a至』［i￠le forces and displacements in granular ma乳erials， Co〃∼ρ財’、 （フεo∼θch、， 20（3），五、＝くノ1、＞［1＋α、、cos2（β一β，）1（A3） 223−244．6）Fioravan芝e， V、， Jamiolkowski， 汽・1，． Lo Presti， D、 C「、 F、， 1〉lanfredil11， G． and Pedroni， S． （1998）： Assessment of 【he coe伍cien芝of韮he ear［h pressure at rest flronl s｝1ear wa、・e velocity measureme搬s，060！8ch11ゆθ，48（5），657−666，7）Ha陰sson，∫．and Svensson，P、（200圭）：Stress disτributiQn i取 unbound a99regate of road s芝ructure：h1貝uellce of surface roほ9h− nessandparticleshar）e，β”〃．五n9．Gθ01、だ1∼y、，60，223−226、8）Harr，M．E、（1977）：A／8chα’∼1（’50∫Pα’』∫’α’1α’θA／θ4’α♪湘 P”o加δ11∫5”c、4ρρ1−oαぐh，McGraw−Hil1，New York．9）HObeda，P、（1988）：Krossn諭gens be｛ydeise pas｛enkvalitet，sarskilIwhereβ，，de負nes tぬe orientation of the maximum normα1compoRent of contact forces，く囲、＞is the average normalcontact force，α耳達（ie且nes the magnltude of（11rectionalvariation of local norm＆I contacξforces．It should benoted由at由e maxlmum value ofプ1，colncides with thenlajor principal traasferred stressσ挙It cεm be shown thatthe contact force componentsプ1＆nclフらcan be related tothe normal and tangential coataαforces via med avseende pa koraform：en正1tteraturstudie，State臓s Vag−odl Tra盤kins撤u【，VTlnotatV68，LinkΦing、10）Jaky，」，（1944）：Thecoe餓c1eRtofearthpressurea甘est，ノ．So（b、ゐ徽凶、COSθ＋五si難θ一孟、（COSθ＋tanψメ、slnθ） GUO AND STOLLE652The <fl>/<j > can then be determined according to Eq.f* cos(e - ,,)cos(A4) (34) as;'f'_ tan(e -,,)f Sln(eCOS'f ;!t) e;!'i,(A5)o, other¥viSe/ll sin(e-< f >< f._>,,)[1 -an Sin 2(e- eo)][1 - c;' sin 2(O- go)]clei - Sinan T con3 - (COS -' ,u + Sinil;!)'l:/2cos(e _,,)[1_an sm 2(e e,,)][1 a) sln 2(e e )]del-an + (Dn(cos q'!'For the case of isotropic or ¥veakly anisotropic materialsIt follo vs that for isotropic materialsin ¥vhich, (a +co*,)/3<< I the above equation may be( :Koisosimplified to<f > = aI - +sin co,,(cos 2 ,, + cosq,;' f.,,) (A6)sini,)3<, f I >)< f._> (A7)1 - sin"o,,¥vhich has the same form as Eq. (2) and is very close toEq. (51).
- ログイン
- タイトル
- Multi-scale Physicochemical Modeling of Soil-cementitious Material Interaction
- 著者
- Kenichiro Nakarai・Tetsuya Ishida・Koichi Maekawa
- 出版
- soils and Foundations
- ページ
- 653〜663
- 発行
- 2006/10/15
- 文書ID
- 20948
- 内容
- ,,,r;,SOILS AND FOUNDATIONSVol. 46,No),653-663, Oct2006Japanese Geotechnical SocielyMULTI-SCALE PHYSICOCHEMICAL MODELING OF SOIL-CEMENTITIOUSMATERIAL. INTERACTIONKENICH:IRO NAKARAli), TETSUYA IsHIDAii and KOICHI lvIAEKA¥vAiii)ABSTRACTA multi-phase physicochemical method for simulating the durability of cementitious composites is used to predictthe long-term degradation of underground concrete and cemented soil by calcium leaching. The objective is to developa unified approach that can be used for both cemented soils and concrete. This paper describes a computational modelbased on physicochemical thermodynamics that can calculate the voids of micron-to-millimeter scaie in soilfoundations as ¥*ell as the gel and capillary pores of nanometer-to-micron scale in cement paste. The proposed modelsho¥vs that the soil-str'ucture interaction of calcium-1eaching transport and underground ¥vater ad¥'ection are ¥'eryimportant ¥vhen assessing long-term durability of cementitious composites.Ke¥_' Ivords: cement, concrete, (durability), ground ¥vater, ieaching, (physico-chenrical pr'operty), soil impro¥'ement,(thermodynamics) (IGC: E1?_)any assessment of the long-term durability of under-INTRODUC.TIONSoil and cementitious composites are the primaryground concrete structures.Cemented soils are nehv kinds of engineering mater'ialsconstituents of ground and infrastructures. Assessing thelong-term serviceability of artificial cementitious compos-that can be used to improve the ground, make use ofsurplus soil, and enhance soil-structure performance.ites coupled with natural soil foundations requires aExamples of such materials are cemented soil and gravel(CSG) (Hirose et al., ,_OO1) and geosynthetic-reinforcedcement treated backfills (Watanabe et al., 7_002). Theunified physicochemical model, especially ¥vhen targetingintermediate materials such as cemented soils. In thispaper, state variables f'or pores in hardened cementhydrates (nanometer-to-micron in size) are integratedcemented soils generally have high ¥vater-to-cement ratiosand contain large voids, and so are thought to deteriorateinto thermodynamic state equilibrium equations thatmore quickly than ordinary concrete due to calciurnhave governing formulae for ¥'oids (micron-to-millimeterin size) in soil particles. The multi-phase multi-scaleconcrete models are extended to the geo-environment andleaching from cement hydrates.In Japan, cemented soils must be tested for hexavalentchromium leaching before they can be used, despite theirused to assess mid-and-long term changes and fluctuations in the material properties of coupled soils andlo¥v cement content per unit volume. Research to date hasstructures (Fig. 1).cemented soils, and there has been little investigation oftheir long-term durability. Particularly needed is a studyof the properties of cemented soils rhat have voids muchlarg)er than the pores in cement paste.The primary objective of this research is to apply thethermodynamic coupled analysis system (Maeka¥va et al.,mainly focused primarily on increasing the strength ofConcrete is bein..*a considered for use as a barriermaterial to solidify radioactive ¥vaste for geologicaldisposal. Because such waste contains materials ¥vith longhalf-lives, the bar 'ier must rernain stable for several tensof thousands of years, ¥vhich is far longer than the1999, '_003; Ishida and Maeka¥¥*a, 2000; Nakarai andlifetimes of convent.ionai infrastructures under normaluse. Ho ¥'ever, the per'formance of these materials overIshida, 2006) that was developed for concrete to foundations ¥vith larger voids in the soil particles. This wouldcreate a single numerical analysis rnethod for evaluatingthe material qualities and pore environments of cementedsoils, non-cemented soils, and concrete.such long periods is difficult to evaluate solely by experi-ments or accelerated tests. These laboratory-scalemethods must be firmly tied to theoretical approaches ifthey are to pro¥'ide reliable assessments of design andperformance. Soil foundations form part of the naturalbarrier, and their characteristics must be considered inl)ll,iii)Assistant Professor, Department of C'ivil Engineering, Gunma University, Japan (nakarai( ,ce.gunma-u.ac.jp).Associate Professor. Department of Civil Engineering, The University of 'Tokyo. Japan.Professor, ditto.The manuscript for his paper lvas received for revie v on February 6, 2006; arjproved on ,Ia}' 29, 2006.¥¥frilten discussions on this paper should be submitted before N"lay I , 2007 to the Japanese Geo echnical Society, 4-38-2, Sengoku, Bunkyo-ku,Tokyo I 12-001 1. Japan. Upon requesthe closing date may be extended one month.65.J" NAKARAI654ConcreteCemented soil Soi] foun dationSoil Porosityce ment hydrate= ; "? ' ;' ; ': ;' " 1' ;;i ? iET AL' ';'SS SVoid among soilE'*Fig. 1.Extended thermodynamic s,stem to soii materials:Size, shape, mix proportions, Equation c!initiel and boundary conditions O : Degree of treedom' 1i i';'7;'--<'-"'-' "f"=' ' 'Temperatufe pofe pressure, concentration of CL. CO-. O. and Ca:'+Tem pe ratu e"'' __::p ressurej Bi-madeil Porosity=hydrationlevel PoreH andConcentra ior!s ;; dis ributionof eachmoisture ; oforasitycam onent interlayerdistriutione & bound ic loridese t.> Gasnd dissoive ;{ 02 cor!centra on irig. 2.Gas and dissolvedi CO. eo centf tion iOverail sci]eme of DuCOM cheru0-physical coupled s)stemTHF.RMODYNAMIC MODELING OF CF,MF,r ITTF.DSOILTllel'moc!y/7an7ic A/7alytica! Systen7The process of cement hydration at an early age iscritical as it determines the long-term properties of acementitious mater'ial. lvlaeka¥va et ai. (1999) ha¥'edeveloped a computational method capable of simulatin_"._multi-scale chemo-physical events in concrete during thehardening stages (Fig. 2). The analytical method consistsof a hydration model incorporating the heat generationand ¥vater consumption properties of cement po¥vders, aover the ¥vide range bet¥veen nanometer and micronscales.Mu!ti-sca!e Pol-e Srructure Mode!A consistent method for analyz,ing natural geo-materials, cemented soils, and concrete must be able to take intoaccount the intrinsic characteristics of the soils. O_ ne keyissue is that the geometry of pores can ¥*ary greatly(Fig. 3). Sandy soils have a skeleton of partic]es, ¥vithlarge airspaces (¥'oids) dispersed throughout the material.In natural cemented soils, ¥vater' and cement cannot fillmicro-pore structure development model. Se¥'eral ¥*erifi-up the airspaces. The connecting pores define the soil'smechanical properties and permeability.In this study, the analytical method incorporates a ne vcations have pro¥'en that these models can simulatemicro-structural component representing the lar Oeearly-age development processes, such as heat generationand moisture profiles, for ar'bitrary mix proportions andairspaces in cemented and natural soils (Fig. 4). Thismeans the expansion of the multi-scale analytical systemenvironmental conditions. In addition, the analyticaiinto the large pores bet¥veen micron and millimetermethod can be used to assess the long-term durability ofrelnforced concrete, including the penetration of chloridescales. The inputs are the pore volume and the a¥'eragepore radius, ¥vhich are set according to the target mixproportion and the properties of the sand. It is assumedmoisture transport/equilibrium in micro pores, and aions and carbon dioxide, the corrosion of embeddedsteel, and calcium-ion leaching (Maekawa et al., ,_003;Ishida and ilvlaeka¥va, 2000; Nakarai and lshida, '_006).The target of this analytical method has been thecementitious material ha¥*ing the fine pores distributedthat the micro-spaces in the large airspaces of the soil areoccupied by ¥vater and do not provide space for cementhydr'ates to solidif.v. The existing model statisticallyexpresses the general pore structure of cemented soil 照SOIL＿CE氏1…三NTITIOUS！q。へTER1。A．L至NTER、へCTION655the pore struc芝ure becomes nner with cement hydr＆tionMix proportions（in volume）and coarser with calcium leacbiag．For thevoids betweensoil particles，a new characteristic value，β、d，is incorpo−1鴨ated to represent廿1e pea鼓pore rad重しls of the soil．丁捻e菖eometric shape of the voids is assumed to be collstantirrespective of hydratior1． In other words， β、d is aC（）nstaL“t．Un−ce囎nted Cemented Soil ＄oiIConcrete八4正’1∼i−5cα1θA40’甜ε’ノ9θT1−αn5po1’∼ノ》04θ1 The flux of liquid condensed waξer in cQn乞inuouspores，denoted byσ1，can be determined by l磁egrating diespec量ac月ux of l圭quid water over the ent圭re pore structureuslng a random pore size（iistribation model（Maekawaetal．，2003）．lndependent airspaceConnected voids 瓢ゴv）2▽P （3）amongsandpa吐icles、v豆1ere，φ is the毛otal poros圭ty（no【 inc正uding inter豆a｝・e1’fig．3・Mix群oport蚤on蹄dvoldi獄so銭m貸皇e劇spores）lm3／m31＆ndηis the viscosity Qf liquld wate1’［Pa−s］．In order to consider tl｝e圭nfiuence of the pore sizeLarge alrspace（micrO∼mmscale）cOo』2Cement paste matrixコ』0、1（nano∼microscale） η一11・exp（舞） （4）狐の℃Φomhe moisture transport，the viscosity oギ、vater in capll−laryαnd gel pores of且ner sizes is calculated as fo璽lows．01Newt一．owhere， ’70 is 芝he viscosity of 重iquid water under i（iealconditio董1s［Pa−sl and O。is the add玉tional G玉bbs energyrequired for the flux of l圭quid water under non−idea正瓜00condiξious［kcal／moll．Forthelarge−radius voids between01Pso1I p＆rtic正es，t紅e additiQn＆l G重bbs energy， G。，can beE−」1 1．OE−9 10E−7 10∈一5 ∼OE−3assumed to bezero，meaningthat the intrinsic vlscosityo￡ Pore raωus（m〉bu至k∼vater is used．Pore dlst将butionFl9・4・MuM−sc田e pore s【rudure modelLEACHING MODEL（Shimomura et aL，1997）．The distribution ofnanometer− Although long−term deterloration of re圭nforced con−crete is caused mai撮y by steel corrosion，mec執anlcaIto−millimeter scale pores is represented by the followingdamage to the concrete ltself ls mostly caused by cbemicalpore density function、 φ（1。）漏φ、dV、・d（1噂）＋φcpレ｛cp（1一）＋φ9［Vgl（1“）＋φlr （1）events tha毛distort the cement hydrate solids．Th圭s paperdescribes calclum leachlng from cement hydrates（Flg．5），、vhich is a common problem wit熱concrete ancl cementedw封ere，φ、d，φ。p，φgl，andφ1，aretheporositiesoft1｝evoidssoils，The leach玉rlg of cεし1cium fro111concrete is a problembetween the soll particles，c＆pillary pores in出e cementpaste，gel pores，an（i interlayer pores，respectively，［m3／for the extremely Iollg−term serviceability of a radioactivem31，μ、、d（1・），V。p（1），αnd殊（1・）are functlons th甑specify thesize distribu芝ion of the voids，capi1正ary pores，and gelpores，respectivdy，as given by芝he follo、v重ng e（luatiol1，which is based on the assump重ion that the Raleigぬ一Ritzwaste depos重亙ory，for wklch use the由ermody服micinteractlon of the geo−environment段nd the underground￠oncrete is a crucial factor．Cemented soil is sometimes inconξilluous contact with groundwater．In such cases，亡hee岱eαof leaching on long−term durabllity needs to bedistr圭bution is ＆PPlic＆ble to each pore i，including 重hestudied．Slnce cemented soils generally have high water一neYv正y def崖ned vo量ds between the so圭1partic玉es、重o−cement ratios and larger vo圭ds than concrete，they are Vi（1｝）躍1−exp（一βi1’）thoughttodeterioratemorerapidlythanconcrete。 4レうi（1’）＝βiノ璽exp（一Biノ呼）41nノ’ （2）ルfαε3Coπ5「εrvα∼io7z oゾ「卜Cヤα！cど乙μηwぬere，βi is a porosity distribution parεしme宅er μ／m】， Momentum，energy，and痴e mass How of mαterlalswhich represents the peak of porosity distr玉bution on amust satisfy the laws of conservation．The following masslogarithmicscale．Forcapillaryandgelpores，theparameters can be c段lculated from the material propertiesconserva芝ion Eq．（5）is applied i勲terms of the totalcalc重um ions 量n the pore solution a勲d the soli（1−phaseof theむydra｛es．In the cεしlculations，the varying micro−calcium in the system，in reference to the equation bystructures are童aken into accoun毛in suc鉦a manner thatG6rardet段L（2002）． 『657SOIしCEM娠NTITIOUS MATER三AL正NτER、へCTION 84、0 ユα 3．5￡30器α 25 Porosity Sma巽 PorosltyLarge Tortuosity Large Tortuosity Small＞8烈 20三 歪5δト 40Fig・6・ IorIuosi重y of pores00P亀1・s轟，、、、，鴨・／m弓405（lshida and Maekawa，2000；Maekawa e宜aL，2003），thenux of ca圭clum lons transported in a porous media takes（a）the following form（Fig．5）．婦（竃1・むピ・沁・）・▽C㎞＋φ・S・u・C㎞（7）Fig。7（a）。駁odelingof重or重uos塁Iyfo罫ceme蝋p段sIe4、0where， Ωa、、。 iS average tOrtUOS重ty， δ撫，。 iS averagecons毛riαivity，Z）i。，is重he di仔usion coef丑cient of a calciumion［m2／sl，▽T＝［∂／∂κ∂／∂y∂／∂婿is the Nabla operator，and uT圃ガ正バ凋is the velocity vector of a cα1cium lou重ransported by a solutiou fまow lm／s】．The capi11＆ry and − 〉ぺ切で⊂㎝gel pores in the cement pasεe and重he voids between theのsoil particles are trea毛ed as量on traasport pathways，段nd＞t勤e authors assume that no ions are trausported in thelnterlayer pores ln the cement paste （lshlda andMaekawa，2000；Maekaw＆et al．，2003）．Tbus，theporosity，φ，can be expressed bythe fo玉10wing equation．φ＝φcp＋φg汁φ、d（8）3．53．02．52、0のoコ1、5ト1．0to0001 0、2 0．3 0、405P・r・sity，Φvdlm3／m31 The丘rst term of Eq．（7）represents the compo【1ent of（b）di建usion driven by the conceutration gradient，whi里e t紅eseco【1d term is 童he component representing ＆dvect量onFig．7（b）。Modeling ofωrωosity for sanddriven by the flow of condensed liquid water ia the pore．The veloclty of t紅e calcium ions rela業ed to advection isassumed to reHect the bulk motion of the玉iquid water andto−cementratiosorleachedcementpaste．Forsoi玉is determined from the transport model for the liquidphase．The dlffusioa coe銀cient of the calcium lons isthe degree of compaction（Van Brakel et aL，1974），ThisexpIlessed by Einstein’s theorem belowl λ…。nmateri＆1s，由e value depends Iargely on the soil type aωwi正1be t紅e case for cemented soil，as weli．Here，it isassumed that重he tortuosity can be identi丘ed simply in D…。n；R・T・ （9）terms of the porosity of cement paste or soil particles．where，R ls the idea正gas consta煎 ［J／mol−K】，T isexpressed by the effective porosity，φpa，【，，as g量vell by z嘉、・戸absolute te組perature IK】，λi。，量s tぬe molar conductivi重y ofan ion ls鷺i2／mol】，zi。，圭s the ion va玉euce，and F is theThe重ortuosi重y of the pores in the cement paste，Ωpa，、。，isEq．（10）（Fig．7（a））シwhich is del’ived flrom the experimen−tal di狂usion coefaclent of c強10ride ions（Maekawa et al．，F＆radayconstantlc／moII．2003）．The重ortuosity of the voi（1s in tむe soil part圭cles， The transpo践properties of ions ln porous materia正s，Ω、、d，ls also assumed to be formulated in the same mamersucb as concrete and ceme貰1te（I and natural soi里s，depe薫1das the poros嚢y，φ、・d，as given by Eq．（11）（Fig，7（b）），withon their pore structures．III this s重udy，the pore struc芝urereferencetoVanBrakeletal．（1974），is computationally char＆cξerlzed by porosity，degree ofsaturation，tortuosity，and constrictivlty（A重kinson et aL， Ωpa，【ご際一L5tanh｛8。0（φp＆，【。一〇．25）｝＋251984）．Tortuosity is （ie且ned in terlns of porosity，εしnd φcp＋φglconstrictivity by the pQre radius玉n the proposed mu重ti−scale analytical system． φpa，、e； （王0） レpas【巳 Ω、d憲一1．5tanh｛4．O（φ、，d−0．15）｝＋2．5 （H） In this study，the tor重uosity factor，9，expresses theincreased length of the actua正 ion tl剛ansport pathwayaccordiag to the tortuosity of the pores （Fig。6）、It isξwhere，φp、、【。is伽e ef罫ective porosity tha亡is the sum of thegel and capillary pores acting as ion transport pathwayst紅ought to be higher for cement paste w圭th nne pores andper unlt volume of cement pas｛e lm3／m3】，and vp、、【，is thelow water−to−cement ratios，and lower for larger w謙er一unit volume of cement paste lm3／m31．For materials such NAKARAI658ET AL.li;S S# {1*s'+_{>1J ol;*== ;, 'l=" == = '5=: I _osc:o ;ol lc:oo =<'1 OoIFig. 8. Constrictivitl.' of pores-10 -9 8-675-4 - 3 2(r 5 k[m])iogoFig. 10^Mode!in"of constrictivit¥.05Pe k radius¥t:: 04al¥{: 03;)/ 1; J>o j-5 O 2.oFlo 9. E,ffcct of electrostatic FepulsionD- alprorninent¥-10-9as cemented soils that contain both pores in harcienedcement paste and ¥*oids bet¥veen soil particles, thelt =/r}ter8ctions areOOmacroscopic a¥'erage tortuosity is determined b¥_' simply/ llFine pore in which/-8/-lCh nge of porosity distributionwith ch nge of pe k radivs-65iog(r[rr]j)Fig, 11.Porosit,. distribution and peak radiusassigning ¥veights in proportion to the por'osities inpoi'e connectivity and the poreEq. (12).oQ*.* = -- " ".*t.' - c**i(c*..Lc l)Q,**i (i_,)c*p + cgj + c.dThe constrictivity is then formulated in order toexpress the effect of the pore connectivity and the electric6i=0.39)tanh 4(lo*(!P'k) 6 ,)040) (13)6i = O for r **k < ac*changes on the ¥valls of the micro-pores during masstransport (Fig. 8). Porosity and pore size distribution¥vere considered by Van Brakel and Heerijes (1974). Poredimensions are thoug:ht to be the main determinant ofconstrictivity (Atkinson et a]., 1984). Van Brakel et al.,'ail effect is expressed asconstrictivity. The constrictivity of the pores in a cementpaste and the voids of the soil particles are defined as afunction of the peak pore radius by Eq. (13) (Fig. 10).* -2'¥vhere, rP*"k is the peak pore radius [m] and ac** is an iondiameter parameter for calcium ions=0.6 x lO9 m. For(1974) and Peterson (1958) reported a significant range ofparameter ,'P"k, the peak radius of a capillary pore isg:iven in the case of hardened cement paste, ¥vhereas forconstrictivity, with a ¥'alue of about O.8 for ordinarythe ¥'oids bet¥veen soil particles, the peak radius of' theporous materials, ¥vhile Atkinson et al. (1984) r'eported a¥'alue of about O.OI for fine pores in cement paste. Poresvoids is used. These ¥*alues are determined from thein cement paste are distributed ¥videly over thenanometer-to-micron range, and pores of differentdimensions are mutuall _' connected in a random manner,The average rate of ion transport is thought to be lo¥ver infine pores due to the interactions bet¥veen the ions and thepore walls as ¥vell as to the smaller size. E.lectr'icalinteractions bet veen the ions and the pore ¥ +alls ha¥'einverse of the pore distribution parameters, B,p and B d,respectively. The peak pore radius, as a parameter in theRaleigh-Ritz distribution, does not directly express thefine pores in ¥vhlch interactions bet¥veen the ions and thepore ¥¥'alls are prominent, but it does determine the shapeof the pore size distribution (Fig. 11). In this study,constrictivity is modeled in this simplified manner as afirst approximation. In the future, a detailed study ofsmaller the por'e size, the greater the infiuence (Fig. 9). Instatistical processing for pore connectivity ¥vill benecessary. In addition, the ion concentration is ansoil voids lvhere the pore siz,e is much larger' than the ioninfluential parameter that also needs to be taken intoradius, the electricai interaction is relati¥'ely small.account (Sato et al., 1995). For materials such asConsequently, the absolute size of mutually connectedpores seems to be the dominant factor behind ion trans-cemented soil that contain both cement paste pores andport.In this stud.¥', the reduced mass transport caused by theis determined by simply assigning ¥veights in proportionbeen cited as a mechanism for' this (Sato et al., 1995); thesoil particle voids, the macroscopic a¥'erage constricti¥*ityto the porosities. rSOIL-CE IENTITIOUS ¥. , ATERIAL INTERACTIO ¥'Table l.659Mix. proportions for cemenl paste and cemented soilUni mass (kg/rn ) VoidsPorosit¥'¥Vater Cement Sand ("' at 7 days (', )l¥: o ¥¥* I C" ( ･ )612O 22O79 1706P50 50s50 5012231573,-26Cemented sandDeionized water Specl men'l2Cement pasteCondition of surface of specimen before immersion tcstsFig. 13.Deien zed w t8r, 4-SPeeime1 om O Imv; 5 x Ocrn *400:5Experiment and anal)sis for immersion test200coo3=, . = (c'P*c,.[)6 >p***=c*p + c l + c*d¥vhere,c.d8,,[ l cerTlented SandE3aoEAnalysisEx perimentFig, 121: 100( 1 4)(1):oCQQ)Jp,**t* is the constricti¥'ity of the pores in the cementOcement paste/ ;i/'_1' Ifl" ';/ i llltr '+' i _._'_ -,L..__--1o lo 20 30405a60Time (day)paste and 6.d is the constr'ictivity of the voids bet¥veen thesoil particles.Detel'ioration of Micl'olpol es by LeachingIt has been reported that the leaching of calcium leadsto a coarse pore structure in cement paste, which mayaccelerate calcium leaching. This study takes into accountthe incremental changes in the amount and size of thepores caused by the dissolution of calciurn hydroxide andC -S-H gel. The changes in the pore structure andFig. 14. Leached calcium from cement paste and cemented sand in theexperiments3EEOo::s600)400e'moisture re-distribution due to calcium leaching areJ::calculated by using the increased pore size and volurne inCQ(vthe existing thermodynamic coupled analysis systemQ)(Nakarai and Ishida, '_006).800// /i200>oSLeaching oj' Ca!ciuln from Cenlented SandIn order to cornpar'e calcium leaching from cementpaste with that. from cemented sand, cylindrical testcemented sand l,cem i'en:ANALYSIS OF CALCIUM LEACHING_l r/ i:sOFig. 15.1/____'/'"'-Ai_l't_ ast,,_,{ _ =* */*l.;o io 20 30 405060Time (day)Cumulative leached calcium in the experimentsspecimens of cement paste and cemented sand ¥vereprepared and subjected to an immersion test. The waterto-cement ratio ¥vas 500/0; the mix proportions are shownin Table I . The amount of calciurn ions leaching into thesolution lvas measured. The cylindrical specimens ¥verethat leached. The amount of calciurn that leached becamezero every 1 5 days ¥vhen the ¥vater was replaced. The totalamount of calcium that leached from the cemented sandwas larger than the amount that leached from the cement50 mm in diarneter and 100 mm in height. After sealedcuring for 7 days, the top and sides of the specimenpaste, in spite of the fact that, at initial immersion, thesurfaces (but not the bottom) ¥vere coated ¥vith rubber,and then immersed in deionized ¥vater at a liquid-t.o-solidsmaller volume of pores than did the cement pasteratio of I to 10 by volume (Fig. 12). The lvater ¥vas stirredat intervals of a few days and replaced every 15 days. Theconditions of the exposed surfaces before immersion aredescribed in Fig. 13. Large voids ¥ver'e visible in thecemented sand.Figure 14 sho¥vs the amount of calcium that leached, asdetermined frorn the chan*'e in the concentration in thewater. Figure 15 sholvs the cumulative amount of calciumcemented sand had smallel' quantities of cement and a(Table 1). The volume of pores is the sum of the volumeof voids bet¥veen the soil par'ticles (determined durin*'mixing) and t.he volume of gel and capillary pores in thecement paste at the age of seven days (as calculated in theanalysis) .A simple one-dimensionai analysis ¥vas carried out(Fig. 12). Input data such as mix proportions andenvironmental conditions ¥vere based on the experiments.While the porosity distributions in the cement paste over NAKARAI ET AL660/a)FF:s/Without advection1400 - - With advection /; / /cemented san/ r ::: I O 4m/cement300pe kz5a;o2001::e)coJ(Ipaste ¥' /--_ '##1 oo//"..¥''¥･ *H> Specimen(D"1u) 1010lu)e)'oQ)'ffl/// /j cemented sand1005l(Ur = I a rme)Water1015Q)*o 1000oCLO I O 20 30 40 50 60-O 05 O OO O 05-a loTime (day)Fig. 16. Leaehed calcium from cement paste and cemented sand in theo loDistance from surface(m)Fig. l?.Distribution of pore water pressure in the sensitivity anal) sisanal) sistime ¥vere calculated, the porosity of the ¥'oids among thesoil particles ¥vas a fixed value determined from the inputdata. In order to reproduce the conditions of the immersion test, an analysis of calcium ieaching, taking intoaccount the concentration gr'adient in the ¥vater aroundthe specimen and the decrease in the concentrationa)>oO>:O: =1 E-7! Cemented sand (r =10 m)'P==k(1)'-radient as ions leached into the ¥vater, vas carried out byQ,connecting the analytical elements representing the:Sdeioniz,ed water. To take into account the effects of threedimensional diffusion in ¥vater as vell as stirrin_"*, thediffusion coefficient of the calcium ions in the deionized¥vater ¥vas set to a value ten times larger than the value inOfree ¥vater. The analysis did not take into account thereplacement of the ¥vater.1 E-5 1 'S(1)1 E-1Cemented1 , sandp==*(ri ,:::::,=TIE-i3 Cement paste,=10 'm)- *i1 E-1 5 io.ooO 02 O 04 O.06 O.08o 10Distance from suriace(m)Fig, 18. ¥_ ioisture fiolv velocit) in sensitivity anall. sisFigure 16 sho¥vs the results of the ana]ysis. Thecalculated results for still ¥vater' ¥vithout advection ¥verecompared first. When the cemented sand ¥vas assumed tohave a fine pore structure comparable to that of thecement paste (peak pore radius: 10-' m), the amount ofcalcium that leached from the cemented sand ¥vas muchsmaller than the amount that leached from cement paste.This is because the ¥'olume of pores and the cementcontent per unit volume are both smaller. On the otherhand, in the analysis that considered the scale of theconnected large voids in the cemented sand (peak poreradius: 104 m), the amount of calcium that leached lvashigher due to the greater diffusion coefficient. Theseanalytical results demonstrate the absolute necessity oftaking into account the characteristics of the pore structure.Comparing the results of the analysis ¥vith those of theexperiment, ho¥ve¥'er, reveals that the amount of leachedcalcium ¥1*as underestimated. The reasons are thought tobe the effects of leached calcium from the sand grains andthe effect of advection due to stirring. In a preliminaryexperiment in vhich the same quantity of sand alone ¥vasimmersed for 15 days, about 80 mg calcium ¥vas leached.This means that sand in_"..redients can leach, but only to alimited extent. In order to maintain a constant concentration in the immersion solution, the solution ¥vas stirred.Because the pore structure of the cemented sand used inthis study ¥vas very coarse, this stirring may ha¥'e causedadvection ¥vithin the specimen, ¥vhich may have accelerated the leachin of ions.To look into this, a sensitivity analysis to determine theeffect of stirring ¥¥'as carried out by applying a smallpressure gradient to the inside of the test specimen in theout¥vard direction, as sho¥vn in Fig. 17. A ¥vater headdifference of O. I mm per 100 mm of depth ¥vas applied. Inthe cement paste and the cemented sand, ¥vhich ¥vasassumed to have fine pores, the ¥vater permeability ¥vasfound to be lolv and there vas practically no transport of¥vater (Fig. 18), so there lvould be no effect on the amountof calcium that leached (Fi**. 16). More specifically, underthe small pressure _9:radient used to simulate stirring, therevas practically no advection effect, and the transport ofions in the specimen lvas governed by diffusion alone. Itshould be noted that the cemented sand had high ¥vaterpermeability and sho¥ved significant transport of vater(Fig. 1 8), ¥vhich resulted in a sharp and high-level increasein the amount of calcium that leached (Fig. 16). Thisconfrms the need to carefully examine the experimentalconditions for their effects on advection, e¥'en though theeffects mav_ be minute. It is also vital to examine thedurability of cemented soil under ground¥vater fio¥v. Todate, no firm conclusions have been dra¥vn re_"*arding anyof these effects, aithough studies ¥vill continue. 「66圭SOIL−C薮！㌧「1薮NTITIOUS！〉1．へ丁嚴R王．へL五NTER、ACTION12A Concrete wltho磁soil Concrete 瓢a鼎，1、職，…騒翻．9 10驚B Concrete with soiIL ∈ ヨ醸 2 翻 ＼ 置 圃 O、8 Soil Concrete圏 麗 囲 rWith soil ’＼ほ ，” VVithout soiIIδ 06鳶50m＄urvey TargetoblectQ o40 0 2の0，5m黛Analysiselemen重s00Figほ9．Analys量s重arge傾ndeiements Concrete footing（WIC讐50％） 膣 Measurement 一……一一Analysis0，00 0，01 0、02 0．03 0、04 0．05 006Dintance至rom surface（m〉夏able2．Mixpropor亘ionsforconcre乳eFig，20， Disεribution of residu謡solid鱗帥ase calci臓篁n r＆〔io w／c Unltmass（kg／m3）No、 （％） WaIer Cement Sand GravdD55 55170309799 1104コ》 300∈∈ 25五θαchiηg oゾCα1ci‘’1η∫ン’01ηCθ〃1θ1π’∼io〃5Co1ηρ05i∫ε5in！o∼hθS乙〃γoμ1∼61i1∼g G11’oμ1∼‘13で 20σ躍 15 The effects of the surroundh199round on the Ieachingof calcium from concrete were analyzed by applying thesite structural survey proposed by Yokozek圭et＆L（2002）、墓to aηo正d underground concrete footing for a four−storiecl、⊇buildillg constructed ln1929．Concrete samples weretakena【4mbelowthegroundsurface＆ndatabout70cm⊆： 歪0、9E… 5Q一一Analysis without soil 1−Analysiswiths。“ rr ／碧 ／ξ i ／ 頚 ／ 頚 ／一H→ 〆〆〆 Soil l Concrete ＿＿＿一一’〆 蓼￡ 0ΦConcrete footing（WIC鷲50％）一5 一4 −3 −2 −1 0Dlntanceデroms麟ace（m）below the groundwater leve1（Fig．19）．The mix propoトtion of the concrete w＆s estimated from the compressiveFig．2LDis｛ribuほon of騒quid−phase c田cium ionstrengt｝1．Table2shows the results of an exanlination ofthe samples．The amount of calcium and silicon weremeasured using an energy dispersive X−ray an段lyzer Figure20shows the ratio of measure（玉and an＆至ytica至（EDX）．The remalning caicium ratio for the solid phasedlstributions of the remaining solid一凶ase calcium for thewas determined using two types of analyses：one analyslsunderground structul『e． Tbe ratio 玉s calculate（i bydlviding the amount of residual solid calcium by thefocused ou the concrete itself，while the o重her examinedthe interaction of the co烈crete with the surrounding so且found＆tion． In由eanalysisof重heconαe芝ealolle，thecoacentrationaverage amoullt of solid calcium in the non−leached p段rt。Figure21shows the dis書ributioll of Iiquid−phase calclum玉on concentrations in the ground and structure（analyzedof c＆1cium in the ground was taken as the boundaryva正ues）。The coup至ed analysis of the interaction of thecondition at the concrete’s free surfaces．The spec重且edconcrete with the surrounding so圭l foundation procluced avalue of1．3mmol／l was measured imhe groundwater in亡he v玉cinity of bui至ding．In童he＆nalys圭s of the interactiondegree of deterioratloa that was closer to the measuredresults tれau the one produced by the＆na正ysis of3ust雛1eof the concrete and the surrounding ground， the soiIconcrete（Fig．19）．As can be seen ln出e coupled an＆1ysis，elements were combined with芝he concrete elements．Inthe concentration of calcium in the ground increasedbecause of mass trαnsport from inside the structurecoasiderationoft虹edepthoflo録di伽slon，thethicknessofthesoileleme麗s∼∼7assetto5．Om．Slnce由erewereno（Fig．21）．The surroanding grouad mαkes the concent影a−datα on the details of the ground proper重ies， it wastion gradient small and reduces the rate of calciumassumed to be ordinary sandy gl齢ound without cemellt．Ieachin9． The m＆ss 宅ransport interaction is vlta至 forBaseci on the assumption，the porosity and peak poreratiollally assessing Iorlg−term calcium leaching and theradiuswerede肋edas35％andLO×10㎜4m，respec−subsequent deterloratlon of cementitious composites in atively．The effective di狂usion coe伍cient of a ca圭cium ion，foun（1ation．includ宝煎g tortuosity （Eq． （11）） and constric重ivity（Eq．（13）），as determlned from these set vαlues，w段s∠、θθぐh’ng wi1h G1’oμηグ／垂450’わillg C‘716iμ1η／011scalculated to be5．9×10覗m2／s in重he soil elements。 In orcler to analyze the ef董をct that ｛he sur1loundingMoisture traasport of the groundwater was Iloξa factorground had on leach宝ng Nvhen the ground was重reated as asince completely saturated states∼、・ere assumed lnanalysis．boundary co隻1dit玉on，a coupled ana至ys宝s of the surround−lng ground and the water environme虚was carried out i=NAKARAI662ET AL,labie 3. Mix proportions for cemented soilNo. ¥V/C _Unit mass (kg/m3) _ Voids; ¥¥rater Cement SandB I OO50l OO150 1000 40 O2 Ox 10'With soil (NO adsorption)EOEEE1,* +-5xi 06/ '.+t ,/ '¥,t/ With soil1 OxlOe:SCemented soil5 Oxl05O:{Cemented soil (W/C=year exposure)Opure water(Adsor ption)With WaterCQA With water...1/roo(/)o olo ooao'l,)o 03o 02Distance from exposure surface (m)BWith soil (without adsorption)Cemented soilJC. With soil (with adsorption)Cemented soilMO.Im-:sCQoooo/e)W'th so'l .(AdSorption)Withsoil¥¥(NoadSorption). =Wlth¥Water" 'i* *,,105O"20E:sC52 Oxl OScemented soil (Wlc::1 ye8r exposu ei5,Flg 22. Analysis elements30oEE 25102.0mDistribution of residllal solid-phase calciumFig. 24/-o 4-O 6-o 2OODistance from exposure surface (m)5 1 5xl06EEFig. 25.Distribution of liquid-phase calcium ionE I OxlO*:;taken into account, the cemented soil deteriorated to aC5coo 50xlO'1cio oOO5 1 O 1 5 20 25coCalcium ion in liquid (mmol/1)Frg 23. So!id-liquid equilibrium relations(Fig. '-)-). The subject of the analysis ¥vas cemented soil¥vith a water-to-cement ratio of 1000/0, c d of 400/0, and apeak pore radius of 106m. The mix proportions arelesser degree than in the case ¥vhere the specimen ¥vas incontact ¥vith ¥vater. This is because the ¥'olume of poresacting as ion path¥vays was reduced. When adsorptionwas taken into account, deterioration developed rapidly.This is because the pores in the ground maintained a lo¥vconcentration of free calcium ions due to the adsorptionof ions and the constantly high concentration gradient inthe cemented soil. These results agree ¥vith past results:cemented soil exposed to clay ground deteriorates fasterthan cemented soil immersed in fresh ¥vater (Ikegamiet al., 2004).listed in Table 3. After sealed-curin*' for seven days, thespecimens ¥ver'e exposed to deionized ¥vater and the'_round environment (with and without adsorption)(Fig. 22). The ground ¥vas saturated, non-cemented soil¥vith a ¥vater content of 600/0, a cvd of 600/0, and a peakCONCLUSIONSThe multi-scale computational system for concrete isextended to cemented soils and used to predict long-termpore radius of 106m. Adsorption was taken intofunctionality under moisture-rich conditions. Theaccount by adoptin_9: a simple linear equilibrium adsorp-micron-to-millimeter scale void structures of soils and thetion cur¥'e, as sho¥vn in Fig. 23. The amount of ionsadsorbed ¥vas determined according to examples takenfrom past research (Usui et al., 2005). Figure 23 alsonanometer-to-micron scale micro-pore structur'es ofcement hydrates ha¥'e been integrated into a singlesho¥vs the solid-liquid equilibriurn curve for the soundportion of the cemented soil at the age of one year.Figure 24 shows the distribution of solid-phase calciumremaining in the cemented soil one year after exposure,¥vhile Fi9:. '_5 sho¥vs the distribution of liquid-phasecalcium ion concentrations. When adsorption ¥vas notmulti-scale theorem. Focusing on the geometricalcharacteristics of pore structures, Iarge-scale voids of soilparticles, including cemented soils, were stochasticall"vmodeled and a thermodynamic theory for state equilibri-um ¥vas de¥'eloped. As for calcium leaching from bothcement paste in concrete and cemented soil, the absolutescale of the pores ¥vas extensively studied and experimen-j 663SOIL−CεへIENTIT五〇USき1．へTER1．へL玉NTER．へCT至ONtal正y ver至丘ed，as wαs t麺e ro王e of pores as ion pat瓦ways．The proposed computational scheme and sensitlvltyall＆lysesmakeitclearthaUhecouplillgofulldergroundconcrete、vith the surrounding foulldation is cruciεtl forrat玉on＆lly assessing the service life of structures ＆ndground e臓v玉ronments． T｝le advection of undergroundwaterwasαlsoquantiHedandrecognizedasαc面calfactor in determlning the extremely long−term service＆bil−ityOfSOil−StrUCtUreSyStemS． degradation process of cenlenししrea〔ed sQil．P”o（『■ノρ’z、CY、1〃∠三ノ∼9’召， Soc．，〔59−3）．1073避G74（lnJa1）anese）6）互shid＆，T、alld Maekawa．K，（2000）：All imegra【ed compu乞a［iol1εd systemfQrmass／ellergygelleraτlon，職1spor【，andmごchanicsQt 貸laterials and s芝rucしures，Co’∼cπ∼’θ五1ひ1一α1二、・q〆一／5C五、Jaぎ）an Socie芝y of C1vil EΩghleers，（36），129−144，71N至aekawa，K．，Chaube，R Palld Kisねi，丁・G999）＝ご、40‘ノθ〃i／1goゾ Co〃c’署∼8Pθノ∫o〃1∼α1∼cθ，E＆FN SPON．LoadQn，1999．8） 汽1aekawa，冠．，Ishida，Tξ逸nd Kfshi，T、（2003）：燕lui吃f−scaie nlode莚ng of co三1crete r）erformance−lntegra【ed maεe互’ial and s乞ructural mechal1玉cs，／．4‘1y．Co1κ7’θ’θτθごh’∼o！．．1（2），91−126，9） Nakarai， K．， Ish1da， T，a職d N玉aekawa， K，（2006）： へlocleling ofACKNOWLEDGMENTS The authors express the圭r sincere apPreciat玉on to I∼厘r．S．Nakaae and Mr．T．Usui for the experiments allddiscussions． This study was financial豆y supPorted byGra飢一in−Aid for Scienti且c Research（S）No．玉5106008，ancl YouPg Scieatists（B）No．16760358． ca1〔：1um leachlng fronl cen〕ent ｝1ydra｛es coupled wi【量1 登董icro−Po「e fQmla【ion，ノ、ぜ4‘1v、C「o’∼（一1烈θτθ（｝ノ∼1∼0／、，4（3）10）Pe芝erse【1，E，E．（1958）ID澄lusioni駿al）oreofvaryingcrossseαion， ．4、∫ C11、五、／、．4（3），343−345、11）SatQ，H、，Yui，M andYoshikawa、棄｛、（1995）l D滑uslonbehavior for Se and Zr in sodium−beΩ｛on1【e．P’『o（一，A／α’θヂ、Rθ5、Soご，Sダ1∼∼ρ．， 353，269−276．12）Shimomura，Tand Maekawa，K、（1997）：Anaiysis of由e drying sllrhlkage behavior Qfl coΩcre｛e us1ng nlicro nlechanical nlodel basedon〔hemicropores【ruct乳圭reof−collcre［e，瓶’9礁1∼θqブREFERENCES1）A【kinson，A．andNickersol1，A．K，（1984）：τiledi伽sionoflons τhroughwa［er−sa膿aζedceme蹴，ノ．A／α’81’、Sご’、，19，3068−3078、2）Bui1，M、，Rever芝ega！，E、and Oliver，，1、（1992）：A model ofエhe Coノ∼c・1祈fθRθ∫θαノ・ch、49，（181），303−322、13） Usui，T，，Isま1ida，丁，，Nakarai，K、andSak1窺1ura，T、（2005）：Calci貝窪｝ 1eaching ar｝田ysis co糠pied with bentoni￡e and surrouding soil，P’』o己 ノρ’∼、Co1∼（7−θre1’15’”￡f’θ．（27）（lnjapanese）．14）VaD Brakel，J、aΩd Heer芝jes，P、NI （1974）：、へnalysis ofd1αus玉oIl in auack of pure wa［er or under sa韮ura【ed l三me solutions on cement， macroporous media i員 【ernls of a porosi｛y． a 芝ortuosity and a 、へSTl〉I SτP 1123，227−241、 cons【rlc【1vi｛y faCtor，／ノπ．／、旋α’αノ∼4Mα∬T’『α1r5卿．蓋7，3） G6rard， B，， Le Be｝lego，C． and Bernard， 0、 （2002）＝Sim｛）h負ed modelingofcalciumleacぬingofconcretein、’ariousenviro臓me瓶s， A／θ！θ∼’αZ5α’∼ゴ3〃・召c’μ∼θ5，35，632−640． 豆093−1103、15）∼Va乞anabe，K，andτateya滋1a，氏1、（2002）：Shaking［abie｛es芝s on a Ilew type bridge abutmellt w琵h geogrid−reinfQrced cenlent treated4）Hirose，T、，Fulisawa，丁，，Nagayama，1、，Yos短da，H．andSasaki， T、（2001）：Designcrlteriafortrapezoid−shapedCSGdams，／ノ∼r、i6）YQkozeki，K、，Watanabe，K、，Furし【sawa，Y．，Daimon，M、，0τsuki， Co’η！ノ∼、ムαヂgθ0α〃1∫2001μ10rん∫hoρ，Dresdel1． N、aΩd Hlsada，M．（2002）：、へnalysisofoldstrucmresandaumerical5） Ikegami， ∼q．， Saτo． H、， 1chlba， T、， 0亡sロki， N．， Nis1琵da， 丁、 modelfordegradaεloηGfcoacreζebycalc紺m1onle霞cllil！9， τerashi，氏’LandOish1，K、「（2004）ISiml）li昌edpredictionmethodfor Co・1α’αθ乙め1”α1ヲ？1’∼’・・（40）・209−22匝・ back聞，P1｝oc、7’h1ノ∼’、Co’∼ゾ0θoεソ1∼’11．，Nice．L
- ログイン
- タイトル
- Viscous Property of Loose Sand in Triaxial Compression, Extension and Cyclic Loading
- 著者
- Takashi Kiyota・Fumio Tatsuoka
- 出版
- soils and Foundations
- ページ
- 665〜684
- 発行
- 2006/10/15
- 文書ID
- 20949
- 内容
- ,SOiLS AND FOU*NDATIONS¥'ol_ 46, i¥'0, 5. 665684, Oct 2006Japanese Geotechnical Societ}VISCOUS PROPERTY OF LOOSE SAND IN 'TRIAXIAL COMPRESSION,EXTENSION AND C 'YCLIC LOADINGTAKASHI KIYOTAi) and FU ,{lO TATSUOKAii)ABSTRACTThe viscous property of sand under triaxial compression (TC), triaxial extension (TE) and cyclic triaxial loadin*'conditions ¥vas evaluated by using reconstituted loose samples of three types of' relatively fine uniform and relativelyangular sand (Silica No. 8, Toyoura and Hostun). The viscous property ¥vas quantified mainly by changing step¥visethe axial strain rate many times and partially by peT'forrning drained sustained loading, both during other¥visemonotonic loading (ML) at a constant strain rate. Such a peculiar feature of viscous property as that the viscous stressincrement decays ¥vith an increase in the irr'ever'sible strain dur'ing ML at a constant strain rate (i.e., the so-calledTESRA viscosity), ¥vhich has been observed vith Toyoura and Hostun sands in pre¥'ious studies, was obser¥'ed alsovith Silica No. 8 sand. The magnitude of ¥'iscous property is represented by the rate-sensitivity coef cient, fi, defined asthe slope of the !1 R/R - Iog {(i*)*r*** /(,;, i*)b*r.** } relation, ¥vhere A R is a sudden change in the principal stress ratio, R(T Icr. , caused by a step chan'e m the rrrevelsible shear straln rate from ( y i*) *f.** to ( p i*)*ft** at a given R value durin_',_other¥vise lvlL. The follolvin*" ¥¥'as found. The same definition for fi is relevant to drained TC and TE tests. In drainedcyclic triaxial loading, the fi value is obtained from the above-sho¥vn equation after re-defining the sign of A R andproportionally scaling the value of R. With the respective type of sand, the fi values under these different loadin :conditions are very similar. The effect of overconsolidation on the fi value is insignificant. Thevalues of these threetypes of sand are similar to each other and also to those of other ordinary types of sand and gra¥'el ha¥'ing lar*'elydifferent particle sizes. The decay rate of viscous stress increment ¥vith an increase in the irreversible shear strain, ¥vhichis another factor of the viscous pr'operty, is rather similar among the three types of sand, Ivhile the decay rate is slightlylo¥ver in ML TC than in ML TE. The effect of o¥'erconsolidation on the decay rate is insignificant,Ke .' words: cyclic triaxial test, Ioading rate effects, sand, triaxial compression, triaxial extension, viscous property(IGC: D61D7)Benedetto et al. (2005) in the torsional shear tests. On theother hand, the relationship among the ¥'iscous propertiesunder the TC, TE and triaxial cyclic loadin*' conditions isINTRODUC1'10NAccording to a number of previous studies that can befound in the literature (e.*'., Murayama et al., 1984;not ¥¥'ell understood. For this reason, it is not knownwhether the viscous property pararneters evaluated underMejia et al., 1988: Yamamuro and Lade, 199,3;the TC and PSC stress conditions can be applied to generai three-dimensional str'ess conditions.In vie¥v of the above, in the present study, the viscousproperties of reconstit.uted loose specimens of three typesMatsushita et al., 1999; Nakarnura et al., 1999; Lade andLiu, 1998, 2001; Howie et al., 2001; Di Benedetto et al.,2002; Tatsuoka et al., 2002; Ku¥vano and Jardine, 2002;Nabvir et al., 2001, 2003a, b; Pham Van Bang and DiBenedetto, 2003; Di Benedetto et al., 2005; Tatsuoka,of relatively fine uniform sands (Silica No. 8, Toyouraand Hostun), having relati¥'ely angular particles, ¥vereevaluated under the drained TC. TE and cyclic triaxialloading conditions at fixed confining pressure. It lvasattempted to find the relevant viscosity parameters thatcan be equally applied to those different loading conditions. The effects of isotropic-stress overconsolidation2004), sand exhibits significant creep deformation andstress relaxation in drained triaxial compression (TC)tests, plane strain compression (PSC) tests and torsionalshear tests. In these previous studies, essentially the sameviscous property was obser¥'ed with fully drained saturated sand (i.e., ¥vith negligible effects of delayed dissipationof excess pore water pressure) and air-dried sand. Thesewere also evaluated to a limited extent. It was also exam-previous studies vere performed mostly under TC orPSC stress conditions, except Nakamura et al. (1999),ined ¥vhether the stress-strain relation of Silica No. 8 sandPham Van Bang and Di Benedetto (2003) and Dihistories includin*' drained sustained loading can also befrom drained TC tests performed for various loadingi] Institute or Indus rial Science, University of 'Tokyo, Japan (kfyota@!iis.u- ok.vo.ac.jp).ii) Department of Civil Engineerin_ . Tokyo Uni¥,'ersity of Science. Ja )an (tatsuoka@ rs.noda tus.ac.jp).'The manuscript for this paper vas received for reviehv on August 2, 2005; approved on "lay 29, 2006Vritten discussions on tiris paper should be submitted befbre May I , 2007 o the ,Japanese Geotechnical Society, 4-38-2, Sengoku, Bunk_vo-ku,Tokyo 1 1'_-OOI , Japan Upon requesi the closing date may be extended one month.665 ilKIYOTA AND TATSUOKAG66fio¥v rule are modelled similarly as the con¥'entionalelasto-plastic theories. So, any elasto-plastic modeld8can be extended to a non-linear three-componentmodel by adding the (7' component appropriately.inviScid corriPonentrILLJP I (5i).The basic ¥'ariable for (7* is not "the general time t ",for ¥vhich it is not possible to define the origin in theobjective ¥vay (e.g.. Tatsuoka et al., '_OOO, 2001). Theviscous stress increment, c!(T', develops by either c!e '*or its rate, c!H y po-eiastic=*, or both and Is al¥vays proportional to.theinstantaneous (Trvalue; i.e , "d(T ¥vhen8"=r,,Iscomponent vjscous component( _iven as:Fig. 1. =0n-linear three-component model (Di Benetietto et al., 2002;Tatsuoka et al., 2002)[d(T '](=) = [cl { (T f (e i') ' g ( i*) }It.) (3)lvhere g (i*) is the viscosity function, ¥vhich is al¥vayssimulated by a non-linear three-component model (described below) using the parameters for the ¥'iscouszero or positive and given as follo¥vs for any strainproperty evaluated from the stress-strain behaviour uponstep changes in the strain r'ate applied durin_ other¥visemonotonic loading at a constant strain rate. Only loosespecimens ¥vere tested, because creep deformation can beobserved more clearly ¥vith looser specimens.ing):¥vhere IA BRIEF RF.VIF,¥V OF PRF.VIOUS STIJDIF.Sn7 are positive material constants. As explained in DiBenedetto et al. (2002) and Tatsuoka ('-004) and alsolater in this paper, these constants for a given type ofNon-!inear Three-con7ponel7t Mode!Although a number of elasto-viscoplastic constitutivemodels have been proposed for saturated clay little hasbeen proposed on the viscous property of sand (e._O.Yamamuro and L.ade, 1993; Di Pr'isco et al., 2000). DiBenedetto et al. (_7002,_005), Tatsuoka et al. (?_OO_ ),Komoto et al. (2003) and Tatsuoka (2004) sho¥ved thatthe viscous properties of a ¥vide ¥'ariet_v of geomaterials(i.e., clays, sands and gra¥'els) observed in dr'ained TC_and PSC_ tests can be described appropriately by the non-linear three-component model having the basic frame¥vork described belo v (Fi_"*. l).1. A given strain increment, de, consists of an elastic(i.e., rate-independent and reversible) component,d8*, and a rate-dependent and irreversible (i.e.,(si*) or stress ((Tr) path (¥vith or ¥¥'ithout cyclic load-[ f (I i'i)J_}J( :O) (4)",g, (b**) = c ' [ i - exp I8***I ,2. de* takes place only in component E,'; and c ,}' andgeomaterial ar'e determined based on the ratesensitivity coefficient, fi. The values of fi of threetypes of sand under various str'ess conditions andloading histories ¥vere evaluated in the present study,as explained later in this paper.Di Benedetto et al. ( _OO?_, 2005), Tatsuoka et al. (2002)and Tatsuoka (2004) sho¥ved that different formulationsof (7 are necessary for different geomaterial types thatexhibit different effects of recent history of ** on thecurrent (T ¥'alue. Firstly, a stress-strain model called thene¥v isotach" ¥vas pr'oposed to describe the ¥'iscousproperty of sedimentary soft rock (Hayano et al., ?_OOl)and some clay types (Tatsuoka et al., 1999c, '_OO'_), forwhich the current a during primary ML is obtained bydirectly integrating Eq. (3) ¥vith respect to 8*' as:inelastic or visco-plastic) component, de'*, ascJe=cl8*+de*' (1)i* i is the absolute value oflaFrom Eqsvhich is(8 ",i*) = a f(s i*) ' g.(i*) (5)(2) and (5), ¥ve ha¥'e:(T = (7 f (e i') ' { I + g, ( i')} (6)obtained by a h _'po-elastic model ha¥'ing a set ofe]astic modulus that are all a function of instantaneous stress state (and straln history ¥vhen relevant)The unique dependency of the current stress, (7, on the(e.g., Hoque and Tatsuoka, 1998, 2001; Tatsuoka etisotach property (Suklje, 1969). It is to be recalled that, inal., 1999a, b).Eq.3. A given effective stress, (T, consists of an inviscid(i.e., rate-independent) component, (Ti, and a viscous(i.e., rate-dependent) component, (T , as:(T = (7 { + (T ' (-?)4. (7is a unique function of irre¥+ersible strain, 8i*, inthe monotonic loading (lvlL) case along a fixed stresspath, in ¥vhich the irr'eversible strain rate, i*=aei'/instantaneous strain rate, , Ivas originally called the(6) (for the lvlL case), the current stress, (7, is a uniquefunction of instantaneous 'rreversible strain rate,**, andalso irreversible strain, 8i*. This difference in the strainor ", in the constitutive modellingrate parameter,results into largely different beha¥'iours, in particular¥vhen the strain rate chan_ es fast and during the stressrelaxation process, and the use of ei* in Eq. (6) is necessary to descrlbe realistically the stress-strain behaviour(Tatsuoka et al., 2000 and ,_OO1).at, is al¥vays positi¥*e irrespecti¥'e of the sign of stressrate, ( . The a f_ e i* relation, ¥vhich becomes hysteret-lc under cyclic loading conditions, and the relatedDecay of Viscous St/-essMatsushita et al. (1999), Tatsuoka et al. ()_OOO,200 1 ) ¥,1SCOSiTY OF SAND IN TRIAXIAL TES'TSr-i3('bC ; I :::r'li"I!rl'l1l;C}Cil )e '¥; 'lll5C ioe}i;h rlll')"CmlLn11dJ.' ' rl/asTiil:: ll-4(ll¥d" dJI n:rlT Ii r ;:lfiilif:';/:s iik i1:i J eiI'! "IIi C;{i"}!t}(C (}i tJJ(,l(,l-il I '- !f L - - "l(}ItCl l li 5t]n};: Inn:i - - }i f}' elic l ) inC '}iT f i Ifh( iTC (}fli: # P4 {f'7C i}fT{!eISilL:ar straln ' = , _ (..* {ob)Fig. 2. Rf]i5:T It :;'}2C*=l:=,[c!{( g,(t")}]{=}'(= =*)" }(8" r)a.*(7)H l" C ; 11J ::': , d : :L t T stl rlla/ H ' Fl:: I I C' }:iii:tl;:::::i: ::::::!'::i 4)cr = [d( ']L'fl'rll'lr' 1'1"r"!i" ))J:=1 ' ' : "'! '¥ i !l3ntch ; l ¥/ / ' L k it) fi Sa trir ued HL stv:1 s nd667t !1(]']lvhere o" is the current viscous stress (1vhen 8**=8*');[c!(r' J{*.*=) is the ¥'iscous stress increment that de¥'eloped inthe past (¥vhen e'*=r) and then has decayed until theplesent (¥¥hen e" 8") [c!{(T g,(8")}](rl is the ¥'iscousstress increment that cleveloped ¥vhen 8 *' =(Eq. (3)); andei* is the lrre¥*ersible strain aT the start of integration,¥'here (T =0. Tatsuoka et al. (2001, '_002) and DiBenedetto et al. (200'_) proposed the follo¥ving polverfunction based on experimental data:gd***1'(8 **relatlons from dralned PSC tests ((r 39' kPa) atdifferent constant i+s and a tes with step changes in i*, saturatedHostun sand (bach A) (iMatsu lita ct al., 1999: 'Tatsuoka ct a].,2000, 2001; Di Benedetto et al. 2002)T) = /'(t(8)¥vhere /'1 is a positive constant smaller than unity. Thepo¥ver form has a fundamental ad¥'antage in the integration of' Eq. (7) (Tatsuoka et al., 200'_).and Di Benedetto et al. (2002) reported that, ¥vith t¥vo fineuniform sands havin_g: relati¥'ely angular particles, Hostunand Toyour'a sands, the viscous stress increment, [d( ' l(*,,according to Eq. (3) decays ¥vith an increase in the strainVVhen /'1 = 1.0, Eq. (7) becomes totally differential,retur'ning to Eq. (5) (the ne¥v isotach model). The decayparameters r; of the tested sands ¥vere evaluated in thepresent study.Due to such decay feature as expressed by Eqs. (7) andduring the subsequent ML. This feature can be seen typically from Fig. 2, which sho¥v the test results obtained(8), the effects of irreversible strain rate,from a series of drained PSC tests at an effective horizontal stress, (Tl(' equal to 39'- kPa on saturated specimens ofthe (T' value during the subsequent loading become rran-air-pluviated RF Hostun sand (batch A).It may be seen that, in continuous ML of drained PSCTESRA model (i.e., temporary or transient effects ofat constanton the viscous stress component). Then, the value of (T'could become either positi¥'e or zero or negative depending on recent loading history e¥'en lvhen *' has ah ays. s that were different by a factor of up to 500(i.e., tests H30'_C through H307C;0=0.01250/0/min),the o¥'erall relationships bet¥veen the principal stressratio, R=(T(lcrl(' and the shear strain, y=8 -eh, fromthese six tests are essentially independent of the axialstrain rate,+. In the other test (HOSO1), the R vaiue sud-denly increases and decreases immediately after. in-creases and decreases step¥vise by a factor of 100. In thistest, as ML continues at a constantafter the respectivesudden change in R, the stress-strain cur¥'e exhibits amarked chan*'e in the tangent modulus and then tends to*'radually converge into the unique stress-strain curvethat is obtained by continuous ML at different s.The decay of the viscous stress increment, [d(T ](*), ¥vithstrain during the subsequent ML at a constant strain(i.e., irreversible strain acceleration),sient, or temporary. The ne v model is therefore called theirreversible strain rate and irreversible strain acceleratlonbeen kept positi¥'e.Rate-Sensitivity Coefficient fiDi Benedetto et al. ('_OO'_) and Tatsuoka et al. ('_002)proposed to express the magnitude of the viscous property of geomaterial as f'ollolvs.The sudden jump in R (at the fixed irreversible shearstrain) by a step¥vise change in the irreversible shear strainrate,*'= : - }f, from ( *')b*r.** to (' **)*f*** is defined asA R =A(( f lo' ). In the drained PSC tests and the drainedTC tests performed in the present study, the value of lo_,_"{( ) /( )b*r ,*} is nearly the same as log{( i,)*f*"/*f*** *** *** *follo¥ving a step change in the strain rate described above,¥vas also observed in other drained PSC tests on air-dried( i') .} The AR/R-loHostun sand (batch B) and saturated Toyoura sand (Di¥vhichBenedetto et al., 2002; Tatsuoka et al., 2002), in torsionalshear tests on air-dried Hostun sand (Di Benedetto et al.,2001) and in drained TC tests on ¥¥'ater-saturated and airdried Toyoura sand (lvlatsushita et al., 1999; Nawir et al.,2003a, b).*', and i s ratei'=a28i'/at2, on{(* *). .+ /() *f'**} relatrons*f* *f'rom these PSC tests are independent of the value of R atwas step vise changed ¥vhile they are highly linearalso as sho¥vn later in this paper. The slope of the relationis defined as the rate-sensiti¥'ity coefficient, fi.Matsushita et al. (1999) sho ved that the P value ofToyoura sand in ch'ained PSC and TC tests are nearly thesame. Na vir et al. (2003a) showed that the P ¥'alue ofWhen the viscous stress incr'ement, Ic!a'](=;, decays ¥vithToyoura sand is rather independent of density, confinin_"*,strain, the stress, a', is no longer a unique function ofand (6)) is unable to describe this peculiar feature ofpressure and vet condition (air-dried or saturated) indrained TC tests.Figure 3 summarises the fi values of several types ofviscous property. Di Benedetto et al. (200'_) and Tatsuokaet al. (2002) modified t.he ne¥v isotach model by introducing the decay function, gd*** (8**- ?), as follows:sand and *･ra¥'el, a crushed concrete aggregate and twokinds of compacted dried clay po¥vder, plotted againstthe mean diameter, D50. The fi value of Silica No. 8 sandinstantaneous e ' and**. The ne¥v isotach model (Eqs. (5) KIYOTA AND TATSUOKA66sI OOo locomp cted 'Hostun 's nd- comp ,cted***ei j(.t)FLJJinomori ei yPolrvder(Li et al 20D4)a 08ca,Silica Xo.S snnd= Drairied TCoven d edcrus ed concr8te80ggregate>pawder} Pharnvan 8ang et 31 (2003) []: J mL na R[versar d ,*: (Yasin et al 2003) /Q) , ,, *] ,.'o oo Nalr* r etO[II (Anh D n etal 20a4)Toyoura sand (fviatsushita et l 999: Modei chi 8 g avelATatsuoka et 81 2003: Hir8k wa. 2003: (Njri3 a '! 2003)i , 2a03a)IE-3 a al o 1 1 IoMean particle diamter, Dso (mm)Fig. 3. P-D<0 re]ations of various granular materials and compactedoven-dried clal.' powder (.see Table A1 in APPENDIX Al for thetest conditions)S'iiell ¥o.S sandMOstUn s ntV = I . 3RF Ilostun snnti:-Cl, o gin lchiba graveiClls nd No8 [] . ･'2005oSilica02 (Kjyota& Tatsuokaro) o u ['tl S llldD, = t} ri7? m {1>, 40{Deng & Ta suok 'c:e)6(t(Matsushit3 et al , 9s9: **Di Benedetto et l . 2aa2: *o,' a4 2a05] * '¥D, = O IS nIIT1t; = 1 64Aqil et l (2005) *C5a a6 oven-dried :alln cl y ,To}'our:1 snndl D*,= f).3i m 71L;.= 1 94oO OlOlParticle dia l eter ( m!l)Fig. 4. Gratn size distributions of tested sandsIt ¥vas confirmed, ho¥vever, that, ¥vith the fine uniformsands used in the present study, the fi vaiues evaluatedbased on axial strains locally measured and thoseplotted in Fig. 3 ¥vas obtained from one of the drained TCexternally measured are essentially the same (Na vir et al. ,tests described in the next section. The data obtainedunder other loading conditions in the present study are'_003a; Enomoto et al., 2006). The volume change of thereported later in this paper. The follo¥ving trends may beseen from Fig:. 3:amount of pore ¥vater expelled from and sucked into thespecimen by measuring the ¥vater height in a burette that1) ¥Vith Toyoura and Hostun sands, the fi values fromdrained TC and PSC tests are essentially the same.¥vas connected to the specimen ¥vith a lo¥v-capacity2) Except for a crushed concrete a gregate (Aqil et al..respective saturated specimen ¥vas obtained from thedifferential pressure transducer.The strains presented in this paper are logarithmicfrom 0.0013 mm to 7.8 mm. A noticeably higher fivalue of a crushed concrete aggregate would be dueones, obtained by integrating strain incr'ements definedbased on respective instantaneous specimen dimensions.Test Mate/'ia!s: The follo¥ving three types of relatively fine and uniform sand ha¥'ing relati¥'ely angularto such a special feature of the particles that stiff andparticles ¥vere used (Fig. 4): Silica No. 8 sand (a .Japanesestrong cores of gra¥rel particles are covered ¥vith arelatively ¥veak and crushable thin layer of mortar.Despite these important findings ¥vith respect tO theviscous property of geomaterial summariz,ed above, mostsand; Dj0=0.077 mm, U*=2.43, G*=2.655, e ,**= I .335and e i*=0.73), chosen to realize more contractive beha¥'iour than Toyoura and Hostun sands when loose because of a more angular particle shape (Kiyota et al.,of the available data were obtained by drained TC andPSC tests, but no systematic data from drained triaxial'_005); Toyoura sand (a Japanese sand; D50 = O. 1 8 mm, U*2005), the range of these fi values is ¥'ery small, beinessentially independent of D50 for a ¥'ery ¥vide rangeextension (TE) tests and drained cyclic triaxial tests canbe found in the literature. lvloreover, all the reconstitut.edspecimens of granular materials tested to evaluate theviscous property reported in the literature ¥vere normallyconsolidated ones, so effects of overconsolidation on thecoefficient fi are not kno¥vn.TEST PROCF.DURF,S= 1.64, G*=2.65, e***=0.99 and emi =0.62); and RFHostun sand (batch B) (a French sand; D50=0.3i mm,U.= 1 94 G =' 65 e =0 95 and e*i =0.55). Toyouraand Hostun sands are quartz-rich subangular sands,¥vhich ¥vere used by Di Benedetto et al. (2002) andTatsuoka et al. (2002) to study the viscous property ofsand. The test conditions are listed in Table 1.Specilllel7s: All the specimens ¥vere prepared by theair-pluviation method. To achieve the isotropic stressconditions at the top of the specimen ¥vhile ensuring freeAppa/'atuS.' An automated tr'iaxial apparatus ¥vasused. The specimens ¥vere 70 mm in diameter and 155 mmin height. To make the specimen deformation as uniformas possible, the top and bottom ends of specimen ¥vereaxial compression during specimen preparation, a collar¥vas set in advance at the top of the split mould andremoved immediately before applying an initial eff ctiveisotropic confining pressure (by partial vacuum) equalvell-lubricated by using a O.3 mm-thick latex rubber diskto 2 kPa to an air-dried specimen (Fukushima andsmeared ¥vith a silicone grease layer having an initialthickness of 0.05 mm (Tatsuoka et al., 1984). The deviator load ¥vas measured with a sensitive and lo¥v-compli-Tatsuoka, 1984). Then, the partial vacuum ¥vas increasedance load cell. As the axial strain ¥vas measuredexternally, the measured axial strains included anas eo in Table 1. The specimen ¥vas then made saturatedunkno¥vn amount of bedding error (Goto et al., 1991).to - )-O kPa ensuring the isotropic stress state at the topof specimen. The initial void ratio at this stage is denotedby supplying carbon dioxides and then de-aired waterfrom the bottom of the specimen and back-pressurized T¥,ISCOSITY OF SA.¥Dlable 1.TeslNoLoading history fmingpressure (kPa)14Toyourasandeo /e*O.927/0_906THO . 943 /O. 9 1 8(consiani slrain raie) 4003Vold ra ios*1,TC(conslant strain rate)1TRIAXIAL TESTSTCO.932/0 912TEO.945/0 922OCRl .OTC100O, 960 /o . 942407TE200O.954/0.9342.08CyclicO 939/0.916l_192/1. l9TC(constant strain rate)TE14SilicaTC(1vlth susiainedloading)o .o 1 95O.0200-o.o0125 - o ･) o.0254:i: O.O0125 - : : O ') O.OIS9O.O0125O.0125O. 1 25l 40190/1. l4004218o.25- O.OI 25Sustained loadinat c!= 300 kPa19O 125Sus ained loadinl 187/1. 130TC1.188/l .135TEl.190/1. 136drained creep for3 minutesO.O0125 - O.25 -l_180/ . 128l.181/1. 131l 7t,)al q=200 kPaO_0125O_OO 1 25 - O.25 O.0272- O O012_-O.25 O_0304l.lS9/1. 13420Cyclic21l.173/1. l2,-:!: O.O0125 - :!: 0.25 O_O'_23I.177/1. 145,,N. ole:2 o1 182/1.120162440l.187/1. 139(constant strain rate)23O OI 251.1S7/l i351 186/l12No SLegcndIniiial isotropic6l 5*)/ m i n ) fi- o,,o0125 - - o ･) o.0242O.94 1 /O 92613(O.OOI 25 - 0.25 O,.0200200llAxial strain ra eO.0125TClo669Triaxiai iest contiitions in the presentecl siuti,E cti¥=e cou'lalerialli¥'HostunsandTCO.918/0_893TE0.926/0 905O O0125 - 0.25 O.0214- O.O0125 - - O.25 0.0275Initial isotropicdrained creep for3 mir utesa) The period ofinitial drained creep immedia el_v before the s art of drained riaxial loading lvas 3 minutes in this test, Ivhile the period inthe other iests of Silica No. 8 sand ¥vas 180 minu es. This perlod 'as 3 minuies in all the iesLs on Toyoura and Hostun sands.b) Theaxial strain rateduring lvlL ¥¥'as equal o0.0125a. hnin, vhicll vas one tenth of O. 1250/6/minute in other similar ests Ncs. 14-16.c) Initial void rario (eo) and consolidated void raiio (e*).with pore pressure equal to 200 kPa.Loac!iilg Method.' With all these three sand types,for a range of overconsolidation ratio (OC*R) up todrained ML TC and TE tests ¥vith a number of stepa number of step changes in . ¥vas performed.All the triaxial tests were performed in an automatedlvay by using a precise gear system dri¥'en by a ser¥'o-changes in . were per'forrned. The follo¥ving other tests¥vere also performed:four. Moreo¥'er, one drained cyclic triaxial test ¥ 'itha) Silica No. 8 sand.' Effects of strain rate on themotor for axial loading together ¥vith an electricalstress-strain behaviour were evaluated by performingfour drained ML TC tests at constants that werepneumatic transducer for cell pressure control (Tatsuokaet al., 1994; Santucci de Magsitris et al., 1999). All thedifferent by a factor of up to 200. In four otherdrained TC tests, sustained loading tests ¥vereperformed during other¥vise ML at a constant ..specimens ¥vere subjected first to compression underMoreover, three drained cyclic triaxial tests with anurnber of" step changes in . ¥vere performed.b) Toyoura salld." The effects of isotropic-stress overconsolidation on the viscous property lvere evaluated400 kPa. The norrnally consolidated (NC) specimens¥vere then subjected to drained creep loading underisotropic stress conditions (hereafter called "isotropic-stress compression") at.=0.0250/0/min to¥vards (Th=isotropic stress conditions (hereafter called "isotropicstress drained creep loading") before the start of drained KIYOTA AND TATSUOKA67040J3540No 17- No lOa)z I O ,,I ( ,,e'O( 30*'*20Be3jle*10_)_, ,,* J OAc);s 2.0E,! I O20e..r)rained TC_.lO* f VN0.9:)_ 1,5=NoI= O Ol 25,,!lO. NO I O:=0 *. No {=:Af:'_ +0*'minlD,ained TC_,,.No 9:･ 1 5= 20 +.¥.o IS:, change from* O_OI 25 " min* +1 O. N'o I O:,*No i ! : = O **. No 12:s1 .oNo 9No I li 3 O, iO T To 18l O'-;,j .)_5lO ' E,,i ,!lo No 11 N09No lONo 12a)O r' to lO ,,20 +=103530>b) 7'1N* 9,5!s30No 18¥No lOll20)No i 1/xNO l?+/10> oooDrained TC.¥. =0.9:'o:No I S:o 4** O Oi25,f O.)･*･tnin'o {O:.* IO ,,. No il･=No 10No 12,lv i)/No I Ib) ¥l!l) 52015c;/N09 ',+.o lo>o= 20 ,).Drained TC.No 9:05. change hom I/IO ,* to 20 *=JNo I I :)6 8>,O 12 14 16o tnin_. I0L, ' No i 2:= E .= IC ;,*ooVertical strain. 8 ("/")40Pig. 5. a) R - 8*, and b) 8,*,: - c* re!ations from ML tests ((T; = 400 kPa)No lOc)with and without strain rate changes (Silica No. 8 sand)... e35triaxial loading at constant (Ti; for a per'iod of 3 minutes¥vith Toyoura and Hostun sands, ¥vhile it ¥vas 1 80 minutes¥vith Silica No. 8 sand, except 3 minutes in test 15. Assho¥vn later in this paper, the perlod of initial isotropicstress drained creep loading had significant effects on thesubsequent stress-str'ain behaviour of NC specimens.¥ lith o¥'erconsolidated specimens of Toyoura sand,, iO; . E E30lOge,:lOg6%- 2.5*!! O NOEg' )* 7_oe,I f I Oe )g /lOPnn {palpal st'sssst'sss :tio:tso' RTll 'i '2(j 8aftsi ()! I OJs- 1.5;t}RlOec-be :: RIo1 8!10*=400 kPa ¥vas follo¥ved by isotropic-stress unloading ate IOe' lOE _e'isotropic-stress drained creep loading for 3 minutes at crj;*= O 012* ;,,!iO. No 10:' lls;c:"'!e 'fgilrTeye･s b e yert csJ suasn'= - 0.0250/0 /min to¥vard (Tl( = 200 kPa (tests 5 and 7) or100 kPa (test 6). Then, the specimens ¥vere subjected toisotropic-stress drained creep loadlng for 3 minutes before the start of drained TC or TE Ioading.30))VISCOSITY IN DRAINED TC)The TESRA viscosity ¥vas obser¥'ed in drained TCtests on Silica No. 8 sand. Figures 5(a) and (b) sho¥v therelationships bet¥veen the principal stress ratio, R, andthe axial strain, e , and bet¥veen the volumetric strain,8 *1' and e from five dramed lvlL TC tests ((Tl; =400 kPa).In the first four tests, the axial strain rate,, ¥vas differ-ent but kept constant, equal to o/lO, o, 10 o and ,_O o,¥vhere 0= 0.01'_50/0/min. In test 18, . was changed step¥vise from ( )b*f ** to (lvlL at a constant)*f*** many times during other¥vise.. The nominal ratio ( .)L,*f***/()*r***ranged from 1/100 to 100.Figures 6(a) and (b) sho¥v the relationships bet¥veen R15lNo iO/,eo¥¥/ ¥20TESRA Viscosity of Si!ica IVo. 8 Sanclo Isd)lO05Drained TCe,No. lO:c,¥. To I S: , change from I !1 O *>ooo5lO= ,T= O 0135 , ;min.15o 2020lrre¥'ersible shear strain. 7 " (?/*)Fig. 6. a) and b) R- !" and c) antl d) 8:', - f" relarions from drainetiML TC tests at different constant strain rates and one test lvithstrain rate changes (Silica No. 8 sand, a; =400 kPa) VISCOSITY OF SAND IN TRIA¥lAL TESTShighly reliable due to unknolvn efi cts of beddin_",_ error.Table 2. Values of t} e parameters In Eq. (lO)To}oura HostunSilica No. 8E.( " Pa)';l6f 1140140#120*, 160to.50504loadlng is purel"v elastic.The elastic shear and ¥'olumetric strains at the end ofthe tests presented in Flg. 6, ¥vhere R is about 3.5, are== Hoque and Ta suoka (1998),, Based on externall} measured axial strains, including lhe BE effects(nat highly reliable)t) rrom the inliial slope of stress-strain curves from Lhe TC tests, usedLo obtain elastic strain incremen s in this studvand the ure elslble sheal straln y*'=ej*-ej:, and bet veen the irre¥*e 'sible volumetric strain, 8:,.1=8:So, E,t = 160 lvlPa ¥vas used so that the initial part ofstress-strain cur¥'e immediately af'ter the srart of TC2ej:,and y'* from these four ML tests presented in Fig. 5.Figures 6(c) and (d) compare the results from test 18 (¥vithstep changes in ,) and test 10 (at a constant , = o). Unfortunately, the ¥'olumetric strain in the slo¥vest lvlL test(test 9) is not reliable probably because of' slo¥v cell ¥vaterO.50/0 and O.'_50/,vhich are significantly smaller than thecorrespondlng irreversible stralns.As long as , is kept constant, any systematic efi cts ofstrain rate on the overall stress-strain relation are notnoticeable (Figs. 5 and 6). On the other hand, ¥*hen , (ory**) is Increased and decreased step¥vise, R exhibits a sud-den Increase and decrease by an amount that incr'eases¥vith an increase in R. These apparently contradictingtrends of behaviour could be explained in a unified lvay¥vhen based on the fact that, in test 18, as ML continuesat a constant , (or ,*') after a sudden change in R, thestress-strain cur¥'e tends to rejoin the one that is obtainedleakage through a latex rubber membrane into the specimen. So, the values of ej*', therefore the values of y*'by continuous ML at different constant , s (or ,'*s). Thistrend in beha¥*lour is indeed of' the TESRA viscosity.presented in Figs. 6(a) and (b) of test 9 Ivere obtained byCorresponding to such significant viscous effects asdescribed above, Silica No. 8 sand exhibited significantsubstltutin_('* the values of 8( rneasured in test 9 into thea¥*erage 8:, - 81: Ielatlon of the other thlee tests at hl'hel, s. This procedure ¥vas necessary also to evaluatechanges in the cross-sectional area of the specimen to obtain the axial stress in test 9.creep deformation. Fi**ures 7 and 8 sho¥¥' the results f'romtest No. 14 and t¥vo other similar tests ¥vith initialisotropic-str'ess drained creep loading for 180 minutes.A broken rectangle in Figs. 7(b) and 8(b) denot.es theThe respective irre¥'ersible strain component, de*'=d8range of strain in, respectively, Figs. 7(a) and 8(a). It may- c!8 *, ¥vas obtained from the ¥'alue of d8* obtained basedbe seen that the creep strain rate increases ¥vith anon the follo¥ving hypo-elastic model (Tatsuoka et al.,increase in the shear stress level and the axial strain rate1999a, b):during drained ML TC immediately before the start ofc!8= d(r( /E : (9a)d8 h = - c!8vhere c!8･ v:1* (9b)and d8 :* are the elastic axial (¥'ertical) and later-al (horizontal) strain increments; Eis the vertical elasticYoung's modulus; and v h is the elastic Poisson's ratiovhen axlally cornpressed at a constant (71(' Eand v ･i* arenot constant during the respective triaxial test at a constant (;i(, but they ar'e a function of instantaneous effectivevertical str'ess, (T(, as follo¥vs:E= E.o ' ((7 ' /(yo)"*' (1 Oa)rate at the start of' drained SL, is equal to the irreverslbleshear strain rate dur'ing ML imrnediately before the startof SL. It may be seen from these test results that the loading late effects due to the ¥'iscous property on the stressstrain behaviour are sig:nificant ¥vith Silica No. 8 sand.One of the complicated issues of the viscous propertyof sand is eft cts of loading history under isotropic stressstate (or more generally the ¥'olumetric creep under general stress conditions) on the viscous beha¥'iour during thesubsequent shearing. Figures 9(a) and (b) sho v the R - y *'and e:*-y** relations from t¥vo other drained ML TCis the constant; and vo is the ¥'alue of v ･1'tests at ( }{ =400 kPa in ¥vhich drained SL was performedat q= 200 kPa for '_4 hours. The specimens ¥¥'ere subjected to isotropic-stress drained creep loadin*' at ar; =400kPa for either 3 minutes or 180 rninutes before the startis equal to (a( /(Tl' )o, ¥ 'hich is the ¥'alue of (T( /of drained ML TC. Figures 9(c) and (d) sho¥v the timev l' = vo ' { ((T( l(Tl{) l(CT( /(TIOo }"'¥vhere E+0 is the value of Epresent case); mvhen (T( l(Tsustained loading (SL). Note that the initial shear strain( 10b)when (T( = (70 ( = 98 kPa in theat( ¥vhen the elastic property becomes isotropic (i.e. , E. =histories of shear and volurnetric strain incr'errlents, Zl yEh; the Young's modulus ¥vhen hor'izontally compressedand A8 *j, during drained SL at q=200 kPa. It may beat a constant (7O. The value of (cr(/crt{)o depends on thespecimen reconstitution rnethod. v0=0.2 and (cr( IcTIO0=seen that the creep strain i'ate is significant in both testsvhile the rate is aft:ected by the period of initial isotropic-1 .O Ivere assumed for these air-plu¥'iated specimens of fineabout 0.0010/0 at dift'erent effective stress states in severaistress drained creep loadin*" before the start of drainedML. This fact indicates that component P (Fig. 1) shouldha¥'e both the Cam-clay type yield locus, vhich developsby volumetr'ic yielding, and the stress ratio-t.ype yield10cus, ¥vhich develops by shear yielding (1.e., the doublehardening). This issue is discussed in detail by Kiyota ettriaxial tests. It seems ho¥vever that the Young'sal. (2005) and Siddiquee et al. (,_006).sand based on the pre¥'ious studies. The other elasticmodulus parameters are listed in Table '-, ¥vhich ¥vereevaluated by applying small unload/reload cycles ofdeviator stressvith a single axial strain amplitude of"modulus. E*, of Silica No. 8 sand obtained as above is not 、672KIYOTA AND TATSUOKA22 ））IsQtK）Plc−Slro3sdrai瞬creepbdbrこshearloaご旧glbri80mmじユo〉 ユ、oo−ごl l8↓18屈 】6召召一N・1415、置0125％nun No17・も、淵OO1250らmmNo】7 ＼、＼、煮』☆撚駕 16Noi4魏 14蕊員ぼ 1．2o l2黛lso！rOPIC甜cssdrai置10dcrccp昌。a麺t嘩＃ユ。・kPa＆3〔1・kPaへ篇川25・。min00 02 0謬 06 08 10 】2 14 16bご恥re shear lo3〔圭inq lb【i8（｝【11in㎜ 1．0 】0a）AxIais：minratelmmごdi飢e1｝b￠lbret縮S1巳rt〔｝fsロS面㍑dloadm里じ一00 0ユ 04 06 08 10 a）12 14 16 ［πeversibleshearstr貸1蓄1．ジ「〔％1 1rreversibleshearstrain．ジ「（％） 10 iOlsotropic−stressd繍￠dcro￠P↑篶lsαTopic−5t嚇dramedcr岬belbre3hoarloadinglbr180minbeR）re shoaτloading R｝r…SO n…in0．8…08訟06RζmgeofF19誘髪（｝6／鮎『縛つ釜04饗0290智鴬04202。／’ S：蕊翼ofsロ賦昌i訪od io＆dl窮匙No lじ00 し｝5 11） ！5 ユ0 25 3りb） 瞥 、 ＼ i φ〆一町 醐瞬” Sτユrτoゼ兜s竃amodloadln罫．NoN ∼ ∼ S脚fsu5庶dl。a占lnさN。ロ験1蝋贈．1きつ〔）0 冒 L ト ー 華o（｝ε磁ofsus幅総d【o認in閏NoI70005 …、0 15 ユ0 25b）3、0 1汀e・・ersiblesl職stra頭．γ匹「（％） ［πeversibleshearstτ且1…1、・「【τ（Ob、 贋06 ≧05ISQtrOPlc−stress dra加ed creep bじ薮》rごshear bad正ng lbr歪80min由ごs塾rt ofsus㎜gd loadi靱9Nol4 05−N・14華0】25％min 噸レ 蓉017＝を，＝00125％一min 跳04 03 003 e引oad［ng る02 q繍200kPa ．生 02 01 質OINol7／Iso柱opic−sビessd面nedcreepMqs “ じ1じ、 じ ㎜of瓢凶ごd 200A測st面ra｛e㎞m司ia監elybε飴re 答 醤014・Sus臨edio蕊面g、 壱04 馨 06l・adingatq一ユ00胱＆300贈a；邑、需㈱5％励c）be恥resh餓rloading偽rl80min 00c）三 一 一， 0．3 03送oぼopic−s注鄭dr血edα即be郵oresh㎝loa面9魚rl80鱒 No14二Sus臨ヒd lo＆dIng三 〇、2 飢q冨300kPa ヤっ 答奮葺釜 01 、Axja！sすぬTate㎞me伽芝elybelbre由e s㎜ofsus蜘ed load血9−No14＝量、鷲O l25％【ロ磁 。障二 一」）『oドノ 02 0 苓 1No l6＝Su5面nedめadlng 一 議q埠200kP＆ 芒 OI／lA：ぬalsα諭烈e痴mediatelybefbre山es甑ofsus腔血ed茎 oo bad加gatT200岬a＆300職も、鎚0125％「顧聴oτ㈱ic−s汀cssd面nedcre叩0 5 10 15 20 25d） Creep業繍e（卜ou6〉befo陀she撚b＆d加9最》r I80r田τ1 OOd）三o5 10 152025 Creeptime（hours）F負9．7．E琵ecIs・fsl・earstressleve1・n：a）Rvers・s7已【andb）ε瓢肇versusFig．8E疲ects・荊匙ia韮s｛ra蓋nra吐e・n＝a）Rversus点ndb）ε銭，lversus γi『rel飢i・ns，andtimehls吐・ries・fc）コンandd）コε、、，ldurlngsus輔 ン1「relaIlo盈s，a翻dtimehis重orlesofc）」γandd）」ε、。匪duri臓gSL ｛ai照ed loadi臓9（SL），drai臓ed ML TC重es｛s（S韮lica No・8s訓d，σ‘竺 400kP践）』 要673VISCOS亘τY OF S、へND至N TR王．へXI．へしTESTS0082、けPo口odoflso！rOPIc−s…ressdramedcrcePo 18 No 15．3IIliFlじ No16 i80駐U飛k006△SilicaN『o、8sand薗004i6目△1、灘』爵賢，，、、撃，編魯㊥ 002霧乞 0001、2一〇〇2翁⇒10一〇〇4△働（1．0 （｝2 〔｝、4 00 08 10 1コ14・N・18、TC，・CR司・σ義・轟4G・kPaβ瓢・・2721一〇〇6△ 1汀e・e酌lcshearstr｛湘．ジ「（％）a）ムN・19TE・CR菰1・、σ卜、・叫・・kP胆・3・4i一〇〇8 001 0、1 1 10 100＿ i o1之a芝ioof1irslle＆rs乳rai【篭ratesわelbreandalierasζepchallgePcrK）d ohSOtro｝）耳c−sττcss d職11ごd crccp No l53nlm− Nol6 180ξnin雛 08 予［「“ま蓄Cr／デbC【brcR二11聾巳ごof l・19．aコ0 06F量9ほ0、」RIR−1・9｛（プ『）3f、脅，／（プ『）憂，。r。，。｝relat韮・nsfr・m鼠drainedIC／o、 垂est（Fig．6）andadrainedTEIest（c，f．，Fig．17）Endof5u5【ユ1＝1￠dIQ“dm9，No聾5…i o4 En己of5幡臨監霞じ註 1Qadl織“ N臼 16愚 021璽㌦Sこユrτof5“駅ユInごd Io“dmg「No l5def玉ned in Fig．6（c）．The TE test data presented l！1Fig．10are exp豆ained later in this papeL h may be seen that t駐eS鵠r10f）us【βlnじdload：ξ燦 Nolbrelation呈s indepenclellt of t｝1e value of1∼ at which the三 〇〇strain rate was changed stepw呈seεしnd essentiα11y linear．05 1．0 ［5 2、0 25 300、0b） 1π￠・・ersibloshe餌漁in．ゾ「（％1脈ing the following equatlon to the TC test dat＆making出erelatlonpassthecoordlnate：∠R／R＝Oand（夕i「）、f、，，／ 墓 D5Pedω・fisoαopic・s臨5d面aedcr岬 ゴ 04 No15＝3m㎞No15（ンi「）bごf。「ピ撚至： 1 重㎜ No，16＝180m㎞∠、 讐e3 1装o、2 The Iineεしr re1＆tion presented ill Fig．10was obtained by！No16 琶 1こ o．1告・1・g・・（細一かln（総い1）whereδis出ecoe伍cientequαltoβ／1nlo．T｝1eβval組eofSilicaNo，8sandin出edrainedTCtestwasO，0272，whichis comparable wit勤tkose of other granular materiεし1s，ex−．へ；x1副sしra甘1rat￠㎜e（i』a【e【y before！he s㎜ofs邸励1edIGa磁ng飢q艦200kPa：￠、＝0125P“’血n 釜00c）蕊cept for c1−ushed concrete aggregate（c．f．，Fig．3）． Equ＆tion（13）can be I・ewrltten to由e lncreme慮＆1form：05‘1RR紹lnR；わ・ゴ（1nアi「）（12）On the other hand，、ve obtai茎1from Eq．（2）： 1∼蹴R f＋R V（13）As4R in Eq．（12）is de負ned at a行xed v＆lue ofジ（1．e．，the緒 l！value when the stl’ess jump starts），疑is e（1ua璽to4R’1騨A．滋al s汀ah1鳳t￠lmmedla【elybelbre偽es厭of4｛Rらg、（夕i「）｝．Tben，from Eqs．（12）and（13），we obtain：瓢臨。dl・adi騨q舅200kPa＝峡騨Oi25％掴Ωd）05 10 E5 20 25 CreePtime（醜ours）Fig、9． E庁ects of dura重ion of iso症ropic creep肇oading on＝段）石∼versus γi「容odb）εt㌔lversusγi『rel段重ions，9nd重imehlstoriesofc）」γ＆ndd） ∠ε、。lduri獄gSL，dralnedMLIC芝ests（SilicaNo，8sand，σ1警400 kPa） ゴ｛R f・9、（アi「）｝ ；わ・グ（lnアi「） （14a） R「十R vIn the case of isotach viscosity，for which R’徽R「・9、．（アi「），、ve obtain： 4｛1∼f・9、（シi「）｝ R f・｛1十9、（アi「）｝Rα∫ε一Sθn5i！ivi∫』y Co（がciε1πβ’11五）ノ’αinθゴTCSinceγi「iscoPst段ntand The viscous property of Silica No，8saucl in drainedEq．（14b），、ve obtain：τC was quanti丘ed as foHows． Figure IO shQws therelationshlpbetween∠RIRandlo9｛（ン1「）af，。，／（ア1「）b。f。，。｝from tesd8（presented in Fig．6（c）），where沼R and R are功・ゴ（1nアIT） （14b）therefore R f is constallt inご｛正n（1十9、（プ「）｝冨か4（ln夕i「）（重4c）工）espite t勤at Eq．（14c）isεしn apProxilnated solution of Eq． KIYOTA AND TATSUOKA674l lode! Simu!ation witll Si!ica No. 8 Salldi 20¥;Iscositv rBmelerslE,'* = O OOe(}6(Il 15It ¥vas examined lvhether the results of Silica No. 8t!minO.OI05) OF O 35 & TTsand, including the behaviour during drained creepbehaviour, can be simulated by the TESRA model usingO 035(b: l)ep O 35 & m= O 05e)_. )*=025&rT 003b =0the parameters for the viscous property determined basedon the P coefficient described above. According to theTESRA model, the ML stress-str'ain relation at any constant strain rate tends to converge to a unique r'eferenceI 10= 6 OI05iP05b *O(X)69stress-strain relation ¥vith an increase in y{*. It is particu- Rsnge oper ted in the -a) I oolarly the case as the stress state approaches the peak state.stlJd 'byN. awiret ai (2003)The reference stress-strain relation (i.e. , the R20E '= O OO006 P /mifollowing this principle. A typical one is presented in Fig.Toyou'a sand (b= O 00382 cx= O 23. m= O O4J Is12(a), ¥vhich ¥vas fitted to become the ultimate relationfor all the segmental R - yi* relations for different strainSilioa sand N 'o 8 (b= O O1 i 82) (x= O 23 m= O OSSiostuu sasd (b= O 00963) oL= O 23, m= O 044!IISl]Ica 5and NoO¥rates in a drained TC test in ¥vhich the axial strain ratevas changed step¥vise many times.The simulated R ( =R f+R ' ) - yi* relation is presented¥Hostun sand¥Toyoura sandl 05- y ** rela-tion) for the respective drained TC test ¥vas determined¥*iscosiiy parenleters ;in Fig. 12(a). The viscous component, R', ¥vas obtainedby directly integratin_g Eq. (16), ¥vhich is derived fromRan_2e operatedin the this studyl ooIE-5 IE-4 IE-3 O Ol OIne 'ersib e shear strain Fa e. d･/*'!d100lO(o/o!min)Eq. (7):= , 1(- )R･ =J: [dRFig. 11. Viscositl.' functions in a full-log plot for: a) Tol.'oura sand indrained TC ( 'alvir et al., 2003a) and b) the materials tested in theJ:= t= [c!{Rr g ( i')}1(.) gd .,(y=' ) (16)present studl_'(12) for the TESRA viscosity, Di Benedetto et al. (2002)and Tatsuoka et al. (2002) used Eq. (i4c) for both typesof viscosity (New Isotach and TESRA) for consistenc}'.By integrating Eq. (14c) ¥vith respect to ", ¥ve obtain:l +g ( i')=c,,'(j, ) (15)i*1b¥vhere cis a constant. The viscosity function (Eq. (4))should be defined to fit Eq. (15) for the range of'* of thedata from which Eq. (15) was derived. That is, Eq. (15) isvalid only for this range of*.Fi*･ure 1 1(a) sho¥vs the upper and lower bounds andavera'e relatronships betl een "I 0+*･, ( *)" and" (ona full'+-logarithmic plot) obtained from the plots forFigure 12(b) is a close-up of part of the ¥vhole stress-strainrelation. Figures 12(c) and (d) sho¥v the measured andsimulated stress-strain relations for another drained TCtest (test 14, Figs. 7 and 8), in ¥vhich one SL ¥vas per-formed at q=300kPa for 24hours. The modelparameters used to simulate the creep behaviour in Figs.12(c) and (d) ¥vere determined based on the fi coefficientobtained from the stress-strain behaviour associated ¥vithstep changes in the strain rate presented in Figs. I '_(a) and(b)It is also to be noted that the creep strain rate is controlled by not only the fi value (i.e., the ¥'iscosity function, g (i')), ¥vhich is independent of the density of sand,among others, but also the stiffness of the R r_ y** relaby trial and error. A relevant value was assumed fortion, ¥vhich is controlled by the density of sand.It may be seen from Figs. 1'_(a) throuc(;h (d) that all theviscous aspects of the shear stress-shear strain beha¥'iourof Silica No. 8 sand observed in these different tests are¥vell simulated by the TESRA model consistently usin._,_(Tparameter ai, ¥vhich represents the upper bound of g (")¥vhen ,i* becomes infinite. Figure 1 1(b) sho vs the averagethe same model parameters for the viscous property.On the other hand, the irreversible shear and volumet-relationships between "I.0+g ( **)" and y** (on a fulllogarithmic plot) from the drained TC tests on the threesand types tested in the present study. The relation for'ric strain relations, includin.++.O those during drained SL,Toyoura sand in drained TC obtained by Na¥ 'ir et al.(2003a). The respective relation has a linear part ¥vith aslope of b = P/In 10 that fits Eq. (15). A parameter j77 forthe average relation is equal to 0.05, ¥vhich was obtainedToyoura sand obtained from the present study(Fig. 11(b)) is ¥vithin the range presented in Fig. 11(a).With Silica No 8 sand, the experimentally obtained valueof b=fi/In 10 is equal to 0.0 _72/In l0=0.01 18, and ai=0.23 ¥vas assumed so that the log {1 +*･,,(j,i*)} -logi'relation becomes linear for the concerned range of strainwas not simulated in the present study. Ho¥vever, itssimulation by the same theor'etical frame¥vor'k as used tosimulate the shear stress-shear strain behaviour becomespossible by assuming that the irreversible volumetricstrain consists of the follo¥ving two components that de-velop in a delayed manner due to the ¥'iscous propertyduring SL, (Kiyota et al., 2005): 1) the component due toshear yielding, obtained from creep shear' strains basedrate. The other parameters necessary for the TESRAon the shear flow characteristics (i.e. , the relationship be-model simulation of Silica No. 8 sand are presented int¥veen the irreversible shear and volumetric strain increments) by shear yielding as observed during lvlL at a rela-Fig. 11(b). jviSCoSrrY OF SAND IN TRIAXIAL TESTS40,-5S ie 35TI Lrlti eI I O;I( = ¥ .L* E-*L - -eIUl(i 30e8 = e..J. t"' ¥,, E s 10 E'., iOO¥1)e merSlmul3t on: 20*/_Ol O ,l20675. .. -' /'s f' 3 *'rI O-* lReference s ress-str :n r F t OnlOlo R ;t :r :nce str ;s:0 ,,¥l}5traln rcratlonrE¥ptrl nemei O , ,V*.- 15!Dmfned TC'(ollours,;]al straln Fate before suslnlned !(x;d n1020lOa)DF2lned creep al q= 3eO Pa i'orminAxial str in rate from lilO to 1..-OG1Io,.= O O i25ooc)OV I * e(} mLn1015lOlrreversible shear strain_l* (o. )lrteh rsib]e shear strain. f" (9･t)O 6(,e,_- 05t:;* - ',1)j¥;lOE¥periment(,T 1.::: 04llO , gt iG1,.. . ･ ' ". SimulationReference stress-strain re ation･Ob);,oSin ula i0 lOg,,l; O,7;)E¥perinlen[ (eDrained TC.= O O 1vDrained creep nl q- 30.;'' Oiee'minkPa for4 I ovrs' ,ia! strain rate befbre sus ained leadin ,= O 1eirninAxi ;! strain rate frorn i!' lO , to 20 *,3 5 6oo8in"eversible shear strain. -/ * (a! )od)5 lO15C25Creep tin e (.hour)lodel of the TC test results of Silica N_ To. 8 sand, (Ti =400 kPa: a) vhole R-y*' relation b) a zoomed uprelation with many step changes in the axial strain rate, c) whole R " relation and d) time histor .' of y" during drained SLrio. 12. Similiation bv the 'TESRAtively fast shear strain rate, ¥vhich can be considered to berate-independent; and ･_) the component due to volumetric yielding, which is necessary as can be seen from thefact that the measured flow characteristics during drainedSL is noticeably different from the one during ML at aconstant strain rate (Figs. 7(b), 8(b) and 9(b)). Furtherstudies will be necessary to develop a relevant rnodel forrate-dependent volumetr'ic yielding.Effects of Isotropic-Stress Overconso!idationFigures 13, 14 and 15 show the R-y'* and 8{ 1 yi'relations from three drained TC tests on air-pluviatedthis trend in behaviour is due to effects of the ratedependent volumetric yielding discussed above.Figure 16 sho¥vs the relationships betlveen A R/R andlo' {( p i') /(p i') *f '} from these tests. The stress-strain* *f*** *relations from the drained TE tests on NC and OCToyoura sand of ¥vhich the data are presented in Fig. 16are shown in the next section. The rate-sensitivitycoefficients, P, obtained for the dlfferent ioadingconditions (TC, TE and triaxial cyclic) and different sandtypes, plotted in Figs. 10 and 16, are listed in Table 3. Theresults of the cyclic triaxial tests presented in Table 3 areexplained later in this paper.The following trends of behaviour rnay be seen fromToyour'a sand either normally consolidated (e.g., OCR =1 .O) or overconsolidated. The value of ( 1" during drainedthese figures and table:ML TC was equal to 400 kPa ¥vhen OCR = I .O; 200 kPal)The trends of viscous behaviour, including the decaymanner of viscous effects with an increase in y ', ofthe OC Toyoura sand specimens, are essentially the2)The rate-sensitivity coefficients, fi, of Toyoura sandwhen OCR=2; and 100kPa ¥1'hen OCR=4. In thesetests, the axial strain rate,*, was stepwise changed manytimes during otherwise ML at a constant . In Fig. 13,the result from a continuous ML test is also presented fora reference. It rnay be seen from Figs. 13(b), 14(b) and15(b) that the rate de:'*!/dyi' (positive for contraction)becomes larger with a decrease in the strain rate. Thistrend in behaviour may also be noted in Fig. 6(d) forSilica No. 8 sand. It may also be seen from these figuresthat this trend is stronger ¥vhen OCR= I . It is likely thatsame as the corresponding NC ones.¥vhen OCR=2 and 4 under the TC Ioading conditions are essentially the same as the NC ones. Theconfining pressure was different for the differentOCRs. However, the effects of confinin_9: pressure onthe fs value are negligible ¥vith Toyoura sand, according to Nawir et al. (2003a). lilKIYOTA AND TATSUOKA6764040No*¥ E<3 :OroYouT s ;Ide 3)e*a) 10E¥.30o 1:C ;a)e*E {o30Tc}1'ovr .s rxi5e .laEC 10l ( , = f I Oc:i,IO1'5, 52020DT ne TC. (; '= 400 kP .15¥. 'e l:= E.,= 0.0]15¥. =(, 3:from15Tlin.10lO04TO'Yours sOS!xTol ura-; ind,.¥*1'.**b) E ']oi, Ielo .= E lO= 02, ･ ; o 3l OE,iO: 06"JNo lt)S 04OCR* 4 ClE*= O Oll5 'h*miTt s ,*TQm . {O tO 20lOx¥o 6 DTainel:1 TC'. e '= 100 kP*.lO to 20 .,Vs,! I OOO,s) -02:'*rJ> =0.4t'); 02Dr sn ;ed TC. e *= 4LX) kJ*¥, e 1::,>t,:: OOo 2Fi(J.=E,* O0125 * rnirL'0.31,*rom4 6 8 iO2= 10o?,S -06146vithout strain rate ciranges (To .'oura sand, OCR = 1 ( : = 400 kPa)40¥. To 6. DFnt:.'d TC. o: .*=E ,* O Oi le u nlin_ E from100P:cToveur **>*arld4lrreYersible6 8 10i2 14shear strain. 7o 216 18 20(/ ). -ri* relations from a Ml. TC test with strainF g 15. R- '* and e'l,lrate changes (Tol. oura sand, OC_R=4, (;!1 = 100 1 Ps)o 06TOVOLib' lldIOcc. Ioo 0430l i' 4lOa 02,5,'o oo20-o 02v 1¥ ).Dr lincljTC cr '= 200 kPa OCR- 2 CI= O 0125-o 04im;J1. , fyom < ;1 O o OlO:'t'!-o os06TovouFs-sandb) E-'10R ¥OTC-OCR* cir,O kPa-= () {': r}C': ¥L) 4 rE-OCR= I r, c ,= 40 kP* r}{} 4L ;Q= r] r,1 e5TC-OCR* ･ ov ¥. O6 TC-OCR= 4 oA-o 08o ol04OCR= 4 O+10 [o 20o 08a)e'-O S8 20lrreversible shear stra in. f (9･ )13. R-yEr and 8:', '* relations from IML TC tests with ande 3b)>t'ei0¥. 07 TE-OC f =;*=c;. = 2r,rj kPa.o = iCO kP2. p= a O C}Oo. a = 2C)a kP10= O 0 5100Ratio oi iir shear strain rates beibTe and afier a step changeOEE, lO" 02E_Fio. 16 Relatlonshlps betl een,:: OO>1 R/R and log (v'.'F ,./ j,'.f"") for'Cand OC Toyoura sand specimens in drained TC and TElO *ce;;-O)¥oe,>. DT ncd TC. CT '* IeO kPe * O Oi25 o tnjTL EOCR= 2 OVISCOSITY IN DRAIl l'ED TRIAXIAL F.XTENSIONfrom E,= ' i O to 2O .Figures 17(a) and (b) sho v the relationships bet¥veen-O 4o 24lrreveTsible6 8 shearO strain.12 146 IS 20'!' ( 'o)R =(7f/a=cTl"I(T( and the absolute ¥'alue of yi*=e:1 e*h*,l y i* j , and bet¥veen e :f 1 and I y =* I from a parr of dramedtriaxial extension (TE) tests with and ¥vithout stepFig. 14. R- r" and L ::,i - ;"' relatrons from a ML TC test 11 tll stralnrate changes (Toyoura sand, OCR = 2, crt; = 200 kPa)changes in the strain rate on NC Ioose specimens of SilicaNo. 8 sand. The corresponding drained TC test data arepresented in Fig. 6.The decay parameter i'j (E.q. (8)) under TC, TE andFigures 18 and 19 sho v similar results for NC and OCcyclic triaxial loading conditions, Iisted in Table 3, are(OCR=2) specimens of Toyoura sand. The corre-discussed later' in this paper.spondin*' drained TC test data are presented in Figs. 13 rVISCOSl'TY OF SAIND IN TRIAXIAL TESTSYable 3.677List of the values of p and ,･1 for the difrerent test conditions3()[LoadinSandOCRiypet)* pep4,0Toyoura.oTECvclicTC02o,0242O5o_0254 o. ll ,o0.0189Drain i Tc¥. e.2:.h:0,4ii lO.=*- 400 kPO{ ll5, tk)mnxirL! 10 Io 20 .b)1-5o 0272lO2(}I2.010TEl¥:ro. 8fo.250.02la)1 52 o o.oi95 o_25TCroVe'eo,02l .OSilicai' u]o.3Ol0.0304xToYQur *se'Id* ;20O E :Ob) ¥. ) I .¥Ne;IieCyclicTCHostunTEloo.0223b)ioO .02 1 4o 25lOo.0275::15[';;'E io,Ola)Defined in }*** and averaged for respective loadirrg condit}ons_b)Dif ;cult to evalua e confidently-F: l,)S-05Dr incd TE Q.'= 4t}O kP02t,>=* E. * O(ll 2ShOOFT rLfronl s< *lO Io 2C, .N0.4-cL'4 6 8o40silie;¥;eNo 13ss:IdO 12 14 i6 IS20 1 1Absclu e value of irreversible shcar strain. ,(e.' )e' 3 5ea)130(rig. 18. a) R- i!"] and b) s;,*, - Iyi*i relations from iML TE tcstso ., .lwith and without strain ratc changes (Toyoura sand, OCR= 1)OE j ( ,'o , llr E, lONO93u _O15eDr:vned TENo 13 E = E*= -OOl**rru}l*ENo !91f )mlOt02C}Silica" 30IL *u;202(o S sanda)c {o+ *,5*/_140353Oe10:: ;iL",+Tc} ]u' "}-sendE ;leS'l( ;, E ioE+i I Ob)l5No i9. 10 ? 'o 13. 5¥+ o 7 DIl ine(iTE e,*= 200 kPl 0 .,-lOe: 2.0SE.,* e.OI 25?ntnOCR- 2 f).frQm E== 10to 2OQe:: 15;>. 2013: c =e 19:0,0O*= O.0125 e, from E10 to 20 ,.(C,= ! I OvS lO)i}'*'i from ML 'TE tcsts with andI O ,:Owithout strain ratc changes (Silica No. 8 sand* OCR= 1. (T ; =400:)kPa):) OO¥. *o 7. Draint:xl T5,= 0_Oi25 I jmlnoand 14. Fi**ures 20 and 21 show the results from a pair ofdrained TC and TE tests on NC Hostun sand. In thesedrained TE tests, (Tl( =400 kPaE :0le2 4 6 8 10 l' 4 16 IS 70 '1,*E, * lO15n n.Absoiute value of irreversible shcar strain, =1"F g 17 a) R l,,*'1; and b) c.*,To"our -s r]db)Drail L'd TE'S 05>:'=',ilo, l()vhen OCR= 1.0 and ,-OOkPa when OCR=2.0.(T '= 2(X) ki)a OCR= 2 efrom s*=*1 O Eo 2e *,2 4 6 8 10 12 146 IS20 1.Absolute value of irreversible shear strain* f (9., )Fig. 19. a) R- i}"'! and b) s::r"i relations from a ML TE testwith strain rate changes (To_voura sand, OCR=2, a ; =200 kPa)In the drained TE tests, R=(Tfl(T is equal to (Tr(/(T(while y*'= e: - e h' is negative. Other different test conditions bet¥veen the drained TE and TC tests are as follows:effecti¥'e confining pressure, p' = ((Tf + (7i + (T )/3 =((T( +2(TtO/3 is ((T +2a )/3, ¥ 'hich increases during1) Ovel'consolidation: In drained /1L TC, the meanML. In drained ML TE, p' Is (a +af)/3, ¥vhich '1KIYOTA AND TATSUOKA678o 084. o35elOzHostun-s Jldo 068ea I o ,30) 5hIOStliM Sallde);:!'E,!lO[].'o 04･ ii/ O 02S. ! lO*,ll OEa oO20-O 025N To 23. D,2Jned TC'. c. T'= 400 kP-O 04E,= O 0 25 9 irnirL E from E,,,*10 to 20 ,,oJ*J *-O OGI!/C!Test 3. TC-OCR= { O. c .= 400 kPil_ = O a 14CTest 4. TE-OCR= I (}. CF = 400 kPa. = a {) 75L¥=Hosturhsa'rd3.0O 08b)O ol10erO10100Ratio of iir shear strain rates before and after a step changee,flO: rr l:fr"! 20'e)ot*Fig. 22. Relarionslvips bet¥ een !fR/R and log (/:･fl"/, I'*F*'*.) for ¥_ 'CE, "I:sHostun sa:nd in TC and TE;> iO¥. 'o 23. DrainL:d TC. (;*'=E iOv>+,= O 0125 9s;TrirLfrom(}O kP2) Illherent Anisotropy: The direction of (7f is or-* *lO Io 20 **: OOthogonal to the direction of the beddin*" plane (i.e.,o l6 8 10 12 14 164gthe horizontal direction during specimen prepara-20tion) in TC tests ¥vhile it is in parallel in TE tests.I･reversible shear strain. T ("/*)'*Fig. 20. a) R- i *': and b) s.*,!iy"I rela:ttons from a ML TC testlvith strain rate changes (Hosiun sand, OC_R = 1, or= 400 1 Pa)40e 3)e30c'HosEun-sandEa) lOEl: 15oN. to 24. D Jlcd TIE, = O Oi25 9 jmjrLe400 kPthat, with the respective sand type (i.e., Silica No. 8, Toy-2 5oura and Hostun sands), the P values obtained based onthe R- I yi*1 relations from the corresponding drainedHOS u;1-sandb) E=]tcl o )//E iloTC and TE tests are similar (c.f., Table 3). These resultssuggest that the fi value evaluated by dr'ained TC tests,¥twhich is the most popular triaxial test method for sandt'and **ravel, can be applied ¥vithout si*･nificant modifications to other general triaxial loading conditions.It may be seen by rigorously examining Figs. 10, 16 andF:10o yc;>>c,/lel/ No 24. Ds ned T-OO22 that the ft value is slightly higher in the drained TEtests than in the drained TC tests under other¥vise thecF";;; 40() kP(Ef o.0125 9tJrnirL , from r !lo te 20 ,,:o2 4 6 8 102 14 16 i8Absolute value of irre¥*ersible shear strain,Fi('.- i yi* I relation is basically similar bet¥veen the respec-(Hostun sand). It may be seen from Fi_ s. lO, 16 and '_2* fil)m E!lO te 20 *:: *0.51 .O in the TC and TE tests, respectively.It may be seen fr'om Figs. 17 through 21 that the R = crf /viscous property in the drained TE tests is also of theTESRA type as in drained TC tests.The A RIR-log { i*). **,/( i') ,f"'} relations fr'omdralned ML TC and TE tests are summariz,ed in Fig:. 10(Silica No. 8 sand). Fig. 16 (Toyoura sand) and Fig. 22i _Ol:(Tf)/((Tf - (T ), is equal to 0.0 andences that can be seen are due likely to the factors listedabove (in particular term 2). It may also be seen that theg,j r I oO . E lOg'parameter, b = ((Tti¥'e pair of drained ML TC and TE tests. Some differ-IQe.20u. 53) Interllrediate Principa/ Stress: The Bishop'scr2S$ 2 Oft * ' txrQ**same test conditions. As mentioned earlier, the stressstate becomes more overconsolidated during dr'ained TE,unlike during ML drained TC. Ho¥vever, it is likely that20 22/ , (9/ )21. a) R- i '*1 antl b) c:* iy"i relations from a ML TEwith strain rate changes (Hostun sand, batch B; OCR= l)testdecreases during ML. Therefore, the stress conditionbecomes more overconsolidated in terms ofp' durin_",_drained ML TE.the effects of this factor are insignificant, as mentionedearlier. It seems, therefore, that the possible factors forthis difference include; a) inherent anisotropy; b) the intermediate principal stress; and c) the stress parameter tobe used to define the rate-sensitivity coefficient. Withrespect to the last term, the principal stress ratio, R = (Tf /(T , may not be relevant to define exactly the same viscosi- Fi=VISC OSITY OF SA ND IN 'IRIAXIAL 'TESIS679},*/ " Iff"/ f ll/ll///>' * l.l/ l!c:; 1,4J':*vS 07/,:*//ll f_;･t/ ' '::$O O1lri'l":']":"i':'1'**' -O 7ceJ:J J - ;C :Fig. 24.-2 l30eE o::25151 O t,lO;20b)Proportional rule to obtain viscous stress for h) ;teretic YF relation8s lO>c1 o:SiUca sand No SlO:sE lO/E Iea)1 OsvS 15" O.5t'lllOt:.> l.Ov'pe 05)>)10i¥. 'o 8. DrainedC> :lic, cr.E,,= O 0125v400kP*mil losl Ocs O_from **,*lO to 20e);: OO-lO_//.l_/* IS3Toyour sand3OOE=ONo 20.e{),Je' -l ODTaine(1 C> :lic.8,= 0,01 251g+ fromlrreversible shear strain. 'f ,*(o/ )cr'= 400 kPa'mirf+"I O to 20 ,J*-i 530Fig, 23. Effects of step changes in the strain rate on the normalizedSilica send ¥. 'o S:1 5stress･strain relation from cyclic triax'ial loading ('1'o . oura sand)ty parameter for the drained TC and TE Ioading conditions, as discussed in Tatsuoka (2006).It may also be seen from Figs. 17(b) through 21(b) that::15OE*e'! lOlarger with a decrease in the strain rate in drained TE testsc iol OE¥* 'o 20. DTnjned C'Yclic. e,*= 400 kP Le':O_ "E = O Oll ' *nxil3t)>VISCOSITY IN CYCLIC TRIAXIAL LOADINGTest Resu!tsFigure 23 sho¥¥'s the results from the following threedrained triaxial tests performed at ( = 400 kPa on looseE fromflOt020 *0.0-3J-Olrreversible shear strain. Jl,( 1.)Fig. 25. Effects of step changes in the strain rate on the normalizedToyoura sand:stress-strain reiation from c .'clic tria, ial loading (Silica No. 8 sand,Test 1.･ the specimen was loaded from the isotropicai = 400 kPa)stress state (point O in Fig. 24) to a maximum stresspoint in TC (point A in Fig. 24) by primary drained TCtraversing the TC and TE stress states:loading at.Y (positive) =R - I in TC,= o (=0.01250/0/min). Loading wasreversed at point A to¥vards the minimum stress pointin TE, followed by another load reversal to TC Ioading. Such load reversal ¥vas repeated. b*, ¥vas changedstep¥vise many times.Test 2: the specimen was subjected to primary drainedTC Ioading at aii = a = 400 kPa.Test 3: the specimen ¥'as subjected to primary drainedvhere R = (Tf lcr= cr( Icrh;Y (ne*'ative) = I -R in TE, where R = (T /a = (71',1(7( (17)Y= O at the isotropic stress state, ¥vhere R = I .Despite that it is subtle, Toyoura sand temporarilysho¥vs a slight rebound in the volumetric strain immediately after a change in the direction of loadin*" from TCto TE (Fig. 23). This trend of behaviour cannot bedrained triaxial tests on Silica No. 8 sand. In Figs. 23 andobserved in Fi**. 25 for Silica No. 8 sand. This may be dueat least partly to extra axial strain incrernents (negative)by bedding error at the top and bottom lubricated ends of25, the stress parameter, Y, defined by Eq. (17) isintroduced to achieve the continuity of stress whenspecimen, ¥vhich are larger with Toyoura sand, ¥vhich iscoarser than Silica No. 8 sand. Another possible reason isTE Ioadin*' at (71" = ( f =400 kPa.Fi**ure '-5 sho¥vs results fr'om one of three similar".i"*iol 0t::the rate d8 :r.1 / ! dy i* ! (positive for contraction) becomesas in drained TC tests.b)-*_,.* 20 * !KIYOTA AND TATSUOKA680stress conditions are repeatedly traversed:o 08o 06Toyoura sandR ' = R * .g, (a)i*) (18)where R f= = is the inviscid principal stress ratio componento.04( 00that is to be substituted into Eq. (1 8) to obtain the viscous-* o ooloading, Rf* js equal to R , and Eq. (18) becomes thestress ratio component, R '. During the primary TC or TE-o 02-o 04:that takes place upon a step change in'o 4. DTained TE.00242No S DTainedCyclicThe relationship bet¥veen the inviscid stress ratio, Y *, andSilica No 8 sand Ao 04fo 02ooothe h reversible shear strain, y ', for the test resultspresent.ed above is schematically depicted in Fig. 24. Forf ccthe Yt - y'* relation, referring to Eq. (17), ¥ve obtain:Yf (positive)=R f_ I in TC_;Yr (negative) = I - R r jn TE (_'O)-o 02Nishi et al. (2002) proposed the follo¥vin*' method to:A-o 04obtain the value of A R + (Eq. (19)). That is, "the in¥'iscide N'o IS Drained TC. P= O 0272 *;-o 06', A R A RA R =R A g ( y*') (19)wlrl-o oso 08;::c (viscosity, the follo¥ving equation, ¥vhich can be derived.from Eq. (18), is assumed to obtain a sudden change in Re ¥*=03.DTainedTC, =001CX) i-O 06o 06orl'Inal equatron R R g ( i*). For the TESRA typea-o 08O Olstress ratio R * at point (1) in Fig. 24, for example, isobtained by substituting Yf= *<(Yf)1 at point (1 ') IocatedA ¥. 'o 19. Draine ! TE. = O 0304¥* 'o 20.2 .22. DrEined CycUc. = O 0223 iAOilOOORatio of irr. shear stTain rates before and af er a step chan_ e.'*..'! *j"*** / hel=**along the primar'v_ TE Ioading branch" into Eq. (7-0). Thevalue of (Yi )1. is obtained by the follo¥ving proportionalrule:(Y ) - (Y )1-(Y )A .(Y ) (21)Frg '6 Companson of jR/R Iog L(/ ")*Ft,*/(y")b,f"'*} relationsfrom drained ML TC, ML TE and cyclic triaxial tests of loose!'- (Y )B_(Yf)Atriaxial tests of loose Toyoura sand (Fig. 23) and Silicawhere (Y )A and (Yf)B are the Yf values at kno¥vn pointsA and B. It is assumed that, ¥vhen unloaded from point A(under TC stress condition) to vards point C (under TEstress condition), the incremental stress-strain relationfrom poim B becomes the same as the one in the primaryTE. Ioadin_"*. ¥vith a shift in the strains. Note that, inFig. 24, the hysteresis loop is not closed, as seen fromFigs. '-3 and 25. For this reason, the proportional rule,Eq. (21), which is more general than the Masing's secondNo. 8 sand (the test presented in Fig. 25 and the other t¥vorule, is relevant (Tatsuoka et al., 2003).tests) ¥vith those from the drained ML TC and TE tests.Some data points, typica]1y point a, obtained from thecyclic triaxial tests deviate largely from those from theML TC and TE tests These data points are those immedi-When follo¥vin*" the proposal described abo¥'e, inFig. 24, the viscous stress component, R , immediatelyafter the start of unloading from point A becomes thesame as the value at the starting point O in the primaryTE Ioading for the same irreversible strain rate, asspecimens of a) Toyoura sand and b) Silica No. 8 sandthat the Toyoura sand specimens ar'e more dilative thanthe Silica No. 8 sand specimens, as seen by comparingFigs. 6(d) and 13(b).Figures 26(a) and (b) compare the ARIR-log{( i').f***/( i*)b,f "} relations from the drained cyclicately after load reversal vith a change in the sign of'*.The deviation tends to disappear as the loading continuesin the same direction.It is seen from the above that Eq. (5) (for the isotachtype), which is R =R*･g.( i*) in the present case, andEqs. (7) and (16) (for the TESRA viscosity) should bemodified to properly describe the viscous property underunloadin*' and reloading conditions, or generally undercyclic loading conditions, in ¥vhich the sign of irreversibleaxial or shear strain rate is changed repeatedly.obser¥'ed in the experiments. Moreover, the ¥'iscous stresscomponent, R ', at point B, ¥vhich is reached by unloading from point A , becomes the same as the value at pointB' during primary. TE Ioading, at ¥vhich R i (and thereforeYr) is the same as point B. Then, the viscous stress com-ponent, R', when unloading continues from point Bto¥vards point C becomes the same as the one for thesame values of Rf and i* during primar)' TE Ioading.Consequently, the viscous stress component can becomecontinuous ¥vhen the stress state returns from an unload-Modlfi cationsNishi et al. (2002) proposed the follo¥ving equation todescribe the isotach type viscous stress component undercvclic triaxial loadin conditions in which the TC and TEing (or reloading) branch to a primary loading branch.The same rule as described above is applied to other subsequent unloading and reloadin_9: branches.Figures 27(a) and (b) compare the relationships ,¥'1SCOSITY OF SAND IN TRIA¥lAL TESTSTo)L ur;O ri.SO 06sand 1makes point a deviate largely from the relation for the1liR=AR (negative). On the other hand, as (Y)1 isO 04a : 1O 02C:O (Tf)negative, and so is R*. Then, the stress ratio, lR-/R*,becomes positive, vhich makes point a located similarlyas the relation for the ML TC* and TE tests in Fig. '-7(a).-C) O-O.()4lvlL TC and TE tests in Fi :. '_6(a). As the value Y at pointa (i.e., (Y)1) is positlve (under TC stress conditions),)hl681=: = e No 3 Drained Tc p'==-O O(,:s'O4 Dri l)2( {] lnedTE P=00242 jos.Drainetic)clic'=(1'ois9It may be seen from Figs. 27(a) and (b) that the scallngrule (Eq. (21)) together vith the sign rule (Eq. ('-?-))appear to be relevant for the c_vclic triaxial loadin_",_conditlons traversing: the TC and TE stress conditions tobecome the same relation as the ML TC and TE ioading:*O OSO.OSconditions.One may consider that the ¥'iscous stress componentO 06during unloading or reloading is obtained only byproportionally scaling the total stress (cr = a r + (T ') and 8 i*O 04relation. In that case, the measured stress jump, A R, isO Olflscaled do¥¥'n by a factor of {(Y' )l-(Yf),A}/{(Yr)B_(Y')A} (smaller than unity) bef'ore being plotted inFig. '-7. This ¥vay of sc.aling makes the data morescattered than the plot presented in Fig:. 27. It seemsO OOC :-O Other'efore that the scaling of the viscous stress componentis not necessary.-O 04-O 06-O OSO1O O1iOlSUMMARY OF VISCOUS PROPERTY OF1 OORatio of irr. shear strain rates before and af'ter a s ep changeGRANULAR MATERIALF o '7 Compa:nson of J R /R*-log {(};i') /(1}i')E ,f< *fl relations*rl** ' '* '*from drained ML TC, ML I'E and c .'clic triaxial tcst of loosespecimens of a) Toyoura sand and b) Silica No. 8 sand'The follo¥ving facts can be reconfirmed from Table 3and Fig. 3:l) Thevalue is essentially independent of loadin_ ._method (PSC, TC, TE and cyclic triaxial).'_) These ft values of' the three different sand types arevery similar to each other.bet¥veen the stress ratio, AR-/R= <, and log ((y='),r* ,l3) These p values are comparable ¥vith those of otherf ,rl'-*"y(*Ib**i*) ,f,,,* } from the same data of ML TC and TE tests andcyclic triaxial tests presented in Figs. '-6(a) and (b). Thefollo¥ving tlvo stress parameters that are different fr'omt.hose in Flg. 26 are used in Fig. 27:1) AR-, Ivhich ha¥'e the same magnitude as AR (themeasured jump in R =(7f/a upon a step change inthe strain rate =A R ') and the same sign as A Y; i,e.,Fig. 3), except for' a relati¥'el}, high¥'alue of crushedconcrete ag regate.The parameter rl of the deca} functron gd .*,() *')(Eq. (8)) defined in terrns of },* for the respecti¥'e test con-dition ¥vas obtained by fitting Eq. (8) to the respective seg-change in the strain rate in all the lvlL TC and TE tests.'hen (Y)j >0 (TC stress conditions)The values of /･1 in each test ¥vere essentially independentAR=-AR= iYof th_e shear stress level ¥vhere the strain rate ¥vas step¥vise¥vhen (Y)1 <0 (TE stress conditions) (22a)2) R*, ¥vhich ha¥'e the same magnitude as the scaledstress ratio, for example, (R)i, at point (1 ') in Fig. 24and the same sign as (Y)1. (Eq. ('-3)): i.e.,chan_"*ed. The aver'age ¥'alue of' /'1 f'or each test conditionar'e listed in Table 3. It was not possible to confidentlye¥'aluate the values of rl dur'ing the unloading andreloading branches because of relatively small viscousstress components. It may be seen from Table 3 that thevalue of rl is similar among the three sand types. TheR* (positive) = (R)1, = (Y)1 + 1.0¥'alue of rl is slightly larger (i.e., a slightly slo¥ver rate ofvhen (Y)1. >0 (TC stress conditions)decay) in TC than in TE, Ivhile the efi cts of OCR are¥'er_v small.R* (negati¥'e)= - (R)1, = (Y)] - 1.0(2?_b)) ･ /, ** , + *i***For example at point a in FiO 23 (( + )b,,f*-=(,i')･ /( i')b,r.,'* 100 and A R is negatrve* * **ft**vhile R is positive. So, the r'atio A R/R is negative,po¥vder of' Fujinomori clay and kaolin (presented inmental R o /(7 i yi'j relation follo¥ving each stepAR-=AR=1]Ylvhen (Y)i, <0 (TE stress conditions)granular materials and compacted o¥'en-driedvhichCONCLUSIONSThe follo¥ving conciusions can be derived from the testdata and their analysis presented above: KIYOTA AND TATSUOKA6s21 . A fine uniform relatively angular sand, Silica No. 8sand, exhibited nearly the same stress-strain relationsin monotonic loadin_ : (ML) drained triaxial compres-RF,FF.RENCESl) Anh Dan> L. Q.. Tatsuoka, Fand Koseki, i. (2006): Viscoussion (TC) tests at constant strain rates that ¥veredifferent by a factor up to 200 under other vise theeffects on the stFess-strain characteristics of gravelly soil in cirainedsame test conditions. On the other hand, the de¥'iatorstress exhibited a significant jump ¥vhen the strainrate was changed step¥vise during other¥vise ML at aconstant strain rate, ¥vhile significant creep strainstook place during drained sustained loading at a constant deviator stress. These apparently contradictingtrends of loading rate effects can be explained in a unified ¥vay ¥vhen based on noticeable decay in a gi¥'enviscous stress increment ¥vith an increase in the irreversible shear strain (called the TESRA ¥'iscosity),2) Aqil. U.. Tatsuoka, F., Uchimura. T., Lohani. T. N. .. Tomiia, Y,and ¥1atsushima* K, (2005): Strength and cieformation characteris-as have been observed lvith To_voura and Hostunsands in the previous studies.2. With Silica No. 8, Toyoura and Hostun sands, the¥'iscous stress increment decays ¥vith an increase inthe strain (i.e., the TESRA type viscosity) in the lvlLtriaxial extension (TE) and cyclic triaxial loadingtests in the similar vay as the lvlL TC tests.3. The rate-sensit!¥'ity coefficients, fi, for the relation-ship bet¥veen the pr'incipal stress ratio, R=(Tflcr ,and the irreversible shear strain, y**, ¥vhich representsthe viscosity of a gi¥*en material, evaluated by the MLTE tests lvas very similar to the ¥*alue e¥'aluated bythe lvlL TC tests. lvloreo¥'er, in both TC and TE tests,the effects of overconsolidation on the fi ¥'alue ¥vereinsignificant. Furthermore, nearly the same P value¥ 'as obtained from cyclic triaxial tests ¥vhen relevant-ly scaling the stress parameter and redefining the signof the stress jump. These results suggest that therate-sensitivity coefficiem, fi, obtained by TC testscan be applied to general triaxial stress conditionswith minor modifications ¥vhen necessarv.4. The values of fi of the tested three types of sands aresimilar to each other, ¥vhile they are also similar tothose of other types of sand and gravel as ¥vell ascompacted oven-dried clay powder having largelyriaxial compression, Ceorec!1. re.st. J . AST*tif 29 (4), 330-340ics of recycled concrete aggrega e as a backfi]1 material, Soi!s anc!Fotinda!ions 45 (4), 53-723) Deng, j. and Tatsuoka. F (2004): Ageing and ¥*iscous effects on thedei'orma ion of clay in ID compression, Pr'oc. GeoF!'ontiel' 2005r_ongress. Geolns[inlte, ASCE, Austin. Texas. GSP 13g. SileCharacterization ar d'lodeling (edsby(ayne el al ).4) Di Benede o, H , Tatsuoka, F and Ishihara, h,l (2002): Timedependent deformation characteris ics of sand and their conslitutive modeling, Soils and Founclations, 42 (2)* 1-22.5) Di Benedetto. H., Tatsuoka. F.. Lo Presti. D , Sauzeat. C_ andGeoffro¥'. H, (2005): Time effects oTthe beha¥*iour or geomaterials,Keyncue lecture, Proc^ 3rc! Int. Synlp Defornla!!on C_ haracler!st!csof Geonlalerials. IS L_von 03 (eds. by Di Benedet o et al.), Balkema,Sept. 2003 2, 59-123.6) Di Prisco. C.. Imposimato. S^ And Vardoulakis, I_ (2000):,Iechanical modelling of drained creep triaxial les s on loose sand,Giolecllniclue, 50 (1), 73-827) Enomoto. T , Tatsuoka, F . Shishime, ,1., Ka¥vabe, S, and DiBenedetto, H (2006): V}scous properly of granular material indrained triaxia] compression. Proc. Geo!ech. Sy'mp Roma (to appear).8) Fukushima, S. and Ta suoka, F (1984): Strength and deformaLiolcharacteristics of satura ed sand at extFemely lo¥v pTessures, Soi!sanc! Founcla!ions, 24 (4), 30-4S.9) Golo. S.. Tatsuoka. F . Shibuya, S . Kirn, Y.-Sand Sato, T(1991): A simple gauge for local small strain measurements in thelabora orv, Soi!s anc! Founc!ations= 31 ( ), 169l80_IO) Hayano, K., ,Iatsumoto, ¥. I., Tatsuoka, F. and Koseki, J (2001):E¥'alualion of time-dependem deformation property of sedimemar) soft rock and its constituti¥'e modelling, Soils and Foundarions,41 (2). 21-38l l) Hiraka va. D^ (2003): Stl dv on residual deformation charac. eristicsof geosyntheric-reinforced soistFuctures, Dr. of Engineeringrllesis, University of Tok.¥'o (in Japanese).i2) Hoque. Eand Tatsuoka, F_ {1998): Aniso ropy in the elasticdeformation of ma erials, Soi!s ancl Foundations, 38 (i), 163-1 7913) Hoque, E and Tatsuoka, F^ (2004): Effects of stress ratio on small-slrain stiffness duriug lriaxial shearing, Gdo,echnique, 54 (7),429-439.14) Ho¥vie, J_ A.. Shozen. T_ and Vaid, Y. P. (2001): Effecof agein_",_different particle sizes (except for recycled crushedconcrete).on stiffness on loose Fraser Rover sand, Ac!vancec! Laborclrolt}'Stress-srrain Tes!in*" of Geomaterials (eds_ by Ta suoka et al.),5. The decay manner of viscous property ¥vith an15) Kiyota, T , Ta suoka, F. and Yamamuro, J. (2005): Drained andincrease in y** is similar' among the three differentundrained creep characteristics of loose saturated sa d anci theirrelation, Proc, GeoF]-on!ier 2005 Con*"ress. Ceolnstilu[e. ASCE,Ausiin, Texas, CJSP 138, Site Characterization and ¥= iodeling (edssand types. The decay rate in the ML TC tests isslightly smaller than in the lvlL TE tests. The effectsof overconsolidation history are ¥'ery small.ACKNOWLF,DC.F.MENTSPart of the experiment on Silica No. 8 sand and itsnumerical simulation ¥vas performedvith the help of lvlr.Alan Ezaoui, from the D partement G6nie Civil etB timent, Ecole Nationaie des Travaux Publics de l'Etat,France, when visiting the Universit_v of Tokyo. The helpof the staff of the CJeotechnica] Laboratory at theUniversity of Tokyo is greatly appreciated. Financialsupport from the IMinistry of Education, Culture andSport, Government of Japan is greatly ackno¥vledged.Balkema. 235243-by,1aynet al.).6) Komoto, N . Nishi, T . Li. J, Z,. and Tatsuoka. F (2003): Viscousstress-strain properties of undisturbed Pleistocene clay and itsconstitutive modelling, Proc. 3rd Int. S;*nl. Defonna!ion Characierislics of Ceomateria!s. IS Lyon 03 (eds. by Di Benedetto e al.),Balkema, September, 2003, 579-587,17) Ku¥vano, R. and , ardine, R. J (2002): Ort measu ing creepbeha¥'iour in granular materials through triaxial esting, CanGeotech. J., 39 (5), 061-l07418) Lade, P V_ ar d Liu, C_.-T. (1998): Experimentai sludy of drainedcreep beha¥'iour of sand, J. Engr*". * lech, ASCE, 124 (8), 9'_920.19) Lacie. P. V. and Liu, C_ -T. (2001): ¥. ,Iodeling creep beha¥'iour ofgranulaF materials, Con7puter Alerhoc!s anc! Adl'a,7ces fnGeomec!1anics (eds. bv Desai et al.), Balkema, 277-284,20) Li, J.-Z , Acosta- ,iartinez, H , Tatsuoka, F^ and Deng, J -L(2004): ¥riscous property of soft clay and itS modelling, Engineering VISCOS韮TY OF SAND正N TRI．へXIAL TESτS683 P’ヤα（漉θα1∼ゴPθ1プ01’〃∼θ∼κ・θoゾ5ψ0θρ051δ，P1｝oc、∫SO∫αんσ2004．351Taζsuoka，F、（2006）：五nelas芝ic delomlation characteris［ics ol 1−6 geonlateria1，Speci＆！Leculre，So1！S’1θ55−5〃て11刀8（∼1∼【1ylo1∵早、／（∼‘15ま’ヂ（∼一21）Ma正sushita，M、，TaIsuoka，F、，Koseki，」、，Cazacliu，β、，D1 η∼θ’π，イ、／0ゴθ1〃∼9α刀6！．41rαひ写Z5，P1’o（・、（9θo∫θ‘1r，εy〃1ρ、（eds，by Ling Benedet｛o，K．and Yasin，S，」、M、（1999）：τime effecζs oo【he pre−peak de妻ormadon properζies of sands，P1’oc、21∼ゴ／1∼∼、Co尺ズ ρ1捗搬’∼正！1｝θρ401’〃∼α∼’on Chα∼ααθ1一’5’ic5毎磁01∼副θ1”α15，∫S ro1｝ノno’99（eds、byJamiolkowskieta1、），βalkema，1，681−689、22）Mejla，C、A、，Vaid，Y、P．aKldNegし！ssey，D、（1988）：TlmedepelldeK1〔 et aL）．March16−17，2006，Roma，36） Tatsuoka． F．， N韮olenkamp， ヂ．， Tor§，T、，and Hillo，丁．（1984）＝ Behavior of lubrication layers of pla［ens in elemen｛｛es｛s，50〃5α1∼4 Fα’！1ゴα1’o∼∼5，24（1），IB−i28、37）Tatsuoka，F、，Sa芝o，丁 ，Park，C．一S、，Kim，Y．一S、，N・1し監kabi，」、N、and behaviourofsalld，P1’oc、11π、Co’アブRhθ010＆γα11グSo〃A1θchαノ1’ぐ5 Koha［a， Y、 （1994）： 汽leasuremen芝s of elastic properζies of （eds、by Keedwem，εlsevier Apl）11ed Science，312弓26、 geomaterialsilllabora［or｝’compressiomests，Gθαθご1∼．7θ甜、／、，23）Murayama，S、，Michih1ro．K、aPdSakagami，τ、（1984）：Creep characterisτics Qf sands，Soπ5α1κノ」Foε〃∼ゴαず’011∫24，（2），1−15、 ASTM．17（1），80−94、38）Ta〔suQka，F，Modoni，G、，J1ang，G、一L、，A君猶Dall，L、Q、，Fiora，24） Nakamura，Y，，Kuwano，」．and壬｛as翻imo乳o，S．（｝999）＝Smallslrain A、，八玉a｛sしKs員ita，NI、alld Koseki，」，（1999a）：Stress−s芝rain behaviour stlf責ness and creep ofτoyoura salld Ineasured by a ho賛ow cylinder a【sma！ls【raiRsofunboundgra且ularmaterialsandl￡s！aboraエory ＆P［）ara毛us，1二》roぐ、21∼‘ノ∫’1r．Co’1ゾニPヂθ一ノi【z〃‘”ぞ0（グb〃nα”01∼C1∼α1’αc一 老ests，Keyl10teLecture，P”oc、駒1甲ん∫hOρo∼』、／0ゴθ1〃n9α1∼4 ∼θノ’加（50∫Gθ01η醒θ廠Z∫，Tor1no，1999，Balkema（eds，by ．44v醐Cθゴτθ5”ノ19．砂U1めα’1∼ゴG1糊ε’1σノー」、愈πθ舶Z5，Ial1瞭y Janliolkowskiαal．），玉・i4玉一148，25｝Naw1r，9，，Kuwa蹴o，R，aad Tats襖oka，R（2001）：Eぼec￡s of s甘ess 21−22，1999．LjsbQa（eds、by Correia），Balkema，17−61．39）Tatsロoka，F．，∫ardille．R，J，，LQPres【i，D、，DiBenedel【o，｝｛、and paIh on the貝ow rule of sand in triaxial compression，〆蓋ゴγ、五αδ． Kodaka，丁「、（1999b）：C豹arac【er1sing ｛he preぜailure defor：11aζion Sr1で55−S〃w〃1 7’θ5’、 （3θ01刀α1θ1ゾαZ∫ （eds． by Ta芝suoka e【 ＆1、）． properdes of geoロ1aterlals，Thenle Lecture for【むe PlePary Sessioll Balkema，287−294、 No， 1， PI−oc． λ！∫「 ∫C Sル1F五， Ha且1burg， September 至997， 4，26） Nawir，棄｛．，Ta［s目oka，F、and Kuwa【10，R （2003a）＝Experiτnell芝ai 2129−2164、 evaluaτlonof由eviscousr）ropert1esofsandinshear，501Z5αノ1ゴ40） Taζsuoka， F．． San［ucci de N正ag1s乳ris． F，， 汽｛omoya， Y． and F加η面∼’oノ∼∫，43（6），B−31、 λ1a「uyanla，N，（1999c）：正so【ach beha、一iour of geonlalerials and註s27） Nawir，H、，Ta｛suoka，F ，and Kuwano，R、（2003b）：Viscous e鐸ects nlodeまi員9， ρroc． 2ノ∼ζノ ∫’∼’， ≦ミw1∼ρ． P’ぞ一∫α’1i’”8 ∠）（ヅ10〃1∼α∼’01r on ［he shear yielding charac【erisζics of saud， So’Z∫ α∼1グ Chα1ηαe’一Z5∫’c50ゾGθo〃∼α∼θ’｝’‘∼∠∫，1S roヂ’ノ∼099，Balkema，Rαter− ヂoμノ∼面”o’∼5，43（6），33−50、 dam，1，491−49928）Nishi，T、，KQmαo，N．and Tatsuok＆，F，（2002）：Simし瓢ialion of4至）Tatsuoka，F，，Sanしucci deMagisこris，F、、Hayano，K，，Momoya，Y， deformationduringcydicioadingofsoilbythegenerai！hree− andKosek1，J （2000）：Somenewaspec【sofτimee貸ec【son由e compo汽e撚modei，Pヂoc、37’1∼／ρ1∼、蜘’、Co厭、Gθαθご1∼、五ン’91召、， s【ress−s【ra1nbeha、’iourofst潰『geo猟aterials，KeynoteLec［ure，7hθ （Osaka〉JGS，（in Japanese）． Gθo’θd∼’∼’cεo∫κα1’‘1So〃∫一Soゾ’Rocん5，Pヂoc．21∼4／1∼r、Co’ゾκσ1’ゴ29）PbamVaΩBang，D、andDi Bellede【【o，脛、（2003）＝E昼ectofs［rain So〃5 α11（ノ 50ゾ’ 1∼oぐん5， Napoli， 1998 （eds． by 狂vangelis【a alld ra芝eo“由ebehav1ouroゼdrysand，P∼oc、3’マ4∫1π．⑤v1刀ρ． Picarelli），Balkema，2，重285−B刀、 P⑳1甲1刀α”o〃Chα1｝ααθ1｝’∫flc50ゾGθo’∼∼α！θ’ゴoZ5，∫5五3’oノ∼03（edsby42）Tatsuoka， F．， Uc騒imura、T、， Hayano， K、， Di BeaedetLo， 9．， Dl Benedetto eこa1、），Balkema，Sep韮、，1，363−373． Koseki，」、and S1ddiquee，M、S、A，（2001）1Time−dependent30）Samuccl de Maglstris，F「．，Kosekl，」、，Amaya，M．蕪amaya，S，． defOrmatiOn CbaraCter1SliCS Of S｛i貿 9eOmaξer1alS ln ea黛ineering Sato． T and τa｛suoka， F．（豆999）：A triaxial tesεing syslem to prac薮ce， ｛he Tわeme Lecture， Pノ’oぐ，2／1ゴ ／’∼∼、 Co1りく、 P1｝θ一ゾi‘7’々‘rθ evaiua【estress−strainbeilaviou罫ofsoils forwidera鷺geofls1rainand 0401’〃∼α！’01∼C11α1’ααθノ”5”C30ゾGθ0〃∼‘”θ1ゾαZ5，TOI−lno，1999（eds． s芝rain ra毛e，0θo’8c1∼、7を∫’、∫．，ASτNi，22（1），44−60． by Jamioikowsk1el al．），Baikema，2，三161−1262，31）Siddlquee，M．S、A、，Taエsuoka，罫、andτanaka，T．（2006）：FEM simuiaエionofζheviscouse窪ec【sonヒhestress−strainbellaviourof43）Tatsし…oka，F，，Isllihara，M、，Di Benedetto，H、and Kuwa鳥Q，R， sand in Plane strain coτnpression，So”5α’∼ゴFヒ）μ11ゴα’ioη∫，46（1）， geoma￡erialsand由eirsimulation，So〃5αηゴFα11∼面’ioノ∼5，42（2）， 99−108、 103−129、32）Suk垂je，L．（1969）：R1∼ε0109’cα1〆i5ρθα∫oゾ50’1A4θご1∼α’∼ic5，酵〆’1の呼一 （2002）：Time−depende凱shear deformation characteristics of44）丁撮suoka， F、， 氏lasuda， T． a鷺d S王ddiquee， L王． S、 A． （2003）： ∫1∼fe13c1θ1∼cθ，Londo“、 氏・lodell霊ng t！1e stress−strain behaviour of sand in cyc巨c plane stra1n33） Tatsuoka，F．（2001）：Impac｛s on geotecllnical engineering of several ioad1ng，Geo｛echnlcaland熱vironmenξa！Engineering，滅Gθαθc1∼、 reCent§ndingSfrOmlabOratOryStreSS−StraimeStSOngeOmateria1S， 五η、”1−oη五’∼grg，ASCE．茎29（6），June1，450−467． 2000Burmister Lecture at Columbia University，Gθo∫θぐ1∼1∼’c3、戸α45）Yamamuro，1、A、and Lade、P、V、（1993）：E貸をc【s of strain rate on 1∼oα4∫，Rα11万σcん∫α’1ゴ勲πh5微伽ノで5（eds．byCorrelaand 玉nsζabili【y of granu藍ar soi王s， Gθo’θc11， 7セs’、 ノ．， AST∼正， 16 （3）， Brandle），Balkema，69一王40、34） Tatsuoka，F．（2004）：E貸セc｛sofviscous proper盛esand ageingon直1e 304−313． stress−strainbehavioufofgeomaζerials．Pヂoc、G1−／σS駒1凹ん∫hoρ （eds、by Yamamuro and Koseki），ASCE Geo［echnical SPT，1｛0 air−dr1edmicacioussandinplanes【raincompressioΩ，P1’oぐ，／ρ’∼、46） Yasil1，S，∫．｝〉1．and Taしsuoka，F．（2003）；Viscous property of a雛 N竹∼、Coπゾニ（フθo’ε【ゾ1，だn9ヂ9，Ak1t＆．Jap＆nese Geo｛ec鼓nical Societ》・． 684KIYOTA AND TATSUOKAAPPENDIXA猟bleA玉。L量sIofβv幽esfromloadingleslsw謎hslepchangesinthes重mlnrate，presen｛edinFi9・3N瓶aIeriaiGrading propertiesOr1磁nalCrushedsandstone：Chiba grave！05亀）竺7、8mm，（molstPmユx漏39．6mm，compaαec玉）Uc竺1L2，De職s註yb∼VeI condltio鷺MoiSt（、私胤5％，S，謹77％）Dense，θ罵0．19（two Range ofε、Test me出od （％／m三n）Ref．βDra玉ned TC a覧 0．0006− 0．0335σ1沖490kPa α06％／miΩAnh Dan eτal．（2006）specimens）G、繍2．71Nlodel Chibagrave1A（air−driedcompaCted）Crushed saadstone：Ai卜dried050竺0、8mm，e筥0．584Dralned TC at O．008− 0，0244and O．556σ貞郡40kPa α00008％／min鍼玉rakawa（2003）（ρ灘L760uに漏2。1，and1。7709／cm3）0ロ葦轟x讐5．Omm，（3、漏2．74，θロ撚皿0．727，θn，iロ漏0．363Ir｛ostun sand（batch B；air−Pluviated）Quartz甲ric員Air−dr玉ed0、漏2．65，QuartZ−r1cllDi Beηede柱o et al・Alr−drledSaturatedθ￠罵0．72Dra玉賑ed TC aζ 0．006− 0．024P島am Van Bangand O。93σ‘竺80，200％ 0、6％／min400匙Paand D玉Benede鷺Oθコ0、658sub−angular，Pずα18mm，U3L64，Al卜driedG、謹2．65，（2003）Dra玉ned PSC at O，000108− 0。0219！Vlatsusl1髭a et al．σll筥400kPa 1。08％／min（1999〉τatsuoka e【al．θ、漏0．674Drained PSC at、0．004− 0，0207and o、673σ卜30 0．4％／mln ando．0226 （2004）and80kPaθnlax瀟0．99，θロ1111筥α62τ〉laISush髭a et a1、（1999）and（2002）θFn…＝1罵0．55ToyourasandDrained PSC at O．00025− 0．0219σ孟漏392kPa O．259も／mlnP5。漏0、31mm，u。讐L94，θ醗該x讐0．95，（a1r−pluvia【e（i）θ。讐0．698and O。700sub−a澱gular，Alr，dr1edθ、漏0。633−0。649Drained TC at O．00008− 0．0269H1rakawa（2003）σ孟罵40kPa O．008％／minS＆turatedθ讐0．658DrainedτC aI O．00108− 0呼0205σ≦罵200kPa LO77％／minSatura覧edθc讐0、605−0、925and a玉卜dr1edMa置susbitae【a1、（1999）Dral鷺ed TC at O。0008− 0。0242暮a、vir e芝 al．σ‘讐玉00− o．12％／m沁（2003a）Dralned TC at O．00125− 0。0272τbepresentstudy600kPaSHica sand0ず0．077mm，No、8U。識2，43，（alr−pluv玉ated）SaturaIedεC竺1，B5σll竺400kPa O．25％〆mlnθ、露2．655，θロ13×質L335，θ臨罵α73，Janlu隷a0∫。竺α16，river sandu。漏L99，（air−piuviated）FC筥7％，Alr−dr1edθo竺0．フ75Drained PSC a【 0、00125− 0．0273and O．821σ‘竺100 α125％／ml厳Yasln et a！、（2003）and400kPaG、瓢2．7，θm：Ex司．173，θ，，，in盤0．690C田shedconcretea黛黛re黛ateP50漏5ふ65，（w司．6．69， 1759／cmG、漏2石5，17、349も，（ρd）ほ、誌N需1．789／cm3F癖nomoriclay31MQist ρd漏L72・3FC讐王、2−2．玉％，0ず0．Oi7mm，Uc罵玉0，P1讐33，LL漏62％Drai資ed TC O、001− 0．0536Aq簸et al．（2005）σ孟＝20kPa O．1％／m1nnearly讐、t’。P己筥L69％A1r−driedθ。盟LO93Drained TC飢 0．002− 0．0444Lietal．（2003）σll漏77kPa α29も／m1n（脂竺4．29％，5，巳f漏8．09％）Air，driedθ。漏L202Drained TC at O．003− 0，0353σ孟漏80kPa Oβ％／mln（w轟r竺256％，S，．評4．68％）Kaoiin3卜05。望0、0013mm，AiトdrledPI罵4玉、6，い，ar讐03％，LL讐79．6動もS，、ユf漏0．5％）Ai卜dried（｝㌦讐α3％，θ。漏玉．38Dra呈nedτC at O．000046− 0．029σA漏王00kPa O．oo玉2？る／min（2005）θc漏L41Drai自ed TC a芒 0。000049− 0、030σ‘漏100kPa O．00B％〆ml鷺S，、ユf轟0，5％）1）Dengand TaτsuokaθC竺co践so玉idate謡vo玉d ratio．2）wユfandS「ほflmeas駄redaftereac蝕εesし3）Tlleβvalue a［ove鷺一dried state was inferred based o【｝［he respec【iveβ一S。relatiorL
- ログイン
- タイトル
- Preliminary Report on the 17 February 2006 Leyte, Philippines Landslide
- 著者
- R. P. Orense・S. E. Sapuay
- 出版
- soils and Foundations
- ページ
- 685〜693
- 発行
- 2006/10/15
- 文書ID
- 20950
- 内容
- .SOILS AND FOUNDATIONS Vol. 46. No. 5. 6S_1"-693, Ocl 2006Japanese Geolechnical Societ)PRELIMINARY REPORT ON THE 17 FEBRUARY 2006 LEYTE,PHILIPPINES LANDSLIDEROLAiN'DO P. OREN'SEi) and S ¥, UEL E.S 4 pU Avii)ABSTRACTFollowing days of hea¥'y rainfall, a large-scale landslide occurred in Southern Leyte Province, Philippines, buryin_",_almost the entire village of' Guinsaugon and causing the death of more than 1000 people. The landslide, ¥vhich occurredalong the steep slope of Mt. Can-abag in the middle of the province, mobilized large amount of rocks and debris ¥vithestimated volume of about 101 5 million m3. This paper discusses the results of the damage investigation conducted inthe ar'ea after the disaster, Ivith emphasis on the general features of the landslide and on the hydro-geological aspects ofthe disaster. Based on the obser'vations made from the field in¥'estigation as ¥vell as additional information obtainedfrom ¥*arious sources, the main causes of the landslide are identified, and several sources of potential hazards arepointed out.Ke¥_' words: landslide, rainfall, site investigation, slope (IGC: B3 IC4)be caused by future disasters.IN'TRODUCTIONAt around 1 1 A.M. on 17 February 2006, a large-scalelandslide buried almost the entire village of Guinsaugon,OUTLINE OF 1'HE AFFECTED AREASt. Bernard tolvn in Southern Leyte, the PhilippinesGeo!o*"ica! alrd Topographica! Settil7gLeyte Island consists of t¥vo political regions: Leytefollo¥ving days of heavy rainfall. The landslide coveredaround 500 houses and a primary school building,and Southern Leyte provinces. The province of SouthernLeyte, Iocated about 675 km southeast of Manila (seeresulting in 139 deaths and 30 injuries ¥vhile 980 people¥vere reported missing, including '-48 school children(based on the report by NDCC (2006) as of 5 P.lvl. 28February 2006). The disaster displaced 3,264 people andFig. 1), is characterized by relati¥'ely flat land alon*' its18,862 people ¥vere affected. The total cost of damage toelevation of 948 m above rnean sea level. An activeinfrastructure and a*"riculture is estimated at USS2.2rnillion (OCHA, 2006).To investigate this disaster, the authors undertook anocular inspection at the site durin*" 12-14 March 2006,volcano, Mt. Cabalian (elev: 945 m), is located near thesoutheastern tip of the island, about 6 km to the east ofcoastal area and rugged mountainous interior region. Thehighest rnountain in the province is Mt. Nacolod ¥vith anSt. Bernard town. This volcano could be a possiblesource of the thick ¥'olcanic materials presently coveringSouther'n Leyte.about four ¥veeks after the disaster. This paper outlinesthe preliminary results of the reconnaissance works, vithemphasis on the hydro-geological causes of the disaster.The general features of the landslide, as ¥vell as the mainfactors lvhich triggered the disaster, are also discussed.It is to be noted that although detailed information areMost towns in the province are surrounded by steepnot yet a¥'ailable and further investigation is necessary tomountainous ran**e as high as 800 m. Guinsaugon villageis located at the foot. of the north¥vest-trending mountainous range. Young volcanic rocks co¥'er the top ofthese mountains. The steep slopes are often planted withcoconut trees, the area's main crop. Ho¥vever, because ofunderstand fully the mechanism involved, it is believedtheir shallow root system, coconut trees are kno¥vn not tothat a quick dissemination of the important findingsobtained will help other resear'chers perform morecontribute to soil stability.in-depth investi**ation on this landslide. Moreover, sincesimilar disasters may occur in other parts of the world,active fault system ¥¥"hich transects the whole PhilippineThe Philippine Fault Zone (PFZ), a 1,200 km-lon_"*.archipelago from the Luzon Island in the north toMindanao Island in the south, traverses throughSouthern Leyte Province, including the town of St.such as in Japan, understanding the mechanism andimpact of this landslide can also assist geo-scientists,engineers and planners in mitigating t.he damage that willBernard. The locations of major fault lines in the region*) Associate Professor, Department of Clvu Engineering, Yamaguchi Universit.v. Ube-shi. Japan (orenseC･yanlaguchi-u,,ac.jp)ii' president, Infra-tech s),stems Consultants, Pasig Cit)', Philippines (sesapuay( ･ yahoo .com) .The mar uscript for this paper ¥vas received for revie¥v on April 24 2006; approved on August 4, 2006¥vritten discussions on this paper shou d be submitted before *¥4ay I , 2007 to the Japanese Geotechnical Society, 4-38-2, Sengoku. Bunkyo-ku,Tok)'o I 12-001 l, Japan. Upon request the closing date may be ex ended one month.685f OREN+SE AND SAPU686Yare sho¥vn in Fig:. )_(a). On the other hand. Fig. 2(b) sho vsthe traces of t¥vo prominent structures in Southern L,eyteas obtained from satellite Ima_"._ery: the north-north¥vesttrending Philippine Fault Zone and a north vest-trendingf'jLUZON,structure oblique to the Philippine Fault. From the'L:--. ;? .Jfigure, it is apparent that the site of the Guinsaugon':Maniri ..j'-)'(1:trT1l¥(landslicie is locatecl at the inter'section of these t vo fal.lltsi(La*'may et al., ,_006)..c¥r+Guinsaugon,*' Il' L. r"."}' [ '.1PiThe Philippine Fault mo¥'es at a rate of approximatelySt. Bernard(Southern Leyie)!,f '_*'.' '" l!2 to 2.5 cm per year (Bar'r'ier et al., 1991 ). Because of this,j ,1 i ;/L' ffc I' !'l'f!'_'*+*sf ' :"" ,, j,'cSouthern Le .*te can be considered as a highly seismicarea. According to data from the Mines and GeosciencesBureau (lvIGB) Region 8, the pro¥'ince has experienced_ Ifr" *' !'!1;9.: ('t .'*"_r'r' V]SAYAS"'f r"""iI ' !j"-hIl')!'!! '' __.1'Jcstrong earthquakes in 1907, 1948 (M6.9) and 1984! '-':' t(lvl6.4). Because of the numerous faults presem in thearea, the underlying rocks are badly broken or fragmented, making them susceptible to ¥veathering and erosion.r"i J _-' 'j--i MINDAijtAOI""- 2 re'i'! f/ , j"L, ri/r' '.1 1.],*As a result, the underlying rocks are ¥¥'eathered and havechanged to clay, resulting in thick surface soil formationin the area.l.r: *'.* -_ I' !o loo 2ao kmPig. l. IMap of the Plli!ippines showing the locaiion of GuinsaugonPast Disasters in the RegionSouthern L,eyte's natural and **eologic features make itsusceptible to landsliding and flooding. On 5th Novembervillage199i, heavy rainfall due to the passage of a typhoon(b )( a)_ :'1?: ir': 'iit{1:' ; {L ;"IT ;i'- ;'f :" ":1i:1 :'i;: ;x/):;f_ i'till:"i -: {{P';'" $ ';;i -r! "'t:1 ' :/ rf;" ;t'ta : *;'sle l "'jS' i '::E';i' /ii'*l ';Ii;. ,t {; tL * /: t /!: *+ -_''(' 1 ;1 ; ::;;::;;] fxf' //j;:i! 1'i(":;::j;i i;/i:/:{;'ti/tl:;i:t;:: Ii;;:!;;:;::il;il:j?::{::; !'{ '---i*'1****' - *'*' =(;ij;;.i v;::;le;'L:; :5tji;:irs;S ?i;; '_S _'/;; ^;;'* :*' s*{ri'- =s_,*/' :i :';'_:'i/';;"<:f' 'S 't ';L ' ' - '#?; 1$ ';iJ; :_; ;f=:1T': 'eIft'l'i; f 4i; :ti'i* i' it- :"_'t:< :i' !';/''i;Ifi. ' 'i I' ';aJ' t i'=r S''-LEYTE ISLAND'$ :'1':!: ? ' s';i!' :" :;i;f' ..**''*i//_! //;:;; ;:l'-' $i'':'ti'"s"':;': {"'GuinS ugon='s': t;;1' "I" = 'J ;'i ;'* '9_:'*s..*'', ;"'**f"::;''.,_...S''* **.*** " * ** ": , """""/"..=_._･*. f.r"sf'l/""*: f"'!^ /;i;! '_' '' 'i;;_ ' *';::,,' ,.'" #""' /;'. .t':.; :: ;i: ; ;: ; fr'Ii_ = _ l{' _' F f: ;;_''s!i! (=' 'i " ':. . tabalian Bay{ :j;1 : i st'_' :s:r'l'{'o5i O km*Fig. 2. Relative !ocation of Guinsaugnn landslide and (a) distribution of faults and trenches in the islan(1 of Le)'te (from iv. Iines and GeosciencesBureau) and (b) estimated location of fauits in Southem Le)'te based on Jh ,RS-1 SAR mosaic (original data from Earth Remotc Sensing DataAnah.'sis Center and modified according to Lagma et al., 2006) .2006LEYTE LAiNDSLiDElOOD9002501 seO20012eOE1 sO80e Sa:10eeOe =503QO o80GE 700- eoo500c> 4ao300:687200c:oooJan Feb Mar Apr May J n Jul A:Jg Sep Oct Nov DecMontho1 fI f 1 1 2!1 O a,20I f21oI f31Fig. 3. Average and maximum monthly rainfall intensities from1980-2005 (based on PAGASA data)Fig. 4. Dai!y rainfall from Ol Januan.'-28 Februarl. 2006 recordednear the landslide sitc (based on PAGASA data)caused flooding in Ormoc City, Iocated in the ¥ "esternside of' Leyte Island. The levels of the t vo rnain riveraverage monthly rainfall durin_g: the typhoon seasonsystems, Anilao and Malbasag, rose and spilled intosetrlements lying alon_ : the riverbanks (Vitug, 1993).a erage drum' the "driest" month (i.e. May) is 91 mm.For the month of February, the average rainfall is 275lvloreover, flashflood s¥¥'ept do¥vn from the hill adjacentto population centers. As a result of this disaster, morethan 4,000 people ¥vere killed and o¥'er '_.OOO more ¥verereported missing. Illegal log:ging ¥vas considered as themm. Overall, the average annua:1 precipitation in Otikonbased on a¥'ailable data from 1980-2005 data is 2545 mm.Records of daily rainfall obtained at the Otikon stationindicate that bet¥veen 8-i6 February 2006, the area vasmain culprit of the disaster, with hills above the citystripped of vegetation necessary to prevent flooding anddrenched by 687.8 mm of rainfall, with the peak dailyerosion.During 17-20 December '-003, Iandslides and debrisFig. 4). It lvas at this time that the landslides occurred insuccession in the nearby Sogod tolvn, as discussed belo¥v.flo¥vs caused by heavy rainfall resulted in death of 207people, mostly in San Francisco to¥vn, Iocated in a smallBecause of concerns regarding possible fiooding andlandsliding, some residents of Guinsaugon left theirisland south of the Leyte mainland. The landslidechanged into debris flo v and deposited huge volume of'soil in the area, engulfing hundreds of houses and otherhomes and evacuated to safer places. After this, rainfallintensity some vhat subsided, vith an intensity of 32.4mm recorded the day prior to the landslide. As a result,civil engineering structures (Sakurai et al., 2004). Rainfallthe people lvho sought refuge came back to their homesrecords fr'om PAGASA (Philippine Atmosphericto resume normal daily activities.(No¥'ember-January) is about 350 mm, ¥vhile therainfall of 171.0mm occurring on 1'_ February (seeGeophysical and Astronomical Services Administration)As mentioned above, the average rainfall in the areaindicate that 699 mm of r'ain f'ell in Southern Leyte withinDecember. Moreover, detailed investigation conductedf'or the month of February is 275 mm, indicating that the9-day rainfall (frorn 8-16 February) prior to the landslideof 687.8 mm is rnore than 2.5 times the monthly average.In fact, the rainfall intensity registered for the wholeafter the disaster sho¥ved that the geolo_ ,_ic structure in themonth of Februar_¥' 2006 was 970.8mm, the highestarea played an important role in causing the disaster.monthly rainfall e¥'er recorded since 1980, including thetyphoon season (see Fig. 3). It is to be noted that severea 3-day period ¥vhen the disaster occurred, almost threetimes the a¥'erage rainfall in the area for the month ofFollo¥ving the 2003 Iandslides, go¥'ernment _･._eologistslisted 82.60/0 of the Southern Leyte province as prone torainfall in the area normally ran between November andgeologic hazards, such as landslides (DENR, 2006).Accordingly, regional geolo*'ists have planned in JanuaryJanuary. Such unusual climatic chan*'es are broughtabout by the appearance of La Niha phenomenon, which2006 to include the to¥vn of St. Bernard as among theareas to be sur'veyed during the year for the plannedgeohazard map, which up to no¥v has only been done forselected urbanized and urbanizing areas in the countryis associated lvith above-normal sea surface ternperaturesin the West Pacific and stronger t.rade vinds. This patterncan significantly enhance rainf'all across the West Pacificregion.(such as Metro Manila, Baguio, etc.). Unfortunately, thelandslide struck before the plan got under¥vay.DESCRIPTI0_¥' OF 'I=HE LA_NDSLIDERainfa!! CharacteristicsFeatu/'es of the Lanc!s!ideC.limate in Southern Leyte is characterized by theabsence of dry season with a ¥'ery pronounced maximurnrain period occurring in the rnonths of' November tofoot of Mt. Can-abag, the 800 m high mountain rangetraversing the interior portion of the Southern LeyteGuinsaugon village is a farming village located at theJanuary. Figure 3 shows the average and maximumPro¥'ince. Based on CY 2006 municipal survey, Guinsau-monthly rainfall intensities from 1980-2005 as recordedgon villa*'e had a population of 1,857 residents and 3,_1by PAGASA rainfall station in Otikon, Libagon to vnhouseholds (Ramos,(about 4 km from Guinsaugon). It can be noted that theoccurred on the eastern slope of the mountain range and_006). The massive landslide V..2006 LFYTE LAN'DSLIDE''e' /30L-aII oljSubrnarine slides,! isiopes atfailure sites 'i o subaerial siides, 1j JLj ooca+e*H/Li Assembiedby Sassa(1992) /) /(to ro)r o20; oooro)v1,/1ooa:c:e)o'CL 'L( ]oooooc(I2 iO>"ScoQ 'J oo'uJGlnsaugonslide a o e o e eeofo8105 10G 107 108 i09 iOio 1011 1012Volurne of Landslide (m3)Fig. 8. Relation betw'een falli b schung (or slope angle c*,.) andvolume of landsiide (based on original piot by To,vhata, 2000)689clebris, ¥¥'ith himself and his house riding on top of thefio ving mass of soils and rocks. Fortunately, he ¥ 'as res-cued do vnslope.Residents intervie ved mentioned t.hat after days ofhea¥'y rain, itvas a sunny dayvhen the landslideoccurred. This is consist.ent ¥vith the rainfall recordsvhich sho¥ ' that only '-.6 mm of rain fell on 17 February,,_006 (see Fig. 4). They heard a loud crash and felt theearth shake before ¥vater mixed ¥vith mud and bouldersfell from the mountain. This clearly points to the role ofantecedent rainfall in trig ering landslides. Water frompre¥'ious rainstorm may ha¥*e made its way from otherparts of the mountain range into the fragmented rocksoverlying mountainside. This allowed ¥vater to pressureto build up vithin the slope, creating a potentially dangerous condition.A report by the Presidential Inter-Agency C*omrnittee(2006) indicates that pre¥'ious events of landslides in thearea have occurred in the past, as extracted from topo-graphic maps and recent photographs. The reportclaimed that the presence of screes, or loose rock debrison the slopes of the mountain (no v covered ¥vith trees),are indications of old landslide events. Old debris flo¥vdeposits are also visible at the base of the mountain (seeFig. 5). Three generations ofvitnesses intervie¥ved at thesite claimed that they have not encountered landslides ofsuch large-scale in the past, indicating that the Guinsaugon landslide may ha¥'e a return period of more than 100years.F'ig. 9. The deposited field has numerous small lril s or hummocks:Inset sllows a 6 m ,vide and 2 m hia l hummockEarthcjuak e EffectThe Philippine Institute of Volcanology and Seismology (Phivolcs) reported that a small earthquake (M2.6)occurred at 10:36 A.lvl. on 17 February, '-006 ¥vith focalobtained for this slide is consistent ¥vith those observed inother subaerial siides, although the plot is some¥¥'hat indepth of 6.0km. The earthquake source is along theLeyte segment of the Philippine Fault System and anepicenter about 20 km from the landslide site (Phi¥'olcs,the lo¥ver limit.Some sur¥'ivors mentioned that durin*' the debris fio¥v,the surface of debris sho ved ¥vave-like pattern as itflolved further from the base. This would probablyexplain the hummocky nature of the deposited materials,as sho¥vn in Fig. 9. As the debris hardened and stabilized,the ¥vave patterns on the surface remained, producingsmall hills within the deposit. One hummock, shown inthe inset of Fig. 9, measures about 6 m ¥vide and ,_ mhigh. Some survivors claimed that the debris flo¥v lastedfor less than three minutes, an assessment which may bedifncult to comprehend in panic situations such as t.hiscase. Nevertheless, assuming that such accurate determination of' time period is possible and the stated du 'ationis correct, this would imply a debris flow velocity ofbetween 80-100 km/hr. This range is consistent ¥vith theestimates made by U.S. Army Corps of Engineers (C.ox,2006). It re*'istered an Intensity 11 based on PEIS(Phivolcs Earthquake Intensity Scaie) in Sogod to¥vn(equivalent to Intensity II-Ill of Rossi-Forel Scale).Similarly, the United States Geologic Survey recorded alvl4.3 earthquake at the same time, Ivith epicenter about4 km north of Guinsaugon and depth of 35 km (USGS,2006). Since both earthquakes occurred at the same time,there is reason to believe that they are one and the same,although the magnitude and locations ar'e different.Unfortunately, the actual rime of occurrence of thelandslide is uncertain. Immediately after the disaster,ne vspaper and television reports indicate that the slidehappened at around 10 A.M. (e.g., PDI, 2006; TimeAsia, '_006). The Presidential Inter-Agency Committee(2006) also indicated in their report that the landslide oc-2006) .curred at about 1000H. Several local people intervie¥vedduring the site visit, ho¥vever, mentioned that the land-It is interesting to note that some parts of the villa*'e¥vere transported as a whole by about 500 to 600 rn do¥vn-slide, accompanied by rumbiin*' noise from the mountain, occurred mid-morning sometime between 10 and 1 1slope. One survivor interviewed mentioned that he wassleeping in his house when the landslide occurred. HeA.M. Local officials of the province claimed that the di-claimed that his house¥'as s¥ 'ept away together'ith thesaster happened at lO:45 A.M., or 9 minutes af'ter theearthquake (C DRC, 2006; PHNO, 2006). Recently, there 'ORENSE AND SAPUAY690Fi**. 11. A large roek boulder at the front end of the debris fiolStCia yFig. 10. Large rock boulders which were transported a considerableSandGravel1 oodistance from the base of the slope:"rf 7Guinsaugon Soil =. +.e- 80is a gro¥ving consensus in the technical community thatthe earthquake happened before the landslide (Catane,2006) ./: .,);Q): 60IA ' ,>(:'a)Thus, considering that the actual time of occurrence ofthe landslide is uncertain, there is some debate on¥vhether it trig*"ered the slide or not. Intervie¥vs conducted¥vith local residents did not yield conclusive evidence.Some residents mentioned that they felt the earth movedbefore the landslide; others contended that they heard aloud noise and ¥vhen they looked at the source of thesound, they sa¥v the mountain crumbling do¥vn.Therefore, in order to ascertain the role of earthquakein the Guinsaugon landslide, it is necessary to establishthe actual time of occurrence of the landslide and todouble check the seismic parameters assigned to theu'CLS40e)oO-20/l:/;./, -Original Ground-1'Hr origjnal Ground-2: : Debris deposit (top)e Debris deposit (midd:e)Debris deposit (bottom)oO OOi O. 1 1 1 O I OOO O1Particle Size (m m)Fi･. i2. Grain size distribution of matcrials obtained at d fferentkocations in Guinsaugonearthquake, such as its magnitude and epicentrallocation. It is ¥vorthy to note that no other landslideswere generated along the trace of the Philippine FaultSystem in Southern Leyte at the same time as the 17February 2006 event.Gellera! Soi! Clla/'acte/'isticsdebris flo¥v (bottom), and the third some¥vhere in bet¥veen(middle).The _g:rain siz,e distribution cur¥'es of the five samplesare shown in Fig. 12. h may be noted that although theoriginal ground and the debris flo¥v deposits includedlarge cobbles and boulders as mentioned abo¥'e, thoseThe materials deposited at the valley floor consistedsizes lvere not represented in the grain size cur¥'es sho¥vnof sandstones, con_ lomerates (sedimentary rocks),mudstones, and breccias (produced by the mo¥'ement ofin the figure because of testin*･ Iimitation. It can be seenthat the original soil cover in the mountain slope has finesthe Philippine fault). Some of the rocks ¥vere huge, morethan 4 m in diameter, and they ¥vere scattered throughoutcontent of about 450/0, consistent lvith the materialsobserved in the slid mass. A view of the area ¥vhere thethe fan of the deposit as they traveled considerabledistance from the mountain source (see Fig. 10). Oneoriginal ground samples lvere obtained is sho¥vn inlarge boulder, measuring about 3.5 m in diameter, can bethe soil covering this par't of the slope.Fig. 13. The inset photo indicates the silty sand nature ofseen at the front end of the deposited debris (see Fig. 1 1).The materials obtained from the slid mass ¥vere veryApparently, this large boulder traveled a distance ofalmost 4 km, indicating the fluid-like behavior of themoving debris.much disturbed as a result of the debris fio¥v as well as theSoil samples lvere obtained at 5 different focations inrescue operations that followed after the disaster. Nevertheless, it can be observed that there is an increase in claycontent of the deposited debris, probably because of theeneral characteristics of the soilcrushing of rock masses dur'ing impact as the mountainin the re*'ion. T¥vo samples ¥vere obtained from theoriginal ground near the bottom ridge (see Fig. 5) northslope crumbled do¥vn. In addition, the falling debris mixed up ¥vith the alluvium comprising the rice field belo¥vof the failed slope. In addition, three samples ¥vere takenthe mountain. Moreover, the preferential grading of the¥vithin the debris flo¥v deposits-one near the base ofdebris is evldent.order to investi ate theslope (referred to as 'top'), another near the toe of the1 Tj.i; :_'*-='*!/"2006 LEYTF LANDSLIDE691; ,.,.##7* +*-''!r'"'i'+'*:*'^" #'. {'+' ;*;!. SS;-" "S i ;'"" ;i/;i-' i(*- S;s ""f ?**:!; - *** +*- ;*"** ** *;: *:* _ _:t+#s' i"' -'/ '!i-::{;t{' " " ' _*'*_'"; i''s-' !';' -:';-;iS **-- i:'i ;/ i; giji": i:" :i- ;:: ;:, ;;. __s' * L *l.'. ^"#'_'"' ''*#. _ ^' _ !:;;t i;:/( !j,;:; i.;;,t; ;;:" * f :'+'1i; i' ^ --* ;;:/';*i; f;:;i,:;!^*+ 'ri ?; ;i'' 'i" ;<!_!* *Fig. 13. Vicw of the ridge adjacent to t le failed slope where sample oforiginal ground was taken: Inset photo sho vs the detail of the sur-^;;s:; ,;'/'_"' x: #f *" -'"' '""}ir (;/'# ..- ..'""');:" .i;* ' '#'#*;" {")i" 1 :''''_*/; . - ". *"" ", -'*i''ii:;,? /'1 is; i li/:!" - i"' i; :;f;:i_* =' 'l*: . .;!' 's-- i'-ma n sea pi"S#'=;#;" ':':face soil in the slopeUnstab!e materiais on'; '' -i_;-' "'* *+i'- ':i!i :::_ *: ' **-*;:-; i' - S-' 'S_** i *'i_^ * * '- ;'"'- * ' +' s+#SS'+ ;:':;:= :i'i<' " +P ; i :*. * { ;tj*:;.'{･ s :ili:() .S }:;.'Li;iS i.;. .:;;'+ ;+ s1***' 't': t "': : ;r' i:t;;; ' ;:"/';."'" :':._ _ _!' .^-*_ _Fig. 15. One of the small river channels within the deposited debriscreated bl_ the damming of the Himbangan Rivervisit that the adjacent area ¥vas well-forested and there¥vas no evidence of deforestation at the site.The role of the earthquake prior to the landslidecannot be established until the actual time of occurrenceof the landslide is clarified. Ne¥'ertheless, it should bepointed out that a perturbation induced by an earthquake, ho¥vever small it is, could amplify in a topograph-ic condition such as in Guinsaugon and could triggermass movement in a fully saturated slope on the verge ofFig. 14. Photo sholving potential sources of instabilitics in the affectedfailure.areaCauSes oJ' the DisasterMost geologrc hazards such as landslides, are part of acomplex chain of cause and effect. The immediate cause isthe triggering mechanism, vhile other underlying factorsdefine the predisposition (proneness or susceptibility) toPossib!e Potentia! HazardsThe changes in the physical landscape in the affectedarea as a result of the landslide in Guinsaugon havebrought about the emergence of future hazards (see Fig.14). The steep slopes at the failure surface, accentuatedby numerous cracks, and the materials that rernain at thef'ailure. Based on the ocular inspection at the site, severalcro¥vn, are potential sources of future landslides.underlying factors can be identified clearly. Because thePhilippine fault line traverses the region, the volcanicrocks in the area are char'acterized by intense fract.uringand weathering, making them unstable and susceptible toLandslide scars adjacent to the failed slope are also indications of potential instabilities.mass movement. Moreover, such condition allo¥vedaccumulation of water in the loose saturated deposit, wasrain¥vater to seep into the r'ock fractures, further ¥veaken-also prevalent. There ¥vere also small river channelstraversing the deposited materials, especially near theing them. The steep terrains of the mountain surroundingthe valley rnake the slope susceptible to iandslide. Thetriggering mechanism, on the other hand, is the heavyDuring the site visit, it was noted that the depositedmat.erials were still saturated and soft. Ponding, orbase of the mountain (see Fig. 15). These river channelscame about as the deposited debris dammed therainfall in the area, made worse by the appearance of LaHimbangan River fio¥ving near the base of the mountain,Niia phenomenon. Intense rainfall softened the soilallo¥ving small tributaries to seek different flo¥v paths.Such conditions may trigger debris flo¥vs in the future.cover, vhich had already been made unstable by the faultline and the previous rainfall.Although initial reports blamed logging in the area asone of the causes, it is belie¥'ed that considering the size ofLANDSLIDES IN OTHER PARTS OF THEthe landslide and the magnitude of antecedent r'ainfall,PROVINCEdef'orestation did not play a significant role in triggeringOthe/' Slope Faiht/'esthe landslide. Moreover, it ¥vas observed during the sitePrior to the Guinsaugon iandslide event, a series of 1OREN+SE AND SAPUAY6 )2S':_:S! '?Agas"Agas " "F';irS!S!x',^'. ** ;j** *s･･ ,'" "* :,･･**_f. *i . **".eee ili;'io : jl: Sej so90di i ; c*sFig. 18. Slope fai ure and road collapse in Lepanto, St. Bermrd townBa y5osLepantoi S 'e ;$Pt F :f:a:Clay;St8ar dG Falre1 oot#"S ; f''caba fianBa y'lc!! s'"'oo- 80jolQ)Fig. 16. Map of Southern Le)te province sho l'ing loca:tions of otherlandslides visited during tl]e tiamage inspection: 60>4:)e)c:40O_c:e)(' 20- :::, as- Lep*"*'CLoO.OOI O. 1 1 OOO.O 1110Particie Size (mm)Pio, 19. Grain size distribution of materials obtained at otherlandslide sitcs in Sout!lern Lel.'teL,iloan buried 4 houses and blocked the only road goin_"._to the Pacific to¥vns. The occupants of the houses ha¥'eevacuated earlier. Another landslide occurred in L.epanto.'¥'illage, also in St. Bernard to¥vn, ¥vhere a portion of the･･･.*mountain collapsed and destroyed the adjoining roadFig, 17, Lands]ide and pavement collapse in the nearby Agas-agns,Sogoti town on 12 rebruar . 2006iandslides and mudslides brou*"ht about by days of heav_vrains occurred in other parts of Southern Leyte Province(see map sho¥vn on Fi_g. 16). O_ n 1'_ February '-006, just5 ciays before the Guinsaugon landslide, three major(see Fig, 1 8). This affected to some extent the transport of_g:oods and personnel to the Guinsaugon landslide site.Less than 2 km a¥vay, another landslide destroyed aportion of the coastal road, allo¥ving only one-1vaypassage of vehicles.Because of these landslides, the pro¥'incial governmentdeclared Southern L.eyte under state of calamity.landslides occurred in succession in Sogod to¥vn, Iocatedjust north¥vest of St. Bernard. One large landslideG/'ail7 Si e Distributionvhere surficial slopeSoil samples ¥vere also obtained at various affectedfailure as ¥vell as pavement collapse occurred. Thevolume of the mater'ia]s in¥'ol¥'ed in the flo¥v ¥vasareas to determine the g:eneral characteristics of the soilinvol¥*ed in the landslides. Aside from those samplecl inestimated at ?-0,000 m3. During the site vlsit a monthCJuinsaugon, t¥vo additional samples lvere obtainedafter the disaster, the roaddirectly at the base of the failed slopes: one sample inAgas-agas slide (see Fig. 17), and another one in Lepantooccurred in Agas-agas (see Fig. 17),vas still closed to traffic,causing inconvenience in accessing the Guinsaugonlandslide site. The t¥vo other landslides have volumesestimated at 15,000m3 and 7_,OOOm3, respectively. Thesliding masses of soil ¥vere deposited along the high¥vay,severely disrupting traffic in the area.In other parts of the pro¥'ince, at least four majorlandslides occurred, Ieaving 9 to¥vns isolated in thePacific and Panaon areas. A Iancislide in Hima_vangan,slide (see Fig. 18).The slide materials under¥vent generally lesserdisplacement compared to those of Guinsaugon, andtherefore, they can be considered as representati¥'e of thesurface soil co¥'er at the sites. Therain size distributioncurves of the t¥vo samples are sho¥vn in Fig. 19. It can beobserved that the t¥vo sets of samples are practically 2006 LEYTE LANDSLIDE-bimilar, ¥vith fines content bet¥veen 8085 /o. This is inag:reernent lvith the ¥'olcanic nature of' the soil in the area.The fines contents of' soils in these regions are much largerthan those in the Guinsaugon slope.CONCLUDli¥G REMARKSThe large-scale landslide in Southern Leyte, ¥vhichcaused the death of' more than I , 100 people, Ivas a cilsas-(. ) )Repol'! on !he Lalic!s!ic!e i,i St. Bel'!!arc!. Sol!ihern Le_vfe. Februar21. 2006, 54) Cox. S. H, (2006): L]'SACH FEST assists U_Sl ri[ es' Le}tesearch and rescue mission, rhe Pacific Collnect!on, Spri l2006,S-9.5) Departrnenl of Enh ironmenand ¥. 'a ural ResaurL: es, DENR (2006):Press Re/ea,se. 22 Pebruarv 20066) C] eagraphicai Sur e} InstituLe, (J S (l006); The position of thelandslide in Le Le island. Philippines as estimated from SpaceShu tle data, hLt ): ,! vhYIY.gsi go jp (in Japanese).ter ¥vaiting to happen. The intensity of the rainf'all prlor7) Heim, A. (1932): Lanc!s!ic!es anr! Hi!man Lil'e,s (Be!: s!iir; l!ncl*tfenichen !eben), (translaied b¥' Skerner, iN.), Bi-'Tech Pubiishers,to the disaster, coupled lvith the existence of ¥veak andf'ragmented rocks due to the presence of the Philippine8) Lagmay, A. N'I. A.. Ong, J. B. T , Ferl andez. D. F., Lal)us,Fault Zone and the steep slopes, ¥vere all in_a*redients f'or adisaster. Although governrnent geologists have already¥･;ancou¥'erl R.,RodolfQ. R. S . Tengonciang, A. P , Soria. J L . Baliaiall, E. G.,Quimba, Z. P , Liichanco. C. L.. PagLlican. E R . Remedio, A. RC., Loren2 o, G. R H.. Avila. F^ B. and Valdibia, ¥'. (2006):identified the area's geologic hazards as early as '-003,Pre!imina/'1' ( :*eo!ogica! Report on rhe Southern Le_,'!e L !nc!s!ir!e,measures to address the percei¥'ed hazards ¥vere nonexistent, or at least, not implemented. As pointed out,9) i¥'a;tional Disaster Coordinaiing Council, l¥TDCC (2006): Cfpc!a!epotential hazards still temain In the area and preventivemeasur'es should be implementecl as soon as possible tominimize damag:e from f'uture disasters.UP-Ateneo Team. 2006 Report, 9,A;o- 16 re Lanc!slic/e a! B!t*"_1'. Guinsaugon. Sl. Bel'ncll'c! Soluhel'nLeyte. http: ,f/¥ 'w v.ndrc go : ph^lO) orfice for the C oordination of Humanilarian Affairs, OCHAC2006): OCHA Sin!cltion Repori No. 8.･ The Phi!ippinesLands!ides, Ref.' OCHA /G VA-2006/9. February 24, 2006, 2.l I ) Philippine Daily Inquirer, PDI (2006): ST,'a!!olt'ec! b_1' !he Ecl, !h-33ACKNO¥VLEDGMEN J'SThe authorsvould like to ackno¥vledge the advice anclcomments pro¥'ided by Dr Sandra Catane and Dr. lvlarkZarco, both of the University of the Philippines. Thediscussions madevith Prof. Masayuki Hyodo ofYamaguchi Uni¥'ersity, as well as the assistance of Mr.Naotaka Kikka¥va, graduate student of' YamaguchiUni¥'ersity, are also appreciated. lvloreo¥'er, Mrs.Lourdes Tibig: of PAGASA assisted in securing: the rainfall data in Otikon. The funding for the site in¥'estigation¥vas provided thr'ough the Project S (InternationalStrategy) of the Faculty of Engineering, YamaguchiUniversity. The authors wish to express their deep gratitude f'or the assistance of the above-narned persons andor :anization.Dead. Hl!'1c!recj_s , liss!jlg in Le.1'1e * luds!ic!es. Februar} IS, 2006.i2) Philippine Headline N. ?e Ys Online. PHNO (.2006): Rains, minorearihquake blamed for landslide in Le.vte. February 7, 2006,http: ./,/ T v¥13) Philil)pi! ene¥ 'sliash org/2004 /02 /hl /hl I 03 ! 28 .hLm ^nstitu e or Volcanolog¥' and Seismology, Phivolcs(2006): Ear!hcluake Bu!!e!!n Afo2, http: /¥Y¥v¥v phlvolcs dost^gov.)h/Earthquake/LaiesrEQ/^14) Presidential In er-Agecy Commi tee (2006): T/1e ! 7 Februa,y 2006Bgl'. C; i!i,Isau*"on. Sot!!he/"n Le_1'te Lanc! !ic!e. Unpublisheci Report,¥. iarch 3. 2006. 30.15) Ramos. N . F. ¥,(2006): Le}te os calls for rescue, Scmtar !¥*eT 's.Februar) 22. 2006.6) Sakurai, ¥¥*., Kano. T , Tsuda, H., Hipolito. D l.. Alpasan, *¥1.T. and Damo. G_ C. R. (2004): The sedimem disasters thatoccurred in SOUtheFn Levle of the Philippines in December 2003. J.Jpn Soc. Fro,s!on Con[ro! Engineering, 57(4), 33-38 (in Japanese)17) Time Asia (2006): Slt'a!lol"ec! b_T' the E'ar[h-Deac!!_1' Lanc!s!ic!e hlthe Ph!!if;Pines C!ai,ns Hunclrec/s ofLil'es, February9, 2006^iS) To¥vhata, I. (2000): Lectul'e i¥ro!es in So!!D_1'namics. Department ofREFERENCESl) Barrier, R.. Huchon. P. and Aurelio, (_ (1991): Philippine fault: Akey for Philippine kinematics, Geo!o*'*'_ ', 19(1), 3235,2) C 'atane. S. (2006): Personal Communication.3) Citi2:ens' Disaster Response Cemer. CDRC (2006): A Pre!ilnincil:yCiYil Engineering. Uni 'ersity of Tok}'o.19) Unitecl S ates Geologic Survey, USGS (2C06): Pre!inlina!Lw Earihquake Repor!' ! fa**"nin!c!e 4.3 Le.vte. Phi!ippines, http: //neic usgs.gov/neis/bulletin/neicJgdn html^20) Vl ug, i¥, . D. (1993): PoLt'erfrorn !he Fores!. PhilipPine Center torInvesligalive Journalism Press,lanila.
- ログイン
- タイトル
- Effects of Pore Fluid Compressibility on Liquefaction Resistance of Partially Saturated Sand
- 著者
- Mitsu Okamura・Yasumasa Soga
- 出版
- soils and Foundations
- ページ
- 695〜700
- 発行
- 2006/10/15
- 文書ID
- 20951
- 内容
- SOiLS AiND FOUNDATiONSVol.46 , ¥. ?o. 5.695700. Oc2006Japanese Geotechnical SacietyEFFECTS OF PORE FLUID COMPRESSIBILITY ON LIQUEFACTIONRESISTANCE OF PARTIALLY SATURATED SANDlvIITsU OKA iURAi) and YASUlvIASA SoGAii)ABSTRACTIt has been recognized that the soil resistance to liquefaction increases significantly as the degree of saturationdecr'eases. Ho vever, the effect of the degree of saturation reported in the literature ¥'aries videly bet veen researchers.In this study, infiuential factors of the liquefaction resistance of partially saturated sand are derived from theoreticalconsideration and effects of the factors are examined through a series of triaxial tests. It ¥vas confirmed that the degreeof saturation has a significant eff:ect on the liquefaction resistance. It also appeared that the liquefaction resistancedepends on the initial confining pressure and the initial pore pressure; the higher the confining pressure and the lo¥verthe initial pore pressure, the higher the liquef'action resistance of partially saturated sand. A unique relationshipbet¥veen liquefaction resistance ratios and the potentiai volumetric strain ¥vas found, ¥vhich enable to estimate theliquefaction resistance of partially saturated sand ¥vith the effects of the three factors taken into account.Ke _' words: confining pressure, degree of saturation, Iiquefaction, sand, triaxial test, voiumetric strain (IGC:D6)ReferenceINTRODUCTIONNatural soil deposits belo¥v the ground ¥vater table areeusually fully or nearly saturated with water (Tsukamotoet al., 2002). Recent investigarions re¥'ealed, ho vever,VAX)t,,that injection of' air in a soil could lo¥ver the degree ofGoto & Shamoto (20C} )Yoshimi et al ( 19 gq)Yasuda et al ( 199q)Ishihara et al ( OOI )A:/:saturation of the soil substantially (Tokimatsu et ai.,Hu mg et al (. 19c)c))AO;-1990; Okamura et al., 2003) and the unsaturated,xVcondition of the desaturated soil lasts for a long time,typically more than tens of years (Okarnura et al., 2006).This fact suggests that desaturation of soils could be an;,..''..v>v vefi ctive ¥vay to enhance the soil resistance to liquefactionin the fieid. It is, theref'ore, necessary to establish apractical method to estimate qualitatively the liquefac-l70tion resistance of partially saturated soils.80De lree olThe effect of degree of saturation on the liquefactionresistance has been studied through laboratory tests. Inthe early research works, degree of saturation of testedspecimens ¥vas mostly in the range close to 1000/0, because90saturation.ooIfoS･ ('/･)rig 1. Results of tests on the effect of degree of saturation ontiquefaction resistance (Liquefaction resistance is normalized ,viththat of full) saturatcd sand)the primary objective in those studies ¥vas to establish thestandard for the laboratory cyclic shear test to avoidundesirable unsaturated condition which resulted in1999; Yoshimi et al., 1989; Yasuda et al., 1999; Ishiharaoverestirnation of the liquefaction r'esistance (e.*'. Martinet al., '_OO1; Goto and Shamoto, 2002). Liquefactionresistances reported by any researchers consistentlyincreased with decreasing the degree of saturation.et al., 1978). Thereafter, partially saturated sands withdegree of saturation do vn to 700/0 were tested by severalresearchers. Figure I depict.s some recent test results inthe literature summarized in the form of t.he relationshipHo¥vever, the liquefaction resistance ratios ¥vere con-bet¥veen the degree of saturation and the liquefactionsiderably different for different sands tested at diff rentcondit.ions, indicating that the degree of saturation mayresistance of the partially saturated sand normalized ¥vithrespect to that of the fully saturated sand (Huang et al.,liquefaction resistances of partially saturated sands.i]ii)not be the only factor dominating the normalizedAssociate PrcfessoF, Gradua e School of Science and Engineering. Ehime University, Japan (okamura( ;,dpc.ehime-u.ac jp).Graduate Student, Kyoto University. Japan (formerly Ehime University)The manuscript f'or this paper ¥vas received for revie¥v on December 8, 2005; approved on May 29, ,-006,¥¥!ritten discussions on this paper should be slibmitted before May I , 2007 to the Japancse Geotechnicai Societ.v, 4-38-2. Sengoku,Tokyo 1 12-001 l, JapanUr)on request the closing date ma.¥' be extended one momh.695Bunkyo-ku, OKA ,IURA AN. D SOGA696As can be seen in Fig, i, existence of air in a soil8,. = Bw /A p (-? )significantly enhances the liquefaction resistance.Resear'chers have paid **reat attention to saturate speci-and ¥*olumetric strain of the fluid (¥vater and air mixture),mens completely for' Iaboratory tests and model groundse*f' is;for shaking table tests to avoid overratin_g soil resistancesto liquefaction. Replacement of air in the void of soils bycarbon dioxide follo¥ved by introducing deaired ¥vaterunder a ¥'acuum pressure is the typical technique that hasbeen developed. V,re, ho¥vever, often observe contradicto-ry phenomenon that a sand deposit in a small containeror a bottle, being almost filled vith ¥vater but containsvisible air bubbles in the deposit, can be easily liquefiedby shaking the container gently. This also alludesexistence of infiuential factors of the liquefactionresistance of a partially saturated sand other than thede9:ree of satur'ation.In this study, influential factors of liquefactionresistance of a par'tially saturated sand are derived fromtheoretical consideration and effects of the factors areexamined throug:h a series of triaxial tests. Results aresummarized in the form ¥vhich can be easily applied toevaluate liquefaction resistances of partially saturated= ApBfI -B.S,B,,S, ')e.f(¥vhere S* is degree of saturation of the soil mass and B*,Bw and Bf are bulk moduli of the air, the ¥vater and thefluid, respectively. Since B, is much higher than B., thesecond term in Eq. (3), S,/Bw' is negligible. IntroducingBoyle's lalv and assuming soil grains to be incompressible, ¥ve obtain the ¥'olumetrlc strain of the soil mass as;8' 4B. (1S)p0+Ap(1e Ap S,)-i+e_ e' 1+e(7*' Ie+e. (1 S,)p O'T (T.¥vhere po and e denote the absolute pressure of the fluidand the void ratio of the soil mass, respectively. Thehig:hest value of the ¥'olumetric strain for the soil isachie¥'ed ¥vhen the Ap attains its possible maximum ¥*aluewhich is equal to the effective confining str'ess, (7.'.. Thissands in situ.FACTORS AFFF.CTING L.IQUEFACTIONRF.SISTANCE OF UNSATIJRATED SANDExistence of air in the pore of a soil is considered toenhance the liquefaction resistance of the soil in t¥vo¥vays. The first mechanism is such that air in the poreplays a role of absorbing generated excess pore pressureshi :hest value of the volumetric strain is hereafter in thispaper termed as potential ¥'olumetric strain, e .TRIAXIAL TF.STIn this study, effects of the factors derived In thepreceding section ¥vere in¥'estigated through a series oftriaxial tests. Three testing parameters including theby reducin*" its volume. The bulk moduius of the poreinitial effecti¥'e confining pressure, cr , the back pressure,fiuid chan*'es significantly by the presence of air bubbles.po, and the degree of saturation, S,, ¥vere varied betweenThe bulk modulus and chan*'e in volume of the poretests ¥vhile the ¥'oid ratio of the specimens ¥vas keptfluid, that is air ¥vater' mixture, may be the factorsdominatin*' this mechanism. The second is the matricconstant throug:hout the test series.suction of unsaturated soils ¥vhich increases the effecti¥'eP/'eparatiol7 of Specil77enToyoura sand ¥vas used in tests conducted in this study.stress and thus the strength of soil mass (Bishop andBlight, 1963). The matric suction depends not only on thedegree of saturation but also on soil par'ticle siz,e. Formost liquefiable soils the matric suction is less signlficantcompared to the effecti¥'e stress of soils at the depth ofpractical concern, say several meters or deeper. For thefine sand used in tests in this study, for instance, thematric suction is at the highest 4 kPa if degree of saturation goes do¥vn to 700/0. In this study the first mechamsmis focused on. The effect of the matric suction is ne9:1ectedor the pressures of air and ¥vater in the pore are assumedto be the same Note that for liquefiable soils ¥vith higherfines contents, such as non-plastic silt and sand containing considerable amount of fines, the effect of the matricThe specific _g:ra¥'ity of the sand is 2.64 and the minimumand the maximum void ratios are e ,i =0.609 and e*** =O.973, respecti¥'ely. Triaxial specimens ¥vere eithersaturated or partiall}., saturated sand. Test specimens¥vere prepared as follo¥vs. Wet sand ¥vith a ¥vater contentof 50/0 ¥vas tamped to a relati¥'e density D,=40 /o in amold with internal dimensions of 50 mm in diameter andlOO mm In high. The sand ¥vas set in the triaxial cell anddeaired ¥vater ¥vas introduced from the pedestal for a¥vhile. Then the back pressure of 98 kPa ¥vas applied and¥'olume of ¥vater pushed into the specimen was measured.The measurement ¥vas continued for an hour since thevolume ¥vas observed to increase gradually probably duesuction could not be negli_"*.ible. Further investi*･ation isto dissolution of air in the pore ¥vater. Volume of air inneeded on this reg:ard.Consider a soil mass with the por'e filled ¥vith air andwater. For a small change in the pore pressure, Zlp, thevolumetric strains of the air and the ¥vater can be ¥vrittenthe specimen ¥vas estimated from Boyle's la v ¥vith themeasured volume of the ¥vater pushed into the specimen.The procedure of introduclng deaired ¥vater and the airby equations;s. = B* /A p ( I )volume estimation ¥vas repeated until the specimencontained predetermined volume of air. It should benot.ed that the adsorption path and the desorption path ofthe soil-water characteristic curves are generally different . L QUEPACTION R SISTANCE OF UN_ 'SATURATED SOILTable 1.Degree of'Triaxial test conditionsPoieniial volumeLricAbsolute backsaturation*, S. (o, )Effec ive confinin :pressure, (J*' (kPa)pressure, po (kPa)l OO49, 981 99Rerati¥*edeosity, D* (?･/o)69 T(97o o008449o-98 . 5)96(95O .OO 1 849s0.0030519 60.00 1 65o 00362199O 006019839 4390i 99O 0151297O OI 13199o 0300297o.0225199O . 045 l297o.033898(s9_0-92.0)8098(78 5-83.0)7098(70.0-72 o)Degree o1 99495 -96 . o).*o19 698strain,saturation in the parentheses was estimated from the measured volume of ¥vater pushed into the specimen by increasin lhe backpressure.(a) S.= I OO b, (r*' = 98 kP L pi) 199 kPa*^ 50v . ;>(b) Sr = 95.401!o'o.;'c :v; !b OS 1>oO-50: OS: 0,1.S Ol:: Ol<;-O Oi; Ox _O I<-O 2o^*e ;'1='V:/>(e'-O 2? 1001 100l'1-P0= 199 kPaOafo _ _50(r*' = 98 kPp^o) 501 v/ c)v2v>(o50'*'.1 -' OlO20Number of cyclesFig. 2.O10Numbcr of' cvcles20'I,pical rime ilistor) from tests on full) saturated and partiail) saturated specimensHo¥vever, the volume of the water pushed in and expelledfrom the specimen during increasin*' and decreasin*' theback pressure ¥vas essentially the same. This is probablydue to the matric suction of this particular sand beingvery lo v in the r'an_g:e of degree of saturation tested in thisTes'ting Pa/'alnetersThree testing parameters derived in the previoussectionver'e varied bet¥veen tests as sho¥vn in Table l. Itshould be noted that the back pressure, po, used through-out this paper is the absolute pressure instead of thestudy.ordinary used gauge pressure. The range of theFor the saturated specimen, deaired ¥vater ¥vas introduced until the Skempton's B value became 0.95 orparameters tested ¥vas ¥vide enough so that the range ofe covers that of possible field situation ¥vhich might behigher. The effective confining pressw'e was kept constantencountered in practice; the initial effective confinin_"*,to 10 kPa throughout the course of the preparation. Onpressur'e ¥vas varied betlveen 19.8 kPa and 196 kPa andcompletion of preparation, the initial effecti¥'e stress andthe ran*'e of S* ¥vas similar to that of the in-situ soilsthe back pressure ¥vere applied and the specimens ¥veredesaturated by the sand compaction pile installationsubjected to the cyclic shear stress ¥vith a frequency of'(Okarnura et al. , 2003, ,_006). The values of the potential¥'olumetric str'ain at the beginnin_ : of cyclic shearing, 8 ,O OI Hz under undrained condition.are also given in Table 1.It should be mentioned that the frequenc)' of shear OKAlvIURA AND SOGA698cycles in the tests being much lo¥ver' than those ofearthquake motions may allow air in the specimen tothe unsaturated sand indicated in Fi**. 2(b) is quite similarto those of the saturated sand except for the applied cyclicdissolve in pore water in accordance to generated excesspore pressure during cyclic shearin_g. According to theHenry's la¥v, a maximum of 3.8 cm3 in volume of air candissolve for the test condition shown in Table I ¥vhen thespecimen '*enerates a 1000/0 excess pore pressure ratio.stress amplitude being considerably higher.Effect of the FactorsHo¥vever, it ¥vas observed in preliminary tests thatback pressure on the liquefaction resist nce. Figure 3amount of air dissol¥'ed in the pore ¥vater in an hour afterdepicts the relationship betlveen cyclic stress ratios andthe number of cycles, N, to cause double amplitude axialstrain, DA, of 50/0 for cases ¥vith cr,'.=98 kPa and p0=199 kPa. As the degree of saturation decreases, the cyclicapplyin*" a back pressure of 98 kPa ¥vas ¥'ery limited,approximately 0.3 cm3 corresponding to an increase inS, of 0.30/0.This section discusses effects of the three factors, that isthe degree of saturation, the confinin*･ pressure and thestress ratio increased irrespective of the number of cycles.RF.SULTS AND DISCUSSIONSStress-strairl Re!atiol7s/1 ipFigure 2 shows t .,pical time histor'ies obtained fromtests on saturated and partially saturated (S*=95.40/0)specimens at the same confining pressure ((7 =98 kPa)and the back pr'essure (p0= 199 kPa). For the satur'atedspecimen, the excess pore pr'essure increased with thenumber of cycles. The axial strain started to increaseswiftly as soon as the excess pore pr'essure approached tothe initial eff cti¥'e confining pressure. This response istypical of a fully saturated loose sand. The response ofThe cyclic stress ratio almost doubled as the de*･ree ofsaturation decreased fr'om 1000/0 to 900/0, ¥vhile in therange of the degree of saturation lo¥ver than 90010 itincreased at a lower rate lvith decreasing the de*"r'ee ofsaturation. Hereafter, in this paper, the cyclic stress r'atioto cause DA=50/0 in 20 cycles is termed as the liquefaction resistance.Illustrated in Fi**. 4 are variations of the cyclic stressratio ¥vith number of cycles for tests in ¥vhich theconfining pressure ¥vas varied bet¥veen tests ¥vhile the0305:-VCr.'= 9S kPa_ pr' = 1 99 kPa)- 040251-:i. 03s 02:-e),, {"*)_ 02J:':):;)>,O lvoOO 70SO] 90O 96A 9SO 15,S'r = 100 'tc 100{5 10Nlumber of c) cles. .¥Oo]oOl litial ef'fective cont ning pressure. (T.' (kPa)Fig. 3. Effect of degree of saturation on the relationship betweenrig. 5. Revoiution ofcl. clic stress ratio and number of c . c]esvith an increase in initial05(a)96 o_p!' = 199 kPa04(b) S* =980. . p,; = 1 99 kPa*' 03' 02iquefaction resistanceeffective confinino* pressure05*rO i OOO' 03-¥ _rT0.4l l {L J r'a'r!6kPa'; dO*'':)rl Tb[;i:j:J6 t'a'.1:'i6kPa) R)>J Ol> OIt)o:'5 iri(,_* . 4.5 10Niumber ol"c¥ cles. AO i OOoOllONtlnrbeToi cycles A'h ,fiect of initia effeetive confining pressure on the relationship between cyclic stress ratio and number of c)cles50 1 OO 699LIQuEF、氏CTION RESISIANcE OF UNS、へTuR、へTED soIL050、5（ωσ，F濫98kl）a．、Sロ冴90％（b｝σ，「皿98kI）a、，∼、、皿70％。τ 04㍉ 0，4ビじ＾ 03＿ 03蓑02罫 02．2つ3，01．婁、O i00500550 100 5 10NUmberolcyclcs．．V50 5 10100NUmbeωfc》clcs．、NFig．6．E耀ec｛ofin漁lporepress巳reonIherelatio賎sh量pbeIweenc》’c置ics［ressra亘loandm鼠mberofc｝『cles（bl resultS t沁m pre、IOus stud｝（alresuksofしestil1禰ssヒud｝（ 」 A」、へbes毛巨t cしぼr㌧e1・9〆6500ε、‘・一10ノ塩 ○つ一○一 つムIo｝lour無sand，Dr篇40％0 98 98 70−100△ 49 98 96＿】00S識nd ∂f ，9r σ♂ μθ Re短re臓ceO Io》oura40％91−IGO9805（Hua口getab△ ro、oura60％90−1009805（Huangota1｝ ｝▽ To｝oura70％91−1009805（Huangetal、｝0 196 98 96−100ムTo・oura60％70−100980監Yoshimieml ｝」』・ 98 196 70−100002 004 ｝蕊 σC「（kPa）ρr’（kPalSr（％）、0＼i。9（6500ピ＋10）＋ Masa 85％94−iGO9867／196（、7asuda0．06（｝PotelltialvolUmetricstra紅1ε、0．02 004et ab006Potennal voiun潅etriC Straln ε玉Fig。7、Relat董onshipbetweenhypothe“calvolumeεricstralna臓dliquefacIionresis重旦nceofpar症ialb『s烈urateds謎騎dnormaiizedwithth撮offully s隷芝ur謎粟ed s＆nd（iegree of saturat玉on alld the back pressure were keptfactors o蹴 the liquefaction resistance discussed aboveconstant．The cyclic stress rat玉o of the partially saturatedqualitatlvely support the idea of the盒rst mechanismξhat，sand is apParent豆y depelldent on the玉nitia圭con行ning Pres−air in the pore plays a role of absorb玉ng generated excesssure．Li（luefactioll resistances are plotted aga圭nst in圭tiaIcoufin量ng pressures圭rl Fig．5．The liquefactionτesistancesofthepartiallysαξuratedsandincreasewi出theinl重i＆1con且鷺重ng Pressures， with the liquefac重ion res量s重ancesbeing higher for lower S，．The至i（1uefaction resistance ofpore pressures by reducing its vQlume．Thus，the liquefac−tion resistance ratio，which隻s the liquefεlction resistanceof a partially sa芝urated sand norma正ized with respect to重hat of the fu玉1y saturated sand，is plottecl against thepotential volumetric str＆in in Fig．7（a）．All the data llesthe partially saturated sand seems to＆pproach to that ofalong a unique cul−ve， conarm三ng that the poten丈ialfu1重ysaturatedsandasthecon且nlngPressuredecreasestovolumetric strain is the determini煎g factor oft難e e窃ect ofzero．hl other words，degree of saturation has a smallerdegree of saturation on th玉s speci負c sand at relativee圧ectontheliqueξactionresistanceofsandunderalowcon負nil19Pressure．Figure6illdicates effects of the backpressure on the cyclic stress ratio。The liquefactiondensity of40％．Data re重rieved from毛he1呈terature三s alsoshown in Fig．7（b）in the same manner．The d飢a plottedin this ngure was obtained from the tests on specimensresistance of the parξia11y saturated s＆n〔iεしpparently de−prepa罫ed using d星鉦ere正1t sand at di拝erent re正εしt圭ve densitypends on the back pressure，which圭s not重he case for satu−and subjected cyclic loadingεLt di郵erent con盒！1ing Pres−rated sand．王n oPPosition to tbe effect of the confiningsuresαs summarized in the figure．Despite重hese differe臓tpressure，the豆iquefaαion resistance decreases as the backconditions，＆H the（iata lies a董ong tぬe same curve as that inpreSSUre lnCreaSeS・Fig．7（a）．Thiscon且mst紅atthee鉦ectofthedegreeofsaturatioll on 正iquefact量on resist＆nce， which is arisen∠，iσμψぐ’ioll Rθ5i5∫α∼zぐθρ〆’∠）θ5ρ々’ノ’α∼θ61Sα11グfrom the丘rst mechanlsm，c＆n be es書imated using this Final至y，the effect of the potentiε芝1volu！netric s芝rain，curve．ε済，givenbyEq，（4）ontheliquefactionresistallcels Figure 7 and Eq． （4） 圭ndicate that the liquefactiondiscussed in this section．All the e仔ects of three inauelltialresistεmce of a soil under a very low confining Pressure is 700OK．へMUR、へ、へND SOG．へ3not th＆t sign韻cant for small scale models飢茎黛but forDel）由飲）蹴gro田1（iie、d ↓Ground、、atertable 謙G LIarger models and centrifuge models。In負eld conditions，providedthatlique負ablefoulldationsollisclesaturatedin一一一：at 蓋01ぬabove G Lsomeway with an 玉n重ention to enhance liquefac毛ion（θ＝06．7’；10kN！m㍉一（i華」L＿一20n1resistance，asigni員cante仔ectcallbeexpectedexceptforsolls at a s｝1allower depth．2 （li．［． 一5nl 1t was found that thereis aunique relationsh量p betweent熱e nonηalized I至quefaction resistance and the potentialG L −2厳1volumetric strain．The iiquefactlon resistance of partlallysaturated sand can be reasonably estlmated from that ofG L．一〇5n！fuHy saturated salld in conjunction with t｝1e potent圭al ＼、 ＼、ミ・⊇繋1、80 90100Degrceofsatura毛ion．5『，・（％）Fig．8．Vari段重沁鷺sofiiquef食ctionresislanceraIiowiII∬，a吐severaIvo墨umetric stra至n using the relationship obta量ned in th量sstudy．This relations麺p may be Iimited for soils with alow matric suction．Fllrther investigation is 勲eeded forthe Iiquefaction resistance of part三al豆y saturated such asnon−plastic silt and saad containing considerable amount dep｛hsof飴es．essentiaIly tbe same irrespective of the degree of satura−REFERENCEStion and t｝1e back pressuτe．This must be a reason why the1）Bishop，A．W．and Blig厩，G，￡．（1963）l Some aspeαs of e貿ectivesoil宝n a smaII scale model foτa shaking tab豆e test at1黛 stressinsaturatedan（玉partlysamra［edso澱s，Gθαθ（hn’σ∼’θ，韮3．envlronment can easily liquefy even if the model ground 177−197、2） GoIo， S． and Shalnoto， Y， （2002）： Estimatiorl metllod for t隔econtains considerable amount of alr bubbles（Okamura liquefaα玉on s【reΩ9こ110f unsa！urated sandy soil（part2），Proc37’1∼and Teraoka，2005）． ゆn、．へ7醒．Co1瑳Gθαθ‘1LEη918，，1987−1988． 丁熱e relationship indicated in Fig。7and Eq．（4）make itpossible to evaluate the liquefact量on resistance ratio for負eld cond嚢ions． Figure 8 dep圭cts variations of the至iquefact量on resistance rat圭o w茎t｝1 the above discussedt振ee factors for a fully submerged uniform sand deposltwithbuoyantunltweighげ薫10kN／m3，voidratioθ瓢0．6and water table being co圭ncided with the gτound璽evel（G．L，．）or at 10m above G．L。互t can be seen that tbeeffects of S，and the ef￡ectlve con負n圭ng Press11τe aτe moτe3）Huang，Y，，τsuc短ya，H．andlshihara，K。G999）IEs［imationof partial saturat1on elぞecτ o【1 1呈q疑efaction resistance of sand using P−wave velocity，P1ηぐ．／（フ55．wηρ．，113，431−434．4）Is賊1ara，K、，Tsuchiya，H．，Hロallg．Y．a自d Kamada，K．（2001）： RecentsεudiesonHquefactio睦res1stanceofsaad−e旋ctofsatura− tlon，Pro‘．4rlr／η’，Co’ゾ、Rθごθ’π．4ゴv‘71κθ111Gθo∼θ‘11．ε‘7π11σμαたθ E1191’9，αηゴSo’10、w1αη11c5，1−75） 釣iart玉a，G．R、，Fi自11，∼V．D．L、and See（玉，H、B，（1978）：E齪eCts of sys葛emcompllanceoniiquefactlontests，ノ．Gθαθ‘17．五η9’8．P’v．． ASCE．茎04（4），463−479．6）Okamura，M．，ls漁ara．M、andOshita，丁．（2003）＝Liq毛！efa面ollsigni負cant t勤an that of tke water table oτthe i勲itial pore resistance of san（i improved widl sand compaction p鉦es，So’Z∫αnゴpressu「e・ Fαぜn面”oη5，43（5），175−187、7）Okam球ra，M，andTeraoka，丁、（2005）：ShaklngIable芝ests［oinves一 芝igatesolldesatura“onasaliquefaαio自co蝋emleasure，Gθαθぐ1LCONCLUDING REMARKS Sρθぐ’α1P‘’か1’ごor’oη 145．．ASCE，282−293． Resistance to liquefaction of partia至1y saturated sand sa田rationan引1quefactionres1stancesofsandimprovedwithsandwas investigated through a series of triax量al tests in this compact1on piles，／．Gθo’θoh．（3θoθノ∼v’1’01L石11911g、，ASCE，B2（2），study． Three parameters obtained from theoreticalcons圭deration，that is the degree of saturation，the initia｝con§ningPτessuτeandtlleinitial貸uidpressurre，wereselected as testing par＆meters in the series of undrained8）Okamura，M．，lshlぬara，M、andτaR1縫ra，K．（2006）：Degreeof 258−264．9） Tokima｛sロ，K．，Yoshimi，Y、and Ari｝zumi，K．〔1990）：Evaluation of l1quefactionres1stanceofsandimprovedb》・deepvibra［ory compaαion．So’1∫αηゴFα〃1面’011∫，30（3），15M58．10）Tsukamoto，Y，Ishlbara，K．，Nakazawa，9、，Kamada，K．andCyCliC tτiaXial teStS． Huang，Y、（2002）：Reslsτance of par［iaHy samrated sa負d 〔Q It is co面rmed that the degree of saturationぬas liquefaction w註h refereace to longitudinal and s騒ear wave veloci−signific＆nt e任ect on tl｝e Iiquefact量on resistance of sand．T』e liquefaction resistance also depends oa the initialcon負ning pressure and the init三al pore pressure．The ef墨ectof the existence of air on the liquefaction resistance玉smore s玉gni員cant foτ soil under the higher confiningpressure and the Iower initial pore pressure。This factimplies that the e行ect of the degree of satllration of soil is ties，50’Z50η‘ノFoμη‘ノα”oη∫，42（6），93−104H）Yasuda，S．，Kobayashi，T，，Fukushima，Y。，Ko』ari，M alld Simazakl，T、（互999）：E霞ectofdegreeofsaturatlo蹟ontheHquefac− 60厳 s重rength of 蒼vlasa， Proご． 34’11 ノρノL 八竹f． Co∼7∫． （3θo’θ‘h． 五ηgrg．，207ロ072．12〉Yoslllml，Y．，Ta麟aka，K．and Toklmatsu，K．（1989）l Liquefac【io“ res1stanceofapartiallysaturatedsand，So’Z5α’1ゴだα〃∼伽’o／1∫， 29（3〉，豆57−162，
- ログイン
- タイトル
- JGS NEWS
- 著者
- 出版
- soils and Foundations
- ページ
- I〜III
- 発行
- 2006/10/15
- 文書ID
- 20952
- 内容
- ログイン