Soils and Foundations
タイトル | 表紙(Soils and Foundations) | ||||
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出版 | Soils and Foundations | ||||
ページ | -〜- | 発行 | 2008/06/15 | 文書ID | 21108 |
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タイトル | Contents(Soils and Foundations) | ||||
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出版 | Soils and Foundations | ||||
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タイトル | Viscous Behaviour of Unbound Granular Materials in Direct Shear | ||||
著者 | A. Duttine・Fumio Tatsuoka・W. Kongkitkul・Daiki Hirakawa | ||||
出版 | Soils and Foundations | ||||
ページ | 297〜318 | 発行 | 2008/06/15 | 文書ID | 21110 |
内容 | 表示 SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 297318, June 2008VISCOUS BEHAVIOUR OF UNBOUND GRANULARMATERIALS IN DIRECT SHEARANTOINE DUTTINEi), FUMIO TATSUOKAii), WARAT KONGKITKULiii) and DAIKI HIRAKAWAiv)ABSTRACTThe viscous properties of a variety of poorly graded unbound granular materials were investigated by direct sheartests on 12 cmcubic specimens. A number of natural sands having dierent particle shapes and sizes as well as uniformglass beads having dierent particle sizes were used. The viscous properties were evaluated by changing the shear displacement rate many times during otherwise monotonic loading (ML) at constant shear displacement rate and normalpressure. Creep loadings were performed in two tests. Dierent types of viscous properties, which are aected by theparticle shape but essentially independent of the particle size, are reported. The viscosity type varies as the shear displacement increases from the prepeak regime towards the residual state. A new viscosity type, called ``Positive &Negative'', was found with relatively round granular materials in the prepeak regime and with relatively angulargranular materials in the postpeak softening regime and at the residual state. Peculiar ``rateindependent unstable behaviour'' is observed with round natural sands and glass beads in the postpeak regime, which is more signicant andfrequent with glass beads. Controlled by the particle size, this behaviour is caused by the socalled stick/slipphenomenon. The viscous properties observed in the DS tests are quantied by the ratesensitivity coecient dened interms of the shear and normal stresses, which are then converted to those dened in terms of the major and minor principal stresses, b13. These b13 values are consistent with those directly obtained by the triaxial and plane strain compression tests. The eects of particle size on the b13 value are negligible and the b13 value tends to decrease as the particleshape becomes more round.Key words: direct shear, particle shape, Positive & Negative, rate sensitivity coecient, stick/slip behaviour,strain/displacement rate, TESRA, unstable behaviour, viscosity, viscous properties (IGC: D6/D7)loading rate eect is the topic of this paper.A number of previous researches showed that, in various types of laboratory stressstrain tests, the stressstrainbehaviour of unbound granular materials (i.e., sands andgravels) is ratedependent even when eects of ratedependent changes in the pore water pressure are negligible with saturated soils or when the specimen consists ofdried particles. The ndings from these studies can besummarized as follows:INTRODUCTIONOne of the important practical geotechnical engineering issues is the accurate prediction of longterm grounddeformation and associated residual displacements ofcivil engineering structures. To this end, the timeeectson the stressstrain behaviour of geomaterial should beunderstood correctly and properly. Even if the inuenceof pore water pressure changes is not involved, the following two types of time eects should be taken into account (e.g., Di Benedetto et al., 2005; Tatsuoka et al.,2008): the ageing eect, which can be dened as ``changeswith time in the intrinsic stressstrain properties due totimedependent changes in interface and/or internal particle properties caused by a physicochemical process''and the ``viscous or loading rate eect'', which can be attributed primarily to the ``viscous deformation and sliding at interparticle contact points and its eects on thestructural stability of a given soil mass''. The viscous ori)ii)iii)iv)1)Four basic viscosity types of geomaterial in shear,Isotach, Combined, TESRA and P&N, have beenrevealed (Tatsuoka et al., 2008). Figure 1 schematically shows the stressstrain curves for these viscositytypes in relation to the reference curve, which is theinviscid stressstrain relation to be obtained by an imaginary monotonic loading (ML) test at zero strainrates. This viscosity type categorisation is made within a nonlinear three component framework (Fig.Postdoctoral Fellow, Institute of Industrial Science, University of Tokyo, Japan (formerly Department of Civil Engineering, ENTPE,France).Professor, Department of Civil Engineering, Tokyo University of Science, Japan (tatsuokars.noda.tus.ac.jp).Lecturer, Department of Civil Engineering, King Mongkut's University of Technology Thonburi, Thailand.Assistant Professor, Department Civil and Environmental Engineering, National Defense Academy of Japan, Japan.The manuscript for this paper was received for review on January 11, 2007; approved on February 5, 2008.Written discussions on this paper should be submitted before January 1, 2009 to the Japanese Geotechnical Society, 4382, Sengoku,Bunkyoku, Tokyo 1120011, Japan. Upon request the closing date may be extended one month.297298DUTTINE ET AL.Fig. 1. Schematic stressstrain curves for four basic viscosity types ofgeomaterial in shear (after Tatsuoka et al., 2008a): with the fourviscosity types, the same stressstrain curve when ·e is equal to ·e0 aswell as the same positive stress jump for a step increase in ·e by afactor of ten are assumedreported similar trends of behaviour of Hostun andToyoura sands in torsional shear (TS) tests.Moreover, in all of these PSC, TC/TE and TS tests,upon a sudden step change in the strain rate duringotherwise ML at a constant strain rate, the stress exhibited a sudden jump that was followed by gradualor fast decay with the stressstrain curve rejoining theoriginal one before a step change in the strain rate.This trend has been called the TESRA viscosity (i.e.,Temporary Eects of Strain Rate and strain Acceleration) (Di Benedetto et al., 2002; Tatsuoka et al.,2002). The Combined viscosity type has the featurescombining those of the Isotach type and the TESRAtype.3) The nonlinear three component framework (Fig. 2)can simulate very well the abovementioned trends ofratedependent stressstrain behaviour (Di Benedettoet al., 2001, 2002; Duttine et al., 2007a; Pham VanBang et al., 2007; Tatsuoka et al., 2002, 2007, 2008).4) The basic viscous properties of a given geomaterialcan be properly quantied by the ratesensitivitycoecient, b13, which is the slope of the DR13/R13|log ( ·g irafter/ ·g irbefore) relation:DR13/R13log s( ·g ir13)after/( ·g ir13)beforetb13Fig. 2. Nonlinear threecomponent framework for constitutivemodeling of the stressstrain behaviour of geomaterial (hs: historyparameter) (after Di Benedetto et al., 2002; Tatsuoka et al., 2002)2)2). The classical Isotach behaviour is dened by theviscous stress component (i.e., sv in viscous body V)that depends on instantaneous irreversible strain andits rate. Then, the shear strength during ML tests increases with strain rate. This viscosity type has beenobserved mainly with more coherent geomaterials,such as sedimentary soft rock and plastic clays(Tatsuoka et al., 2004, 2006, 2007, 2008).A poorly graded ne angular sand, Hostun sand,either airdried or drained saturated, exhibited arather unique stressstrain curve in continuous MLplane strain compression (PSC) tests at constant butstrain rates dierent by a factor up to 500 (Matsushita et al., 1999). This nding was reconrmed bydrained triaxial compression (TC) tests on anothertype of poorly graded angular ne sand, Silica No. 8sand (Kiyota and Tatsuoka, 2006). With the sametypes of sands, signicant creep deformation andstress relaxation took place in PSC tests (Matsushitaet al., 1999), TC tests (Matsushita et al., 1999; Kiyotaand Tatsuoka, 2006; Enomoto et al., 2007; PhamVan Bang et al., 2007, among others) and triaxial extension (TE) tests (Kiyota and Tatsuoka, 2006). DiBenedetto et al. (2001) and Duttine et al. (2007a) also5)(1)where DR13 is a sudden change in the eective principal stress ratio R13s1/s3 caused by a step changein the irreversible shear strain rate from ( ·g ir13)before to( ·g ir13)after at a given R13 value and ·g ir13 is the irreversibleshear strain equal to ·eir1| ·eir3 (Tatsuoka et al., 2002,2004, 2006). In addition:a) the eects of conning pressure and dry densityon b13 are insignicant in drained TC on Toyourasand (Nawir et al., 2003). Kiyota and Tatsuoka(2006) showed that the same denition of b13 isrelevant to both TC and TE stress conditions forToyoura, Hostun and Silica No. 8 sands and alsothat the eects of overconsolidation on b13 arenegligible (with Toyoura sand).b) Tatsuoka et al. (2006), Tatsuoka (2007) andEnomoto et al. (2007) evaluated the eects ofparticle size, grading uniformity and particlecrushability on b13 by performing a series ofdrained TC tests on a wide variety of granularmaterials. They showed that, for a wide range ofthe mean particle diameter D50 from 0.0013 to 7.8mm, the eects of D50 on b13 are insignicant except for saturated clay for which the eects ofpore water on b13 are signicant, and that thevalue of b13 tends to increase with an increase inthe coecient of uniformity as well as particlecrushability.Tatsuoka (2007, 2008) and Enomoto et al. (2007)also reported results from a set of TC tests performedon relatively round granular materials: a granulatecomposed of sti particles of Aluminium Oxide(corundum) and natural poorly graded ne sands. Asschematically depicted in Fig. 1, another very specicVISCOUS BEHAVIOUR OF GRANULAR MATERIALSviscous response, named P&N, was observed: i.e., inthe ML tests at a constant but dierent strain rates,the materials became stier and stronger with adecrease in the strain rate. This surprising behaviourhas been called ``negative Isotach viscosity'', opposed to ``positive Isotach viscosity''. In addition,the materials also showed a sudden `TESRA' increase (which is positive in its nature) in their viscousstress component upon a strain rate step increase,followed by decay with irreversible strain. Dierentfrom the TESRA viscosity, the stress decayed towarda residual value that is lower than the one that wouldhave been obtained if ML had continued at the previous lower strain rate. These trends became more obvious after the peak stress state. This peculiar type ofviscosity has therefore been called the Positive andNegative (P&N) viscosity.Despite these signicant ndings, the viscous behaviour in the postpeak regime and at the residual state isonly very poorly understood. In view of the above, thepresent study aims at:1) providing data from direct shear (DS) tests to obtainan overall picture of the viscous properties of granular material for a wide range of strain from the prepeak to the residual state;2) evaluating the inuence of particle shape on the viscous properties of granular materials; and3) quantifying the viscous properties of granularmaterials in DS and then relating them to those evaluated previously by TC and PSC tests.299Fig. 3. Dierent types of DS shear boxes (modied from Shibuya etal., 1997)DIRECT SHEAR APPARATUS (DSA)The DSA has a number of inherent drawbacks, mostlyoriginating from inevitably nonuniform stress and strainconditions associated with a progressive failure in thepotential (horizontal) shear zone. Numerical studies ofthe deformation and failure of granular material in DS byFEM or more recently by DEM showed that the principalaxes of distributed contact force and initial rupture zonemay rst develop diagonally, not horizontally from thespecimen edges (Potts et al., 1987; Cui and O'Sullivan,2006). To minimize the eects of these inherent drawbacks and to match as much as closely to a ``quasisimpleshear'' mode in the potential horizontal shear zone, attempts have been made to optimize the DSA design bymodifying the conventional type (Jewell and Wroth,1987; Shibuya et al., 1997; Lings and Dietz, 2004). Referring to Fig. 3, the conventional DSA is categorized intotype A, whereas the improved types into types B and C.The major problems with type A concern: a) the rotationof the upper box; and b) the side wall frictions. That is,the normal load is applied to the centre of the top loadingplaten that is not xed against rotation. As a consequence, when subjected to lateral shearing, the distribution of normal stress along the central horizontal shearplane becomes inevitably biased (so does the shear stress)to maintain the equilibrium of moment within the specimen, which results in a more progressive mobilization ofFig. 4.3)Direct shear apparatus constructed in this study (type B in Fig.the shear strength along the central horizontal plane.Moreover, unless the vertical movement of the top shearbox is free, the vertical load applied at the top loadingplaten becomes dierent from the value acting on theshear plane due to the vertical friction acting along the inner walls of the top shear box caused by the volumechanges of the specimen. To alleviate these problems, thetop loading platen is xed against rotation with types Band C. With respect to the side wall friction, the verticalload W is basically free from these eects in type B,whereas, with type C, the vertical load should be measured at the bottom of the lower shear box (Wlower in Fig.3; Shibuya et al., 1997).The DSA used in this study (Fig. 4) is type B and wasdesigned and constructed following the above mentionedconsiderations. The specimen size is 12 cm~12 cm~12300DUTTINE ET AL.Fig. 5. Horizontal frictional stress tf at the bottom of the lower DSbox, dense glass beads (D500.2 mm) (a test reported in Fig. 19)Fig. 6. Variation of local and average normal stresses on the top of theupper DS box, dense Toyoura sand (a test reported in Fig. 8)cm, having the following characteristic features:1) The lower box (No. 8 in Fig. 4) moves on a lowfriction supporting rail (No. 12). The upper box (No. 7)is xed horizontally by means of two rigid stoppingplates (No. 5) while lowfriction ball bearings (No. 6)allow its free vertical displacements. The horizontalfriction acting between the lower box and the rail ismeasured with a pair of friction load cells (No. 14).Figure 5 shows results from a typical test on glassbeads of D500.2 mm. The total friction in terms ofaverage horizontal shear stress tf acting at the bottomof the lower box is very low, about 0.5z of theaverage vertical stresses sv employed in the presentstudy (i.e., 50 and 100 kPa). The friction load cellswere used in the latter stage of the present study. Theshear load measured with shear load cell (No. 10) wasthen corrected for this friction. Based on the resultsfrom these latter stage tests, the measured shear loadwere otherwise corrected for the similar tests performed at the initial stage of the study (before installing the friction load cells). The results from the testsperformed before and after installing the frictionload cells are essentially the same.2) By independently controlling the airpressures supplied to a pair of doubleaction air cylinders (No. 1)by means of a computer servocontrolled system, theoverturning moment caused by the applied lateralshear load is compensated to keep the upper shearbox level and, at the same time, to maintain theaverage vertical load at a prescribed value. Therefore, the dierence between the normal loads appliedby two aircylinders becomes larger with an increasein the applied lateral shear load, as can be seen typically from Fig. 6 (for a test on Toyoura sand). Here,sv.rear and sv.front are the averaged local normal stresses obtained by dividing the normal loads applied bythe aircylinders with a half of the crosssectionalarea of the specimen. sv.rear is much higher than sv.frontand the ratio sv.rear/sv.front is around ve at the peakstress state and subsequent states. Therefore, if thetwo aircylinders apply the same normal load, theupper shear box should rotate signicantly, associated with a signicantly nonsymmetric stress distribution of the vertical stress along the shear zone. Thenormal stress distribution along the central shearzone can become uniform only by keeping the uppershear box level (Shibuya et al., 1997).3) A piece of sponge tape (No. 9) is glued to the lowerperiphery of the upper box rstly to prevent sandfrom spilling out from the opening during shearingand secondly to prevent the inside volume of theshear box from increasing because of shear displacement so that the volume change takes place in thespecimen due solely to the dilatation or contractionof sand. As sponge is easy to compress and swell, itexhibits negligible vertical and shear force unless it isextremely compressed.4) The relative shear displacements between the upperand lower shear boxes, which are hereafter reported,were measured by using a laser displacement transducer (No. 11) xed to the lower box with a target onthe upper box. The lateral displacements of the lowershear box, which included errors due to the testingsystem compliance, were measured by using a LVDTxed on the bottom platen (No. 4'). Yet, the maximum dierence between the two measurements,which was observed at the peak shear stress, was verysmall, of the order of 0.3 mm.5) The shear displacement was imposed in an automated way by using a high precision gear loading devicedriven by a servomotor (Santucci de Magistris et al.,1999; Tatsuoka et al., 2000). The applied displacement rate basically ranged from 0.008 mm/m to 0.8mm/m.The proper performance of this DSA was examined byconducting a series of ML tests on dense specimens ofToyoura sand. The test results were very consistent withthose from tests using other similar DS apparatuses (Quiet al., 2000; Wu et al., 2008).VISCOUS BEHAVIOUR OF GRANULAR MATERIALSTable 1.Physical properties of the materials tested in this studyMaterialGsD50 (mm)Toyoura2.648Hostun(2)emax(2)Ucemin0.1801.6250.5920.9782.6580.3401.4210.6211.034(1)2.6580.2902.4270.6711.174Silica No. 6a2.6470.1601.7220.7121.168Albany2.6710.3002.2000.5050.804SLB2.6600.6811.4300.4900.790Ticino2.6800.5271.5210.5900.960Ottawa2.6700.1741.7600.5150.864Monterey2.6400.4841.400Silica No. 6GB0.40GB0.20GB0.15GB0.10GB0.07GB0.05(1)(2)(3)2.4972.4972.4972.4972.4972.4970.4000.2000.1500.1000.0700.0500.5500.8601.205(3)0.5770.7261.188(3)0.5930.7831.092(3)0.5780.7331.093(3)0.5980.7871.181(3)0.6000.7941.322(3)0.5980.835GRANULAR MATERIALS TESTEDThe granular materials tested in this study (Table 1,Fig. 7 and Photo 1) are all poorly or uniformly graded.The following eight types of natural quartzdominatedsands from largely dierent origins were used: Toyoura(Japan), Hostun (France), Ticino (Italy), Silica No. 6a(Japan), Albany (Australia), Ottawa (Canada), Monterey(USA) and Silver Leighton Blizzard (SLB) (UK). Themean particle size D50 ranges from 0.16 to 0.68 mm.Toyoura, Hostun, Ticino and Silica No. 6a are relativelyangular, whereas Albany, Ottawa, Monterey and SLBare relatively round. Glass beads having the followingdierent sizes were also used as granular materials havingan extreme particle shape (i.e., spherical): 0.05 mm, 0.07Used in drained TC in previous studies (see Fig. 29).Determined according to the guideline JSF.T 1611990 edited by theJapanese Geotechnical Society.Based on the data provided by the manufacturer (TGK Co. Ltd.).Fig. 7.Photo 1.301Grading curves of the materials tested in this studyParticle pictures and particles shape classication of the materials used in this study302DUTTINE ET AL.Table 2.(1)List of the test conditions for the tests referred in this paperMaterialDr0 (z)(1)sv (kPa)(2)Initial opening(cm)Shear loadinghistoryUse ofbottom LCsNos. of relatedguresToyoura95.041000.200VDR(3)No6811202829Hostun90.251000.370VDRNo811202829(4)Hostun94.541000.370CPYes24Silica No. 6a93.74500.160VDRNo91220222829Albany94.921000.300VDRNo1315202829Albany103.111000.370CPYes24SLB91.621000.550VDRNo1315202829Ticino94.481000.500VDRNo91220212829Ottawa88.871000.180VDRNo1416202829Monterey93.431000.475VDRNo1416202829GB0.40104.201000.450VDRNo172023(5)Yes1720GB0.4090.731000.460GB0.20103.671000.250MLYes51920GB0.20104.511000.200VDRNo2829GB0.15100.391000.250VDRNo19202829GB0.10101.831000.200MLYes1920GB0.10100.571000.200VDRNo2829GB0.0793.84500.140VDRYes19202829GB0.0598.3250Initial relative density before consolidation;ML0.100(2)Average normal pressure;mm, 0.10 mm, 0.15 mm, 0.2 mm and 0.4 mm. Silica No.6 sand was used in drained TC by Enomoto et al. (2007).The experimental program is summarized in Table 2.All the specimens were dense and airdried. The specimens of Toyoura sand were prepared by pluviating airdried particles from a hopper composed of four 1.5 mmsieves covering the whole area of the shear box. Thespecimens of the other types of material were prepared bymultilayer volumecontrolled tamping: i.e. the specimenbeing divided into a number of sublayers (typically 7 or8), each sublayer is successively tamped with a squaresteel rod very carefully so that the prescribed mass andheight of the specimen is precisely achieved. All the testswere performed at a constant average normal pressure svof 50 or 100 kPa. As typically seen from Fig. 6, the valueof sv was kept highly constant. The initial opening between the upper and the lower boxes was adjusted byplacing a set of copper spacers having a prescribed thickness between the upper and lower boxes. The initial opening before consolidation was set between 10 and 20 timesD50 of the respective materials. From the completion ofthe specimen preparation until the end of consolidation,the vertical and horizontal displacements and the shearand normal loads were continuously monitored to ensurea minimum disturbance of the specimen. During shearing, the tolerance for the feedback of the tilting of the toploading platen, detected as the dierence between theVDR(3)Variable displacement rate;Yes(4)Creep periods;19202829(5)Continuous ML.measurements of the two vertical LVDTs (No. 4 in Fig.4), was }0.004 mm. This value was determined based onthe accuracy and response of the measuring and loadingsystems.EXPERIMENTAL RESULTSAngular Sands (Hostun, Toyoura, Silica No. 6a andTicino)Figure 8 presents the stress ratio (tvh/svRDS)sheardisplacement (s) relations and the vertical displacement(d, positive in compression)s relations from two tests onHostun and Toyoura sands. These two sands have beenextensively used in laboratory stressstrain tests at theUniversity of Tokyo, the ENTPE and the Tokyo University of Science: Tatsuoka et al. (1986a), Park and Tatsuoka (1994), Matsushita et al. (1999) and Yasin et al. (2000)in drained PSC tests; Goto (1986), Tatsuoka et al.(1986b), Di Benedetto et al. (2001, 2005), Pham VanBang et al. (2003, 2007) and Kiyota and Tatsuoka (2006)in drained TC tests, Tatsuoka et al. (1986c), Di Benedettoet al. (2001, 2005) and Duttine et al. (2007a, 2007b) indrained TS tests; and Qui et al. (2000), Wu et al. (2006)and Duttine et al. (2006) in drained DS tests. In these studies, these two sands exhibited very similar mechanicalbehaviour and it is also the case in the DS tests (Fig. 8). Inthese tests, the shear displacement rate s· was stepwiseVISCOUS BEHAVIOUR OF GRANULAR MATERIALS303Fig. 8. RDSs and ds relations from two DS tests on dense specimens of Hostun and Toyoura sands (subangular to angular): a) whole relationsand; zoomsup: b) prepeak, c) postpeak and d) residual statechanged many times during otherwise ML at a constant s· .Figures 8(b), (c) and (d) are the zoomedup RDSs andds relations. Dierent trends of stress response upon astep change in s· may be seen. That is, in the prepeak regime (Fig. 8(b)), immediately after s· is suddenly reducedby a factor 10, tvh exhibits a sudden decrease, which isfollowed by decay during the subsequent ML at a lower s·towards the stress level reached if the ML had continuedat the previous higher s· . This trend of viscous behaviour,called the TESRA viscosity, can be observed similarlywith both sands in the prepeak regime. This test result isconsistent with the one that has been observed in thedrained TC and PSC tests (Kiyota and Tatsuoka, 2006;Pham Van Bang et al., 2007; Matsushita et al., 1999). Ifthe shear strain takes place only in the shear zone, theaverage shear strain in the shear zone can be obtained bydividing a given shear displacement by the shear zonethickness. However, the actual strain distribution in theDS specimen is much more complicated and the shearzone thickness is not necessarily equal to the thickness ofa single shear band (e.g., Wu et al., 2008). Therefore, itwas not attempted to evaluate the shear strains in theshear zone in the present study.It was found rst by the present study that the TESRAviscosity remains valid only until just after the peak stressstate but the viscosity type gradually changes to anotherand this trend becomes more obvious at later stages in thepostpeak regime toward the residual state (Figs. 8(c) and(d)). This another viscosity type is characterised by theresidual shear stress observed during the subsequent MLat a higher constant s· being lower than the value thatwould have been obtained if the ML had continued at theprevious lower s· without a step increase, and vice versa.As discussed earlier, this viscosity type has been called the``Positive and Negative (P&N)'' viscosity, as it comprisesof a positive viscous component responsible for the temporary shear stress increase upon an increase in s· (or anincrease in the shear strain rate), which always competeswith a negative viscous component responsible for thelower residual shear stresses at a higher s· (or a highershear strain rate). It is to be noted that the relevantparameter to describe the viscous shear stress decay is theirreversible (or inelastic) strain (or shear displacement) increment, not the general time increment (Tatsuoka et al.,2002; Di Benedetto et al., 2001), for example, as seenfrom Figs. 2 and 8(b), the decay rates of the shear stressdecrease that has taken place upon step decrease in s· (orthe shear strain rate) with shear displacement (or shearstrain) is nearly the same for dierent values of s· , but thedecay rates with time are totally dierent (i.e., by a factorof 10 in the case of Fig. 8(b)).Figure 9 shows results similar to Fig. 8, from the DS304DUTTINE ET AL.Fig. 9. RDSs and ds relations from two DS tests on dense specimens of Silica No.6a and Ticino sands (subangular to angular): a) whole relationsand; zoomsup: b) prepeak, c) postpeak and d) residual statetests on two others relatively angular sands, Ticino andSilica No. 6a. The same trends of viscous behaviour canbe seen as Hostun and Toyoura sands: i.e., a progressivetransition from the TESRA viscosity in the prepeak regime to the clear P&N viscosity at the residual state.The P&N viscosity is not totally new. That is, a similartrend of P&N viscosity has been observed in the prepeakregime in drained TC tests (Tatsuoka et al., 2008). TheP&N viscosity (a fortiori the TESRA viscosity) has alsobeen recognised as one of the possible friction laws inGeophysics. Constitutive rate and statedependent friction laws (such as socalled Dieterich law, Ruina law orPRZ law) have been introduced since the 1980's to initially simulate the rock friction then the gouge friction andthe sliding stability of solids (e.g., Marone, 1998; Rice etal., 2001) based on results from related experiments. Inthe experiments, the gouges were often simulated by thinlayers of granular quartz sand and their frictional characteristics were evaluated by means of an annular simpleshear apparatus (Chambon et al., 2002) and a DSA (Mairand Marone, 1999). They have reported remarkable similar trends of shear displacement rateweakening frictionat large shear displacements as observed in the presentstudy. However, a transition of viscosity type with sheardisplacement (or shear strain) and possible eects of particle shape on the viscosity type and transition patternFig. 10. Denitions of the physical quantities used to express the ratesensitivity coecients (Eq. (2))have not been reported.From Figs. 8 and 9, it may be seen that the ds relationship exhibits insignicant or little ratedependency. Thisfeature is discussed in detail later.Quantication of viscous properties: By referring toEq. (1), the viscous properties observed in the DS testswere quantied by the following parameters (Fig. 10, inthe case of a step increase in s· ):DRDS/RDSlog (·s irafter/·s irbefore)bDSD(RDS)r/(RDS)rlog (·s irafter/·s irbefore)(bDS)r(2a)(2b)VISCOUS BEHAVIOUR OF GRANULAR MATERIALSFig. 11.Fig. 12.305Variation with shear displacement of: a) and c) bDS and (bDS)r; and b) and d) u, Hostun and Toyoura sands (subangular to angular)Variation with shear displacement of: a) and c) bDS and (bDS)r; and b) and d) u, Silica No. 6a and Ticino sands (subangular to angular)(bDS)rbDSu(2c)where bDS is the ratesensitivity coecient, where DRDS isthe jump in RDStvh/sv taking place upon a step changein the irreversible shear displacement rate, s· ir, from s· irbeforeto s· irafter when the stress ratio is equal to RDS. Note thats· irafter/·s irbefore is nearly the same as s· after/·sbefore under the test306DUTTINE ET AL.conditions in this study. (bDS)r is the residual ratesensitivity coecient (Enomoto et al., 2007), where D(RDS)rdenotes the residual value of DRDS after it has fullydecayed during the subsequent ML. u is the viscositytypeparameter: i.e., u0 for the TESRA viscosity and uº0for the P&N viscosity, while u1.0 for the classicalIsotach viscosity. Note that any value below 1.0 is possible.The values of bDS and ( bDS)r, therefore the value of u,are not necessarily constant in a given DS test as seenfrom Figs. 11 and 12. In these and other similar gures,the range of the data is indicated by a band to illustratethe general trend. The peak stress strange dened by RDSvalues larger than around 80z of the peak value is alsoindicated. From Figs. 11 and 12, one may note the following similar trends:a) bDS is kept rather constant for a wide range of s except for Silica No. 6a sand, with which bDS graduallydecreases with s (Fig. 12(a)). Yet, the variation ismuch smaller than that of ( bDS)r.b) ( bDS)r and therefore u show a clear transition fromessentially null values (i.e., the TESRA viscosity) until around the peak stress state towards negativevalues (i.e., the P&N viscosity) in the postpeak regime. Then, these parameters are kept rather constant at the residual state.Round Sands (Albany, SLB, Ottawa and Monterey)The test results for Albany, SLB sands and Ottawa,Monterey sands are presented in Figs. 13 and 14. In thesetests, the P&N viscosity is obvious already in the prepeakregime and around the peak stress state (Figs. 13(b) and14(b)). With Albany sand, this trend is consistent with theone in the TC test (Tatsuoka et al., 2008). However, inthe postpeak strainsoftening regime (Figs. 13(c) and14(c)), the viscous property gradually becomes verypeculiar, of which the trend is more obvious at the residual state (Figs. 13(d) and 14(d)); that is:a) Despite that tvh suddenly increases upon a stepwiseincrease in s· , the increase is noticeably smaller thanthe one with relatively angular materials (Figs. 8 and9).b) Immediately after a sudden increase in tvh (as described above), tvh exhibits a sudden and large temporary drop towards a value much lower than thesubsequently observed residual strength (i.e., unstable behaviour). This stress drop is associated with astrong contraction of the material.c) Subsequently, tvh gradually recovers towards theresidual value, which is however still lower than thevalue that would have been obtained if ML had continued at the previous lower s· .Fig. 13. RDSs and ds relations from two DS tests, dense Albany and SLB sands (relatively round): a) whole relations and; zoomsup: b) prepeak,c) postpeak and d) residual state (SD: stress drop during ML)VISCOUS BEHAVIOUR OF GRANULAR MATERIALS307Fig. 14. RDSs and ds relations from two DS tests, dense Ottawa and Monterey (relatively round): a) whole relations and; zoomsup: b) prepeak,c) postpeak and d) residual stated)Upon a stepwise decrease in s· , a clear P&N viscosityresponse is exhibited without the unstable behaviourdescribed above, as relatively angular sands.The trends a, c and d indicate that the basic viscositytype in the postpeak regime and at the residual state ofthese relatively round sands is still the P&N viscosity. Onthe other hand, the trend b (unstable behaviour) is obviously a dierent phenomenon. Moreover in the case ofAlbany and SLB sands, as indicated by a notation SD inFig. 13(c) and (d), similar sudden and signicant shearstress drops, associated with a strong contraction, occurred occasionally during otherwise continuous ML at arelatively low s· . Therefore, it is very likely that this unstable behaviour, followed by stress recovery, is not a viscous response of the sand but is linked to the socalledstick/slip phenomenon (discussed later).Figures 15 and 16 show how bDS, ( bDS)r and u changewith s in the DS tests on, respectively, Albany and SLBsands and Ottawa and Monterey sands. Unlike relativelyangular sands, the increase in tvh upon a step increase in s·is sometimes very dicult to dene when compared withthe decrease in tvh upon a step decrease in s· . Thus, the bDSvalue (therefore the u value) was evaluated based on onlythe sudden decrease in tvh upon a step decrease in s· . Onthe other hand, the values of ( bDS)r were evaluated basedon both increases and decreases in the residual shearstress upon step increases and decreases in s· . The following trends may be seen from these gures:1) bDS is rather constant for a wide range of s overdierent regimes (i.e., prepeak, postpeak and residual), similar as the relatively angular sands.2) ( bDS)r is consistently negative with all these relativelyround sands, compared with consistently positivevalues of bDS.3) ( bDS)r of the relatively round sands is generallynoticeably lower than the relatively angular materials, resulting in relatively lower negative values of u.4) ( bDS)r, therefore u, is rather constant over a wholerange of s in the present study with Albany sand(Figs. 15(a) and (b)) and Monterey sand (Figs. 16(c)and (d)). On the other hand, with SLB sand (Figs.15(c) and (d)) and Ottawa sand (Figs. 16(a) and (b)),( bDS)r, therefore u, decreases with s at large ratesaround the peak stress state, in a similar way as therelatively angular sands.These facts reconrm that the viscosity type of theserelatively round sands is basically of the P&N type as therelatively angular sands in the postpeak regime and atresidual state, although the parameters representing theviscosity are quantitatively dierent.308DUTTINE ET AL.Fig. 15.Fig. 16.Variation with shear displacement of: a) and c) bDS and (bDS)r; and b) and d) u, Albany and SLB sands (relatively round)Variation with shear displacement of: a) and c) bDS and (bDS)r; and b) and d) u, Ottawa and Monterey sands (relatively round)Spherical Granular Materials (Glass Beads)A series of DS tests were performed on glass beads ofdierent particle sizes (i.e., uniform spherical granularmaterials). Figures 17(a), (b) and (c) show the test resultsVISCOUS BEHAVIOUR OF GRANULAR MATERIALSFig. 18.Fig. 17. RDSs and ds relations from two DS tests (ML and VDR),dense glass beads with D500.4 mm: a) whole relations and;zoomsup: b) prepeak and c) residual statefor D500.4 mm. It may be seen that signicant shearstress drop occurs repeatedly and frequently, which issystematically associated with a contraction of the specimen, from slightly before the peak stress state until theresidual state. Each stress drop is immediately followedby its recovery associated with dilation. At the residualstate, the shear stress drops signicantly even from thesocalled residual shear strength towards a lower value.309Ilustrating: a) slip; and b) stick phenomenaThis result indicates that the force chains in the shearzone are somehow destructed in this event. These trendscan be explained by a very simple physical model shownin Fig. 18. In the course of shearing, an assembly consisting of uniform spherical particles would exhibit a suddendrop in the shear stress when particles slide over the crestof the neighbouring particles towards the adjacent porespace (i.e., slip eects associated with volume contraction). Then, the shear stress would be recovered by the``climbing'' of the same particles towards the crest of thenext neighbouring particles (i.e., stick eects associatedwith volume expansion). This phenomenon is basicallyrateindependent.The following may be conceived from the above:a) The frequency of this event per shear displacement isinversely proportional to the particle size.b) The minimum value of RDS in the respective eventscan be interpreted as the coecient of physical friction at the interparticle contact points. Then, theshear stress drop in the respective events is independent of particle size.c) The amount of specimen contraction is proportionalto the particle size.To examine these inferences, other DS tests were performed on glass beads having dierent particle sizes: i.e.continuous ML tests on glass beads of D500.2 mm and0.1 mm (Figs. 19(a) and (b)); and a variable shear displacement rate test on D500.05 mm (Figs. 19(c) and(d)). It may be seen from Figs. 19(a) and (b) that glassbeads of D500.2 mm and 0.1 mm exhibited similar unstable behaviour as glass beads of D500.4 mm (Fig. 17).On the other hand, it may be seen from Figs. 19(c) and(d) that glass beads of D500.05 mm exhibited muchmore stable behaviour with otherwise very similar trendsof viscous behaviour as the relatively round naturalsands. The results from other DS tests performed on glassbeads having intermediate sizes, D500.15 mm and 0.07mm (Figs. 19(e) and (f)), showed consistent results: i.e.unstable behaviour when D500.15 mm and stable behaviour when D500.07 mm.These test results indicate that the inference a) is ratherrelevant: i.e. the minimum shear displacement intervalbetween two consecutive events at the residual statedecreases with a decrease in D50, being 0.118 mm (for D500.4 mm); 0.075 mm (D500.2 mm); 0.074 mm (D50310DUTTINE ET AL.Fig. 19. RDSs and ds relations from DS tests, dense glass beads; D50: a) 0.2 mm (ML); b) 0.1 mm (ML); c) and d) 0.05 mm (VRD); e) 0.15 mm;and f) 0.07 mm0.15 mm) and 0.048 mm (D500.1 mm). On the otherhand, the latter part of the inference b) is not relevant,which is due seemingly to the following factor. That is,for given dimensions of DSA, the number of uniformlygraded glass beads decrease inverseproportionally withan increase in the particle diameter. With a decrease inthe number of particles of a given assembly, the probability that a sucient amount of particles are arranged in thesame conguration to undergo simultaneous loss of stable interparticle contacts, therefore resulting into unstable global stressdisplacement behaviour, increases andvice versa. Figure 20 shows the relationships between theaverage ratio of the shear stress drop to the instantaneousshear stress, (DRDS)drop/RDS, and D50 from the DS tests onthe uniform glass beads. A trend that the stress drop increases with an increase in the particle size is obvious,conrming the inference cited above. Also plotted in Fig.20 are the data of the poorly graded natural sands testedin the present study; the trend of the stress drop increasing with the particle size is not noticeable. The dierenttrends between the glass beads and the relatively roundnatural sands can be attributed to the fact that the particle shape of the relatively round natural sands is notspherical and the grading is not as uniform as the glassVISCOUS BEHAVIOUR OF GRANULAR MATERIALSbeads. Furthermore, the stress drop is consistently nonewith the poorly graded relatively angular natural sands.We can therefore conclude that the possibility of the occurrence of the unstable global behaviour increases with adecrease in the number of particle for a given mass ofgranular material associated with an increase in D50, withan increase in the roundness of particle and with adecrease in the uniformity coecient. Finally, the inference c) was dicult to examine, as the specimen volumevariations in the respective events were too small to evaluate condently this issue.In view of the above, it is likely that the unstable globalbehaviour observed with the poorly graded relativelyround natural sands is due to the stick/slip phenomenonThis phenomenon is however aected by a complicatedcoupling between the particle size, the specimen size, s·and sv. It is also not yet understood why the stick/slipFig. 20. Stress drop ratio in function of D50 from the DS tests performed in the present studyFig. 21.311phenomenon occurs more systematically when suddenlyincreasing s· .Flow CharacteristicsThe ow characteristics (i.e., the relationship betweenthe ratio of irreversible vertical displacement rate to irreversible shear displacement rate, &d ir/&s ir, and the instantaneous stress ratio, RDS) for the dierent types ofgranular material are examined below. In the following,&d/&s is analysed in place of &d ir/&s ir, because they arevery similar except for the initial stage.Figures 21 and 22 present a set of local RDSd, RDSsand ds plots, related to each other, around the peakstress and residual states, typical of relatively angularsands. From Fig. 21, one may note that &d/&s is insensitive to the respective step changes in s· : for example, insections S to F, no discontinuity is observed in the &d/&svalue along the ds relation when tvh exhibits signicantjumps. This fact supports the framework of the nonlinear threecomponent model (Fig. 2), for which theow rule should be described in terms of the nonviscous(inviscid) stress (sf), not in terms of the total stress (ssf{sv). This remains valid also in the postpeak softeningregime (Figs. 8(c) and 9(c)). Hostun and Toyoura sandsdo not exhibit any signicant variations in the value of&d/&s upon a jump of tvh either at the residual state (Fig.8(d)). However, as can be seen from Fig. 22, with SilicaNo. 6a sand, at the residual state, the ow characteristicsare not controlled fully by the instantaneous inviscidstress nor by the instantaneous total stress: for example,for the same total stress at points a and b, the value of&d/&s at point a is signicantly larger than the one atpoint b. In summary, it is likely that the ow characteristics are basically controlled by the instantaneous inviscidstress but may become noticeably stresshistory dependent at the residual state.The same trends of ow characteristics as mentionedFlow characteristics at the peak stress state, Ticino sand (relatively angular) (see Fig. 9)312DUTTINE ET AL.Fig. 22.Fig. 23.Fig. 24.Flow characteristics at the residual state, silica No. 6a sand (relatively angular) (see Fig. 9)Flow characteristics at the residual state, glass beads (D500.4 mm, Dr0104.20%, sv100 kPa) (see Fig. 17)DS tests including creep periods, Hostun (relatively angular) and Albany (relatively round): a) whole relations and b) zoomsupVISCOUS BEHAVIOUR OF GRANULAR MATERIALS313above are observed with round sands in the prepeakstrainhardening and postpeak strain softening regimes(Figs. 13(b) and (c); and Figs. 14(b) and (c)). However, atthe residual state (Figs. 13(d) and 14(d)), once the stick/slip phenomenon becomes active, the ow characteristicsbecome totally dierent (Fig. 23). The RDSd relation during the stick/slip phenomenon is highly reversible.Creep DeformationTwo tests including creep periods were conducted on arelatively angular and relatively round sands having similar values of D50, Hostun and Albany sands (Fig. 24). Itmay be seen that both sands exhibit noticeable creepstrains while the creep strain during otherwise the sameconditions is smaller with relatively round sand which exhibits P&N behaviour (Albany sand) than with relativelyangular sand which exhibits TESRA behaviour (Hostunsand). Similar observations in TC were reported byTatsuoka (2007) and Enomoto et al. (2007). Analysis ofthese trends by the model (Fig. 2) is reported by Kongkitkul et al. (2008).Fig. 25. Mohr's circles of: a) incremental strain; and b) stress, undersimple shear conditionsCOMPARISON AMONG VISCOUS PROPERTIES INDS, TC AND PSCAs mentioned in Introduction, a number of previousstudies (e.g., Tatsuoka et al., 2002, 2006; Kiyota andTatsuoka, 2006) have shown that the viscous propertiesare consistent under the PSC, TC and TE test conditionswhen expressed by the ratesensitivity coecient b13 dened as R13s1/s3 (Eq. (1)). In the following, it is examined whether the viscous properties observed in the DStests quantied as bDS (Eq. (2a)) are consistent with thevalues of b13 (Eq. (1)) evaluated by the TC and PSC tests.To the end described above, the magnitudes and directions of the principal stresses, s1 and s3, in the DS testswere estimated from the measured shear and normalstresses, tvh and sv, on the horizontal planes by introducing a couple of assumptions. The rst assumption is that,except for the initial small strain level, the principal axesof stress and irreversible strain increment are coaxial(Davis, 1968). This assumption was validated by simpleshear tests on rectangular prismatic specimens of sand using the Cambridge Simple Shear Apparatus in the late60's (Cole, 1967; Stroud, 1971) and later by torsionalsimple shear tests on hollow cylindrical specimens of sandusing a torsional shear apparatus (Pradhan et al., 1988a,b). It is assumed hereafter that the deformation in theshear zone in the DS specimen is under the simple shearcondition and the strain increments are nearly the same asthe irreversible strain increments. Figure 25(a) shows theMohr's circle of incremental strain in soil under the simple shear conditions. By assuming the coaxiality, theMohr's circle of stress can be constructed for the principal direction of strain increments determined by a givendilatation angle c (arctan s| _d/·st) (Fig. 25(b)).Another assumption is necessary to determine theMohr's circle of stress after a shear stress jump upon astepwise change in s· . The following two possible assumpFig. 26. Estimated Mohr's circle of stress in DS after a step increase inthe displacement rate assuming: a) a constant dilatancy angle; andb) an elastic responsetions were considered:1) The dilatancy angle remains constant while the coaxiality between the principal directions of stress andirreversible strain increment is maintained. TheMohr's circle of stress immediately after a shearstress jump can then be constructed (Fig. 26(a)).2) The stressstrain behaviour during a shear stressjump immediately after a step change in s· is essentially elastic due to a very high changing rate of s· . Thisinference is supported by the predictions based onthe nonlinear three component model (Fig. 1): i.e.,s· ir can change only at a rate that is much lower than a314DUTTINE ET AL.Fig. 27.b13(c)/b13(e) as a function of RDS and cgiven s· , immediately after a step change in s· . Then,the total lateral stress sh is kept nearly constant whenthe shear stress jumps by Dtvh under the constantnormal stress (sv). Then, we have another Mohr'scircle of stress (Fig. 26(b)).Two dierent sets of the principal stress incrementsDs1 and Ds3 obtained based on these two assumptionsresult in two dierent values of b13: b13(c) and b13(e), as detailed in APPENDIX A. It seems that the actual behaviour is in between these two cases. As the measured dierence is not signicant (as shown below), it is very dicult,if not impossible, to examine which of them is morerelevant. For this reason, the results obtained by thesetwo assumptions are equally presented below.Figure 27 shows the relationships between the ratio ofthe ratesensitivity coecients (Eq. (1)), b13(c) and b13(e), asa function of RDStvh/sv, and the dilatancy angle, c, according to Eq. (A11) (APPENDIX A). The two assumptions give the same result (i.e. b13(c)/b13(e)1.0) at theresidual state, where c is essentially zero. It can be seenthat the ratio b13(c)/b13(e) is not largely dierent from 1.0(i.e., 0.9¿1.0) for the ranges of RDS and c in the presentÆcÆ09). This variancestudy (i.e. 0.4ÃRDSÃ0.9 and 179(c)(e)in b13 /b13 is otherwise of the same order as the one inthe measured values of bDS shown in Figs. 11, 12, 15 and16.Firstly, Figs. 28(a) and (b) show a set of theoreticalrelationships (Eq. (A10b) in APPENDIX A), which wereobtained by analysis for constant values of RDS and c, reÆcÆ09spectively, where s1.0ÆRDSÆ0.5; 209tin Fig.ÆÆÆÆ28(a) and s0.8 RDS 0.4; 209 c 09tin Fig. 28(b).Secondly, these gures show continuous data points foreach DS test that were obtained following a number ofdierent steps:a) An analytical expression of the ds relation is obtained by tting of a 6th to 7th order polynomialfunction. This polynomial function is dierentiatedwith respect to the variable s to obtain an analyticalexpression of the cs relationship.b) An analytical expression of the RDSs relation is obFig. 28. Estimated ratios b13(e)/bDS as a function of RDS and c for DStests on: a) natural sands; and b) glass beadstained by tting of the following function:RDS(s)s ¥sØ 2s {s» ¥R ¥Ø 1{e1ppnpRr{(Rp|Rr)¥e ({1{e|2.k.(s|s )`s|sp`sr|p1||2.k.s1{e)|2.k.(s|sp)»m(3)where Rp is the stress ratio RDS at the peak state; Rr isthe stress ratio RDS at the residual state; sp is the sheardisplacement at the peak state; sr is the shear displacement at the residual state; n and m are two constants; and k is another constant equal to 100.c) An analytical expression of the RDSc is obtained bycombining steps a) and b), which is then incorporated into Eq. (A10b) to obtain continuous data pointsof the ratio b13(e)/bDS.These multiple steps were necessary to capture as closelyas possible the continuous change in the ratio b13(e)/bDSwith the dilatancy angle c.It may be seen from Figs. 28(a) and (b) that, in therespective tests, the ratio b13(e)/bDS varies noticeably whenthe stress state moves from the peak state towards theresidual state. This fact is taken into account in the following when comparing the values of b13(e) and b13(c) fromVISCOUS BEHAVIOUR OF GRANULAR MATERIALSa)b)c)d)Fig. 29. Comparison of a) b13(c) and b) b13(e) from DS tests on naturalsands and glass beads and b13 values from TC and PSC tests onnatural sands (1)Matsushita et al., 1999; Tatsuoka et al., 2003;Nawir et al., 2003; 2)Matsushita et al., 1999; Di Benedetto et al.,2002; Pham Van Bang et al., 2003; 3)Tatsuoka et al., 2008)the DS tests with the values of b13 from the TC and PSCtests. The same analysis for b13(c) (based on Eq. (A7) inAPPENDIX A) is not shown in this paper, but it is verysimilar to the one presented in Figs. 28(a) and (b).Figures 29(a) and (b) compare the values of b13(c) andb13(e) from the DS tests on natural sands and glass beadsperformed in the present study with the b13 values directlyevaluated previously by the drained TC and PSC tests onthe natural sands as indicated in the caption of thegures. The values of b13(c) and b13(e) from the DS tests performed on natural sands are those at the residual state.The ranges of the b13(e) value obtained from Figs. 28(a)and (b) and those of the b13(c) value are also indicated. Onthe other hand, the values of b13(c) and b13(e) from the DStests performed on the glass beads are those evaluatedaround the peak stress state. This is because, with mosttypes of glass beads tested in the present study, it was verydicult to condently dene stable bDS values at the residual state due to the signicant rateindependent unstablebehaviour that took place frequently. The ranges of b13(e)(Fig. 28(b)) and b13(c) from the postpeak regime towardsthe residual state are also indicated. The following trendsmay be noted:315With all the poorlygraded granular materials examined, the ranges of b13 from the DS, TC and PSCtests are very similar. This fact indicates that thequantication of viscous properties by b13 (Eq. (1)) isrelevant and consistent under all these dierent testconditions.When comparing carefully the data at the peak stressstate for the respective types of natural sands, thevalues of b13(c) and b13(e) from the DS tests are slightlylarger than the b13 values from the TC and PSC tests.In the same time, the respective b13(c) values are closerto the corresponding b13 values from the TC andPSC tests.With both data sets obtained by the DS tests and theTC and PSC tests, any meaningful and consistenteects of D50 on the b13 values cannot be noted.Large part of the scatter in the measured b13 valuescan be explained by the fact that the b13 value tendsto decrease as the particles become more roundtowards spherical. These trends of behaviour areconsistent with the results from drained TC tests performed on a much wider range of granular materials(Enomoto et al., 2007; Tatsuoka et al., 2006).With glass beads, the values of b13(c) and b13(e) at thepeak stress state and their lower bounds in the postpeak regime tend to decrease with an increase in D50from about 0.15 mm. This trend of behaviour islinked to the fact that, after the rateindependent unstable behaviour due to the stick/slip phenomenonbecomes frequent in the postpeak regime, the valueof bDS upon a step increase in s· tends to become ultimately zero. It should be noted however that theseunstable behaviour and its eects on the viscousproperties are likely to be aected by the ratio of themean particle size to the specimen size.CONCLUSIONSThe following conclusions can be derived from the DStest results and their analysis presented in this paper:1) The poorly graded granular materials exhibitednoticeable ratedependent shear stress (tvh)shear displacement (s) behaviour. The following dierent viscosity types were observed according to the particleshape, while the viscous properties graduallychanged as s increased for a wide range from the prepeak hardening regime to the postpeak strain softening regime towards the residual state: a) The relatively angular granular materials exhibited the socalled TESRA viscosity in the prepeak regime. Theviscosity type changed to the Positive & Negative(P&N) viscosity in the postpeak regime and at theresidual state; and b) The relatively round granularmaterials exhibited the P&N viscosity already in theprepeak regime, which remained so but accompanied by rateindependent unstable behaviour in thepostpeak strainsoftening regime and at the residualstate.2) The unstable behaviour, which is due seemingly to3163)4)5)DUTTINE ET AL.the socalled stick/slip phenomenon, became morepredominant with more round poorly graded granular materials and became most predominant withuniformly graded glass beads. The particle size had adirect inuence on this trend of behaviour.The ow characteristics of unbound angular andround granular materials were basically rateindependent, indicating that it is relevant to express theow characteristics in terms of the inviscid stresscomponent according to the nonlinear threecomponent model.By introducing several assumptions, the values of theratesensitivity coecient b13 dened in terms of themajor and minor principal stresses, s1 and s3, wereestimated from the values of the ratesensitivitycoecient bDS dened in terms of the shear and normal stresses, tvh and sv, that were evaluated by theDS tests. These estimated values of b13 were verysimilar to those directly measured by the TC and PSCtests. Therefore, the quantication of the viscousproperty by the ratesensitivity coecient b13 isrelevant and rather general.With poorly graded granular materials, the b13 valuesevaluated by the DS, TC and PSC tests are rather independent of particle size while the b13 valuedecreased as the particle became more round.ACKNOWLEDGEMENTSThe rst author gratefully acknowledges the nancialsupport of the Japan Society for the Promotion ofScience. The help of the respective French and Japaneseundergraduate students Mr. Blanc, M. and Ms Fujimura,S. in conducting the experiments must be appreciated.The consistent help of the colleagues at the I.I.S., theUniversity of Tokyo, in particular Prof. Koseki, J. andMr. Sato, T., providing dierent types of sand tested inthis study, is also deeply appreciated. The authors wouldlike also to thank Prof. Di Benedetto, H. (ENTPE,France) for many discussions and fruitful remarks.REFERENCES1) Chambon, G., Schmittbuhl, J. and Corfdir, A. 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Conf. on Hard Soils and Soft Rocks, Napoli, 2,12851371.Tatsuoka, F., Ishihara, M., Di Benedetto, H. and Kuwano, R.(2002): Timedependent deformation characteristics of geomaterials and their simulation, Soils and Foundations, 42(2), 103129.Tatsuoka, F. (2004): Eects of viscous properties and ageing on thestressstrain behaviour of geomaterials, Geomechanics Testing,Modeling and Simulation, Proc. GIJGS Workshop, Boston,ASCE Geotechnical Special Publication GSP No. 143 (eds. byYamamuro and Koseki), 160.Tatsuoka, F., Kiyota, T. and Enomoto, T. (2006): Viscous properties of geomaterials in drained shear Geomechanics Testing,Modeling and Simulation, Proc. 2nd GIJGS Workshop, Osaka,ASCE Geotechnical Special Publication GSP No. 156 (eds. by Ladeet al.), 285312.38) Tatsuoka, F. (2007): Inelastic deformation characteristics of geomaterial, Soil StressStrain Behavior: Measurement, Modellingand Analysis (eds. by Ling et al.), Proc. 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(2000): Stress historydependentdeformation characteristics of dense sand in plane strain, Soils andFoundations, 40(2), 7798.APPENDIX A: EVALUATION OFRATESENSITIVITY COEFFICIENT b13 IN DSBy assuming the coaxiality between the principaldirections of stress and irreversible strain rate, thedilatancy angle c and the stress state are related to eachother as follows (Fig. 25(b)):sh|sv2tvhtan c(A1)The coordinates of the centre C of the Mohr's circle (sC,0) are then given by:sh|svsv{tvh tan c2sCsv{(A2)The radius of the Mohr's circle, r, is given by:4r 2(sh|sv)2{4t 2vh; r12(sh|sv)2{4t 2vh(A3)The principal stresses, s1 and s3 are therefore obtained from Eqs. (A1) through (A3):is1sC{rsv{tvh tan c{ 1 4t2vh{4t2vh¥tan2 csv{tvh (tan c{ 1{tan2 c)k2j1k2222ls3sC|rsv{tvh tan c| 2 4tvh{4tvh¥tan csv{tvh (tan c| 1{tan c)(A4)By assuming that the dilatancy angle (Fig. 25(a)) is kept constant immediately after a step change in s· , the principalstress increments, Ds1 and Ds3, can be obtained as showin in Fig. 26(a) or simply by dierentiating Eq. (A4) under theconditions dc0 and dsv0:Ds1Dtvh (tan c{ 1{tan2 c): Ds3Dtvh (tan c| 1{tan2 c)(A5)By noting that DR13/R13D(s1/s3)/(s1/s3)Ds1/s1|Ds3/s3 and by assuming that log ss· after/·sbeforet§log s( ·g ir13)after/( ·g ir13)beforetin the shear zone in the DS specimen, we obtain from Eq. (1):Ds1/s1|Ds3/s3log (·safter/·sbefore)(A6)b13By substituting Eqs. (A4) and (A5) into Eq. (A6), and referring to RDStvh/sv, we obtain:«$«2 1{tan2 c2 1{tan2 cDtvh/tvhbDS1/RDS|RDS{2 tan clog (·safter/·sbefore) 1/RDS|RDS{2 tan cb13b(e)13 $(A7)On the other hand, if we assume an elastic response upon a step change in s· , which leads to Dsh0, the Mohr's circleexpands at the xed centre C with Ds1|Ds3 (Fig. 26(b)). The new radius r? is then expressed as follows, referring toEq. (A1):318DUTTINE ET AL.(sh|sv)2;4r?2(tvh{Dtvh)2{r? (tvh{Dtvh)2{t2vh tan2 c(A8)By referring to Eq. (A3), the principal stress increments, Ds1 and Ds3, are obtained as:iDs1r?|rtvhkjk« Ø »« Ø »Dtvh 2{tan2 c| 1{tan2 ctvh1{$Dtvh 21{{tan2 c| 1{tan2 ctvhlDs3|Ds1|tvh(A9)$By substituting Eqs. (A4) and (A8) into Eq. (A6), we obtain:Ø 1{Dtt » {tan c| 1{tan cvh(e)13b13b 222vhlog (·safter/·sbefore)«2(1{RDS¥tan c)1/RDS|RDS{2 tan c$(A10a)By using the Taylor's expansion law with respect to the variable Dtvh/tvh and noting that (Dtvh/tvh)2 91.0, we obtain:/Dtvh1{tan2 c2(1{RDS¥tan c)1tvh2(1{RDS¥tan c)(e)b13 §bDS¥21{tan c 1/RDS|RDS{2 tan clog (·safter/·sbefore) 1/RDS|RDS{2 tan c«$(A10b)From Eqs. (A7) and (A10b), we obtain the following approximated equation:1{tan2 cb(c)13§1{RDS¥tan cb(e)13(A11) | ||||
ログイン | |||||
タイトル | Cyclic Triaxial Tests on Asphalt Concrete as a Water Barrier for Embankment Dams | ||||
著者 | S. Feizi-Khankandi・A. A. Mirghasemi・A. Ghalandarzadeh・K. Hoeg | ||||
出版 | Soils and Foundations | ||||
ページ | 319〜332 | 発行 | 2008/06/15 | 文書ID | 21111 |
内容 | 表示 SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 319332, June 2008CYCLIC TRIAXIAL TESTS ON ASPHALT CONCRETE AS AWATER BARRIER FOR EMBANKMENT DAMSSIAMAK FEIZIKHANKANDIi), ALI ASGHAR MIRGHASEMIii),ABBAS GHALANDARZADEHiii) and KAARE HOEGiv)ABSTRACTThe seismic behavior of asphaltic concrete used in embankment dams subjected earthquake loads has been studied.In order to evaluate the dynamic behavior, an extensive series of monotonic and cyclic tests were carried out on triaxialspecimens of asphalt concrete used in hydraulic structures. The MTSdynamic equipment at the Norwegian Geotechnical Institute (NGI) was used for this purpose. Temperature and frequency eects on specimen behavior and on specimen degradation have been studied under the cyclic loads in both isotropic and anisotropic initial stress conditions.For investigation of the fatigue behavior, thousands of cyclic loads were imposed on some of the specimens.Moreover, to study any sign of material degradation due to the cyclic loading, the postcyclic monotonic stressstraincurve was compared with the corresponding curve for specimens that were not rst subjected to cyclic loading. Geotechnical parameters to be used in dynamic numerical analysis models are also presented.Key words: asphaltic concrete core dams, cyclic tests, monotonic tests, seismic behavior (IGC: H4/M3)dam and showed that relatively large shear strains mayoccur in the top of the core if the dam slopes are verysteep. However, he concluded that rockll dams withasphaltic concrete core in general have a favorable seismic protection.Meintjes and Jones (1999) analyzed the Ceres dam located in South Africa. They also used the Newmarkmethod to estimate permanent shear displacements. Thepredicted behavior of the dam was satisfactory.Gurdil (1999) performed seismic analyses the Koprudam in Turkey. His analyses were based on the equivalentlinear method. He concluded that some cracking may occur in the core, near the crest level. However, the selfhealing behavior of asphaltic concrete will solve thisproblem.Ghanooni and Mahinroosta (2002) performed dynamic analyses on a typical 115 m high asphaltic concrete corerockll dam. They concluded that, in nonlinear analyses,the top section of the core experiences small tensile stresses which are less than asphalt material strength.FeiziKhankandi et al. (2004) performed a 3D analysison a typical 60 m high asphaltic concrete core dam. Theyconcluded that as in the case of 2D analysis, the top section of the core experiences some tensile stresses, butsomewhat more than in the 2D analysis. Furthermore,they concluded that although there is a possibility ofsome cracking in the top of the asphaltic core, the damINTRODUCTIONThe sealing of earth and embankment dams by meansof asphalt concrete cores has attained importancethroughout the world. This kind of material is virtuallyimpervious, exible, and resistant to erosion and agingand exhibits viscoelastoplastic behavior (ICOLD, 1992;Hoeg et al., 2007). In regions with cold and rainyweather, construction of this kind of dam is easier thanthat of clay core dams. For many years, monitoring ofthese dams has indicated their suitable behavior duringconstruction and operation. However, little informationexists on the behaviour of asphalt concrete core damssubjected to seismic loads. There are only a few publisheddocuments providing information on the behavior ofasphalt concrete used as impervious water barriers indams during and after earthquake shaking.Previous Numerical StudiesValstad et al. (1991) analyzed the Storvatn dam locatedin Norway using a Newmark approach to compute theearthquake induced permanent displacements along thecritical sliding surfaces. They studied whether the permanent shear displacements of a dam due to severe shakingmay be so great that a thin core may be sheared otoward the dam crest.Hoeg (1993, 2005) presented the results of Storvatni)ii)iii)iv)Ph.D. Student, School of Civil Eng., College of Engineering, University of Tehran, Iran (sfeiziut.ac.ir).Associate Professor, ditto (aghasemiut.ac.ir).Assistant Professor, ditto (aghalandut.ac.ir).Professor, Norwegian Geotechnical Institute (NGI) and University Of Oslo Norway (kaare.hoegngi.no).The manuscript for this paper was received for review on March 5, 2007; approved on February 14, 2008.Written discussions on this paper should be submitted before January 1, 2009 to the Japanese Geotechnical Society, 4382, Sengoku,Bunkyoku, Tokyo 1120011, Japan. Upon request the closing date may be extended one month.319320SIAMAK ET AL.could be designed to behave safely.Previous Experimental WorkThe rst experimental research in the eld of seismicbehavior of asphaltic concrete core dams was performedby Breth and Schwab (1973). Their study was based onnite element analysis of a dam with a height of 180 m.They devised an interesting setup to impose computedcyclic horizontal shear stresses on representative elementsof the asphaltic concrete core. They concluded that thecyclic loads did not change the structural strength of theasphalt concrete which behaved like an elastic body.Ohne et al. (2002) performed oneway uniaxial cyclictests on the specimens drilled out from Higashifuji damin Japan (the asphaltic concrete face dam was damagedby an earthquake in 1996). Twenty stress cycles were applied at each static stress level. They dened the dynamicyield strain for the asphalt material. The authors concluded that the observed cracks that opened in the facingof the dam were caused by cyclic compression stresses.Wang (2005) reported a series of cyclic loading tests ontriaxial specimens of asphaltic concrete. He showed thatthere was no sign of cracking or degradation of the specimens.Salemi (2005) performed some numerical and experimental tests for Meyjaran dam in Iran with a heightof 60 m. Small scale physical models of asphalt core damswere also tested in a centrifuge under impact loads. Sheconcluded that her numerical analysis corresponded wellwith data recorded in the model and mentioned that theasphaltconcrete core behaves safely, even under a verysevere earthquake.It is important to determine the level of tensile stressand the amount of tensile strain that asphalt concrete in adam core can sustain before it cracks. This strain level isclearly a function of temperature and rate of loading. Inearthquake prone regions, the asphalt concrete mix isusually made with a soft grade bitumen and/or an added(0.51)z bitumen content to increase the exibility andductility and the tensile cracking strain (Hoeg et al.,2007).The tensile or breaking strength of asphalt concretedecreases with the time of loading or with the increase intemperature. The tensile strength of an asphalt mix is ofthe order of 10z of the compression strength of theasphalt concrete (Creegan and Monismith, 1996). Themost recent paper discussing the tensile strength and tensile cracking strain is the one presented by Nakamura etal. (2004). The main goal of their study was to comparethe engineering properties of conventional asphalt concrete with a special admixture (called Superexphalt).The Superexphalt has a much lower tensile strength anda higher tensile cracking strain than conventional asphaltconcrete used in hydraulic structures.PURPOSE AND SCOPE OF THE PRESENTRESEARCHMany researches have been done on the asphalt concrete on the road and aireld pavements. However, onthe water barrier for hydraulic structures such asphalticconcrete core or face dams, there is not much research inthe literature about the behavior of asphalt concrete, especially during an earthquake occurrence.To investigate the stressstrain behavior of asphalt concrete under static and dynamic loads and for determination of geotechnical parameters of this material, monotonic and cyclic tests were performed. At least 50 and atmost 10000 cycles were applied to the samples in dierentconning pressures, temperatures and frequencies. Thetests were done in both isotropic and anisotropic conditions. In addition, some monotonic tests were carried outbefore and after cyclic tests to investigate postcyclic behavior of asphalt concrete and loading eect on thematerial strength.In this research, the laboratory investigations are divided into three sections. In the rst, monotonic tests wereperformed to determine stressstrain behavior of theasphalt concrete before application of the cyclic loads.Triaxial cyclic tests in both isotropic and anisotropic conditions were carried out in the second part of this study.Performing monotonic tests after application of the cyclic loads, to compare the results with rst section was thethird part of the study.Briey, the following topics form the main scope of thepresent experiment:ÉMaterial degradation due to cyclic loading (speciallyafter 50 cycles)ÉEects of dierent parameters on the behaviour ofspecimensÉPossible cracking of samples due to cyclic loadsÉBehaviour of specimens under thousands of cyclicloadsÉDetermination of geotechnical parameters to be used inthe numerical analysisÉPostcyclic behaviour of asphalt concretePREPARATION OF THE ASPHALT CONCRETESPECIMENTSAll specimens were prepared in the asphalt laboratoryof KoloVeidekke in Norway. Firstly, small size specimens were prepared based on the standardized Marshalmethod. The size distribution of the sand and gravel inthe asphalt concrete mix complied with the Fuller's equation (Hoeg, 1993; Creegan and Monismith, 1996):Pi100Ø dd »imax0.41z(1)Where: Pi is the percent by weight smaller than theequivalent grain size dimension di. These initial tests wereaccomplished to reach the optimum percent of the bitumen value to mix with the aggregates. The used bitumenwas of grade B60 and the tests were done with the bitumen percentages by weight of 5, 6, 6.5, 7 and 7.5. Thetype of asphalt binder used is important, because theshear modulus and the damping ratio are dependent onthe properties of asphalt binders as well. There is a wide321CYCLIC TRIAXIAL TESTS ON ASPHALT CONCRETErange of bitumen grades to be chosen for hydraulicasphalt concrete. The asphalt binder type selection depends on specic project conditions and behavior requirements of asphalt concrete including its degree ofpenetration.Based on the Marshal's test results, the value of 7.0percent by weight was selected for the mix. The laboratory triaxial specimens were prepared in a mould with a diameter of 100 mm and a height of 200 mm. Dry aggregates and the added ller, in accordance with the calculated weight based on Fuller's equation were put insidethe oven to reach a temperature of 1529C. Besides, bitumen was put inside another oven for preheating and toreach a temperature of 1459C (Baron et al., 1955). Bothof these materials remained inside the oven for ten hours.After this period, the calculated weight for bitumen wasadded to the aggregates and then placed in a mixer fornearly three minutes. A standard Marshall tamping hammer was used with 30 blows per layer for compaction ofthe samples (one blow per second). This hammer has aweight of 4.5 kg and the height of its drop is 45 cm. Thespecimens were built in four layers of equal thickness. Airvoid of all samples was obtained to be less than 1z.Wang and Hoeg (2002) showed that this compactionprocedure gives specimens that have the same compressive strength, but a somewhat higher compression modulus than eld specimens drilled out of a dam core compacted by a light vibratory roller.Later on, the samples were trimmed with a special sawto a length of 200 mm. During trimming of specimens, avery high sensitive trimmer was used and the surface ofthe samples were cut and polished with very high degreeof precision to decrease the bedding error eect duringthe tests. Figure 1 shows prepared samples for an example. Flatness, roughness and parallelism for the specimenends had the ability to satisfy the suggested criteria byJapanese Geotechnical Society, 2000 and ASTM D399991.MONOTONIC TRIAXIAL TESTSMonotonic triaxial compression tests were used tostudy the stressstrainstrength behavior of asphalt concrete. Six monotonic tests were performed in dierentconning pressures (Table 1). All prepared specimenswere put inside the cooling room with temperature of 59Cbefore starting the monotonic tests. Specimens weretaken from the cooling room and were set up within atriaxial cell. In all tests, there were membranes usedaround the specimens. The triaxial cell was lled with deaerated water and then the equipment was put inside a bigcell used to retain a constant temperature during the test.All monotonic tests were performed by use of straincontrolled compression loading system. After applying thepredened conning pressure and reaching to a constanttemperature, the axial load was applied up to the failurepoint. The imposed axial strain rate was 2z per hour. Alltests were continued to a very large axial strain (about20z). At that stage, the specimens had a pronouncedbarrel shape and were seriously cracked. During the test,the amount of axial stress, axial strain and volumetricstrain were recorded by the electronic sensors used forthis purpose.Presentation of the ResultsTable 1 presents the summary of results for monotonictriaxial tests. Figures 2 and 3 show the values of deviatorstress and volumetric strain versus axial strain for imposed conning pressures (250, 500 and 1000 kPa). Forall conning pressures, the same stressstrain trend is seenin Fig. 2. As expected, the higher is the value of conningpressure, the more is the amount of failure axial strain.Values of axial strain at failure point for s31000, 500and 250 kPa are 15, 6 and 5 percent respectively. Also,the curves show a good harmony between two repeatedtests in the same conning pressures. This similarity iseven more evident in higher conning pressures. This isbecause, with the increasing conning pressure, the samples, to some extent, behave like rigid materials.Equivalent Young modulus (E ) was derived from theinitial stage of the curve, up to an axial strain of 1z:Table 1.Fig. 1.Picture of prepared samplesResults of monotonic triaxial testsTestNo.s3(kPa)E(MPa)s1s3 (kPa)at failureT1T2T3T4T5T625025050050010001000135110150150160150252221973129333238793793Temperature(9C)Axial strainat failure (z)55.55.5661515322SIAMAK ET AL.Fig. 2.of the aggregate alone, which show a modulus increasingmarkedly with increasing conning pressures. However,for the strain values more than 1z, a signicant increasein shear strength is observed while increasing conningpressures.To study the eect of reduction of bitumen viscosity,supplementary triaxial tests results were reported byHoeg, 1993. The results showed that the same geotechnical parameters are observed with 5.9z B180 and 8zB60.Figure 3 shows the relation between volumetric and axial strains. The results show that with the increase in theconning pressure, the value of dilatancy decreases. Upto an axial strain of 3z, however, the amount of dilatancy is small, e.g., less than 0.5z. Moreover, this gureshows a very little volumetric compression at the initialstage of the tests. It is quite common, as in the rst seconds after the load application; little spaces existing inside the specimens raze. After a few seconds, the volumeshows expansion. This important phenomenon is due tothe opening of small ssures. Although no visible cracksmay appear, the dilatation may lead to an increase inpermeability. However, the increase in permeability onlyoccurs when ssures get opened in consequence of sheardeformations at a stress level which causes specimenfailure.Deviator stress axial strain curvesTRIAXIAL TESTS WITH CYCLIC LOADINGFig. 3.Degree of dilatancy as a function of conning pressuresdeaE(2)For conning pressures of 250 to 1000 kPa, the range ofthe secant modulus is between 110 MPa and 150 MPa(Table 1).As previously known, the value of elasticity modulus isa function of many parameters like porosity and conning pressure (Kramer, 1996). In other words:E1zf (e, s?0, . . .)K~f (e)~f (s?0)(3)where: K is a constant parameter and e is the specimenvoid ratio.In all specimens, the amount of void ratio is less than1z. Therefore:E1zA~s y0(4)where: A is a constant parameter.Based on the monotonic tests results (Fig. 2), the valueof y in the above relation is calculated and the followingequation is dened for asphalt concrete materials:E1zA~s 0.180(5)Young modulus for asphalt concrete does not show asubstantial increase while increasing the conning stress.This is in contrast with the results from triaxial samplesTwentyfour cyclic triaxial tests were carried out in thisresearch (Table 2). The specimens were loaded under initial isotropic condition (kcs1/s31.0) and anisotropicconditions (kc2.0 and 3.0). During the tests, theamount of anisotropy coecient was xed by applyingthe desired loads from the load cell of triaxial equipment.The conning pressure was varied from 85 kPa to 500kPa. As the behavior of the asphaltic concrete core nearthe top of the dam is of most concern when it is subjectedto the cyclic loads of earthquake, this range of conningstress was selected. The cell pressure was generated by thepressurized deaired water where the cell was fully undercomputer controlled data acquisition system.The specimens with rubber membranes were placed inthe triaxial cell and then subjected to a conning pressure. Moreover, the triaxial cell was put inside a biggercell connected to a water pumping system. This systemhad the capability of applying any temperature to thepumped water. In the duration of 12 hours, the temperature gradually reached a predened value. All tests wereperformed at two dierent temperatures, T59C and T189C. These temperatures were chosen from the temperature monitoring of the embankment dams (Dannicli, 1996). Conditions inside a dam will be rather constant, and selected temperatures to cover some typicalvariation, were set to T59C and T189C; T59C, asan assumed yeararound temperature inside a typical damin sunarctic climate and T189C, as an assumed yeararound temperature inside dam in countries with tropicalor subtropical climate. On the other hand, in embank323CYCLIC TRIAXIAL TESTS ON ASPHALT CONCRETETable 2.Summarized information of cyclic triaxial testsTest No.s3 (kPa)KcT 9CFrequency (Hz)Number of cyclesG (GPa)Type of loadingF1500152501.80AF2500152501.75AF3500252502.50BF4500252502.30BT5250152501.40AT6250252501.67BT7250352501.70BT8250252501.72B and CF950015250, 400, 502.00AF1150035250, 100003.75BE1285152 and 1050, 2000, 501.30AE1385252 and 1050, 1000, 1000, 501.33BF14500252 and 1050, 1000, 1000, 503.20BF15500352 and 1050, 1000, 1000, 50004.00BT16250252 and 1050, 1000, 1000, 501.6BF175003182, 5 and 1050, 50, 50, 501.75B and CT182503182, 5 and 1050, 50, 50, 501.25BE19851182, 5 and 1050, 50, 50, 500.85AT202501182, 5 and 1050, 50, 50, 500.92AF215001182, 5 and 1050, 50, 50, 501.00AT222503182, 5 and 1050, 50, 50, 501.80BE23851182, 5 and 1050, 50, 50, 500.75AF245003182, 5 and 1050, 50, 50, 501.90Bment dams with clay cores, the eect of reservoir temperature is not an important factor, while in asphaltic concrete core dams, it would be. As known, nearly six toeight percent of bitumen is used in the mix design ofasphalt concrete. Since the asphalt binder is a temperature dependent material, the temperature has a signicanteect on the specimens' behavior. Therefore, the selection of a suitable asphalt binder to mix with aggregates isof great importance. The recommendation of selectingtype B180 in cold regions like Norway and type B60 intropical areas such as Iran are examples of this fact.Although the results of numerical analysis show that thegreater part of the earthquake energy is in the frequencyrange of 2 to 5 Hz and all prepared specimens were imposed to loadings of 2 Hz frequency, there were alsosome extra tests carried out in higher frequencies of 5 and10 Hz.Denition of LoadingFigure 4 shows for instance, the applied cyclic loads onthe samples subjected to a conning pressure of 500 kPa.The value of axial stress starts from 500 kPa, reaching1000 kPa and then decreasing to nearly 0.0 kPa. Inanisotropic conditions (Kc3.0 as an example, Fig. 5(a)),Fig. 4. Eective axial stressloading time, s3500 KPa and Kc1.0(Type A)the starting point is 1500 kPa, reaching 3000 kPa andthen decreasing to nearly 0.0 kPa (cyclic load}1500kPa).In most of previous works, regarding the connementsof setting up the loading equipment, there was no possibility of applying the twoways loads to asphalt concrete. Consequently, the upper part of the cyclic loadingrecords was applied to specimens (as indicated in Fig.5(b)). This type of loading was also used for some tests inthe present study.In brief, the following types of cyclic loading used in324SIAMAK ET AL.Fig. 5.Fig. 6.Cyclic stressstrain hysteresis loop, Test T5Fig. 7.Cyclic stressstrain hysteresis loop, Test T20Fig. 8.Cyclic stressstrain hysteresis loop, Test F4Eective axial stressloading time, s3500 KPa, Kc3.0this research can be noted:Type A: Isotropic condition with symmetric cyclic loading (Kc1.0)Type B: Anisotropic condition with nonsymmetric cyclicloading (Kc2.0, 3.0)Type C: Anisotropic condition with oneside cyclic loadingPresentation of the ResultsThe MTS system was scheduled to control the numberof cycles. Table 2 summarizes the dierent parameters ofthese performed cyclic tests. For all specimens, the number of cycles applied at a given load level was set to 50.This number of cycles corresponds to a loading inducedby an earthquake with the magnitude of 7.5 in Richterscale (Kramer, 1996). However, for tests F9 to F24 inTable 2, there were staged cycles planned and applied;for example, in test F9, 50 cycles, 400 cycles and then 50cycles were applied. Moreover, there were small intervals(about ve seconds) between each stage and the next forbetter observation of the asphalt concrete degradationbehaviour during the cyclic loading.Figures 6 to 11 show the hysteresis loop of the cyclicloading as examples. The hysteresis loops were plottedfor the rst, ftieth, hundredths and thousandths cycles.The value of shear stress versus axial strain has beenpresented in these gures. The initial value of the loopswas obtained from the value of axial and conning pressures. The starting point position in the hysteresis loop isdened as follows (Figs. 6 to 11):s |s3iY positionShear Stress in the loop 12jlX positionShear Strain in the loop0.0kkThe results are described as follows in two categories;isotropic condition (Kc1.0) and anisotropic states withthe values of Kc2.0 and Kc3.0.First, for the isotropic condition (Tests T5 and T20);Figs. 6 and 7 have been plotted for instance, at two dierent temperatures of T59C and T189C.Figures 8 and 9 (Tests F4 and E13) are indicated for ananisotropic state with anisotropy coecient which has thevalue of 2.0 (Kc2.0). In these tests, the temperatureremained constant at T59C.Figures 10 and 11 (Tests F15 and T18) are shown for anCYCLIC TRIAXIAL TESTS ON ASPHALT CONCRETEFig. 9.Fig. 10.Cyclic stressstrain hysteresis loop, Test E13Cyclic stressstrain hysteresis loop, Test F15325tained results are aected by two sources of error; compliance and bedding error. The compliance of the loadingsystem, consisting of all parts (top and bottom platensand connections) between where the specimen deformation is monitored and the specimen shall be determined(Tatsuoka and Shibuya, Kohata, 1992, 1995). In thepresent study, errors due to apparatus compliance wereevaluated with reasonable certainty by careful calibrationin the laboratory. For this purpose, a cylindrical steeldummy of a similar size and length to asphalt concretespecimens was placed into the location normally occupiedby the specimen where some calibration tests were performed. The Young Modulus of the dummy specimenhad a minimum of ten times the modulus of the asphaltconcrete (ASTM D 399991). Based on the obtainedresults, the correction coecient was dened and used inthe main tests.On the other hand, to decrease the eect of bedding error, the surface of specimens was cut and polished withvery high accuracy (Fig. 1). In addition, bedding errorcould cause lower stiness in initial cycles and higher stiness in later cycles that was not observed in hysteresisloops (Figs. 6 to 11). Therefore, the eect of bedding error can be ignored in these tests with the above considerations.Dynamic Properties for Asphalt ConcreteIn the cyclic triaxial tests, the axial stiness and damping parameters can be directly obtained by analyzing thedeviator stressaxial strain loops (Fig. 12). Cyclic triaxialtests are traditionally oriented to analyses of cyclic behavior, described by the relationship between the deviator/radial eective stress ratio (q/s?r) and the number ofcyclic loads. The upper part of the shear stressaxialstrain hysteresis curves is used to calculate the shearmodulus. The following relations would then be used forthis purpose:t, g(1{n)ea2eaEGFig. 11.Cyclic stressstrain hysteresis loop, Test T18anisotropic state with anisotropy coecient of 3.0 (Kc3.0) for two dierent temperatures of T59C and T189C.Accuracy of MeasurementsThe delity of the results depends on the accuracy ofthe measurements of both stresses and strains. The obE2(1{n)(6)Where: tshear stress, eaaxial strain, gshear strainand nPoisson ratio.Table 2 presents the complete information for all performed tests. The shear modulus increases from 1.5 GPain the isotropic condition to nearly 4.0 GPa foranisotropic state with anisotropy coecient of Kc3.0,at a low temperature of T59C. For the higher temperature (T189C), the value of shear modulus decreased tohalf or less as much as the mentioned values. Althoughthe amount of shear modulus can change during cyclicloading, the 10th cycle was chosen to calculate the shearmodulus. While it is observed that in the isotropic condition and low temperature, the conning stress does nothave signicant eect on the shear modulus, its eect increases with increase of anisotropy and temperature. Bythe following equation, the damping ratio (D) is calculat326SIAMAK ET AL.Table 3. Comparison of dynamic parameters between asphalt concrete and the other materialsFig. 12. Cyclic triaxial test(a) Loads on asphalt concrete specimen(b) Interpretationed as:1 WD~100(z)4p WSD(7)where, WD is the damping energy in a single loading cycleand WS is the equivalent elastic energy Based on thepresented curves, the areas of the hysteresis loops and theindicated triangle were calculated. The values of thedamping ratio range between 0.066 and 0.35. In the sameasphalt binder percent, binder type B180 causes thedecrease of the shear modulus while increasing the damping ratio compared to type B60 (Hoeg, 1993).To show the characteristics of asphalt concrete relativeto the other geotechnical materials, dynamic propertiesof asphalt concrete were compared with those of other geotechnical materials (Table 3). Based on the stinessvalues, asphalt concrete can be laid between soft rocksand soils. In comparison with crushedrock (G0§2000 to500 MPa), roundgravel (G0§150 to 300 MPa), sandygravel (G0§100 to 200 MPa) and sand (G0Ã100 MPa)(Kokusho and Esashi, 1981), asphalt concrete is a stiermaterial. It should be emphasized that the presentedrange of shear modulus is aected by the value of conning stress and void ratio. The results in Table 2 show thatthe amount of shear modulus for asphalt concrete rangesbetween 700 MPa to 4 GPa. These values correspond wellto sedimentary soft rocks (Tatsuoka and Shibuya, 1992)and plastic concrete used as a cuto wall in the embankment dams (MahabGhodss, 2007). In addition, lowamplitude shear modulus for undistributed gravellysand(Kokusho and Tanaka, 1994) ranges between 1 GPa to 5GPa which, can be considered to be similar to that ofasphalt concrete.On the other hand, it should be noted that the dampingratio percentage obtained in present study for the asphaltconcrete is high, (especially in higher temperatures whichis about 5z to 35z). Coarse material and plastic concrete can be put in this damping range.MaterialGsec (MPa)Damping (z)Asphalt concrete700¿40005¿30Crushed rock200¿5002¿35Round rock150¿3002¿20Sandygravel100¿2005¿20Sandº1002¿15Plastic concrete500¿50002¿30Investigation of Dierent Parameters on Dynamic PropertiesFigures 13, 14 and 15 present the eect of dierentparameters such as conning stress, anisotropy, loadingfrequency, temperature and hysteresis loop shapes on theshear modulus and damping ratio. In the following paragraphs, the eects of the abovementioned factors are described in detail.a) Eect of anisotropyIn each part of Fig. 13, the temperature and anisotropycoecient were xed while the conning pressure wasvaried. It can be seen that the dynamic shear modulus ofasphalt concrete is strongly dependent upon the shearstrain. At low strain amplitudes, the shear modulus ishigh, but it decreases while the strain amplitude increasing. Moreover, by comparing Figs. 13(a) with (d) (at T59C) or Figs. 13(b) with (e) (at T189C), it can be seenthat the higher the value of anisotropy coecient, thehigher the amount of shear modulus that is obtained.This is because at higher values of anisotropy state, theamount of smean(s1{s3/2) increased and this was themain reason for the shear modulus augmentation.b) Eect of temperatureComparison of shear modulus presented at the sameanisotropy coecients in Figs. 13 ((a) and (b) at Kc1.0)or Figs. 13 ((d) and (e) at Kc3.0) stands for decreasingthe shear modulus as the temperature increases. In addition, the temperature has an important eect on thethreshold point position in Gg curves. It is clear thatwith the increase in the temperature, the amount of shearmodulus falls faster.Figure 14 shows the damping ratio versus axial strainin dierent conning stresses at two dierent temperatures of T59C and T189C. Figure 14(a) shows that incomparison with shear modulus, damping ratio is not signicantly dependent on the shear strain amplitude.However, its value increases gradually with increase ofthe shear strain level. It is observed that dependency onthe strain is more distinct at the higher temperature of T189C than that at a lower temperature of T59C (Fig.14(b)). Furthermore, by increasing the temperature, thedamping ratio increases. That is because in high temperatures, viscosity of asphalt concrete causes the material toeasily absorb the applied energy. Therefore, the dissipated energy in a single loading cycle and consequently theCYCLIC TRIAXIAL TESTS ON ASPHALT CONCRETEFig. 13.327Eects of s3 and Kc on straindependent modulus at two dierent temperatures of 59C and 189Cdamping ratio increases.c) Eect of conning stressThe eect of conning stress on shear modulus is alsoillustrated in Fig. 13. For an example in Fig. 13(a), at theconstant temperature and anisotropy coecient, thehigher values of conning stress, the higher amount ofshear modulus is obtained. Comparison between Fig.13(a) and (d) (or Fig. 13(b) and (e)) shows that at a highlevel of anisotropy such as Kc3.0, the eect of conningstress is more distinct. In addition the threshold point occurs at higher amplitudes of shear strain in comparisonwith a low conning stress. This point is observed in Figs.13(a), (c) and (d) as examples. Figure 14(a) shows that bydecreasing the conning pressure from 500 kPa to 85kPa, the damping ratio increases from 5z to 35z respectively.d) Eect of hysteresis loops shapesBecause of the dierence between the curve inclinationsin compression and extension regions, two types of shearmodulus, Gc and Ge, were calculated from the hysteresisloops (Figs. 6 to 11 and 12). The eects of conning stress(Fig. 15(a)), anisotropy coecient and the temperature(Figs. 15(b) and (c)) were plotted separately for these twotypes of modulus. It shows that the value of shear modulus in compression region is more than two times of thevalue in extension side in the same temperature and conning stress (GcÆ2Ge). It is clearly seen in Fig. 15(c) thatwith increasing conning stress and/or anisotropycoecient at the constant temperature, the values of Gcand Ge increase. Moreover, Fig. 15(b) shows that thevalues of Gc and Ge decrease at the higher temperature.e) Eect of reversal coecient (rc)Reversal Ratio is introduced by the reversal coecient(rc), which is the proportion of the positive portion in applied cyclic shear stress to the whole domain of the shearstress. The eect of stress reversal ratio in the Glog N diagram has been also studied, (where N is the number ofapplied cycles.)Figure 16 shows the Glog N curves for dierent valuesof rc. It is observed that the larger the value of rc, thehigher is the curve in the Glog N diagram. This meansthe potential for degradation increases when the extension mode has become more predominant. In addition,this gure shows that in lower values of rc (such as rc0.5), the amount of degradation for shear modulus is lessthan that of higher values (rc0.85). In addition, this328SIAMAK ET AL.Fig. 16.GLog N curves for dierent values of rcFig. 17.Eect of cycles number on shear modulusFig. 14. Eects of conning stress and temperature on straindependent damping ratioFig. 15. Comparison between shear modulus in extension and compression states at two temperatures of 59C and 189C with dierentconning stressesgure shows that increasing the number of cycles causeddecrease of shear modulus.f) Eect of number of cyclesFigure 17 presents the eect of the number of cycles onmodulus reduction behavior at dierent conning stresses, anisotropy coecients and temperatures. The value ofshear modulus is plotted in the rst and ftieth cycles. Itis seen that holding constant the values of conningstress, anisotropy coecient and temperature, by increasing the number of cycles, the amount of shear modulusdecreases (Figs. 17(a), (b) and (c)). This reduction behavior is more distinct at a low level of shear strain. In addition, the shear modulus reduction behavior is moreCYCLIC TRIAXIAL TESTS ON ASPHALT CONCRETEprevailing in a low conning stress (s3250 kPa) thanhigher conning stresses (Fig. 17(a) for an example). Atthe same temperature and conning stress, comparisonbetween Figs. 17(a) and (b) shows that with increase ofanisotropy coecient, the eect of the number of cyclesdecreases. In other words, in the same cycle number, thespecimens degradation with a higher value of anisotropycoecient (Kc3.0) is less than that of Kc2.0. Figures17(b) and (c) shows that the value of temperature has asignicant inuence on the dynamic properties of asphaltconcrete between the rst and ftieth cycles. Indeed, inhigh temperatures, the threshold point for Gg curves occurs at a low level of shear strain.Strain Values and Specimens CrackingIn the present research, because of using ASTM standards at the laboratory, the external transducers wereused to measure deformations. Though the researchdevelopments in advanced triaxial equipments (e.g., Tatsuoka et al., 1992, 1995) have shown that shear strains aslow as 0.001z can be resolved in static (e.g., Goto et al.,1991) and cyclic triaxial tests by using local displacementtransducers, however, with proper mounting as well ascarefully calibrating the high resolution transducer andby considering the eects of equipment compliance andbedding error (ASTM D 399991), the reliability of theresults can be put in an acceptable range.As expected, the value of strain was very small. Hence,a very high precision electronic displacement transducerwas used to record the value of displacement during thecyclic loads. According to ASTM D 531192 and399991, displacement measuring devices such as LVDTmay be used if they have an accuracy of }0.02z of theinitial specimen height. Since specimens height in thepresent study was 200 mm, the accuracy of }0.04 mmhad to be the minimum required accuracy for the usedLVDT. The LVDT used at the laboratory satised thiscondition very well and other criteria suggested in theASTM standards.Figure 18 summarizes the axial strain (De) for performed tests at the end of the loading in dierent frequencies. In high speeds of cyclic loading, the strain valuesdecrease ( F5 Hz and 10 Hz). Since, in higher loadingspeeds, asphalt concrete cannot show its exibility andviscosity behavior very well, consequently the axial strainvalues are less than those of low speeds. Good compaction of the samples was one of the reasons of rather smalldisplacements. In addition, the value of axial strain increases with the increase of conning pressure. Withreference to Figs. 13 and 15, it is obvious that the temperature has the largest eect on the strain values. As expected, the higher the value of temperature, the greater is theamount of axial strain.After the cyclic tests, specimen surfaces were well inspected. In addition, some specimens were cut horizontally and vertically to investigate the cracking in the interior surfaces (Fig. 19). There was not any sign ofcracks, even after 10000 cycles. This shows a goodresponse of the asphalt concrete specimens resistingFig. 18.Fig. 19.329s3De curves for dierent values of frequencyCross setion of the specimen after 10000 cyclesagainst cyclic loads.Degradation of the Asphalt Concrete SpecimensThe shape and inclination of the hysteresis curveswould be good criteria to investigate the material degradation. Hence, the average inclination of the rst hysteresis loop was calculated and compared with the slopes ofother loops. This comparison showed that by increasingthe number of cycles, the amount of curves inclinationdecreased (Figs. 6 to 11 and 17). It was also observed thatthe value of shear modulus was gradually decreasing during the cyclic loading. Some tests were run with thousands of load cycles to study whether there is a longtermdegradation (fatigue) phenomenon which was not foundnoticeable to be the case up to 10000 cycles (Fig. 19).Figures 6 to 11 show that the banana shape was seen inthe extension mode. In the presented gures (Figs. 6 to11), the curves' inclination in extension mode is less thanthat of the compression mode. Therefore during the cyclic triaxial tests, specimen strength reaches the failureline in extension mode. Consequently the values of axialstrain increases. With the application of compressionloads, the specimens' behaviour is changed. However,some residual strain remains. It is one of the explicationsto describe the banana shape in the extension region.Anisotropy in asphalt concrete; because of the directionof compaction, is another reason to make the bananalooking shape in the extension mode.330SIAMAK ET AL.Description of Dierent Behaviors of the Asphalt ConcreteDuring the cyclic triaxial tests of asphalt concrete, twodierent behaviors were observed; Extension and Compression, which are summarized in Table 4. According tothis table, the extension behavior may occur in a low levelof conning stress such as near the dam crest and hencethis part of dam is more vulnerable during the cyclic loading.Table 4 shows that during the cyclic tests with highervalues of Kc, the compression behavior occurs. Althoughthe amount of strain is very small, the loads compress thematerial. For anisotropic condition, changing the temperature, conning pressure and loading frequency aectthe strain values only and do not alter the general behavior (compression) of the specimens.As mentioned above, the extension behavior is onlyseen in the isotropic state (Kc1.0). Increasing the temperature or decreasing the conning pressure are the mainfactors causing extension. In this state, compression behavior was just seen at a low temperature (T59C) andhigh conning pressures (s3250,500 kPa) while extension behavior was seen in other cases.Since the extension behavior is just observed at Kc1.0, the eects of temperature and conning stress on thegeneral behavior of asphalt concrete is explained more inthe following paragraphs:a) Eect of temperature (in isotropic condition)The cyclic tests were performed at two dierent temperatures, T59C and T189C. As presented in Table4, in the constant conning stress, extension behavior occurred in a higher temperature. For the reason that in ahigher temperature, the eect of material viscosity ismore distinct and the increment of conning pressurescan not substantially aect the compression behavior ofthe material. It should be noted that the prepared specimens for the cyclic tests are bitumen rich. The so called``Rich'' is used for the specimens with the high percentage of the bitumen. In a low temperature (T59C), thesample behaves rigidly. With increasing temperature, thecompaction, mixture quality of aggregate with bitumenand the particles interlocking are more inuential.b) Eect of conning stress (in isotropic condition)The cyclic tests were performed in three dierent conning pressures, s385, 250 and 500 kPa. By increasingthe conning pressure, the compression behavior is moredistinct than that of extension; this is specically moreremarkable at low temperatures. At the temperature of T189C, in all conning pressures, the extension behaviorwas observed while at the temperature of T59C, thisbehavior was just seen at s385 kPa. In other words, in alow level of conning pressure (s385 kPa), only the extension behavior is observed and the temperature eectcan be negligible.Near the dam crest the amount of conning pressure isnot considerable. It is also well established that this partof the core is very vulnerable during the earthquake.Therefore, special control of the dam during the construction on this region would be necessary.POSTCYCLIC BEHAVIOUR OF THE ASPHALTCONCRETE SAMPLESAfter an earthquake shocking, the structures shouldretain their eciency and operate normally. The mentioned period is titled the ``postcyclic operation time''.To simulate this occurrence, after completing the cyclictests, some specimens were selected to be imposed bymonotonic loading. The postcyclic monotonic stressstrain curve would be compared to the correspondingcurve for the specimens not rst subjected to cyclic loadFig. 20. Post cyclic behaviour (stressstrain curve), s3500 KPa, T59CTable 4. Dierent types of asphalt concrete behavior during the cyclicloadings3(kPa)85Kc1.0T59CT189CExtensionExtensionKc2.0T59CKc3.0T59CT189C250Compression Extension Compression Compression Compression500Compression ExtensionFig. 21. Post cyclic behaviour (stressstrain curve), s3250 KPa, T189CCYCLIC TRIAXIAL TESTS ON ASPHALT CONCRETEing, to study any sign of material degradation due to thecyclic loading. Figure 20 shows the comparison of thestressstrain curve for one of the specimens before andafter the cyclic loading at a low temperature of T59C.The cyclic tests were performed at dierent anisotropystates (Kc1.0 and Kc3.0). The amount of degradationis nearly 15 percent at the pick point of the curve. In addition, the gure shows a similar overall behavior for thesamples before and after subjecting to cyclic loading.Figure 21 shows the monotonic test results for thespecimen after cyclic loading in a high temperature (T189C). The gure shows the same behavior trend for thetests before and after the cyclic loading in a high temperature of T189C like T59C.It can be concluded that the asphalt concrete retains itseciency after cyclic loads application and the postcyclicbehaviour of this material is still suitable.SUMMARY AND CONCLUSIONSLack of high quality experimental data on the asphaltconcrete subjected to earthquake loading was the mainincentive to perform this research. The outcome of thepresent study shows the behavior of asphalt concrete under cyclic loading. During the design procedure, it isnecessary to have exact material properties to control thedam stability.The results obtained from the present study can besummarized as follows:ÉTriaxial monotonic tests were performed to study thestressstrain behavior of asphalt concrete material.Strength and stiness increased with higher conningstress, s3. Based on the monotonic tests results, theYoung's secant modulus at 1z axial strain is proposedto be E1zA~s0.180 . In addition, higher conningstresses imposed on the specimens caused lowerdilatancy and volume expansion during shearing.ÉIn the cyclic triaxial tests, fty cycles were imposed onthe specimens to simulate earthquake excitations. Insome cases, the cyclic loads were continued to thousands of cycles. However, there was no signicantdegradation detected on the specimen behavior. Nocracks on the specimen surfaces were detected, even after 10000 cycles.ÉMany factors inuence the dynamic properties of theasphalt concrete, such as conning stress, stressanisotropy, loading frequency and temperature. Theeects of the mentioned factors are more distinct onthe shear modulus than on the damping ratio. The dynamic shear modulus of asphalt concrete is strongly dependent on the shear strain.ÉThe damping ratio increases with the increase of dynamic strain at lower stress ratios (Kc), while being constant at higher stress ratios.ÉThe cyclic strain values were less than 0.20z for theperformed tests. The cyclic amplitude remains constanteven for a large number of cycles. The smallest valuesof strain occur for low temperatures and high frequency loading.331ÉAfter the completion of cyclic loading, monotonic testswere carried out on the samples to investigate the postcyclic behaviour. The results show that the asphalt concrete behaves much the same way as prior to cyclicloading. However, by increasing the temperature, theamount of degradation increases. Postcyclic behaviour shows that the reduction in shear strength after cyclic loading is insignicant. The increase of permeability only occurs when ssures get opened near the failurelevel in monotonic loading.ÉThis study shows that asphaltic concrete is resistant toearthquake excitations. The earthquake has to be verystrong to cause any detrimental cracking or materialdegradation of the properties of a ductile asphalticconcrete core in embankment dam.ACKNOWLEDGMENTThe present research was supported by the Iran WaterResources Management Organization (IWRMO) andMahabGhodss consulting engineers in Iran and the contractor KoloVeidekke in Norway. The authors appreciate the assistance of laboratory employees at the Norwegian Geotechnical Institute and KoloVeidekke duringthe experimental work.NATATIONThe following terms are utilized in this research:e: void ratio of specimensn: porosity of specimensy: Poisson ratios3: conning stress, is a pressure applied into the triaxialcells1: axial stress, is applied in the axial direction of thespecimen, while lateral stress is applied in the radial direction of the specimensd: deviator stress, is the dierence between major andminor principal stresses in a triaxial testKc: anisotropic stress ratio, is calculated by dividing theaxial stress by lateral stress (Kcs1/s3)Reversal ratio, is introduced by the reversal coecient(rc), which is the relative value of positive portion of applied cyclic shear stress to the whole domain of shearstressG: shear modulus, is calculated from hysteresis loops. Gcand Ge are dened for the compression and extensionregions inclination, respectivelyD: damping ratio, is carried out from hysteresis loopsDegradation, is the reduction amount of materialstrengthThreshold point, is the point that separates the constantand falling parts of the Gg curveCompression behavior, is the shortening of thespecimen's height under the cyclic loadingExtension behavior, is the elongation of the specimen'sheight under the cyclic loading332SIAMAK ET AL.REFERENCES1) Baron, W. F. and Van Asbeck (1955): Bitumen in Hydraulic Engineering, Shell Petroleum Co., Ltd., 1, London, England.2) Breth, H. and Schawab, H. H. (1973): Zur Eignung des asphaltbetons fur die Innendictung von Staudammen, Wassewirtschaft, 69,Heft 11, 348351, Stuttgart, Germany.3) Creegan, P. and Monismith, C. (1996): Asphaltic Concrete WaterBarriers for Embankment Dams, ASCE Press.4) Dunnicli, J. (1996): Geotechnical Instrumentation for MonitoringFiled Performance, 2nd Edition.5) FeiziKhankandi, S., Mirghasemi, A. A. and Ghanooni, S. (2004):3D seismic analysis of asphaltic concrete core rockll dams, ICGEConference, 220225, UAE.6) Ghanooni, S. and Mahinroosta, R. (2002): Seismic analysis anddesign of asphaltic concrete core embankment dams, Journal ofHydropower and Dams, 6, 7578.7) Goto, S., Tatsuoka, F., Shibuya, S., Kim, Y. S. and Soto, T.(1991): A simple gauge for local small strain measurements inlaboratory, Soils and Foundations, 31(11), 169180.8) Gurdil, A. F. (1999): Seismic behavior an Asphaltic Concrete coredams, Proc. 1st Symposium on Dam Foundation, Antalya, Turkey.9) Hoeg, K. (1993): Asphaltic Concrete Cores for EmbankmentDams, Norwegian Geotechnical Institute, Oslo, Norway.10) Hoeg, K. (2005): Earthquake resistance of Asphaltic concrete core,Report No. 200510311, Oslo, Norway.11) Hoeg, K., Valstad, T., Kjaernsli, B. and Ruud, A. M. (2007):Asphalt core embankment dams: recent case studies and researches,Journal of Hydropower and Dams, 13(5), 112119.12) ICOLD Press (1982, 1992): Bituminous Cores for Earth and Rockll Dams, Bulletin 42 and 84.13) International Navigation Association Press (1997): Seismic DesignGuidelines for Port Structure, working group No. 34 of the Maritime Commission International Navigation Association.14) Japanese Geotechnical Society (2000): Standards of JapaneseGeotechnical Society for Laboratory Shear Test, Japan.15) Kokusho, T. and Esashi, Y. (1981): Cyclic triaxial test on sands andcoarse materials, Proc. 10th ICSMFE, (Quoted by Ishihara 1986),Stockholm, Sweden.16) Kokusho, T. and Tanaka, Y. (1994): Dynamic properties of gravellayers investigated by insitu freezing sampling, Proc. GroundFailure under Seismic Conditions, ASCE Annual Convention, Atlanta, USA.17) Kramer, S. (2007): Geotechnical earthquake engineering, Cut ofWall for Gotvand Dam, Prentice Hall, Inc, USA, 1996MahabGhodss report, Iran.18) Meintjes, H. A. C. and Jones, G. A. (1999): Dynamic analyses ofthe new cores dam, Proc. 12th Regional Conference for Africa onSMGE, Durban, South Africa.19) Nakamura, Y., Okumura, T., Narita, K. and Ohne, Y. (2004): Improvement of impervious asphalt mixture for high ductility againstearthquake, Proc. 4th International Conference on Dam Engineering, 1820, China.20) Ohne, Y., Nakamura, Y., Okumura, T. and Narita, K. (2002):Earthquake damage and its remedial measure for earth dams withasphalt facing, Proc. 3rd USJapan Workshop on Earthquake Engineering for Dams, 1526, Japan.21) Salemi, S. (2005): Dynamic behavior investigation of asphaltic concrete core Rockll Dams, IUST University, PhD Dissertation, Iran.22) Tatsuoka, F. and Shibuya, S. (1992): Deformation characteristicsof soils and rocks from eld and laboratory tests, Report of the Institute of Industrial Science, University of Tokyo.23) Tatsuoka, F. and Kohata, Y. (1995): Stiness of hard soils and softrocks in engineering applications, Report of the Institute of Industrial Science, University of Tokyo.24) Valstad, T., Selness, P. B., Nadim, F. and Aspen, B. (1991): Seismic response of a rockll dam with an asphaltic concrete core,Journal of Water Power and Dam Construction, 43, 16.25) Wang, W. (2005): Cyclic Tests on Asphalt Concrete, Xi'an University Press, China.26) Wang, W. and Hoeg, K. (2002): Eects of compaction method onthe properties of asphalt concrete for hydraulic structures, International Journal on Hydropower and Dams, 9(6), 6371. | ||||
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タイトル | Residual Deformation of Geosynthetic-reinforced Sand in Plane Strain Compression Affected by Viscous Properties of Geosynthetic Reinforcement | ||||
著者 | W. Kongkitkul・Daiki Hirakawa・Fumio Tatsuoka | ||||
出版 | Soils and Foundations | ||||
ページ | 333〜352 | 発行 | 2008/06/15 | 文書ID | 21112 |
内容 | 表示 SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 333352, June 2008RESIDUAL DEFORMATION OF GEOSYNTHETICREINFORCEDSAND IN PLANE STRAIN COMPRESSION AFFECTED BYVISCOUS PROPERTIES OF GEOSYNTHETIC REINFORCEMENTWARAT KONGKITKULi), DAIKI HIRAKAWAii) and FUMIO TATSUOKAiii)ABSTRACTA series of plane strain compression (PSC) tests were performed on large sand specimens unreinforced or reinforcedwith prototype geosynthetic reinforcements, either of two geogrid types and one geocomposite type. Local tensilestrains in the reinforcement were measured by using two types of strain gauges. Sustained loading (SL) under xedboundary stress conditions and cyclic loading (CL) tests were performed during otherwise monotonic loading at a constant strain rate to evaluate the development of creep deformation by SL and residual deformation by CL ofgeosyntheticreinforced sand and also residual strains in the reinforcement by these loading histories. It is shown thatthe creep deformation of geosyntheticreinforced sand develops due to the viscous properties of both sand and geosynthetic reinforcement, while the residual deformation of geosyntheticreinforced sand during CL (dened at the peakstress state during CL) consists of two components: i) the one by the viscous properties of sand and reinforcement; andii) the other by rateindependent cyclic loading eects with sand. The development of residual deformation ofgeosyntheticreinforced sand by SL and CL histories had no negative eects on the subsequent stressstrain behaviourand the compressive strength was maintained as the original value or even became larger by such SL and CL histories.The local tensile strains in the geosynthetic reinforcement arranged in the sand specimen subjected to SL decreasednoticeably with time, due mainly to lateral compressive creep strains in sand during SL of geosyntheticreinforcedsand. This result indicates that, with geosyntheticreinforced soil structures designed to have a suciently high safetyfactor under static loading conditions because of seismic design, it is overly conservative to assume that the tensile loadin the geosynthetic reinforcement is maintained constant for long life time. Moreover, during CL of geosyntheticreinforced sand, the residual tensile strains in the geosynthetic reinforcement did not increase like global strains in thegeosyntheticreinforced sand that increased signicantly during CL. These dierent trends of behaviour were also dueto the creep compressive strains in the lateral direction of sand that developed during CL of geosyntheticreinforcedsand.Key words: creep, cyclic loading, bre bragg grating, geocomposite, geogrid, plane strain compression, reinforcedsoil, relaxation (IGC: D6/K14)number of GRSRWs with fullheight rigid facing havebeen constructed by the staged construction procedure aspermanent RWs allowing a limit amount of deformation,while they exhibited satisfactory postconstruction performance, including those during the 1995 Kobe Earthquake (e.g., Tatsuoka et al., 1997, 1998). In addition, anumber of unreinforced soil structures that weredamaged by earthquakes were reconstructed to GRSstructures, including GRSRWs with fullheight rigid facing, in Japan (Tatsuoka et al., 2007a, b).The current design method of GRS structures is mostlybased on the ``limit equilibriumbased stability analysis'',in which the design tensile strength of reinforcement layerarranged at a certain vertical spacing is specied to beINTRODUCTIONA great number of important permanent soil structureswith a design life of typically 50 years have been designedand constructed reinforced with polymer geosyntheticreinforcement. Presently, various dierent types ofgeosyntheticreinforced soil (GRS) structures can befound, including soil retaining walls (RWs), bridge abutments, steep slopes of embankment, dykes and earthlldams, shallow foundations, etc. The popularity of GRSstructures results from a high costeectiveness becauseof a rapid construction speed, a relatively small construction space required and a high postconstruction performance including high seismic stability. In particular, ai)ii)iii)Lecturer, Department of Civil Engineering, King Mongkut's University of Technology Thonburi, Thailand.Assistant Professor, Department of Civil and Environmental Engineering, National Defense Academy of Japan, Japan.Professor, Department of Civil Engineering, Tokyo University of Science, Japan (tatsuokars.noda.tus.ac.jp).The manuscript for this paper was received for review on May 31, 2007; approved on April 8, 2008.Written discussions on this paper should be submitted before January 1, 2009 to the Japanese Geotechnical Society, 4382, Sengoku,Bunkyoku, Tokyo 1120011, Japan. Upon request the closing date may be extended one month.333334KONGKITKUL ET AL.higher than the lateral earth pressure per reinforcementlayer that is activated by selfweight of the backll andsurcharge on the backll crest as well as seismic load(e.g., FHWA, 2001; AASHTO, 2002). The design tensilestrength of geosynthetic reinforcement is usually obtained by reducing the ultimate tensile strength obtainedby tensile loading tests at a relatively high strain rate using several reduction factors that account for installationdamage, chemical and/or biological degradation, thepossibility of creep rupture and a global safety factor fora given structural type. Due to the use of a creep reduction factor in design, it is often considered wrongly thatcreep is a degrading phenomenon. Moreover, the creepreduction factor is determined assuming that the tensileload activated in respective geosynthetic reinforcementlayers arranged in a GRS structure is maintained constantthroughout specied design life. It is obvious that this assumption could be relevant only when the stressstrainproperties of both soil and geosynthetic reinforcementare rateindependent. However, this assumption is notrealistic, because both soil (e.g., Matsushita et al., 1999;Di Benedetto et al., 2002, 2005; Tatsuoka et al., 2000,2001, 2002, 2008; Tatsuoka, 2004, 2007; Kiyota and Tatsuoka, 2006; Anh Dan et al., 2006; Pham Van Bang etal., 2007; Duttine et al., 2008; Kongkitkul et al., 2008)and polymer geosynthetic reinforcement (e.g., Bathurstand Cai, 1994; Leshchinsky et al., 1997; Shinoda andBathurst, 2004; Hirakawa et al., 2003; Kongkitkul et al.,2004a, 2007a, d; Kongkitkul and Tatsuoka, 2007) exhibitsignicant ratedependent stressstrain or loadstrain behaviour (e.g., creep deformation and stress/load relaxation) due to their viscous properties. Tatsuoka et al.(2004, 2006) and Kongkitkul et al. (2007d) argued thatthe possibility of creep rupture is overestimated while thetensile rupture strength under given loading conditions atthe end of a given life time is underestimated in the current design method and they proposed a new method notusing a creep reduction factor.This research was undertaken rst to reconrm the arguments above by performing a series of plane straincompression (PSC) tests on relatively large specimens(230 mmwide, 243 mmdeep in the plane strain directionand 570 mmhigh, Fig. 1) of airdried Toyoura sandunreinforced or reinforced with prototype geosyntheticreinforcement, either of two geogrid types and one geocomposite type. By using large specimens, it becamepossible to measure local tensile strains activated in layersof prototype reinforcement arranged in a sand specimenby means of electricresistant strain gauges or optical sensors, depending on the reinforcement type.A number of PSC tests have been performed to evaluate the eects of mechanical properties (i.e., tensile ultimate strength and stiness) and geometric properties(i.e., surface roughness, shape, covering ratio and so on)of polymer geosynthetic reinforcement as well as arrangements of reinforcement layers on the deformation andstrength characteristics of geosyntheticreinforced soil(e.g., Tatsuoka and Yamaguchi, 1986; Ling and Tatsuoka, 1994; Peng et al., 2000; Roh and Tatsuoka, 2002;Fig. 1. Large PSC specimen of reinforced Toyoura sand: a) dimensions; and b) s2 surface at ev8.0% (PET GCreinforced sand): alocal strain eld was constructed by the photogrametric method ina rectangular zone of broken lineKongkitkul et al., 2007b, c, e). The rst advantage of thePSC test over the triaxial compression test is that thestressstrain conditions are more representative of typicalprototype GRS structures. Furthermore, local strain distributions in the specimen can be evaluated by photogrametric analysis of pictures of the s2plane of the specimentaken during loading (e.g., Yoshida and Tatsuoka, 1997;Kongkitkul et al., 2007c).Signicant residual deformation may develop ingeosyntheticreinforced soil during sustained loading(SL) due to the viscous properties of sand and geosynthetic reinforcement. In addition, signicant residualdeformation may also develop in reinforced soil duringcyclic loading (CL), also aected and controlled by theviscous properties of sand and polymer geosynthetic reinforcement. Despite a number of previous studies described above, the ratedependent behaviours of polymergeosyntheticreinforced soil during SL and CL and theirrelation have been studied only to a very limited extentand therefore are understood only very poorly. This current situation is due mainly to very complicated interactions between the ratedependent behaviours of soil andgeosynthetic reinforcement (e.g., Kongkitkul et al.,2007b, c). With respect to the residual deformation characteristics of reinforced sand during CL, the rateindependent cyclic loading eect on the residual deformation of sand, which is dened and explained later in thispaper, should also be taken into account in addition tothe viscous properties of soil and geosynthetic reinforcement. This study was performed also to understand themechanism of the residual deformation of reinforcedsand during CL and the associated loadstraintime behaviour of geosynthetic reinforcement arranged in sand.TESTING METHODSGeosynthetic Reinforcement Types and their Mechanicaland Geometric PropertiesThe following three types of prototype geosynthetic335GEOSYNTHETICREINFORCED SANDTable 1. List of geosynthetic reinforcement types and their strengthand stiness values at a strain rate of 1.0%/minFig. 2. a) PET GG, b) PVA GG, both with four electricresistantstrain gauges adhered to a longitudinal member and c) PET GCwith FBG sensors inserted in three longitudinal yarnsFig. 3. Tensile loadtensile strain relations of geosynthetic reinforcement types used in the present studyreinforcement were used:1) Polyester geogrid (PET GG, Fig. 2(a)): Both longitudinal and transversal members are made of polyester bre. This is relatively weak while having acovering ratio (CR, dened as the area covered by thereinforcement per unit area) equal to 22.2z.2) Polyvinyl alcohol geogrid (PVA GG, Fig. 2(b)):Both longitudinal and transversal members are madeof polyvinyl alcohol bre. This is relatively strongwhile having CR25z.3) Polyester geocomposite (PET GC, Fig. 2(c)): This ismade by sewing yarns of polyester bre (i.e., PETyarns) onto a sheet of polypropylene (PP) nonwoven geotextile. The PP nonwoven geotextile function as drainage only, bearing negligible tensile load,while the PET yarn bears the major tensile load. Before the use of PET GC in the present study, all thePET yarns of the original PET GC were tightlybonded for the full length to the PP nonwoven geotextile sheet by using rapidhardening highstrengthglue to prevent any slippage in the longitudinal direction between them when loaded inside the backll.The strength and stiness of a sand specimen reinforced with this ``fully unied PET GC'' in PSC testswere signicantly higher than those when reinforcedwith the original PET GC (Kongkitkul et al., 2007e).Figure 3 compares the tensile loadtensile strain (Te) reReinforcementnameUltimate tensilestrength, Tult(kN/m)Secant stinessat a strain of 5z,J5z (kN/m)PET GG39.2220PVA GG85.2910PET GC61.9458lations from a series of continuous monotonic loading(ML) tensile tests at dierent constant strain rates rangingfrom 0.01 to 20z/min on the three types of geosyntheticreinforcement. A pair of rollerclamps was used to gripthe ends of the respective specimens to avoid the ruptureof the specimens near the gripping locations (e.g.,Hirakawa et al., 2003; Kongkitkul et al., 2004a, b,2007a). It is readily seen from Fig. 3 that the rupture tensile strength and tensile stiness are highest with PVAGG, intermediate with PET GC and lowest with PETGG. Moreover, the Te relations exhibit a noticeable ratedependency and a high strainnonlinearity. Table 1 summarises the rupture tensile strength values (Tult) and thesecant tensile stiness values at the tensile strain of 5z( J5z) obtained at a strain rate of 1.0z/min.Measurements of Local Tensile Strains in the ReinforcementOne layer of, respectively, PET GG, PVA GG andPET GC equipped with strain gauges to locally measuretensile strains activated in the reinforcement was arranged at the third level from the top (i.e., slightly abovethe central height) in the respective PSC specimens (Fig.1(a)). With PET GG and PVA GG, a pair of electricresistant strain gauges (SGs) was arranged at four positions, about 50 mm apart in the s3 direction along thecentral strand (Figs. 2(a) and (b)). To ensure smooth surface of the strand before attaching SGs and to provide anextra working space, the strand at the respective positionswhere SGs were to be equipped was rst sandwiched by apair of small smoothsurface plastic sheets and thenultrasonicwelded including the plastic sheets and thestrand. Then, a pair of SGs was attached to the upper andlower faces of the welded plastic sheets at the same position of the strand. Subsequently, the attached SGs wereconnected to cables (Figs. 2(a) and (b)) and nally covered with silicone for protection against damage. TheSGs formed a Wheatstone bridge of ``oppositeside twoactivegauge twowire system'' consisting also of a pair ofxed resistances outside the PSC specimen (Fig. 4(a)) toeliminate reading errors of strain generated by bending ofthe strand.As the structure of a geogrid is not homogeneous in thelengthwise direction of the strand due to a grid structure,the local tensile strain is highly nonuniform along thestrand. Moreover, readings from SGs may be signicantly dierent from actual local tensile strains at a given location of the strand of a given geogrid due to eects of336KONGKITKUL ET AL.Fig. 4. a) Wheatstone bridge of ``oppositeside twoactivegauge twowire system'' for SGs and b) principle of FBG sensorssystem compliance. For these reasons, local tensile strainsmeasured with SGs could be largely dierent from globalaveraged tensile strains measured for some large gaugelength spanning over multiple grids, as pointed out byBathurst et al. (2002). Figure 5(a) shows the relationshipsbetween the global averaged tensile strain for a gaugelength equal to 5 cm and the local tensile strain measuredwith SGs attached (as shown in Fig. 5(b)) obtained fromrespectively two tensile loading tests on respectively PETGG and PVA GG at a strain rate of 0.1z/min. It may beseen that the global average tensile strain is larger by afactor of 3.8 on average than the tensile strains measuredlocally with SGs. Therefore, only the trends of behaviourseen from the time histories of local tensile strains measured with SGs are discussed in this paper. When the localtensile strains are numerically analysed based on a constitutive model of geogrid, this dierence between theglobal averaged tensile strain and the local tensile strainmeasured with SGs is taken into account.Tensile strains in the PET yarn of PET GC were measured with three Fibre Bragg Grating (FBG) sensors (Fig.4(b)) printed on an optical bre inserted into the threeselected PET yarns separated about 50 mm in the s3direction (Fig. 2(c)). The locations of the three FBG sensors were also separated about 50 mm in the s2 direction(i.e., the direction that is perpendicular to that of thePET yarns). The FBG is diracting elements printed on aphotosensitive core of a single mode optical bre. Onlyone spectral component satisfying the Bragg relation isreected by the grating when light of a broadband sourceis coupled into a bre with a FBG. The grating reects aspectral peak based on the grating spacing; therefore,changes in the length of the bre due to tension or compression change the grating spacing and the wavelength(l) of light that is reected back (Briançon et al., 2004,Fig. 5. a) Relationships between global averaged tensile strain for agauge length of 5 cm and local tensile strain measured with SGs andb) locations of SGs along a strand, tensile loading tests at a strainrate of 0.1%/min2006; Nancey et al., 2006). In this study, the three FBGsensors having the characteristic wavelengths of 1530,1535 and 1540 nm were connected in series on a single optical line (i.e., multiplexed); thus, the locations of eachsensor can be distinguished. The tensile strain incrementsfrom each FBG sensors were obtained from thewavelengthshifts (i.e., Dl1, Dl2 and Dl3; Fig. 4(b)) ofthe reected light, by using a spectral analyser. This strainmeasuring method is explained more in detail in Kongkitkul (2007f). The relationships between the globalaveraged tensile strains and the local tensile strains measured with FBG sensors could not be obtained because itwas not possible to grip the ends of a PET GC specimenequipped with an optical bre without damaging the optical bre for tensile loading tests.PSC Specimens, Measuring Devices and Loading SystemPSC tests were performed on large specimens (Fig. 1)made of dense (Dr§90z) airdried Toyoura sand (Kongkitkul et al., 2007e, f). It is a natural quartzrich poorlygraded ne subangular sand. The batch of Toyoura sandused in this study had Gs2.65; D500.2 mm; Uc1.20;emax0.98 and emin0.62. The specimens were eitherunreinforced or reinforced with dierent types of reinforcement listed in Table 1. Six reinforcement layers havingthe same area as the horizontal crosssection of the PSCspecimen were arranged at an equal vertical spacing of9.5 cm (Fig. 1(a)). The reinforcement layer equipped withlocal strain gauges was placed at the third level from theGEOSYNTHETICREINFORCED SAND337Fig. 7. a) Bottom face of the specimen cap with a vertical hole to extend the cables outside the specimen and b) highvacuum grease toseal the hole on the top face of the specimen capFig. 6. Preparation of reinforced sand specimens, showing the thirdPET GG layer attached with electricresistant strain gauges to locally measure tensile straintop. To ensure as much as possible a high homogeneity inthe sand density and to minimise the eects of bedding errors at the interface between each reinforcement layerand the adjacent sand on the global axial strain of thespecimen (e.g., Kongkitkul et al., 2007b), the specimenswere prepared as follows (Fig. 6):1) Airdried Toyoura sand was pluviated through airinto the rectangular prismatic specimen mould at acontrolled falling height of about 30 cm from thebottom of a multiplesieve pluviating device, asshown in Fig. 6(a). The sand was supplied from ahole at the bottom of a liftedup sand bucket via aexible plastic tube. This procedure continued untilthe transient surface of sand became slightly higherthan the specied level of the respective reinforcement layers.2) The surface of each sand layer was levelled byvacuuming extra sand via a vertical metal pipe whilecontinuously controlling the level of the bottom ofthe vertical metal pipe, as shown in Fig. 6(b). In sodoing, the vertical metal pipe was xed to a horizontal Lbeam with a specied length of the pipe belowthe Lbeam. Then, a controlled negative pressure wassupplied to the pipe and the sand surface was levelledby gradually sliding the Lbeam placed on the top ofthe mould.3) Each reinforcement layer was placed on thesmoothened sand surface, Fig. 6(c). Then, somesmall amount of sand was placed on the reinforcement layer (Fig. 6(d)) and then manually spread overthe whole area of the reinforcement layer.4) The sand layer including the reinforcement layer wastamped by hand using a rubber hammer to minimisethe bedding errors at the interface between the adjacent sand and the reinforcement layer while achieving the specied sand dry density, Fig. 6(e).Steps 14 were repeated for the respective reinforcementlevels. At step 4, when arranging the reinforcement layerequipped local strain gauges, prior to tamping, the cablesfrom the local strain gauges (Fig. 2) were placed horizontal in the s3direction on the transient sand surface untilreaching the side wall of the mould as the cables wereconnected with the reinforcement in this direction (Fig.2). After tamping, the cables were horizontally rearranged again and then bent up in the vertical directionalong the left side (from the front) of the specimen andkept so at the subsequent steps. Then, when the step 4was nished for the last (i.e., top) reinforcement layer,the cables were bent rst horizontally at the left side ofthe mould and then vertically up at the position of thevertical hole of the cap (explained later). Subsequently,the nal step 1 was executed until the sand lledup themould, while the cables were vertically held at the abovementioned position. It is to be noted that, as the cableswere much more extensible than the reinforcement used,it was considered that only negligible tensile force wouldbe activated by the cables during the PSC tests. The unreinforced PSC specimen was made only by lling up sanduntil the top of the mould at step 1.After having smoothened the nal top surface of specimen by using a sharp edge (Fig. 6(f)), the cables were extruded out of the PSC specimen via a vertical hole drilledthrough the specimen cap (Fig. 7(a)). Then, the cap wasplaced on the top of the specimen and a latex rubbermembrane was sealed to it. Subsequently, the hole wassealed with highvacuum grease (Fig. 7(b)) to preventleakage that might take place via the hole when applyingthe negative pressure to the specimen.The two s2 faces of the specimen were welllubricatedby smearing a 0.05 mmthick layer of Dow highvacuumsilicon grease between the lateral conning platens andthe 2 mmthick specimen membrane while the top andbottom ends of the specimen by placing a 0.3 mmthicklatex rubber sheet smeared with a 0.05 mmthick of thesame grease (Fig. 7(a), Goto et al., 1993). A number ofphotos of the latex rubber membrane at the s2 face, onwhich markers had been printed at a 1 cm spacing in bothvertical and horizontal directions (Fig. 1(b)), were takenthrough the Acrylic conning platen during each test.These photos were analysed subsequently by the photogrametric method (Kongkitkul et al., 2007c).An axial load cell having a capacity of 100 kN (Fig.7(b)) was used to measure the axial load applied to the topof the specimen. Despite it being very small, the verticalfriction activated on the s2 faces was measured with apair of load cells arranged at the bottom of the two conning platens to correct the axial load measured with the338KONGKITKUL ET AL.axial load cell. Conning pressure, s?c, of 30 kPa was applied to the specimen by partial vacuuming and measuredwith a pressure transducer. The average axial strain, ev,of the PSC specimen was obtained by measuring the vertical displacements of the loading piston with a pair ofLVDTs, while the average lateral strain by measuring thelateral displacements at the midheight of specimen by using a pair of laser displacement transducers (Fig. 1(a)).An axial loading system having a capacity of 500 kNand consisting of a hydraulic jack system and a precisepressurecontrolled unit was used. The rate and directionof the vertical displacement of the loading piston of thehydraulic jack were controlled in an automated way sothat the distance between this loading piston and thepiston of a small gear system, measured with a highprecision LVDT, was always kept zero, while the vertical position of the piston of the small gear system was controlled very accurately to realise the specied time historyof the axial compression of the specimen (Tatsuoka et al.,1999; Anh Dan et al., 2006).PSC Loading SchemesThe following three loading schemes were employed,extending those employed by Kongkitkul et al. (2007f):a) Monotonic loading (ML) at a constant axial strainrate, ·ev, equal to 0.04z/min until the axial strain, ev,becomes 8.0z.b) Sustained loading (SL), lasting for six or three hoursper stage, at several or many stages during otherwiseML at ·ev0.04z/min and also during otherwisetwo cycles of global unloading and reloading, applied before ev becomes 8.0z.c) Cyclic loading (CL) with 200 cycles of a deviatorstress amplitude, Dq, equal to 150 kPa at several ormany stages during otherwise ML at ·ev0.04z/min.Local tensile strains in reinforcement were not measuredin the ML PSC tests of loading pattern a).RESULTS FROM MONOTONIC AND SUSTAINEDLOADING TESTSContinuous Monotonic Loading TestsAs the stresses are highly nonuniform inside the reinforced sand specimen, the shear stress state of the specimen is expressed in terms of ``the apparent average stress v is the average vertiratio, R'' dened as s?v/s?c; where s?cal stress; and s?c is the conning pressure (30 kPa).Figure 8 compares the R cev relations from four continuous ML tests at ·ev0.04z/min towards the residual stateon the sand specimens unreinforced or reinforced witheither PET GG or PVA GG or PET GC. The reinforcedsand specimens are much stronger than the unreinforcedone due to signicant tensile reinforcing eects providingadditional conning pressure to the sand. Also, the reinforced sand specimens are stier and the stiness is largerwhen reinforced with a stier reinforcement (Fig. 3;Table 1). However, the dierence in the stiness amongthe three reinforced specimens is much smaller than theFig. 8. Re v relations of unreinforced and reinforced sand specimenssubjected to continuous MLFig. 9. Contours of local maximum shear strain when ev4.0%, sandreinforced with: a) PET GG, b) PVA GG and c) PET GCone among the three reinforcements in their tensile loading tests (Fig. 3). Moreover, despite that the tensile rupture strength and stiness of the fully unied PET GC arelower than PVA GG (Fig. 3; Table 1), the specimen reinforced with this reinforcement type is noticeably strongerthan the PVA GGreinforced sand. These results indicateimportant positive eects of a high CR on the compressive strength. On the other hand, the initial stiness ofRe v relation at small vertical strains of the PET GCreinforced sand is particularly low. This trend is due likely toextra compression of the PP nonwoven geotextile layers.Figure 9 compares the contours of local maximumshear strain obtained from a photogrametric analysis(Kongkitkul et al., 2007c), gmaxe1|e3, when ev4.0zin the three reinforced sand specimens. The area shown inFig. 9, which is free from any obstacle, covers the seconddown to the fth reinforcement layers (Fig. 1(b)). It maybe seen that the strain localisation is most intense in thePET GGreinforced sand specimen (i.e., the weakest reinforced sand specimen). By comparing Figs. 9(a) and (b)for the PET GG and PVA GGreinforced sand specimens, it is seen that, for similar interface conditions between the reinforcement and the sand, the number ofshear band, which controls the compressive strength ofreinforced sand, increases with a decrease in the tensileGEOSYNTHETICREINFORCED SANDstiness of reinforcement. Furthermore, as signicantstrainsoftening behaviour takes place quickly in a shearband, once clear multiple shear bands develop, thestrength of reinforced sand cannot increase at a high ratewith the average axial strain or even strainsoftening maystart during subsequent loading. With the PET GCreinforced sand specimen (Fig. 9(c)), on the other hand, anysignicant strain localisation with welldened shearbands could not be observed at ev4.0z, where the peakstrength is not yet attained. This is due likely to a higherCR (i.e., 100z) of PET GC, which prevents direct contact of sand particles above and below the respective PETGC layers and therefore restrains the formation of shearband.Sustained Loading TestsA set of sustained loading (SL) tests were performedduring otherwise primary loading at ·ev0.04z/min onthree sand specimens reinforced with PET GG, PVA GGand PET GC. Figures 10(a), 11(a) and 12(a) present theRe v relations from these tests, which are compared withthose from continuous ML tests (Fig. 8). With the PETGCreinforced sand, SL tests were performed also duringotherwise two cycles of global unloading and reloading(Fig. 12(a)). The respective SL stages lasted for six hours339with the PET GG and PVA GGreinforced sand specimens and three hours with the PET GCreinforced one.Figures 10(b), 11(b) and 12(b) show the zoomedup portions of Figs. 10(a), 11(a) and 12(a). Figures 10(c), 11(c)and 12(c) show the distributions of measured local tensilestrain, elocal (positive in tension), at the respective SLstages (see Figs. 10(b), 11(b) and 12(b) for the respectivemoments in Re v relations). Figures 10(d), 11(d) and12(d) respectively show the distributions of the ratio ofthe local tensile strain, elocal, in the reinforcement (shownin Figs. 10(c), 11(c) and 12(c)) to the average axial strain,ev (positive in compression), at the respective SL stages inthese three specimens. Figure 13 shows the time historiesof creep axial strain at SL stages during primary loading,unloading and reloading, obtained from the test on thePET GCreinforced sand specimen, presented in Fig.12(a). Figure 14 compares the relationships between thecreep axial strain measured at the end of each SL stage at thefor six hours, Dev, and the average stress ratio, R,SL stage. The Dev values of the PET GCreinforced sandwere obtained by extrapolating those measured for threehours. The following trends of behaviour may be seenfrom Figs. 10 to 14:1) Signicant creep axial strains took place at these SLstages, which can be attributed to the viscous properFig. 10. a) Re v relation of PET GGreinforced sand subjected to SL during otherwise ML, b) zoomup of Fig. 10(a); and distributions of: c) localtensile strain and d) normalised local tensile strain in the PET GG during SL stages340KONGKITKUL ET AL.Fig. 11. a) Re v relation of PVA GGreinforced sand subjected to SL during otherwise ML, b) zoomup of Fig. 11(a); and distributions of: c) localtensile strain and d) normalised local tensile strain in the PVA GG during SL stages2)3)ties of sand and geosynthetic reinforcement whileaected by their interactions. The creep axial strainincreased with an increase in the shear stress level inthe respective PSC tests (Fig. 14). This can be explained theoretically such that the creep axial strain isbasically inversely proportional to the tangent stiness of the Re v relation at the stress level of the concerned SL, while the tangent stiness decreases withan increase in the stress level. A similar trend withgeosyntheticreinforced sand was reported also byTatsuoka et al. (2004) and Kongkitkul et al. (2007b).This trend of behaviour is consistent with the onethat has been observed with sand alone (e.g., DiBenedetto et al., 2002; Tatsuoka et al., 2002, 2008;Duttine et al., 2008; Kongkitkul et al., 2007b, 2008)and geosynthetic reinforcement alone (e.g., Hirakawa et al., 2003; Kongkitkul et al., 2004a, b, 2007a).For the same reason as above, the creep axial strainof reinforced sand by SL at a certain R generally increased with a decrease in the stiness of the Re v relation among the three reinforced sand specimens.The creep axial strain increment became negativeduring SL at unloaded stress state and the amount ofnegative creep strain increased with a decrease in thestress level (Fig. 13(a)). On the other hand, it became4)5)positive again during SL, during otherwise globalreloading, but it is much smaller than the one by SLat the same stress level during primary loading (Fig.13(b)). These facts indicate that the creep deformation of a given GRS structure can be eectivelydecreased by relevant preloading history.When ML at ·ev0.04z/min was restarted at the endof each SL stage, the Re v relation exhibited somestress range with relatively high initial stiness.However, the initial stiness immediately after therestart of ML was much lower than the elastic onewhile the Re v relation started yielding without showing a clear yield point, followed by slow rejoining tothe primary Re v relation from the respective continuous ML tests (Fig. 8). These trends of behaviourhave also been observed with smallsize geosyntheticreinforced sand specimens (96 mmwide, 62 mmdeep in the plane strain direction and 120 mmhigh)in drained PSC (Kongkitkul et al., 2007b). This issueis discussed in detail later in this paper.In the test results presented in Figs. 10 and 11, duringsubsequent loading after the respective SL stages, thereinforced sand became even stier and strongerwhen compared with the behaviour during continuous ML. This trend of behaviour is due likely to aGEOSYNTHETICREINFORCED SAND341Fig. 12. a) Re v relation of PET GCreinforced sand subjected to SL during otherwise ML, b) zoomup of Fig. 12(a); and distributions of: c) localtensile strain and d) normalised local tensile strain in the PET GC during SL stagesFig. 13. Time histories of creep axial strain at SL tests during otherwise monotonic loading, unloading and reloading on PET GCreinforced sand:a) lm, no, pq and rs and b) de, no and rs at R12better interlocking between the grid structure and thesand particles that developed during SL. It is likelythat this factor is a function of not only averagestrain but also elapsed time (i.e., a kind of positiveageing eects).These test results in terms 4) and 5) indicate that creepdeformation of geosyntheticreinforced sand is not adegrading phenomenon, but it is merely a result of interacting viscous behaviours of sand and geosynthetic reinforcement that may include some positive ageing eects.6) The trend of the local tensile strains, elocal, measuredby means of FBG sensors is consistent with the one ofthe local tensile strains measured by means of electricresistant SGs.7) The elocal values measured at the all locations noticeably decreased with time at the all SL stages (e.g., hi342KONGKITKUL ET AL.Fig. 14. Relationships between creep axial strain Dev and averagestress ratio Rin Figs. 10(c) and 11(c); lm in Fig. 12(c)). Therefore,in all the cases, the ratio of the local tensile strain,elocal, in the reinforcement to the average axial compressive strain in the reinforced sand signicantlydecreased with time at the respective SL stages (Figs.10(d), 11(d), and 12(d)). This trend of behaviourshould be explained by relative largeness between thefollowing two factors that aect the development oftensile strain in the geosynthetic reinforcement:a) an increase in elocal imposed by laterally expanding creep strains of sand caused by vertical creepcompressive strains of sand due to sustained vertical load (i.e., the Poisson's eect); andb) a decrease in elocal associated with lateral compressive creep strains of sand caused by tensileforce of geosynthetic reinforcement.The test results in Figs. 10(d), 11(d) and 12(d) indicate that, at these SL stages, the eects of factor b)overwhelmed those of factor a), resulting in a noticeable decrease with time in the tensile strain of geosynthetic reinforcement. If the tensile strains in the geosynthetic reinforcement had been kept constant under loading conditions, the tensile force in the geosynthetic reinforcement should have decreased withtime due to the phenomenon of load relaxation.Therefore, it is certain that, at these SL stages, thegeosynthetic tensile force signicantly decreased withtime.8) With the PET GCreinforced sand, the elocal values atpoint t in Fig. 12(c) (when R22during ML after thesecond global unload/reload cycle) is similar to thosemeasured at point m (when R20at the end of SLduring otherwise primary loading) while signicantlysmaller than those measured at point l (when R20at the start of SL) despite the R and ev values are larger at point t than at l (Fig. 12(a)). This result also suggests that the tensile load signicantly decreased notonly during SL lm but also during the subsequentglobal unload/reload cycle. This result explains why,in Figs. 12(a) and 12(b), the Re v relation passes signicantly below point m during global reloadingfrom point s. On the other hand, the elocal value iskept essentially constant during SL stages at unloaded state pq (Fig. 12(c)). A minute increase at the twoouter locations during SL stage pq may be due todelayed rebound of sand in the lateral direction according to a decrease in the reinforcement tensileforce by global unloading of R.With respect to term 4) (about the stressstrain behaviourimmediately after ML is restarted after SL), Fig. 15(a)shows the result from a PSC test on a smaller specimen(96 mmwide, 62 mmdeep in the plane strain directionand 120 mmhigh) of unreinforced Toyoura sand at thesame conning pressure as in the present study, whereRs?1/s?3 s?v/s?c (i.e., s?1 and s?3 are always equal torespectively s? v and s?c in the case of PSC test on unreinforced sand) (Kongkitkul et al., 2007b). In this gure, SLand stress relaxation (SR) tests were performed for respectively three hours during otherwise ML at ·ev0.04z/min. Figures 15(b), (c) and (d) show the resultsfrom three tensile loading tests on the three reinforcement types (PET GG, PVA GG and PET GC), in whichSL and load relaxation test were performed during otherwise ML at constant tensile strain rates equal to 0.01, 0.1or 1.0z/min. The following common trends of behaviour of sand alone and reinforcement alone may be seen:1) The stressstrain relation of sand and the loadstrainrelations of geosynthetic reinforcement exhibit signicant creep deformation and stress (or load) relaxation.2) Immediately after the restart of ML following the SLor SR stage, these relations exhibit a very high tangent stiness, close to the elastic value.3) Subsequently, the relations exhibit a very clear yieldpoint, followed by quick rejoining to the respectiveoriginal ones obtained by continuous ML at the sameconstant strain rate.These trends of behaviour cannot be seen in the results ofgeosyntheticreinforced sand (Figs. 10, 11 and 12).The high stiness behaviour of both Re v relations ofsand alone and Te relations of geosynthetic reinforcement alone observed immediately after the restart of MLat the original constant strain rate following a SL stage(Fig. 15) can be explained as a result of a step increase inthe strain rate from a very small value at the end of SLstage to a higher value during continuous ML (e.g.,Kongkitkul et al., 2007a). Figures 16(a) and (b) show thetime histories of axial strain and its rate during a typicalSL stage in the PSC test on Toyoura sand presented inFig. 15(a). The time history of measured creep strain(Fig. 16(a)) was tted by a set of polynomial functions(e.g., Kongkitkul et al., 2007a, c). These tted equationswere then dierentiated to obtain the creep strain rate(Fig. 16(b)). Figures 17(a) and (b) show similar timehistories of axial strain and its rate during SL at R12from the PSC test on PET GGreinforced sand (Fig. 10).It may be seen from Figs. 16(b) and 17(b) that the axialstrain rate has decreased signicantly during the respective SL stages and, upon the restart of ML, the strain ratesuddenly increased in a similar way, by a factor of about875 from 7.6~10|7z/s to 6.67~10|4z/s (the valueGEOSYNTHETICREINFORCED SAND343Fig. 15. a) Re v relation of Toyoura sand alone in smallsize PSC test (after Kongkitkul et al., 2007b); and tensile loadtensile strain relations of: b)PET GG, c) PVA GG (after Hirakawa et al., 2003) and d) PET GC (after Kongkitkul et al., 2004b), during and after sustained loading andstress (or load) relaxation compared with the ones from continuous MLFig. 16. Time histories of: a) creep axial strain and b) creep axialstrain rate, of SL test performed at R6on the Toyoura sandalone presented in Fig. 15(a)Fig. 17. Time histories of: a) creep axial strain and b) creep axialstrain rate, of SL test performed at R12on the PET GGreinforced sand presented in Fig. 10344KONGKITKUL ET AL.during ML) in Fig. 16(b) and about 250 from 2.7~10|6z/s to 6.67~10|4z/s in Fig. 17(b). Despite these similar trends of strain rate behaviour, the stressstrain behaviour of geosyntheticreinforced sand did not exhibit aclear yield point and fast rejoining to the original stressstrain relation after ML was restarted at the originalstrain rate following the respective SL stages, as mentioned above. It is very likely therefore that, during SL ofreinforced sand, the tensile force in the geosynthetic reinforcement signicantly decreased and, correspondingly,the local conning pressure in sand decreased signicantly. This inference is consistent with the observation thatthe tensile strains in the reinforcement decreased duringSL stages (term 7 described above).Estimate of Tensile Force in Geosynthetic ReinforcementA typical time history of tensile load activated in thegeosynthetic reinforcement during SL of reinforced sandin drained PSC described above was estimated based onthe time history of tensile strain activated in the reinforcement as follows.Figure 18(a) shows the time histories of individual local tensile strains measured with SGs from the PSC teston PET GGreinforced Toyoura sand described in Fig.10 and their average. The measured strains and theiraverage are plotted in the original scale and the scale factored by a ratio of 3.84 based on the result of calibrationtests presented in Fig. 5(a). Figure 18(b) shows the timehistories of factored averaged tensile strain in PET GGbefore and during SL at R12.This test result is a typicalone that was used in the simulation shown below. In thisgure, it is assumed that ML has continued at a constantstrain rate that is equal to the one during ML immediatelybefore the start of this SL stage in the experiment,without intermissions of SL at R4and 8. This simplication procedure does not aect noticeably the timehistories of simulated tensile force during the analysed SLstage. The time history of strain rate that was used in thesimulation was obtained from the time history of factored averaged measured tensile strain tted by a nonlinear function presented in Fig. 18(c). In Fig. 18(b), thetime history of strain obtained by simulation assumingthat the tensile load were kept constant at the initial valuethroughout the SL stage is also presented.The simulation was performed based on the nonlinearthreecomponent model, which is described in APPENDIX A. Hirakawa et al. (2003) and Kongkitkul et al.(2004a, 2007a) showed that this model is able to simulatevery well the loadstraintime relations of a number ofdierent types of geosynthetic reinforcement subjected toa wide variety of loading histories, including ML atdierent strain rates, step changes in the strain rate, SL atxed load and load relaxation and so on.Figures 19 and 20 show the relationship between thetensile load and the tensile strain and the time history oftensile load that were obtained by simulation based onthe measured time history of tensile strain of PET GG. InFig. 19, the inviscid load and strain relation under loading conditions starting from the origin (T0 and e0) asFig. 18. a) Time histories of individual local tensile strain and theiraverage in the original and factored scales, b) time histories of factored averaged tensile strain before and during SL at R12and c)zoomup of the time history of strain increment during SL shown inFig. 18(b), PET GGreinforced Toyoura sand (Fig. 10)well as the one under unloading condition starting frompoint A (explained below) are presented. Here, the `loading' (approaching the tensile rupture condition) and `unloading' (becoming more remote from the tensile rupturecondition) are dened based on the sign of irreversiblestrain rate, ·eir. The unloading inviscid tensile load andstrain relation was obtained without introducing anypurely elastic zone as explained briey below. The detailsare described by Kongkitkul et al. (2004a).1) Unloading branches of inviscid load and irreversiblestrain relation starting from dierent tensile loadGEOSYNTHETICREINFORCED SAND345Additionally in Fig. 20, the time histories of tensileload obtained by simulations performed based on the following various assumptions, which are actually notrelevant, are also plotted:1) the tensile load was always constant and the same asthe initial value (i.e., the SL condition);2) the strain rate was always kept zero (i.e., the loadrelaxation condition); and3) the measured strain rate was always elastic one (i.e.,the purely elastic unloading condition).A given strain rate of geogrid (positive in tension), ·e, during SL of reinforced sand, which is always negative in thepresent case, consists of irreversible and elastic components, ·eir and ·ee, as follows until point A:Fig. 19. Simulated relationship between tensile load and tensile strainof PET GG for the time history of tensile strain presented in Fig.18(b)·e (negative) ·eir (positive){ ·ee (negative).Note that negative ·ee means that the tensile load rate,T,_ was negative. At point A, ·eir becomes zero, after which·eir becomes negative: i.e.,·e (negative) ·eir (negative){ ·ee (negative).Fig. 20. Time histories of tensile load in the PET GG during SL of reinforced sand at R12,compared with those obtained by simulations for various assumptionsvalues were obtained by performing experiment including global unload/reload cycles.2) As the shape of the unloading tensile loadstraincurves is noticeably dierent from that of primaryloading curve, an imaginary primary unloading curvehaving a shape similar to the shape of actual unloading curve was introduced.3) Unloading curves starting from dierent tensile loadvalues were obtained by parallelshifting this imaginary primary unloading curve without scaling, basedon the fact that the shape of the actual unloadingcurves starting from dierent tensile loads were essentially similar.4) A polynomial function was tted to this imaginaryprimary unloading curve ensuring that it can be ttedwell to the relation between the inviscid tensile loadand the irreversible tensile strain (i.e., the unloadingTe relation at the zero irreversible strain rate) inferred based on the test result.The tensile load and elastic strain relation that passesthrough point A is also presented.The Te curve simulated based on the measured timehistory of ·e (negative) is smooth at Point A. This relationbecomes closer to and more remote from the elastic relation passing through point A, respectively, when approaching and leaving point A. It may be seen from thesegures that, during this SL stage, the PET GG tensileload decreases relatively fast, noticeably faster than theone under the load relaxation condition. It may also beseen that the tensile strain (positive) is wrongly predictedto increase with time if it is assumed that the tensile loadwere kept constant. On the other hand, the decrease inthe tensile load is overestimated if it is assumed that thetensile strain increment were always elastic. The simulation shown above is typical of those at the SL stages in thePSC tests on reinforced sand performed in the presentstudy.CYCLIC LOADING TESTSTests Results of Reinforced SandTwo hundred cycles per stage with a double amplitudedeviator stress, Dq, equal to 150 kPa, equivalent to DR5, were applied at three and seven stages during otherwiseprimary ML at ·ev0.04z/min on two sand specimensreinforced with PET GG and PVA GG, respectively.During cyclic loading (CL) tests, ·ev was also equal to0.04z/min. The maximum stress levels during therespective CL stages were the same as the ones at the respectively corresponding SL stages. Figures 21(a) and22(a) show the whole stressstrain relations, which arecompared with those from the continuous ML tests at thesame ·ev (Fig. 8). Figures 21(b) and 22(b) show thezoomedup stressstrain curves. Figures 21(c) and 22(c)show the distributions of local tensile strain, elocal, in thereinforcement at the respective CL stages (see Figs. 21(b)and 22(b) for the respective moments in the Re v relations). Figures 21(d) and 22(d) show the distributions ofthe ratio of the local tensile strain, elocal, in the reinforce346KONGKITKUL ET AL.Fig. 21. a) Re v relation of PET GGreinforced sand subjected to CL during otherwise ML, b) zoomup of Fig. 21(a); and distributions of: c) localtensile strain and d) normalised local tensile strain in the PET GG during CL stagesment (shown in Figs. 21(c) and 22(c)) to the average compressive axial strain at the respective CL stages of reinforced sand specimen. Figures 23(a) and (b) show therelationships between the local tensile strain increment,Delocal, that developed at dierent locations in the reinforcement during the unloading and reloading branches ineach cycle between R7and 12 and the number of loading cycles, Nc, obtained from these CL tests. Figure 24compares the relationships between the residual strain dened as the axial strain increment at the maximum stresslevel that accumulated by CL for six hours, Dev, and theaverage stress ratio, R, at the respective CL stages. Notethat yielding that takes place when the stress level increases for the rst time is one of the major causes for thedevelopment of residual strain that takes place when R increases rstly to higher values, such as loading from pointc to point d in Figs. 21(b) and 22(b), in the course of cyclic loading. In the following, the residual strain is dened zero at the rst maximum stress point, such as pointd, to exclude the eects of this factor. The followingtrends of behaviours may be seen from Figs. 21 to 24:1) Signicant residual axial strains of reinforced sanddeveloped at the all CL stages, which could be attributed to the following two factors:i) Viscous properties of sand and geosyntheticreinforcement together with their interactions.This factor becomes more important with an increase in the loading period. In CL tests, thisfactor is aected to some extent by the numberof loading cycles, Nc, and the cyclic stress amplitude.ii) Rateindependent cyclic loading eects withsand. This factor becomes more important withan increase in Nc and the cyclic stress amplitude.On the other hand, this factor can be ignoredwith polymer geosynthetic reinforcement (Kongkitkul et al., 2004a).2) In all the cases, the dierence between the absolutevalues of the local tensile strain increments, Delocal,during unloading and reloading in respective loadingcycles decreased at a fast rate with an increase in Ncand became nearly zero after some large Nc (Fig. 23).This means that the behaviour became graduallymore elastic with cyclic loading and nally nearlyelastic.3) Residual tensile strain increments by CL were notsmall at the lowest stress level examined (i.e., at R8) (Fig. 24). Then, with an increase in R to 12, theywere maintained similar with the sand specimen reinforced with PET GG or decreased with the sandGEOSYNTHETICREINFORCED SAND347Fig. 22. a) Re v relation of PVA GGreinforced sand subjected to CL during otherwise ML, b) zoomup of Fig. 22(a); and distributions of: c) localtensile strain and d) normalised local tensile strain in the PVA GG during CL stages4)specimen reinforced with PVA GG. This may be duelikely to that a good interlocking between the geogridand the adjacent sand had not been developed beforethe rst CL stage at R8.At higher R values,however, the residual strains by CL increased with anincrease in R. This trend is the same as the residualstrains by SL (Fig. 14). Furthermore, the residualstrain by CL was smaller with the sand reinforcedwith stier reinforcement (i.e., PVA GG), similarlyto the case in the SL tests (Fig. 14). It was also thecase in the PSC tests on smaller size sand specimensreinforced with the same geosynthetic reinforcementtypes (Kongkitkul, 2004). These two similar trends ofresidual deformation by CL and SL of geosyntheticreinforced sand described above indicate that the viscous properties of sand and geosynthetic (factors i)have strong eects on the development of residualstrain by CL in reinforced sand.The Re v relation immediately after the restart of MLat the original strain rate (i.e., 0.04z/min) followingthe respective CL stages did not exhibit a clear yieldpoint at any stress level higher than the maximumlevel during CL, without exhibiting any large stressrange in which the tangent stiness was very high.Subsequently, the Re v relation tended to only very5)6)slowly rejoin the primary Re v relation from therespective continuous ML tests. This is similar to thetrend observed immediately after the restart of MLfollowing respective SL stages described in the precedent section.The PET GGreinforced sand specimen became evenstier and stronger by prepeak CL histories (Fig.21). This may be due to the development of better interlocking between the grid structure and the sandparticles during CL. This trend is similar as those observed when ML was restarted at the original strainrate after a SL stage. On the other hand, with thePVA GGreinforced sand specimen (Fig. 22), thistrend is not obvious, perhaps masked by a variancebetween the two dierent specimens, as seen from alower initial stiness in the test with CL stages than inthe continuous ML test (Fig. 22(a)).The local tensile strains, elocal, measured at dierentpositions along the respective reinforcement layers atthe last peak stress state at the end of the respectiveCL stages are not always smaller than those at therst peak stress state at the CL stage (Figs. 21(c) and22(c)), unlike the case of SL (Figs. 10(c) and 11(c)).This dierence is due to an additional increase in thelateral strain in sand by factor ii (rateindependent348KONGKITKUL ET AL.Fig. 23. Local tensile strain increments (absolute values) during unloading and reloading in each cycle between R7and 12 plottedagainst the number of cycle: a) PET GG and b) PVA GGFig. 25. Relationships between cyclic residual strain and creep strainobtained from tests on: a) PET GGreinforced sand and b) PVAGGreinforced sandand 22(d)). This dierence is because of residualcompressive strain in the lateral direction of sand dueto the viscous properties of sand (factor i above).Fig. 24. Relationships between cyclic residual strain Dev obtained atthe elapsed time of six hours and average stress ratio Rcyclic loading eect with sand in the CL tests). In allthe cases, however, the ratio of the local tensilestrain, elocal, in the reinforcement to the average axialcompressive strain in the reinforced sand specimensignicantly decreased during the respective CLstages (Figs. 21(d) and 22(d)), like the case of SL(Figs. 10(d) and 11(d)). This is due to that the residual local tensile strain, Delocal, by CL increased at arate that is much lower than the one at which the axial strain of reinforced sand increased (Figs. 21(d)Comparisons between Trends of Residual Strain by SLand CLFigures 25(a) and (b) compare the relationships between the residual axial strains that developed by CL andSL in which the peak average stress ratio, R, during theCL is the same as the one during the respective SL stagesfor the PET GG and PVA GGreinforced sand specimens. The data points along the respective solid relationsindicate the axial strain increments that had developeduntil the elapsed times of 10, 20, 40, 80, 160 and 320minutes since the start of respective CL or SL stages,while the broken lines indicate the results at the respectivesame R values. The following trends of behaviour may beseen:1) The general trends of the residual strains that tookplace by these two dierent loading schemes (i.e., SLand CL) under otherwise the same conditions aresimilar to each other, showing that these residualstrains should have a common factor (i.e., factor iexplained before).GEOSYNTHETICREINFORCED SAND2)The increasing rate with an increase in R of the residual strain by SL (i.e., creep strain) was generallymuch larger than that of the residual strain by CL, inparticular when the loading duration was relativelyshort. This means that the creep strain is much moresensitive to the stress level.3) For the rst 10 minutes (i.e., for around the rst oneto four cycles), the creep strain was consistently larger than the one by CL at any average stress ratio (except at R8).However, with an increase in the loading duration (i.e., an increase in Nc in the CL tests),the residual axial strain by CL became larger than thecreep strain for the same duration. This trend isstronger at lower R values.These results mean that the residual strain by CL can beattributed to the two dierent factors discussed earlier:factors i) and ii), indicating the following:1) the importance of factor i) relative to that of factorii) increases with an increase in R; and2) the importance of factor ii) relative to that of factori) increases with an increase in Nc (and also the cyclicstress amplitude): i.e., the eect of factor ii) becomesmore important with an increase in the loading duration for a given loading frequency than that of factori).These trends of behaviour have also been observed intriaxial tests with CL and SL stages during otherwise ML349on Toyoura sand alone (Tatsuoka, 2007). Figures 26 and27 show, respectively, the loading histories (i.e., CL andSL stages during otherwise ML) and the results from twoconsolidated drained triaxial tests (s?c40 kPa) on denseairdried Toyoura sand having similar relative densities,around 90z. Figure 28 compares the residual shearstrains developed by CL and SL histories for a short duration (i.e., the rst 100 seconds or the rst one cycle) andthose for a long duration (i.e., the whole 50,000 secondsor the whole 500 cycles). The four data points of therespective relations were obtained at four deviator stressFig. 27. Results from the tests using loading histories described in Fig.26: a) test A and b) test B (after Tatsuoka, 2007)Fig. 26. Loading histories employed in a pair of CDTC tests on Toyoura sand to evaluate the importance of inviscid cyclic loadingeect: a) test A and b) test B (after Tatsuoka, 2007)Fig. 28. Comparison between residual strains by cyclic and sustainedloading histories for short and long durations from CDTC on Toyoura sand (after Tatsuoka, 2007)350KONGKITKUL ET AL.levels, equal to q (sustained deviator stress)qmax (thepeak deviator stress during CL)60, 90, 120 and 150 kPa(see Fig. 26).The trends of behaviour seen from Fig. 25, in particular at low R (8), are basically the same as those seenfrom Fig. 28. This is a natural consequence because thereinforcing eects were still low at this low average stressratio. On the other hand, in Fig. 25, with an increase inR, due likely to an increase in the reinforcing eects, theincreasing rate with time of the residual strain by CL andthat of creep strain became similar, unlike the trend seenin Fig. 28. That is, with an increase in R, the eects ofviscous properties of geosynthetic reinforcement becomemore important even on the residual strains by CL.Therefore, we can conclude that the residual strain ofgeosyntheticreinforced sand that takes place by CL, inparticular slow CL as performed in this study, cannot beproperly predicted without taking into account the viscous properties of geosynthetic reinforcement as well asthose of sand.CONCLUSIONSThe following conclusions can be derived from the testresults and their analysis presented in this study:1) Signicant residual deformation took place ingeosyntheticreinforced sand by sustained loading(SL) and also by cyclic loading (CL). The residualstrain by SL is due to factor i): the viscous propertiesof both sand and geosynthetic reinforcement, aected by their interactions, which increases with an increase in the loading period and the load level. On theother hand, the residual strain by CL is due also tofactor ii): the rateindependent cyclic loading eectswith sand, which increases with an increase in thenumber of loading cycles for a given period of loading and the cyclic stress amplitude, in addition to factor i).2) The stiness and strength of geosyntheticreinforcedsand did not decrease, or even increased in somecases, by such SL and CL histories in the prepeak regime. Therefore, the development of residual strainby SL and CL in geosyntheticreinforced sand is nota degrading phenomenon, but it is due merely toeects of factors i) and ii). These eects eventuallydisappear as the strain increases during subsequentloading.3) The tensile strain in the geosynthetic reinforcementarranged in sand signicantly decreased with timeduring SL of geosyntheticreinforced sand due tocompressive creep strain in the lateral direction insand caused by tensile load in the reinforcement,despite that the global axial strain of thegeosyntheticreinforced sand signicantly increasedwith time (factor i). During SL of geosyntheticreinforced sand, the tensile load in the geosynthetic reinforcement decreased signicantly at a rate higherthan the one during the load relaxation stage at a xed strain. The tensile loadstrain state became evenunder unloading conditions of geosynthetic reinforcement during SL of geosyntheticreinforced sand.This nding suggests that it is overly conservative toassume in design that the tensile load in the geosynthetic reinforcement arranged in soil structures subjected to longterm static working load is maintainedconstant.4) During CL of geosyntheticreinforced sand, the tensile strain in the geosynthetic reinforcement arrangedin sand did not increase, despite that the global residual axial strain of geosyntheticreinforced sand increased signicantly.5) It is necessary to take into account the eects of theviscous properties of both soil and geosynthetic reinforcement when properly evaluating the residualdeformation characteristics of geosyntheticreinforced soil by not only SL but also CL.ACKNOWLEDGEMENTThe study was nancially supported by the Ministry ofEducation, Culture, Sports, Science and Technology, theJapanese Government, the Japan Society for the Promotion of Science and the Tokyo University of Science. Theauthors are also grateful to Mr. T. Kanemaru, Graduatestudent, Tokyo University of Science for his help in performing the experiment, to Mr. T. Masuo and Mr. S.Ihara of Taiyo Kogyo Co. Ltd., Japan, for providing thegeogrids, to Dr. T. Hirai, Dr. J. Nishimura and Mr. N.Kiyokawa of Mitsu Chemicals Industrial Products, Ltd.,Japan and Dr. K.H. Loke of Polyfelt Asia Sdn. Bhd.,Malaysia, for providing the geocomposite and supportingthe tensile strain sensors and devices regarding the opticalmeasuring sensors, and to Mr. K. Hara of Taiyo KogyoCo. Ltd., Japan, for ultrasonicwelding of plastic sheetson geogrids. This study was performed while the rstauthor was staying at the Department of Civil Engineering, Tokyo University of Science.REFERENCES1) AASHTO (2002): Standard Specications for Highway Bridges,American Association of State Highway and Transportation Ocials, 17th Edition, Washington, DC.2) Anh Dan, L. Q., Tatsuoka, F. and Koseki, J. 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(2007d): Creeprupture curve for simultaneous creep deformation and degradationof geosynthetic reinforcement, Geosynthetics International, 14(4),189200.22) Kongkitkul, W., Hirakawa, D., Tatsuoka, F. and Kanemaru, T.(2007e): Eects of geosynthetic reinforcement type on the strengthand stiness of reinforced sand in plane strain compression, Soilsand Foundations, 47(6), 11091122.23) Kongkitkul, W., Kanemaru, T., Hirakawa, D. and Tatsuoka, F.(2007f): Relaxation of tensile load mobilised in geosynthetic reinforcement arranged in sand, Proc. 13th Asian Regional Conferenceon SMGE, Kolkata.24) Kongkitkul, W., Tatsuoka, F., Duttine, A., Kawabe, S., Enomoto,T. and Di Benedetto, H. (2008): Modelling and simulation of ratedependent stressstrain behaviour of granular materials, Soils andFoundations, 48(2), 175194.25) Leshchinsky, D., Dechasakulsom, M., Kaliakin, V. N. and Ling,H.I. 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(1997):Geosyntheticsreinforced soil retaining walls as important permanent structures, 19961997 Mercer Lecture, Geosynthetics International, 4(2), 81136.35) Tatsuoka, F., Koseki, J., Tateyama, M., Munaf, Y. and Horii, N.(1998): Seismic stability against high seismic loads of geosyntheticreinforced soil retaining structures, Keynote Lecture, Proc. 6th Int.Conf. on Geosynthetics, Atlanta, 1, 103142.36) Tatsuoka, F., Modoni, G., Jiang, G.L., Anh Dan, L. Q., Flora,A., Matsushita, M. and Koseki, J. (1999): Stressstrain behaviourat small strains of unbound granular materials and its laboratoryrests, Keynote Lecture, Proc. of Workshop on Modelling and Advanced Testing for Unbound Granular Materials, January 21 and22, 1999, Lisboa (ed. by Correia), Balkema, 1761.37) Tatsuoka, F., Santucci de Magistris, F., Hayano, K., Momoya, Y.and Koseki, J. (2000): Some new aspects of time eects on thestressstrain behaviour of sti geomaterials, Keynote Lecture, TheGeotechnics of Hard SoilsSoft Rocks, Proc. 2nd Int. Conf. onHard Soils and Soft Rocks, Napoli, 1998 (eds. by Evamgelista andPicarelli), Balkema, 2, 12851371.38) Tatsuoka, F., Uchimura, T., Hayano, K., Di Benedetto, H.,Koseki, J. and Siddiquee, M. S. A. (2001): Timedependent deformation characteristics of sti geomaterials in engineering practice,Theme Lecture, Proc. 2nd Int. Conf. on Prefailure DeformationCharacteristics of Geomaterials, IS Torino '99, Balkema (eds. byJamiolkowski et al.), 2, 11611262.39) Tatsuoka, F., Ishihara, M., Di Benedetto, H. and Kuwano, R.(2002): Timedependent shear deformation characteristics of geomaterials and their simulation, Soils and Foundations, 42(2),103129.40) Tatsuoka, F. (2004): Eects of viscous properties and ageing on thestressstrain behaviour of geomaterials, GeomechanicsTesting,Modeling and Simulation, Proc. GIJGS Workshop, Boston,ASCE Geotechnical Special Publication GSP No. 143 (eds. byYamamuro and Koseki), 160.41) Tatsuoka, F., Hirakawa, D., Shinoda, M., Kongkitkul, W. andUchimura, T. (2004): An old but new issue; viscous properties ofpolymer geosynthetic reinforcement and geosyntheticreinforced35242)43)44)45)46)47)KONGKITKUL ET AL.soil structures, Keynote Lecture, Proc. 3rd Asian Regional Conference on Geosynthetics (GeoAsia 2004), Seoul, 2977.Tatsuoka, F., Kongkitkul, W. and Hirakawa, D. (2006): Viscousproperty and timedependent degradation of geosynthetic reinforcement, Proc. 8th International Conference on Geosynthetics (eds.by Kuwano and Koseki), Yokohama, Japan, 4, 15871590.Tatsuoka, F. (2007): Inelastic deformation characteristics of geomaterial, Special Lecture, Soil StressStrain Behavior: Measurement, Modeling and Analysis, Proc. of Geotechnical Symposium inRoma, March 16 & 17, 2006, Springer (eds. by Ling et al.), 1108.Tatsuoka, F., Koseki, J., Tateyama, M. and Hirakawa, D. (2007a):Recent developments of geosyntheticreinforced soil structures tosurvive strong earthquakes, Proc. 4th International Conference onEarthquake Geotechnical Engineering, June 2528, 2007, Thessaloniki, Greece, (W11003), 256273.Tatsuoka, F., Tateyama, M., Mohri, Y. and Matsushima, K.(2007b): Remedial treatment of soil structures using geosyntheticreinforcing technology, Geotextiles and Geomembranes, 25(45),204220.Tatsuoka, F., Di Benedetto, H., Enomoto, T., Kawabe, S. andKongkitkul, W. (2008): Various viscosity types of geomaterials inshear and their general expression, Soils and Foundations, 48(1),4160.Yoshida, T. and Tatsuoka, F. (1997): Deformation property ofshear band in sand subjected to plane strain compression and its relation to particle characteristics, Prof. 14th ICSMFE, Hamburg,Germany, 237240.APPENDIX A: NONLINEARTHREECOMPONENT MODEL FORGEOSYNTHETIC REINFORCEMENTAccording to Hirakawa et al. (2003) and Kongkitkul etal. (2004a, 2007a), the tensile load, T, is obtained by adding the viscous component, T v, to the inviscid components, T f, at the same irreversible strain, eir, while the tensile strain rate, ·e, is obtained by adding the elastic component, ·ee, to the irreversible component, ·eir, at the samevalue of T as:[T](e )[T f(eir)](e ){[T v(eir, ·eir, hs)](e )irire·e ·e { ·eirir(A3b)irf [d(T )e[(T v)TESRA](e )irirvteir1] ¥[r1(eir)]e |tiriso (t)gv( ·eir)a*¥( ·eir/ ·eir0 )1{b*(A4b)where: a*, b* and ·e are constants. Kongkitkul et al.(2007a) proposed to combine Eqs. (A4a) and (A4b) inthat Eq. (A4a) is activated when the encountered strainrate is high and Eq. (A4b) when the strain rate is low.r1(eir) is the decay function, that decreases with eir.Tatsuoka et al. (2002) proposed the following forms forr1(eir):ir0For eir0:r1(eir)riFor 0ºeirÃeirr1:r1(eir)(A5a)« Ø »$eirri{rf ri|rf{¥cos p¥ ir22er1c(A5b)For eirÀeirr1: r1(eir)rf(A5c)where: ri, rf, c and ·eirr1 are constants controlling the decayrate with eir of the viscous load component. u(eir) is theviscosity type parameter. Tatsuoka et al. (2008) and Kongkitkul et al. (2008) proposed the following forms foru(eir), analogous to Eq. (A5):For eir0:u(eir)uiniFor 0ºeirÃe :iru(A6a)« Ø »$uini{uend uini|uendeir{¥cos p¥ ir22euu(eir)cu(A6b)where uini, uend, cu and eiru are constants controlling thetransition with eir of the viscosity type parameter, u.Hirakawa et al. (2003) and Kongkitkul et al. (2007a)reported that PET GG, the same as the one used in thisstudy, has the viscous properties of the socalled ``combined type'', having a constant u value equal to 0.8.Therefore, Eq. (A6) becomes unnecessary. For the viscosity function, Kongkitkul et al. (2007a) reported that a0.70; m0.12 and ·eirr10|4z/s for Eq. (A4a); and a*0.20, 1{b*0.32 and ·eir010|3z/s for Eq. (A4b) arerelevant for this PET GG. To simulate the decay characteristics of this PET GG, they selected ri1.0 and rf0.15 (both dened for eir expressed in z); and c0.4;and eirr10.6 in their simulation.where:irwhere: a, m and ·e are constants controlling the quantityof T v for a given ·eir and T f.On the other hand, Di Benedetto et al. (2005) chose thefollowing function for gv( ·eir):(A2)ir[(T v)iso](e )[T f(eir)¥gv( ·eir)](e )(A4a)irrFor eirÀeiru : u(eir)uend[T v](e )u(eir)¥[(T v)iso](e ){[1|u(eir)]¥[(T v)TESRA](e ) (A3a)irgv( ·eir)a¥[1|exp s1|(` ·eir`/ ·erir{1)mt] (Æ0)(A1)The current value of T v (when the irreversible strain is eir)is obtained as:ir2002; Tatsuoka et al., 2002):(A3c)where: eir1 is the value of eir at the start of integration inEq. (A3c), which is 0.0 in this study. gv( ·eir) is the viscosityfunction, for which the following nonlinear function hasbeen proposed for geomaterials (Di Benedetto et al.,(A6c) | ||||
ログイン | |||||
タイトル | Effect of Slope on P-Y Curves Due to Surcharge Load | ||||
著者 | K. Muthukkumaran・R. Sundaravadivelu・S. R. Gandhi | ||||
出版 | Soils and Foundations | ||||
ページ | 353〜361 | 発行 | 2008/06/15 | 文書ID | 21113 |
内容 | 表示 SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 353361, June 2008EFFECT OF SLOPE ON PY CURVES DUE TO SURCHARGE LOADK. MUTHUKKUMARANi), R. SUNDARAVADIVELUii) and S. R. GANDHIiii)ABSTRACTAn extensive program of laboratory model tests was undertaken to study the eect of slope on py curves due to surcharge load in dry sand. The paper concerns the method developed in a series of laboratory model tests to experimentally determine py curves. Bending moment curves are dierentiated by using curve tting method of cubic polynomial function. The study includes eect of slope angle and relative density on bending moment, lateral soil resistance,lateral deection and nondimensional py curves. The nondimensional py curves for piles on sloping ground undersurcharge load are developed modifying API RP 2A (2000) method by including a Reduction Factor (R) using the experimental results.Key words: bending moment, py curves, sloping ground, soil resistance, surcharge load (IGC: E/E12/E14)dolph, 1981). However, the load deection behaviour oflaterally loaded piles is highly nonlinear and hence requires a nonlinear analysis. Poulos and Davies (1980) andBudhu and Davies (1987) modied the elastic solutions toaccount for nonlinearity using yield factors, the modulusof subgrade reaction approach was extended to accountfor the soil nonlinearity. This was done by introducingpy curves (Matlock, 1970; Reese and Welch, 1975).Experimental studies were performed to examine theperformance of piles under lateral loads. Alizadeh andDavison (1970) described a pile testing program conducted to determine the lateral loaddeection behaviour forindividual vertical and batter piles and the eect of sanddensity on the pile response. The results showed the signicant eect of the relative density of sand on pile behaviour. Prakash and Kumar (1996) developed a methodto predict the load deection relationship for single pilesembedded in sand and subjected to lateral load, considering soil nonlinearity based on the results of 14 fullscalelateral pile load tests. However all these studies have beendirected towards the response of individual piles or pilegroups subjected to lateral load at pile head (direct lateralload) on horizontal ground. Very few research workshave been carried out on piles subjected to lateral load onsloping ground (Mezazigh and Levacher, 1998; Clarlesand Zhang, 2001).When piles situated in sloping ground are subjected tohorizontal movement (passive loading), horizontal pressures are developed between the pile and the soil withconsequent development of bending moments and deections in the piles. This phenomenon is analogous as to thephenomenon of negative friction developed in piles byINTRODUCTIONPiles are frequently used to support structures subjected to lateral forces and moments such as oshore structures, harbour structures, high rise buildings and bridgeabutments. The governing criterion in designing pilefoundations to resist lateral loads in most cases is themaximum deection of the foundation rather than its ultimate capacity. The maximum deection at the pile headis important to satisfy the serviceability requirements ofthe superstructure while the bending moment is requiredfor the structural sizing of piles.Early research on single pile was directed mainlytowards estimating the ultimate capacity, assuming thatthe deformations would be acceptable if an adequate factor of safety against ultimate failure was used to determine the allowable load capacity. Broms (1964) developed solutions for the ultimate lateral resistance of a pileassuming distribution of lateral pilesoil pressures andconsidering the statics of the problem. Two modes offailure yielding of the soil along the length of the pile(shortpile failure), and yielding of the pile itself at thepoint of maximum moment (longpile failure) are consider. Narashimha Rao et al. (1998) investigated the lateral load capacity of pile groups in soft marine clay andthey found that the lateral load capacity mainly dependson rigidity of pile soil system.Many analytical approaches have been developed in recent years for the response analysis of laterally loadedpiles. The approaches assume either the theory of subgrade reaction (e.g., Matlock and Ripperger, 1956) or thetheory of elasticity (e.g., Poulos, 1971; Pise, 1984: Rani)ii)iii)Lecturer, Department of Civil Engineering, National Institute of Technology, India (kmknitt.edu and kmk_iitmyahoo.com).Professor, Department of Ocean Engineering, Indian Institute of Technology Madras, India.Professor, Department of Civil Engineering, Indian Institute of Technology Madras, India.The manuscript for this paper was received for review on May 1, 2007; approved on February 5, 2008.Written discussions on this paper should be submitted before January 1, 2009 to the Japanese Geotechnical Society, 4382, Sengoku,Bunkyoku, Tokyo 1120011, Japan. Upon request the closing date may be extended one month.353354MUTHUKKUMARAN ET AL.vertical movement of the surrounding soil. The analysisof piles in soil undergoing lateral movement is studied byPoulos (1973). Ito and Matsui (1975) proposed an empirical equation for the estimation of lateral force acting onstabilizing piles. Stewart et al. (1993), Bransby and Springman (1996), Kim and Barker (2002) and Cai and Ugai(2003) have also studied the eect of lateral soil movement on pile behaviour. However, the studies on behaviour of piles on sloping ground under surcharge load arelimited. Hence, the need for new research is necessary inthis area. A study was accordingly undertaken to determine the eect of slope and surcharge load on py curves.The objective was to estimate a Reduction Factor that canbe applied on the py curves for single piles in horizontalground.The paper describes the details of the experimental studies and the response of piles under surcharge load.METHODSoilpile interaction problems are three dimensionaland are presently very complex to be solved by theoreticalor numerical methods. Tests at full scale are impracticalor very expensive due to large number of tests required.Laboratory model test makes it possible to investigatethis kind of problems by instrumenting the model pileswith strain gauges, to measure the bending moments. Thepy reaction curves are obtained by double dierentiationand double integration of experimental bending moments.Fig. 1.Experimental set upThe objective of this paper is to study the eect of slopeon py curves under surcharge load for exible long pilesinstalled at the crest of the slopes in dry river sand. Threeslopes were tested (1V:1.5H, 1V:1.75H & 1V:2H) withthree dierent relative densities of 30z, 45z and 70z ofthe sand.tank size is 1.3~0.6~1 m deep. To avoid any side friction between the tank wall and soil, two layers of plasticsheets are coated with silicon grease bonded to the insideof the tank wall. The surcharge load is applied throughhydraulic jack, which is xed to the loading frame. Thecapacity of the jack is 250 kN and ram diameter is 75mm. The test pile is placed at the top edge of the slopingground (slope crest) for all slope angles under consideration. In order to distribute the surcharge load as uniformly as possible, a 450~350~10 mm thick steel plateis used to transfer the load from the jack to the soil.MODEL STUDYTEST PILEThe dimensions of the model pile testing are determined by a dimensional analysis (Buckingham Pi theorem). There are ve variables, which are displacement( y), pile diameter (d ), area (A), lateral force (F ) and pilelateral stiness (EI ). In order to comply with completesimilitude between the model and the prototype, the scaling factors are 1/N, 1/N, N 2, N 2, N 4. Accordingly, themodel pile was 25 mm in outer diameter, 23 mm in innerdiameter, and 700 mm in length. The model pile is modeled as an equivalent prototype pile (1:30 scale) with anouter diameter (d ) of 750 mm, bending stiness (EIp) of330 MNm2, and equivalent diameter to thickness ratio(d/t ) of 50.An aluminium pipe pile having an outer diameter of 25mm with 1mm wall thickness is used as a test pile. Thetotal length of the model pile is 700 mm and the embedment depth is 550 mm. The exural stiness of the pile isdetermined by considering a simply supported beam test.The exural stiness of the pile is 416~106 Nmm2. Themodel pile is instrumented with electrical resisting typestrain gauges of 3 mm in length, 120 ohms resistance (R)and a gauge factor (K) of 2. A total of 24 strain gaugesare used each at 50 mm spacing in both compression andtension side of the pile. The instrumentation details areshown in Fig. 2. The strain gauges used are calibrated byconducting a bending test. The strain response is linearwith the bending moment and the calibration constant isobtained from the slope of the straight line, which is 14.2Nmm per micro strain. (1~10|6 mm/mm).TEST PROGRAMEXPERIMENTAL SETUPThe experimental setup is shown in Fig 1. The test355PY CURVES DUE TO SURCHARGE LOADFig. 3.Fig. 2.Details of instrumented pilePLACEMENT OF SANDThe test is conducted in dry river sand. The propertiesof the sand are; Eective particle size (D10) is 0.26 mm,Average particle size (D50) is 0.54 mm, Coecient ofUniformity (Cu) is 2.4, Coecient of Curvature (Cc) is1.1, Specic Gravity (Gs) is 2.65, Maximum Dry Density(gmax) is 17.9 kN/m3 and Minimum Dry Density (gmin) is15.3 kN/m3. To achieve uniform density in the tank, apipe and cone arrangement called sand raining device isfabricated. This arrangement contains a hopper connected to a 940 mm long pipe and an inverted cone at the bottom. The hopper has a holding capacity of about 80 N ofsand. The sand passes through a 25 mm internal diameterpipe and is dispersed by 609due to the inverted coneplaced at the bottom. The height of fall is measured fromthe bottom of the pipe using an adjustable length pointerxed at the bottom. The sand raining device is shown inFig. 3. This arrangement is calibrated by a number of trials to get the height of fall corresponding to 30z, 45zand 70z of relative density.TEST PROCEDUREThe test pile is placed in position and then the soil islled to the required depth by sand raining method. Therelative density of 30z, 45z and 70z is selected suchthat, the relative density is covered in the led conditionfrom loose state to dense state. The slope is varied as1V:1.5H, 1V:1.75H and 1V:2H. These slopes are likely tobe unstable due to external load. The surcharge load isapplied up to 50 kN with 10 kN increments. The pilesused in berthing structure generally have tie beam at thetop. The tie beam stiness is modeled by providing rigidDetails of sand raining devicelink between the pile and the horizontal beam facing CD(Fig. 1) xed in the side wall of the tank. The horizontaldisplacement of the pile head and the strain at variouslevels in the piles are measured at each load increments.Vertical settlements are also measured for few tests and itis observed to be negligible. The mechanical dial gaugesare used to measure the horizontal displacement. Amanual compensating strain meter with full bridge circuitis used to measure bending strain along pile length at various elevations. The lateral deection and strain readingsare recorded for each increment of load.RESULTS AND DISCUSSIONSEect of Slope on Bending MomentTypical bending moment variations are shown in Figs.4 to 6 for 30z, 45z and 70z relative density with1V:1.5H and 1V:2H slope respectively. From all thegures it can be seen that the increase in surcharge loadincreases the bending moment. This is due to increasinglateral soil movement. The maximum bending moment of24000 Nmm is observed in 30z relative density with1V:1.5H slope and minimum bending moment of 13200Nmm is observed in 70z relative density with 1V:2Hslope. The depth of maximum bending moment is observed at 12D and 14D for slope angle of 1V:1.5H and1V:2H respectively. However the change in relative density does not have signicant inuence on the depth ofmaximum bending moment for atter slope of 1V:2H.Eect of Steepness of Slope and Relative Density onMaximum Bending MomentFigure 7 shows the eect of slope on maximum bending moment for 30z, 45z and 70z relative density with50 kN surcharge load. The increase in steepness of slopeincreases the maximum bending moment for all three relative densities. The increase in steepness of slope from1V:2H to 1V:1.5H increases the maximum bending mo356MUTHUKKUMARAN ET AL.Fig. 4. Bending moment vs depth for 1V:1.5H slope with 30% relativedensityFig. 7. Eect of steepness of slope on maximum bending moment for50 kN surcharge loadFig. 5. Bending moment vs depth for 1V:2H slope with 45% relativedensityFig. 8. Eect of relative density on maximum bending moment for 50kN surcharge loadment by 11z, 23z and 23.5z for relative density of30z, 45z and 70z respectively. The maximum reduction is observed in atter slope of 1V:2H with 70z relative density. Figure 8 shows the eect of relative densityon maximum bending moment for 1V:1.5H, 1V:1.75Hand 1V:2H slope with 50 kN surcharge load. The increasein relative density reduces the maximum bending momentfor all three slope angles. The increase in relative densityfrom 30z to 70z reduces the maximum bending moment by 25z, 20z and 37z for slope angle of 1V:1.5H,1V:1.75H and 1V:2H respectively.Fig. 6. Bending moment vs depth for 1V:2H slope with 70% relativedensityEstimation of Soil Resistance and DeectionThe soil resistance (p) and lateral deection ( y) alongthe pile shaft are obtained from the measured bendingmoment in the experiments using an approach similar tothat presented by Matlock and Ripperger (1956) and Naggar and Wei (1999).The distribution of the bending moment along the pileshaft is curve tted by a cubic polynomial function, i.e.,PY CURVES DUE TO SURCHARGE LOADM(x)ax3{bx2{cx{d357(1)Where x is the depth below the sand surface, and a, b, c,and d are constants obtained from the curvetting process. The distribution of the soil resistance along the pileshaft is obtained by double dierentiating the bendingmoment, i.e.,d 2MP(x) 2 6ax{2bdx(2)The deection of the pile along its shaft is obtained bydouble integrating the bendingmoment function, i.e.,1y(x)EIwhich yieldedy(x)1EI{f{f}[M(x)dx]dx(3)}a 5 b 4 c 3 d 2x { x { x { x {Fx{G126220(4)In Eq. (4), a, b, c, and d are the curvetting constantsand EI is the exural rigidity of the pile. F and G are integrating constants which are obtained from the boundary conditions. Two boundary conditions are used to obtain the integral constants of F and G. First boundarycondition is, slope is zero at the maximum bending moment occurring depth (i.e., when xdepth of maximumbending moment, dy/dx0). Second boundary condition is, deection is zero at the pile tip (i.e., xl, y0.where l is the depth of embedment). The curvettingprocedure is introduced to smoothen the bending moment diagram in order to reduce the scatter of experimental errors.The obtained soil resistance along the depth of pile for45z relative density with slope angles of 1V:1.5H,1V:1.75H and 1V:2H are shown in Figs. 9 to 11 and theobtained corresponding deections along the depth ofpile are shown in Figs. 12 to 14. From all the gures, it isobserved that the increase in surcharge load increases thesoil resistance and deection. The negative soil resistanceFig. 9.Soil resistance vs depth for 45% relative density with 1V:1.5HFig. 10. Soil resistance vs depth for 45% relative density with1V:1.75HFig. 11.Soil resistance vs depth for 45% relative density with 1V:2HFig. 12. Deection vs depth for 45% relative density with 1V:1.5Hslope358MUTHUKKUMARAN ET AL.Fig. 13. Deection vs depth for 45% relative density with 1V:1.75HslopeFig. 14.Deection vs depth for 45% relative density with 1V:2H slopebelow |500 mm depth indicates that the mobilization ofpassive resistance is in the embankment side. The deection obtained below |450 mm is almost equal to zero for45z relative density with 1V:1.5H slope.Eect of Slope on Non Dimensional py CurvesThe ultimate soil resistance ( pu) is calculated using theequation given in API RP 2A (2000). These two equations (Eqs. (5) and (6)) are used to calculate the ultimatesoil resistance of piles in horizontal ground and theseequations can not be used for piles located on slopingground.where,pus(C1Z{C2D)gZ(5)pudC3DgZ(6)puultimate resistance (force/unit length)Fig. 15. Non dimensional py curve for 30% relative density with1V:1.5H slopeFig. 16. Non dimensional py curve for 45% relative density with1V:1.5H slope(kN/m) (sshallow, ddeep)geective soil unit weight (kN/m3)Zdepth in (m)qangle of internal friction of sand. (degrees)C1, C2, C3Coecients determine based on angle of internal frictionDaverage pile diameter (m)Equation (5) is used for shallow depths and Eq. (6) is usedfor deeper depths. The coecients C1, C2 and C3 are obtained based on the angle of internal friction. The maximum lateral deection ( ymax) is taken as the maximumdeection observed from the experimental results. pu andymax are used to obtain the nondimensional parametersfor p and y respectively.The non dimensional py curves for 30z, 45z and70z relative densities with 1V:1.5H slope are shown inFigs. 15 to 17. From these gures, it is observed that theincrease in depth increases the ( p/pu). This is due to theincrease in passive resistance for increase in overburden359PY CURVES DUE TO SURCHARGE LOADFig. 17. Non dimensional py curve for 70% relative density with1V:1.5H slopeFig. 19. ( y/ymax)/( p/pu) vs (y/ymax) for 45% relative density at Z12DFig. 18. Eect of slope on non dimensional py curve for 30% relativedensity at Z12DFig. 20.pressure of the soil mass as depth increases. The increment is more in 1V:2H slope than 1:1.5H slope which canbe seen from Fig. 18.The normalized py curves are further normalized toobtain the ( p/pu) for all slopes and relative densities.These types of normalized plots are presented by Wu etal. (1998). The values of y/ymax are further divided byp/pu and then the plot is drawn between y/ymax and( y/ymax)/(p/pu). In horizontal ground the value of p/pu istaken as 1, when the soil resistance reaches to ultimatelevel (the mobilization of passive resistance at the failurestage is equal to the ultimate passive resistance of thesoil). Figures 19 and 20 show the eect of slope on( y/ymax)/( p/pu) vs ( y/ymax) plot for 45z and 70z relativedensity at a depth of Z12D. The values of p/pu are theslopes of ( y/ymax)/( p/pu) vs ( y/ymax) curve are taken fromthe plot for dierent relative density with dierent slopeangle. The values of p/pu obtained from experiments arepresented in Table 1.( y/ymax)/( p/pu) vs (y/ymax) for 70% relative density Z12DConstruction of Lateral LoadDeection (py) Curve forSloping GroundThe API RP 2A (2000) method for construction of pycurves in horizontal ground is modied for piles in sloping ground under surcharge load using the reduction factor (R) as given in Eq. (7)pA~R~pu~tan h«k~Z~yA~R~pu$(7)Afactor to account for cyclic or static loading condition. Evaluated by;A0.9 for cyclic loadingA(3.00.8 Z/D)Æ0.9 for static loadingRfactor to account the slope of the ground surfacepuultimate bearing capacity at depth Z (kN/m)kinitial modulus of subgrade reaction (kN/m3)Zdepth in meterylateral deection in meter360MUTHUKKUMARAN ET AL.Table 1.Values of p/pu obtained from experimentsRelative densitySlopeZ/Dp/pu30z30z30z30z30z30z30z30z30z45z45z45z45z45z45z45z45z45z70z70z70z70z70z70z70z70z70z1V:1.5H1V:1.5H1V:1.5H1V:1.75H1V:1.75H1V:1.75H1V:2H1V:2H1V:2H1V:1.5H1V:1.5H1V:1.5H1V:1.75H1V:1.75H1V:1.75H1V:2H1V:2H1V:2H1V:1.5H1V:1.5H1V:1.5H1V:1.75H1V:1.75H1V:1.75H1V:2H1V:2H1V:2H8101281012810128101281012810128101281012810120.470.600.690.640.660.700.640.740.800.500.620.720.660.740.800.690.780.830.540.690.750.680.750.830.710.800.85Fig. 21.p/pu value obtained from the experimental results is usedto predict R using the multiple regression analysis. In themultiple regression analysis, R is used as dependent variable and slope (S) and Z/D as independent variables. Thefollowing Eq. (8) is obtained based on the multipleregression analysis.R0.74{0.0378(Z/D)|0.6315(S); RÃ1(8)Zdepth in meterDdiameter of pile in meterSslope angle in radians (applicable in the range of 0.66to 0.50)The scatter plot of reduction factor (R) is shown in Fig.21. The value of R2 is equal to 0.9639 and the maximumerror is 0.06725 and hence the t is very good. The variation of R as a function of Z/D for 1V:1.5H, 1V:1.75Hand 1V:2H slope are shown in Fig. 22. The increase inZ/D increases R and the value of R1 is observed at Z/D18, 16.5 and 16 for 1V:1.5H, 1V:1.75H and 1V:2Hslopes respectively.CONCLUSIONS1.The results of the model study are used to modify theAPI method for construction of py curves for pilesin horizontal ground under surcharge load for theanalysis and design of piles in sloping ground. Theeect of sloping ground is included using a reductionfactor 'R' in the modied approach. The value of theR is observed to increase from 0.31 to 0.42 at Z/D0as slope is varied from 1V:1.5H to 1V:2H. As Z/DFig. 22.Scatter plot for reduction factor (R)Variation of reduction factor (R)increases, R increases and the limiting value of 1 forR is observed at Z/D18, 16.5 and 16 for 1V:1.5H,1V:1.75H and 1V:2H slopes respectively.2. The reduction factor R is obtained based on theresults of a single pile located at the slope crest.Therefore, the application of the reduction factor Ris limited to single pile located at the slope crest.3. The increase in steepness of slope from 1V:2H to1V:1.5H increases the maximum bending moment by11z, 23z and 23.5z for relative density of 30z,45z and 70z respectively. The increase in relativedensity from 30z to 70z reduces the maximumbending moment by 25z, 20z and 37z for slopeangle of 1V:1.5H, 1V:1.75H and 1V:2H respectively.4. The increase in steepness of slope from 1V:2H to1V:1.5H reduces the maximum soil resistance by 3z,6z and 8z for relative density of 30z, 45z and70z respectively. The increase in relative densityfrom 30z to 70z increases the maximum soilresistance by 15z, 19.8z and 17.5z for slope of1V:1.5H, 1V:1.75H and 1V:2H respectively.PY CURVES DUE TO SURCHARGE LOADREFERENCES1) Alizadeh, M. and Davission, M. T. (1970): Lateral load test on pileArkansas River Project, Journal of Soil Mechanics and FoundationDivision, ASCE, 96, 15831603.2) American Petroleum Institute (APIRP2A) (2000): Recommended practices for planning, designing and constructing xed oshoreplatforms, Washington.3) Bransby, M. F. and Springman, S. M. (1996): 3D nite elementmodeling of pile groups adjacent to surcharge loads, J. of Computers and Geotechnics, 19(4), 301324.4) Broms, B. B. (1964): Lateral resistance of piles in cohesionless soils,J. Soil Mech. Found. Engg. Div., ASCE, 90(SM3), 123156.5) Cai, F. and Ugai, K. (2003): Response of exible piles under laterally linear movement of the sliding layer in landslides, Canadian Geotechnical Journal, 40, 4653.6) Charles, W. W. Ng. and Zhang, L. M. (2001): Threedimensionalanalysis of performance of laterally loaded sleeved piles in slopingground, Journal of Geotechnical and Geoenvironment Engineering, ASCE, 127(6), 499509.7) Ito, T. and Matsui, T. (1975): Methods to estimate lateral force acting on stabilizing piles, Soils and Foundations, 15(4), 4359.8) Kim, J. S. and Barker, R. M. (2002): Eect of live load surchargeon retaining walls and abutments, Journal of Geotechnical and GeoEnvironment Eng., ASCE, 127(6), 499509.9) Matlock, H. and Ripperger, E. A. (1956): Procedure and instrumentation for tests on a laterally loaded pile, Proc. 8th TexasConference on Soil Mechanics and Foundation Engineering,Bureau of Engineering Research, University of Texas, Special Publication 29, 139.10) Matlock, H. (1970): Correlations for design of laterally loadedpiles, Proc. 2nd Annual Oshore Tech. Conf., Houston, Texas,577593.11) Mezazigh, S. and Levacher (1998): Laterally loaded piles in sand:12)13)14)15)16)17)18)19)20)21)22)361slope eect on py reaction curves, Canadian Geotechnical Journal,35, 433441.Nagger, M. H. EI. and Wei, J. Q. (1999): Response of tapered pilessubjected to lateral loading, Canadian Geotechnical Journal, 36,5271.Narasimha Rao, S., Ramakrishna, V. G. S. T. and Babu Rao, M.(1998): Inuence of rigidity on laterally loaded pile groups in marine clay, Journal of Geotechnical and Geo Environmental Engineering, ASCE, 124(6), 542549.Pise, P. J. (1984): Lateral response of freehead pile, Journal ofGeotechnical Engineering, ASCE, 110, 18051809.Poulos, H. G. (1971): Behaviour of laterally loaded piles: I. singlepiles, Journal of Soil Mechanics and Foundations Divisions,ASCE, 97(SM5), 711731.Poulos, H. G. (1973): Analysis of piles in soil undergoing lateralmovement, Journal of Soil Mechanics and Foundations Divisions,ASCE, 99(SM5), 391406.Poulos, H. G. and Davis, E. H. (1980): Pile Foundation Analysisand Design, John Wiley and Sons, New York.Prakash, S. and Kumar, S. (1996): Non linear lateral pile deectionprediction in sand, Journal of Geotechnical Engineers, ASCE, 112,130138.Randolph, M. F. (1981): The response of exible piles to lateralloading, G áeotechnique, 31(2), 247259.Reese, L. C. and Welch, R. C. (1975): Lateral loading of deep foundations in sti clay, J. Geotech. Engg, Div., ASCE, 101(GT7),633649.Stewart, D. P., Jewell, R. J. and Randolph M. F. (1993): Numerical modeling of piled bridge abutments on soft ground, Computersand Geotechnics, 15, 2346.Wu, D., Broms, B. B. and Choa, V. (1998): Design of laterallyloaded piles in cohesive soils using py curves, Soils and Foundations, 38(2), 726. | ||||
ログイン | |||||
タイトル | Mechanical Behavior of Bentonite-sand Mixtures as Buffer Materials | ||||
著者 | Toshiyuki Mitachi | ||||
出版 | Soils and Foundations | ||||
ページ | 363〜374 | 発行 | 2008/06/15 | 文書ID | 21114 |
内容 | 表示 SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 363374, June 2008MECHANICAL BEHAVIOR OF BENTONITESAND MIXTURESAS BUFFER MATERIALSTOSHIYUKI MITACHIi)ABSTRACTFor the purpose of establishing the method for estimating insitu mechanical behavior of articial buer materials,stressdeformation behavior of bentonitesand mixtures were investigated through oedometer test, consolidated undrained triaxial compression test and expansive stressstrain measuring test by changing the clay content as 30, 50, 70and 100z, and by changing the range of initial dry density of mixture from 1.4 to 1.8 g/cm3. Oedometer test resultssuggest that the magnitude of consolidation yield stress almost coincides with the maximum expansive stress ( p?s)max irrespective of bentonitesand mix proportion, initial density of mixture and the magnitude of molding stress at thespecimen making. Strong correlation between consolidation stress and initial tangent modulus during undrained triaxial compression test is observed, and it is found that the reduction rate of rigidity is hardly dependent on the specimenmaking method, molding stress and the consolidation stress. From the two series of expansive stressstrain measuringtests, it is recommended to perform the measurement of expansive stress by feed back system with the load cell installed at the base of the specimen. A unique relationship is found between the maximum expansive stress (p?s)max versusbentonite specic volume vb, which is dened as the specic volume calculated by excluding the volume of sand particles. The line showing the unique log vb versus log (p?s)max relationship can be recognized as the state boundary lineprescribing onedimensional expansive stressstrain behavior of the bentonitesand mixtures.Key words: bentonite, buer material, consolidated undrained triaxial test, inltration test, oedometer test, swellingbehavior (IGC: D3/D5/D6)deformation to verify the equations proposed by them.Tanaka and Nakamura (2005) investigated the eects ofseawater and hightemperature history on the swellingcharacteristics of bentonite. Based on the mechanical behavior of bentonitebased buer materials obtained bylaboratory tests, Namikawa et al. (2004) investigated theapplicability of constitutive equations which were originally proposed to apply nonswelling clay. Kurikami etal. (2004) extended the model for evaluating swellingcharacteristics of saturated buer material proposed byKomine and Ogata (2003) to unsaturated media, and applied to coupled thermal, hydraulic and mechanical analysis.Based on the concept that the maximum water volumeabsorbed by unit volume of smectite is constant, Cui etal. (2004) reported that the swelling deformation of bentonitesand mixtures was uniquely characterized by usingthe void ratio of smectite, which was dened by thevolume ratio of water and smectite.In this study, oedometer test and consolidated undrained (CU) triaxial test were performed under highstress level up to 5 MPa. From the test results, mechanical properties of bentonitesand mixtures under a widerange of stress and strain were investigated. The eect ofINTRODUCTIONAt present, bentonitesand mixture is expected to bethe most appropriate as a buer material of highlevelradioactive waste products when they are disposed in thedeep ground. Therefore, it is important to establish themethod for estimating insitu mechanical behavior ofbuer materials. For this purpose, it is necessary to clarify the stressdeformation behavior of buer materials under various conditions. Up to this time, research worksconcentrating on individual subjects have been performed. One dimensional consolidation tests and consolidated undrained triaxial tests have been performed forcompacted bentonitesand mixtures under high stress level (Graham et al., 1989; Borgesson and Hokmark, 1991;JNC Report, 1999). In order to quantify the swellingcharacteristics of bentonite buer materials, Komine(2001) and Komine and Ogata (2003) performed a seriesof swelling tests and proposed equations for evaluatingswelling characteristics of bentonitesand mixtures. Further, they performed a series of model test (Komine et al.,2004) to simulate the process of lling up the space between the buer material and a wall of the disposal pit,and/or between the buer and an overpack by its swellingi)Professor, Department of Civil Engineering, Nihon University and Emeritus Professor of Hokkaido University, Japan (mitachieng.hokudai.ac.jp).The manuscript for this paper was received for review on April 18, 2007; approved on February 5, 2008.Written discussions on this paper should be submitted before January 1, 2009 to the Japanese Geotechnical Society, 4382, Sengoku, Bunkyoku, Tokyo 1120011, Japan. Upon request the closing date may be extended one month.363364MITACHITable 1.TypeIndex properties of materialsBentonite(Kunigel V1)Sand(Silicasand No. 7)Natype32.692 g/cm3Soil density (rS)2.799 g/cmLiquid limit (vL)498.6zPlastic limit (vP)39.4zPlasticity index (IP)459.2Smectite content60zdierent methods of making specimen on the triaxial testresults was also examined. For the purpose of investigation on the expansive stressstrain behavior, two series oftests were performed; (i) swelling test and (ii) inltrationtest. Through the systematic and comprehensive experiments, new signicant ndings are presented andmethods for characterizing mechanical parameters required for the numerical analysis of stressdeformationbehavior of articial buer system are proposed.Fig. 1. Specimen preparation for a) oedometer test and expansivestressstrain measurement test and b) triaxial compression testSPECIMEN PREPARATIONBentonite material used in this study is Kunigel V1which is most frequently used for the study of buermaterial in Japan. Silica sand No. 7 is used as a sandmaterial. Index properties of these materials are shown inTable 1. Smectite content of bentonite was measured bythe methylene blue test. Referring to the specication ofthe buer material for radioactive waste disposal projectin Japan, bentonitesand mix proportion a in mass wasmainly specied as 70z in this study. Experiments usingspecimens with 30z, 50z and 100z of bentonite content were also performed as a comparison. The conditions of specimen preparation are as follows:Compacted SpecimenBentonite powder was mixed in a dry state with sand asspecied, 70z30z in mass for making a70z specimen and statically compacted in the mold (Fig. 1) whoseinner diameter was 60 mm for oedometer test and onedimensional expansive stressstrain measurement test(Fig. 1(a)), and 35 mm for triaxial test (Fig. 1(b)). Molding pressure was changed from 4 MPa to 15 MPa depending on the bentonitesand mix proportion and target drydensity. Compacted specimens with a height of 10 mmand 70 mm respectively for the oedometer and triaxialtests, were sustained to be saturated (Fig. 2) for 3 to 5months by supplying 2 MPa of deaired water from thebottom surface of the specimen and by loading negativestress of |90 kPa on the top surface under the connement of all circumferential surfaces of the mold. Thedegree of the specimen calculated before triaxial testshowed 100}2z and pore water pressure coecient Bvalue was measured to be B»0.95 as mentioned in thenext section. Specimens made by this method are called asCOMspecimens.Fig. 2. Two types of mold for saturating specimen for consolidationand expansive stressstrain measurement test (a) and c)) and triaxialtest (b) and d))Specimen Made by Cold Isostatic PressingBentonitesand mixture compressed under 5 MPaisotropic stress by Cold Isostatic Pressing method wastrimmed to be 35 mm diameter and 70 mm height fortriaxial test; then the specimen was saturated by the sameprocedure as COMspecimen. Cold Isostatic Pressingmethod is a kind of technique of forming powderedmaterial into various shapes by pressurizing the powdercontained with rubber bag under high hydraulic pressureand under normal temperature. Specimens made by thismethod are called as CIPspecimens.TEST CONDITIONOedometer TestTest apparatus used for incremental loading consolidation test in this study is able to apply any amount of consolidation stress up to 5 MPa by using air pressurethrough belloframcylinder. In order to minimize the error of displacement measurement during consolidation,porous metal plates and high polymer lms were installedas the loading plates and lters at the top and bottom ofBEHAVIOR OF BENTONITESAND MIXTURESFig. 4.Fig. 3. Triaxial test apparatus equipped with high torque digital servomotorthe specimen. Also, to obtain consolidation yield stressand compression/swelling indices with higher accuracy,multistages of loading, unloading and reloading wereperformed on the 60 mm diameter and 10 mm heightspecimens, regardless of load increment ratio. In thispaper, the test name is denoted as COM7016 for example,in which COM means the method of specimen making, 70refers to the bentonite content a in percent and 16 means10 times the value of dry density rd in g/cm3.Consolidated Undrained Triaxial TestA series of consolidated undrained triaxial tests wasperformed by using a newly developed triaxial apparatusequipped with high torque digital servomotor (see Fig.3). The apparatus has the following special features;1) Strain controlled monotonic and cyclic loading canbe performed in the wide strain range of 1~10|6zto 20z under the maximum cell pressure of 3MPa.2) Accurate pore water pressure measurement is possible by using ush diaphragm type of pressuretransducer installed in the pedestal, in which thesurface of the diaphragm is located just below thebottom of the specimen. Moreover, a ``pool'' withdeaired water is attached to the pedestal to avoidentrapping air during the mounting of the specimen (see Fig. 4).In this test, dimension of the specimen is 35 mm diameter and 70 mm height, and the dry density is speciedas rd1.6 g/cm3. Test specimens were prepared by COMand CIP method. After mounting the specimen on thetriaxial apparatus, deaired water was supplied to thespecimen under the application of negative cell pressure365Devices for accurate pore water pressure measurementand negative back pressure to make the specimen fullysaturated. After that, 500 kPa of cell pressure and 400kPa of back pressure was applied and then Bvalue waschecked, and isotropic consolidation under 0.5, 1.0, 1.5,2.0 and 2.5 MPa of eective consolidation stress wasstarted after conrming B»0.95.The drainage during isotropic consolidation was forcedto radial direction through the lter paper wrappedaround the specimen. To ensure the drainage route underhigh conning pressure, specimen was wrapped twicewith two sheets of lter paper having no slits. Axial loadwas measured by a load cell set up inside the triaxial cell.Isotropic consolidation stress was increased by a rateof 4 kPa/min up to the prescribed stress and consolidation was terminated at the time when the volume changeDV versus logarithm of time t curve reaches 2tline, beingstraight and parallel to the steepest slope line obtainedfrom the observed DV versus log t curve. After the completion of isotropic consolidation, undrained triaxialcompression test was performed under an axial strain rateof 0.001z/min. Considering extraordinary high conning stress during undrained testing, the author performeda preliminary test by using 0.003z/min and 0.001z/min(which is oneftieth of recommended value by JGS standard, 2000) of strain rate. After examining the test resultsshown in Fig. 5, in which the eect of dierent measurement system and rate of strain are revealed, the authordecided to select strain rate as 0.001z/min.The test name is denoted as COM7025 for example, inwhich the interpretations of COM and 70 are the same asthose in the oedometer test, and 25 means 10 times thevalue of eective consolidation stress in MPa.Expansive StressStrain Measurement TestAs mentioned previously, two series of tests referredto, in this paper as swelling test and inltration test wereperformed to investigate onedimensional expansivestressstrain behavior of bentonitesand mixtures. The366MITACHIFig. 5. Test results for comparing the eects of location of the porewater pressure measurement transducer and rate of strain in the undrained triaxial compression testterm ``expansive stress'' is preferably used in this paperdening the stress acting on the rigid conning boundarysurface originated from the ``swelling pressure'' developed in the interlayer water of smectite. Expansive stressmay usually be 1 to 2 orders smaller than the swellingpressure as shown by Nakano et al. (1984) and Fujita etal. (1995).Expansive stress measuring apparatus capable of applying back pressure is used in this study and is shown inFig. 6. Porous metal plates and high polymer lms are installed as the loading plates and lters at the top and bottom of the specimen.Swelling TestSwelling test specimens were statically compacted tothe prescribed dry density by using a mold in which thespecimen conning ring was installed (see Fig. 1). Aftercompaction, 60 mm diameter and 10 mm height specimenwith conning ring was extruded from the mold and installed in the expansive stress measuring apparatus. Inorder to ensure the contact between the specimen and theloading piston, preloading axial stress of 30 kPa was applied to the specimen. Then keeping vertical displacementto be zero, deaired water was supplied through upperand lower parts of the apparatus, and expansive stresswas measured by two load cells, one installed on the loading piston, and the other at the base. Figure 7 is an example of preliminary test result on expansive stress p?s versustime relationship observed up to 10000 minutes. From thegure, it can be seen that p?s reaches its maximum value( p?s)max at around 2000¿3000 minutes and its value continues to be almost constant. Based on this result, swelling test was continued up to 5000 minutes and the measured maximum vertical stress was dened as maximumexpansive stress ( p?s)max. In this study, following twomethods of measuring expansive stress were adopted.1) Measurement by feedback system (Fig. 8(a))In order to avoid the underestimation of the expansivestress due to the deection of the loading frame, load cellFig. 6.Fig. 7.Expansive stressstrain measuring apparatusExpansive stress vs. time during swellingFig. 8. Schematic representation of the dierence of measuring expansive stress by a) feed back (FB) system and b) nonfeed back (NFB)systemand others, the expansive stress is measured by usingfeedback system, in which the axial displacement is automatically controlled by belloframcylinder through electropneumatic transducer to minimize the axial displacement (to be less than 0.0065 mm). In this paper, thismethod is called as FB system.2) Measurement by non feedback system (Fig. 8(b))For the purpose of comparison, the expansive stress ismeasured without using feedback system. This measurBEHAVIOR OF BENTONITESAND MIXTURES367ing system is called as NFB system.The test name for the expansive stress measurementmentioned above is denoted as FB7016 for example, inwhich FB means feedback measurement system, 70means bentonite content a in percent and 16 means 10times the value of dry density rd in g/cm3.To prove the validity of the test results of swelling testmentioned above, another series of swelling tests bymeasuring expansive (or compressive) strain under constant vertical stress was performed by using the same apparatus shown in Fig. 6. Specimens were set up by thesame procedure as expansive stress measuring test, andmaximum expansive stress measured by FB and NFB system was applied to the specimen as prescribed verticalstress. Keeping the vertical stress to be constant, deairedwater was supplied through upper and lower parts of theapparatus, and vertical displacement was measured. Thetest name is denoted as RNFB 7016, in which the meaningof 70 and 16 are the same as expansive stress measuringtest and RNFB means the application of vertical stresscorresponding to the maximum expansive stress obtainedby NFB system.Inltration TestTesting apparatus and specimen preparation are thesame as above mentioned swelling test. Bentonitesandmixtures (a70 and 100z) in dry state were staticallycompacted to obtain the dry density of 1.4, 1.5 and 1.6g/cm3, and the height as 5 mm and 10 mm under a stressof about 5 MPa using a 60 mm diameter mold in whichthe specimen conning ring was installed. After that, 60mm diameter and 5 mm or 10 mm height specimen withconning ring was extruded from the mold and installedin the expansive stress measuring apparatus.Firstly, dry state specimens were compressed by incremental loading of 20 minutes interval up to theprescribed vertical stress, then deaired water was supplied through the upper and lower part of the apparatusand vertical stress or vertical strain was measured depending on the following two test conditions.1) Vertical stress constant conditionAfter the incremental loading up to the prescribedvertical stress, the stress is kept constant and vertical strain is measured over a period of three days.2) Vertical strain constant conditionIn this case, vertical stress is measured while keeping the vertical displacement to be zero.To clarify the dierence of the stressstrain conditionsof the specimen from those of swelling test mentioned inthe previous section, the present author refers to thisseries of tests as inltration test. In this test, deairedwater is supplied after completion of the incrementalloading compression up to the prescribed vertical stress,while in the swelling test the supply of deaired water wasstarted immediately after application of small amount ofcontact pressure of 30 kPa.Fig. 9. elog p? relationship obtained by oedometer test for (a) a70%, (b) a50% and (c) a100% specimensTEST RESULTS AND DISCUSSIONConsolidation Test ResultsVoid ratio e versus consolidation stress p? relationshipobtained from incremental loading consolidation test isillustrated in Fig. 9. Figure 9(a) shows the test results onthe specimens of a70z made by COM method. Figures9(b) and (c) illustrate the results obtained from the testsperformed on the a50z and a100z specimens for368MITACHITable 2Compression and swelling indicesCCCSCS/CCCOM70160.4070.1840.452COM70180.2710.2570.948COM100160.3720.3060.823Kiyohoro0.2320.0470.202Hachirougata0.6600.2210.334Kurihama0.6690.1060.240MCkaolin0.6340.1730.273NSFClay0.4850.1700.351Higashiogishima0.4200.0570.136the comparison.In Fig. 9(b) for the specimens of a50z, it is seen akind of inection at about 1.3 MPa which is corresponding to the void ratio of e0.46 at which sand particles in the mixture contact with each other. Probably dueto the increase of bentonite contents, e versus log p?curves show almost linear variation in the normally consolidated range and such a behavior mentioned above isnot seen for both cases of a70z and a100z.Compression and swelling indices Cc and Cs obtainedfrom the consolidation tests on a70z and a100zspecimens are listed in Table 2. Swelling indices were obtained as an average slope of the unloading and reloadingcurves. Test results performed on various nonswellingclays (MCkaolin and NSFclay are obtained commercially in a state of powder, and others are retrieved fromnatural clay deposits in undisturbed state) are also shownfor the comparison.The cause of the greater Cs value of bentonitesandmixtures compared with other clays is considered to bedue to the high smectite content of bentonite and its increase with both density and mix proportion. As seen inthe table, Cs/Cc for bentonitesand mixtures are as largeas 0.4¿0.9 (which are similar to those reported byNamikawa et al., 2004) compared with nonswelling clayof 0.1¿0.3.Oedometer test results by JNC (Japan Nuclear CycleDevelopment Institute, 2002) on the specimen of 60 mmdiameter and 20 mm height with a70z and rd1.6g/cm3 give relatively smaller values of Cc0.27 and Cs0.16 when compared with the results of present study ofCOM7016. As the maximum consolidation stress was19.6 MPa for JNC experiment, there might be a possibility of underestimation of void ratio change due to relatively large friction between the conning ring and specimen, the height of which was twice that in the presentstudy. The occurrence of inection of the curve as mentioned previously on a50z specimen in Fig. 9 (b)might be also possible for higher stress range of JNC experiment on a70z specimen.Consolidation yield stress p?c is evidently smaller thanthe molding stress at the time of making the specimen asTable 3. Comparison of consolidation yield stress p?c, molding pressure and maximum expansive stress ( p?s)maxp?cmolding pressure( p?s)maxCOM5016300 kPa4.47 MPa312 kPaCOM5018448 kPa10.35 MPa562 kPaCOM7016470 kPa6.42 MPa524 kPaCOM70181091 kPa14.50 MPa920 kPaCOM10016944 kPa8.35 MPa818 kPaFig. 10.p?c( p?s)max relationshipcan be seen from Table 3, in which maximum expansivestress ( p?s)max is also tabulated, where ( p?s)max is the maximum value of expansive stress obtained by the swellingtests mentioned in the previous section. As shown in Fig.10, the values of p?c seem close to ( p?s)max irrespective of thebentonitesand mix proportion, initial density of mixtureand the magnitude of molding stress. As explained in theprevious section, specimens for consolidation test wererstly compacted in the mold in dry powder state andthen they were sustained to be saturated under the connement of all circumferential surfaces of the mold.Therefore the stress condition in the mold seems like thatin a swelling test mentioned previously, and the expansivestress exerted in this condition may play a role of preconsolidation stress.Figure 11 illustrates the coecient of hydraulic conductivity k versus bentonite density rb relationship obtained from the normally consolidated stress range,where bentonite density is dened as the density calculated by excluding the volume of sand particles from that ofbentonitesand mixture as shown in the following equation:rbMb/(V|Vs)( rd|Ms/V )/(1|Vs/V )a¥rd/s1|(1|a)rd/rsst(1)where, Mb and Ms are respectively the mass of bentoniteand silica sand in the bentonitesand mixture, Vs andV are the volume of sand and bentonitesand mixturerespectively, a is bentonitesand mix proportion(Mb/M ), and rss (Ms/Vs) and rd (M/V ) are thedensity of sand particle and dry density of bentonitesandmixture, respectively.BEHAVIOR OF BENTONITESAND MIXTURESFig. 11.369krb relationshipThe Coecient of hydraulic conductivity k versus rbrelationships obtained by JNC (2002) on a70z specimen are also plotted in the gure. Figure 11 shows thelinearly decreasing trend of the hydraulic conductivity kwith the increase of bentonite density rb, and k value is inthe order of 10|11¿10|12 cm/s at the bentonite density of1.3¿1.8 g/cm3.Consolidated Undrained Triaxial Test Resultsq versus ea RelationshipThe principal stress dierence q normalized by eectiveconsolidation stress p?0 versus axial strain ea relationship isillustrated in Fig. 12. Test results with CIPspecimens( rd1.7 g/cm3) and COMspecimens ( rd1.6 g/cm3) fora50z are shown in Figs. 12 (a) and (b), respectively.Normalized stressstrain behavior of the specimens madeby the same method almost coincides with each other, excluding CIP5005, CIP5010 and COM5005.Figure 12(c) illustrates the normalized stressstrain behavior for a70z and rd1.6 g/cm3 specimen. As seenin the gure, q/p?0 for low consolidation stress ofCOM7005 is greater than other specimens of higher consolidation stress. As the maximum expansive stress fora70z specimen is 524 kPa (see Table 3), the state ofstress consolidated at 0.5 MPa is corresponding to theoverconsolidation state since the consolidation yieldstress is close to the maximum expansive stress as mentioned in the previous section. Hence the stressstrain behavior of COM7005 is close to the behavior of overconsolidated clays. Similar trend is seen in Figs. 12(a) and (b)for the specimens of a50z consolidated at low stresslevel.Eective Stress PathsFigure 13 shows the eective stress paths for CIP50,COM50 and COM70 specimen. The specimens whichbehave close to the overconsolidated clay in the stressstrain relationship as shown in Fig. 12 show smallerFig. 12. q/p?0 versus ea relationship for (a) CIP (a50%) specimen,(b) COM (a50%) and (c) COM (a70%) specimensdecrement of eective mean stress in the undrained shearstress path compared with those specimens consolidatedby higher stresses. Critical state stress ratio M calculatedby excluding the data consolidated at low stress level areM0.57 for COM70 specimens, M0.77 for COM50specimens and M0.84 for CIP50 specimens, respectively.Modulus of DeformationFor the evaluation of the reduction of deformationmodulus with the increase in axial strain, the initial tangent modulus Emax for the small strain range (ea0¿0.005z) and the secant modulus Esec are investigated.Void ratio e versus logarithm of consolidation stress p?0370MITACHIFig. 14.Fig. 15.eln p?0 relationshipeln Emax relationshipFig. 13. Eective stress paths during undrained test on (a) CIP (a50%), (b) COM (a50%) and (c) COM (a70%) specimensrelationship obtained from the isotropic consolidationstage and e versus ln Emax relationship are shown in Figs.14 and 15, respectively. As shown in these gures, strongcorrelation between eln p?0 and eln Emax for bentonitesand mixture is observed, which is the same trend asreported by Shibuya et al. (1999) and Kawaguchi et al.(2004) for nonswelling clays.Dening the slopes of eln p?0 and eln Emax as l and n,the ratio of n/l for COM70, COM50 and CIP50 are calculated as 1.125, 0.812 and 0.857, respectively. The ratiosn/l for the same bentonitesand mixture of COM andCIP are assumed to be similar value.Figure 16 shows the change of the secant modulus Esecwith the increase in axial strain, where Esec is normalizedby Emax. At the small strain range up to 0.005z, somescattering is seen but any regular trend is not found out.With the increase in axial strain, almost all the curvesFig. 16.Esec/Emaxea relationshipconverge to a single curve. Therefore, it may be concluded that the reduction rate of rigidity in bentonitesandmixture with the strain increase is hardly dependent onthe specimen making method, molding pressure and theconsolidation stress.371BEHAVIOR OF BENTONITESAND MIXTURESFig. 17.( p?s)maxrd relationshipFig. 18. Expansive stress measurement by load cells installed at thetop and bottom of the specimen during swelling test under FB andNFB system of measurementExpansive Stress Measured by Swelling TestAs mentioned previously, expansive stress in the swelling test was measured by two measuring system (FB andNFB) and by two load cells mounted on the loadingpiston and on the base. For example, the expansive stressobtained by FB system and measured by the load cellmounted on the loading piston is denoted now onward asFB (top).Figure 17 shows the maximum expansive stress ( p?s)maxvs. initial dry density of mixture rd relationship obtainedfrom the swelling test on a50z and 70z specimens. Asshown in the gure, the expansive stresses obtained by FB(top) are larger than those measured by FB (base) sinceFB (top) includes the upward friction force between thespecimen and the conning ring caused during control forminimizing the vertical displacement as shown in Fig. 18.On the other hand, NFB (base) is slightly larger thanNFB (top) due to the downward friction force betweenthe specimen and the conning ring developed accompanying with the slight upward movement caused by thedeformation of the loading frame and load cell in theNFB measuring system. In Fig. 17, maximum expansivestresses obtained by Komine and Ogata (2002) are alsoplotted, in which the expansive stress were measured byNFB system and by the load cell installed at the top of theFig. 19.Fig. 20.( p?s)maxrb relationshipestime relationshipspecimen. It should be reminded that there are dierencesin two points of test condition between the present paperand Komine and Ogata (2002). In the experiment of Komine and Ogata, specimen height is half that of thepresent investigation and smectite content of the bentonite is 48z, which is lower than that of the present testof 60z. The dierence of the smectite content mightcome from the dierence of batches even in the same bentonite sample of Kunigel V1 produced by the same company.Expansive stresses measured by FB system are alwaysgreater than those measured by NFB system and thedierence is 10z to 20z even in the comparison betweenFB (base) and NFB (base). As almost all values reportedtill now by other researchers were measured by NFB(top), the dierence becomes as large as 15 to 35z if wecompare FB (base) with NFB (top). From the test resultsmentioned above, it is recommended that the measurement of the expansive stress be performed by FB (base)system.Figure 19 shows the maximum expansive stress ( p?s)maxversus bentonite density rb relationship for a30 to100z specimens. Unique relationship between ( p?s)maxand rb is found irrespective of mix proportion and initialdensity of mixture rd.372MITACHITo prove the validity of the expansive stress measuredby swelling test mentioned above, another series of swelling tests by measuring expansive (or compressive) strainduring keeping the vertical stress to be constant was performed. Figure 20 shows the expansive strain es versustime relationship measured for the specimens of a70zand the initial density rd of 1.6 and 1.7 g/cm3, where expansive strain is dened as the ratio of swelling displacement to the initial height of specimen. Vertical stressesapplied for the specimens were determined based on themeasured values by FB and NFB system in the swellingtest under the condition of keeping zero vertical displacement.At the initial loading stage, the expansive strain showsnegative value due to the vertical compression of 0.2¿0.3mm. After that, the expansive strain value tends tobecome constant. In the test RFB7016, the maximum expansive stress of 524 kPa obtained from FB7016 specimen was applied. Maximum expansive strain obtainedfrom the test was (es)max0.4z, which was less than halfof that obtained by RNFB7016 ((es)max1.0z) in whichthe vertical stress was applied based on the NFB7016 testresults. The same trend is seen for the specimens ofRFB7017 and RNFB7017. As it is considered that the expansive strain will not occur when the applied verticalstress is exactly the same value of true expansive stress,the validity of the FB measuring system of expansivestress is ensured.StressVolume Change Behavior during Inltration TestFigure 21 shows the change of bentonite specicvolume vb versus vertical stress relationship in loglogplot obtained from a series of inltration tests under constant vertical stress condition for two samples of a100z and initial dry density of rd1.4 g/cm3 specimen,where vb1{eb, and eb is bentonite void ratio calculatedby excluding (when aº100z) the volume of sand particles. In Fig. 21 log vb versus log (p?s)max relationship forthe range of vb1.8 to 2.4 obtained by swelling test menFig. 21. log vblog p? relationship during incremental loading compression and const. stress inltration test (a100% and rd1.4g/cm3)tioned in section 4.3 is also illustrated. The relationshipbetween bentonite density rb (which is dened as Eq. (1))and bentonite specic volume vb is represented as follows:rbMb/(Vb{Vv)(Mb/Vb)/(1{eb)rsb/vb(2)where, Mb is mass of bentonite, Vb and Vv are thevolumes of bentonite and voids in the bentonitesandmixture, respectively, and rsb is density of bentonite particle.In this series of tests, specimens are rstly subjected incremental loading compression up to the vertical stress of0.4 MPa and 0.8 MPa, respectively. After that, inltration test is started by supplying deaired water throughupper and lower parts of the apparatus while keeping thevertical stress constant as 0.4 MPa or 0.8 MPa, respectively. During the inltration test, compressive volumechange is observed for the specimen started inltration atthe stress of 0.8 MPa as indicated by downward headedarrow in Fig. 21, whereas the specimen started inltration at 0.4 MPa shows expansive volume change as indicated by an arrow heading upward direction. Moreover,it can be seen that the data points after completion of inltration test locate close to the log vb versus log ( p?s)maxline obtained from the swelling test.In Fig. 22 all the data of log vb versus log p? relationship obtained from the series of inltration tests excluding the plot of incremental loading compression up to theparticular stress state before starting inltration areshown together with the log vb versus log ( p?s)max line ttedfor the points obtained by the series of swelling tests mentioned in the previous section 4.3. The same trend illustrated in Fig. 21 is observed on a70z specimen asshown in Fig. 22, where the test number is denoted as7014 for example, in which 70 means bentonite content ain percent and 14 means 10 times the value of initial drydensity rd in g/cm3.Inltration test results under constant vertical straincondition are also plotted in Fig. 22. In this case, for thespecimens compressed up to the stress of 0.2 MPa (testNo. 10014a and 10016h) and 0.4 MPa (test No. 10014b),Fig. 22. log vblog p? relationship obtained by const. stress and const.strain inltration tests (a70% and 100%)BEHAVIOR OF BENTONITESAND MIXTURESthe stress increased as shown by arrows heading to theright with the progress of inltration, whereas the stressdecreased when the inltration started after the incremental loading up to 1.0 MPa (test No. 10014c) as shown byan arrow heading to the left in the same gure. As seen inFig. 22, nal points of inltration test performed underboth conditions of constant stress and constant strain locate close to the log vb versus log ( p?s)max line obtainedfrom the swelling tests.Cui et al. (2006) reported similar results in terms oflog em versus log p? relationship obtained by a series ofinltration test under constant vertical stress conditionfor the mixture of bentonite and Toyoura sand, where emwas dened as the void ratio of montmorillonite. Whenthey made the specimen for their tests, they changed thecombination of initial dry density and water content ofthe bentonitesand mixture depending on the test condition, while the initial state of all specimens in the presentstudy is started from dry condition.From the results mentioned above, it can be said thatthe compressive volume change may occur depending onthe density and the stress state at the start of inltration,even in the bentonitesand mixture possessing high swelling potential. Moreover, the existence of a uniquerelationship between vb and ( p?s)max, which can be recognized as the state boundary line, is suggested irrespectiveof previous stressvolume change history.CONCLUSIONSFrom the series of consolidation, triaxial compression,expansive stressstrain measuring tests on bentonitesandmixtures with varying clay contents of 30, 50, 70 and100z, and varying initial dry density of 1.4, 1.5, 1.6 and1.7, 1.8 g/cm3, the following conclusions were obtained:1) The ratio of swelling index to compression indexCs/Cc obtained from oedometer tests is as large as0.45 for COM7016 specimen, which is considerablylarger than those of nonswelling clays of 0.1 to 0.3.The magnitude of consolidation yield stress almostcoincides with the expansive stress irrespective ofbentonitesand mix proportion, initial density ofmixture and the magnitude of molding stress at thespecimen making.2) Strong correlation between eln p?c and eln Emax obtained from consolidated undrained triaxial compression test for bentonitesand mixture is observed,and the reduction rate of rigidity of bentonitesandmixture is hardly dependent on the specimen makingmethod, molding pressure and the consolidationstress.3) Expansive stresses measured by feedback (FB) system are always greater than those measured by nonfeed back (NFB) system and the dierences becomeas large as 15 to 35z if we compare FB (base) withNFB (top), where ``base'' and ``top'' refer to the location of the load cell installed in the expansive stressmeasuring apparatus. Therefore, it is recommendedthat the measurement of the expansive stress be per4)5)373formed by FB (base) system.Unique relationship between the maximum expansivestress ( p?s)max and the bentonite density rb is foundfrom the results of swelling test irrespective of themix proportion and the initial density of mixture.Even in the case of bentonitesand mixture possessing high swelling potential, compressive volumechange may occur depending on the density and thestress state at the start of inltration. A uniquerelationship is found between the maximum expansive stress ( p?s)max versus bentonite specic volume vb,irrespective of initial dry density and of claysandmix proportion. The line showing the unique log vbversus log ( p?s)max relationship can be recognized asthe state boundary line prescribing expansive stressstrain behavior of the bentonitesand mixtures.ACKNOWLEDGMENTSThis study is nancially supported by the Ministry ofEducation, Culture, Sport and Science of Government ofJapan. The author greatly appreciates the assistance provided by Messrs. Kowase, Y., Ebisu, T., Tanimura, M.,Komatsu, K., Todate, T. and Asano, J. in performingthe experiments, while they were students of HokkaidoUniversity. The author also wishes to thank the concerned persons of the IshikawajimaHarima Heavy Industries Co., Ltd. for their provision of CIP specimens.NOTATIONBSkempton's pore water pressure coecientCIPSpecimen making by Cold Isostatic PressmethodCOMSpecimen making by static compaction in themold in dry powder stateEmaxInitial tangent modulus obtained by consolidated undrained triaxial compression testEsecSecant modulus obtained by consolidated undrained triaxial compression testFBExpansive stress measurement by Feed Backsystem during swelling testNFBExpansive stress measurement by Non FeedBack system during swelling testRFBExpansive strain measurement by applyingmaximum expansive stress measured by FB systemRNFBExpansive strain measurement by applyingmaximum expansive stress measured by NFBsystemebBentonite void ratiop?0Eective consolidation stressp?cConsolidation yield stress( p?s)maxMaximum expansive stress obtained by swellingtestqPrincipal stress dierencevbBentonite specic volume calculated by excluding the volume of sand particlesMCritical state stress ratio q/p?374MITACHIaBentonitesand mix proportionlSlope of eln p?c curvenSlope of eln Emax curveeaAxial strain measured during triaxial compression testesExpansive strain measured during swelling test(es)maxMaximum expansive strain measured by swelling testrbBentonite density calculated by excluding thevolume of sand particlesrdDry density of bentonitesand mixturersbDensity of bentonite particlerssDensity of sand particleREFERENCES1) Borgesson, L. and Hokmark, O. (1991): Interim report on thelaboratory and theoretical work in modeling the drained and undrained behavior of buer material, SKB TECHNICAL REPORT.2) Cui, H., Sun, D. A., Matsuoka, H. and Xu, Y. F. (2004): Swellingcharacteristics of sandbentonite mixtures under onedimensionalstress, Journal of JSCE, No. 764, III67, 275285 (in Japanese).3) Fujita, T., Chijimatsu, M., Kanno, T., Kobayashi, A., Moro, Y.and Nakano, M. (1995): On the modeling of the expansive stress ofBentonite Buer Material, Proc. 50th Annual Conf. on JSCE, IIIA, 2829.4) Graham, J., Saadat, F., Gray, M. N., Dixon, D. A. and Zhang, Q.Y. (1989): Strength and volume change behavior of a sand bentonite mixture. Can. Geotech. J., 26, 292305.5) Japanese Geotechnical Society (2000): Standard Method for Consolidated Undrained Triaxial Compression Test on Soils with PoreWater Pressure Measurements (JGS 05232000).6) Japan Nuclear Cycle Development Institute (1999): Technical condence on the disposal facilities for high level radioactive wastes2nd Report.7) Japan Nuclear Cycle Development Institute (2002): Technical condence on the disposal facilities for high level radioactive wastes2002 year Report.8) Kawaguchi, T., Mitachi, T. and Shibuya, S. (2004): Quantifyingdeformation modulus of reconstituted clays at small strains, Journal of JSCE, No.638, III49, 179191 (in Japanese).9) Komine, H. (2001): Evaluation of swelling characteristics of buerand backll materials considering the exchangeable cations compositions of bentonite and its applicability, Proc. 15th ICSMGE, 3,19811984.10) Komine, H. and Ogata, N. (2002): Swelling characteristics of sandbentonite mixture and various kinds of bentonite, Journal of JSCE,No. 701, III58, 373385 (in Japanese).11) Komine, H. and Ogata, N. (2003): New equations for swelling characteristics of bentonitebased buer materials, Canadian Geotechnical Journal, 40(2), 460475.12) Komine, H., Ogata, N., Nakasima, A., Takao, H., Ueda, H. andKimoto, T. (2004): Evaluation of selfsealing property of bentonitebased buer by onedimensional model test, Journal of JSCE, No.757, III66, 101112 (in Japanese).13) Kurikami, H., Chijimatsu, M., Komine, H., Kobayashi, A. andOhnishi, Y. (2004): Coupled thermal hydraulic and mechanicalanalyses to evaluate swelling characteristics, Journal of JSCE, No.771, III68, 2131 (in Japanese).14) Nakano, M., Amemiya, Y., Fujii, K., Ishida, T. and Ishii, A.(1984): Inltration and expansive pressure in the conned unsaturated clay, Transaction of JSIDRE No. 112, 5566 (in Japanese).15) Namikawa, T., Hirai, T., Tanai, K., Yui, M., Shigeno, Y., Takagi,K. and Ohnuma, M. (2004): Study on applicability of elastoviscoplastic models to mechanical properties of compacted bentonite,Journal of JSCE, No. 764, III67, 367372 (in Japanese).16) Shibuya, S., Mitachi, T., Tanaka, H., Kawaguchi, T. and Lee, I.M. (1999): Measurement and application of quasielastic propertiesin geotechnical site characterization, Proc. 11th Asian RegionalConf. on SMGE, Theme Lecture 1, 85156, Korea.17) Tanaka, Y. and Nakamura, K. (2005): Eect of seawater and hightemperature history on swelling characteristics of bentonite, Journal of JSCE, No. 806, III73, 93111 (in Japanese). | ||||
ログイン | |||||
タイトル | Large-scale Shake Table Experiment and Numerical Simulation on the Nonlinear Behavior of Pile-groups Subjected to Large-scale Earthquakes | ||||
著者 | Masahiro Shirato・Yoshinori Nonomura・Jiro Fukui・Shoichi Nakatani | ||||
出版 | Soils and Foundations | ||||
ページ | 375〜396 | 発行 | 2008/06/15 | 文書ID | 21115 |
内容 | 表示 SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 375396, June 2008LARGESCALE SHAKE TABLE EXPERIMENT AND NUMERICALSIMULATION ON THE NONLINEAR BEHAVIOR OF PILEGROUPSSUBJECTED TO LARGESCALE EARTHQUAKESMASAHIRO SHIRATOi), YOSHINORI NONOMURAii), JIRO FUKUIiii) and SHOICHI NAKATANIiv)ABSTRACTThis paper describes the results of largescale shaketable experiments involving a 3~3 pilegroup. The pilegroupwas embedded in dry sand and subjected to sinusoidal waves and an earthquake motion recorded from the 1995 Hyogoken Nanbu (Kobe) earthquake. The load transfer between soil and pile was derived and the group eect was captured. Numerical simulations were also performed using a BeamonNonlinearWinklerFoundation approach with anew hysteretic py curve. A comparison of the experimental and numerical results revealed that the numerical simulation is capable of accounting for the soilpile interaction observed in the experiment.Key words: group eect, numerical simulation, pile group, shake table test, soilpile interaction (IGC: E12/E14/H1)Alternatively, many 1 G largescale laboratory experiments and centrifuge model experiments have been conducted using shake tables. For example, Wang et al.(2000) and Tokimatsu et al. (2005) investigated largescale earthquake situations using 1 G largescale shake table experiments, while Curras et al. (2001) performedcentrifuge shake table experiments. Miyamoto et al.(2004) carried out an experimental and modeling study ofthe dynamic response of a groupedpile foundation toground motions induced by largescale mining blasts;however, further research eorts are required. Additionalexperimental case studies that are made available to thepublic will continue to be welcomed in the future, as realdesign cases involve a diverse range of conditions.Although experimental methods should be chosen interms of factors such as the aim, scale, time, and cost,largescale experiments that consider the dynamicresponse of pile foundations subjected to large earthquakes remain limited in number. In particular, highwaybridge foundations in Japan have a standard nominalcentertocenter pile spacing of 2.5times the pile diameter, yet there are only a few experimental data concerning pile foundations with such closely spaced piles. Inaddition, the development of a suitable dataprocessingmethod, data interpretation, and the choice and arrangement of relevant sensors for largescale shake table testsof pile groups remain challenging tasks.In this context, we conducted a series of largescaleINTRODUCTIONAs a result of the disastrous consequences of recent severe earthquakes such as the damage to infrastructure associated with the 1995 Hyogoken Nanbu (Kobe) earthquake (Public Works Research Institute, 1996), the current seismic design of highway bridges in Japan againstlarge earthquakes is expected to: (1) control damage inthe nonlinear region beyond the elastic limit and (2) continue to provide emergency transportation services following a large earthquake, even if the structure hadsuered a certain degree of damage. Therefore, it isnecessary to develop designcalculation methods to assessthese requirements. Equally, it is quite useful to havebenchmark datasets that can assess the capabilities of numerical simulations. In terms of foundations, groupedpile foundations are one of the most commonly usedfoundation types throughout the world.Onsite realtime observations are considered to be oneof the best ways to assess the behavior of groupedpilefoundations during earthquakes; however, such an approach is timeconsuming in terms of the potentially longwait involved for a large earthquake that poses the nonlinear behavior of the groupedpile foundation. There arefew reports that document the behavior of groupedpilefoundations for highway bridges during seismic events(Ohiraet al., 1985; Tazoh et al., 1988), even when considering smallscale earthquakes.i)ii)iii)iv)Senior Researcher, Center for Advanced Engineering Structural Assessment and Research, Public Works Research Institute, Japan (shiratopwri.go.jp).Researcher, Public Works Research Institute, Japan.Advanced Construction Technology Center, Japan.Chief Researcher for Bridge Management Technology and Substructures, Center for Advanced Engineering Structural Assessment andResearch, Public Works Research Institute, Japan.The manuscript for this paper was received for review on January 24, 2007; approved on February 5, 2008.Written discussions on this paper should be submitted before January 1, 2009 to the Japanese Geotechnical Society, 4382, Sengoku,Bunkyoku, Tokyo 1120011, Japan. Upon request the closing date may be extended one month.375376SHIRATO ET AL.shake table experiments of model pilegroups. The pilegroup specimens had a nominal centertocenter spacingof 2.5times the pile diameter. Waves with high acceleration intensities were then applied to the shake table. Inthis paper, rstly, relevant methods of dataanalysis aresought to estimate the load transfer between the soil andpiles. Second, typical experimental results are summarized, especially for maximum response properties andsoilpile interactions including hystereses of py curvesand group eects. Third, a method is proposed to incorporate the group eect into hysteretic singlepile pycurve models. In the end, a numerical simulation is conducted as an example of a means of benchmarking numerical techniques using the present experimental data.Fig. 1.Detailed results of the shaketable experiment areavailable as a technical report from the Public WorksResearch Institute, Tsukuba, Japan (Fukui et al., 2006);the report includes a DVDROM that contains digitaldata of the experiment results, so that readers who wantto examine the experimental results from their viewpointswill also be able to access the required relevant data set.LARGESCALE SHAKETABLE EXPERIMENT OFA GROUPEDPILE FOUNDATIONTest Layout and SequenceThe pile groups and sensor layouts are shown in Fig. 1.The experiments were conducted using an 8~8 m largeDiagram of the test setup (e.g., the Weight M is mounted as the topweight)377SEISMIC BEHAVIOR OF PILEGROUPTable 1.Weight casesWeightTable 3.MassN (None)ThicknessRun WeightWaveTest sequence in Series 2SoilSoilAssumed RecordedDtable acc. table acc. depth H density r r(z)22(t/m3)(m/s )(m)(m/s )0 kg0 mm302 kg32 mm1MSweep0.500.572.9931.59467.1M (Medium)1509 kg160 mm2MSinusoidal1.00.92H (Heavier)2867 kg320 mm3MSweep0.500.574MKobe8.188.192.9951.59266.75MSweep0.500.552.9541.61473.26MStepincreasing6.06.177HSweep0.500.572.8811.65584.8L (Lighter)Table 2Run WeightWaveTest sequence in Series 1Assumed RecordedSoilSoilDtable acc. table acc. depth H density r r22(m/s )(m/s )(m)(t/m3) (z)1NSinusoidal3.02.782.9911.58263.68HKobe8.188.192NSinusoidal3.02.729HSweep0.500.572.8691.66286.83NSweep0.500.594LSweep0.500.582.9591.59968.710HStepincreasing6.06.235LSinusoidal1.00.9211MSweep0.500.552.8611.66788.16LSinusoidal3.02.7212MSinusoidal5.05.097LSinusoidal4.03.972.9071.62877.013MSinusoidal1.00.892.8431.67890.98MSweep0.500.5914MSweep0.500.569MSinusoidal1.00.93After2.8421.67891.010MSinusoidal3.02.7811MSinusoidal4.03.9312MSinusoidal5.05.342.8921.63679.413MSinusoidal6.06.322.8651.65183.714LSinusoidal6.06.522.8411.66687.615MKobe8.188.822.8371.66888.2After2.8331.67088.9Note: Not measuredSoil depth H, soil density r, and soil relative density Dr represent thestate right before each Run.After: showing the conditions after all exciations in the correspondingSeriesacc.: Accelerationscale shaketable and a large exible shear stack housed inthe Public Works Research Institute, Tsukuba, Japan.The shake table was rocked in a northsouth direction, asshown in Fig. 1. The ground level (GL}0 m) was denedat a height of 3 m from the base of the exible shearstack. As listed in Table 1, four kinds of top weights wereused, namely Weights N, L, M, and H, which will be explained later. Tables 2 and 3 provide lists of experimentalruns. The experiments were conducted using two dierentsetups, referred to as Series 1 and 2. Each series consistsof several runs, and the jth run of the Series i is hereafterreferred to as Run ij. Series 1 was designed to enable theobservation of basic features of soilpile load transfer,while Series 2 was designed to obtain benchmark data forevaluating the capability of numerical models ofgroupedpile foundations.Note: Not measuredSoil depth H, soil density r, and soil relative density Dr represent thestate right before each Run.After: showing the conditions after all exciations in the correspondingSeriesacc.: AccelerationPile GroupsThe specimens were made of steel and comprised a topweight, a support column, a pile cap, and a pilegroup.The pilegroups comprised a 3~3 box arrangement ofnine steel piles. As shown in Fig. 1, the piles in the north,middle, and south rows are labeled piles N (north), pilesM (middle), and piles S (south), respectively, and thenumbers 1 through 3 are assigned to the piles from westto east in each pile row, i.e., pile N1, pile N2, and pileN3 in terms of the N row. The nominal centertocenterdistance was 2.5times the pile diameter. The necessity ofthis spacing distance is explained in the Introduction, andwe considered that it is useful to have a middle row to understand the group eect for typical pile groups.The length from the top to the bottom of each pile was3000 mm. The piles were embedded into the pile cap andwelded to lib plates inside the pile cap. The lower 2850mm of the piles was buried and the upper 150 mm wasleft exposed to acquire a head clearance for the construction of the soil deposit beneath the pile cap. It was alsoexpected that the extrusion of the piles from the groundsurface would generate a deeper depthtomaximumbendingmoment, leading to an increased correspondingoverburden pressure in the soil. Each pile base was supported by a pinned supporting device of 130 mm inheight, as shown in Photo 1, and the supporting devices378SHIRATO ET AL.Photo 1.Hinge device located at the base of each pileFig. 2.Typical crosssection of a pilewere attached to a steel plate with a wide base.The base plate was hooked into the ditch on the base ofthe exible shear stack to prevent it from moving backand forth, but it was free to move upward. At the planning stage, we assumed that the overburden load fromthe soil deposit to the base plate would prevent the pilegroup specimens from moving upward; however, thepiles were unexpectedly uplifted during several runs thatinvolved larger accelerations. The uplift during the excitations is described from the experimental data later inthe text.A typical pile crosssection is shown in Fig. 2. The pileswere hollow steel pipes with a roundcornered rectangular section, a width of 125 mm, and a wall thickness of4.5 mm. The rectangular section provided ample roomwithin the pile to install sensors and sucient strength toensure that the piles did not yield. A steel plate of 4.5 mmthickness and 116 mm width was installed inside everypile with angles guiding along the centerline of each pile.The positions of the installed steel plates and angles werearranged such that they can be assumed to make aminimal contribution to the bending stiness of the pilesin response to the inputted motions. The steel plates andangles extended up to a height of 3100 mm from the baseof each pile. The plate was xed to the pile using bolts at13 depths: GL {0.05 m, |0.10 m, |0.25 m, |0.35 m,|0.45 m, |0.65 m, |0.75 m, |0.85 m, |1.05 m,|1.45 m, |1.85 m, |2.25 m, and |2.65 m. These werethe same depths as the accelerometers arranged in thepiles, as is explained later. It should be noted that themeasured values of axial strains in the piles were alwayssmaller than the yield strain in each run.In terms of the normal crosssection, the mass per unitlength of the pile was 22.5 kg/m and the sectional areaand the moment of inertia of the crosssections were3.085~103 mm2 and 5.107~106 mm4, respectively. Thesevalues took into account the contributions of the steelplates and angles within the piles as well as the piles themselves. The average values of Young's modulus and yieldstress were 20.2 kN/mm2 and 425.6 N/mm2, respectively,as obtained using a standard JIS material tests (JapaneseIndustrial Standard, 2004) of three specimens that werecut from a separate piece of the same pipe. The calculatedbending rigidity, EI, is 997 kN¥m2, in which EYoung'smodulus and Ithe moment of inertia of the crosssection. Bending tests of the piles were also performed. Inthis test, a pile specimen was supported at both ends anda lateral load was applied at the midspan of the specimen.The bending strains that developed in the piles subjected to lateral loads indicate that a value of EI1000 kN¥m2 is acceptable. Therefore, this study takes 1000 kN¥m2to be a representative value of the bending rigidity of thepiles.The pile cap was 250 mm high, 1200~1200 mm in planview, and had a mass of 764 kg. The square crosssectioncolumn that supported the top weight was 300 mm high,1000~1000 mm in plan view, and had a wall thickness of24 mm and a mass of 321 kg.As has been described above, Table 1 lists the involvedtop weights. Weight N indicates that no top weight wasused on the support column. Weight H was the heaviestand it was designed to carry as heavy as possible while thepile material would not yield during the excitations,based on a preliminary design calculation result. WeightL was a steel plate with a thickness of 32 mm, a length of1200 mm, a width of 1000 mm, and a total mass of 302kg. Weight M comprised 5 steel plates, with each platehaving a thickness of 32 mm, a length of 1200 mm, and awidth of 1000 mm; accordingly, the total height was 160mm and the total mass was 1509 kg. Weight H was constructed by placing four additional steel plates uponWeight M. The added plates were 40 mm thick, 1200 mmlong, and 900 mm wide. The mass of Weight H was 2867kg, and its total height was 320 mm. These plates were arranged symmetrically about the centerline of each pilegroup specimen, with the long side oriented parallel tothe shake direction.Flexible Shear Stack and Soil DepositThe exible shear stack consisted of 17 layered frameswith a total height of 3.5 m. Each layer was 0.2 m deepexcept for the bottom layer, which was 0.3 m deep. Adjacent layers were able to move back and forth relative toeach other, with a maximum relative movement of 40mm. Therefore, the maximum possible average shearstrain in the soil was approximately 10z.The soil deposit was constructed following the placement of the groupedpile specimen in the shear stack.Once a soil deposit was constructed, it was used duringthe entire experimental series. After Series 1, the soil wasremoved from the shear stack and a new soil deposit wasmade for Series 2. Airdried Tohoku silica sand #6 was379SEISMIC BEHAVIOR OF PILEGROUPFig. 3.Particlesize distribution within Tohoku silica sand #6Fig. 4.used for the soil deposit. Physical test results for this sandwere as follows: rs2.653 g/cm3, rdmax1.712 g/cm3,rdmin1.397 g/cm3, and D500.365 mm. The particle sizedistribution of the sand is shown in Fig. 3. The soildeposit was constructed to a height of 3 m and a targetrelative density Dr of 65z. The internal friction angle, q,obtained by isotropic consolidated drained triaxial compression tests was 40.99at a relative density of Dr65z(the soil density was 1.587 g/cm3). The internal frictionangle was estimated under the assumption of c0, inwhich cadhesion. The relationship between Young'smodulus and the conned stress was obtained by isotropic consolidated undrained cyclic triaxial compressiontests, as follows:E01.691(s?c)0.5364~104(kN/m2),(1)where s?cconned stress (also kN/m2).The relationships between G/G0g and hg obtainedfrom the cyclic triaxial compression tests are shown inFig. 4, in which Gsecant shear modulus, G0smallstrain shear modulus, hequivalent damping ratio, andgshear strain. A leastsquare method derives a ttedcurve with the hyperbolictype function proposed byHardin and Drnevich (1972):1GgG01{gr(2)where gr0.0487z, in which gr is the reference strain.The depths of the accelerometers in the soil depositswere measured both during the construction and removalof the soil deposits, as the soil deposit gradually settledduring the excitations. The ratios of the change in depthof each accelerometer before and after the experimentwere largely unchanged at all soil depths. Therefore, it isassumed that the soil deposit contracted at a constant rateover the depth of the soil.The soil deposit height, H, was measured when theshake table was completely shut down between experimental runs. These measurements provide the instantaneous average density, r. The instantaneous averagesoil density, r, is calculated by dividing the total soil massby the instantaneous height H of the soil deposit and theplan area within the exible shear stack. These values arelisted in Tables 2 and 3, in which the tabulated values ofG/G0g and hg relations at Dr65%the height of the soil deposit, H, and the density and relative density of the soil deposit, r and Dr, correspond tothe values obtained immediately prior to the corresponding runs.InstrumentationAccelerometers, strain gauges, load cells, and displacement transducers were used as sensors. All sensors werezerocleared immediately before each shake table run.The horizontal response of the shaketable was measured using accelerometers and laser displacement transducers (LDTs), while the horizontal and rocking motionsof the supported structure and the horizontal motions ofthe piles and soil were captured using accelerometers.Vertical arrays of accelerometer were located in the soildeposit on the east, west, and north sides of the pilegroup. Small pieces of acrylic sheet were attached to theaccelerometers, horizontally and vertically, to movetogether with the soil and thereby prevent rotation of theaccelerometers during excitation.The load transfer between soil and pile was directlymeasured in Series 1 using the load cells embedded in thepiles, although use of the load cells in this way made itimpossible to assume relevant stress and strain distribution around the opening areas. All nine piles were ttedwith load cells at crosssections at GL |0.35 m and|0.75 m. Details of the pile crosssections around theload cells are shown in Fig. 5. The anges were cut out toinstall the load cells at the above crosssections in eachpile; consequently, the values of the crosssectionalparameters at the crosssections around the load cellswere dierent from those of the normal section.Although strain gauges were also arranged on the piles,even in Series 1, the strain gauge data for Series 1 is notused in this paper because of the diculty involved in estimating the inuence of the deformation around theopening parts on the measured strain gauge values.The load transfer between soil and pile in Series 2 wasestimated based on the bending strains in the piles. Therefore, the entire lengths of the piles had no decit in crosssections, as load cells were not used. In addition, the useof piles with no decit in crosssections facilitates themodeling of the piles via computer simulations. PilesN1, N2, M1, and M2 were tted with strain gauges at13 crosssections, and piles S1 and S2 were tted with380SHIRATO ET AL.Fig. 5.Crosssection at which load cells embedded in piles for Series 1 testsFig. 6.Original input base accelerationsstrain gauges at 9 crosssections. The strain gauges wereattached at the same crosssections at which horizontalaccelerometers were installed. The depthtomaximumbending moment and soil resistance stress were assumedto appear at approximately GL |0.60 m based on a preliminary design calculation; accordingly, the strain gaugeswere arranged more densely at around that depth.Applied WavesOriginal input base (i.e., table) accelerations to theshake table are plotted in Fig. 6. As Series 1 was designedto observe the basic features of soilpile load transfer, asimple wave form of stationary harmonic sinusoidalwaves were mainly applied, with a frequency of 2 Hz, duration periods of approximately 30 sec, and constant acceleration levels of 1, 3, 4, 5, and 6 m/s2. A sweepsinusoidal wave with a small acceleration level (or sweepwave) was also inputted in the run immediately before orafter each run with a large input acceleration level to conrm the characteristic vibration properties of the soil andfoundation. The acceleration level was set to remain constant at 0.50 m/s2, while the frequency level was gradually increased from 1 over a frequency level lager than 20Hz, then the acceleration was manually decreased to zero.As Series 2 was designed to obtain benchmark data forestimating the capabilities of numerical models of pilegroups for real earthquakes, we used the NS componentof the earthquake motion recorded by JMAKobe duringthe 1995 Hyogoken Nanbu earthquake (hereafterreferred to as the Kobe earthquake), where JMA standsfor the Japan Meteorological Agency. This motion has amaximum acceleration of 8.18 m/s2. In Run 28, thephase angle was set to the opposite of that in Run 24 tobalance the accumulation of residual displacement of thetest specimen in a particular direction stemming from thestrong motion. Accordingly, the signs of both theplanned and measured maximum accelerations on theshake table in Run 24 and Run 28 are opposite. A stepincreasing type of sinusoidal wave (or stepincreasingwave) was also used in Series 2. The wave was set to maintain a constant frequency of 2 Hz, while the accelerationamplitude was increased in a stepwise manner from 1, 3,4, 5, up to 6 m/s2 during each excitation. The stepincreasing wave was used, so that, just in case, the datacould be alternative to the results of typical sinusoidalwave runs in Series 1. It is worth mentioning that we haveconrmed that the observed soilpile interactions weresimilar when using the stationary harmonic sinusoidalwaves and when using the stepincreasing type ofsinusoidal waves (Fukui et al., 2006).The output acceleration on the shake table was dierent from the input acceleration signal to the shake table ineach run; this is also shown in Tables 2 and 3 as the dierence in the recorded and expected maximum acceleraSEISMIC BEHAVIOR OF PILEGROUPtions. Nonetheless, the wave accelerations in this paperare always presented along with the originally plannedmaximum acceleration levels. The dierence is associatedwith the reproducibility of the shake table system.ANALYSIS OF EXPERIMENTAL DATABecause all sensors were zerocleared immediately before every run, the state immediately prior to each run isregarded as the initial state for that run. The positivedirection of lateral soil resistance is from south to north,and the positive direction for both acceleration and displacement is to the south.Estimation of the Soil Resistance Stress p upon the PilesIn Series 1, a pair of load cells installed at a singlecrosssection were used to measure the increase ordecrease in earth pressure on each side of the pile, pS andpN, relative to the state immediately prior to the experimental run, as illustrated in Fig. 7. The superpositionof the load cell values on both sides is expected to give thelateral soil resistance stresses upon the pile at the crosssection during the excitation.In Series 2, the lateral soil resistance stresses at crosssections with strain gauges were derived by the doublenite dierentiation of the measured moment distribution versus depth, based on the BernoulliEuler beam theory as follows:.Mi{1|Mi Mi|Mi|1|1lili|1pi(3)(li{li|1)/2Dwhere pi (kN/m2)the soil resistance stress at the ithcrosssection, and Mi|1, Mi, and Mi{1 (kN¥m)the measured bending moments at the (i|1)th, ith, and (i{1)thcrosssections, respectively, D (m)pile width, and li andli{1 (m)the distances between the (i|1)th and ithcrosssections and between ith and (i{1)th crosssections. Eq. (3) does not consider the eect of the inertialforce in the pile body. The time history of p at any crosssection located between crosssections with strain gaugescan be estimated using linear interpolation.We also estimated the value of p for several experimental runs incorporating the eect of the inertial force intoFig. 7. Schematic diagrams of a beam on Winkler foundation in anx1x2 Cartesian coordinate system and earth pressures to a pile atrest position (dash lines) and at a deformed position (solid lines)381Eq. (3) and found that the dierence in p estimated whenconsidering and ignoring the eect of the inertial forcecan be approximately 10z at most. The dierence waslarger at small amplitudes of p. Therefore, we judgedthat the eect of the inertial force can be ignored for theexamination of the experimental data in this paper.This data processing scheme generally worked well asshown in the indepth experimental report (Fukui et al.,2006). For example, the open circles in Figs. 8(a) and (b)plot the distributions of p versus depth via the originaldata processing scheme at a sequential time of 9.30 sec inRun 24, Kobe wave run, at which larger soil reactionstresses appeared, and at a sequential time of 8.52 sec inthe same run, at which the displacement of the pile relative to the soil was very small and the values of p weresupposed to be almost zero over the entire length. Only inFig. 8(b), a bumpy distribution is noticeable, indicatingthat the margin of error in the obtained values of p via theoriginal data processing scheme may not be minor whenthe values of `p` are very small or almost zero.Therefore, as implemented in the data interpretation ofsome experiments of piles subjected to lateral loads (e.g.,Kikuchi, 2002; Shirato et al., 2006b), we further prepreprocessed the bending moment distribution in pile, using a smoothing spline algorithm with a thirdorder polynomial and then moved to the original data processingscheme. Because the strain gauges were densely arranged,the preprocessing was applied from GL |0.26 mthrough to |1.45 m, which will be paid attention to inthe data analysis below. A relevant value of the smoothing parameter was determined by trialanderror visualinspections for several soil resistance stress distributionsFig. 8. Observed typical soil reaction stress distributions versus depthduring Run 24 (Righthand side of the gures show the enlargedviews of the distributions. Open circles: Original data, Filled circles: Modied through an additional smoothing preprocessing)382SHIRATO ET AL.for several runs, so that the distributions of soil resistancestress, p, versus depth satised the following conditions:1. The predominant trend in the original distributionof p, prior to the additional smoothing preprocessing, remained visible.2. A bumpy highorder uctuation was not stressedin the distribution of p obtained via Eq. (3).The examples of data that were modied via the additional smoothing preprocessing are also shown with the lledcircles on the righthand side enlarged views of Figs. 8(a)and (b). On the one hand, as compared in the righthandside gure of Fig. 8(a), when the values of `p` are larger,the dierence is little in the distributions of p obtainedwith the original and modied data processing schemes,i.e. the open circles and lled circles in the gure, respectively. On the other hand, the righthand side gure ofFig. 8(b) reveals that the unrealistic scattering in thevalues of p obtained via the original data processingscheme was improved in the values of `p` obtained viathe modied data processing scheme.AccelerationIn terms of shake table accelerations, the values obtained from the two accelerometers on the shake table areaveraged for any given time. Unless stated otherwise, thetop weight motion refers to the motion at the gravity center. The records of the two accelerometers on the top ofthe top weight and at the center of the supporting columnare linearly interpolated. Accelerations at any depth within the soil and groupedpile model are generally estimated using a linear interpolation and extrapolation inthe vertical direction from two accelerometer records atneighboring depths; however, for accelerations of thesoil, the acceleration at any depth shallower than theshallowest accelerometer position was regarded as beingthe same as that of the shallowest accelerometer record;likewise, the acceleration at any depth deeper than thedeepest accelerometer position was taken to be the sameas that of the deepest accelerometer record. The soil accelerations recorded by the arrays of A1 and A3 wereaveraged for any given time with respect to the depth ofthe accelerometers; these values are considered torepresent the soil acceleration record at the corresponding depth.Because subsidence of the soil deposit was observed,the depths of the accelerometers in the soil deposit werereestimated for each run. Then, the depth of the soildeposit was assumed to be maintained during the subsequent run.We compared the changes in the heights of the accelerometer positions at the times that they were placedand removed before and after each experiment series. Asa result, the volume fraction is assumed to be homogeneous at all depths during each run. However, the settlement of the soil deposit was not measured at every run.To approximate the progressive settlement of the soildeposit, the evolution of soil settlement is assumed toproceed according to the Arias intensity, Iar, as shown inFig. 9. The evolution of soil settlement was representedFig. 9. Evolution of the soil deposit settlement with the change in Arias intensity Iaby the change in the ratio of the soil deposit depths immediately prior to the run, h, to the initial soil deposit depth,h0, i.e., h/h0. The Arias intensity Iar is dened as:fa(t) dtp2GIar/02(4)where Iar (m/s)Arias intensity, G (9.8 m/s2)acceleration due to gravity, and a(t) (m/s2)the shake tableacceleration at time t. The Arias intensity is associatedwith the input energy. While we concede that the validityof this assumption should be examined based on theresults of future shaketable experiments, this assumption can be used as a rst approximation. For example,Fig. 9 shows that the settlement trends in Series 1 and 2are dierent, and we infer that the amplitudes and typesof inputted motions, as well as the input energy, are likelyto inuence the settlement trend.DisplacementDisplacement time histories are derived from thetrapezoidal double integration of acceleration time histories. Acceleration time histories were ltered in terms offrequency with a highpass lter before the double integration process; the accelerations shown in this paperare nonltered values. Finally, the pile displacement relative to the soil displacement, y, at a depth of x2 is derivedusing the pile and ground displacements at equivalentdepths.Figure 10 shows the lters that were eventually adopted for each type of wave, namely the sinusoidal, stepincreasing, and Kobe waves, and compares the horizontalshaketable displacements obtained from two dierentsources: accelerometer records and LDT records. A lterwas determined according to the specic type of the inputmotion. The transition band in the frequency of the lterwas dened using a cosine function with the boundaryfrequencies of fstop and fpass, as given in the lters shown inFig. 10. The values of fstop and fpass are tailored to eachwave type (sinusoidal wave, stepincreasing wave, andKobe wave) by trial and error such that the derived shaketable displacement time histories approximate those captured by the LDT as much as possible. The determinedlter was applied to all acceleration records of the soiland pilegroup specimens as long as it was compatible interms of the type of input motion.SEISMIC BEHAVIOR OF PILEGROUPFig. 10.383Highpass lter and the identied shake table displacementAlthough the information on the actual residual displacement and longer period components was susceptibleto being lost as the lowfrequency components were removed by the highpass lters, the risk is unavoidable andnecessary when using this kind of approach. For example, because of the vibration characteristic of the shaketable system, the table displacement measured with theLDTs in Run 26 contains a large undulation with a muchlonger vibration period compared to the frequency of theinput base acceleration, while that measured from the acceleration time history does not have, where the main frequency component of the applied wave was 2 Hz and thehigher threshold of the transition band of the highpasslter was 1 Hz as also shown in Fig. 10. However, themain vibration components were not be removed and theinuence of the undulating longperiod component ofdisplacement on the real deformation component of soiland pile that induced the lateral soil resistance to pilesshould be considerably small, compared to the inuenceof the main vibration component of 2 Hz. In otherwords, the undulating longperiod component of displacement can be regarded as the rigid movement component of the system. Therefore, we can at least capture thevariation in the displacement from the undulating baseline.For runs with the Kobe wave, a further special treatment was required prior to the above general process. Inthe Kobe wave runs, acceleration records had considerable residual values after the excitation. This may be because those particular accelerometers were inclined at aparticular time during the excitation. If this type of acceleration record is integrated just once, without anyltering process, the base line of the velocity time historyhas a breaking point, as shown in Fig. 11. Because it isimpossible to remove this eect via the general lteringprocess, a further process was introduced for the Kobewave runs, prior to the above general ltering process, toremove this distortion that resulted from the inclinationof the accelerometer. The time when the accelerometerFig. 11. Recorded acceleration of weight and velocity obtained with aonetime integration for Run 24was inclined was roughly estimated and the gravity component of acceleration was removed from the acceleration time history, assuming: (1) the mean recorded acceleration during the last few seconds agreed with thegravity acceleration component and (2) the predominantinclination of the accelerometer occurred with a particular large pulse of the applied motion and the degree of inclination did not change during the rest of the excitation.The process we did is summarized as follows:1. We calculated the mean accelerations, a1 and a2,from 0 sec (the beginning of the record) to 3 secand from 37 sec to 40 sec (the end of the record),respectively.2. The time at a temporary breaking point, tb, that indicates the time when the inclination occurred wasassumed; a1 was subtracted from the accelerationrecord from 0 sec to tb, and a2 was subtracted fromtb to 40 s.3. The processed acceleration record was then integrated once, and the velocities at times t0 and40 sec were obtained.4. We then determined the time of tb that yielded thederived velocities of zero at times t0 sec and t384SHIRATO ET AL.40 sec, repeating steps 2 and 3 by trial and error;this value was then used in the subsequent generalprocess.TYPICAL OBSERVED RESPONSETypical observed responses are shown herein.Figure 12 shows recorded accelerations at three depthsin the soil deposit and at the base (i.e., shake table). Thephases at dierent depths were similar to each other ineach run, and the acceleration levels basically increased asthe depth became shallower except for the Kobe waverun. In Kobe wave runs, the input base acceleration amplitude was so large that the soil became highly nonlinear,resulting in the decrease in the acceleration as the waveapproached the soil surface.Figure 13 shows the Fourier spectrum ratio of thehorizontal acceleration records at the soil (Ground) at adepth of GL |0.10 m to the table and that of thehorizontal acceleration records at the top weight to theFig. 12.table, respectively, for Run 21 with Weight M. On thebasis of the results of sweep wave runs, the natural frequency of the soil deposit was approximated as 8 Hz andthose of the structural models were approximated as1517 Hz for the cases involving the Weight M and 1314Hz for the cases involving the Weight H, respectively.When using the Weights N and L, a noticeable peak didnot appear in the Fourier spectra in the range smallerthan 20 Hz and their natural frequencies are consideredto be larger than 20 Hz.The eects of the dierence in input base accelerationlevel on the response were examined in Fig. 14, in whichthe observed maximum horizontal soil accelerations at adepth of GL |0.10 m, maximum topweight horizontalaccelerations, maximum bending moments of Pile M1 ata depth of GL |0.10 m, and maximum topweight displacements relative to the base (or table) are plottedagainst the maximum base input acceleration levels for allexcitation runs except for the sweep wave runs. Regarding the accelerations, the observed values tend to increaseTypical recorded accelerations in soil and at baseSEISMIC BEHAVIOR OF PILEGROUP385Fig. 13. Fourier spectrum ratios of horizontal acceleration records atthe soil surface or the top weight to that at the base (Run 21)Fig. 15. Maximum and minimum soil displacements relative to theshake table (Runs 19 to 113)Fig. 14. Observed maximum responses versus maximum base acceleration levelswith increase in the base input acceleration levels andhave sort of a cuto limit at larger base excitation levelslike the Kobe wave runs. This is also because the soilbecame highly nonlinear during the Kobe wave runs.The maximum and minimum soil displacements relative to the shake table displacement are plotted in Fig. 15for Runs 19 to 113; sinusoidal waves with dierent baseacceleration levels were applied. It is intriguing that thedistribution of soil displacement shows a linear trendwith depth. A distribution such as a quarter of awavelength of a cosine curve is generally assumed in design practice. While a cosine curvelike distribution canappear in a homogeneous medium that has a constantdistribution of shear stiness with depth, the rigidity ofthe sand deposit actually increases with increasing depthand overburden pressure. Figure 16 shows a theoretical equation for displacement distributions with depth indams and embankments (Ohmachi and Tokimatsu,1983). The equation considers dierent types of shearstiness distributions with depth: GAzn, where Aconstant, zdepth, and nconstant. Although the equaFig. 16. Horizontal displacement versus depth in a homogeneous elastic mediation for a semiinnite medium is not given, the overalltendency is likely to be similar. Based on Eq. (1), the soilshear stiness in the present experiment is almost proportional to the square root of the conning pressure, or thesquare root of depth. Accordingly, the experiment displacement distribution is a straight line rather than aquarter of a wavelength of a cosine curve.COMPARISON OF TYPICAL DATAANALYSISRESULTS OBTAINED USING DIFFERENTMETHODSA typical set of data analysis results obtained usingdierent methods are explored herein.Soil Resistance StressThe soil resistance stresses, p, at depths GL |0.35 m386SHIRATO ET AL.Fig. 17.Comparison of recorded soil resistance stress for Series 1 (soild lines) and Series 2 (dash lines)and |0.75 m measured with load cells in Series 1 and estimated from strain gauge data in Series 2 are comparedherein; Runs 19 to 113 (sinusoidal waves) and Run 26(stepincreasing type of sinusoidal wave) are used forcomparison, and the results are shown in Fig. 17. Thesoil resistance stresses in Fig. 17 were the maximum andminimum values in the time histories and the minimumvalues were plotted after reversing the sign. The corresponding displacement relative to soil, y, in Fig. 17 wasrepresented by the displacement at the middle row pile ofthe rst trailing piles and transferred into the half amplitude. As for the positive and negative peak values next toeach other in the time history of y, the half amplitudeswere calculated as ([the positive peak value]|[the negative peak value])/2 and the maximum half amplitude waspicked up. Then, it was nondimensionalized with the pilewidth, D. As for Run 26, the maximum and minimumsoil resistance stresses and the maximum half amplitudesof y at every input acceleration step of 100 to 600 gal wereextracted and plotted. The soil resistance stresses obtained with two types of observation methods are similar,indicating the measured soil resistance stresses are acceptable.The soil resistance of the back bone curve of py loopstends to converge to a particular strength as the displacement level increases. The soil resistance intensities of theleading, rsttrailing, and secondtrailing piles (Piles N,M, and S or vice versa) dier markedly, even at the samedisplacement levels, while those of the center and sidepiles (Piles 1, 2, or 3) are largely similar.DisplacementFigures 18 and 19 show time histories of the soil surface displacement and weight displacement derived according to the process described above and from imageFig. 18. Time histories of soil surface displacement in Runs 24 and28Fig. 19.Time histories of weight displacement in Runs 24 and 28SEISMIC BEHAVIOR OF PILEGROUPprocessing of the video recordings for Runs 24 and 28,although the video camera and a video recorder used inthis study were consumer models with a data acquisitionrate of 30 Hz; this rate is slower than those of other sensors by a factor of 101 or 102. Because of the lteringprocess removing lowfrequency components, the baselines in the time histories of displacements obtained fromacceleration time histories are not fully reproduced andthe residual displacements are not captured. However, itis conrmed that the present procedure of identifying displacement from acceleration records can account forboth the amplitude from the base line and the phase characteristics for the periods of main motion at least.OBSERVED TYPICAL py CURVES AND GROUPEFFECTSA typical set of py curves are examined and then thegroup eciency is estimated herein.py LoopsAssociated with a depth of GL |0.35 m for Pile N1during a time window of 1011 sec in Runs 110 and112, respectively, Fig. 20 shows the time histories of thedisplacements of soil (or ground) and pile, and the pilerelative to the soil, y, normalized with the pile width, D,Fig. 20.387the soil reaction stresses measured at the northside andsouthside load cells, pN and pS, respectively, and the soilresistance stress to the pile, ppNpS as well as the corresponding py loops, where the load cell values were positive when the load cell was in tension. Both runs wererocked by sinusoidal waves, but the base acceleration levels were dierent. Run 110 involved a base accelerationlevel of 300 gal, while Run 112 involved a base acceleration level of 500 gal. In terms of each Run, the fourpoints labeled A through D are plotted on the time histories and the py loop, showing the timings at which y/Dreached the negative peak (A), came back to zero (B),reached the positive peak (C), and came back to zeroagain (D). In Fig. 20(a), the dierence in the soil and piledisplacements is indiscernible.Regarding the time histories of the load cell values, pNand pS, the intensity of pN periodically varied largely onthe negative side while the intensity of pS continued to bealmost zero, so that the positive and negative amplitudesof p were dierent. This dierence arose from the groupeect. Pile N1 was a corner pile and it became a leadingpile when the values of p and y/D decreased. In addition,the fact that the values of pN and pS periodically becamepositive indicates that either loosening or separation occurred between the pile and the surrounding soil andeither an active earth pressure or zero earth pressure apTime histories of the load cell values at a depth of GL |0.35 m in Pile N1388SHIRATO ET AL.peared.Generally, the py loops in Fig. 20 are asymmetric andthey have similar loop shapes of py curves to those observed in an experiment of single piles subjected to lateralcyclic load at the pile top (Shirato et al., 2006b), whichappear to consist of triangles. However, the path CDA ofthe py loops in Fig. 20, especially for Run 112 with alarger base acceleration level, also indicates that the pyloop shape in the shake table experiment was aected bythe opening or loosening between the soil and pile. Afterthe displacement y reverses at Point C, the soil resistancep in the following py path has a tendency to initially increase (as with Path CD), although the tendency soon disappears, especially around y0 (see the path aroundPoint D), where the loop might be aected by the loosening. In the end, p surges sharply (Path DA) after the displacement level y/D reaches a certain level.Although it seems that, in Run 112 with a base acceleration level of 500 gal, the py loop had a tendency asthough the positive peak value of p appeared when thedisplacement of the pile relative to the soil, y, reachedzero, we do not infer that this tendency is a general feature in the load transfer between soil and pile. Strictlyspeaking, the phases of the soil displacement time histories at a point in the vicinity of the pile and the free eldare unlikely to be completely identical and the dierenceis likely to increase with increase in the base accelerationlevel. As for Run 110 with a base acceleration level of300 gal, pN, pS, and y/D almost simultaneously reachedtheir peak values at the times designated with A and C,while, as for Run 112 with a base acceleration level of500 gal, the timings when the values of pN and pS reachedthe peaks and when the value of y/D reached the peakswere clearly dierent.For Run 112, Fig. 21 shows typical dynamic pycurves at a depth of GL |0.35 m (i.e., `z/D`2.8) forall the piles in the time window of t2021 sec. Nine pyloops are arranged in the graph, corresponding to the pilearrangement. Because the piles in the N and S rows are alternately the leading row and second trailing row duringan excitation, the py loops of the piles in the S row andthe N row appear upsidedown and ipped side to sidewith respect to each other. In contrast, for the py loopsof the piles in the M row, there is no large discrepancy inthe amplitude of p when pÀ0 and when pº0.The piles in the M row were always the middle piles; accordingly, the soil resistance to the M row was alwayssmaller than that to the S row or the N row. The py loopsof the Mrow piles do not show the characteristic featuresthat indicate the occurrence of an opening or a looseningbetween the soil and pile. It is considered that the soil between the piles was constrained by the surrounding pilesand moved together with the Mrow piles as a unitedbody.Group EciencyA pmultiplier approach has been suggested by Brownet al. (1988). Pmultipliers soften the shape of the singlepile py curves, together with the decrease in the ultimatesoil resistance, accounting for the group eects on thelateral load transfer between soil and pile. The adjustedpy curves are described as follows:pG( y)h~pS( y)where pG( y)adjusted py curve that considers the soilresistance stress upon a pile within the pilegroup, pS( y)single pile py curve model when there is no group eect,and hnondimensional group eciency and the socalled pmultiplier. One of the physical understandingsfor pmultipliers is that the soil resistance area to a pile asa pilegroup may reduce because of the overlapping of thesoil resistance areas of the neighboring piles, i.e., socalled shadowing eects, which also have been suggestedby Brown et al. (1988). Because of its simplicity, pmultipliers have been empirically estimated from load testson pile groups and such values have been adopted in design codes like API design recommendations (API 1987)and AASHTO design specications (AASHTO, 1998).On the other hand, ymultipliers are considered inelasticitybased studies, such as:pG( y)pS(z~y)Fig. 21. Observed py loops for each pile at GL |0.35 m for Run112 (t2021 sec)(5)(6)where znondimensional group eciency and the socalled ymultiplier. Because p and ymultipliers are likelyto consider shadowing eects and elasticity, respectively,the use of both p and ymultipliers can make the physicalmeaning clearer. For example, the Japanese Specications for Highway Bridges (Japan Road Association,2002) apply both p and ymultipliers to design static pycurves for pile groups. In this study, for the sake of dataprocessing simplicity, the experimental pmultipliers areanalyzed below.The group eciency for each pile is estimated. First,the maximum and minimum values of the soil resistancestresses, p, at depths GL |0.35 m and |0.75 m are extracted from the time histories of p within time windowsof t1011 sec and t2021 sec in Run 19 to 113(sinusoidal wave runs), as well as from the time windowsthat correspond to the fth vibration period at eachSEISMIC BEHAVIOR OF PILEGROUPacceleration level of 100 gal to 600 gal in Run 26 (stepincreasing type of sinusoidal wave run) at depths of GL|0.26 m, |0.45 m, |0.65 m, |0.85 m, and |1.10 m.Namely, the group eciencies up to a depth of ninetimesthe pile diameter will be obtained. Second, within thesame time windows and at the same depths, the maximum half amplitudes of y were obtained, as has beendone for Fig. 17. In the end, the group eciency, h, iscalculated relative to the instantaneous leadingrow corner piles.The group eects for the leadingrow corner piles areassumed to be acceptably small in the present shaketableexperiment, using the following past experimental facts.Fukui et al. (1997) investigated several previous experiments of pilegroups with a nominal pile spacing of 2.5times the pile diameter, as well as experiments involvingsingle piles. They reported that when the piles are subjected to static lateral loads, the group eciency h for theleading piles is generally between 0.8 and 1.0. Mokwa andFig. 22.Duncun (2001) compiled the results of many previous experiments involving model pilegroups subjected to lateral loads and found that the group eciency of the leadingrow piles is approximately 0.83 for a centertocenter pilespacing of 2.5times the pile diameter. In addition, thecorner piles in the leading row are expected to be lessaected than the other piles in the same row based on theshadowing eect theory.The results are shown in Figs. 22 and 23, where PileS1 was the reference leading corner pile. Each data setfor each depth is designated by a particular symbol, andthe plotted values of y/D correspond to the displacements of individual piles. Even though the mobilized displacement level of the reference pile (Pile S1) did notperfectly coincide with those of individual piles, the experiment result showed they can be regarded almost identical. It should be noted that the value of h when Pile N1is the reference leading corner pile was also analyzed; theresult is very similar to that shown in Figs. 22 and 23.Pilegroup eciency in the horizontal soil resistance relative to the soil resistance to a corner pile of S1 (Runs 19 to 113)Fig. 23.389Pilegroup eciency in the horizontal soil resistance relative to the soil resistance to a corner pile of S1 (Run 26)390SHIRATO ET AL.Figures 22 and 23 show that the dierence in the mobilized soil resistance, p, is found clear between the leadingrow piles and the trailing row piles, while the dierenceappears largely similar between the center piles numberedwith 2 and the outside piles numbered with 1 and 3, as theshadowing eect theory suggests.The facts that the trend of h decreases with increasingdisplacement level and such a trend does not vary withdierent depths merit attention. As for the former fact,Figs. 22 and 23 also conrm that the group eciency (pmultiplier), h, rapidly decreases; it eventually convergesto certain values once y/D has reached 0.01. Based onpreviously published experimental data, Mokwa andDuncun (2001) also demonstrated that the group eciency h generally tends to converge to constant values at adisplacement level of approximately 5z of the pile diameter.INCORPORATION OF PMULTIPLIERS INTOHYSTERETIC py CURVESThe sectional forces and strengths of piles vary frompile to pile within a pile group. This occurs because, inaddition to the change in the axial forces of the piles related to the horizontal and rotational movement of the pilecap, the group eect is evident in the horizontal soilpileload transfer.Therefore, group eects should be considered inhorizontal seismic soilpile interactions when undertakingseismic design. The py curve model or nonlinear beamon nonlinear Winkler foundation model is one of themost popular choices in assessing the dynamic behaviorof pile groups in the event of large earthquakes. Therefore, in this section we describe a method that can be usedto apply the pmultiplier approach, even to hysteretic pycurves.The shake table experiment shows that the value of thepmultiplier converges to a certain value as long as thedisplacement level is greater than 1z of the pile diameter.Therefore, it can be considered that the dependency of hon the displacement level is likely to be negligible in seismic design against large earthquakes, as during largeearthquakes piles can reach a displacement level of several percent of the pile diameter. For example, a displacement level of 1z of the pile diameter is allowed even inthe case of small to mediumscale earthquakes whendesigning Japanese highway bridges (Japan Road Association, 2002). The shake table experiment also shows thatthe value of the pmultiplier is independent of depth. Asit turns out, it is not necessary to change the pmultiplierwith changing displacement level or depth.Figure 24 provides a graphical description of theproposed method. Two pmultipliers of h and h? alternating with the sign of p are applied to the correspondingsinglepile py curve:pG( y)zzh~pS( y)zz, if pÆ0pG( y)zzh?~pS( y)zz,if pº0(7)where pG( y)zz is a hysteretic py curve at depth z for aFig. 24.Modeling of pilegroup eects in dynamic py curvespile in a pilegroup, pS( y)zz is any hysteretic py curvemodel for a virtual isolated single pile at the same site,and h and h? are nondimensional pmultipliers. For example, a corner pile in a group will alternately becomeboth a leading pile and a trailing pile during an earthquake. Therefore, the two values of h and h? are introduced.NUMERICAL SIMULATIONAs mentioned in the Introduction, one of the important aims of the experiment was to generate a benchmark data set that can be used to assess the capabilitiesof numerical simulations in terms of the behavior ofgroupedpile foundations subjected to large earthquakes.This section describes a simulation for Run 24 withthe Kobe wave. It is worth noting that a comparison ofthe experimental and numerical results for Run 28 reveals the same trends as those revealed in an equivalentcomparison for Run 24. In both runs, the shake tablewas rocked by the Kobe wave. More detailed calculationresults are presented elsewhere (Fukui et al., 2006).Summary of the ModelA schematic diagram of the computational model isshown in Fig. 25. A beam on nonlinear Winkler foundation (BNWF) approach is employed, and the innitesimaldeformation theory is applied.The top weight is modeled using a lumped mass thattakes the mass and rotational inertia into account. Twolumped masses with weights and rotational inertia are arranged at the midheights of the pier and the pile cap.These lumped masses are connected using rigid beam elements. Rigid beam elements are also arranged along thebase of the pile cap and rigidly connected to the piles. Thepiles are modeled using linear elastic BernuolliEulerbeam elements with lumped masses arranged at everynode. The piles are assigned a Young's modulus of E200 kN/mm2, the moment of inertia of the crosssectionof I5.0~106 mm4, and sectional area of A2085 mm2;however, for further simplicity, the three piles in eachrow are dealt with together as a single beam with the secSEISMIC BEHAVIOR OF PILEGROUPFig. 26.Fig. 25.Schematic diagram of the numerical modeltional values equivalent to the sum of the three piles. Theelement length is set to 50 mm (0.4D, where D is thepile width) such that the depths of the accelerometers embedded in the piles correspond to the nite element nodesof the piles.Each pile is considered to be supported horizontally bylateral soilpile interaction springs that express the lateralsoilpile interactions. The springs are distributed at thenite element nodes of the pile because of the limitationsof the commercial niteelement code used for the simulation. This represents a challenge in terms of furthersimplifying the numerical model. The loaddisplacementrelationship of the lateral spring at the upper node of abeam element for a pile is estimated from the soilparameters at the midheight point in that beam element.The loaddisplacement relationship is described based ona py curve, in which psoil resistance stress to a pile andythe corresponding displacement of the pile relative tothe fareld. The spring load is obtained by simply multiplying p by the element width and the element length.We use a hysteretic rule of py that was developed at thePublic Works Research Institute, Tsukuba, Japan; this isdescribed later in the text.A relevant pmultiplier is also applied depending on theposition of the pile. The pmultiplier is obtained on thebasis of the shadowing eect theory.For the sake of data processing simplicity, we considerthree lateral loaddisplacement springs at the same depth,as the beam elements of the three piles are already integrated into a single beam element.At the pile tips, nonlinear vertical joint elements are arranged to account for the uplift of the foundation observed in the experiment. The loaddisplacement curve ofthe joint elements is described below. The axial soilresistance to a pile is represented by a single joint elementat the pile tip; no sidedistributed vertical springs are arranged on the side of the pile. While the vertical displacement at the pile tip is described in terms of the joint elements, horizontal displacement is xed and rotation isfree to occur. The three vertical joint elements in eachrow of piles are also integrated.We input the observed freeeld ground motion at each391Hysteretic mechanism for py curves for single pilesdepth directly into each end of the lateral soilpile interaction springs at the corresponding depth, although freeeld excitations are commonly computed with a relevantmethod when the BNWF approach is used. Given that weespecially focus on the capability of a model using a pycurve to dynamically analyze pilegroups, it is preferablethat the numerical results are unaected by shortcomingsin the numerical predictions of soil motions.For simplicity, the damping matrix is set to be proportional to the initial stiness matrix. Ultimately, the damping is assumed to be 2z for the rst characteristic vibration mode of the soilfoundation system, as we considerthat this assumption may be valid. Because the experiment was conducted within a closed space inside the exible shear stack, the damping caused by the nonlinearity inpy curves should be much larger than the other dampingfactors. This damping component is also stipulated to beproportional to the initial rigidity of the system. A timestep of 0.001 sec is used in the numerical time integration.Hysteretic Rule of the py CurveA hysteretic rule of py curve proposed by the PublicWorks Research Institute (Shirato et al., 2006a) is usedfor the simulation, and the group eect is incorporatedusing the method proposed above. Figure 26 illustratesthe essence of the hysteretic rule of py curves. Thismodel is proposed based on the behavior of soil elementssubjected to cyclic compressionextension deformation,as well as the behavior of single piles subjected to cycliclateral loads with dierent cyclic loading patterns. Themodel is devised to account for the fact that mobilizedlateral soil resistances to single piles can change whensubjected to fullyreversed cyclic loading and onesidedcyclic loading. The model also performed reasonably inthe dynamic analysis reported in Shirato et al. (2005),simulating a centrifuge shakingtable experiment of extendedpile shafts in clay that was originally performedby Boulanger et al. (1999).Although the choice of the shape of the backbone pycurve is optional, this paper employs an elastoperfectplastictype bilinear skeleton curve as used in previousstudies; this is described with an initial gradient of backbone py curve, kH (kN/m3), and the ultimate soilresistance, pU (kN/m2). The initial gradient, kH, is given392SHIRATO ET AL.as follows:kHakk0,(8)where k0 (kN/m )unloading gradient in the hystereticpy curve. The unloading gradient is assumed to have aclose relationship with the unloading rigidity of the surrounding soil or the soil rigidity at a lowstrain level,while the initial gradient of the backbone curve can be determined via a tting process to observational monotonicpy curves. Accordingly, the nondimensional correlationfactor, ak, is introduced. Because the initial gradient ofthe backbone curve is dierent from the unloadinggradient, the hysteretic loops are made even if `p` has notreached pu.The unloading path from the last displacement reversalpoint R1 on the backbone curve to p0 is a straight linewith the unloading gradient k0. The subsequent loadingpath from p0 (point Z1) is bound for point R1*, which isthe point that is opposite point R1 about the origin, wherepoint Z1 is the fully unloaded point from point R1 and thecombination of the lines of R1Z1R1* is referred to as theexternal curve. A path unloading from a point R2 on theexternal curve R1Z1R1* and consequently returning tothe backbone curve is referred to as the reference curve(R2Z2P). The reference curve is bound for point T1.Point T1 is the intersection point of the lines Z1*R1 andZ1T1, and point Z1* is the point that is opposite point Z1about the origin. Line Z1T1 has a gradient of kHr, wherekHr is termed the reference reloading gradient and is dened as kHrmk0 using a nondimensional parameter, m.Because the modication factor m is introduced, thereversed loading path from the external curve is boundfor a point that is dierent from the original unloadingpoint R1 on the backbone curve, as illustrated in Fig.26(c).The reference reloading gradient, kHr, is assumed to besimilar to the initial gradient of the backbone curve. Forfullyreversed cyclic loading, the py curve follows apeakoriented rule, as shown in Fig. 27.Internal curves that move inside the curves of R1Z1R1*and R2Z2P always trend toward point T2 or T3, depending on the traveling direction. Points Z2, T2, Z3, and T3are set in the same manner as Z1 and T1.Finally, the pmultipliers, h and h?, are applied depending on the position of the pile in accordance with the3Fig. 27.Typical hysteretic curve of py in fullyreversed cyclic loadingconceived method described in the previous section.Parameter Settings for the py CurveThe parameters for py curves are given with referenceto previous numerical simulations (Shirato et al., 2005,2006a, 2006c).When a pile is subjected to a large displacement, soilresistances will become noticeably plastic. Accordingly,the ultimate soil resistance stress, pu, is rst xed, whilethe rst gradient is then set empirically. We use the ultimate soil resistance given by Kishida and Nakai (1979),assuming an admissible plastic ow onto a horizontal underground plane:Ø p4 | q2 » 1|sin q3¥¥exp Ø p|q » tan qpqcos q{2}cos Ø { »42cospusv|KA(9)where svoverburden stress at a depth of x2, qinternalfriction angle, and KARankin's active earth pressurecoecient:KAtan2Ø p4 | p2 »(10)The unit soil mass is given as 1.6 t/m3 based on Table 3and we use q40.99obtained from the results of laboratory tests.We obtain the unloading gradient, k0, asØ »E0(x2)D~B0B0k0(x2)n(11)where E0 (kN/m2)the small strain deformationcoecient of soil at each depth, x2 (m)depth, ntheconstant that represents the loadingwidthdependency ofsubgrade reaction coecients, D (m)pile width, and B0(m)reference width in terms of the loadingwidth dependency. In addition, s?c in Eq. (1) is replaced with amean eective stress estimated by sm(1{2K0)sv(x2)/3(kN/m2), where sv(x2) is the eective overburden stress atdepth x2 and K0 is the coecient of earth pressure at rest,as estimated by K01|sin q.In Eqs. (8) and (11), the soil resistance to the pile isproportional to the soil rigidity (Gazetas and Dobry,1984), and the modication concerned with the foundationwidth dependency of the subgrade reactioncoecient is applied with a power of the foundationwidth (Yoshida and Yoshinaka, 1979; Japan Road Association, 2002), where B00.3 m and n|3/4 wereused (Yoshida and Yoshinaka, 1979; Japan Road Association, 2002). It turns out that the form of Eq. (11) is similar to the subgrade reactionintensity equation in theJapanese Specications for Highway Bridges (JapanRoad Association, 2002).Previous numerical simulations (Shirato et al., 2005,2006a, 2006c) suggest that the parameter used to describethe initial rigidity of the backbone curve, ak, is in the order of 10|2 to 10|1 when we assign the small strain shearmodulus of soil, E0, the result of typical cyclic triaxial393SEISMIC BEHAVIOR OF PILEGROUPFig. 28. Estimation of the areas of apparent soil resistance, A, and thegroup eects, h, based on the shadowing eect theoryFig. 29.Resistance zone for a single pilecompression, where the small strain shear modulus E0 ateach depth can be evaluated using Eq. (1). We undertookpreliminary tests of ak0.01 and 0.1 via numerical simulations of Run 24 and Run 28; the values of the otherparameters were unchanged. The numerical results showthat the overall trends of the calculated and observed timehistories are in good agreement; however, the use of ak0.1 was considered to make the system somewhat stier,as higherfrequency components appear in accelerationtime histories compared to those in the experimentaldata. Therefore, all numerical results shown hereafter arecalculated with ak0.01.In terms of the loadingpattern dependency, we set thereference reloading gradient, kHr, and the initial backbone curve gradient, kH, to be equal, based on previousresults (Shirato et al., 2005, 2006a, 2006c).As has been proposed previously, with regard to thenumerical simulations for pilegroups subjected to largescale earthquakes, it is not considered to inadvertentlyobtain unrealistic numerical results even when the pmultipliers that are relevant for the ultimate soil resistancelevels are applied to entire displacement levels. Therefore, as a typical pmultiplier approach, the shadowingeect theory is applied even to smaller soil resistancestress levels, although it should be originally relevant forthe soil resistance stress level close to the ultimate. Kosaet al. (1998) estimated the value of h for previously published in situ pilegroup load tests, following the shadowing eect theory, and concluded that the method originally proposed in DIN4014 (Deutsches Institut f äur NorFig. 30. Recorded behavior of Pile N1 and Pile S1 in the directionparallel to the pile axis in Run 24 and an approximated backbonecurve (solid lines: experimental results, dashed lines: approximatedbackbone curves of the experimental results)mung, 1987) approximated the observed values; theirmethod is illustrated in Fig. 28. The reference resistancearea to a single pile, A0, is a trapezoidal area that is 3Bwide and 6B long, as shown in Fig. 29, where Bpile diameter. The area of apparent soil resistance for each pile,A, decreases, and it can be estimated by subtracting thearea of the overlapping zones from the original resistancearea A0. Ultimately, h is obtained as the ratio A/A0. Finally, the average pmultipliers, h and h?, are estimatedto be 0.98 for the leading rows and 0.52 for the trailingrows, as shown in Fig. 28; these are applied to the pycurves of the single pile. Although the pmultipliers arecalculated as shown in Fig. 28 in this study, further investigations are needed to conrm the means of estimatingpmultipliers: for example, empirical pmultipliers alsohave been proposed by Brown et al. (1988), Mokwa andDuncan (2001), Rollins et al. (1998) etc.EndPile Springs and Modeling of Side Resistance toPilesFigure 30 shows the observed relationships between theaxial force at the pile top and the axial displacement atthe pile end in Run 24. This result encourages us to setan assumed axial pile resistance property. The axialforces N are estimated from the axial strain at a positionof GL{0.05 m, with the pile's Young modulus E200kN/mm2 and crosssectional area A3.085~103 mm2.The displacement at a pile end, dv, is approximated bysubtracting the elongation of the pile from the pile topdisplacement. The vertical displacement at the pile tops isestimated from analysis of the video images. The elongations of the piles are approximated by multiplying the axial strain at GL{0.05 m by the pile length.Eventually, the endpile springs with a nonlinear elasticproperty,dvaN{bN 3,(12)are adopted, in which N (kN)axial load, dv (mm)axial displacement at the end of a pile, and a and bconstants. From the viewpoint of physical behavior, the springs shrink by only a minor amount, even for large compressive loads, while they expand readily under large tensile forces. From the viewpoint of the numerical simula394SHIRATO ET AL.tion, it appears to be better that the transition betweencompression and extension is smooth in terms of theloaddisplacement relationship; this ensures that no impact forces are generated at the transition point. The assumed behavior is given via trialanderror visual estimations. The coecients a and b in Eq. (12) are eventuallygiven as a5.105~10|2 mm/kN and b2.572~10|5mm/kN3.Because all of the soil resistance in the direction of thepile axis is included in the endpile spring, the axial sideresistance component is not arranged.CALCULATED AND OBSERVED DYNAMICSOILFOUNDATION INTERACTIONSFigure 31 shows the calculated and recorded relationships for Run 24 between lateral acceleration and lateraldisplacement at the top weight, where the lateral displacement is the displacement relative to the groundsurfacedisplacement. The numerical result shows excellent agreement with the experimental result.Several types of calculated and recorded responses ofthe top weight motion are compared in Fig. 32. From topto bottom, the time histories of horizontal acceleration,horizontal displacement, and rotation are shown. Discrepancies in the horizontal acceleration and displacement between the calculation and experiment are barelydiscernible. The timings when each wave motion crossesover the abscissa and reaches each peak are successfullypredicted. This fact proves that the hysteretic rule of pyused herein works very well in estimating hysteretic foundation behavior in random loading conditions. However,the calculated peak rotation angle is approximately halfof the experimental value, while the calculated time history of the peak rotation angle shows similar trends to therecorded time history. This may reect the fact that theinversed pilebase springs remain stier than the actualcondition.The calculated and experimental distributions of peakbending moment are compared in Fig. 33. The calculation is only able to successfully predict the experiment onthe negative side. This is one of the outcomes that need tobe improved in the future. The timings at which peakpositive bending moments appeared in the piles tend tocorrespond to the timings at which the superstructure rotated in the negative direction. As examined above, thecalculated peak negative rotation angle is underestimatedby as much as half of the recorded values; this may be attributed to a discrepancy between the calculated and observed bending moment for this period. The calculatedand recorded time histories of the bending moment at adepth of GL |0.45 m in Pile N1 are shown in Fig. 34.The phase characteristics of the calculation and the experiment are in good agreement.The calculated and recorded peak soil resistances areshown in Fig. 35 and the calculated and recorded pyFig. 31. Calculated and recorded lateral acceleration and lateral displacement curves at the top weight in Run 24Fig. 33. Calculated and recorded distributions of the peak pilebending moment versus depth in Run 24Fig. 32. Calculated and recorded response time histories of the topweight motion in Run 24Fig. 34. Calculated and recorded response time histories of the bending moment at a depth of GL |0.45 m in pile N1 for Run 24SEISMIC BEHAVIOR OF PILEGROUPFig. 35. Calculated and recorded peak soil resistance distributions versus depth in Run 24Fig. 36. Calculated and recorded dynamic py curves at a depth of GL|0.45 m in Run 24curves at a depth of GL |0.45 m are compared in Fig.36. They are in good agreement. As seen in Fig. 36, thedisplacement level of the pile relative to soil almostreached 20z of the pile width, where the pile width is 125mm. The calculated curves envelop the experimentalcurves, and the calculated curves have similar loop shapesto the experimental ones. As seen in the experimentalresults, the current py curve model also expresses a cleardiscrepancy in the amplitudes in p of the positive andnegative values, especially for piles N1 and S1 (cornerpiles).CONCLUDING REMARKSThis paper reports on the results of largescale shaketable experiments of a pile group that has the typicalnominal piletopile spacing of Japanese highwaybridgefoundations. We also analyzed soilpile interactions onthe basis of the experiment results. We then provided anexample of the use of experimental data to benchmark anumerical model of pilegroups. The main results of ourstudy are summarized in the following points.1. We examined dataprocessing methods for largescale shake table experiments of pile groups anddemonstrated the capability of these methods interms of capturing soilpile interactions. Accelerometers and strain gauges worked in identifying displacement time histories and the time395histories of soilpile load transfer; however, theuse of a VCR and load cells is also very helpful inverifying the dataprocessing process from accelerometer and strain gauge records.2. On the basis of the experimental results, the groupeect observed in lateral load transfer between thesoil and piles in the experiment did not vary withdepth. Although the group eect increased with increasing relative displacement between the soil andpiles, the eect approaches a particular value whenthe displacement level is greater than approximately y/D1z. Therefore, for large earthquakes thegroup eect can be expressed solely in terms of theposition of the pile in the pile group.3. We proposed a method that can be used to incorporate the group eect during large earthquakesinto any hysteretic py curve models.4. We demonstrated the usefulness of the shaketableexperiment data in terms of assessing the accuracyof numerical models of pile groups. A numericalsimulation that uses the hysteretic py curve modelproposed by Shirato et al. (2006a) and that incorporates the group eects as conceived in this paperis capable of accounting for the experimentalresult.The authors hope that the digital data of Public WorksResearch Institute's shaketable test (Fukui et al., 2006)and cyclic lateral load experiment of single piles (Shiratoet al., 2006a, 2006b) will be widely used for the development of numerical models of soilpile interactions duringlarge earthquakes.ACKNOWLEDGMENTSThe authors acknowledge the assistance of Mr. S.Tanimoto in helping to operate the experiment equipment. The authors also thank Prof. N. 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ログイン | |||||
タイトル | Linear Model to Predict Soil-gas Diffusivity from Two Soil-water Retention Points in Unsaturated Volcanic Ash Soils | ||||
著者 | A. C. Resurreccion・Toshiko Komatsu・Ken Kawamoto・Masanobu Oda・Seiko Yoshikawa・P. Moldrup | ||||
出版 | Soils and Foundations | ||||
ページ | 397〜406 | 発行 | 2008/06/15 | 文書ID | 21116 |
内容 | 表示 SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 397406, June 2008LINEAR MODEL TO PREDICT SOILGAS DIFFUSIVITY FROM TWOSOILWATER RETENTION POINTS IN UNSATURATED VOLCANIC ASH SOILSAUGUSTUS C. RESURRECCIONi), TOSHIKO KOMATSUii), KEN KAWAMOTOii),MASANOBU ODAii), SEIKO YOSHIKAWAiii) and PER MOLDRUPiv)ABSTRACTRisk assessment and design of remediation methods at soil sites polluted with gaseous phase contaminant require anaccurate description of soilgas diusion coecient (Dp) which is typically governed by the variations in soil airlledporosity (va). For undisturbed volcanic ash soils, recent studies have shown that a linear Dp(va) model, taking into account inactive airlled pore space (threshold soilair content, va, th), captured the Dp data across the total soil moisturerange from wet to completely dry conditions. In this study, we developed a simple, easy to apply, and still accuratelinear Dp(va) model for undisturbed volcanic ash soils. The model slope C and intercept (interpreted as va, th) were derived using the classical Buckingham (1904) Dp(va) powerlaw model, vXa , at two soilwater matric potentials of pF 2(near eld capacity condition) and pF 4.1 (near wilting point condition), and assuming the same value for the Buckingham exponent (X2.3) in agreement with measured data. This linear Dp(va) prediction model performed better thanthe traditionallyused nonlinear Dp(va) models, especially at dry soil conditions, when tested against several independent data sets from literature. Model parameter sensitivity analysis on soil compaction eects showed that a decrease inslope C and va, th due to uniaxial reduction of airlled pore space in between aggregates markedly aects the magnitudeof soilgas diusivity. We recommend the new Dp(va) model using only the soilair contents at two soilwater matricpotential conditions (eld capacity and wilting point) for a rapid assessment of the entire Dpva function.Key words: airlled porosity, soilgas diusion coecient, soilgas diusivity, soilwater retention, volcanic ash soil(IGC: D4/E14)Several predictive models for soilgas diusivity,Dp/Do (where Do is the gas diusion coecient in freeair), as a function of soilair content (va, m3 soilair m|3soil) have been proposed. These include both empirical,soiltype independent models and some recent and moreconceptual soilwater retention (poresize distribution)dependent models. The early Dp/Do models of Buckingham (1904) and Penman (1940) require only va to estimate Dp, whereas the later Millington and Quirk (1960,1961) Dp/Do models also include the soil total porosity(F, m3 pore space m|3 soil). These soiltype independentDp/Do models performed poorly when tested against Dpmeasurements on soils with dierent texture (includingvolcanic ash soils) and across a wide interval of soilmoisture conditions (Moldrup et al., 1999, 2000, 2003).However, the Millington and Quirk (1961) Dp/Do modelis still today the most widely used model when investigating the diusion of gaseous phase contaminants in soil(e.g., Jury et al., 1983; H äohener and Surbeck, 2004).To take into account the eect of soil type on Dp, Moldrup et al. (1996, 1999, 2000) developed the soilwaterINTRODUCTIONThe movement of gaseous phase contaminants in soil(e.g., volatile organic chemicals as a result of spills orleaks from underground tanks) is generally controlled bygas diusion through tortuous airlled pathways in between soil particlewater complexes (Hers et al., 2002).An accurate prediction of the soilgas diusion coecient(Dp) and its dependency on the soil moisture conditions inthe unsaturated zone are, therefore, essential to realistically simulate the migration of soilgaseous contaminantsand to quantify the associated risk from soil contamination (Petersen et al., 1996). This is especially the case forsoils in urban areas where the degree of soil compactionbelow buildings will additionally inuence the magnitudeof Dp. Since measurements of Dp are highly time consuming and require specialized measurement apparatus (Rolston and Moldrup, 2002) that is not available in mostsoils and geotechnical laboratories, a prediction modelfor Dp requiring easily obtainable input parameterswithout sacricing prediction accuracy is needed.i)ii)iii)iv)Dept. of Engineering Sciences, University of the PhilippinesDiliman, Philippines (acresurrecciup.edu.ph).Graduate School of Science and Engineering, Saitama University, Japan.Department of Hilly Land Agriculture, National Agricultural Research Center for Western Region, Kagawa, Japan.Environmental Engineering Section, Dept. of Biotechnology, Chemistry and Environmental Engineering, Aalborg University, Denmark.The manuscript for this paper was received for review on May 25, 2007; approved on February 5, 2008.Written discussions on this paper should be submitted before January 1, 2009 to the Japanese Geotechnical Society, 4382, Sengoku,Bunkyoku, Tokyo 1120011, Japan. Upon request the closing date may be extended one month.397398RESURRECCION ET AL.characteristic (SWC)based Dp/Do models. These SWCbased Dp/Do models performed superior to the soiltypeindependent models when estimating Dp for dierent soiltypes (Moldrup et al., 1999, 2000, 2004). For wellaggregated volcanic ash soils, however, the SWCbasedDp/Do models had a tendency to underestimate Dp at intermediate soil moisture conditions (soilwater matricpotentials between pF 2 and pF 4.2; where pFlog (|c,soilwater matric potential in cm H2O)) and largelyoverestimated Dp at air and ovendry conditions (Moldrup et al., 2003; Resurreccion et al., 2007a, b).The SWCbased Dp/Do models do not consider theeect of isolated airlled pore space entrapped by interconnected water lms in between soil aggregates. This inactive airlled pore space governs the magnitude of Dp atvery high soilwater content, as reported by severalauthors (Call 1957; Troeh et al., 1982; Freijer, 1994).Resurreccion et al. (2007a, b) showed that a linear Dp/Domodel, proposed by Moldrup et al. (2005a) and takinginto account the inactive pore space (threshold soilaircontent, va, th) well captured the observed linear Dp(va) behavior of undisturbed, unsaturated volcanic ash soils.The two model parameters (slope C and intercept va, th),however, have yet to be linked to measurable soil physicalcharacteristics (e.g., soilwater retention).Alternatively, Moldrup et al. (2005b) revisited theBuckingham (1904) powerlaw model (vXa ) and suggestedthe possibility of linking the exponent X with soilmoisture condition in terms of the soilwater matricpotential c or pF. Moldrup et al. (2005b) showed that Xis expected to vary between 2 for drier soil and graduallyincreases to 2.5 or more for wetter soil, based on data for44 dierently textured undisturbed soils. In this study, wewill combine the approaches of Moldrup et al. (2005a, b)to arrive at a simple and easy applicable model for soilgas diusivity taking into account both inactive airlledpore space and soilwater retention.Volcanic ash soil diers from normal mineral soils because this soil usually possesses dual porosity aggregatedstructure including high amounts of Allophane, a claymineral with a hollow particle structure. These allophanicvolcanic ash soils have unique physical and chemicalproperties, including high water retention, gooddrainage, and high nutrient availability that make themsuitable for agricultural production (Shoji et al., 1993).In Japan, it extends to most of the Kanto region in EastJapan (Takahashi and Shoji, 2002) including highly urbanized areas within the Tokyo metropolis.The objectives of this study are (1) to develop a simple,predictive Dp/Do model for unsaturated volcanic ash soilsbased on only two welldened points on the soilwaterretention curve, (2) to test the performance of this newDp/Do model against independent soilgas diusivity datafrom literature covering a wide range of soilmoistureconditions, soil texture, and bulk densities, hereundercomparing model performance with that of existingpredictive Dp/Do models, and (3) to evaluate the eects ofbulk density on the sensitivity Dp/Do based on the newmodel and supporting measurements.MATERIALS AND METHODSData from LiteratureWe considered 24 Dp/Do data sets for undisturbed volcanic ash soils from Osozawa (1998) and Resurreccion etal. (2007a, b) where Dp was measured on 100 cm3 coresamples. Each undisturbed (intact) soil sample was collected by inserting a 100cm3 core into the soil. The soilsample was removed using a hand shovel, trimmed,sealed with a vinyl tape, and stored at 2¿59C beforelaboratory analyses. Measurements of Dp were conductedat a wide range of soil moisture conditions and with anumber of intact samples measured for Dp at air andovendry conditions. Some of the data sets from Osozawa (1998) in this study were also used by Moldrup et al.(2003) in testing the performance of SWCbased Dp/Domodels.The undisturbed volcanic ash soils were taken fromdierent locations in Japan, and are labeled according tothe sampling location (name of the local area). The datafrom Osozawa (1998) consist of 20 soils collected fromTsumagoi (10 soils), Kyushu (5 soils), and Miura (5 soils).Measurements of Dp and soilwater retention at soilwater matric potential intervals between pF 1 and 4.2were conducted on triplicate samples and the mean valuewas used in the analysis. Tsumagoi and Kyushu soils werecharacterized as humic to highly humic volcanic ash soilsfrom agricultural and grass lands, respectively; whileMiura soils were characterized as light clay volcanic ashsoil. Two Tsumagoi soils were also measured for Dp atairdry condition.The remaining four volcanic ash soils are from Resurreccion et al. (2007a, b) and were sampled from NishiTokyo (1 soil) and Fukushima (3 soils). NishiTokyo soildata represent 12 intact soil samples collected along atransect in a pasture eld and characterized as highly organic loam with approximately 11z organic matter content, while 36 intact soil samples from Fukushima weretaken from a forest site at three depths (12 intact soil samples per depth) with a steep organic matter gradient. Measurements of Dp and soilwater retention were done at thesoilwater matric potential intervals between pF 1 and4.1. Dp was measured for 19 samples at airdry conditionand for 10 samples at ovendry condition out of the 48samples in total. The remaining soil samples collapsedduring the drying process and therefore did not allowmeasurements of Dp at air and ovendry conditions. Weadopted the value of pF 6 as the soilwater matric potential at airdry condition following Poulsen et al. (2006).The soil physical and geotechnical indices of all undisturbed volcanic ash soils in this study are given inTable 1. Data on texture, liquid, and plastic limits ofsoils from Osozawa (1998) were obtained from similarsoil series at dierent places from the sampling points ofOsozawa (1998); whereas data on texture, liquid, andplastic limits of NishiTokyo and Fukushima Andisolswere results of direct measurements on samples takenfrom the actual sampling location.399TWO SOILWATER RETENTION POINTS IN UNSATURATED VOLCANIC ASH SOILSTable 1. Soil properties for the 24 Andisols used in this study including soilair content data at pF 2 and 4.1 (4.2). Data from Osozawa (1998),Resurreccion et al. (2007a, b), and this studyParticledensity(Mg m|3)Bulkdensity(Mg m|3)2.472.462.412.392.822.572.572.552.562.56TotalPorosity(m3 m|3)SoilAir Content, e(m3 m|3)Gas diusivity,Dp/DoSand* Silt*(z)(z)Clay* Gravel*(z)(z)0.570.730.610.400.690.570.760.720.630.7730.6§nm26.5§nmnmnmnmnmnmnm35.2§nm38.4§nmnmnmnmnmnmnm34.2§nm35.2§nmnmnmnmnmnmnm0§nm0§nmnmnmnmnmnmnm0.7700.7050.7450.8340.7560.7780.7060.7170.7540.70088ö135ö172önmnmnmnmnmnmnm59ö75ö83önmnmnmnmnmnmnm0.3420.0840.0610.2790.1710.3530.1700.1340.3570.1650.5230.2920.2370.4890.2550.5170.3410.2760.5390.3000.1030.0020.0010.0690.0260.1150.0150.0100.0900.0120.2310.0590.0400.2430.0570.2120.0890.0640.2020.0642.512.502.682.662.520.790.710.490.670.62nmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnmnm0.6870.7150.8190.7500.753nmnmnmnmnmnmnmnmnmnm0.2240.2670.2300.3210.2840.3770.4460.3870.4580.4600.0290.0590.0340.0820.0740.1350.1910.1290.1940.2012.452.592.622.582.580.740.560.520.810.7533.1§48.0§31.2§18.8§16.6§36.3§28.3§28.9§37.6§46.8§30.6§23.7§39.9§43.6§36.6§4.4§3.2§8.1§0.6§0§0.6970.7830.8020.6850.708100ö158ö163ö86ö94ö70öö126öö128öö58öö65öö0.1410.0870.1030.1950.1960.3320.1610.2070.3200.3470.0200.0120.0140.0290.0320.1100.0400.0510.0800.091NishiTokyo2.630.7725.652.122.300.71072530.1400.3700.0190.120Fukushima 1Fukushima 2Fukushima 32.352.562.710.510.650.6431.643.049.247.236.641.520.919.68.80.50.80.90.7800.7400.760127971068476710.2900.2600.2100.4600.4100.3600.0500.0600.0400.1500.1500.130SoilTsumagoiTsumagoiTsumagoiTsumagoiTsumagoiTsumagoiTsumagoiTsumagoiTsumagoiTsumagoiMiuraMiuraMiuraMiuraMiuraKyushuKyushuKyushuKyushuKyushu123456789101234512345Liquid PlasticlimitlimitpF 2pF 4.1 (4.2)õ pF 2pF 4.1 (4.2)õõMeasurements of soilwater retention and Dp were done at pF 4.1 for NishiTokyo and Fukushima volcanic ash soils, and at pF 4.2 for Tsumagoi,Miura, and Kyushu volcanic ash soils.* Sand, silt and clay fractions of NishiTokyo and Fukushima soils were classied according to Japan Geotechnical Society (JGS) while other soilswere classied according to International Society of Soil Science (ISSS).§Data from the Department of Environmental Chemistry, National Institute of AgroEnvironmental Sciences (1976).öData from Wada (1986).ööData from Osozawa (1998).nmnot measuredNew Data Representing Dierent Compaction LevelsIn the present study, disturbed soil was also collected atthe same soil site in NishiTokyo. The disturbed soil waspassed through a 2mm sieve and repacked onto 100 cm3soil cores (in triplicate) at bulk densities of 0.6, 0.7, and0.73 Mg m|3, thus representing three dierent levels ofuniaxial compaction. Soilwater retention and Dp weremeasured on these repacked samples at pF 1, 1.5, 1.8, 2,2.3, 3, 4.1, and 6 (airdry condition).Measurement MethodsFor all data sets, the same experimental methods formeasurements of soilwater retention and Dp were used.Soilwater retention was measured using a drainingcurve, using either a hanging water column for pFÃ2(i.e., cÆ|100 cm H2O) or a pressure plate extractor forpFÀ2 (i.e., cº|100 cm H2O). Resurreccion et al.(2007a, b), however, used only the pressure plate extractor across the entire pF interval. Firstly, soil core sampleswere immersed in a basin containing water (treated withsodium azide, NaN3, to prevent fungal growth) tosaturate the soil samples by capillary action. Soil sampleswere kept for 5 to 7 days at a constant water level around2¿5 mm below the upper edge of the soil core. Aftersaturation, the soil samples were then drained subsequently to dierent pF conditions where Dp was measuredat each drainage step. Before measurements of Dp, soilsamples were weighed to determine the soilwater contentat each pF. For soil samples successfully measured for Dpat air and ovendry conditions, the samples were placedinside a convective airow oven which was set at 209Cfor 5 to 7 days for airdry condition, and at 1059C for 2days for ovendry condition.The soilgas diusion coecients (Dp) were measuredby the method of Currie (1960) as recommended by Rolston and Moldrup (2002). The apparatus uses a diusionchamber with oxygen as the experimental gas at 209C (seeFig. 1). The diusion chamber was ushed with 100znitrogen gas while the upper end of the soil core was exposed to the atmosphere. Once the slide plate is opened toestablish contact between soil sample and diusion chamber, oxygen from the atmosphere diuses through the soilsample into the diusion chamber while nitrogen gasdiuses through the soil sample into the atmosphere. The400RESURRECCION ET AL.Dp (va)10/3DoF2(5)SoilWater Characteristic (SWC) Based ModelsThe recent Dp(va)/Do models developed by Moldrup etal. (1996, 1999, 2000, 2005a) linked soilgas diusivity tosoil type through the pore size distribution (PSD)parameter b by using the Campbell (1974) soilwaterretention model,Ø»cuce u sFig. 1. Schematic diagram of the experimental apparatus used tomeasure soilgas diusion coecient, Dpoxygen concentration inside the diusion chamber wasmeasured using an electrode sensor. Oxygen consumption in the soil samples was considered negligible for theshort measurement time (Schjønning, 1985). Mixing ofair within the small diusion chamber was assumed to occur instantly. The calculation of the soilgas diusioncoecient, Dp, was done according to Rolston and Moldrup (2002).MODELS FOR SOILGAS DIFFUSIVITYSoilType Independent ModelsBuckingham (1904) suggested that the soilgas diusion coecient depends on soilair content following apowerfunction,Dp(va)XDo(1)Buckingham suggested the Buckingham exponent X approximately equals to 2 based on measurements of Dp onsand, loam, and clay soils.The Penman (1940) model assumed a linear variationof Dp/Do with soilair content,Dp0.66vaDo(2)Call (1957) modied the Penman model by assuming10z of the total soil volume consisted of isolated (inactive) airlled pores. This model successfully describedthe diusion of ethylene dibromide in a sandy loam soil.The Call (1957) Dp/Do model is given as,Dp0.66(va|0.1)DoDp (va)2Do F2/3(4)where F is the soil total porosity (m pore space m soil).The Millington and Quirk (1961) Dp(va)/Do model is,3|3(6)where c is the soilwater matric potential (cm H2O), ce isthe airentry potential (cm H2O), u is the volumetric soilwater content (m3 m|3), us is the soilwater content atsaturation (m3 m|3), and b (À0) is the slope of the SWCcurve in a log (|c) versus log (u) plot. The SWCbasedDp(va)/Do models include the BuckinghamBurdineCampbell (BBC) model (Moldrup et al., 1999), the va, 100dependent (macroporositydependent) model (Moldrup etal., 2000), and the ThreePorosity Model (TPM, Moldrup et al., 2004).The BBC Dp(va)/Do model (Moldrup et al., 1999) is,Ø »vaDpF2DoF2{3b(7)where the expression, F2, is a reference gas diusivity atcompletely dry conditions, following Buckingham(1904). The exponent 2{3/b is analogous to the Burdine(1953) capillary tube model for unsaturated hydraulicconductivity.The va, 100dependent Dp(va)/Do model (Moldrup et al.,2000) is,Ø »Dpva(2v3a, 100{0.04va, 100)Dova, 1002{3b(8)where va, 100 is reference soilair content equal to theamount of pore space at soilwater matric potential ofc|100 cm H2O. In Eq. (8), an empirical relationbetween gas diusivity at c|100 cm H2O and themacroporosity (va, 100) replaces the Buckingham expression in the BBC model (F2 in Eq. (7)).Moldrup et al. (2004) combined the BBC (Eq. (7)) andthe macroporositydependent (Eq. (8)) Dp/Do models toreduce the necessary parameter input from soilwaterretention data yielding the ThreePorosity Model (TPM).The TPM is given as,Ø»vaDpF2DoF(3)Millington and Quirk (1960, 1961) used a mechanistic approach to develop nonlinear Dp(va)/Do models. The Millington and Quirk (1960) Dp(va)/Do model is given as,|bXT(9)where XT is a tortuosityconnectivity factor calculated as,logX TØ 2v3a, 100{0.04va, 100F2va, 100logFØ »»(10)TWO SOILWATER RETENTION POINTS IN UNSATURATED VOLCANIC ASH SOILSNew TwoRetentionPoint (2RP) ModelTo develop a simpler and easily applicable gas diusivity model, we consider a linear socalled PenmanCalltype Dp(va)/Do model (Moldrup et al., 2005a),DpC(va|va, th)Doif vaÆva, th(11a)Dp0Doif vaºva, th(11b)where C is the slope of the linear Dp(va)/Do model, andFig. 2. Plot of the soilgas diusivity against soilair content forTsumagoi and NishiTokyo volcanic ash soils. A linear t to eachDp/Do data set and the Millington and Quirk (MQ, 1961) model,Eq. (5), are also shown401va, th is the threshold soilair content below which soilgasdiusivity becomes negligible (ceases due to the inactiveor remote airlled pore space created by interconnectedwater lms). Both C and va, th are likely dependent on soilpore size distribution (i.e., soilwater retention) and soilstructure (e.g., aggregation) (Moldrup et al., 2005a).Figure 2 shows measurements of Dp on two undisturbed soil samples from NishiTokyo and Tsumagoi,supporting a highly linear relation between Dp/Do and va,starting from the threshold soilair content (va, th) up tothe airdry soil moisture condition. This linear behaviorof Dp(va)/Do was also observed for all NishiTokyo andFukushima undisturbed soils, as already reported byResurreccion et al. (2007a, b), and on the 20 data setsfrom Osozawa (1998).Since the PenmanCall type Dp(va)/Do modelrepresents a linear function of va, only two points (i.e.,vaDp/Do coordinates) on the prediction line are sucientto derive the model parameters (slope C and interceptva, th). In order to dene the prediction line, it is necessaryto estimate the gas diusivities at two appropriatelyselected values of va based on the soilwater retentioncurve. In this study, the Buckingham (1904) power function vXa , is used to estimate the Dp/Do values at the twochosen values of soilair content.For the classical Buckingham (1904) powerlaw modelto accurately estimate Dp/Do the Buckingham exponentX has to vary with va and, thus, with soilwater matricpotential (pF), as illustrated in Fig. 3(a) for the soilmoisture conditions at pF 3 and 6. Data for threeFukushima soils with Dp measured up to airdry condition suggested that X has to vary symmetrically with soilwater matric potential (expressed as pF) with a minimumFig. 3. (a) Plot of Dp/Do against soilair content for 13 intact volcanic ash soil samples from Fukushima 05 cm, 1520 cm and 5560 cm depths atsoilwater matric potentials of pF 3 and 6 (airdry, as lled out symbols). The Buckingham (1904) Dp/Do powerlaw model tted to the Dp/Dodata at pF 3 and 6 is also shown. (b) Plot of the average of Buckingham exponent (X) values at each pF measurement for three Fukushima soillayers. The symmetric X(pF) function tted to the average XpF data (excluding data at pF 1) in this study (solid line) and to individual soilfrom Fukushima are also shown. Data from Resurreccion et al. (2007b)402RESURRECCION ET AL.(va, 4.1)2.3|(va, 2)2.3va, 4.1|va, 2(12)Cwhere va, 2 and va, 4.1 are soilair content values at pF 2 and4.1, respectively. The threshold soilair content, va, th, iscalculated as,Øva, thva, 4.1 1|Fig. 4. Model concept for the tworetentionpoint (2RP) soilgasdiusivity model, Eq. (11). The Dp/Do values at the two soilwaterretention points are estimated from the Buckingham (1904) powerlaw model, vXa , assuming the same value of X2.3 at both retention pointsX value occurring at around pF 3 (Fig. 3(b)). This soilwater matric potential (pF 3) was suggested as the soilwater retention point where separation between interand intraaggregate pore space region takes place(Kawamoto and Aung, 2004). At this pF condition, maximum continuity (connectivity) of airlled pore spacelikely occurs because voids between aggregates are almostcompletely drained eliminating the interconnected waterlms between waterlled aggregates resulting in a minimum water blocking eect (and, therefore, minimum Xvalue). This is in agreement with the Dp/Do data of Moldrup et al. (2005b) for 44 dierently textured undisturbedsoils.Figure 4 illustrates the proposed linear Dp/Do modelnamed as the TwoRetentionPoint (2RP) Dp/Do model.Two va values from the soilwater retention curve wereselected at the soilwater matric potential conditions ofpF 2 (c|100 cm H2O) and pF 4.1 (c|12600 cmH2O). The soilmoisture condition at pF 2, where largepores larger than 30 mm are likely to be drained, is closeto the natural eld capacity for a wide range of soils(Beukes, 1987). The soilmoisture condition at pF 4.1 isclose to the wilting point condition where water becomesunavailable for the plants to use (Hillel, 1998; So, 1998).The two pF values near eld capacity and wilting pointconditions typically correspond to va values that are farfrom each other. This reduces the prediction error propagated across the entire va values when the Dp/Do values atpF 2 and 4.1 are slightly under or overestimated by theBuckingham Dp/Do powerlaw model, vXa . Following thetted symmetric XpF function in Fig. 3(b), the same Xvalues (2.3) at both pF 2 and 4.1 were used in the Buckingham (1904) powerlaw model leading to the derivationof the expression for the slope C of the 2RP Dp/Do modelas,(va, 4.1)1.3C»(13)where the expression inside the parenthesis in Eq. (13) isthe fraction of airlled pores less than 0.2 mm that constitutes the threshold soilair content for soilgas diusion.In order to use the 2RP Dp/Do model, values of va, 2 andva, 4.1 have to be either measured or estimated. When measurements are not available, the soilair content at pF 2(va, 2) can be deduced from the soilwater content at eldcapacity. The eld water capacity is the remaining soilwater content in the soil drained a few days after rainfallor irrigation (when free drainage is negligible). On theother hand, measurement of the soilair content at pF 4.1would require a pressure plate apparatus to drain the soilto near wilting point conditions. However, with limiteddata, the soilair content at pF 4.1 can be estimated usingpedotransfer functions from clay, silt, and sand fractions(Givi et al., 2004).The soilwater retention hysteresis aects the calculation of the soilair content both at pF 2 and pF 4.1.However, in this study, the new 2RP model is developedbased on the soilair content calculated from the maindrying curve of soilwater retention. The eect of hysteresis on the conguration of the airlled pore connectivityis outside the scope of this paper and should be furtherstudied.Statistical AnalysesTo compare the dierent predictive Dp/Do models, theroot mean square error (RMSE, Eq. (14)) was used forthe best overall t compared to measured data.RMSE1nnS (d )i1i2(14)where di is the dierence between the predicted and themeasured values of Dp/Do at a given soilair content, andn is the number of measurements.RESULTS AND DISCUSSIONModel TestsThe performances of the soiltype independent (Eqs.(1) to (5)), the SWCbased (Eqs. (7) to (10)) and the 2RP(Eq. (11) with Eqs. (12) and (13)) Dp(va)/Do models testedagainst the Dp measurements in this study (24 volcanicash soils with a total of 424 data points) are shown in Fig.5 and Table 2. For the 20 soils from Osozawa (1998), thesoilair content at pF 4.2 was used in Eqs. (12) and (13) asva, 4.1 since measurements at pF 4.1 were not available.In general, the traditional soiltype independent andSWCbased Dp(va)/Do models largely overestimatedTWO SOILWATER RETENTION POINTS IN UNSATURATED VOLCANIC ASH SOILS403Fig. 5. Scatterplot comparison of predicted and measured gas diusivities (24 soils, 424 data points). Test of (a) Buckingham(1904), Eq. (1), (b)Penman (1940), Eq. (2), (c) Call (1957), Eq. (3), (d) Millington and Quirk (MQ, 1960), Eq. (4), (e) Millington and Quirk (MQ, 1961), Eq. (5), (f)the BuckinghamBurdineCampbell (BBC), Eq. (7), (g) Macroporositydependent, Eq. (8), (h) TPM, Eq. (9 and 10), and (i) the tworetentionpoint (2RP), Eq. (11, 12, 13), Dp/Do models. Data are from Osozawa (1998) and Resurreccion et al. (2007a, b)Table 2. Test of ten predictive gas diusivity models against Dp/Dodata for 24 soils (424 data points) used in this study. Root MeanSquare Error (RMSE, Eq. (14)) is given for each model for all dataas well as for data divided into pFÃ3 and pFÀ3Dp/Do ModelBuckingham (1904)EquationNumber(1) withX2(2)(3)(4)(5)Penman (1940)Call (1957)Millington and Quirk (1960)Millington and Quirk (1961)BuckinghamBurdineCampbell, BBC(7)Moldrup et al. (1999)Macroporositydependent(8)Moldrup et al. (2000)ThreePorosity Model, TPM(9, 10)Moldrup et al. (2004)Modied Buckingham(1) with(this study)X2.3TwoRetentionPoint, 2RP(11, 12, 13)(this study)RMSEAll data pFÃ3 pFÀ30.0600.021 0.1080.1110.0550.0910.0810.0980.0430.0310.0330.0560.017 0.1010.0520.017 0.0940.0580.017 0.1050.0480.018 0.0850.0260.017 0.0420.1370.0770.1630.143measured Dp values at air and ovendry conditions (Fig.5(a)(h)). At pFº4.2, the classical Penman (1940), Call(1957), and Millington and Quirk (1960) Dp(va)/Domodels overestimated Dp/Do data (Fig. 5(b)(d)) whilethe commonly applied Millington and Quirk (1961)Dp(va)/Do model underestimated measured gas diusivities (Fig. 5(e)).The original Buckingham Dp(va)/Do model, Eq. (1),performed surprisingly well in predicting Dp/Do values(RMSE0.060, Fig. 5(a) and Table 2). When X was modied to 2.3, signicant improvement in the predictionperformance of the Buckingham Dp(va)/Do model wasobtained, reducing the RMSE to 0.048. The performanceof the Buckingham vXa model, with X2.3, became comparable to the performance of the SWCbased Dp(va)/Domodels (BBC with RMSE0.056, the va, 100dependentmodel with RMSE0.052, and TPM with RMSE0.058; see Fig. 5(f)(h) and Table 2).The 2RP Dp(va)/Do model well captured the linearDp(va)/Do behavior across the entire soil moisture conditions (RMSE0.026, Fig. 5(i) and Table 2). In contrastto the nonlinear, SWCbased Dp/Do models, no large404RESURRECCION ET AL.Fig. 6. Plot of gas diusivity against soilair content for individual undisturbed samples from (a) Tsumagoi, (b) Fukushima 05 cm depth and (c)NishiTokyo having decreasing soil total porosity values. The Millington and Quirk (MQ, 1961) model (Eq. (5)), the BuckinghamBurdineCampbell (BBC) model (Eq. (7)), and the tworetentionpoint (2RP) model, Eqs. (11), (12), (13), are also shownprediction errors at high soilair content were observed.Resurreccion et al. (2007a) suggested that the much lowermeasured Dp values at pFÀ4.1 compared to thosepredicted by the SWCbased power law Dp/Do modelswere due to an increase in tortuosity for soilgas diusionin the remote airlled pore space within the soil aggregates when soil samples were drained past pF 3.Eects of Soil Compaction on Gas DiusivityThree individual undisturbed volcanic ash soils fromTsumagoi, Fukushima, and NishiTokyo shown in Fig.6(a)(c) dier in bulk density and porosity due to dierent soil compaction conditions. The 2RP Dp/Do modelperformed better than the MQ (1961) and the SWCbasedBBC Dp/Do models, as also suggested in Fig. 5. Further,the values of the threshold soilair content, va, th, were observed to increase with increasing slope C, consistent withthe derived expression for va, th (Eq. (13)).An increase in bulk density due to soil compactionreduces the amount of total pore space, and consequentlydecreases the continuity of airlled pores primarily in theinteraggregate pore space region. Osozawa (1998) hasshown for a volcanic ash soil compacted at 50, 100, and200 kPa that uniaxial compaction mainly reduces typically larger pores (macropores) À30 mm, i.e., mainlyreduces interaggregate pores without reducing the intraaggregate porosity. This results in water blocking eectsbetween aggregates at wet conditions, giving low valuesof slope C and va, th at high bulk density, in agreementwith data for the three dierently compacted soils in Fig.6(a)(c).To illustrate the eect of soil compaction, a model sensitivity analysis using the 2RP model to predict Dp at airdry condition under increasing soil dry bulk density (rd)by using a Tsumagoi sample (particle density, rs, of 2.41Mg m|3, bulk density of 0.4 Mg m|3, and macroporosity, va, 2, of 0.28 m3 m|3; see Table 1) is shown in Fig. 7.The relation between soil dry bulk density (rd) and soiltotal porosity (F) is given byFig. 7. Eect of uniaxial compaction on soilgas diusivity at pF 6(airdry). The compaction was assumed to aect only the macropores, va, 2, between aggregatesF1|rdrs(15)The analysis assumes that the increase in bulk density (rd)due to uniaxial compaction reduces the total porosity calculated following Eq. (15). The change in the total porespace, F, is reected only on the reduction of larger interaggregate pores, va, 2. Further, since the intraaggregatepores are not likely aected by soil compaction, thedierences between va, 4.1 and va, 2 and between va, 6 (airlled porosity at pF 6) and va, 4.1 were kept constant andassumed equal to 0.2 m3 m|3 (i.e., from the initial dierence in soilair content in between pF 2 and pF 4.1 and inbetween pF 4.1 and pF 6 for the Tsumagoi sample). Theanalysis showed that the slope C and intercept va, thdecreased with increase in rd, and consequently decreasedthe calculated value of Dp at pF 6, in full agreement withthe measurements for the three volcanic ash soils in Fig.6(a)(c).The variation of C and va, th with bulk density and thedecrease in Dp at pF 6 (airdry condition) shown in Fig. 7TWO SOILWATER RETENTION POINTS IN UNSATURATED VOLCANIC ASH SOILS405Fig. 8. Plot of gas diusivity against soilair content for three repacked volcanic ash soils from NishiTokyo at (a) 0.6, (b) 0.7 and (c) 0.73 Mg m|3dry bulk densities. The Millington and Quirk (MQ, 1961) model (Eq. (5)), the BuckinghamBurdineCampbell (BBC) model (Eq. (7)), and thetworetentionpoint (2RP) model, Eqs. (11), (12), (13), are also shownis supported by the measurements of Dp on repackedNishiTokyo volcanic ash soil compacted at three bulkdensities, seen in Fig. 8. Similar to the observations inFig. 6(a)(c) and what is suggested by the model sensitivity analysis in Fig. 7, the slope C and va, th decreased asbulk density increased. The decrease of C and va, th withthe increase in rd implies that at a given soilair contentwithin intermediate soilmoisture conditions (i.e., exceptat high soilair contents) the soilgas diusivity increasedwith a decrease in bulk density. This is in agreement withCurrie (1984) and further supported by the ndings ofFujikawa and Miyazaki (2005) based on measurementson repacked volcanic ash soil within the range of soilaircontent vaº0.4 m3 m|3.Lastly, the new 2RP model predicted excellently themeasured Dp values on repacked NishiTokyo volcanicash soils at three dierent bulk densities (Fig. 8), whilethe widely used MQ (1961) and BBC Dp/Do models performed poorly. Thus, the new 2RP model seems promising for predicting gas diusivities across moisture conditions (from wet to dry) in both noncompacted and compacted volcanic ash soils.CONCLUSIONSIn this study, we developed an easily applicable, linearsoilgas diusivity model that uses only two points on thesoilwater retention curve. The performance of this socalled 2RP Dp/Do model proved superior to the widelyused Millington and Quirk (1961) and to nonlinear Dp/Domodels that require the full range of soilwater retentiondata.The 2RP model was tested for Japanese Andisols within the following parameter intervals: 0.68¿0.78 totalporosity (m3 pore space m|3 soil), 0.57¿0.81 bulk density (Mg dry soil m|3 soil), and less than 20 percent soilorganic matter.As illustrated by both the new model and gas diusivitymeasurements, soil compaction has a large eect on gasdiusivity in volcanic ash soils because of a decrease inthe void space, mainly taking place between aggregates.We recommend the use of the new 2RP Dp/Do modelfor prediction of gas diusivity and calculation of gasdiusive transport in volcanic ash soils, especially underdry moisture conditions where the 2RP model is signicantly more accurate than previous models while requiring the same or less data input.ACKNOWLEDGEMENTThis study was made possible by the GrantInAid forScientic Research no. 18360224 from the Japan Societyfor the Promotion of Science (JSPS) and by a grant fromthe Innovative Research Organization, Saitama University. This study was in part supported by the projects GasDiusivity in Intact Unsaturated Soil (``GADIUS'') andSoil Infrastructure, Interfaces, and TranslocationProcesses in Inner Space (``Soilitis'') from the DanishResearch Council for Technology and ProductionSciences. We would like to acknowledge the supportfrom the University of the PhilippinesDiliman.REFERENCES1) Beukes, D. J. (1987): Comparison between hydraulic conductivityand related properties of a ne sand and a ne sandy loam duringinsitu drainage, South African J. Plant and Soil, 4, 151158 (inAfrikaans with English summary).2) Buckingham, E. (1904): Contributions to our knowledge of the aeration of soils, USDA. Bur. Soil Bul., 25, U.S. Gov. Print. Oce,Washington, DC.3) Burdine, N. T. (1953): Relative permeability calculations fromporesize distribution data, Trans. AIME, 198, 7178.4) Call, F. (1957): Soil fumigation: V, Diusion of ethylene dibromidethrough soils, J. Sci. Food Agric., 8, 143150.5) Campbell, G. S. 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ログイン | |||||
タイトル | Effects of Water Content Distribution on Hydraulic Conductivity of Prehydrated GCLs against Calcium Chloride Solutions | ||||
著者 | Takeshi Katsumi・Hiroyuki Ishimori・Atsushi Ogawa・Satoshi Maruyama・Ryoichi Fukagawa | ||||
出版 | Soils and Foundations | ||||
ページ | 407〜417 | 発行 | 2008/06/15 | 文書ID | 21117 |
内容 | 表示 SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 407417, June 2008EFFECTS OF WATER CONTENT DISTRIBUTION ONHYDRAULIC CONDUCTIVITY OF PREHYDRATED GCLSAGAINST CALCIUM CHLORIDE SOLUTIONSTAKESHI KATSUMIi), HIROYUKI ISHIMORIii), ATSUSHI OGAWAiii),SATOSHI MARUYAMAiii) and RYOICHI FUKAGAWAiv)ABSTRACTWhen geosynthetic clay liners (GCLs) are applied as bottom liners at waste containment facilities, they are naturallyprehydrated by absorbing moisture in the underlying base layers. In order to evaluate the eects of cations contained inwaste leachates, this study investigated the eects of the water content distribution of the GCLs prehydrated with actual soils on their hydraulic conductivities against CaCl2 solutions. The ``prehydration tests'', which were conductedprior to the hydraulic conductivity tests, showed that the water content distribution of the prehydrated GCLs dependson the properties of the GCLs and the base layers. In particular, drastic dierences between GCLs with powdered bentonite and GCLs with granular bentonite were observed in the prehydration water content and its distribution. Prehydrated GCLs with powdered bentonite had a higher water content and a more homogenous distribution than thosewith granular bentonite. The hydraulic conductivity tests showed that most of the prehydrated GCLs exhibit a lowhydraulic conductivity of k§1.0~10|8 cm/s against CaCl2 solutions with 0.10.5 M. However, GCLs with granularbentonite may be dicult to homogeneously prehydrate and exhibit an unstable hydraulic conductivity, which variesfrom k2.9~10|9 cm/s to k1.5~10|6 cm/s. The homogeneity of the water content distribution has been considered an important factor to obtain a required barrier performance under prehydration conditions, which are naturally generated in actual sites.Key words: chemical resistance, geosynthetic clay liner, hydraulic conductivity, prehydration (IGC: D4)mechanical behavior involved in overlapping and partialdeformation (Barroso et al., 2006; Daniel et al., 1997;Dickinson and Brachman, 2006; Giroud et al., 2002;LaGatta et al., 1997; Rowe and Orsini, 2003; TouzeFoltzet al., 2006; Viswanadham et al., 1999), the transportproperties of chemical solutions (Lake and Rowe, 2000,2004), the hydraulic conductivity against chemical solutions and longterm stability (Jo et al., 2001; Katsumi etal., 2005, 2007; Kolstad et al., 2004a; Petrov and Rowe,1997; Ruhl and Daniel, 1997; Shackelford et al., 2000;Shan and Lai, 2002), and so on. Although most of thesereports focus on the performance evaluation of the GCLsthemselves, few reports investigate the eects of geological and hydrological conditions in actual sites on the performance of the GCLs.Prehydration is one factor that aects the barrier performance of GCLs in actual sites. Prehydration hydratesthe bentonites in the GCLs before exposing to chemicalsolutions such as waste leachates. Because chemical solutions seriously deteriorate the swelling capacity and barriINTRODUCTIONGeosynthetic clay liners (GCLs) are manufactured clayliners, which consist of a thin layer of bentonite glued to ageomembrane or encased by geotextiles. Due to their relatively low cost, easy installation, longterm stability,deformability, and excellent barrier performance towater, GCLs are eective barrier materials that can beused as alternatives or combined with previous barriermaterials. Thus, GCLs have been used all over the worldfor various applications such as to seal ponds, lagoons,and landlls.GCLs are increasingly being used as a component ofpresent bottom liner systems in waste containment facilities. However, basic performance and fundamental factors in addition to estimating the performance in thepeculiar conditions of a waste containment facility mustbe considered when designing a bottom liner system.Many researchers have studied the performance of GCLsin a laboratory setting; for example, the hydraulic andi)ii)iii)iv)Associate Professor, Graduate School of Global Environmental Studies, Kyoto University, Japan (tkatsumimbox.kudpc.kyotou.ac.jp).Department of Civil Engineering, Ritsumeikan University, Japan.Formerly Graduate Student, ditto.Professor, ditto.The manuscript for this paper was received for review on June 29, 2007; approved on April 8, 2008.Written discussions on this paper should be submitted before January 1, 2009 to the Japanese Geotechnical Society, 4382, Sengoku,Bunkyoku, Tokyo 1120011, Japan. Upon request the closing date may be extended one month.407408KATSUMI ET AL.er performance of bentonites (Laird, 2006; Norrish,1954; Norrish and Quirk, 1954; Posner and Quirk, 1964;Rowe, 1998, 2005; Rowe et al., 2004; Slade and Quirk,1990; Slade et al., 1991), prehydration has been considered an eective measure for improving barrier performance and chemical resistance of bentonites (Daniel etal., 1993; Lee and Shackelford, 2005; Shackelford, 1994;Vasko et al., 2001). When GCLs are applied to bottomliners at waste containment facilities, the GCLs are naturally prehydrated because the bentonites in the GCLs absorb moisture in the underlying base layer on which theGCLs are installed.It is important to clarify the prehydration eects on thehydraulic conductivity of the entire prehydrated GCL inorder to improve the design of bottom liner systems inwaste containment facilities. However, limited data onthe barrier performance of GCLs naturally prehydratedon an unsaturated base layer soil has been reported. Thisstudy aims to investigate (1) the heterogeneity of thewater content distribution of prehydrated GCLs, (2) thehydraulic conductivity of the prehydrated GCLs againstCaCl2 chemical solutions, and (3) the relationship between the water content distribution and the hydraulicconductivity of the prehydrated GCLs.BACKGROUNDWhen GCLs are used as hydraulic barrier materials tocontain chemical substances, barrier performance deterioration must be closely monitored. The barrier performance of GCLs directly exposed to leachates at wastecontainment facilities deteriorates because the bentonitein GCLs has insucient swelling against electrolyticchemical solutions. It has been reported that the hydraulic conductivity value increases as the concentrationand/or ionic valence of the electrolytic solution increases(Jo et al., 2001; Katsumi et al., 2007; Kolstad et al.,2004a; Shan and Lai, 2002). Because deterioration is dueto such chemical attacks, many researchers have developed and proposed methods to improve the chemicalresistance of GCLs. Some methods include (1) to usechemical resistance bentonites (Katsumi et al., 2006,2008; Kolstad et al., 2004b, 2006; Lo et al., 1994, 1997;Onikata et al., 1996, 1999a, 1999b; Trauger and Darlington, 2000; Lo and Yang, 2001; Gates, 2004; Gates et al.,2004; Yang and Lo, 2004), (2) to hydrate bentonites before exposing to chemical solutions (Daniel et al., 1993;Lee and Shackelford, 2005; Shackelford, 1994; Vasko etal., 2001), and (3) to conne bentonites with a highereective pressure (Katsumi et al., 2005; Petrov and Rowe,1997).Hydrating bentonites before exposing to chemical solutions is called ``prehydration''. Bentonites prehydratedwith pure water have been considered to have a lowerhydraulic conductivity to chemical solutions than nonprehydrated bentonites (Daniel et al., 1993; Lee andShackelford, 2005; Vasko et al., 2001). These reportsrepresent the necessary water contents to satisfy the required barrier performance. For example, Bonaparte etal. (1996) have considered that the prehydration watercontent of GCLs exhibits 40100z in actual sites, butthey did not show the hydraulic conductivity values of theprehydrated GCLs. Moreover, Vasko et al. (2001) haveinvestigated the water content and its distribution of theprehydrated GCLs, and then evaluated the hydraulic conductivity values. However, their GCL prehydrationmethod diers from the actual process that GCLs absorbmoisture from the unsaturated base layers; they usedlter papers instead of the base layers. Hence, it shouldbe claried how prehydration eects induced in actualsites inuence the water content distribution, itshomogeneity, and the hydraulic conductivity of GCLs.Although Lee and Shackelford (2005) showed thehydraulic conductivity of prehydrated GCLs againstchemical solutions, the prehydrated GCLs were preparedby permeating the fresh water into them in the apparatusfor the hydraulic conductivity tests before permeating thechemical solutions.These reports are not applicable when bentonitematerials are heterogeneously prehydrated. Even if thesuciently swelled parts included in the heterogeneouslyprehydrated bentonite material can exhibit the lowhydraulic conductivity, the insuciently swelled parts exhibit the high hydraulic conductivity so that the hydraulicconductivity of the entire bentonite material with theheterogeneous water content distribution becomes high.In the base layer at real sites, GCLs are rarely prehydrated without heterogeneity of the water content distribution. Thus, it is necessary to investigate the barrier performance of GCLs prehydrated on a base layer soil considering the real prehydration process.EXPERIMENTAL METHODSTo investigate the prehydration eects on barrier performance of GCLs, a prehydration test was initially conducted to prepare the prehydrated GCLs before thehydraulic conductivity test. Fortynine GCL specimenswere prehydrated under the various testing conditions.Among the 49 GCL specimens, 25 specimens were usedfor the hydraulic conductivity test to evaluate thehydraulic conductivity, while others were used to evaluate the water content distribution (in particular, theaverage and the heterogeneity of its distribution) of theGCLs. Finally, the prehydration eects on the barrierperformance of GCLs were discussed by relating thewater content distribution of a GCL to its hydraulic conductivity. Detailed experimental conditions and methodsare described below.Materials UsedTwo types of GCLs where sodium bentonite was encapsulated between a polypropylene woven geotextile anda polypropylene nonwoven geotextile by needlepunchingbers were used. One had powdered bentonite (BentoxNPS 49001), while the other had granular bentonite(Bentox NPS 49002). The mass per unit area of eachGCL was 4.73 kg/m2 (the data provided by the manufac409PREHYDRATION EFFECT ON GCLSTable 1.Properties of bentonites in GCLs usedPropertyUnitStandardSoil particle densityNatural water contentPlastic limitLiquid limitHydraulic conductivitySwell indexMethylene blue consumptionChemical compositionSiO2Al2O3Fe2O3TiO2CaOMgOK2ONa2OP2O5MnOIgnition loss[g/cm3][z][z][z][cm/s][mL/2 gsolid][mmol/100 g]JIS A 1202JIS A 1203JIS A 1205JIS A 1205ASTM D 5084ASTM D 5890JBAS 107 91JIS M 8853[z][z][z][z][z][z][z][z][z][z][z]Powderedbentonite GCLGranularbentonite GCL2.83910.0251.0619.52.24~10|933.0104.02.8038.5052.2630.06.71~10|928.059.6518.297.150.412.023.140.462.600.130.016.1562.5320.524.550.161.202.430.522.380.050.005.66turer), and the initial thickness was 6.07.0 mm. Table 1summarizes the basic properties.Prehydration TestPrehydration tests were conducted (1) to prepare theprehydrated GCLs before the hydraulic conductivity testand (2) to evaluate the eects of the prehydration condition on the water content distribution. Figure 1 shows theapparatus for the prehydration test. In order to focus onthe prehydration process generated at an actual site, thistest simulated a process where an installed GCL washydrated by absorbing moisture from base layer soil.The following procedure was used. According to JIS A1210, Toyoura sand or decomposed granite soil wascompacted at a water content (15z or 20z) using a compaction test mold, which measured 10 cm in diameter,12.7 cm in height, and 1,000 cm3 in volume. Table 2 andFig. 2 show the basic properties of Toyoura sand anddecomposed granite soil. The water retention curves wereevaluated according to JGS 01512000, ``Test Methodfor Water Retentivity of Soils''. The compacted soil wasremoved to an acrylic mold, which had a 10 cm diameterand 15 cm height, and was used as the base layer of theprehydration test. Next, the GCL was trimmed to a 10 cmdiameter and then it was placed on the base layer with aconning pressure of 5 kPa. The acrylic mold with thebase layer was placed in a water tank, which was 60 cm inwidth ~30 cm in depth ~35 cm in height, with orwithout a water level of 1 cm as water supply source, andthe tank was closed. Following this, the tank was placedin a constant temperature room controlled at 209C. Theprehydrated GCL was prepared by removing from theacrylic mold after the GCL was hydrated for a curingperiod of Æ7 days. Total number of the GCLs subjectedto various conditions of prehydration was 49 as listed inTable 3.After the prehydration test, 25 specimens of the preFig. 1.Apparatus for prehydration testhydrated GCLs were used for the hydraulic conductivitytest as shown in the following subsection, while otherswere used to investigate the water content distribution.The water content distribution was evaluated by measuring the water content values of 16 species of a prehydrated GCL, which is divided as shown in Fig. 3. From theirwater content values, the average, wave, and the standarddeviation, wstd, the coecient of variation, dcov, were evaluated as follows:wavewstd1nnSwi11nwstdwavedcov(1)inS (w |wi1iave)2(2)(3)where n is the number of the sampling species (n16 inthis study). The average water content distribution, wave,indicates the prehydration water content, and thecoecient of variation in the water content distribution,dcov, indicates the heterogeneity of the distribution.410KATSUMI ET AL.Table 2.Properties of base layer soils usedPropertyUnitStandardToyoura sandDecomposedgranite soilSoil particle densityNatural water contentOptimum water contentHydraulic conductivitySoil pHElectric conductivitySoil particle size distribution2000Àmm200075 mm755 mmº5 mmChemical compositionSiO2Al2O3Fe2O3TiO2CaOMgOK2ONa2OP2O5MnOIgnition loss[g/cm3][z][z][cm/s][][S/m]JIS A 1202JIS A 1203JIS A 1210JIS A 1218JGS 0211JGS 0212JIS A 12042.6300.0517.001.42~10|28.040.022.6770.4510.903.73~10|57.930.020.00100.000.000.0015.6469.0612.692.6294.042.780.580.240.160.111.420.320.010.010.331.00Fig. 2[z][z][z][z][z][z][z][z][z][z][z][z][z][z][z]Water retention curves of base layer soilsHydraulic Conductivity TestTwentyve specimens of the GCLs prepared in theabove prehydration tests were used for the hydraulic conductivity test in order to discuss the prehydration eecton the barrier performance of GCLs against the permeation of chemical solutions. Calcium chloride solutionswith a molar concentration of 0.10.5 M were used as thepermeant liquids to clarify the prehydration eects on thehydraulic conductivity of GCLs: this concentration levelhas an inuence to deteriorate nonprehydrated GCLs(Katsumi et al., 2007). The hydraulic conductivity testwas conducted according to ASTM D 5084, ``StandardTest Methods for Measurement Hydraulic Conductivityof Saturated Porous Materials Using a Flexible Wall Permeameter''. Figure 4 shows the apparatus. The hydraulicJIS M 8853conductivity test was performed using a exiblewall permeameter with a cell pressure between 2030 kPa and anaverage hydraulic gradient of 90 in a constant temperature room controlled at 209C.To prepare the specimen, the prehydrated GCL was cutinto a diameter of 6 cm. Here the average and variance ofthe water content of the GCLs were indirectly estimatedfrom the water content values of the remaining bentonitepieces after this trimming. The prepared specimen wassandwiched between two lter papers attached with thewoven geotextiles, and placed in the apparatus. The sidesof the specimen were restrained with a rubber membrane,which received a hydraulic pressure of 2030 kPa by lling an outside cell with water so that the solution couldpermeate through the specimen without leaking out ofthe specimen. The hydraulic conductivity tests were continuously performed, and lasted at least a year to investigate the longterm change in the hydraulic conductivity.RESULTS AND DISCUSSIONWater Content Distribution after PrehydrationThe prehydration tests focused on evaluating the following eects: (1) the type of soil material used as thebase layer, (2) the initial water content of the soil, (3) thewater supply from the water table like groundwater, (4)the type of bentonite contained in the GCL, (5) the contact face, woven side or nonwoven side of the GCL, onthe base layer, and (6) the curing period during prehydration. Although the base layer is compacted under thesame condition according to JIS A 1210 in all the prehydration tests, the physical heterogeneity in the base layer also aects the prehydration eects. But, this studydoes not evaluate the eects of the heterogeneity in the411PREHYDRATION EFFECT ON GCLSTable 3.Results of prehydration testsPrehydration conditionBase layer typeTest No.#01#02#03#04#05#06#07#08#09#10#11#12#13#14#15#16#17#18#19#20#21#22#23#24#25#26#27#28#29#30#31#32#33#34#35#36#37#38#39#40#41#42#43#44#45#46#47#48#49ResultGCL type and curing conditionsNoteEnd of testingPrehydration water content1Soil type andits water contentSupply fromwater table?BentoniteformContactface withbase layerCuringperiod[day]wave [z]wstd [z]dcov []Toyoura sand (15z)NoNoYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesNoNoYesYesNoNoNoNoYesYesYesYesYesYesYesYesNoNoNoYesYesYesYesYesYesYesYesYesPowderedPowderedGranularGranularGranularGranularGranularGranularGranularGranularGranularGranularPowderedPowderedPowderedPowderedPowderedPowderedPowderedPowderedPowderedPowderedPowderedPowderedPowderedGranularPowderedPowderedPowderedGranularGranularPowderedPowderedPowderedPowderedPowderedPowderedGranularPowderedPowderedGranularGranularGranularPowderedPowderedPowderedPowderedPowderedPowderedWNWWWWWWWNWNWNWNWWWWWWNWNWNWNWWNWWNWWWWWWWWWWWWWWWWWWWWWWWWW77777313131773131777313177731777777731731773131319377317313177731319389.7110.882.282.9106.5136.2141.3147.843.583.280.1119.5109.7134.1144.6177.1192.1134.1155.8162.9188.8100.189.5118.4120.748.752.380.589.678.7145.2126.5138.5177.1189.7200.6177.576.198.8110.2103.4144.9160.4120.5138.4146.4175.4266.1192.610.74.833.031.321.218.818.719.311.530.610.429.111.011.917.39.422.69.015.811.419.910.511.08.59.76.35.37.21.614.45.86.213.97.418.313.98.811.73.70.518.45.44.34.48.817.12.543.86.90.120.040.400.380.200.140.130.130.260.370.130.240.100.090.120.050.120.070.100.070.110.100.120.070.080.130.100.090.020.180.040.050.100.040.100.070.050.150.040.000.180.040.030.040.060.120.010.160.04Toyoura sand (20z)Decomp. granite soil (15z)Decomp. granite soil (20z)Continues tohydraulicconducitivty test?YesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYes1The values of the GCLs used for the hydraulic conductivity tests are evaluated from the water contents of bentonite pieces left when GCL istrimmed to 6 cm in the diameter for the test.base layer. Table 3 summarizes the results of the prehydration tests. Heterogeneity of bentonite mass per areain GCL might also aect the prehydration eect. In thisstudy, however, the eect of this heterogeneity on theprehydration was not investigated, because the GCL cannot be accurately divided into small species to measurethe distribution of mass per unit area.Figures 5(a) and (b) show the water content distribution of the GCL after prehydration when Toyoura sandand decomposed granite soil with an initial water contentof 15z were used as the base layer, respectively. Thewater content distribution of each soil is almost the same.Figures 5(b) and (c) show the eects of the water supplyfrom the water table like groundwater on the water con412KATSUMI ET AL.Fig. 3.Fig. 4.Division of prehydrated GCLApparatus for hydraulic conductivity testtent distribution after prehydration. A dierence in theprehydration water content, which is the average watercontent distribution, is observed. The base layer with thewater table increased the prehydration water content to144.6z. However, the base layer without the water tablealso increased although the increased prehydration watercontent reached only 89.7z. Hence, in actual sites, thepresence of a groundwater table and the depth from theground surface to the groundwater table are importantfactors, which aect the prehydration eect.Figures 5(c) and (d) show the water content distribution of GCLs that contains powdered bentonite andgranular bentonite, respectively. The bentonite form signicantly aects the average and the coecient of variation of the prehydration water content distribution. Thepowdered bentonite increases the prehydration watercontent more than granular bentonite. In addition, powdered bentonite homogenizes the water content distribution after prehydration more than granular bentonite. Itis probably because, even when one bentonite granulargets wet, it may not be easy for the pore water in thegranular to freely disperse to another neighboring granular beyond the space between these granules. Therefore,using a GCL containing powdered bentonite eectivelyimproves both the prehydration water content and theheterogeneity of its distribution in a short curing period.However, a longterm curing period improves the prehydration water content and the heterogeneity of its distribution, even if a GCL containing granular bentonite isused. Figures 5(e) and (f) show the water content distribution when the curing period is 31 days; in contrast,Figs. 5(c) and (d) show the water content distributionwhen the curing period is 7 days. Increasing the curingperiod from 7 to 31 days homogenize the water contentdistribution of both GCLs. In particular, a signicantchange appears in the water content distribution of theGCL with granular bentonite. The prehydration watercontent increased from 82.9z to 141.3z, while thecoecient of variation decreased from 0.38 to 0.13.Figures 6 and 7 show the eects of the curing period onthe prehydration water content and the heterogeneity ofits distribution, respectively. These gures include all theexperiment results shown in Table 3. Increasing of thecuring period improves the prehydration water contentand the heterogeneity of its distribution in all the prehydration conditions tested. However, a curing periodgreater than certain days did not cause a signicantchange in either the prehydration water content or heterogeneity. The curing period is dependent on the soil properties of the base layer, the GCL properties, and the actual depth from the ground surface where the GCL is installed to the water table; In this experiment, a curingperiod longer than 31 days did not cause a signicantchange in either the prehydration water content orheterogeneity.Hence, it is concluded that prolonging the curingperiod and employing GCLs with the powder bentoniteare eective measures for enhancing the prehydrationwater content and for homogenizing the water contentdistribution. However, as for the contact face (nonwovenside or woven side) of GCLs with the base layer, therewas no clear eect on the water content distribution afterprehydration.Hydraulic Conductivity of Prehydrated GCLsThe purpose of the hydraulic conductivity tests was toevaluate the hydraulic conductivity of the prehydratedGCLs against aggressive chemical solutions, and to discuss the prehydration eect by comparing the prehydrated GCLs to nonprehydrated GCLs in the hydraulic conductivity. Table 4 summarizes the results of the hydraulicconductivity tests. This table shows the relations betweenthe water content distribution of the GCLs and theirhydraulic conductivity values. The water content distribution of the GCLs, which were used in the hydraulicconductivity test, was indirectly estimated from the waterPREHYDRATION EFFECT ON GCLS413Fig. 5. Distribution of prehydration water content of GCLs; where Powd.Bpowdered bentonite GCL, Gran.Bgranular bentonite GCL,DGSdecomposed granite soil, TSToyoura sand, and WLwater levelFig. 6.Eect of curing period on prehydration water contentcontent values of the bentonite pieces that remained whenthe prehydrated GCLs were trimmed from a diameter of10 cm to 6 cm. Trimming was necessary in order for thesamples to work in the hydraulic conductivity test. Thehydraulic conductivity value was determined by conducting a longterm test, which lasted at least a year, and theFig. 7. Eect of curing period on heterogeneity of prehydration watercontent distributionchemical equilibrium state was checked before the testwas terminated.Figure 8 shows examples of data obtained in the longterm hydraulic conductivity tests. The thickness of GCLswas observed by the cathetometer once a day, and then414KATSUMI ET AL.Table 4.Results of hydraulic conductivity tests using CaCl2 solutionsPermeant solution(CaCl2 solution)Test No.#27#44#36#11#04#10#05#12#06#08#39#13#32#19#20#16#21#17#45#33#48Testing material (GCL)End of testing (Hydraulic conductivity test)Molar conc.[M]pH[]Prehydration water contentECBentonite form Prehydration[S/m]wave [z] wstd [z] dcov []0.108.5616.850.258.8836.700.509.2462.40PowderedPowderedPowderedPowderedGranularGranularGranularGranularGranularGranularGranularGranularPowderedPowderedPowderedPowderedPowderedPowderedPowderedPowderedPowderedPowderedPowderedPowderedPowderedNPPPPNPPPPPPPPNPPPPPPPPPNPPPPFig. 8. Changes in the hydraulic conductivity, the thickness, and thevolumetric ow rate of GCLs containing granular bentonite withtime52.3120.5200.680.182.983.2106.5119.5136.2147.898.8109.7126.5155.8162.9177.1188.8192.1138.4138.5266.15.34.413.910.431.330.621.229.118.819.33.711.06.215.811.49.419.922.68.813.943.80.100.040.070.130.380.370.200.240.140.130.040.100.050.100.070.050.110.120.060.100.16Time[year]PVF[]pH[]EC[S/m]k[cm/s]º1º2º2º1º1º2º2º2º2º2º2º2º1º2º2º2º2º2º2º2º2º1º1º1º112.2253.0943.4478.659.4530.8182.6918.9225.0157.3014.3183.8610.6093.6943.9639.85123.8892.7491.2579.1824.8023.7232.4119.2619.698.197.067.316.536.696.896.806.686.556.566.576.786.816.7217.8118.0016.6016.9838.8039.6038.7039.7040.9038.0066.0076.5065.7073.501.83~10|86.16~10|91.19~10|92.06~10|83.37~10|53.41~10|91.78~10|81.48~10|62.91~10|91.12~10|81.13~10|81.60~10|89.29~10|61.21~10|81.45~10|86.63~10|93.20~10|82.07~10|83.92~10|95.55~10|97.74~10|92.80~10|52.92~10|84.64~10|84.11~10|8the hydraulic conductivity was evaluated using the latestthickness. The hydraulic conductivity of prehydratedGCLs to CaCl2 solutions was rst as low as that of GCLto water, but gradually increased with time. When theconcentration of the permeant liquids was low, thehydraulic conductivity of the prehydrated GCLs settleddown in k§1.0~10|8 cm/s. The euent liquid was usedto measure its pH and electric conductivity. In order toreach the chemical equilibrium state before the test is terminated, the electric conductivity ratio of the inuent andeuent should fall within 0.91.1 according to ASTM D6766 ``Standard Test Method for Evaluation of Hydraulic Properties of Geosynthetic Clay Liners Permeated withPotentially Incompatible Liquids''.Figure 9 shows the eects of the prehydration watercontent on the hydraulic conductivity of prehydratedGCLs against 0.10.5 M CaCl2 solutions. When the watercontent was À50z, the prehydration water content barely inuenced the hydraulic conductivity of the prehydrated GCL. The hydraulic conductivity of the prehydratedGCLs was approximately 1.0~10|8 cm/s even when themolar concentration of the permeant CaCl2 solution wasmore than 0.25 M, which signicantly aects the decreasein the hydraulic conductivity of nonprehydrated GCLs.All the prehydrated GCLs with powdered bentonite indicated the low hydraulic conductivity of §1.0~10|8cm/s. In contrast, one of prehydrated GCLs with granular bentonite indicated the high hydraulic conductivity of1.5~10|6 cm/s, although the others indicated the lowhydraulic conductivity. Thus, it might be concluded thatPREHYDRATION EFFECT ON GCLSFig. 9.415Eects of the prehydration water content on the hydraulic conductivity of GCLsFig. 10. Eects of the heterogeneity of the water content distributionon the hydraulic conductivity of GCLsGCLs with granular bentonite do not necessarily obtainthe low hydraulic conductivity by the prehydration. Itmay be because the water content distribution of the prehydrated GCLs with granular bentonite became easilyheterogeneous as shown in Fig. 5. Even if the sucientlyswelled parts included in the heterogeneously prehydrated GCL can exhibit the low hydraulic conductivity, theinsuciently swelled parts exhibit the high hydraulic conductivity so that the hydraulic conductivity of the entireGCL with the heterogeneous water content distributionbecomes high.Figure 10 shows the eects of the heterogeneity of thewater content distribution on the hydraulic conductivityof prehydrated GCLs. In this study, it was not clearlyrecognized that the hydraulic conductivity of prehydratedGCLs was increased with the heterogeneity (thecoecient of variation) of the water content distribution.It may be because the way to evaluate the heterogeneityof the water content distribution of GCLs used for thehydraulic conductivity tests was not applicable. Thewater content distribution was indirectly estimated fromthe water contents of bentonite pieces left when GCL istrimmed to 6 cm in the diameter for the hydraulic conductivity test. The water content distribution estimatedby this way may not be the exact water content distribution of the GCL used for the hydraulic conductivity test.Although the eects of the heterogeneity of the watercontent distribution on the hydraulic conductivity cannotbe clearly shown by this evaluation, GCLs with granularbentonite would be prehydrated more heterogeneouslythan those with powdered bentonite. One of the prehydrated GCLs with granular bentonite would indicatethe higher hydraulic conductivity than the others due touncertainty of their prehydration. The homogeneity ofthe water content distribution of the prehydrated GCLhas been considered an important factor for improvingthe chemical resistance.Figure 11 shows the hydraulic conductivity values ofnonprehydrated and prehydrated GCLs. The prehydration treatment maintains an extremely low hydraulic conductivity even to the permeation of the aggressive chemical solutions such as CaCl2 solutions. In particular, theeect of the prehydration treatment greatly appears in thehydraulic conductivity when the CaCl2 solution with ahigh concentration permeates into the GCL. The nonprehydrated GCL is deteriorated by the permeation of aCaCl2 solution with a molar concentration of 0.5 M sothat the hydraulic conductivity increases up to k2.8~10|5 cm/s, while the prehydrated GCLs against the 0.5 MCaCl2 solution showed k§1.0~10|8 cm/s. The threeorders of magnitude dierence appears in the hydraulicconductivity between the nonprehydrated GCL and the416KATSUMI ET AL.Fig. 11. Comparison between nonprehydrated GCLs and prehydrated GCLs in the hydraulic conductivityprehydrated GCL. It is concluded that prehydrationeectively improves the chemical resistance of GCLs.CONCLUSIONSWhen GCLs are applied as bottom liners at waste containment facilities, the GCLs are naturally prehydratedby absorbing moisture from unsaturated base layers. Inconsideration of the prehydration process at actual sites,this study investigated the eects of the water content distribution of prehydrated GCLs on their barrier performance against CaCl2 solutions, which were used to simulate waste leachates. From the prehydration test and thehydraulic conductivity test, the following conclusionswere obtained.(1) Prehydrated GCLs with powdered bentonite havethe higher water content as the average and morehomogeneous water content distribution than those withgranular bentonite. Hence, GCLs with powdered bentonite can be highly and homogenously prehydrated. Furthermore, employing GCLs with powdered bentonite isan eective method for improving barrier performanceagainst chemical attack.(2) The curing period for prehydration inuences thewater content and the homogeneity of prehydratedGCLs. In this experimental condition, when the curingperiod is prolonged from 7 to 31 days, the water contentincreases and its coecient of variation, which is aparameter that indicates the heterogeneity of the watercontent distribution, decreases. However, the change inthe water content and its coecient of variation is negligible when the curing period was prolonged from 31 to 93days.(3) Although GCLs with granular bentonite are lowlyand heterogeneously prehydrated, prolonging the curingperiod improves their water content distribution.(4) Most of the prehydrated GCLs exhibit a lowhydraulic conductivity of k§1.0~10|8 cm/s againstCaCl2 solutions with concentrations between 0.1 and 0.5M. This hydraulic conductivity value is about 1,000 timeslower at the maximum than that of the nonprehydratedGCLs.(5) However, prehydrated GCLs have been considered not to exhibit such a low hydraulic conductivitywhen the water content distribution of the prehydratedGCLs was strongly heterogeneous. Heterogeneous prehydration permits the parts, which are insucientlyswelled with a low water content, to pass the permeant solutions. The hydraulic conductivity values of such heterogeneously prehydrated GCLs will widely vary. It was easyfor GCLs with granular bentonite to be heterogeneouslyprehydrated.To maintain the required barrier performance forGCLs installed as largescale bottom liners at waste containment facilities, it is important to consider the eectsof geological and hydrological conditions such as notonly retention characteristics, groundwater level but alsophysical heterogeneity of base layer soils (the physicalheterogeneity eects are not investigated in this paper)when designing the GCL and the curing period.ACKNOWLEDGMENTSHelpful comments and discussions were provided byProfessor Masashi Kamon (Kyoto University). The GCLswere provided by Marubeni Tetsugen Co., Ltd. Assistance with the experimental work was provided byformer students of Ritsumeikan University, includingShugo Numata, Masato Yokoi, and Kazuyoshi Hanamoto.REFERENCES1) Barroso, M., TouzeFoltz, N., Maubeuge, K. and Pierson, P.(2006): Laboratory investigation of ow rate through compositeliners consisting of a geomembrane, a GCL and a soil liner, Geotextiles and Geomembranes, 24, 139155.2) Bonaparte, R., Othman, M. A., Rad, N. R., Swan, R. H. and Vander Linde, D. L. (1996): Evaluation of various aspect of GCL performance, Report of 1995 Workshop on Geosynthetic Clay Liners,EPA/600/R96/149.3) Daniel, D. E., Shan, H.Y. and Anderson, J. D. (1993): Eects ofpartial wetting on the performance of bentonite component of a geosynthetic clay liner, Geosynthetics '93, 3, 14821496.4) Daniel, D. E., Trautwein, S. J. and Goswami, P. K. 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(2004): Flow of gasoline through composite liners, Journal of Environmental Engineering, 130(8),886890. | ||||
ログイン | |||||
タイトル | Formulation of a Dusty Gas Model for Multi-component Diffusion in the Gas Phase of Soil | ||||
著者 | Yoshihiko Hibi | ||||
出版 | Soils and Foundations | ||||
ページ | 419〜432 | 発行 | 2008/06/15 | 文書ID | 21118 |
内容 | 表示 SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 419432, June 2008FORMULATION OF A DUSTY GAS MODEL FOR MULTICOMPONENTDIFFUSION IN THE GAS PHASE OF SOILYOSHIHIKO HIBIi)ABSTRACTSoil vapor extraction and bioventing have been utilized for purication of contaminated soil or groundwater. It isnecessary to predict the movement of gas phase components in soil for the design of soil vapor extraction and bioventing systems. Though chemical substances migrate with advection and diusion in gas phase of soil, we investigatedmulticomponent diusion systems in gas phase of soil. Numerical modeling for multicomponent diusion is useful tothe prediction of the movement of components. A dusty gas model for multicomponent diusion systems has not sofar been formulated by the Finite Element Method; furthermore it has not been applied for assessing the movement ofcomponents in the gas phase of soil. Accordingly, a dusty gas model for three gas phase components was formulatedby the Finite Element Method in this study, and the concentrations of components in binary and multicomponent gassystems were calculated by numerical methods developed in this study. As a result, it was found that the dusty gasmodel must be applied for study of diusion in a multicomponent gas system; and the study showed that the dierence between molecular weights of gas phase components inuenced the movement of components in the gas system.Key words: dusty gas model, nite element method, multicomponent diusion, numerical analysis, unsaturated soil(IGC: E13)hexane gas in a binary gas system composed of air andthese gases by numerical models applying Fick's law.Fick's law can be applied for diusion in a binary gas system, and is represented byINTRODUCTIONSoil vapor extraction and bioventing have been usedto purify contaminated soil and groundwater (Shan andJavandel, 1992). In soil vapor extraction, gas phase soilcomponents are extracted by a vacuum pump and harmful gases are adsorbed onto activated carbon. In bioventing, oxygen is pumped into the soil to support the growthof microbes which break down the organic liquid contaminants present in the soil. In these cases, the gasphases present in the soil (oxygen, nitrogen, harmful gas,etc) disperse and advect in a multicomponent gas system.It is important to predict the migration of components inthe gas phase by a numerical model. The prediction of gasmigration by numerical modeling is useful to the designof soil vapor extraction and bioventing systems.Previous studies (Abriola and Pinder, 1985; Sleep andSkyes, 1993) have developed a numerical model with multiphase ow, gas ow, and advectivedispersion transportof components in the vapor zone. Fick's law was formulated in that model for dispersion of components in thevapor zone. Moreover, Lenhard et al. (1995), Kneafseyand Hunt (2004), Jellali et al. (2003), Mendoza and Frind(1990), Mendoza and Frind (1990), Sleep and Sykes(1989), Corapcioglu and Baeh (1987), CostanzaRobinson, and Brusseau (2002), Baehr and Corapcioglu (1987)have simulated the migration of trichloroethylene ori)Ni|Dij;ci(1)where Ni is the molar ux [mol/L2T] of component i in abinary gas system, Dij is a binary molecular diusioncoecient [L2/T] between component i and component j,and ci is the molar concentration [mol/L3] of componenti. Actually the components in the gas phase of soil maydiuse in a multicomponent gas system in most cases,but there are a few cases in which the components diusein a binary gas system. The application of Fick's law isrestricted to systems that exhibit binary gas diusion. Advection of chemical components is signicantly in themulticomponent gas system and has been solved formass transfer in groundwater. However, multicomponent diusion in gas phase of soil has not been investigated except for Fick's law. Accordingly, we investigatemulticomponent diusion in this study.A diusion coecient which considers molecular diusion in a multicomponent gas system can be employed inplace of the binary diusion coecient in Eq. (1) as longas each component is present in low concentrations. Inthis case, the molecular diusion coecient can be givenby Blanc's law (Poling et al., 2001) if the concentration ofDepartment of Environmental Science and Technology, Faculty of Science and Technology, Meijo University, Nagoya, Japan(hibiyccmfs.meijou.ac.jp).The manuscript for this paper was received for review on August 27, 2007; approved on February 5, 2008.Written discussions on this paper should be submitted before January 1, 2009 to the Japanese Geotechnical Society, 4382, Sengoku, Bunkyoku, Tokyo 1120011, Japan. Upon request the closing date may be extended one month.419420HIBIeach component is very low.1XjSDJ1ijDim(2)nIn the equation, Dim is a molecular diusion coecient[L2/T] in the multicomponent gas system, Xj is the molarfraction [dimensionless] of component j, and n is thenumber of components. Hoeg et al. (2004) simulated themigration of low concentration gas phase 1,1,1trichloroethane, 1,1,2 trichloroethane, and trichloroethylene in soil by a numerical model applying Eqs. (1) and(2). The results of the simulation were compared withresults of experiments carried out by Fischer et al. (1996),and it was demonstrated that the results of simulationwere consistent with experimental results.Poling et al. (2001) indicated that Eq. (2) was derivedfrom StefanMaxwell equations (Curtiss and Hirschfelder, 1949) as follows:S X N D|X N ;cnJ1J» iijjijii(3)Equation (3) represents the diusion of components inmulticomponent systems with accuracy, and can be applied to molecular diusion in multicomponent gas systems even if the concentration of each component is high.The diusion in Eq. (3) occurs when molecules collidewith each other, as shown in Fig. 1.Baehr and Bruell (1990) carried out experiments on theadvectivediusion of hexane, benzene, and isooctane inoxygen and nitrogen gas systems in the vertical direction.The concentrations of the organic species were predictedby Fick's law or the StefanMaxwell equations, assumingthat the molar ux of oxygen approaches zero over time.It was found by comparison between the predicted concentration and the concentration observed in the advectivediusion experiments that the concentration predicted by Fick's law was similar to the concentration given bythe StefanMaxwell equations. Massmann and Farrier(1992) reported similar results by demonstrating uxes oftrichloroethylene in oxygen and nitrogen gas systemswhich were calculated by multicomponent equations or asinglecomponent equation derived from Fick's law. TheFig. 1.multicomponent equations (called ``dusty gas'' modelequations) were derived from the StefanMaxwell equations with Knudsen diusion ux and viscous ux. Knudsen diusion occurs when molecules collide with surfacesof soil particles, as shown in Fig. 1. Massmann and Farrier (1992) concluded that it was possible to apply a Fick'slawtype equation when the permeability is more than10|10 cm2.The above mentioned results were derived for conditions of restricted permeability, or where some of the molar uxes in Eq. (3) were zero, i.e., when the ux of somecomponents was stagnant. However, Eq. (3) cannot besolved for the molar fraction or concentration and themolar ux of each component unless it is assumed thatsome molar ux is zero, or has a dened relationship toanother molar ux.Therefore it is not suitable to apply Fick's law Eq. (1)to multicomponent gas systems, suggesting the use of thedusty gas model equations. On the other hand, the dustygas model equations have never been completely formulated with either the Finite Element Method (FEM) or theFine Dierence Method (FDM). This study attempts tosolve the dusty gas model equations by FEM, and severaldierent gas systems will be simulated by the numericalmodel developed in this study. The results will demonstrate the dierence between the diusion coecient calculated by Eq. (2) and the diusion coecient calculatedby the dusty gas model in a binary gas system, and thedierence between the concentration simulated by the numerical model using Eqs. (2) and (1) and the concentration simulated by the numerical model developed in thisstudy.NECESSITY FOR THE DUSTY GAS MODELMason (1967) and Mason and Malinauskas (1983) derived multicomponent diusion equations with diusionux and viscous ux depending on temperature from adusty gas model, and Cunningham and Williams (1980)explained the process of induction for StefanMaxwellequations and multicomponent diusion equations, adding a term for the Knudsen diusion to the StefanMaxwell equations. Knudsen diusion is a phenomenonwherein molecules of gas diuse by colliding with the surSchemata of Molecular diusion and Knudsen diusion421FORMULATION OF A DUSTY GAS MODELfaces of soil particles. Reinecke and Sleep (2002) demonstrated a relationship between the Knudsen coecient,soil permeability, and the Klinkenberg parameter(Klinkenberg, 1941), and Thostenson and Pollock (1989)investigated the inuence of Knudsen diusion ux onmulticomponent diusion in the soil gas phase.The dusty gas model equation without viscous ux under constant temperature is,XiNj|XjNi Nj| ;cjSDijDii1»nidiusion coecient without soil particles (Millingtion,* and D *BA take account of tortuosity t1959). The D AB[dimensionless], which inuences the paths of components in the soil gas phase.*D ABD *BA(4)A Comparison between an Equation based on Fick's Lawand an Equation Derived by the Dusty Gas ModelThe dusty gas model for a binary gas system can be expressed for components A and B as follows.Component AXANB|XBNA NA| ;cADABDA(5a)XBNA|XANB NB| ;cBDABDB(5b)Component BIn these equations, XA and XB are molar fractions[dimensionless] of component A and component B, NBand NA are molar uxes [mol/L2T] of components A andB, and cA are cB molar concentrations of components Aand B [mol/L3], DAB is the molecular diusivity [L2/T] ofcomponent A in component B or B in A, and DA and DBare the Knudsen diusivities [L2/T] of components A andB, respectively.On other hand, the following equation may be derivedby Graham's law (Cunningham and Williams, 1980) forbinary system when the total gas pressure is constant inan analytical domain.1/2NAM 1/2A {NBM B 0(6)where MA and MB are the molecular weights [M/mol] ofcomponent A and component B, respectively.By substituting Eqs. (6) into (5) and rearranging, NAand NB can be obtained as follows,NA|;cAØ »XA MADAB MBNB|XB1{DAB DA1/2(7a){;cBØ »XB MBDAB MA1/2XA1{{DAB DB(7b)By comparison between Eqs. (1) and (7), moleculardiusion coecients in Eq. (1) correspond with the D *AB* dened from Eq. (7). Because particles of soiland D BAresist molecular diusion in the soil gas phase, themolecular diusion coecient with soil particles presentin the system is generally smaller than the molecularØ »XB MBtDAB MAjwhere Di is the Knudsen coecient [L2/T], and the secondary term of the left side indicates Knudsen diusion.Ø »XA MAtDAB MB11/2XB1{{tDAB DA11/2XA1{{tDAB DB(8a)(8b)A molecular diusion equation in the form of Fick'slaw taking account of tortuosity can be expressed for themolar ux of component A as follows:NA|tDAB;cA(9)Furthermore, a molecular diusion coecient takingaccount of tortuosity for component A approximates Eq.(10) when the component is present at low concentration.*D AB1(10)1XB{tDAB DAEquation (8a) without a Knudsen diusion coecientis consistent with the binary diusion coecient of Eq.(9) if the molecular weight of component A is equal to themolecular weight of component B. Then, assuming thatthe concentration of component A is very low, XB approximates 1.0. As a result, Eq. (10) without a Knudsendiusion coecient is almost equal to the binary diusioncoecient of Eq. (9). If XB is below 1.0 and Knudsendiusion is taken account of, Eq. (10) is inconsistent withthe binary diusion coecient of Eq. (9).Therefore Eq. (10) has the limitation when the equation is applied to the binary diusion coecient. On theother hand Eq. (8a) can be applied for every situation encountered in a binary gas system without the limitation.The above mentioned conditions for application of Eqs.(8), (9) and (10) are arranged in Table 1.A Comparison with Molecular Diusion Coecients inthe Binary Gas SystemMolecular diusion coecients have been calculatedby Eqs. (8a) and (10), and the results are illustrated inFigs. 2 and 3. Chemical and physical parameters used inthese calculations are indicated in Table 2.The binary diusion coecient in Eq. (9) has beenTable 1. A comparison between conditions for application of eachmodelModelEquationDusty Gas Model(8)Fick's lawBlanc's law(9)(10)Conditions for applicationWithout any restriction.In all cases for multicomponent gassystem.In binary gas system.In cases that concentration of thediusing gas is dilute.422HIBIFig. 2. Diusion coecients for binary gas system consisting ofmethane gas and air in the gas phase of soil. Circles in case of adierence between molecular weights, and triangles in case of equalmolecular weightsFig. 3. Diusion coecients for binary gas system consisting oftrichloroethylene and air in the gas phase of soil. Circles in case of adierence between molecular weights, and triangles in case of equalmolecular weightsTable 2. Parameters for calculation of molecular diusion coecientsfor binary gas systemParameterTortuosity, tComponent A : air Molecular weight, MAComponent B: methane Molecular weight, MBTCE Molecular weight, MBMolecular diusion coecient between air andmethane, DABMolecular diusion coecient between air andTCE, DABValue and/or Units0.128.75 g/mol16.04 g/mol131.4 g/mol2.2~10|1 cm2/s7.6~10|2 cm2/scompared with the diusion coecient calculated by Eq.(8a) or Eq. (10) in a binary diusion system consisting ofair and methane. This situation implies that methane, oflower density than air, inltrates through the airgas system by molecular diusion. Figure 2 shows the relationship between the molar fraction of methane in an airmethane system and the relative diusion coecientwhich divides the diusion coecient of Eq. (8a) or Eq.(10) by the diusion coecient of Eq. (9).Relative diusion coecients calculated by Eq. (8a) orEq. (10) exceed 1.0, and increase with the molar fractionof methane as shown in Fig. 2. It is found by a comparison between the molecular diusion coecients calculated by Eqs. (8a) and (10) that the relative diusioncoecient given by Eq. (10) is larger than that given byEq. (8a). Actually, the relative diusion coecient givenby Eq. (10) should become 1.0 for the case of a moleculardiusion coecient in a binary gas system without Knudsen diusion and a dierence in the molecular weight.The relative diusion coecient given by Eq. (10)becomes 1.02 as shown in Fig. 2 when the molar fractionof methane is 0.02 and 1.05 when the molar fraction ofmethane is 0.05. Therefore, Eq. (2) can be applied onlywhere the molar fraction of methane is relatively low.The molecular diusion coecient given by Eq. (10) isnot equal to the binary molecular diusion coecient forhigh concentrations of methane. Equation (10) must notbe employed under conditions of high concentrationcomponents diusing in a gas system. The moleculardiusion coecient given by Eq. (8a) or Eq. (8b) shouldbe equal to the diusion coecient in Eq. (9) if themolecular weight of component A is consistent with thatof component B and Knudsen diusion does not occur ingas system. The diusion coecient given by Eq. (8a)diers from the diusion coecient in Eq. (9) by reasonof the ( XA/tDAB)( MA/MB)1/2 term included in the numerator of Eq. (8a). The relative diusion coecient given byEq. (8a) as shown in Fig. 2 becomes 1.03 when the molarfraction of methane is 0.05 and 1.06 when it is 0.10.Therefore the molecular diusion coecient is highly inuenced by the dierence in the molecular weight, andthe binary diusion coecient of Eq. (9) can not be usedwhen simulating a system of gases that are of signicantlydierent molecular weights.Figure 3 shows the relationship between the molarfraction of trichloroethylene (TCE) and a relative diusion coecient obtained by Eq. (8a) or Eq. (10) in a binary gas system consisting of air and TCE. The molecularweight of TCE is heavier than that of air, as shown inTable 2. The relative diusion coecient calculated byEq. (10) is more than 1.0, similar to the case of themethaneinair system, and Eq. (10) can be used for simulations of the molecular diusion only if the concentration of TCE is suciently low. On the other hand, the relative diusion coecient calculated by Eq. (8a) does notexceed 1.0, and decreases with increasing TCE molarfraction. The relative diusion coecient given by Eq.(8a) is 0.95 as shown in Fig. 3 when the molar fraction ofTCE is 0.05, and 0.90 when TCE molar fraction is 0.10.The diusion coecient given by Eq. (8a) may becomesmaller than that in Eq. (9) if the molecular weight of thegas diusing into the system is heavier than that of themajority gas.It was found in this investigation that Eq. (10) can beused for simulations of the molecular diusion only if theconcentration of gas diusing into the system is very dilute, and that Eqs. (8a) and (8b) must be used for simulations of systems with gas phase components that dier inmolecular weight. The total molar diusion ux NT is dened as the sum of the molar diusion gas ux ND [mol/L2T], given by Eq. (9) representing Fick's law, and a none423FORMULATION OF A DUSTY GAS MODELquimolar diusion gas ux NT [mol/L2T] (Thorstensonand Pollock, 1989, Cunnigham and William, 1980),which occurs by reason of the dierence in gas molecularweight. The dierence between the diusion coecientsgiven by Eq. (8a) and the binary diusion coecient inEq. (9) is a reason for the nonequimolar diusion.Component BFORMULATION OF MOLECULAR DIFFUSIONEQUATIONS FOA A THREECOMPONENT GASSYSTEM IN THE GAS PHASE OF SOILIn these equations, XC is a molar fraction [dimensionless]of component C, NC is a molar ux [mol/L2T] of component C, cC is a molar concentration of component C[mol/L3], DBC is a binary molecular diusion coecient[L2/T] of component B in component C or C in B, DAC isa binary molecular diusion coecient [L2/T] of component A in component C or C in A and DC is the Knudsendiusion coecient [L2/T] of component C, respectively.The equation of Graham's law for three componentscan be expressed as follows.It was found in the binary gas system that a dierencebetween molecular weights is very important, and Eq.(10) must be used when the concentration of the components diusing into the gas system is very low. Thenmigrations of three components in a threegas system inthe soil gas phase will be simulated by the dusty gas modeland Fick's law with Eq. (9). The results reported heremake it clear that the dusty gas model is very signicantfor multicomponent diusion in soil gas phases.The dusty gas model for three components can be expressed as follows.Component AXANB|XBNA XANC|XCNA NA{| ;cAtDABtDACDANA|Ø»(11a)ػػØػػwhere D A*, D *B, and D *C in Eq. (13) are dened as follows:1D A*XC1XB{{tDAB tDAC DAØ1D *BXAXC1{{tDAB tDBC DBØ1XB1XA{{tDAC tDBC DC»»»(12)Arranging (11), NA, NB and NC can be given as the following equation.XCXC;cC{NA{NBXAXAXAXB1XB1XB1{{tDAC{{tDBC{{tDAC tDBC DCtDAC tDBC DCtDAC tDBC DC»(11c)1/21/2NAM 1/2A {NBM B {NCM C 0ØNC|ØXCNA|XANC XCNB|XBNC NC{| ;cCtDACtDBCDCXBXB;cB{NA {NCXC1XC1XC1XAXAXA{{tDAB{{tDBC{{tDAB tDBC DBtDAB tDBC DBtDAB tDBC DB»(11b)Component CXAXA;cA{NB{NCXC1XC1XC1XBXBXB{{tDAB{{tDAC{{tDAB tDAC DAtDAB tDAC DAtDAB tDAC DANB|D *CXBNA|XANB XBNC|XCNB NB{| ;cBtDABtDBCDB(14a)(14b)ugػػØ(13a)(13b)(13c)» Ø& cAD *AXAD *AXA;¥( D *A;cA)|;¥NB |;¥NC&ttDABtDAC»(15a)ugØ» Ø&cBD *BXBD B*XB;¥( D B*;cB)|;¥NA |;¥NC&ttDABtDBC»(15b)(14c)Substituting Eqs. (13) and (14) into equations of theconservation of mass law for each gas phase componentof soil, the constituted equations Eq. (15) for each component in the soil gas phase can be induced as follows:ugØ» Ø& cCD *CXCD *CXC;¥( D C*;cC)|;¥NA |;¥NB&ttDACtDBC»(15c)where ug is the gaslled porosity.A dierential equation like Eq. (15) can generally besolved approximately by means of the Finite ElementMethod (FEM) or Finite Dierence method (FDM). FEMhas an advantage that any shape of element can be usedfor discretization of the analytical domain. On the other424HIBIhand, quadrilateral elements except for the rectangle cannot be used in FDM, and rectangular elements are generally employed in FDM. FDM is superior to FEM fortracking the mass balance between that of a componentinjected into or discharged out of the analytical domainand changes of mass of a component in the analyticaldomain. However the Lumping method veried by Milly(1985) or Celia (1990) is able to improve mass balancewhich is calculated from the concentration of the component given by means of FEM, and the accuracy of themass balance obtained by means of FEM with the Lumping method is as precise as that obtained by means ofFDM. Therefore the Galerkin Finite Element Method(GFEM) is applied to solve Eq. (15) in this study, and ifFi is a basic function at node i for discretization of theanalytical domain, each variable in Eq. (15) may be approximated by Fi as follows.npugS Fiugi1npckS Ficki1(16a)ifor k Component A, B, Ci(16b)npD k*S FiD *k for kComponent A, B, C(16c)XkS FiXkfor kComponent A, B, C(16d)NkS FiN*k for kComponent A, B, C(16e)ii1npi1npi1iiIn these equations, a subscript i is the nodal numbergiven at a node in the discrete domain, and the variableswith subscript i are the physical or chemical values at eachnodal number. Then np is the number of nodes.When GFEM and Green's integral theorem are appliedto Eq. (15), a weight function is equal to the basic function. Furthermore the time terms in Eq. (15) can be madediscrete by the implicit Euler method, and the Picard iteration method is employed for linearization of the approximate equations of Eq. (15) because these equations arenonlinear in molar fractions of the components. As aresult, the approximate equations of Eq. (15) with theLumping method can be obtained as follows.fu F dVc {SfD * ;F ¥;F dVc1D *XuF dVc {S;F ¥F dVNf DDt fD *X{S{;F ¥F dVNf DfF q ¥ndV1DtVt{Dt, mgVt{Dt, m{1Aiit{Dt, mgnpAj1tAiit{Dt, mnpj1npj1t{Dt, mAAt{Dt, mt{Dt, mit{Dt, m{1Ajjt{Dt, miABViACVAVt{Dt, mCjijt{Dt, mBjt{Dti AVffD * ;F ¥;F dVc1D *XuF dVc {S;F ¥F dVNf DDt fD *X{S{;F ¥F dVNf DfF q ¥ndV1DtnpVt{Dt, m{1ugt{Dt, mFidVc Bi{Sj1Vt{Dt, mgnpBj1tBiit{Dt, mnpj1t{Dt, mBBt{Dt, mt{Dt, mit{Dt, mBt{Dt, mCjjijt{Dt, mAjt{Dti BVffD * ;F ¥;F dVc1D *XuF dVc {S;F ¥F dVNf DDt fD *X{S{;F ¥F dVNf DfF q ¥ndV1DtnpVt{Dt, m{1ugt{Dt, mFidVc Ci{Sj1Vt{Dt, mgnpj1CVtCiit{Dt, mBCnpj1t{Dt, mCCVCt{Dt, mit{Dt, mCjt{Dt, mBjiIn the foregoing, unknown variable become NA, NB, NC,cA, cB and cC, and superscripts t or t{Dt indicate a timestep in which time t elapses or time is incremented by Dt,and m or m{1 is an iteration number of the Picard iteration method. The terms ug, D A*, D B*, D *C, X A, X B and X Care averages of the respective values of ug, D *A, D *B, D *C,XA, XB and XC within each element, V is the wholevolume [L3] of the analytical domain, and V is a boundary of the analytical domain. Furthermore, n is normalvector to boundary V. The terms qA, qB, and qC are molaruxes [mol/L2T] of components A, B, and C at theVfor i1¿np(17b)t{Dt, m{1CjjACVit{Dt, m(17a)t{Dt, m{1BjjABViBCVBVfor i1¿npjt{Dti Ct{Dt, mAjfor i1¿np(17c)boundaries, respectively, and are dened as follows:D *AXAD *AXANB|NCtDABtDAC(18a)D *BXBD *BXBNA|NCtDABtDBC(18b)D C*XCD *CXCNA|NBtDACtDBC(18c)qAD A*;cA|qBD *B;cB|qCD *C;cC|The coecients D *A, D B*, and D C* can be calculated from425FORMULATION OF A DUSTY GAS MODELvariables than the number of the constituted equations.Therefore NA, NB and NC in Eq. (17) is given from aprevious iteration step by mean of Picard iterationmethod. These variables must be obtained from the latestconcentrations of the components in the Picard iterationstep. Values of NA, NB and NC may be obtained by Eqs.(11) and (12).By substituting Eq. (12) into Eq. (11b) and rearranging, Eq. (20) can be obtained as follows:molar fractions XA, XB and XC, and each molar fractioncan be divided by the concentration of each component asfollows.Xkck/c, for kcomponent A, B, C(19)where c is the total concentration (cA{cB{cC) [mol/L3]in the analytical domain. Accordingly D *A, D *B, D *C, XA,XB and XC can be obtained from the concentration ofeach component. It is necessary to assign NA, NB, NC forthe solutions of Eq. (17) because there are more unknownØ{ ( MtD/M )BA1/2AB» Ø»}11111XB{|XB{{NBtDBCtDBC DBtDAB tDBC|{1/2}1( MC/MA)|XBNC|;cBtDABtDBC{{}(20a)1( MB/MA)1/2|XC NBtDACtDBCØ{ ( MtD/M )C{A1/2AC» Ø»}11111XC {|XA{{NC|;cCtDBCtDBC DCtDAC tDBC|(20b)Utilizing GFEM for the discretization, the approximate equations substituted for Eq. (20) at each nodal point become:1111( M /M )1f{Ø tD |tD »X {Ø tD |tD »X {tD {D }F F dVN1( M /M ){Sf{ tD |tD }X F F dVN |SfF ;F dVc (i1¿np)( M /M )1|XF F dVNS f{ tDtD }( M /M )11111{Sf{Ø tD |tD »X {Ø tD |tD »X {tD {D }F F dVN|SfF ;F dVc (i1¿np)npSj1BAABVnpj1npj11/2BCC1/2AABVBABC1/2ACVBCnpj1Bnpj1VAijt{Dt, mC1/2ACVt{Dt, mBBCABt{Dt, mBijt{Dt, mCit{Dt, mABCt{Dt, m{1CjjBCiBjnpj1Vit{Dt, m{1Bjt{Dt, mBjj(21a)t{Dt, m{1BjACt{Dt, mCjNB and NC can be given by the abovementioned Eq. (21)from cA, cB, XA, XB and XC which have been calculated onthe previous Picard iteration step. On the other hand NAcan be calculated by Eq. (12) for Graham's law. Theterms NA, NB, and NC given by Eqs. (12) and (21) are substituted into Eq. (17), and cA, cB, and cC on the latestPicard iteration step are calculated by Eq. (17). This numerical model is called the DG model hereafter.Figure 4 shows a calculation owchart for this numerical model. As presented in Fig. 4, molar fractions of eachcomponent are calculated from the initial concentrationsof each component. Then the initial molar uxes NB andNC are obtained based on the initial molar fractions byEq. (21), and the initial NA is calculated from NB and NCby Eq. (12). The values of NA, NB, and NC given here areutilized to calculate cA, cB and cC by Eq. (17) on the nextPicard iteration step. NA, NB, and NC are then updated bycalculating from the new cA, cB and cC values. The nalvalues for cA, cB and cC are determined when these concentrations converge to within a preset tolerance, andthe simulation can be advanced to next time step.However the simulation is interrupted when cA, cB and cCBCt{Dt, mBBCCijt{Dt, m{1Cj(21b)do not converge within the desired tolerance. Thesimulation is complete when the elapsed time in the simulation is equal to the specied maximum time.VALUATION OF THE DEVELOPED NUMERICALMODEL FOR THE MULTICOMPONENT GASSYSTEM IN GAS PHASE OF SOILIn this section we illustrate dierences between the numerical model developed in this study (the DG Model)and the numerical model with a diusion coecient calculated by Eq. (2) which can be used when the concentrations of components diusing into gas phase of soil arevery low. It has been described for the binary gas systemin this study that a dierence between molecular weightsof components inuences the diusion in multicomponent gas system, and that the diusion coecient of Eq.(2) derived from the dusty gas model could only be applied under restricted conditions, i.e., when the gas concentration is very low. However, Eq. (2) is very convenient for simulation of multicomponent gas systemsbecause the constituted equations are simpler and the426HIBITable 3. Parameters for simulations of multicomponent gas systemsif the molecular weight of gas diusing into an analytical domain islighter than that of other gasFig. 4. The owchart of the numerical simulation developed from thedusty gas model in this study for mass transfer of multiple components in the gas phase of soileort of computation can be decreased. The concentration at which Eq. (2) can be applied for multicomponentgas systems can be decided by a comparison between theconcentrations of components calculated by use of theDG model and the concentration given by Eq. (2), and itshall be veried that the DG model developed in thisstudy is useful for multicomponent gases in the gasphase of soil.The constituted equations with diusion coecient calculated by Eq. (2) can be obtained from the conservativelaw and Fick's law. These constituted equations were already formulated by means of GFEM to compute theconcentration of components in the soil gas phase. Thisnumerical model is called modied Fick's law model (theMF model) thereafter.The Case of Gas with Lower Molecular Weight than theSurrounding GasesA simulation of methane diusing into a region full ofoxygen and nitrogen was carried out in this study becauseit illustrates the dierence between distributions of concentrations given by means of the DG model and thoseParameterValue and/or UnitsTortuosity, tComponent A Oxygen Molecular weight, MAComponent B Nitrogen Molecular weight, MBComponent C Methane Molecular weight, MCMolecular diusion coecient between oxygenand nitrogen, DABMolecular diusion coecient between oxygenand methane, DABMolecular diusion coecient between nitrogenand methane, DBC0.432.00 g/mol28.01 g/mol16.04 g/mol2.08~10|1 cm2/s2.27~10|1 cm2/s2.13~10|1 cm2/sgiven by means of the MF model. One dimensionalelements were employed for both numerical models. Theanalytical domain specied over 0 mÃXÃ10 m, andelements with nodal spacing of 0.05 m were used for bothnumerical models. The initial concentrations were:oxygen, 8.3 mol/m3; nitrogen, 33.3 mol/m3; andmethane 0 mol/m3 in 0ºXÃ10 m, except for X0 m asan initial condition. The total concentration was 41.6mol/m3 in 0 mÃXÃ10 m.Methane molar fractions of 0.05, 0.10, 0.20 or 0.50were specied at X0 m during the simulations. Theconcentrations of oxygen, nitrogen, and methane werespecied to be 8.3, 31.22, and 2.08 mol/m3 respectivelywhen the molar fraction of methane was 0.05; 8.3, 29.14,and 4.16 mol/m3 respectively when methane was set to0.10; 8.3, 24.98, and 8.32 mol/m3 respectively when 0.20;and 8.3, 12.54, and 20.8 mol/m3 respectively when 0.50.On the other hand the molar uxes of each component at10 m were specied to be zero during the simulation, thusensuring that no component was injected into the analytical domain or discharged from the analytical domain onthe boundary located at 10 m.Table 3 indicates the physical and chemical parametersused for simulations in the present study. Diusioncoecients of each component are similar, however themolecular weight of methane is approximately half thatof oxygen or nitrogen as shown in Table 3.Figure 5 shows the concentration distributions ofoxygen, nitrogen, and methane at an elapsed time of 8000seconds when the molar fraction of methane is 0.05 atX0 m. As shown in Fig. 5, no dierence can be distinguished between the distributions of the methane concentrations given by means of the DG model and that givenby the MF model, and it can be seen that both concentrations are similar. On the other hand the concentration ofoxygen given by means of the DG model is 1.4 mol/m3smaller than that given by the MF model at 10 m, and inversely the concentration given by the DG model fornitrogen is 1.4 mol/m3 larger than that given by means ofthe MF model. These tendencies of migrations withoxygen and nitrogen can be conrmed in Fig. 6 which illustrates the distributions of the concentrations of oxygenand nitrogen when the molar fraction of methane is 0.10at X0 m, but the dierence between the concentrationsFORMULATION OF A DUSTY GAS MODEL427Fig. 5. Distributions of concentrations of oxygen, nitrogen, andmethane after 8000 seconds of simulation for a molar fraction ofmethane of 0.05. White circles represent concentrations given byDG model, and lled circles the case of MF modelFig. 6. Distributions of concentrations of oxygen, nitrogen, andmethane after 8000 seconds of simulation for a molar fraction ofmethane of 0.10. White circles represent concentrations given byDG model, and lled circles the case of MF modelgiven by the two models for methane is not distinct because this dierence becomes 0.08 mol/m3 at X10 m.Figure 7 shows distributions of each concentrationwhen the molar fraction of methane is set to 0.20 at X0m, and Fig. 8 shows concentration distributions for amethane molar fraction of 0.50. As shown in Fig. 7, thedierences between the concentrations given by the DGand MF models are more obvious than those shown inFig. 6, and the dierence between concentrations ofmethane given by each numerical model becomes 0.35mol/m3. A larger dierence in predicted methane concentrations appeared for a molar methane fraction of 0.5, asseen in Fig. 8. The results shown in Figs. 7 and 8 conrmthat the dierences between the concentrations of oxygenand nitrogen given by the DG model and MF model increase with the molar fraction of methane at X0 m.Therefore the diusion coecient calculated by Eq. (2)can be used for the multicomponent gas system simulation with a molar fraction of methane of 0.10 or less, ifthe diusing component has a lighter molecular weightthan those of the components lling the domain. The DGmodel composed in this study must be used to simulatethe migrations of each component in a multicomponentgas system if the molar fraction of methane exceeds 0.10.However, regarding the migrations of components whichinitially exist in the domain, the distinct dierence between the results given by the DG and MF models ispresent for the entire range of methane molar fraction.The Case of Gas with Higher Molecular Weight than theSurrounding GasesThe DG and MF models have been evaluated in theprevious section for the condition of a lower molecularweight component diusing through a domain of highermolecular weight gases. Applicability of these models willbe examined for the condition of a diusing component428HIBIFig. 7. Distributions of concentrations of oxygen, nitrogen, andmethane after 8000 seconds of simulation for a molar fraction ofmethane of 0.20. White circles represent concentrations given byDG model, and lled circles the case of MF modelFig. 8. Distributions of concentrations of oxygen, nitrogen, andmethane after 8000 seconds of simulation for a molar fraction ofmethane of 0.50. White circles represent concentrations given byDG model, and lled circles the case of MF modelwith higher molecular weight than the background gases.The extent of the analytical domain, the discretizationscheme, and the initial and boundary conditions areequivalent in the case of methane.Table 4 indicates the physical and chemical parametersused for the simulations presented here, with TCE as thediusing gas. The molecular weight of TCE is approximately four times that of oxygen and nitrogen as shownin Table 4, and the diusion coecient between TCE andoxygen or nitrogen is approximately 1/3 that betweenoxygen and nitrogen.Figure 9 shows distributions of oxygen, nitrogen, andTCE concentrations when the mole fraction of TCE is0.05 at X0 m after an elapsed simulation time of 30000seconds. Figure 10 shows these concentrations for an initial TCE fraction of 0.10, Fig. 11 for 0.20, and Fig. 12for 0.50.It can be seen in Fig. 9 that the concentrations given bythe DG model for oxygen and nitrogen are similar toTable 4. Parameters for simulations of multicomponent gas systemsif the molecular weight of the gas diusing into an analyticaldomain is heavier than that of other gasParameterValue and/or UnitsTortuosity, tComponent A Oxygen Molecular weight, MAComponent B Nitrogen Molecular weight, MBComponent C TCE Molecular weight, MCMolecular diusion coecient between oxygenand nitrogen, DABMolecular diusion coecient between oxygenand TCE, DABMolecular diusion coecient between nitrogenand TCE, DBC0.432.00 g/mol28.01 g/mol131.4 g/mol2.08~10|1 cm2/s7.60~10|2 cm2/s7.60~10|2 cm2/sthose given by the MF model. However, the dierences inpredicted TCE concentrations given by the DG modeland the MF model are slightly greater than those predicted in the case of methane. The concentration given by theFORMULATION OF A DUSTY GAS MODEL429Fig. 9. Distributions of concentrations of oxygen, nitrogen, andtrichloroethylene at 30000 seconds for a molar fraction oftrichloroethylene of 0.05. White circles represent concentrationsgiven by DG model, and lled circles the case of MF modeFig. 10. Distributions of concentrations of oxygen, nitrogen, andtrichloroethylene at 30000 seconds for a molar fraction oftrichloroethylene of 0.10. White circles represent concentrationsgiven by DG model, and lled circles the case of MF modeDG model for TCE is 0.058 mol/m3 lower than that givenby the MF model.The concentration of TCE given by the DG model is1.76 mol/m3 at X10 m as shown in Fig. 10, while thatgiven by the MF model is 1.99 mol/m3 at X10 m, adierence of 0.23 mol/m3, just as shown in Fig. 10. Thedierence between both concentrations is 5.5 percent ofthe boundary value concentration of 4.16 mol/m3 specied and X0 m. The oxygen and nitrogen dierences ofthe concentrations given by the DG model are indicatedin Fig. 10. The concentration of oxygen given by the DGmodel is slightly lower than that given by the MF model,while the DG model predicts a higher nitrogen concentration than the MF model, as shown in Fig. 10. Thesedierences in regard to oxygen, nitrogen, and TCEbecome greater as the concentration of TCE at X0 mincreases, as can be seen by comparing Figs. 10 and 11.When the molar fraction of TCE is 0.50 at X0 m, thedierence between the TCE concentrations given by theDG model and MF model is 6.37 mol/m3, the dierencebetween the concentrations for oxygen is 3.3 mol/m3, andthe dierence between the concentrations for nitrogen is3.1 mol/m3, as shown in Fig. 12.Therefore the concentration calculated for the component diusing into the domain is dierent depending onthe type of numerical method used, even if the molarfraction of TCE is very low (0.05) at X0 m, when themolecular weight of the diusing component is higherthan that of the components which initially exist in thedomain. The concentrations simulated by the DG andMF models for oxygen and nitrogen are similar when themolar fraction of TCE is 0.05 at X0 m; however dierences between the concentrations simulated by the twomodels for TCE, oxygen, and nitrogen at X10 m increase with increasing molar fraction of TCE at the inletof the diusing component.Consequently, the diusion coecient calculated byEq. (2) for a diusing component of higher molecular430HIBIFig. 11. Distributions of concentrations of oxygen, nitrogen, andtrichloroethylene at 30000 seconds for a molar fraction oftrichloroethylene of 0.2. White circles represent concentrationsgiven by DG model, and lled circles the case of MF modeFig. 12. Distributions of concentrations of oxygen, nitrogen, andtrichloroethylene at 30000 seconds for a molar fraction oftrichloroethylene of 0.5. White circles represent concentrationsgiven by DG model, and lled circles the case of MF modeweight than those of the surrounding components mustnot be used in the case that the concentration of thediusing component is very low. The DG model developed in this study may be used in this case.by means of the dusty gas model and Graham's law, ascompared with the diusion coecient in Fick's law. Theconcentration of an actual gas phase pollutant in the soilis likely to extend over a large range, since the gas phasemolar fraction will be high in the vicinity of the volatileliquid pollution source and will drop o with distancefrom the liquid source. Consequently it was illustrated inthis study that the dusty gas model must be applied formulticomponent gas systems in the gas phase of soil.The numerical model to simulate mass transfer of multiple components in the soil gas phase has been developedby means of FEM from the duty gas model for a multicomponents gas system. The diusion coecient calculated by Eq. (2) which is applied for gas phase diusion ofa component with very low concentration has often beenused instead of the diusion coecient in Fick's law.Complexity of the calculation can be avoided by employing Eq. (2), reducing the eort of computation.CONCLUSIONBy comparison between a Fick's law of diusioncoecient for a binary gas system and a diusioncoecient derived by means of the dusty gas model andGraham's law for the binary gas system with a very dilutediusing gas, it became obvious that the diusioncoecient given by means of the dusty gas model andGraham's law could be used only if the concentration ofthe diusing gas is considerably dilute. Furthermore, itwas found in this study that the dierence in componentmolecular weights inuences the diusion coecient in abinary gas system when the diusion coecient is givenFORMULATION OF A DUSTY GAS MODELHowever, it was found in this investigation that Eq. (2)could be applied for multicomponent gas systems onlyfor concentrations of the diusing component that didnot exceed 0.10, even in the case of methane which islighter than the molecular weights of the surroundingcomponents. It was also found that Eq. (2) could not beemployed to simulate mass transfer for componentswhich were heavier than the molecular weights of the surrounding components in a multicomponent gas system,even if the molar fraction of this component was 0.05 at aboundary of the domain. The distributions of the concentrations simulated by the DG model were dierent thanthose simulated by the MF model, and it has been conrmed that the DG model developed in this study must beapplied for modeling multicomponent diusion in thesoil gas phase.Only diusion has been estimated in this study; a complete model must also include advection. It may be possible to introduce the dusty gas model into the diusionadvection or dispersionadvection equations by means ofthe numerical model developed in this study.NOTATIONcciDiDijDimtotal concentration [mol/L3]molar concentration [mol/L3] of component iKnudsen coecient [L2/T]binary molecular diusion coecient [L2/T] betweencomponent i and component jmolecular diusion coecient [L2/T] in the multicomponent gas system»/Ø»/Ø»/Ø/Ø Ø »/Ø Ø »D *A1XC1XB{{tDAB tDAC DAD *B1XC1XA{{tDAB tDBC DBD *C1XAXB1{{tDAC tDBC DCD *AB1XA M AtDAB MB1/2D *BA1XB MBtDAB MA1/2»1{ »DXB1{tDAB DA{XAtDAB{BD *A average of the respective values of D *A within eachelementD B* average of the respective values of D *B within eachelementD *C average of the respective values of D *C within eachelementMi molecular weights [M/mol] of component im iteration number of the Picard iteration methodFi basic function at node iNi molar ux [mol/L2T] of component iND molar diusion gas ux [mol/L2T]NN nonequimolar diusion gas ux [mol/L2T]NT total molar diusion ux [mol/L2T]431nnnpqinormal vector to boundary Vthe number of nodesthe number of componentsmolar uxes [mol/L2T] of components i at theboundarytelapsed timeV whole volume [L3]Xi molar fraction [dimensionless] of component iX j average of the respective values of Xi within each elementDt increment of elapsed timeug gaslled porosityug average of the respective values of ug within each elementttortuosity [dimensionless]V boundary of an analytical domainREFERENCES1) Abriola, L. and Pinder, G. 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ログイン | |||||
タイトル | Undrained End Bearing Capacity of an Improved Soil Berm in an Excavation | ||||
著者 | Y. D. Zhang・T. S. Tan・C. F. Leung | ||||
出版 | Soils and Foundations | ||||
ページ | 433〜445 | 発行 | 2008/06/15 | 文書ID | 21119 |
内容 | 表示 SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 433445, June 2008UNDRAINED END BEARING CAPACITY OF AN IMPROVEDSOIL BERM IN AN EXCAVATIONY. D. ZHANGi), T. S. TANii) and C. F. LEUNGii)ABSTRACTFor a wide excavation in soft soil, the excavation can be stabilized by an embedded improved soil berm to increasewall stability and control soil movement. An embedded sti berm essentially behaves like a horizontal pile subjected toa load applied by the retaining wall and derives its resistance to horizontal movement from both end bearing and interfacial shear resistance on the top and bottom of the berm. This resistance helps to restrain the wall from moving inwards to the excavated side. However, to date, there is no known reported literature on the determination of the undrained ultimate bearing capacity of such a berm, especially for the unit end bearing, qb. In this paper, the undrainedend bearing of an improved berm under a plane strain condition was determined. The undrained end bearing capacitywas rst derived using a solution from a proposed upper bound analysis based on observations from centrifuge testsand then modied, taking on the basis of an equivalent nite element analyses. The proposed end bearing capacity factor Nc lies between the upper bound and lower bound solutions. The solution showed that the undrained end bearingcapacity is not a constant but decreases during the excavation process. Furthermore, it was shown that the existence ofan improved soil berm will provide an additional pressure relative to the passive pressure to control the wall displacement.Key words: bearing capacity, excavation, nite element, improved berm, upper bound (IGC: E6/H2)INTRODUCTIONIn an excavation in soft ground with a signicant thickness of soft soil below the nal excavation level, the maximum deection of the retaining wall often occurs belowthis level. This poses a challenge to restrain the wallmovement at this location, as conventional bracing usingsteel struts can not be installed below the formation level.One approach to overcome this is to improve a layer ofsoil at this location of maximum deection through jetgrouting or deep mixing to form an improved soil raft.The eectiveness of these ground improvement techniques in controlling the lateral movement of the retaining wall and the associated ground movements has beenproven in many successful engineering cases (Tanaka,1993; Ou et al., 1996; O'Rourke et al., 1997; Hu et al.,2003).Ou et al. (1996) classied the typical layout of soil improvement in practice into three patterns, namely block,column and wall types as shown in Fig. 1. Depending onthe size and depth of excavation, thickness of the softclay, soil properties and issue of economics etc, one of thethree types may be adopted and the improvement couldbe full (i.e. improvement is from one side of the excavation to the other side) or partial (i.e. the improvementarea is within a certain distance from the wall) (Ou et al.,i)ii)Fig. 1. Typical schemes of soil improvement in excavation: (a) Blocktype, (b) Column type and (c) Wall type (after Ou et al., 1996)1996; O'Rourke et al., 1997; Hsieh et al., 2003).For the case of partial improvement of the block typeas shown in Fig. 1, in this paper, the nomenclature ``anembedded improved soil berm'' is used; ``embedded'' toconvey the idea that this is improved below the soil surface and ``berm'' to emphasize that one end of this improved soil layer is in contact with the wall while the otheris resting against the soil as shown schematically in Fig.2. To a large degree, such an embedded berm behaves likea horizontal pile subjected to a load applied by the retaining wall and derives its resistance from both end bearingand interfacial shear resistance on the top and bottom ofthe berm. This resistance helps to restrain the retainingPostdoctoral Research Fellow, Centre for Soft Ground Engineering, National University of Singapore, Singapore.Professor, Centre for Soft Ground Engineering, National University of Singapore, Singapore (cvetantsnus.edu.sg).The manuscript for this paper was received for review on May 11, 2007; approved on March 17, 2008.Written discussions on this paper should be submitted before January 1, 2009 to the Japanese Geotechnical Society, 4382, Sengoku, Bunkyoku, Tokyo 1120011, Japan. Upon request the closing date may be extended one month.433434ZHANG ET AL.Fig. 2. Bearing capacity components of an improved soil berm in anexcavationwall from moving inwards to the excavated side. Theprincipal dierence between such an embedded berm anda typical pile is that in an excavation, the overburdenabove the berm is being reduced as the excavationprogresses causing the pressure acting on top of the bermand from below the berm to become unequal and thisoverall interaction will aect the mechanism for mobilization of end bearing capacity and thus the overallresistance mobilized.Embedded improved soil berm has been used in a number of cases. Ooi et al. (2002) reported a 14.3 m deep excavation supported by 22.6 m wall with its toe into marine clay in Boston. To increase the stability of the walland reduce the wall movement, a certain area of theground on the passive side next to the wall is improved using jet grouting technique. With this partial soil improvement and other measures, the strut levels was reducedfrom 4 levels to only one top strut to leave larger clearance for construction of the tunnel box. Also, in caseswhere the thickness of the soft soil is uneven or where theretaining support systems vary across excavations, partialimprovement could be carried out within the deeper areaof soft soil to avoid excessive sway movement of theretaining system. Page et al. (2006) reported the use ofsuch a berm in the construction of the undergroundKallangPaya Lebar Expressway (KPE), a jet grout bermwas constructed within the deep marine clay area wherethe base of marine clay is steeply sloping across the excavation. In another project in the mid 1990's, during theconstruction of a shopping mall next to the Singapore'sMass Rapid Transit Pasir Ris Station, only a part of thesoil next to the station is improved using deep cementmixing to ensure that the excavation induced movementto the station is controlled to less than 10mm, a designrequirement.However, to date, there is little research conducted onthe use of such a system of partial soil improvement, oran improved soil berm. In this paper, the undrained endbearing of an improved soil berm under a plane straincondition is established through the use of an analyticalupper bound solution, which is then subsequently modied using results from nite element analysis. The upperbound limit analysis is conducted to determine the keyparameters governing the capacity. The mechanism offailure used in the upper bound analysis is establishedfrom centrifuge tests that were conducted as part of thisresearch. After that, results from nite element analysesare used to improve the estimation of the end bearingcapacity factor and provide further clarication on themechanism that was used in the limit analysis. The analytically developed upper bound solution is then modiedby backanalyzing the results from FE analyses. In thepresent study, the nite element analysis is used to complement the analytical upper bound limit analysis. Such asolution not only can be used for design purposes butmore importantly, also provides a better understandingof how the change in these parameters with the progressof excavation aects the capacity. Such a ``feel'' isdicult to get from numerical analysis alone.UNDRAINED END BEARING CAPACITY OF ANIMPROVED BERMThe ultimate load capacity Qu of an improved soil bermunder axial load as shown in Fig. 2 can be regarded as thesum of the endbearing load Qb and the shaft resistanceload Qs as follows:QuQb{QsAbqb{(As fU{As fL)(1)where Ab is the cross sectional area of the improved soilberm, qb is the unit end bearing capacity of the improvedsoil berm, As is the contact area at the top and bottomsurfaces of the improved soil berm and fU and fL are theunit mobilised interfacial shear resistance between thesoil and the upper and lower surface of the berm, respectively.The bearing capacity of foundations is generally calculated using Terzaghi's equation (Terzaghi, 1943). Theunit end bearing resistance is assumed to comprise threebasic components as follows:gBNg2qbcuNc{gDNq{(2a)where D and B are the depth and width of a foundationrespectively; Nc, Nq, Ng are nondimensional bearingcapacity factors and are functions of the soil friction angle, q. Nc is also a function of the ratio of the depth overwidth of the foundation, D/B. For an undrained case involving saturated clay, the bearing capacity could be expressed in terms of total stresses with Nq1 and Ng0.In such a case, Eq. (2a) becomes:qbcuNc{gD(2b)where Nc is a function of D/B only under undrained condition (Skempton, 1951).One important objective of this paper is to determinethe value of Nc for the case of an improved soil berm andto verify whether Nq1 for an undrained case. The valueof Nc is rst obtained by an upper bound solution.435IMPROVED SOIL BERM IN AN EXCAVATIONFig. 3. Total displacement vectors at 40 mm excavation depth (modelscale). (a) 2 cm thick berm and (b) 3 cm thick bermPROPOSED UPPER BOUND SOLUTION FOR ENDBEARINGTo determine an upper bound solution for the endbearing, it is necessary to calculate the work done by internal stresses and external loads during an incrementalmovement of a kinematically admissible mechanism(Chen, 1975; Atkinson, 1993). Thus, for an upper boundsolution, it is important to have an idea of the actualfailure mechanism for such an embedded berm. In thepresent case, this is provided by imaging data from centrifuge tests conducted as part of the present study andshown in Fig. 3 (Zhang, 2004). The displacement vectorsshown have been established by determining the movement of a grid of patches through the use of a techniqueknown as Particle Image Velocimetry (White et al., 2003;Zhang et al., 2005). From the movements shown in Fig.3, a failure mechanism as shown in Fig. 4(a) is assumed.In deriving the upper bound solution, the soil is assumedto have a unit weight of g, an undrained soil strength ofcu, and the base of the berm is smooth.If the berm moves with a horizontal velocity V0, theother velocities in this admissible mechanism could be determined from Fig. 4(b) as follows:V0;sin aV1V0;VvV1 cos atan aFig. 4. (a) A proposed upper bound failure mechanism and (b) Velocity diagramV2 V0Vv;cos (909|b) tan a sin bØ»1;tan a tan bV12V1 sin a|V2 sin (909|b)V0 1|where V1 is the velocity of the triangular block in Fig.4(a); V2 is the velocity of the block above the berm; V12 isthe relative velocity between these two blocks. a and b aretwo angle variables involved in the failure mechanism.For this mechanism, the external work done E is:EqbDV0|qbDV0|1gD(D tan a)Vv|gC(D tan a)Vv21gD2V0|gCDV02(3)where C is the vertical distance from the excavation baseto the top surface of the berm at each excavation stage orembedment depth of the improved soil berm and D is thethickness of the improved soil berm.The internal work done W is composed of three parts,namely:WcucuDCV1{2cuV2{cu( D tan a)V12cos acos (909|b)D V0CV0{2cucos a sin acos (909|b) tan a sin b436ZHANG ET AL.Ø1tan a tan b{cu( D tan a)V0 1|»(4)By equating E and W, the resulting upperbound solutionobtained is:qb2Ccucu{{cu tan acos a sin a D tan a sin2 bØcuC1{gD{tan b2D|»(5)To obtain the upperbound solution, a and b has to besuch that qb is a minimum. This implies:&qb0&aFig. 5.Bearing capacity factor for the upper bound mechanism&qband0&bIn the present form, it is dicult to solve for the two optimum angles directly. However the upper bound solutionof Eq. (5) could be rearranged into:qbcu1{tan2 aC 1{tan2 b{2cutan aD tan a tan2 bØC 1cu{{gD{cu tan a|D 2tan b»(6)using the relations:sin a1tan a; and cos a.21{tan a(1{tan2 a)Fig. 6.Let stan a, ttan b and mC/D, where the ratio mcould be thought of as an embedment ratio for an embedded improved soil berm. Then Eq. (6) could be simpliedas:«qbcu 2s{» $ØØ12m112m{1{ 2 |{gD m{stt2»(7)The upperbound solution could now be obtained withrespect to variables s and t as follows:&qb&qb0 and0&s&tA system of two equations is then obtained:2m1{2m{ 2t2|0s24m 1{ 0st 3 t 2|t2 |m{16m21{2mby:ØqbNc1cu{gD m{(8)(9)(10)(11)If these relations for s and t are placed into Eq. (7), thecorresponding upperbound solution obtained is given12»(12)WhereNc11{1|1{16m2m(13)Clearly, Nc1 is dependent on the value of m (C/D), asshown in Fig. 5. a and b are also dependent on the valueof m, as given by the relations below and shown in Fig. 6.2 m 1{2m 1809Ø 2 |m{16m»p2 |m{16m 1809barctan Ø»p1{2maarctanSolving Eqs. (8) and (9), the optimum s and t could be determined:2 2 m 1{2ms|m{16m2Two variable angles for the upper bound failure mechanism22(14)(15)Examining Eq. (13), it is clear that this will give problems when m approaches zero, that is approaching a situation where there is no cover to the berm. For example, ifm approaches close to zero, that is when there is almostno cover at all, Eq. (13) will become indeterminate. Whatthis is signalling is that as the cover reduces, the mechanism that has been assumed for the limit analysis is no longer valid. How small should m be before this change occurs is an interesting question by itself.Strictly speaking, if m0, Nc should be 2 (qb2cu{gD(C/D{1/2)), implying that the soil surrounding theend of the berm is in a passive state of failure. If the over437IMPROVED SOIL BERM IN AN EXCAVATIONall situation is undrained, then the angle of the slip planeto the horizontal should be 459according to Rankine'stheory. Thus, a modication is needed for Eq. (13) in thecase of very small m (the denition of ``small'' will be established subsequently). This small m will also indicatethat when the cover above the berm reduces to below this,there is a slight change in the way the berm fails.A reasonable assumption is that as the cover of soilabove the berm thins out, the slip plane will become continuous. In Fig. 4(b), a continuous failure plane meansthat V1V2 and V120, which leads to:b909|a(16)Combining Eqs. (5) and (16) gives:Ø cos a1sin a{2CD tan a1cos a{tan a|tan a »C 1{gD Ø { »D 2c2CC1{1 »{gD Ø { »Øsin a cos a DD 22c1(17)(2m{1){gD Ø m{ »2sin 2aqbcu2uuIt is obvious that the optimum solution for this failuremechanism is when a459. In this case, the corresponding upper bound solution is:ØqbNc2cu{gD m{Nc22{4m2{4»1, where2CD(18)1|1{16m,2m1for mÆ ; and41{NcNc22{4m,for 0ÃmÃ14qbNccu{gDØ DC { 12 »(19)This process also helps to clarify the denition of howsmall the value of m should be before the failure mechanisms transits. This also means that as the cover over theberm becomes thin, the slip plane will become continuous. The limit of this is m0.25, in other word with acover onequarter of the berm thickness. Variation of Ncwith m, as dened by Eq. (19), is plotted in Fig. 5. Theupper bound solution for the end bearing capacitybecomes:(20)where Nc is given by Eq. (19). Equation (20) can be usedto evaluate the end bearing capacity of an embedded improved soil berm in an excavation. Comparing with Eq.(2b), the upper bound solution for Nq is also equal to 1and is independent of m.One interesting observation is that the failure mechanism proposed above for the analysis of a berm used to restrain a retaining wall is similar to that proposed by Daviset al. (1980) for the collapse of a plane strain tunnel, whoused the failure mechanism shown in Fig. 7 to determinethe upper bound solution. There are three variable anglesinvolved in this mechanism, and the upper bound solution was found by optimizing with respect to these threevariable angles. The solution is:(ss|sT)Ncu{gDIn Eq. (18), Nc2 is 2 when m0 and increases linearlywith m. The variation of Nc2 with m is also presented inFig. 5. The point of intersection between Nc1 and Nc2 is m1/4, and the value of Nc at this point is 3. Furthermore,if this value of m is substituted into Eqs. (14) and (15), aand b have the same value of 459, which is consistent withthe assumption in deriving Eq. (18). Thus, for the modication, Nc2 is used for 0ÃmÃ1/4 while Nc1 is used formÆ1/4, that is, the bearing capacity factor Nc of an improved berm is as follows:NcNc1Fig. 7. A collapsein upper bound failure mechanism for a planestrain tunnel (after Davis et al., 1980)N4Ø DC { 12 »C 1{D 4with tan atan b2(21)(22)C 1p{ and d .D 42According to Davis et al. (1980), this solution is alsoapplicable to the case of a blowout failure for a planestrain tunnel, though the direction of the movement ofthe failure body would be reversed. In essence, this typeof failure is similar to the failure of the end bearingcapacity of an improved berm. Figure 5 shows the bearing capacity factor Nc obtained in previous section andthe number N from Davis et al.'s solution. It could beseen that the value of Nc derived in this paper is close tothe value of N from Davis et al.'s solution. The smalldierence reects the slightly dierent failure mechanisms in the two problems.The key parameters contributing to the end bearingcapacity from the upper bound analysis are captured inEq. (20). These parameters are the undrained shearstrength cu, unit weight of soil g, embedment depth of theimproved soil berm C and thickness of the improved soilberm D. As the upper bound solution would normallyoverestimate the end bearing capacity factor Nc, in thefollowing section, nite element analyses have been conducted to improve the estimation of Nc, and to modifythe above proposed upper bound solution.438ZHANG ET AL.Table 1. Methods for calculating end bearing capacity and horizontalstress for an improved soil bermMethod End bearing from upper bound Measured horizontal stressTotalNetØqbNccu{gD m{ØqbnetNccu{gD m{1212»»(1|k0)qmØqmnetqm|k0gD m{12»FINITE ELEMENT ANALYSISPotts (2003) summarized the solution requirements satised by three categories of analysis (Closed form, simple and numerical analysis) in his 42th Rankine Lecture.For a complete solution, the basic requirements ofequilibrium, compatibility, material behaviour and theload and displacement boundary conditions must all besatised. For the upper bound limit analysis, the requirements of equilibrium and the force boundary conditionsare not met and kinematically admissible failure mechanism is postulated based on observations or assumption.For this reason, upper bound solution over predicts theresults. This is also true for this case to determine the endbearing capacity of an improved soil berm.It is interesting to note that Ukritchon et al. (2003)adopted the numerical limit analysis to evaluate the undrained stability of braced excavations in soft clay, inwhich the upper and lower bound limits are solved numerically by linear programming methods. It is reportedthat the numerical limit analysis is able to bound the stability number within }5z through careful discretizationof the upper and lower bound meshes. The numericallimit analysis requires no postulation of failure mechanisms. However, this method is still under the frameworkof limit analysis and as such the limitations of limit analysis as in Table 1 still exist for the numerical limit analysis.Moreover, the numerical limit analysis, unlike the otherfull numerical methods such as nite element and nitedierence methods, is not capable of dealing with stability problems involving time dependent behaviour including consolidation/swelling and dynamic behaviour.Another powerful approach, besides the analyticalmethods, is the nite element analysis. All the four requirements stated above are met, and the geometry andboundary conditions of a specic problem can be accurately modeled. The nite element method has beenwidely used to evaluate various stability problems such asslope stability (Griths and Lane, 1999), bearing capacity(Potts, 2003; Griths, 1982; Zdravkovic et al., 2003) andbasal stability of an excavation (Faheem et al., 2003;Hashash and Whittle, 1996). Griths (1982) evaluatedthe ability of the FEM to calculate the three bearingcapacity factors in Eq. (2a). It is concluded that the FEMcould be used to predict the bearing capacity of a surfacefooting, and in particular, the FE results showed goodagreement with closed form solutions for Nc and Nq.Zdravkovic et al. (2003) evaluated the change of the ultiFig. 8.Nodes and stress points for 15node triangular elementmate undrained bearing capacity under dierent consolidation ratios using the nite element method, whichwould be dicult to evaluate by other traditional analytical methods. This clearly demonstrated the exibility andversatility of the nite element method in dealing withcomplex stability problems. Therefore, in this study, theFE method is adopted to improve the estimation of theend bearing factor Nc and to demonstrate that Nq is equalto 1 based on Eq. (20).In the present FE study, 15node cubic strain triangularelements are chosen in the mesh used to predict the bearing capacity factors since Borst and Vermeer (1984) andSloan and Randolph (1982) have shown that such 15nodes triangular elements are very accurate and able toproduce high quality stress results for dicult problems,such as the collapse load calculation. The 15node triangular element provides a fourth order interpretation ofdisplacement and the numerical integration involvestwelve Gauss stress points as shown in Fig. 8.The displacement control method is chosen to predictthe collapse load as the improved soil berm behaves morelike a rigid foundation rather than a exible foundation.The commercial software Plaxis v7.2 Professional(Brinkgreve and Vermeer, 1998) was used to calculate thecollapse load F (kN/m) using the elasticperfectly plasticMohrCoulomb model. This software is able to providethe displacementload curve and furthermore the appliedexternal load can be obtained directly during the calculation process. Furthermore, Plaxis also allows the users tospecify the tensile stress induced in the soil. However, forthe present study, no tensile stress in the soil was allowed.Therefore, the possible eect of the tensile stress on theend bearing capacity of an improved soil berm is eliminated. In the case of a weightless soil, the bearing capacity factor could be determined from the collapse load bythe equation:Fcu BNc(23)where B is the width of the footing.Verication ProblemA traditional plane strain bearing capacity problem fora strip foundation with dierent embedment depth D wasevaluated using the FEM to verify its ability to predict thebearing capacity factor Nc in an undrained condition.Figure 9 presents two meshes, one for a surface footingand another for a footing with D/B4. The meshesIMPROVED SOIL BERM IN AN EXCAVATIONFig. 9.Typical FEM meshes for vertical footingsFig. 11.Fig. 10.439Typical FEM meshes for improved soil bermsBearing capacity factors for vertical footingaround the footing were more rened to ensure more accurate results. The width of the footing, B, was assumedto be 2 m. Because of symmetry, only half of the footingwas analysed. The soil was assumed to be weightless withan undrained shear strength cu of 20 kN/m2. The bearingcapacity was mobilised by applying a prescribed verticaldisplacement at all the nodes within the footing. Valuesof Nc obtained from FE analyses were compared withthose from Skempton (1951) and shown in Fig. 10. Thisshows close agreement though the value of Nc for large mfrom the FE analyses is a little higher (7.9) than the valueof 7.5 from Skempton's result. However, Meyerhof(1951) provided a solution for the bearing capacity of apurely cohesive material and the maximum value of Nc is8.28 for a smooth deep strip foundation. Compared withthe solutions by Skempton and Meyerhof, the present FEresults give an intermediate solution for large m. What isimportant here is that the above analysis demonstratesthat FEM is suitable for analysing the bearing capacityproblem.Computation of Nc of an Improved Soil BermIn order to compute the endbearing capacity factor Ncin Eq. (2b) of an improved soil berm, it is necessary to assume that the soil is weightless. Otherwise, the contribution of the soil's weight to the total end bearing capacityneeds to be separated rst. However as the eect of theFig. 12. End bearing capacity factor Nc for improved soil berm fromFEM analysisweight of soil and undrained shear strength were presentsimultaneously in the FE analysis, it is dicult to distinguish them. This isolation means that the undrainedshear strength will govern the endbearing capacity. Inthis case, Nc could be calculated directly using Eq. (23)once the other parameters are established.The undrained shear strength in this analysis was assumed to be 20 kN/m2. The thickness of the berm, D, was2 m. The embedment depth of the berm, C, is varied forthe parametric study. The length of the berm, L, is 10 m,which is long enough to avoid the inuence from the endof the berm that is in contact with the retaining wall. Infact, the length of the berm needs to exceed the passive inuence zone to behave eectively (Thanadol, 2002).Figure 11 shows two meshes for the cases of mC/D0and mC/D4. To simplify the analysis, the retainingwall was treated as a boundary on rollers, with verticalmovement only and no horizontal movement was allowed. Finally, the berm is assumed to behave like a rigidbody, and was replaced by a set of equivalent boundaryconditions. At the top and bottom surface of the berm,only horizontal movement was allowed and verticalmovement was not allowed. This treatment allows theisolation of the endbearing capacity from the interfacialshear resistance that would otherwise be mobilised by the440ZHANG ET AL.improved soil berm.The computed Nc is presented in Fig. 12 which showsthat Nc starts from 2.037 for m0 and reaches a maximum of 8 for mÆ8. For m0, the calculated Nc is closeto Rankine's earth pressure theory. At the other extreme,the calculated maximum Nc is nearly the same value as avertical strip footing. This nding is reasonable since forhigh m values, the failure mode of the end bearing of animproved soil berm becomes a local shear failure just likethe failure mode of a vertical deep foundation. This observation is also consistent with Meyerhof (1973) who hasshown that the breakout coecients of vertical anchors atgreat depths in clay were the same as the bearing capacityfactors of deep foundations.Computation Nq of of an Improved Soil BermThe second part of the endbearing capacity comesfrom the soil weight. To evaluate the contribution of selfweight alone, it is assumed that the soil has a unit weightof 15 kN/m3 but the soil is cohesionless. However, usingcu0 would have caused the analysis to be unstable. Instead, a nominal undrained shear strength of 0.2 kPa wasused in the FEM analysis. The value of Nq correspondingto the particular m(C/D) is obtained using the equation:FNq qDF(24)1gD m{D2where q is the average surcharge due to the weight of soilacting on the berm tip. For the undrained case, the theoretical solution shows that Nq should be equal to 1. Thepreviously proposed upper bound solution has alsoshown that Nq1 for the undrained condition.Figure 13 shows the variation of the value of Nq withthe value of m. As can be seen, the calculated Nq value isslightly larger than 1, but decreases with increasing m.This slight deviation from 1 is probably due to the use ofa nominal shear strength for the sake of numerical stability. However, with increase in the value of m, the contribution of a small undrained shear strength to endbearingcapacity becomes negligible and Nq approaches 1.Ø»Fig. 13. Bearing capacity factor Nq for improved soil berm from FEManalysisIndependence of Nc and NqThe independence of Nc and Nq was examined using thefollowing approach. Firstly, the collapse load F of an improved soil berm was computed when both undrainedshear strength and soil weight are included in the FE analysis. Secondly, it is reasonable from earlier sections to assume Nq1. Then, Nc can be calculated from Eq. (23) toarrive at the following equation:1F|gD m{2F|NqqN c(25)cu DcuDØ»Finally, the calculated Nc obtained here is compared withthe Nc obtained in the previous section where the soil isweightless. If these two are quite close, it can be safelyconcluded that the terms Nc and Nq are independent.Otherwise, Nc and Nq are dependent.The comparison is shown in Fig. 12 and shows that Ncvalues calculated using the two dierent ways are virtually identical. Therefore, it can be concluded that the termsNc and Nq are independent and the contributions from theundrained shear strength and soil's weight to total endbearing capacity are independent. This also supports thepresent approach to isolate Nc and Nq.MODIFIED UPPER BOUND SOLUTIONFigure 14 shows that the value of Nc from the proposedupper bound solution is larger than the corresponding Ncfrom the FE analysis, while the FE solution lies betweenthe upper bound and lower bound solutions proposed byDavis et al. (1980). The main reason the upper bound solution of Nc is higher than that of the FE solution is likelyto be due to the assumption of full mobilisation of theundrained shear strength on the slip planes for the upperbound analysis. For a deep foundation, the failure modewill be a local shear failure rather than a general shearfailure and thus full mobilisation is unlikely.To obtain a more accurate upper bound solution andprovide an empirical solution to evaluate the value of Nc,the upper bound solution proposed earlier would need tobe modied. This modication was implemented throughthe introduction of a mobilisation factor l to modify theFig. 14.End bearing capacity factors from dierent solutions441IMPROVED SOIL BERM IN AN EXCAVATIONundrained shear strength on the two parallel slip planesof the improved soil berm. This concept is similar to the``equivalent free surface'' used by Meyerhof (1951) toderive the bearing capacity of strip foundations. Thevalue of l is expected to vary with m. The relationship ofl and m will be determined in this section, after which, Ncobtained from the modied upper bound analysis will becompared with that from the FEM analysis.Earlier, Eq. (5) was established to be the solution forthe proposed upper bound analysis, assuming full mobilisation of shear strength along the entire slip plane.However, if a mobilisation factor l is introduced, the external work E remains unchanged but the internal workW becomes:WcuD V0CV0{2lcucos a sin acos (909|b) tan a sin bØ1tan a tan b{cu (D tan a)V0 1|»Nc1|1{16lm2lm1{Obviously, Nc from the modied solution is equal tothat in Eq. (13) if l1. There are three unknown variables in this equation, namely Nc, l and m. To determinethe relationship between l and m, the true Nc needs to beestablished. In the present study, Nc from the FEM analysis was used to backanalyze the relationship between land m, which is shown in Fig. 15. This gure shows thatthe relationship between l and m can be divided intothree zones. The rst zone is mÃ1, where the value of ldecreases rapidly. The second region is 1ÃmÃ2 andwhere the value of l decreases very slightly. The thirdregion lies in 2ÃmÃ9, where the value of l decreases(26)Consequently, the unit end bearing capacity qb for themodied upper bound isCcucu{2l{cu tan acos a sin aD tan a sin2 bqbØcuC1|{{gDD 2tan b»(27)Following the same working procedure, Nc for the modied upper bound becomes:Fig. 16.(28)Fig. 15.Relationship between l and mDisplacement contours at dierent values of m442ZHANG ET AL.almost linearly with increasing m. The division ofrelationship between l and m into three zones can be understood from the point of view of failure modes. WhenmÃ1, the failure mode is dominated by a general shearfailure, which means that failure planes will extend up tothe ground surfaces as can be seen from the displacementcontours in Fig. 16. The failure mode observed is close tothat used in the upper bound analysis. This also explainsthe fact that Nc from the upper bound solution in thiszone is close to that from the FEM analysis as shown inFig. 14. In the zone of 2ÃmÃ9, the failure mode isdominated by local shear failure, which means that thefailure planes will not extend up to the ground surface.This can also be observed in Fig. 16, which shows an increase of displacement contour lines around the berm anda decrease of contour lines extending to the surface whenm increases. This also accounts for the observation thatNc from the upper bound solution increasingly deviatesfrom the FE analysis as shown in Fig. 14. The zone of1ÃmÃ2 is the transition from a general shear failure to alocal shear failure. Here, Nc from the upper bound solution begins to deviate from the FE analysis.To back analyse the value of l to be used in the modied upper bound analysis, the nearly linear relationshipbetween l and m in the zone of 2ÃmÃ9 was approximated by a linear relation and then extrapolated to the rangeof 0.25ÃmÃ2. This extrapolation will not aect the calculated Nc values signicantly, as discussed later. In theregion of 0ÃmÃ0.25, the value of l is set to 1. The ttedrelation is also presented in Fig. 15. With this tted relation, the complete description of the modied upperbound solution is given by Eq. (20) with the value of Nc asfollows:11|1{16lm, for ºmÃ8; (29a)2lm4NcNc1 1{NcNc22{4m,for10Ãmà .4where l|0.0468m{0.8101,for(29b)1ºmÃ8.4(30)in the above equation, l is the mobilization factor, whichis dependent on the embedment ratio m.It is important to note that the maximum Nc is reachedat m8 and is then a constant thereafter as shown earlier. This value of m can be called the critical embedmentratio mcr. Therefore, if the real value of m is bigger than8, a value of 8 should be used in Eqs. (29) and (30) tocompute Nc. Nc calculated using this modied upperbound solution is also presented in Fig. 14 and beingback analyzed, agreed well with and almost identical tothat of the FE analysis.IMPLICATIONS OF THE MODIFIED UPPERBOUND SOLUTIONThe importance of the modied upper bound solutionof Eqs. (20), (29) and (30) lies in not only providing asemianalytical solution in determining the end bearingcapacity but also oering an insight into the mechanismof the changing end bearing capacity during excavationprocess as well as laying the foundation for further experimental and numerical study (Zhang, 2004).For the improved soil berm in an excavation, with theprogress of excavation, the embedment ratio m decreasesand the value of Nc will decrease according to Eqs. (29)and (30) when m is less than 8. At the same time, the overburden gD(m{1/2) also decreases. Thus both contributors to the end bearing capacity on the right side of Eq.(20) decrease with the progress of excavation. On theother hand, with increasing excavation, the wall movement increases which means a greater mobilisation of endbearing capacity and consequently this means a lower factor of safety for the end bearing capacity.Furthermore, Eqs. (20), (29) and (30) show that thepresence of an improved soil berm will supply an additional pressure relative to the passive pressure to controlthe wall displacement, provided that the length of theberm is long enough to ensure that the end bearing failurezone lies outside the general passive zone of the excavation (Thanadol, 2002). The additional pressure is thedierence between qb and pp which is the passive pressure(2cu{gD(C/D{1/2)) for the improved soil berm. Thisadditional pressure is given by:Dp(Nc|2)cu(31)This additional pressure acting on the wall will increasethe stability of the wall and consequently reduce the wallmovement. Obviously, this additional pressure wouldalso decrease as the embedment ratio m drops and nallyequals to zero when it reaches is the passive state. Fromthis point of view, it is preferable to treat the ground before commencement of any excavation to better utilisethe improvement eect of the improved soil berm.It should be also noted that the end bearing capacityprovided in Eq. (20) together with the modied upperbound solution is the total maximum stress between thesoil and the berm which includes initial contact stress dueto soil weight before the berm is loaded. For the case ofan improved soil berm, the initial contact stress is thetotal horizontal stress at rest. During excavation, it is themobilised horizontal stress over and above the initialhorizontal stress that is helpful to control the wall movement. The maximum horizontal stress that can bemobilised to resist the wall movement is the net end bearing capacity qbnet, which can be obtained from the totalbearing capacity minus the inital total horizonal stress atrest. Therefore, to obtain the net end bearing capacityqbnet of improved soil berm, the initial horizontal stressshould be subtracted from Eq. (20) as following:ØqbnetNccu{gD m{»1(1|K0)2(32)where K0 is the coecient of total earth pressure at rest.To provide a feel for the modied upper bound solution developed, the results of a centrifuge test will bepresented. In this test, the embedment depth C beforeIMPROVED SOIL BERM IN AN EXCAVATION443end bearing through increasing the total contact stress between berm and soil. It is precisely this combined eect oftwo opposing trends that causes the nearly constantmeasured total horizontal stress. If the initial stress at K0condition at each excavation step is separated from thetotal calculated end bearing capacity and measured totalend bearing as the way presented in Table 1, the net endbearing capacity and net/mobilised end bearing could beobtained as shown in Fig. 18. It is clear that the mobilisedend bearing keeps increasing while the net end bearingcapacity continues decreasing during the excavation process. Furthermore, it can also be seen from Fig. 17 that themeasured lateral stress begins to be larger than the passivepressure after 4.5 m excavation.Fig. 17. Total end bearing capacity, measured horizontal stress andpassive stress with excavation depth at the middle level of bermFig. 18. Net end bearing capacity and mobilised end bearing with excavation depth at the middle level of bermany excavation is 10 m (all dimensions are given in prototype scale) and the thickness of the improved berm D is 2m. A total stress transducer was placed at the far end ofthe berm away from the wall and right in the center tomeasure the total horizontal stress. Other details of thecentrifuge test could be found in the thesis by Zhang(2004).The variation of calculated end bearing capacity fromthe modied upper bound analysis and the measured endbearing with excavation depth for the test are shown inFig. 17. Two trends are discernable. As expected, with increasing excavation depth, the calculated end bearingcapacity decreases with excavation depth, a direct resultof the reduction in embedment depth C. On the otherhand, the actual horizontal stress from measurement isvirtually constant, and in fact increases slightly withdepth. This is not obvious but logical. With increasingdepth of excavation, the total vertical stress is beingreduced and if the wall and berm are not allowed tomove, the total horizontal stress is also being reducedcorrespondingly to comply with the K0 condition.However, the wall and berm in fact needs to move due tolateral unloading eect which leads to mobilisation of theCONCLUSIONSAn embedded improved soil berm in an excavationbehaves like a horizontal pile in that it mobilises its endbearing and shaft shear resistance to restrain the wallfrom moving inwards to the excavated side. The undrained bearing capacity of a berm is the sum of the undrained end bearing capacity and undrained shearresistance. But unlike a pile, in a berm the conningstresses on top and bottom are changing all the time withexcavation and this complicates its mechanics. In thisresearch, the end bearing capacity of the berm is established through stages shown in Fig. 19. The main conclusions from this research can be summarised as follows:1) An upper bound failure mechanism for the improved soil berm in an excavation was proposedbased directly on observations from centrifugetests to estimate the undrained end bearing capacity qb. It is shown that qb comprises two parts (qbNccu{gD(C/D{1/2)); one is due to undrainedshear strength cu and the other due to soil weight.The key parameters governing the end bearingcapacity can be determined from the upper boundsolution.2) As upper bound solution would overestimate theend bearing capacity provided by the improved soilberm, a modied upper bound solution whichcombines the results of the upper bound solutionand FE analysis was then developed to improve theestimation of qb. The end bearing capacity factorNc presented here lies between the upper boundand lower bound solutions provided by Davis et al.(1980).3) In the FE analysis, a procedure for estimating qb isintroduced. It is conrmed that the contributionfrom the soil weight and undrained shear strengthto qb is independent.4) Under plane strain condition, undrained end bearing capacity factor Nc increases nonlinearly from 2to 8 as the embedment ratio m increases from 0 to8 and afterwards. It is shown that the existence ofan improved soil berm will provide an additionalpressure relative to the passive pressure to increasestability of the wall and consequently control the444ZHANG ET AL.Fig. 19.5)Flow chart of determination of end bearing capacity of improved soil bermwall displacement.Both undrained end bearing capacity factor Nc andoverburden on the improved berm reduce with excavation depth, as such the undrained end bearingcapacity is not a constant but decreases during theexcavation process. Therefore it is preferable totreat the ground before commencement of any excavation to better utilise the improvement eect ofthe improved soil berm.REFERENCES1) Atkinson, J. H. (1993): An Introduction to the Mechanics of Soiland Foundations through Critical State Soil Mechanics, McGrawHill, London.2) Borst, R. D. and Vermeer, P. A. (1984): Possibilities and limitations of nite elements for limit analysis, G áeotechnique, 34(2),199210.3) Brinkgreve, R. B. J. and Vermeer, P. A. (1998): Finite ElementCode for Soil and Rock Analyses: Version 7.4) Chen, W. F. (1975): Limit Analysis and Soil Plasticity, Elsevier,New York.5) Davis, E. H., Gunn, M. J., Mair, R. J. and Seneviratne, H. N.(1980): The stability of shallow tunnels and underground openingsin cohesive material, G áeotechnique, 30(4), 397416.6) Faheem, H., Cai, F. and Hagiwara, T. (2003): Twodimensionalbase stability of excavations in soft soils using FEM, Computersand Geotechnics, 30(2), 141163.7) Griths, D. (1982): Computation of bearing capacity factors usingnite elements, G áeotechnique, 32(3), 195202.8) Griths, D. and Lane, P. A. (1999): Slope stability analysis by niteelement, G áeotechnique, 49(3), 387403.9) Hashash, Y. and Whittle, A. J. (1996): Ground movement prediction for deep excavations in soft clay, Journal of Geotechnical Engineering, 122(6), 474486.10) Hsieh, H. S., Wang, C. C. and Ou, C. Y. (2003): Use of jet grouting to limit diaphragm wall displacement of a deep excavation,Journal of Geotechnical and Geoenvironmental Engineering,129(2), 146157.11) Hu, Z. F., Yue Z. Q., Zhou, J. and Tham, L. G. (2003): Design andconstruction of a deep excavation in soft soils adjacent to the Shanghai Metro tunnels, Canadian Geotechnical Journal, 40(5),933948.12) Meyerhof, G. G. (1951): The ultimate bearing capacity of foundations, G áeotechnique, 2(4), 301332.13) Meyerhof, G. G. (1973): Uplift resistance of inclined anchors andpiles, Proc. 8th ICSMFE, Moscow, USSR, 2.1, 167172.14) Ooi, P. S. K., Walker, M. P. and Smith, J. D. (2003): Performanceof a singlepropped wall during excavation and during freezing ofthe retained soil, Computers and Geotechnics, 29(5), 387409.15) O'Rourke, T. D., Dewsnap, J. and Stewart, H. E. (1998): CaseHistory of an Excavation Stabilized by Deep Mixing Methods,Designing and Construction of Earth Retaining Systems, Geotechnical Special Publicaton, 83, 4162.16) Ou, C. Y., Wu, T. S. and Hsieh, H. S. (1996): Analysis of Deep excavation with column type of ground improvement in soft clay,Journal of Geotechnical engineering, 122(9), 709715.17) Page, R. J., Ong, J. C. W. and Osborne, N. (2006): Jet grouting forexcavations in soft claydesign and construction issues, International Conference on Deep Excavations, 2830 June, Singapore.18) Potts, D. M. (2003): Numerical analysis: a virtual dream or practical reality?, G áeotechnique, 53(6), 535573.19) Skepmton, A. W. (1951): The bearing capacity of clays, Proc. Conference on Settlement of Structures, Pentech press, London, 1,180189.20) Sloan, S. W. and Randolph, M. F. (1982): Numerical prediction ofcollapse loads using nite element methods, International Journalfor Numerical and Analytical Methods in Geomechanics, 6(1),4776.21) Tanaka, H. (1993): Behavior of braced excavations stabilized bydeep mixing method, Soils and Foundations, 33(2), 105115.22) Terzaghi, K. (1943): Theoretical Soil Mechanics, Wiley, New York.23) Thanadol, K. (2002): Behaviour of an embedded improved soilberm in an excavation, PhD Thesis, Department of Civil Engineering, National University of Singapore.24) Ukritchon, B., Whittle, A. J. and Sloan, S. W. (2003): Undrainedstability of braced excavations in clay, Journal of Geotechnical andGeoenvironmental Engineering, 129(8), 738755.IMPROVED SOIL BERM IN AN EXCAVATION25) White, D. J., Take, W. A. and Bolton, M. D. (2003): Soil deformation measurement using particle image velocimetry (PIV) and photogrammetry, G áeotechnique, 53(7), 619631.26) Zdravkovic, L., Potts, D. M. and Jackson, C. (2003): Numericalstudy of the eect of preloading on undrained bearing capacity, International Journal of Geomechanics, 3(1), 110.27) Zhang, Y. D., Tan, T. S. and Leung, C. F. (2005): Application of445particle imaging velocimetry (PIV) in centrifuge testing of uniformclay, The International Journal of Physical Modelling in Geotechnics, 5(1), 1728.28) Zhang, Y. D. (2004): An embedded improved soil berm in an excavationMechanisms and capacity, PhD Thesis, Department ofCivil Engineering, National University of Singapore. | ||||
ログイン | |||||
タイトル | Rate-dependent Response of Dense Sand in Cyclic Triaxial Tests | ||||
著者 | L. A. Salvati・L. Q. AnhDan | ||||
出版 | Soils and Foundations | ||||
ページ | 447〜451 | 発行 | 2008/06/15 | 文書ID | 21120 |
内容 | 表示 SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 447451, June 2008RATEDEPENDENT RESPONSE OF DENSE SANDIN CYCLIC TRIAXIAL TESTSL. A. SALVATIi) and L. Q. ANHDANii)ABSTRACTA number of cyclic triaxial tests were performed on Monterey No. 0/30 and Sacramento River Sand to investigatethe eect that loading frequency has on the response of sands. The tests were performed on dense, air pluviated sandwith loading frequencies of 0.1 and 1.5 Hz at varying conning pressures, cyclic shear stresses, and peak shear stresses.Under certain loading conditions, the frequency of loading did have a noticeable eect on the response of the sand;larger axial strains were measured in the samples that were subjected to the lower frequency of loading. This dierencein response measured at the two loading frequencies occurred mainly in the rst few cycles of loading, when the dierence in the strain rates was the greatest. Conditions that resulted in larger axial strains, such higher stress levels andlarger cyclic shear stresses, also resulted in a greater dierence between the axial strains measured at the two loadingfrequencies.Key words: cyclic, loading rate, sand, triaxial (IGC: D6/D7)0.001z. In addition, plane strain compression tests wereperformed on Hotsun sand in which the strain rate wasincreased and decreased around a baseline value, andthese were compared to a series of tests that were run atseveral dierent but constant strain rates in Matsushita etal. (1999). While there was little dierence in response between the tests performed at constant strain rates, thestiness of the samples increased and decreased as the axial strain rate was increased and decreased during testswith varying strain rates. Based on these and similar testsperformed on other sands and gravels, Tatsuoka et al.(1999) argued that granular materials were sensitive tochanges in strain rate rather than to the strain rate itself.The change in strain rate does seem to have a much greater inuence on the response, but some tests on granularmaterials have shown dierences in response betweentests performed at dierent constant strain rates. Santucci de Magistris et al. (1999) noted that the strain rateaected the stiness of a silty sand at strains less than0.001z, although the change in strain rate had more inuence on the response than the actual value of strain ratewith increasing strain levels.The above recent work has mainly focused on monotonic loading with creep and stress relaxation. The purpose of this study is to examine the eect that the loadingrate has on the cyclic response of granular materials.Therefore, cyclic triaxial tests were performed on drysands at dierent loading frequencies under a range ofconditions. These tests and their results, which will bediscussed in subsequent sections, will contribute to theINTRODUCTIONTrac loading on highway and railway embankments,wind or seismic loading on bridges, buildings or otherstructures, and water uctuation on earth dams are sometypical repeated/cyclic loads in geotechnical engineering.Depending on the soil characteristics, the repeated/cyclicloading may lead to damage of structures or require continuous maintenance operations. Good understanding ofstressstrain response of repeated/cyclically loadedgranular materials helps designers or engineers to providerational design solutions and more cost eective construction procedures. Recent researches have found thatgranular materials including sands show ``apparent'' viscosity properties such as creep, relaxation and loadingrate (Tatsuoka, 2007; Di Benedetto, 2007). As noted inTatsuoka (2007), a better understanding of how the rateof loading inuences the soil stiness and deformationunder monotonic and cyclic loading is needed, especiallyfor sand, since rate eects in granular materials are notwell understood.Several studies have investigated how creep in sandscan lead to instabilities (e.g., Lade, 1994; Lade et al.,1997), and recent studies have documented the ratedependency in sands in plane strain compression andtriaxial tests (Tatsuoka et al., 1999; Di Benedetto et al.,2002; Tatsuoka et al., 2002). Di Benedetto and Tatsuoka(1997) developed a rheological model based on the creepand stress relaxation observed in tests performed onsand, gravel, soft rock and clays, even at strains less thani)ii)Clare Boothe Luce Asst. Prof., Dept. of Civil Eng. and Geol. Sciences, 156 Fitzpatrick Hall, Univ. of Notre Dame, USA.Transportation Engineer, California Department of Transportation, USA (aileellisassoc.com).The manuscript for this paper was received for review on October 30, 2006; approved on April 8, 2008.Written discussions on this paper should be submitted before January 1, 2009 to the Japanese Geotechnical Society, 4382, Sengoku, Bunkyoku, Tokyo 1120011, Japan. Upon request the closing date may be extended one month.447448SALVATI AND ANHDANTable 1.Properties of Monterey No. 0/30 and Sacramento River Sand2SandeminemaxGsCuD60/D10CcD30/(D*60D10)D60(mm)Monterey No. 0/30Sacramento River0.540.590.890.912.642.701.291.310.980.970.380.24understanding of ratedependent response in granularsoils. The results of these tests can be used to improveconstitutive models that include rate eects (e.g., DiBenedetto et al., 2002; Tatsuoka et al., 2002), which canlead to improved predictions of deformations at dierentrates of loading.MATERIALS USEDTwo sands, Monterey No. 0/30 Sand and SacramentoRiver Sand, were used in the tests, and their propertiesare shown in Table 1. These two materials were selectedbecause they have been used in numerous other studies,and they have dierent particle angularities. The Monterey No. 0/30 Sand is a highly uniform, subroundedbeach sand, and it was modied slightly by removing theparticles with diameters less than 0.075 mm. TheSacramento River Sand is a subangular to subroundedsand, and it was modied so most of the sand particleswith diameters larger than 0.297 mm and smaller than0.15 mm were removed.TEST METHODSDry pluviation was used to prepare the samples, whichwere 70 mm (2.8 inches) in diameter and approximately150 mm (5.9 inches) in height. The relative density ofsamples ranged from Dr86z to 89z for the MontereyNo. 0/30 Sand and Dr87z to 90z for the SacramentoRiver Sand. Dense samples were used to minimize theeects of nonuniformity between dierent samples. Inthe stresscontrolled triaxial tests, the samples weresheared monotonically at a rate of 50 kPa/min to a givenmean shear stress (qmean), and then 100 cycles ofloading/unloading were applied at either 0.1 Hz or 1.5Hz. These tests were performed on dry sands so any possibility of viscous eects resulting from the pore watercould be avoided. Internal LVDTs, held in place by tworings that surround the sample, were used to measure axial strain.Since the objective of this study is to investigate theeect of loading frequency on the response of sand, it isdesirable to minimize the dierences between the samples, which are inherent to testing natural materials.Therefore, the axial strains that were measured after themean shear stress was reached (and cyclic loading was initiated) are reported as ea, fm in addition to the typical axialstrains, ea, which are measured from the beginning of thetest. These measures are illustrated in Fig. 1.Fig. 1.Denition of terms and symbols used with a typical testTEST RESULTSA series of triaxial tests with varying cyclic shear stresses (qcyclic), conning pressures (s3), and peak stresses(qpeak) were performed to in order to investigate theresponse of the sands at the dierent loading frequencies.The conning pressures used in the tests ranged from 65kPa to 200 kPa. As an example of the eect of conningpressure, Fig. 2(a) shows the results from tests performedon Monterey Sand with qpeak300 kPa and qcyclic150 kPa. The conning pressures for the tests were s365 kPa, s3100 kPa, and s3150 kPa, which correspond to peak stress levels of 5.6, 4 and 3, respectively.For the tests performed at s3150 kPa, the axial strainsafter 100 cycles are nearly identical for the two frequencies of loading. However, in the tests performed at s3100 kPa and s365 kPa the axial strains measured at theend of the 100 cycles were smaller for the tests run at thehigher frequency. Figure 2(b) shows the deviatoric stressvs. axial strain for the test on Monterey 0/30 Sand withs365 kPa, as an example of the typical response.The cyclic stresses (qcyclic) used in the test series rangedfrom 50 to 300 kPa. Figure 3 shows the results of testsperformed on Sacramento River Sand with s3100 kPa,qpeak300 kPa, and qcyclic150 kPa, 100 kPa, and 50kPa. With increasing cyclic stresses, an increasing dierence in axial strains was recorded at the two loading frequencies. Similar tests were performed with a higher s3and qpeak, 200 kPa and 600 kPa respectively. The cyclicstresses in these tests were 100 kPa and 300 kPa. As seenin Fig. 4, the dierence in the response between the twoloading frequencies was more pronounced at the highercyclic stress. Results from the entire test series are given inTable 2 and summarized in Fig. 5. The dierence between the axial strains measured at the two loading fre449DENSE SAND IN CYCLIC TRIAXIAL TESTSquencies increased with increasing qcyclic/s3 for bothsands.served rate eects for multiplephase testing, especiallysince the resilient modulus test, which is commonly usedTwoPhase TestsIt is interesting to examine the implications of the obFig. 3. Cyclic triaxial tests of Sacramento River Sand with s3100kPa and varying qcyclicFig. 2. Cyclic triaxial tests of Monterey No. 0/30 Sand with qpeak300kPa and varying s3: a) axial strain measured from qmean and b)deviator stress vs. axial strain for s365 kPaTable 2.aFig. 4. Cyclic triaxial tests of Monterey No. 0/30 Sand with s3200kPa and varying qcyclicResults from cyclic triaxial testsSandqpeak (kPa)qcyclic (kPa)qmean (kPa)s3 (kPa)Final Dea, fm(mm/mm)~10|4Final Dea(mm/mm)~10|4Dierence in finalea valuesa (z)Monterey300300300300300600600600150150150100503001003001501501502002503005003006510015010010020020015043.78.50.54.305.91.375.339.210.40.51.114.41.875.311.811.10.61.41.56.93.427.6Sacramento300300300300300600600150150150100501003001501501502002505003006510015010010020020017.96.40.93.90.56.28.517.96.40.94.10.68.99.37.69.73.56.81.29.311.5Dierence in nal ea values (z)[(ea(100 cycles)f0.1 Hz|ea(100 cycles)f1.5 Hz)/ea(100 cycles)f0.1 Hz]~100450SALVATI AND ANHDANFig. 6. Results from a two phase cyclic triaxial test with qcyclic increasingFig. 5. Inuence of qcyclic/s3 for cyclic triaxial tests with dierentloading ratesin pavement design, is a multiplephase test performed ata single loading frequency. In the LTPP 46 Protocol(Alavi et al., 1997), the sample is prestrained and thensubjected to a series of increasing cyclic shear stresses at agiven conning pressure. Next, the conning pressure isincreased for base/subbase soils or decreased for subgrade soils, and the cyclic shear stresses are increasedagain. To investigate the inuence that the rate of loadingmight have on tests with similar loading sequences, twophase tests were completed. In the twophase tests, oncethe 100 cycles of loading at a given s3, qmean, and qcyclicwere completed, the sample was subjected to a second 100cycles (the second phase) with a dierent value of s3 orqcyclic.Sacramento River Sand was subjected to 100 cycles ofloading with s3100 kPa, qmean250 kPa, and qcyclic50kPa. Then the soil was subjected to 100 cycles of loadingwith qcyclic100 kPa. The results are shown in Fig. 6. Itshould be noted that the origin of axial strain for the second phase in Fig. 6 has been shifted to the same origin asthe axial strain in the rst phase for comparison. In therst 100 cycles of loading there was a small but noticeabledierence in the recorded axial strain at the two dierentloading frequencies. However, even though the cyclicshear stresses in the second phase were larger, there wasvery little dierence in the axial strains measured at thetwo dierent frequencies of loading.The eect of varying conning pressure in the secondphase was also investigated. The Sacramento River Sandwas subjected to a 100 cycles of loading with qmean150kPa, qcyclic150 kPa, and s3150 kPa. Then, in the second phase, s3 was dropped to 100 kPa and the samplewas subjected to 100 cycles of loading with qmean150kPa and qcyclic150 kPa. There was a small dierence inthe axial strains measured at the two loading frequenciesin the rst phase, but in the second phase there wasFig. 7.Results for a two phase cyclic triaxial test with s3 decreasingalmost no dierence, as shown in Fig. 7. A test in whichthe conning pressure was increased in the second phasewas also performed. Although the test results are notshown, little axial strain and almost no dierence between the axial strains were measured at the dierentloading frequencies in the second phase of the test.DISCUSSIONThe behavior of ratedependent geomaterials isthought to be directly related to the strain rate or changein strain rate, but it is the rate of loading that is oftenknown or constrained in practice. In this study, densesands were loaded at 0.1 and 1.5 Hz. The strain rate washigher for the higher loading frequency at the beginningof the test, but after the rst few cycles of loading the rateof strain for the higher loading frequency dropped signicantly. After the rst ve to twenty cycles, the strainrates for the dierent loading frequencies were very similar, as seen in Fig. 8. Correspondingly, the greatest dierence in response between tests run at the two loading frequencies occurred during the rst ve to twenty cycles,which can be seen in Figs. 2 through 4. In the rst few cycles, the sample subjected to the slower rate of loading exDENSE SAND IN CYCLIC TRIAXIAL TESTS451two loading frequencies as shown in Fig. 9. When therate of loading aected the results, the dierence inresponse occurred mostly in the rst ve to twenty cycles,when the dierence in strain rate was the greatest. In thetwophase tests performed, the ratedependent responsewas observed in the rst phase but not the second phasefor the conditions and sands tested.ACKNOWLEDGEMENTSTests presented in this paper were performed at theUniversity of Notre Dame.Fig. 8.Strain rates during a stress controlled cyclic triaxial testFig. 9. Eect of loading frequency in cyclic triaxial tests with increasing axial strainperienced more axial strain. However after the rst ve totwenty cycles of loading, the dierence in axial strain between the two loading rates remained nearly constant forthe remainder of the test. This also agrees with the studiesdiscussed earlier, that found changes in strain rate toresult in the greatest dierence in response.SUMMARYThis paper has presented the results of cyclic triaxialtests that were performed on dense Monterey No. 0/30and Sacramento River Sand at loading frequencies of 0.1Hz and 1.5 Hz. Under certain loading conditions the rateof loading had a noticeable eect; the stiness of the samples subjected to a higher frequency of loading was higherthan the stiness of the samples loaded at a lower frequency. Larger dierences in the strains were measured atthe two loading frequencies in the tests with larger cyclicshear stresses, as shown in Fig. 5. However, other factorssuch as the stress level may inuence the ratedependentresponse. Overall, in the tests presented in this paper,loading conditions that resulted in higher levels of strainresulted in greater dierence in the response between theREFERENCES1) Alavi, S., Merport, T., Wilson, T., Groeger, J. and Lopez, A.(1997): LTPP Materials characterization program: Resilient modulus of unbound materials (LTPP Protocol P46) laboratory startupand quality control procedures, Report No. FHWARD96176,Federal Highway Administration, Washington, DC.2) Di Benedetto, H. and Tatsuoka, F. (1997): Small strain behavior ofgeomaterials modelling of strain rate eects, Soils and Foundations, 37(2), 127138.3) Di Benedetto, H., Tatsuoka, F. and Ishihara, K. (2002): Timedependent shear deformation characteristics of sand and their constitutive modelling, Soils and Foundations, 42(2), 122.4) Di Benedetto, H. (2007): Small strain behaviour and viscous eectson sands and sanclay mixtures, Proc. StressStrain Behaviour:Measurement, Modeling and Analysis, Springer,159190.5) Lade, P. V. (1994): Creep eects and cyclic instability of granularsoils, Journal of Geotechnical Engineering, 120(2), 404419.6) Lade, P. V., Yamamuro, J. A. and Bopp, P. A. (1997): Inuenceof time eects on instability of granular materials, Computers andGeotechnics, 20(3/4), 179193.7) Matsushita, M., Tatsuoka, F., Koseki, J., Cazacliu, B., Benedetto,H. and Yasin, S. J. M. (1999): Time eects on the prepeak deformation properties of sands, Proc. 2nd International Symposium onPrefailure Deformation Characteristics of Geomaterials, Balkema,1, 681689.8) Santucci de Magistris, F., Koseki, J., Amaya, M., Hamaya, S.,Sato, T. and Tatsuoka, F. (1999): A triaxial testing system to evaluate stressstrain behavior of soils for wide range of strain and strainrate, Geotecnical Testing Journal, 22, 4460.9) Tatsuoka, F., Modoni, G., Jiang, G., AnhDan, L. Q., Flora, A.,Matsushita, M. and Koseki, J. (1999): Stressstrain behaviour atsmall strains of unbound granular materials and its laboratorytests, Proc. Workshop on Modelling and Advanced Testing for Unbound Granular Materials, Balkema, 1761.10) Tatsuoka, F., Santucci de Magistris, F., Hayano, K., Momoya, Y.and Koseki, J. (2000): Some new aspects of time eects on thestressstrain behaviour of sti geomaterials, Proc. 2nd International Conference on Hard Soils and Soft Rock, Balkema, 2,12851371.11) Tatsuoka, F., Uchimura, T., Hayano, K., Di Benedetto, H.,Koseki, J. and Siddiquee, M. S. A. (2001): Timedependent deformation characteristics of sti geomaterials in engineering practice,Proc. 2nd International Symposium on Prefailure DeformationCharacteristics of Geomaterials, Balkema, 1, 11611262.12) Tatsuoka, F., Ishihara, K., Di Benedetto, H. and Kuwano, R.(2002): Timedependent shear deformation characteristics of geomaterials and their simulation, Soils and Foundations, 42(2),103129.13) Tatsuoka, F. (2007): Inelastic deformation chracteristics of geomaterial, Proc. StressStrain Behaviour: Measurement, Modelingand Analysis, Springer, 1108. | ||||
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タイトル | JGS NEWS | ||||
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出版 | Soils and Foundations | ||||
ページ | I〜II | 発行 | 2008/06/15 | 文書ID | 21121 |
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