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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
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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
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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
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タイトル Effect of Slope on P-Y Curves Due to Surcharge Load
著者 K. Muthukkumaran・R. Sundaravadivelu・S. R. Gandhi
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ページ 353〜361 発行 2008/06/15 文書ID 21113
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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
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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
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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
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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
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ページ 407〜417 発行 2008/06/15 文書ID 21117
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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
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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
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タイトル Rate-dependent Response of Dense Sand in Cyclic Triaxial Tests
著者 L. A. Salvati・L. Q. AnhDan
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ページ 447〜451 発行 2008/06/15 文書ID 21120
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  • Viscous Behaviour of Unbound Granular Materials in Direct Shear
  • 著者
  • A. Duttine・Fumio Tatsuoka・W. Kongkitkul・Daiki Hirakawa
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  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 297–318, 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 diŠerent particle shapes and sizes as well as uniformglass beads having diŠerent 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. DiŠerent types of viscous properties, which are aŠected 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 signiˆcant 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 quantiˆed by the rate­sensitivity coe‹cient deˆned interms of the shear and normal stresses, which are then converted to those deˆned 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 eŠects 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 coe‹cient, stick/slip behaviour,strain/displacement rate, TESRA, unstable behaviour, viscosity, viscous properties (IGC: D6/D7)loading rate eŠect 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 eŠects of rate­dependent changes in the pore water pressure are negligi­ble with saturated soils or when the specimen consists ofdried particles. The ˆndings 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 time­eŠectson the stress­strain behaviour of geomaterial should beunderstood correctly and properly. Even if the in‰uenceof pore water pressure changes is not involved, the fol­lowing two types of time eŠects should be taken into ac­count (e.g., Di Benedetto et al., 2005; Tatsuoka et al.,2008): the ageing eŠect, which can be deˆned 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 eŠect'', which can be at­tributed primarily to the ``viscous deformation and slid­ing at inter­particle contact points and its eŠects 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 (tatsuoka—rs.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.297 298DUTTINE ET AL.Fig. 1. Schematic stress–strain 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 EŠects 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 quantiˆed by the rate­sensitivitycoe‹cient, b13, which is the slope of the DR13/R13|log ( ·g irafter/ ·g irbefore) relation:DR13/R13log s( ·g ir13)after/( ·g ir13)beforetb13Fig. 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 deˆned 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 ˆne 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 diŠerent by a factor up to 500 (Matsushi­ta et al., 1999). This ˆnding was reconˆrmed bydrained triaxial compression (TC) tests on anothertype of poorly graded angular ˆne sand, Silica No. 8sand (Kiyota and Tatsuoka, 2006). With the sametypes of sands, signiˆcant 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 eŠective prin­cipal stress ratio R13s1/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 eŠects of conˆning pressure and dry densityon b13 are insigniˆcant in drained TC on Toyourasand (Nawir et al., 2003). Kiyota and Tatsuoka(2006) showed that the same deˆnition of b13 isrelevant to both TC and TE stress conditions forToyoura, Hostun and Silica No. 8 sands and alsothat the eŠects of over­consolidation on b13 arenegligible (with Toyoura sand).b) Tatsuoka et al. (2006), Tatsuoka (2007) andEnomoto et al. (2007) evaluated the eŠects 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 eŠects of D50 on b13 are insigniˆcant ex­cept for saturated clay for which the eŠects ofpore water on b13 are signiˆcant, and that thevalue of b13 tends to increase with an increase inthe coe‹cient 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 stiŠ particles of Aluminium Oxide(corundum) and natural poorly graded ˆne sands. Asschematically depicted in Fig. 1, another very speciˆc VISCOUS BEHAVIOUR OF GRANULAR MATERIALSviscous response, named P&N, was observed: i.e., inthe ML tests at a constant but diŠerent strain rates,the materials became stiŠer 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. DiŠerentfrom 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 signiˆcant ˆndings, 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 in‰uence 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. DiŠerent types of DS shear boxes (modiˆed 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 ˆrst develop diagonally, not horizontally from thespecimen edges (Potts et al., 1987; Cui and O'Sullivan,2006). To minimize the eŠects 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 ˆxed 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 diŠerent 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 ˆxed against rotation with types Band C. With respect to the side wall friction, the verticalload W is basically free from these eŠects 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~12 300DUTTINE ET AL.Fig. 5. Horizontal frictional stress tf at the bottom of the lower DSbox, dense glass beads (D500.2 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 ˆxed 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 D500.2 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 diŠerence 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 ˆve at the peakstress state and subsequent states. Therefore, if thetwo air­cylinders apply the same normal load, theupper shear box should rotate signiˆcantly, associ­ated with a signiˆcantly 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 ˆrstly 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) ˆxed 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 LVDTˆxed on the bottom platen (No. 4'). Yet, the maxi­mum diŠerence 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 diŠerent 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 followingdiŠerent 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 161–1990 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 classiˆcation of the materials used in this study 302DUTTINE 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 relatedˆguresToyoura95.041000.200VDR(3)No6–8–11–20–28–29Hostun90.251000.370VDRNo8–11–20–28–29(4)Hostun94.541000.370CPYes24Silica No. 6a93.74500.160VDRNo9–12–20–22–28–29Albany94.921000.300VDRNo13–15–20–28–29Albany103.111000.370CPYes24SLB91.621000.550VDRNo13–15–20–28–29Ticino94.481000.500VDRNo9–12–20–21–28–29Ottawa88.871000.180VDRNo14–16–20–28–29Monterey93.431000.475VDRNo14–16–20–28–29GB0.40104.201000.450VDRNo17–20–23(5)Yes17–20GB0.4090.731000.460GB0.20103.671000.250MLYes5–19–20GB0.20104.511000.200VDRNo28–29GB0.15100.391000.250VDRNo19–20–28–29GB0.10101.831000.200MLYes19–20GB0.10100.571000.200VDRNo28–29GB0.0793.84500.140VDRYes19–20–28–29GB0.0598.3250Initial 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 diŠerence between theVDR(3)Variable displacement rate;Yes(4)Creep periods;19–20–28–29(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/svRDS)–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 stepwise VISCOUS 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. DiŠerent 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 ˆrst 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 diŠerent values of s· , but thedecay rates with time are totally diŠerent (i.e., by a factorof 10 in the case of Fig. 8(b)).Figure 9 shows results similar to Fig. 8, from the DS 304DUTTINE 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 eŠects of par­ticle shape on the viscosity type and transition patternFig. 10. Deˆnitions of the physical quantities used to express the rate­sensitivity coe‹cients (Eq. (2))have not been reported.From Figs. 8 and 9, it may be seen that the d­s relation­ship exhibits insigniˆcant or little rate­dependency. Thisfeature is discussed in detail later.Quantiˆcation of viscous properties: By referring toEq. (1), the viscous properties observed in the DS testswere quantiˆed by the following parameters (Fig. 10, inthe case of a step increase in s· ):DRDS/RDSlog (·s irafter/·s irbefore)bDSD(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 coe‹cient, where DRDS isthe jump in RDStvh/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 test 306DUTTINE ET AL.conditions in this study. (bDS)r is the residual rate­sensitiv­ity coe‹cient (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., u0 for the TESRA viscosity and uº0for the P&N viscosity, while u1.0 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 ˆgures,the range of the data is indicated by a band to illustratethe general trend. The peak stress strange deˆned 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 diŠerent phenomenon. Moreover in the case ofAlbany and SLB sands, as indicated by a notation SD inFig. 13(c) and (d), similar sudden and signiˆcant 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 di‹cult to deˆne 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 ˆgures:1) bDS is rather constant for a wide range of s overdiŠerent 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 reconˆrm 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 diŠerent. 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 ofdiŠerent particle sizes (i.e., uniform spherical granularmaterials). Figures 17(a), (b) and (c) show the test results VISCOUS BEHAVIOUR OF GRANULAR MATERIALSFig. 18.Fig. 17. RDS­s and d­s relations from two DS tests (ML and VDR),dense glass beads with D500.4 mm: a) whole relations and;zooms­up: b) pre­peak and c) residual statefor D500.4 mm. It may be seen that signiˆcant 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 signiˆcantly 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 eŠects 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 eŠects 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 coe‹cient 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 diŠerent particle sizes: i.e.continuous ML tests on glass beads of D500.2 mm and0.1 mm (Figs. 19(a) and (b)); and a variable shear dis­placement rate test on D500.05 mm (Figs. 19(c) and(d)). It may be seen from Figs. 19(a) and (b) that glassbeads of D500.2 mm and 0.1 mm exhibited similar un­stable behaviour as glass beads of D500.4 mm (Fig. 17).On the other hand, it may be seen from Figs. 19(c) and(d) that glass beads of D500.05 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, D500.15 mm and 0.07mm (Figs. 19(e) and (f)), showed consistent results: i.e.unstable behaviour when D500.15 mm and stable be­haviour when D500.07 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 D500.4 mm); 0.075 mm (D500.2 mm); 0.074 mm (D50 310DUTTINE 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 (D500.1 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 su‹cient amount of particles are arranged in thesame conˆguration 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,conˆrming 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 diŠerenttrends 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 glass VISCOUS 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 coe‹cient. Finally, the infer­ence c) was di‹cult to examine, as the specimen volumevariations in the respective events were too small to evalu­ate conˆdently 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 phenomenon‚This phenomenon is however aŠected 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 diŠerent 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 signiˆcantjumps. This fact supports the framework of the non­linear three­component model (Fig. 2), for which the‰ow rule should be described in terms of the non­viscous(inviscid) stress (sf), not in terms of the total stress (ssf{sv). This remains valid also in the post­peak softeningregime (Figs. 8(c) and 9(c)). Hostun and Toyoura sandsdo not exhibit any signiˆcant 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 signiˆcantly 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 (D500.4 mm, Dr0104.20%, sv100 kPa) (see Fig. 17)DS tests including creep periods, Hostun (relatively angular) and Albany (relatively round): a) whole relations and b) zooms­up VISCOUS 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 diŠerent (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 coe‹cient b13 de­ˆned as R13s1/s3 (Eq. (1)). In the following, it is exam­ined whether the viscous properties observed in the DStests quantiˆed 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 ˆrst 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 stress–strain 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 a 314DUTTINE 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 diŠerent sets of the principal stress incrementsDs1 and Ds3 obtained based on these two assumptionsresult in two diŠerent 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 diŠer­ence is not signiˆcant (as shown below), it is very di‹cult,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 coe‹cients (Eq. (1)), b13(c) and b13(e), asa function of RDStvh/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 diŠerent 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 ˆgures show continuous data points foreach DS test that were obtained following a number ofdiŠerent steps:a) An analytical expression of the d­s relation is ob­tained by ˆtting of a 6th to 7th order polynomialfunction. This polynomial function is diŠerentiatedwith respect to the variable s to obtain an analyticalexpression of the c­s relationship.b) An analytical expression of the RDS–s 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 ˆtting 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 RDS–c 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) from VISCOUS 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 theˆgures. 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 verydi‹cult to conˆdently deˆne stable bDS values at the resid­ual state due to the signiˆcant 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 thequantiˆcation of viscous properties by b13 (Eq. (1)) isrelevant and consistent under all these diŠerent 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 consistenteŠects 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 eŠects on the viscousproperties are likely to be aŠected 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 diŠerent 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 to 3163)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 in‰uence on this trend of behaviour.The ‰ow characteristics of unbound angular andround granular materials were basically rate­in­dependent, indicating that it is relevant to express the‰ow characteristics in terms of the inviscid stresscomponent according to the non­linear three­compo­nent model.By introducing several assumptions, the values of therate­sensitivity coe‹cient b13 deˆned in terms of themajor and minor principal stresses, s1 and s3, wereestimated from the values of the rate­sensitivitycoe‹cient bDS deˆned 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 quantiˆcation of the viscousproperty by the rate­sensitivity coe‹cient 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 ˆrst author gratefully acknowledges the ˆnancialsupport 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 diŠerent 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. onDeformation Characteristics of Geomaterials, Sept. 1999, Torino,1, 681–689.Nawir, H., Tatsuoka, F. and Kuwano, R. (2003): Experimentalevaluation of the viscous properties of sand in shear, Soils andFoundations, 43(6), 13–31.Park, C.­S. and Tatsuoka, F. (1994): Anisotropic strength anddeformations of sands in plane strain compression, Proc. 13thICSMFE, New Delhi, 13(1), 1–4.Pham Van Bang, D., Di Benedetto, H., Duttine, A. and Ezaoui, A.(2007): Viscous behaviour of sands: air­dried and triaxial condi­tions, International Journal for Numerical and Analytical Methodsin Geomechanics, published online on March 8th, 2007.Potts, D. M., Dounias, G. T. and Vaughan, P. R. (1987): Finite ele­ment analysis of the direct shear box test, G áeotechnique, 37(1),11–23.Pradhan, T. B. S., Tatsuoka, F. and Horii, N. (1988a): Simpleshear testing on sand in a torsional shear apparatus, Soils andFoundations, 28(2), 95–112.Pradhan, T. B. S., Tatsuoka, F. and Horii, N. (1988b): Strengthand deformation characteristics of sand in torsional simple shear,Soils Foundations, 28(3), 131–148.Qiu, J.­Y., Tatsuoka, F. and Uchimura, T. (2000): Constant pres­sure and constant volume direct shear tests on reinforced sand,Soils and Foundations, 40(4), 1–17.Rice, J. R., Lapusta, N. and Ranjith, K. (2001): Rate and state de­ 317VISCOUS BEHAVIOUR OF GRANULAR MATERIALS28)29)30)31)32)33)34)35)36)37)pendent friction and the stability of sliding between elasticallydeformable solids, Journal of the Mechanics and Physics of Solid,49, 1865–1898.Santucci de Magistris, F., Koseki, J., Amaya, M., Hamaya, S.,Sato, T. and Tatsuoka, F. (1999): A triaxial testing system to evalu­ate stress­strain behaviour of soils for wide range of strain andstrain rate, Geotechnical Testing Journal, ASTM, 22(1), 44–60.Shibuya, S., Mitachi, T. and Tamate, S. (1997): Interpretations ofdirect shear box testing of sands as quasi­simple shear, Ge áotech­nique, 47(4), 769–790.Stroud, M. A. (1971): The behaviour of soils at low stress levels inthe simple shear apparatus, PhD Thesis, Cambridge University.Tatsuoka, F., Sakamoto, M., Kawamura, T. and Fukushima, S.(1986a): Strength and deformation characteristics of sand in planestrain compression at extremely low pressures, Soils and Founda­tions, 26(1), 65–84.Tatsuoka, F., Goto, S. and Sakamoto, M. (1986b): EŠects of somefactors on strength and deformation characteristics of sand at lowpressures, Soils and Foundations, 26(1), 105–114.Tatsuoka, F., Sonoda, S., Hara, K., Fukushima, S. and Pradhan,T. B. S. (1986c): Failure and deformation of sand in torsionalshear, Soils and Foundations, 26(4), 79–97.Tatsuoka, F., Santucci de Magistris, F., Hayano, K., Momoya, Y.and Koseki, J. (2000): Some new aspects of time eŠects on thestress­strain behaviour of stiŠ geomaterials, Keynote Lecture, Proc.2nd Int. Conf. on Hard Soils and Soft Rocks, Napoli, 2,1285–1371.Tatsuoka, F., Ishihara, M., Di Benedetto, H. and Kuwano, R.(2002): Time­dependent deformation characteristics of geomateri­als and their simulation, Soils and Foundations, 42(2), 103–129.Tatsuoka, F. (2004): EŠects 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), 1–60.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.), 285–312.38) Tatsuoka, F. (2007): Inelastic deformation characteristics of ge­omaterial, Soil Stress­Strain Behavior: Measurement, Modellingand Analysis (eds. by Ling et al.), Proc. Geotechnical Symposiumin Roma, 16–17 March 2006, 1–109.39) Tatsuoka, F., Di Benedetto, H., Enomoto, T., Kawabe, S. andKongkitkul, W. (2008): Various viscosity types of geomaterial inshear and their general expression, Soils and Foundations, 48(1),41–60.40) Wu, P. K., Matsushima, K. and Tatsuoka, F. (2006): EŠects ofspecimen size and some other factors on the strength and deforma­tion of granular soil in direct shear tests, Geotechnical TestingJournal (accepted, to be published in Vol. 31–1, Jan. 2008).41) Yasin, S. J. M. and Tatsuoka, F. (2000): Stress history­dependentdeformation characteristics of dense sand in plane strain, Soils andFoundations, 40(2), 77–98.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|svsv{tvh tan c2sCsv{(A2)The radius of the Mohr's circle, r, is given by:4r 2(sh|sv)2{4t 2vh; r12(sh|sv)2{4t 2vh(A3)The principal stresses, s1 and s3 are therefore obtained from Eqs. (A1) through (A3):is1sC{rsv{tvh tan c{ 1 4t2vh{4t2vh¥tan2 csv{tvh (tan c{ 1{tan2 c)k2j1k2222ls3sC|rsv{tvh tan c| 2 4tvh{4tvh¥tan csv{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 diŠerentiating Eq. (A4) under theconditions dc0 and dsv0:Ds1Dtvh (tan c{ 1{tan2 c): Ds3Dtvh (tan c| 1{tan2 c)(A5)By noting that DR13/R13D(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)b13By substituting Eqs. (A4) and (A5) into Eq. (A6), and referring to RDStvh/sv, we obtain:«$«2 1{tan2 c2 1{tan2 cDtvh/tvhbDS1/RDS|RDS{2 tan clog (·safter/·sbefore) 1/RDS|RDS{2 tan cb13b(e)13 $(A7)On the other hand, if we assume an elastic response upon a step change in s· , which leads to Dsh0, the Mohr's circleexpands at the ˆxed 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:iDs1r?|rtvhkjk« 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)13b13b 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
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 319–332, 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 eŠects 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 ˆrst 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 rockˆll 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 corerockˆll 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 oŠtoward 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 (sfeizi—ut.ac.ir).Associate Professor, ditto (aghasemi—ut.ac.ir).Assistant Professor, ditto (aghaland—ut.ac.ir).Professor, Norwegian Geotechnical Institute (NGI) and University Of Oslo Norway (kaare.hoeg—ngi.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.319 320SIAMAK ET AL.could be designed to behave safely.Previous Experimental WorkThe ˆrst experimental research in the ˆeld of seismicbehavior of asphaltic concrete core dams was performedby Breth and Schwab (1973). Their study was based onˆnite 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 deˆned 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(0.5–1)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 Super‰ex­phalt).The Super‰ex­phalt 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 airˆeld 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 diŠerentconˆning 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 eŠect on thematerial strength.In this research, the laboratory investigations are divid­ed into three sections. In the ˆrst, 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 ˆrst section was thethird part of the study.Brie‰y, the following topics form the main scope of thepresent experiment:ÉMaterial degradation due to cyclic loading (speciallyafter 50 cycles)ÉEŠects of diŠerent 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):Pi100Ø 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 wide 321CYCLIC TRIAXIAL TESTS ON ASPHALT CONCRETErange of bitumen grades to be chosen for hydraulicasphalt concrete. The asphalt binder type selection de­pends on speciˆc 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 ˆller, 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 ˆeld 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 eŠect 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 D3999–91.MONOTONIC TRIAXIAL TESTSMonotonic triaxial compression tests were used tostudy the stress­strain­strength behavior of asphalt con­crete. Six monotonic tests were performed in diŠerentconˆning 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 ˆlled 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 thepredeˆned conˆning 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 conˆning pressures (250, 500 and 1000 kPa). Forall conˆning pressures, the same stress­strain trend is seenin Fig. 2. As expected, the higher is the value of conˆningpressure, the more is the amount of failure axial strain.Values of axial strain at failure point for s31000, 500and 250 kPa are 15, 6 and 5 percent respectively. Also,the curves show a good harmony between two repeatedtests in the same conˆning pressures. This similarity iseven more evident in higher conˆning pressures. This isbecause, with the increasing conˆning 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)55.55.5661515 322SIAMAK ET AL.Fig. 2.of the aggregate alone, which show a modulus increasingmarkedly with increasing conˆning pressures. However,for the strain values more than 1z, a signiˆcant increasein shear strength is observed while increasing conˆningpressures.To study the eŠect 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 theconˆning 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 ˆgureshows a very little volumetric compression at the initialstage of the tests. It is quite common, as in the ˆrst 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 ˆssures. Although no visible cracksmay appear, the dilatation may lead to an increase inpermeability. However, the increase in permeability onlyoccurs when ˆssures 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 conˆning pressuresdeaE(2)For conˆning 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 conˆn­ing pressure (Kramer, 1996). In other words:E1zf (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:E1zA~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 deˆned for asphalt concrete materials:E1zA~s 0.180(5)Young modulus for asphalt concrete does not show asubstantial increase while increasing the conˆning 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 (kcs1/s31.0) and anisotropicconditions (kc2.0 and 3.0). During the tests, theamount of anisotropy coe‹cient was ˆxed by applyingthe desired loads from the load cell of triaxial equipment.The conˆning 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 conˆningstress 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 conˆning 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 predeˆned value. All tests wereperformed at two diŠerent temperatures, T59C and T189C. These temperatures were chosen from the tem­perature monitoring of the embankment dams (Dan­nicliŠ, 1996). Conditions inside a dam will be rather con­stant, and selected temperatures to cover some typicalvariation, were set to T59C and T189C; T59C, asan assumed year­around temperature inside a typical damin sun­arctic climate and T189C, as an assumed year­around temperature inside dam in countries with tropicalor sub­tropical climate. On the other hand, in embank­ 323CYCLIC 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 eŠect 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 signiˆcanteŠect 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.Deˆnition of LoadingFigure 4 shows for instance, the applied cyclic loads onthe samples subjected to a conˆning 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 (Kc3.0 as an example, Fig. 5(a)),Fig. 4. EŠective axial stress­loading time, s3500 KPa and Kc1.0(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 conˆnementsof 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 in 324SIAMAK ET AL.Fig. 5.Fig. 6.Cyclic stress–strain hysteresis loop, Test T5Fig. 7.Cyclic stress­strain hysteresis loop, Test T20Fig. 8.Cyclic stress­strain hysteresis loop, Test F4EŠective axial stress­loading time, s3500 KPa, Kc3.0this research can be noted:Type A: Isotropic condition with symmetric cyclic load­ing (Kc1.0)Type B: Anisotropic condition with non­symmetric cyclicloading (Kc2.0, 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 diŠerent 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 ˆve 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 ˆrst, ˆftieth, hundredths and thousandths cycles.The value of shear stress versus axial strain has beenpresented in these ˆgures. The initial value of the loopswas obtained from the value of axial and conˆning pres­sures. The starting point position in the hysteresis loop isdeˆned as follows (Figs. 6 to 11):s |s3iY positionShear Stress in the loop 12jlX positionShear Strain in the loop0.0kkThe results are described as follows in two categories;isotropic condition (Kc1.0) and anisotropic states withthe values of Kc2.0 and Kc3.0.First, for the isotropic condition (Tests T5 and T20);Figs. 6 and 7 have been plotted for instance, at two diŠer­ent temperatures of T59C and T189C.Figures 8 and 9 (Tests F4 and E13) are indicated for ananisotropic state with anisotropy coe‹cient which has thevalue of 2.0 (Kc2.0). In these tests, the temperatureremained constant at T59C.Figures 10 and 11 (Tests F15 and T18) are shown for an CYCLIC TRIAXIAL TESTS ON ASPHALT CONCRETEFig. 9.Fig. 10.Cyclic stress­strain hysteresis loop, Test E13Cyclic stress­strain hysteresis loop, Test F15325tained results are aŠected 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 3999–91). Based on the obtainedresults, the correction coe‹cient was deˆned and used inthe main tests.On the other hand, to decrease the eŠect of bedding er­ror, the surface of specimens was cut and polished withvery high accuracy (Fig. 1). In addition, bedding errorcould cause lower stiŠness in initial cycles and higher stiŠ­ness in later cycles that was not observed in hysteresisloops (Figs. 6 to 11). Therefore, the eŠect of bedding er­ror can be ignored in these tests with the above considera­tions.Dynamic Properties for Asphalt ConcreteIn the cyclic triaxial tests, the axial stiŠness 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 eŠective 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)ea2eaEGFig. 11.Cyclic stress­strain hysteresis loop, Test T18anisotropic state with anisotropy coe‹cient of 3.0 (Kc3.0) for two diŠerent temperatures of T59C and T189C.Accuracy of MeasurementsThe ˆdelity of the results depends on the accuracy ofthe measurements of both stresses and strains. The ob­E2(1{n)(6)Where: tshear stress, eaaxial strain, gshear strainand nPoisson 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 coe‹cient of Kc3.0,at a low temperature of T59C. For the higher tempera­ture (T189C), 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 conˆning stress does nothave signiˆcant eŠect on the shear modulus, its eŠect in­creases with increase of anisotropy and temperature. Bythe following equation, the damping ratio (D) is calculat­ 326SIAMAK 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 stiŠnessvalues, 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 stiŠermaterial. It should be emphasized that the presentedrange of shear modulus is aŠected by the value of conˆn­ing 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 cut­oŠ 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 DiŠerent Parameters on Dynamic Prop­ertiesFigures 13, 14 and 15 present the eŠect of diŠerentparameters such as conˆning stress, anisotropy, loadingfrequency, temperature and hysteresis loop shapes on theshear modulus and damping ratio. In the following para­graphs, the eŠects of the above­mentioned factors are de­scribed in detail.a) EŠect of anisotropyIn each part of Fig. 13, the temperature and anisotropycoe‹cient were ˆxed while the conˆning 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 T59C) or Figs. 13(b) with (e) (at T189C), it can be seenthat the higher the value of anisotropy coe‹cient, 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) EŠect of temperatureComparison of shear modulus presented at the sameanisotropy coe‹cients in Figs. 13 ((a) and (b) at Kc1.0)or Figs. 13 ((d) and (e) at Kc3.0) stands for decreasingthe shear modulus as the temperature increases. In addi­tion, the temperature has an important eŠect 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 diŠerent conˆning stresses at two diŠerent tempera­tures of T59C and T189C. Figure 14(a) shows that incomparison with shear modulus, damping ratio is not sig­niˆcantly 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 T189C than that at a lower temperature of T59C (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 the CYCLIC TRIAXIAL TESTS ON ASPHALT CONCRETEFig. 13.327EŠects of s3 and Kc on strain­dependent modulus at two diŠerent temperatures of 59C and 189Cdamping ratio increases.c) EŠect of conˆning stressThe eŠect of conˆning stress on shear modulus is alsoillustrated in Fig. 13. For an example in Fig. 13(a), at theconstant temperature and anisotropy coe‹cient, thehigher values of conˆning 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 Kc3.0, the eŠect of conˆningstress is more distinct. In addition the threshold point oc­curs at higher amplitudes of shear strain in comparisonwith a low conˆning stress. This point is observed in Figs.13(a), (c) and (d) as examples. Figure 14(a) shows that bydecreasing the conˆning pressure from 500 kPa to 85kPa, the damping ratio increases from 5z to 35z respec­tively.d) EŠect of hysteresis loops shapesBecause of the diŠerence 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 eŠects of conˆning stress(Fig. 15(a)), anisotropy coe‹cient 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 con­ˆning stress (GcÆ2Ge). It is clearly seen in Fig. 15(c) thatwith increasing conˆning stress and/or anisotropycoe‹cient 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) EŠect of reversal coe‹cient (rc)Reversal Ratio is introduced by the reversal coe‹cient(rc), which is the proportion of the positive portion in ap­plied cyclic shear stress to the whole domain of the shearstress. The eŠect 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 diŠerent 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 ˆgure shows that in lower values of rc (such as rc0.5), the amount of degradation for shear modulus is lessthan that of higher values (rc0.85). In addition, this 328SIAMAK ET AL.Fig. 16.G­Log N curves for diŠerent values of rcFig. 17.EŠect of cycles number on shear modulusFig. 14. EŠects of conˆning 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 diŠerentconˆning stressesˆgure shows that increasing the number of cycles causeddecrease of shear modulus.f) EŠect of number of cyclesFigure 17 presents the eŠect of the number of cycles onmodulus reduction behavior at diŠerent conˆning stress­es, anisotropy coe‹cients and temperatures. The value ofshear modulus is plotted in the ˆrst and ˆftieth cycles. Itis seen that holding constant the values of conˆningstress, anisotropy coe‹cient 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 more CYCLIC TRIAXIAL TESTS ON ASPHALT CONCRETEprevailing in a low conˆning stress (s3250 kPa) thanhigher conˆning stresses (Fig. 17(a) for an example). Atthe same temperature and conˆning stress, comparisonbetween Figs. 17(a) and (b) shows that with increase ofanisotropy coe‹cient, the eŠect of the number of cyclesdecreases. In other words, in the same cycle number, thespecimens degradation with a higher value of anisotropycoe‹cient (Kc3.0) is less than that of Kc2.0. Figures17(b) and (c) shows that the value of temperature has asigniˆcant in‰uence on the dynamic properties of asphaltconcrete between the ˆrst and ˆftieth 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 eŠects of equipment compliance andbedding error (ASTM D 3999–91), 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 5311–92 and3999–91, 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 satisˆed 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 diŠerent frequen­cies. In high speeds of cyclic loading, the strain valuesdecrease ( F5 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 conˆning pressure. Withreference to Figs. 13 and 15, it is obvious that the temper­ature has the largest eŠect 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 diŠerent 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 ˆrst 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 ˆgures (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 DiŠerent Behaviors of the Asphalt Con­creteDuring the cyclic triaxial tests of asphalt concrete, twodiŠerent behaviors were observed; Extension and Com­pression, which are summarized in Table 4. According tothis table, the extension behavior may occur in a low levelof conˆning 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, conˆning pressure and loading frequency aŠectthe 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 (Kc1.0). Increasing the tem­perature or decreasing the conˆning pressure are the mainfactors causing extension. In this state, compression be­havior was just seen at a low temperature (T59C) andhigh conˆning pressures (s3250,500 kPa) while exten­sion behavior was seen in other cases.Since the extension behavior is just observed at Kc1.0, the eŠects of temperature and conˆning stress on thegeneral behavior of asphalt concrete is explained more inthe following paragraphs:a) EŠect of temperature (in isotropic condition)The cyclic tests were performed at two diŠerent tem­peratures, T59C and T189C. As presented in Table4, in the constant conˆning stress, extension behavior oc­curred in a higher temperature. For the reason that in ahigher temperature, the eŠect of material viscosity ismore distinct and the increment of conˆning pressurescan not substantially aŠect 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 (T59C), thesample behaves rigidly. With increasing temperature, thecompaction, mixture quality of aggregate with bitumenand the particles interlocking are more in‰uential.b) EŠect of conˆning stress (in isotropic condition)The cyclic tests were performed in three diŠerent con­ˆning pressures, s385, 250 and 500 kPa. By increasingthe conˆning pressure, the compression behavior is moredistinct than that of extension; this is speciˆcally moreremarkable at low temperatures. At the temperature of T189C, in all conˆning pressures, the extension behaviorwas observed while at the temperature of T59C, thisbehavior was just seen at s385 kPa. In other words, in alow level of conˆning pressure (s385 kPa), only the ex­tension behavior is observed and the temperature eŠectcan be negligible.Near the dam crest the amount of conˆning 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 e‹ciency 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 ˆrst subjected to cyclic load­Fig. 20. Post cyclic behaviour (stress­strain curve), s3500 KPa, T59CTable 4. DiŠerent types of asphalt concrete behavior during the cyclicloadings3(kPa)85Kc1.0T59CT189CExtensionExtensionKc2.0T59CKc3.0T59CT189C250Compression Extension Compression Compression Compression500Compression ExtensionFig. 21. Post cyclic behaviour (stress­strain curve), s3250 KPa, T189C CYCLIC 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 T59C.The cyclic tests were performed at diŠerent anisotropystates (Kc1.0 and Kc3.0). The amount of degradationis nearly 15 percent at the pick point of the curve. In addi­tion, the ˆgure 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 (T189C). The ˆgure shows the same behavior trend for thetests before and after the cyclic loading in a high tempera­ture of T189C like T59C.It can be concluded that the asphalt concrete retains itse‹ciency 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 stiŠness increased with higher conˆningstress, s3. Based on the monotonic tests results, theYoung's secant modulus at 1z axial strain is proposedto be E1zA~s0.180 . In addition, higher conˆningstresses imposed on the specimens caused lowerdilatancy and volume expansion during shearing.ÉIn the cyclic triaxial tests, ˆfty cycles were imposed onthe specimens to simulate earthquake excitations. Insome cases, the cyclic loads were continued to thou­sands of cycles. However, there was no signiˆcantdegradation detected on the specimen behavior. Nocracks on the specimen surfaces were detected, even af­ter 10000 cycles.ÉMany factors in‰uence the dynamic properties of theasphalt concrete, such as conˆning stress, stressanisotropy, loading frequency and temperature. TheeŠects 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 insigniˆcant. The increase of permeabil­ity only occurs when ˆssures 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: conˆning 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 diŠerence between major andminor principal stresses in a triaxial testKc: anisotropic stress ratio, is calculated by dividing theaxial stress by lateral stress (Kcs1/s3)Reversal ratio, is introduced by the reversal coe‹cient(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 deˆned 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 loading 332SIAMAK 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, 348–351, Stuttgart, Germany.3) Creegan, P. and Monismith, C. (1996): Asphaltic Concrete WaterBarriers for Embankment Dams, ASCE Press.4) DunnicliŠ, 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 rockˆll dams, ICGEConference, 220–225, UAE.6) Ghanooni, S. and Mahin­roosta, R. (2002): Seismic analysis anddesign of asphaltic concrete core embankment dams, Journal ofHydropower and Dams, 6, 75–78.7) 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), 169–180.8) 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. 20051031–1, 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), 112–119.12) ICOLD Press (1982, 1992): Bituminous Cores for Earth and Rock­ˆll 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, 1996–Mahab­Ghodss 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, 18–20, 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, 15–26, Japan.21) Salemi, S. (2005): Dynamic behavior investigation of asphaltic con­crete core Rockˆll Dams, IUST University, PhD Dissertation, Iran.22) Tatsuoka, F. and Shibuya, S. (1992): Deformation characteristicsof soils and rocks from ˆeld and laboratory tests, Report of the In­stitute of Industrial Science, University of Tokyo.23) Tatsuoka, F. and Kohata, Y. (1995): StiŠness 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 rockˆll dam with an asphaltic concrete core,Journal of Water Power and Dam Construction, 43, 1–6.25) Wang, W. (2005): Cyclic Tests on Asphalt Concrete, Xi'an Univer­sity Press, China.26) Wang, W. and Hoeg, K. (2002): EŠects of compaction method onthe properties of asphalt concrete for hydraulic structures, Interna­tional Journal on Hydropower and Dams, 9(6), 63–71.
  • ログイン
  • 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
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 333–352, 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 ˆxedboundary 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 (deˆned 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 eŠects with sand. The development of residual deformation ofgeosynthetic­reinforced sand by SL and CL histories had no negative eŠects 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 su‹ciently 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 signiˆcantly during CL. These diŠerent 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, ˆbre 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 speciˆed 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 diŠerent types ofgeosynthetic­reinforced soil (GRS) structures can befound, including soil retaining walls (RWs), bridge abut­ments, steep slopes of embankment, dykes and earth­ˆlldams, shallow foundations, etc. The popularity of GRSstructures results from a high cost­eŠectiveness 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 (tatsuoka—rs.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.333 334KONGKITKUL ET AL.higher than the lateral earth pressure per reinforcementlayer that is activated by self­weight of the backˆll andsurcharge on the backˆll 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 speciˆed 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) exhibitsigniˆcant 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 ˆrst to reconˆrm 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 eŠects of mechanical properties (i.e., tensile ulti­mate strength and stiŠness) 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 ev8.0% (PET GC­reinforced sand): alocal strain ˆeld was constructed by the photogrametric method ina rectangular zone of broken lineKongkitkul et al., 2007b, c, e). The ˆrst 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).Signiˆcant residual deformation may develop ingeosynthetic­reinforced soil during sustained loading(SL) due to the viscous properties of sand and geosyn­thetic reinforcement. In addition, signiˆcant residualdeformation may also develop in reinforced soil duringcyclic loading (CL), also aŠected 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 eŠect on the residual deforma­tion of sand, which is deˆned 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 geosynthetic 335GEOSYNTHETIC­REINFORCED SANDTable 1. List of geosynthetic reinforcement types and their strengthand stiŠness 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 ˆbre. This is relatively weak while having acovering ratio (CR, deˆned 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 ˆbre. This is relatively strongwhile having CR25z.3) Polyester geocomposite (PET GC, Fig. 2(c)): This ismade by sewing yarns of polyester ˆbre (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 backˆll.The strength and stiŠness of a sand specimen rein­forced with this ``fully uniˆed PET GC'' in PSC testswere signiˆcantly higher than those when reinforcedwith the original PET GC (Kongkitkul et al., 2007e).Figure 3 compares the tensile load–tensile strain (T­e) re­ReinforcementnameUltimate tensilestrength, Tult(kN/m)Secant stiŠnessat 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 diŠerent 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 stiŠness 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 stiŠness 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 ˆrst 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 ˆnally co­vered with silicone for protection against damage. TheSGs formed a Wheatstone bridge of ``opposite­side two­active­gauge two­wire system'' consisting also of a pair ofˆxed 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 signiˆcant­ly diŠerent from actual local tensile strains at a given lo­cation of the strand of a given geogrid due to eŠects of 336KONGKITKUL 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 diŠerent 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 diŠerence 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 ˆbre 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 diŠracting elements printed on aphotosensitive core of a single mode optical ˆbre. Onlyone spectral component satisfying the Bragg relation isre‰ected by the grating when light of a broadband sourceis coupled into a ˆbre with a FBG. The grating re‰ects aspectral peak based on the grating spacing; therefore,changes in the length of the ˆbre due to tension or com­pression change the grating spacing and the wavelength(l) of light that is re‰ected 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 re‰ected 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 ˆbre without damaging the opti­cal ˆbre 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 ˆne sub­angular sand. The batch of Toyoura sandused in this study had Gs2.65; D500.2 mm; Uc1.20;emax0.98 and emin0.62. The specimens were eitherunreinforced or reinforced with diŠerent 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 the GEOSYNTHETIC­REINFORCED 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 eŠects 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 a‰exible plastic tube. This procedure continued untilthe transient surface of sand became slightly higherthan the speciˆed 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 ˆxed to a horizon­tal L­beam with a speciˆed 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 speciˆed sand dry density, Fig. 6(e).Steps 1–4 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 ˆnished for the last (i.e., top) reinforcement layer,the cables were bent ˆrst horizontally at the left side ofthe mould and then vertically up at the position of thevertical hole of the cap (explained later). Subsequently,the ˆnal step 1 was executed until the sand ˆlled­up 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 ˆlling up sanduntil the top of the mould at step 1.After having smoothened the ˆnal 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 conˆning 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 conˆning 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 con­ˆning platens to correct the axial load measured with the 338KONGKITKUL ET AL.axial load cell. Conˆning 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 speciˆed 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 ·ev0.04z/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 ·ev0.04z/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 stressš v is the average verti­ratio, R''˜ deˆned as šs?v/s?c; where s?cal stress; and s?c is the conˆning pressure (30 kPa).Figure 8 compares the R˜ c­ev relations from four continu­ous ML tests at ·ev0.04z/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 signiˆcant tensile reinforcing eŠects providingadditional conˆning pressure to the sand. Also, the rein­forced sand specimens are stiŠer and the stiŠness is largerwhen reinforced with a stiŠer reinforcement (Fig. 3;Table 1). However, the diŠerence in the stiŠness 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 ev4.0%, 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 stiŠness of the fully uniˆed 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 eŠects of a high CR on the compres­sive strength. On the other hand, the initial stiŠness 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), gmaxe1|e3, when ev4.0zin the three reinforced sand specimens. The area shown inFig. 9, which is free from any obstacle, covers the seconddown to the ˆfth 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 tensile GEOSYNTHETIC­REINFORCED SANDstiŠness of reinforcement. Furthermore, as signiˆcantstrain­softening 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, anysigniˆcant strain localisation with well­deˆned shearbands could not be observed at ev4.0z, 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 ·ev0.04z/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) Signiˆcant 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 stages 340KONGKITKUL 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 whileaŠected 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 stiŠ­ness of the R­e˜ v relation at the stress level of the con­cerned SL, while the tangent stiŠness 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 stiŠness 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 eŠectivelydecreased by relevant pre­loading history.When ML at ·ev0.04z/min was restarted at the endof each SL stage, the R­e˜ v relation exhibited somestress range with relatively high initial stiŠness.However, the initial stiŠness 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 stiŠer and strongerwhen compared with the behaviour during continu­ous ML. This trend of behaviour is due likely to a GEOSYNTHETIC­REINFORCED 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 R12˜better 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 eŠects).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 eŠects.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., h­i 342KONGKITKUL ET AL.Fig. 14. Relationships between creep axial strain Dev and averagestress ratio R˜in 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 signiˆcantlydecreased 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 aŠect 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 eŠect); 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 eŠects 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 signiˆcantly decreased withtime.8) With the PET GC­reinforced sand, the elocal values atpoint t in Fig. 12(c) (when R22˜during ML after thesecond global unload/reload cycle) is similar to thosemeasured at point m (when R20˜at the end of SLduring otherwise primary loading) while signiˆcantlysmaller than those measured at point l (when R20˜at 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 signiˆcantly 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 sig­niˆcantly 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 conˆning pressure as in the present study, whereRs?˜1/s?3 šs?v/s?c (i.e., s?1 and s?3 are always equal torespectively s?š v and s?c in the case of PSC test on unrein­forced sand) (Kongkitkul et al., 2007b). In this ˆgure, SLand stress relaxation (SR) tests were performed for re­spectively three hours during otherwise ML at ·ev0.04z/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 sig­niˆcant 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 stiŠness, 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 stiŠness 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 ˆtted by a set of polynomial functions(e.g., Kongkitkul et al., 2007a, c). These ˆtted equationswere then diŠerentiated 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 R12˜from 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 signiˆcantly 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 value GEOSYNTHETIC­REINFORCED 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 R6˜on 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 R12˜on the PET GG­rein­forced sand presented in Fig. 10 344KONGKITKUL 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 signiˆcantly decreased and, correspondingly,the local conˆning pressure in sand decreased signiˆcant­ly. 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 R12.˜This test result is a typicalone that was used in the simulation shown below. In thisˆgure, 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 R4˜and 8. This simpliˆ­cation procedure does not aŠect 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 ˆtted 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 ofdiŠerent types of geosynthetic reinforcement subjected toa wide variety of loading histories, including ML atdiŠerent strain rates, step changes in the strain rate, SL atˆxed 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 (T0 and e0) 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 R12˜and 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 deˆned based on the sign of irreversiblestrain rate, ·eir. The unloading inviscid tensile load andstrain relation was obtained without introducing anypurely elastic zone as explained brie‰y below. The detailsare described by Kongkitkul et al. (2004a).1) Unloading branches of inviscid load and irreversiblestrain relation starting from diŠerent tensile load GEOSYNTHETIC­REINFORCED 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 R12,˜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 diŠerent 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 diŠerent 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 diŠerent tensile loads were es­sentially similar.4) A polynomial function was ˆtted to this imaginaryprimary unloading curve ensuring that it can be ˆttedwell 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 theseˆgures 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 DR˜5, were applied at three and seven stages during otherwiseprimary ML at ·ev0.04z/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 reinforce­ 346KONGKITKUL 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 diŠerent locations in the reinfor­cement during the unloading and reloading branches ineach cycle between R7˜and 12 and the number of load­ing cycles, Nc, obtained from these CL tests. Figure 24compares the relationships between the residual strain de­ˆned 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 ˆrst time is one of the major causes for thedevelopment of residual strain that takes place when R˜ in­creases ˆrstly 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 de­ˆned zero at the ˆrst maximum stress point, such as pointd, to exclude the eŠects of this factor. The followingtrends of behaviours may be seen from Figs. 21 to 24:1) Signiˆcant 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 aŠected to some extent by the numberof loading cycles, Nc, and the cyclic stress ampli­tude.ii) Rate­independent cyclic loading eŠects 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 diŠerence 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 ˆnally nearlyelastic.3) Residual tensile strain increments by CL were notsmall at the lowest stress level examined (i.e., at R˜8) (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 sand GEOSYNTHETIC­REINFORCED 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 ˆrst CL stage at R8.˜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 stiŠer 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 eŠects 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 stiŠness 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 evenstiŠer 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 diŠerent specimens, as seen from alower initial stiŠness in the test with CL stages than inthe continuous ML test (Fig. 22(a)).The local tensile strains, elocal, measured at diŠerentpositions along the respective reinforcement layers atthe last peak stress state at the end of the respectiveCL stages are not always smaller than those at theˆrst peak stress state at the CL stage (Figs. 21(c) and22(c)), unlike the case of SL (Figs. 10(c) and 11(c)).This diŠerence is due to an additional increase in thelateral strain in sand by factor ii (rate­independent 348KONGKITKUL ET AL.Fig. 23. Local tensile strain increments (absolute values) during un­loading and reloading in each cycle between R7˜and 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 diŠerence 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 R˜cyclic loading eŠect 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 specimensigniˆcantly 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 diŠerent 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 ˆrst 10 minutes (i.e., for around the ˆrst oneto four cycles), the creep strain was consistently larg­er than the one by CL at any average stress ratio (ex­cept at R8).˜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 diŠerent 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 eŠect 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?c40 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 ˆrst 100 seconds or the ˆrst 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 loadingeŠect: 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 eŠects 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 eŠects, 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 eŠects 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) Signiˆcant 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, aŠect­ed 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 eŠectswith 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 stiŠness 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 toeŠects of factors i) and ii). These eŠects eventuallydisappear as the strain increases during subsequentloading.3) The tensile strain in the geosynthetic reinforcementarranged in sand signiˆcantly 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 signiˆcantly increasedwith time (factor i). During SL of geosynthetic­rein­forced sand, the tensile load in the geosynthetic rein­forcement decreased signiˆcantly at a rate higherthan the one during the load relaxation stage at a ˆx­ed strain. The tensile load­strain state became evenunder unloading conditions of geosynthetic reinfor­cement during SL of geosynthetic­reinforced sand.This ˆnding 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 signiˆcantly.5) It is necessary to take into account the eŠects 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 ˆnancially 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 ˆrstauthor was staying at the Department of Civil Engineer­ing, Tokyo University of Science.REFERENCES1) AASHTO (2002): Standard Speciˆcations for Highway Bridges,American Association of State Highway and Transportation O‹­cials, 17th Edition, Washington, DC.2) Anh Dan, L. Q., Tatsuoka, F. and Koseki, J. 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GI­JGS Workshop, Boston,ASCE Geotechnical Special Publication GSP No. 143 (eds. byYamamuro and Koseki), 1–60.41) Tatsuoka, F., Hirakawa, D., Shinoda, M., Kongkitkul, W. andUchimura, T. (2004): An old but new issue; viscous properties ofpolymer geosynthetic reinforcement and geosynthetic­reinforced 35242)43)44)45)46)47)KONGKITKUL ET AL.soil structures, Keynote Lecture, Proc. 3rd Asian Regional Confer­ence on Geosynthetics (GeoAsia 2004), Seoul, 29–77.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, 1587–1590.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.), 1–108.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 25–28, 2007, Thes­saloniki, Greece, (W1–1003), 256–273.Tatsuoka, F., Tateyama, M., Mohri, Y. and Matsushima, K.(2007b): Remedial treatment of soil structures using geosynthetic­reinforcing technology, Geotextiles and Geomembranes, 25(4–5),204–220.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),41–60.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, 237–240.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 )irirvteir1] ¥[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 eir0:r1(eir)riFor 0ºeirÃeirr1:r1(eir)(A5a)« Ø »$eirri{rf ri|rf{¥cos p¥ ir22er1c(A5b)For eirÀeirr1: r1(eir)rf(A5c)where: ri, rf, c and ·eirr1 are constants controlling the decayrate with eir of the viscous load component. u(eir) is theviscosity type parameter. Tatsuoka et al. (2008) and Kon­gkitkul et al. (2008) proposed the following forms foru(eir), analogous to Eq. (A5):For eir0:u(eir)uiniFor 0ºeirÃe :iru(A6a)« Ø »$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 a0.70; m0.12 and ·eirr10|4z/s for Eq. (A4a); and a*0.20, 1{b*0.32 and ·eir010|3z/s for Eq. (A4b) arerelevant for this PET GG. To simulate the decay charac­teristics of this PET GG, they selected ri1.0 and rf0.15 (both deˆned for eir expressed in z); and c0.4;and eirr10.6 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
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 353–361, 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 eŠect 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 diŠerentiated by using curve ˆtting method of cubic polynomi­al function. The study includes eŠect of slope angle and relative density on bending moment, lateral soil resistance,lateral de‰ection 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 de‰ection behaviour oflaterally loaded piles is highly nonlinear and hence re­quires a nonlinear analysis. Poulos and Davies (1980) andBudhu and Davies (1987) modiˆed 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 load–de‰ection behaviour forindividual vertical and batter piles and the eŠect of sanddensity on the pile response. The results showed the sig­niˆcant eŠect of the relative density of sand on pile be­haviour. Prakash and Kumar (1996) developed a methodto predict the load de‰ection 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 de‰ec­tions 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 oŠshore struc­tures, harbour structures, high rise buildings and bridgeabutments. The governing criterion in designing pilefoundations to resist lateral loads in most cases is themaximum de‰ection of the foundation rather than its ul­timate capacity. The maximum de‰ection 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 (kmk—nitt.edu and kmk_iitm—yahoo.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.353 354MUTHUKKUMARAN 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 eŠect 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 eŠect 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 diŠerentiationand double integration of experimental bending mo­ments.Fig. 1.Experimental set upThe objective of this paper is to study the eŠect 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 diŠerent 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 ˆxed 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 ˆve variables, which are displacement( y), pile diameter (d ), area (A), lateral force (F ) and pilelateral stiŠness (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 stiŠness (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 stiŠness of the pile isdetermined by considering a simply supported beam test.The ‰exural stiŠness 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 test 355P­Y 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; EŠective particle size (D10) is 0.26 mm,Average particle size (D50) is 0.54 mm, Coe‹cient ofUniformity (Cu) is 2.4, Coe‹cient of Curvature (Cc) is1.1, Speciˆc 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 pointerˆxed 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 isˆlled 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 ˆled 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 stiŠness is modeled by providing rigidDetails of sand raining devicelink between the pile and the horizontal beam facing CD(Fig. 1) ˆxed 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 de‰ection and strain readingsare recorded for each increment of load.RESULTS AND DISCUSSIONSEŠect 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 theˆgures 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 signiˆcant in‰uence on the depth ofmaximum bending moment for ‰atter slope of 1V:2H.EŠect of Steepness of Slope and Relative Density onMaximum Bending MomentFigure 7 shows the eŠect 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 mo­ 356MUTHUKKUMARAN ET AL.Fig. 4. Bending moment vs depth for 1V:1.5H slope with 30% relativedensityFig. 7. EŠect 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. EŠect 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 eŠect 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 De‰ectionThe soil resistance (p) and lateral de‰ection ( 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 ˆtted 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 curve­ˆtting proc­ess. The distribution of the soil resistance along the pileshaft is obtained by double diŠerentiating the bendingmoment, i.e.,d 2MP(x) 2 6ax{2bdx(2)The de‰ection 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 curve­ˆtting 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 xdepth of maximumbending moment, dy/dx0). Second boundary condi­tion is, de‰ection is zero at the pile tip (i.e., xl, y0.where l is the depth of embedment). The curve­ˆttingprocedure 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 de‰ections along the depth ofpile are shown in Figs. 12 to 14. From all the ˆgures, it isobserved that the increase in surcharge load increases thesoil resistance and de‰ection. 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. De‰ection vs depth for 45% relative density with 1V:1.5Hslope 358MUTHUKKUMARAN ET AL.Fig. 13. De‰ection vs depth for 45% relative density with 1V:1.75HslopeFig. 14.De‰ection 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 de‰ec­tion obtained below |450 mm is almost equal to zero for45z relative density with 1V:1.5H slope.EŠect 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)pudC3DgZ(6)pu–ultimate 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)g–eŠective soil unit weight (kN/m3)Z–depth in (m)q–angle of internal friction of sand. (degrees)C1, C2, C3–Coe‹cients determine based on angle of in­ternal frictionD–average pile diameter (m)Equation (5) is used for shallow depths and Eq. (6) is usedfor deeper depths. The coe‹cients C1, C2 and C3 are ob­tained based on the angle of internal friction. The maxi­mum lateral de‰ection ( ymax) is taken as the maximumde‰ection 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 ˆgures, it is observed that theincrease in depth increases the ( p/pu). This is due to theincrease in passive resistance for increase in overburden 359P­Y 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 Z12DFig. 18. EŠect of slope on non dimensional p­y curve for 30% relativedensity at Z12DFig. 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 eŠect of slope on( y/ymax)/( p/pu) vs ( y/ymax) plot for 45z and 70z relativedensity at a depth of Z12D. The values of p/pu are theslopes of ( y/ymax)/( p/pu) vs ( y/ymax) curve are taken fromthe plot for diŠerent relative density with diŠerent slopeangle. The values of p/pu obtained from experiments arepresented in Table 1.( y/ymax)/( p/pu) vs (y/ymax) for 70% relative density Z12DConstruction of Lateral Load–De‰ection (p­y) Curve forSloping GroundThe API RP 2A (2000) method for construction of p­ycurves in horizontal ground is modiˆed for piles in slop­ing ground under surcharge load using the reduction fac­tor (R) as given in Eq. (7)pA~R~pu~tan h«k~Z~yA~R~pu$(7)A–factor to account for cyclic or static loading condi­tion. Evaluated by;A0.9 for cyclic loadingA(3.0–0.8 Z/D)Æ0.9 for static loadingRfactor to account the slope of the ground surfacepu–ultimate bearing capacity at depth Z (kN/m)k–initial modulus of subgrade reaction (kN/m3)Z–depth in metery–lateral de‰ection in meter 360MUTHUKKUMARAN 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.R0.74{0.0378(Z/D)|0.6315(S); RÃ1(8)Z–depth in meterD–diameter of pile in meterS–slope 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 ˆt 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 R1 is observed at Z/D18, 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. TheeŠect of sloping ground is included using a reductionfactor 'R' in the modiˆed approach. The value of theR is observed to increase from 0.31 to 0.42 at Z/D0as 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/D18, 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, 1583–1603.2) American Petroleum Institute (API–RP–2A) (2000): Recommend­ed practices for planning, designing and constructing ˆxed oŠshoreplatforms, Washington.3) Bransby, M. F. and Springman, S. M. (1996): 3­D ˆnite elementmodeling of pile groups adjacent to surcharge loads, J. of Com­puters and Geotechnics, 19(4), 301–324.4) Broms, B. B. (1964): Lateral resistance of piles in cohesionless soils,J. Soil Mech. Found. Engg. Div., ASCE, 90(SM3), 123–156.5) Cai, F. and Ugai, K. (2003): Response of ‰exible piles under lateral­ly linear movement of the sliding layer in landslides, Canadian Geo­technical Journal, 40, 46–53.6) 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), 499–509.7) Ito, T. and Matsui, T. (1975): Methods to estimate lateral force act­ing on stabilizing piles, Soils and Foundations, 15(4), 43–59.8) Kim, J. S. and Barker, R. M. (2002): EŠect of live load surchargeon retaining walls and abutments, Journal of Geotechnical and GeoEnvironment Eng., ASCE, 127(6), 499–509.9) 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, 1–39.10) Matlock, H. (1970): Correlations for design of laterally loadedpiles, Proc. 2nd Annual OŠshore Tech. Conf., Houston, Texas,577–593.11) Mezazigh, S. and Levacher (1998): Laterally loaded piles in sand:12)13)14)15)16)17)18)19)20)21)22)361slope eŠect on p­y reaction curves, Canadian Geotechnical Journal,35, 433–441.Nagger, M. H. EI. and Wei, J. Q. (1999): Response of tapered pilessubjected to lateral loading, Canadian Geotechnical Journal, 36,52–71.Narasimha Rao, S., Ramakrishna, V. G. S. T. and Babu Rao, M.(1998): In‰uence of rigidity on laterally loaded pile groups in ma­rine clay, Journal of Geotechnical and Geo Environmental En­gineering, ASCE, 124(6), 542–549.Pise, P. J. (1984): Lateral response of free­head pile, Journal ofGeotechnical Engineering, ASCE, 110, 1805–1809.Poulos, H. G. (1971): Behaviour of laterally loaded piles: I. singlepiles, Journal of Soil Mechanics and Foundations Divisions,ASCE, 97(SM5), 711–731.Poulos, H. G. (1973): Analysis of piles in soil undergoing lateralmovement, Journal of Soil Mechanics and Foundations Divisions,ASCE, 99(SM5), 391–406.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 de‰ectionprediction in sand, Journal of Geotechnical Engineers, ASCE, 112,130–138.Randolph, M. F. (1981): The response of ‰exible piles to lateralloading, G áeotechnique, 31(2), 247–259.Reese, L. C. and Welch, R. C. (1975): Lateral loading of deep foun­dations in stiŠ clay, J. Geotech. Engg, Div., ASCE, 101(GT7),633–649.Stewart, D. P., Jewell, R. J. and Randolph M. F. (1993): Numeri­cal modeling of piled bridge abutments on soft ground, Computersand Geotechnics, 15, 23–46.Wu, D., Broms, B. B. and Choa, V. (1998): Design of laterallyloaded piles in cohesive soils using p­y curves, Soils and Founda­tions, 38(2), 7–26.
  • 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
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 363–374, June 2008MECHANICAL BEHAVIOR OF BENTONITE­SAND MIXTURESAS BUFFER MATERIALSTOSHIYUKI MITACHIi)ABSTRACTFor the purpose of establishing the method for estimating in­situ mechanical behavior of artiˆcial buŠer 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 speciˆc volume vb, which is deˆned as the speciˆc 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, buŠer material, consolidated undrained triaxial test, inˆltration test, oedometer test, swellingbehavior (IGC: D3/D5/D6)deformation to verify the equations proposed by them.Tanaka and Nakamura (2005) investigated the eŠects ofseawater and high­temperature history on the swellingcharacteristics of bentonite. Based on the mechanical be­havior of bentonite­based buŠer 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 buŠer 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 deˆned 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 eŠect ofINTRODUCTIONAt present, bentonite­sand mixture is expected to bethe most appropriate as a buŠer material of high­levelradioactive waste products when they are disposed in thedeep ground. Therefore, it is important to establish themethod for estimating in­situ mechanical behavior ofbuŠer materials. For this purpose, it is necessary to clari­fy the stress­deformation behavior of buŠer 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 buŠer 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 ˆlling up the space be­tween the buŠer material and a wall of the disposal pit,and/or between the buŠer and an overpack by its swellingi)Professor, Department of Civil Engineering, Nihon University and Emeritus Professor of Hokkaido University, Japan (mitachi—eng.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.363 364MITACHITable 1.TypeIndex properties of materialsBentonite(Kunigel V1)Sand(Silica­sand No. 7)Na­type—32.692 g/cm3Soil density (rS)2.799 g/cmLiquid limit (vL)498.6z—Plastic limit (vP)39.4z—Plasticity index (IP)459.2—Smectite content60z—diŠerent 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) inˆltrationtest. Through the systematic and comprehensive experi­ments, new signiˆcant ˆndings are presented andmethods for characterizing mechanical parameters re­quired for the numerical analysis of stress­deformationbehavior of artiˆcial buŠer 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 buŠermaterial 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 speciˆcation ofthe buŠer material for radio­active waste disposal projectin Japan, bentonite­sand mix proportion a in mass wasmainly speciˆed 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 asspeciˆed, 70z–30z in mass for making a70z 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 conˆne­ment of all circumferential surfaces of the mold. Thedegree of the specimen calculated before triaxial testshowed 100}2z and pore water pressure coe‹cient 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 ˆlms were installedas the loading plates and ˆlters at the top and bottom of BEHAVIOR 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 speciˆedas rd1.6 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 eŠective consolidation stress wasstarted after conˆrming B»0.95.The drainage during isotropic consolidation was forcedto radial direction through the ˆlter paper wrappedaround the specimen. To ensure the drainage route underhigh conˆning pressure, specimen was wrapped twicewith two sheets of ˆlter 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 conˆn­ing stress during undrained testing, the author performeda preliminary test by using 0.003z/min and 0.001z/min(which is one­ˆftieth of recommended value by JGS stan­dard, 2000) of strain rate. After examining the test resultsshown in Fig. 5, in which the eŠect of diŠerent 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 eŠective consolidation stress in MPa.Expansive Stress­Strain Measurement TestAs mentioned previously, two series of tests referredto, in this paper as swelling test and inˆltration test wereperformed to investigate one­dimensional expansivestress­strain behavior of bentonite­sand mixtures. The 366MITACHIFig. 5. Test results for comparing the eŠects 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 paperdeˆning the stress acting on the rigid conˆning 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 ˆlms are in­stalled as the loading plates and ˆlters 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 conˆning ring was installed (see Fig. 1). Aftercompaction, 60 mm diameter and 10 mm height specimenwith conˆning 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 theˆgure, 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 deˆned 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 de‰ection of the loading frame, load cellFig. 6.Fig. 7.Expansive stress­strain measuring apparatusExpansive stress vs. time during swellingFig. 8. Schematic representation of the diŠerence 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 measur­ BEHAVIOR 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.Inˆltration TestTesting apparatus and specimen preparation are thesame as above mentioned swelling test. Bentonite­sandmixtures (a70 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 conˆning ring was installed. After that, 60mm diameter and 5 mm or 10 mm height specimen withconˆning 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 diŠerence of the stress­strain conditionsof the specimen from those of swelling test mentioned inthe previous section, the present author refers to thisseries of tests as inˆltration 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) a70%, (b) a50% and (c) a100% 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 a70z made by COM method. Figures9(b) and (c) illustrate the results obtained from the testsperformed on the a50z and a100z specimens for 368MITACHITable 2‚Compression 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 a50z, it is seen akind of in‰ection at about 1.3 MPa which is corre­sponding to the void ratio of e0.46 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 a70z and a100z.Compression and swelling indices Cc and Cs obtainedfrom the consolidation tests on a70z and a100zspecimens 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 a70z and rd1.6g/cm3 give relatively smaller values of Cc0.27 and Cs0.16 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 conˆning ring and speci­men, the height of which was twice that in the presentstudy. The occurrence of in‰ection of the curve as men­tioned previously on a50z specimen in Fig. 9 (b)might be also possible for higher stress range of JNC ex­periment on a70z 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 wereˆrstly compacted in the mold in dry powder state andthen they were sustained to be saturated under the con­ˆnement 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 coe‹cient of hydraulic con­ductivity k versus bentonite density rb relationship ob­tained from the normally consolidated stress range,where bentonite density is deˆned as the density calculat­ed by excluding the volume of sand particles from that ofbentonite­sand mixture as shown in the following equa­tion:rbMb/(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 Coe‹cient of hydraulic conductivity k versus rbrelationships obtained by JNC (2002) on a70z speci­men are also plotted in the ˆgure. 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 diŠerence q normalized by eŠectiveconsolidation stress p?0 versus axial strain ea relationship isillustrated in Fig. 12. Test results with CIP­specimens( rd1.7 g/cm3) and COM­specimens ( rd1.6 g/cm3) fora50z 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 a70z and rd1.6 g/cm3 specimen. As seenin the ˆgure, q/p?0 for low consolidation stress ofCOM7005 is greater than other specimens of higher con­solidation stress. As the maximum expansive stress fora70z 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 a50z consolidated at low stresslevel.EŠective Stress PathsFigure 13 shows the eŠective 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 (a50%) specimen,(b) COM (a50%) and (c) COM (a70%) specimensdecrement of eŠective 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 areM0.57 for COM70 specimens, M0.77 for COM50specimens and M0.84 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 (ea0¿0.005z) and the secant modulus Esec are investigated.Void ratio e versus logarithm of consolidation stress p?0 370MITACHIFig. 14.Fig. 15.e­ln p?0 relationshipe­ln Emax relationshipFig. 13. EŠective stress paths during undrained test on (a) CIP (a50%), (b) COM (a50%) and (c) COM (a70%) specimensrelationship obtained from the isotropic consolidationstage and e versus ln Emax relationship are shown in Figs.14 and 15, respectively. As shown in these ˆgures, 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.Deˆning 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 a50z and 70z specimens. Asshown in the ˆgure, 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 conˆning 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 conˆning 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 diŠerencesin 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 diŠerence of the smectite content mightcome from the diŠerence 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 thediŠerence 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 diŠerence 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 a30 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 a70zand the initial density rd of 1.6 and 1.7 g/cm3, where ex­pansive strain is deˆned 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)max0.4z, which was less than halfof that obtained by RNFB7016 ((es)max1.0z) 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 Inˆltration TestFigure 21 shows the change of bentonite speciˆcvolume vb versus vertical stress relationship in log­logplot obtained from a series of inˆltration tests under con­stant vertical stress condition for two samples of a100z and initial dry density of rd1.4 g/cm3 specimen,where vb1{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 vb1.8 to 2.4 obtained by swelling test men­Fig. 21. log vb­log p? relationship during incremental loading com­pression and const. stress inˆltration test (a100% and rd1.4g/cm3)tioned in section 4.3 is also illustrated. The relationshipbetween bentonite density rb (which is deˆned as Eq. (1))and bentonite speciˆc volume vb is represented as follows:rbMb/(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 ˆrstly subjected in­cremental loading compression up to the vertical stress of0.4 MPa and 0.8 MPa, respectively. After that, inˆltra­tion 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 inˆltration test, compressive volumechange is observed for the specimen started inˆltration atthe stress of 0.8 MPa as indicated by downward headedarrow in Fig. 21, whereas the specimen started inˆltra­tion 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 in­ˆltration 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 inˆltration tests exclud­ing the plot of incremental loading compression up to theparticular stress state before starting inˆltration areshown together with the log vb versus log ( p?s)max line ˆttedfor 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 a70z 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.Inˆltration 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 inˆltration tests (a70% and 100%) BEHAVIOR OF BENTONITE­SAND MIXTURESthe stress increased as shown by arrows heading to theright with the progress of inˆltration, whereas the stressdecreased when the inˆltration started after the incremen­tal loading up to 1.0 MPa (test No. 10014c) as shown byan arrow heading to the left in the same ˆgure. As seen inFig. 22, ˆnal points of inˆltration 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 ofinˆltration test under constant vertical stress conditionfor the mixture of bentonite and Toyoura sand, where emwas deˆned 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 inˆltration,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 diŠerences 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 inˆltration. A uniquerelationship is found between the maximum expan­sive stress ( p?s)max versus bentonite speciˆc 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 ˆnancially 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.NOTATIONBSkempton's pore water pressure coe‹cientCIPSpecimen making by Cold Isostatic PressmethodCOMSpecimen making by static compaction in themold in dry powder stateEmaxInitial tangent modulus obtained by consolidat­ed undrained triaxial compression testEsecSecant modulus obtained by consolidated un­drained triaxial compression testFBExpansive stress measurement by Feed Backsystem during swelling testNFBExpansive stress measurement by Non FeedBack system during swelling testRFBExpansive strain measurement by applyingmaximum expansive stress measured by FB sys­temRNFBExpansive strain measurement by applyingmaximum expansive stress measured by NFBsystemebBentonite void ratiop?0EŠective consolidation stressp?cConsolidation yield stress( p?s)maxMaximum expansive stress obtained by swellingtestqPrincipal stress diŠerencevbBentonite speciˆc volume calculated by exclud­ing the volume of sand particlesMCritical state stress ratio q/p? 374MITACHIaBentonite­sand mix proportionlSlope of e­ln p?c curvenSlope of e­ln Emax curveeaAxial strain measured during triaxial compres­sion testesExpansive strain measured during swelling test(es)maxMaximum expansive strain measured by swell­ing testrbBentonite density calculated by excluding thevolume of sand particlesrdDry density of bentonite­sand mixturersbDensity of bentonite particlerssDensity of sand particleREFERENCES1) Borgesson, L. and Hokmark, O. (1991): Interim report on thelaboratory and theoretical work in modeling the drained and un­drained behavior of buŠer 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, III–67, 275–285 (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 BuŠer Material, Proc. 50th Annual Conf. on JSCE, III­A, 28–29.4) 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, 292–305.5) Japanese Geotechnical Society (2000): Standard Method for Con­solidated Undrained Triaxial Compression Test on Soils with PoreWater Pressure Measurements (JGS 0523–2000).6) Japan Nuclear Cycle Development Institute (1999): Technical conˆ­dence on the disposal facilities for high level radioactive wastes—2nd Report.7) Japan Nuclear Cycle Development Institute (2002): Technical conˆ­dence on the disposal facilities for high level radioactive wastes—2002 year Report.8) Kawaguchi, T., Mitachi, T. and Shibuya, S. (2004): Quantifyingdeformation modulus of reconstituted clays at small strains, Jour­nal of JSCE, No.638, III–49, 179–191 (in Japanese).9) Komine, H. (2001): Evaluation of swelling characteristics of buŠerand backˆll materials considering the exchangeable cations compo­sitions of bentonite and its applicability, Proc. 15th ICSMGE, 3,1981–1984.10) Komine, H. and Ogata, N. (2002): Swelling characteristics of sand­bentonite mixture and various kinds of bentonite, Journal of JSCE,No. 701, III–58, 373–385 (in Japanese).11) Komine, H. and Ogata, N. (2003): New equations for swelling char­acteristics of bentonite­based buŠer materials, Canadian Ge­otechnical Journal, 40(2), 460–475.12) Komine, H., Ogata, N., Nakasima, A., Takao, H., Ueda, H. andKimoto, T. (2004): Evaluation of self­sealing property of bentonite­based buŠer by one­dimensional model test, Journal of JSCE, No.757, III–66, 101–112 (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, III–68, 21–31 (in Japanese).14) Nakano, M., Amemiya, Y., Fujii, K., Ishida, T. and Ishii, A.(1984): Inˆltration and expansive pressure in the conˆned unsatu­rated clay, Transaction of JSIDRE No. 112, 55–66 (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, III–67, 367–372 (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, 85–156, Korea.17) Tanaka, Y. and Nakamura, K. (2005): EŠect of seawater and high­temperature history on swelling characteristics of bentonite, Jour­nal of JSCE, No. 806, III–73, 93–111 (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
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 375–396, 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 eŠect 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 eŠect, 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 eŠorts 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 hadsuŠered 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(Ohira˜et 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 (shirato—pwri.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.375 376SHIRATO 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, ˆrstly, 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 eŠects. Third, a method is proposed to incor­porate the group eŠect 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 mm2MSinusoidal1.00.92———H (Heavier)2867 kg320 mm3MSweep0.500.57———4MKobe8.188.192.9951.59266.75MSweep0.500.552.9541.61473.26MStep­increasing6.06.17———7HSweep0.500.572.8811.65584.8L (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)1NSinusoidal3.02.782.9911.58263.68HKobe8.188.19———2NSinusoidal3.02.72———9HSweep0.500.572.8691.66286.83NSweep0.500.59———4LSweep0.500.582.9591.59968.710HStep­increasing6.06.23———5LSinusoidal1.00.92———11MSweep0.500.552.8611.66788.16LSinusoidal3.02.72———12MSinusoidal5.05.09———7LSinusoidal4.03.972.9071.62877.013MSinusoidal1.00.892.8431.67890.98MSweep0.500.59———14MSweep0.500.56———9MSinusoidal1.00.93———After————2.8421.67891.010MSinusoidal3.02.78———11MSinusoidal4.03.93———12MSinusoidal5.05.342.8921.63679.413MSinusoidal6.06.322.8651.65183.714LSinusoidal6.06.522.8411.66687.615MKobe8.188.822.8371.66888.2After————2.8331.67088.9Note—: 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 deˆnedat 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 diŠerentset­ups, 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 N–1, pile N–2, and pileN–3 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 eŠect 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 devices 378SHIRATO 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 su‹cient 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 stiŠness 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 ˆxed 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 EYoung'smodulus and Ithe 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 EI1000 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 was 379SEISMIC 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: rs2.653 g/cm3, rdmax1.712 g/cm3,rdmin1.397 g/cm3, and D500.365 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 Dr65z(the soil density was 1.587 g/cm3). The internal frictionangle was estimated under the assumption of c0, inwhich cadhesion. The relationship between Young'smodulus and the conˆned stress was obtained by isotrop­ic consolidated undrained cyclic triaxial compressiontests, as follows:E01.691(s?c)0.5364~104(kN/m2),(1)where s?cconˆned stress (also kN/m2).The relationships between G/G0­g and h­g obtainedfrom the cyclic triaxial compression tests are shown inFig. 4, in which Gsecant shear modulus, G0smallstrain shear modulus, hequivalent damping ratio, andgshear strain. A least­square method derives a ˆttedcurve with the hyperbolic­type function proposed byHardin and Drnevich (1972):1GgG01{gr(2)where gr0.0487z, 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 Dr65%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 ˆttedwith 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 diŠerent 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 di‹culty involved in es­timating the in‰uence 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 deˆcit in cross­sections, as load cells were not used. In addition, the useof piles with no deˆcit in cross­sections facilitates themodeling of the piles via computer simulations. PilesN­1, N­2, M­1, and M­2 were ˆtted with strain gauges at13 cross­sections, and piles S­1 and S­2 were ˆtted with 380SHIRATO 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 con­ˆrm 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 2–8, thephase angle was set to the opposite of that in Run 2–4 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 2–4 and Run 2–8 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 haveconˆrmed 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 diŠer­ent from the input acceleration signal to the shake table ineach run; this is also shown in Tables 2 and 3 as the diŠer­ence in the recorded and expected maximum accelera­ SEISMIC BEHAVIOR OF PILE­GROUPtions. Nonetheless, the wave accelerations in this paperare always presented along with the originally plannedmaximum acceleration levels. The diŠerence 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 doubleˆnite diŠerentiation 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 eŠect 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 eŠect 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 diŠerence in p estimated whenconsidering and ignoring the eŠect of the inertial forcecan be approximately 10z at most. The diŠerence waslarger at small amplitudes of p. Therefore, we judgedthat the eŠect 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 2–4, 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 2–4 (Right­hand side of the ˆgures show the enlargedviews of the distributions. Open circles: Original data, Filled cir­cles: Modiˆed through an additional smoothing preprocessing) 382SHIRATO ET AL.for several runs, so that the distributions of soil resistancestress, p, versus depth satisˆed 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 modiˆed via the addition­al smoothing pre­processing are also shown with the ˆlledcircles on the right­hand side enlarged views of Figs. 8(a)and (b). On the one hand, as compared in the right­handside ˆgure of Fig. 8(a), when the values of `p` are larger,the diŠerence is little in the distributions of p obtainedwith the original and modiˆed data processing schemes,i.e. the open circles and ˆlled circles in the ˆgure, respec­tively. On the other hand, the right­hand side ˆgure 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 modiˆed 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 deˆned 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 ˆrst approximation. For example,Fig. 9 shows that the settlement trends in Series 1 and 2are diŠerent, and we infer that the amplitudes and typesof inputted motions, as well as the input energy, are likelyto in‰uence the settlement trend.DisplacementDisplacement time histories are derived from thetrapezoidal double integration of acceleration time histo­ries. Acceleration time histories were ˆltered in terms offrequency with a high­pass ˆlter before the double in­tegration process; the accelerations shown in this paperare non­ˆltered 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 ˆlters that were eventually adopt­ed for each type of wave, namely the sinusoidal, step­in­creasing, and Kobe waves, and compares the horizontalshake­table displacements obtained from two diŠerentsources: accelerometer records and LDT records. A ˆlterwas determined according to the speciˆc type of the inputmotion. The transition band in the frequency of the ˆlterwas deˆned using a cosine function with the boundaryfrequencies of fstop and fpass, as given in the ˆlters 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 determinedˆlter 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 ˆlter and the identiˆed 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 ˆlters, 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 2–6 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 high­passˆlter was 1 Hz as also shown in Fig. 10. However, themain vibration components were not be removed and thein‰uence 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 in‰uenceof 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 anyˆltering process, the base line of the velocity time historyhas a breaking point, as shown in Fig. 11. Because it isimpossible to remove this eŠect via the general ˆlteringprocess, a further process was introduced for the Kobewave runs, prior to the above general ˆltering 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 2–4was 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, ša1 and ša2,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; ša1 was subtracted from the accelerationrecord from 0 sec to tb, and ša2 was subtracted fromtb to 40 s.3. The processed acceleration record was then in­tegrated once, and the velocities at times t0 and40 sec were obtained.4. We then determined the time of tb that yielded thederived velocities of zero at times t0 sec and t 384SHIRATO 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 diŠerent 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 2–1 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 as15–17 Hz for the cases involving the Weight M and 13–14Hz 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 eŠects of the diŠerence 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 M–1 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 base SEISMIC BEHAVIOR OF PILE­GROUP385Fig. 13. Fourier spectrum ratios of horizontal acceleration records atthe soil surface or the top weight to that at the base (Run 2–1)Fig. 15. Maximum and minimum soil displacements relative to theshake table (Runs 1–9 to 1–13)Fig. 14. Observed maximum responses versus maximum base acceler­ation levelswith increase in the base input acceleration levels andhave sort of a cut­oŠ 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 1–9 to 1–13; sinusoidal waves with diŠerent 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 stiŠness 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 diŠerent types of shearstiŠness distributions with depth: GAzn, where Aconstant, zdepth, and nconstant. Although the equa­Fig. 16. Horizontal displacement versus depth in a homogeneous elas­tic mediation for a semi­inˆnite medium is not given, the overalltendency is likely to be similar. Based on Eq. (1), the soilshear stiŠness in the present experiment is almost propor­tional to the square root of the conˆning 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 usingdiŠerent methods are explored herein.Soil Resistance StressThe soil resistance stresses, p, at depths GL |0.35 m 386SHIRATO 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 1–9 to 1–13 (sinusoidal waves) and Run 2–6(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 ˆrst 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 2–6, 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, ˆrst­trailing, and second­trailing piles (Piles N,M, and S or vice versa) diŠer 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 2–4 and2–8Fig. 19.Time histories of weight displacement in Runs 2–4 and 2–8 SEISMIC BEHAVIOR OF PILE­GROUPprocessing of the video recordings for Runs 2–4 and 2–8,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 ˆlteringprocess 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 conˆrmed 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 e‹ciency is estimated herein.p­y LoopsAssociated with a depth of GL |0.35 m for Pile N–1during a time window of 10–11 sec in Runs 1–10 and1–12, 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, ppN–pS 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 diŠerent. Run 1–10 involved a base accelerationlevel of 300 gal, while Run 1–12 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 diŠerence 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 diŠerent. This diŠerence arose from the groupeŠect. Pile N–1 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 N–1 388SHIRATO 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 1–12 with alarger base acceleration level, also indicates that the p­yloop shape in the shake table experiment was aŠected 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 y0 (see the path aroundPoint D), where the loop might be aŠected 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 1–12 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 ˆeldare unlikely to be completely identical and the diŠerenceis likely to increase with increase in the base accelerationlevel. As for Run 1–10 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 1–12 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 diŠerent.For Run 1–12, 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 t20–21 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 E‹ciencyA 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 eŠects 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 eŠect,and hnondimensional group e‹ciency 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 eŠects, 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 speciˆcations (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 Run1–12 (t20–21 sec)(5)(6)where znondimensional group e‹ciency and the so­called y­multiplier. Because p­ and y­multipliers are likelyto consider shadowing eŠects and elasticity, respectively,the use of both p­ and y­multipliers can make the physicalmeaning clearer. For example, the Japanese Speciˆca­tions 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 e‹ciency 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 t10–11 sec and t20–21 sec in Run 1–9 to 1–13(sinusoidal wave runs), as well as from the time windowsthat correspond to the ˆfth vibration period at each SEISMIC BEHAVIOR OF PILE­GROUPacceleration level of 100 gal to 600 gal in Run 2–6 (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 e‹ciencies 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 e‹ciency, h, iscalculated relative to the instantaneous leading­row corn­er piles.The group eŠects 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 e‹ciency 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 e‹ciency 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 lessaŠected than the other piles in the same row based on theshadowing eŠect theory.The results are shown in Figs. 22 and 23, where PileS–1 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 S–1) 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 N–1is the reference leading corner pile was also analyzed; theresult is very similar to that shown in Figs. 22 and 23.Pile­group e‹ciency in the horizontal soil resistance relative to the soil resistance to a corner pile of S–1 (Runs 1–9 to 1–13)Fig. 23.389Pile­group e‹ciency in the horizontal soil resistance relative to the soil resistance to a corner pile of S–1 (Run 2–6) 390SHIRATO ET AL.Figures 22 and 23 show that the diŠerence in the mobi­lized soil resistance, p, is found clear between the leadingrow piles and the trailing row piles, while the diŠerenceappears largely similar between the center piles numberedwith 2 and the outside piles numbered with 1 and 3, as theshadowing eŠect theory suggests.The facts that the trend of h decreases with increasingdisplacement level and such a trend does not vary withdiŠerent depths merit attention. As for the former fact,Figs. 22 and 23 also conˆrm that the group e‹ciency (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 e‹cien­cy 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 eŠect is evident in the horizontal soil­pileload transfer.Therefore, group eŠects 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)zzh~pS( y)zz, if pÆ0pG( y)zzh?~pS( y)zz,if pº0(7)where pG( y)zz is a hysteretic p­y curve at depth z for aFig. 24.Modeling of pile­group eŠects in dynamic p­y curvespile in a pile­group, pS( y)zz 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 2–4 withthe Kobe wave. It is worth noting that a comparison ofthe experimental and numerical results for Run 2–8 rev­eals the same trends as those revealed in an equivalentcomparison for Run 2–4. 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 inˆnitesimaldeformation 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 E200 kN/mm2, the moment of inertia of the cross­sectionof I5.0~106 mm4, and sectional area of A2085 mm2;however, for further simplicity, the three piles in eachrow are dealt with together as a single beam with the sec­ SEISMIC 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 ˆnite 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 theˆnite element nodes of the pile because of the limitationsof the commercial ˆnite­element 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 psoil resistance stress to a pile andythe corresponding displacement of the pile relative tothe far­ˆeld. 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 eŠect 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 ˆxed and rotation isfree to occur. The three vertical joint elements in eachrow of piles are also integrated.We input the observed free­ˆeld 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 free­ˆeld 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 unaŠected by shortcomingsin the numerical predictions of soil motions.For simplicity, the damping matrix is set to be propor­tional to the initial stiŠness matrix. Ultimately, the damp­ing is assumed to be 2z for the ˆrst 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 eŠect 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 diŠerent 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 given 392SHIRATO ET AL.as follows:kHakk0,(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 ˆtting process to observational monotonicp­y curves. Accordingly, the nondimensional correlationfactor, ak, is introduced. Because the initial gradient ofthe backbone curve is diŠerent 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 p0 is a straight linewith the unloading gradient k0. The subsequent loadingpath from p0 (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 de­ˆned as kHrmk0 using a nondimensional parameter, m.Because the modiˆcation factor m is introduced, thereversed loading path from the external curve is boundfor a point that is diŠerent 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 ˆrst ˆxed, whilethe ˆrst 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 { »42cospusv|KA(9)where svoverburden stress at a depth of x2, qinternalfriction angle, and KARankin's active earth pressurecoe‹cient:KAtan2Ø p4 | p2 »(10)The unit soil mass is given as 1.6 t/m3 based on Table 3and we use q40.99obtained 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 deformationcoe‹cient of soil at each depth, x2 (m)depth, ntheconstant that represents the loading­width­dependency ofsubgrade reaction coe‹cients, 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 eŠective stress estimated by sm(1{2K0)sv(x2)/3(kN/m2), where sv(x2) is the eŠective overburden stress atdepth x2 and K0 is the coe‹cient of earth pressure at rest,as estimated by K01|sin q.In Eqs. (8) and (11), the soil resistance to the pile isproportional to the soil rigidity (Gazetas and Dobry,1984), and the modiˆcation concerned with the foun­dation­width dependency of the subgrade reactioncoe‹cient is applied with a power of the foundationwidth (Yoshida and Yoshinaka, 1979; Japan Road As­sociation, 2002), where B00.3 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 Speciˆcations 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 triaxial 393SEISMIC BEHAVIOR OF PILE­GROUPFig. 28. Estimation of the areas of apparent soil resistance, A, and thegroup eŠects, h, based on the shadowing eŠect 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 ak0.01 and 0.1 via numerical simu­lations of Run 2–4 and Run 2–8; 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 ak0.1 was considered to make the system somewhat stiŠer,as higher­frequency components appear in accelerationtime histories compared to those in the experimentaldata. Therefore, all numerical results shown hereafter arecalculated with ak0.01.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 shadowingeŠect 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 eŠect theory, and concluded that the method original­ly proposed in DIN4014 (Deutsches Institut f äur Nor­Fig. 30. Recorded behavior of Pile N–1 and Pile S–1 in the directionparallel to the pile axis in Run 2–4 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 Bpile 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 conˆrm 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 2–4. 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 E200kN/mm2 and cross­sectional area A3.085~103 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,dvaN{bN 3,(12)are adopted, in which N (kN)axial load, dv (mm)axi­al displacement at the end of a pile, and a and bcon­stants. 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 simula­ 394SHIRATO 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 coe‹cients a and b in Eq. (12) are eventuallygiven as a5.105~10|2 mm/kN and b2.572~10|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 2–4 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 re‰ect the fact that theinversed pile­base springs remain stiŠer 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 N–1 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 2–4Fig. 33. Calculated and recorded distributions of the peak pile­bend­ing moment versus depth in Run 2–4Fig. 32. Calculated and recorded response time histories of the topweight motion in Run 2–4Fig. 34. Calculated and recorded response time histories of the bend­ing moment at a depth of GL |0.45 m in pile N–1 for Run 2–4 SEISMIC BEHAVIOR OF PILE­GROUPFig. 35. Calculated and recorded peak soil resistance distributions ver­sus depth in Run 2–4Fig. 36. Calculated and recorded dynamic p­y curves at a depth of GL|0.45 m in Run 2–4curves 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 N–1 and S–1 (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 groupeŠect observed in lateral load transfer between thesoil and piles in the experiment did not vary withdepth. Although the group eŠect increased with in­creasing relative displacement between the soil andpiles, the eŠect approaches a particular value whenthe displacement level is greater than approximate­ly y/D1z. Therefore, for large earthquakes thegroup eŠect 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 eŠect 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 eŠects 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. Yoshida of To­hoku­Gakuin University for providing useful commentsand suggestions that helped to improve this paper.REFERENCES1) AASHTO (1998): LRFD Bridge Design Speciˆcations SI Units 2ndEdition, Washington D. C., AASHTO (including interims for 1999through 2002).2) American Petroleum Institute [API] (1987): Recommended practicefor planning, designing, and constructing ˆxed oŠshore platforms,API Recommended Practice 2A (RP 2A), 17th Edition.3) Boulanger, R. W., Curras, C. J., Kutter, B. L., Wilson, D. W. andAbghari, A. (1999): Seismic soil­pile­structure interaction experi­ments and analyses, J. of Geotech. and Geoenvr. Engrg., ASCE,125(9), 750–759.4) Brown, D. A., Morrison, C. and Reese, L. C. (1988): Lateral loadbehavior of pile groups in sand, J. of Geotech. Engrng., ASCE,114(11), 1261–1276.5) Curras, C. J., Boulanger, R. W., Kutter, B. L. and Wilson, D. W.(2001): Dynamic experiments and analyses of a pile­group­support­ed structure, J. of Geotech. and Geoenvr. Engrg., ASCE, 127(7),585–596.6) Deutsches Institut f äur Normung (1987): DIN4014.7) Fukui, J., Kimura, Y. and Okoshi, M. (1997): Strength and ductil­ity characteristics of pile foundations, Proc. 2nd Italy­Japan Wor­ 3968)9)10)11)12)13)14)15)16)17)18)SHIRATO ET AL.kshop on Seismic Design and Retroˆt of Bridges, TechnicalMemorandum of PWRI, (3503), PWRI 255–274.Fukui, J., Nakatani, S., Shirato, M. and Nonomura, Y. (2006):Large­scale shake table experiments of grouped­pile foundations,Technical Memorandum of PWRI, (4015), Public Works Research(in Japanese).Gazetas, G. and Dobry R. (1984): Horizontal response of piles inlayered soils, J. of Geotech. Engrg., ASCE, 110(1), 20–40.Hardin, B. and Drnevich, V. (1972): Shear modulus and dampingin soils: design equations and curves, J. of Soil Mech. and Founda­tion Div., ASCE, 98(SM7), 667–692.Japan Road Association (2002): Speciˆcations for HighwayBridges., Tokyo, Maruzen.Japanese Industrial Standard (2004): JIS Z 2241:1998 Method ofTensile Test for Metallic Materials, Japanese Standard Association.Kikuchi, Y. (2002): Lateral resistance of soft landing moundlessstructure with piles, Ph. D. Thesis, University of Tokyo (inJapanese).Kishida, H. and Nakai, S. (1979): Analysis of a laterally loadedpipe with non­linear subgrade reaction, Trans. of A.I.J., (281),41–53 (in Japanese).Kosa, K., Suzuki, N., Kimura, M., Kimura, Y. and Morita, Y.(1998): Lateral loading test of full­scaled pile foundation focusedon ultimate behavior, J. of Geotech. Engrg., JSCE, (596/III–43),249–260 (in Japanese).Miyamoto, Y., Hijikata, K. and Tanaka, H. (2004): Seismic designof a structure supported on pile foundation considering dynamicsoil­structure interaction, Proc. 3rd UJNR Workshop on Soil­Structure Interaction (eds. by M. Celebi, M.I. Todorovska, I. Oka­wa, and M. Iiba), Menlo Park, CA, USA.http://www.pwri.go.jp/eng/ujnr/tc/a/ssi_w3/index.html.Mokwa, R. and Duncan, J. (2001): Laterally loaded pile groupeŠects and p­y multipliers, ASCE Geotechnical Special Publication,Foundation and Ground Improvement, (GSP 113), 728–742.Ohira,˜A., Tazoh, T., Nakahi, S. and Shimizu, K. (1985): Observa­tion and analysis of earthquake response behavior of foundationpiles in soft soil deposit, J. of Struct. Mech. and Earthq. Engrg.,JSCE (362/I–4), 417–426 (in Japanese).19) Ohmachi, T. and Tokimatsu, K. (1983): Formulation of a practicalmethod for three dimensional earthquake response analysis of em­bankment dams, Proc. JSCE, (333), 71–80 (in Japanese).20) Public Works Research Institute (1996): Report on the disastercaused by the 1995 Hyogoken Nanbu Earthquake, J. of Research,Public Works Research Institute, 33.21) Rollins, K., Peterson, K. and Weaver, T. (1998): Lateral load be­havior of full­scale pile group in clay, ASCE J. of Geotech. andGeoenv. Engrng., 124(6), 468–478.22) Shirato, M., Yoshida, N., Fukui, J. and Nonomura, Y. (2005): Asimulation with a beam­on­nonlinear Winkler spring model for theseismic behavior of extended pile­shafts in soft clay, J. of Struct.Engrg., JSCE, 51A, 739–750 (in Japanese).23) Shirato, M., Koseki, J. and Fukui, J. (2006a): A new nonlinear hys­teretic rule for Winkler type soil­pile interaction springs that con­siders loading pattern dependency, Soils and Foundations, 46(2),173–188.24) Shirato, M., Koseki, J., Fukui, J. and Kimura, Y. (2006b): EŠectsof stress­dilatancy behavior of soil on load transfer hysteresis insoil­pile interaction, Soils and Foundations, 46(3), 281–298.25) Shirato, M., Nonomura, Y., Nakatani, S. and Kulhawy, F. (2006c):Numerical and large­scale experimental study on seismic behaviorof pile foundations, Proc. 8th National Conference on EarthquakeEngineering, EERI, CD­ROM.26) Tazoh, T., Shimizu, K. and Wakahara, T. (1988): Seismic observa­tions and analysis of grouped­piles, Dynamic response of pile foun­dations­experiment, analysis and observation, Geothicnical SpecialPublication, ASCE, (11), 1–20.27) Tokimatsu, K., Suzuki, H. and Sato, M. (2005): EŠects of dynamicsoil­pile­structure interaction on pile stresses, J. of Struct. and Con­st. Engrg., AIJ, (587), 125–132 (in Japanese).28) Wang, H., Murono, Y. and Nishimura, A. (2000): Experimentalstudy on dynamic interaction of pile foundations and soil usingmockup model, J. of Struct. Mech. and Earthq. Engrg., JSCE,661(I–53), 57–69 (in Japanese).29) Yoshida, I. and Yoshinaka, R. (1979): A method to estimate modu­lus of horizontal subgrade reaction for a pile, Soils and Founda­tions, 12(3), 1–17.
  • 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
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 397–406, 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 diŠusion coe‹cient (Dp) which is typically governed by the variations in soil air­ˆlledporosity (va). For undisturbed volcanic ash soils, recent studies have shown that a linear Dp(va) model, taking into ac­count inactive air­ˆlled 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 ˆeld capacity condition) and pF 4.1 (near wilting point condition), and assuming the same value for the Buckin­gham exponent (X2.3) 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 eŠects showed that a decrease inslope C and va, th due to uniaxial reduction of air­ˆlled pore space in between aggregates markedly aŠects the magnitudeof soil­gas diŠusivity. We recommend the new Dp(va) model using only the soil­air contents at two soil­water matricpotential conditions (ˆeld capacity and wilting point) for a rapid assessment of the entire Dp­va function.Key words: air­ˆlled porosity, soil­gas diŠusion coe‹cient, soil­gas diŠusivity, soil­water retention, volcanic ash soil(IGC: D4/E14)Several predictive models for soil­gas diŠusivity,Dp/Do (where Do is the gas diŠusion coe‹cient 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 diŠerent 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 diŠusion of gaseous phase contaminants in soil(e.g., Jury et al., 1983; H äohener and Surbeck, 2004).To take into account the eŠect 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 diŠusion through tortuous air­ˆlled pathways in be­tween soil particle­water complexes (Hers et al., 2002).An accurate prediction of the soil­gas diŠusion coe‹cient(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 in‰uence 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 sacriˆcing prediction accuracy is needed.i)ii)iii)iv)Dept. of Engineering Sciences, University of the Philippines­Diliman, Philippines (acresurrecci—up.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.397 398RESURRECCION ET AL.characteristic (SWC)­based Dp/Do models. These SWC­based Dp/Do models performed superior to the soil­typeindependent models when estimating Dp for diŠerent 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 pFlog (|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 theeŠect of isolated air­ˆlled pore space entrapped by inter­connected water ˆlms in between soil aggregates. This in­active air­ˆlled 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 diŠerently 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 diŠusivity taking into account both inactive air­ˆlledpore space and soil­water retention.Volcanic ash soil diŠers 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 well­deˆned points on the soil­waterretention curve, (2) to test the performance of this newDp/Do model against independent soil­gas diŠusivity 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 eŠects 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 fromdiŠerent 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 ˆeld 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 diŠerent 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 diŠusivity,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 classiˆed according to Japan Geotechnical Society (JGS) while other soilswere classiˆed 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).nmnot measuredNew Data Representing DiŠerent 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 diŠerent 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 diŠerent 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 air­‰ow oven which was set at 209Cfor 5 to 7 days for air­dry condition, and at 1059C for 2days for oven­dry condition.The soil­gas diŠusion coe‹cients (Dp) were measuredby the method of Currie (1960) as recommended by Rol­ston and Moldrup (2002). The apparatus uses a diŠusionchamber with oxygen as the experimental gas at 209C (seeFig. 1). The diŠusion 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 diŠusion cham­ber, oxygen from the atmosphere diŠuses through the soilsample into the diŠusion chamber while nitrogen gasdiŠuses through the soil sample into the atmosphere. The 400RESURRECCION ET AL.Dp (va)10/3DoF2(5)Soil­Water Characteristic (SWC) Based ModelsThe recent Dp(va)/Do models developed by Moldrup etal. (1996, 1999, 2000, 2005a) linked soil­gas diŠusivity tosoil type through the pore size distribution (PSD)parameter b by using the Campbell (1974) soil­waterretention model,Ø»cuce u sFig. 1. Schematic diagram of the experimental apparatus used tomeasure soil­gas diŠusion coe‹cient, Dpoxygen concentration inside the diŠusion 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 diŠusion chamber was assumed to oc­cur instantly. The calculation of the soil­gas diŠusioncoe‹cient, Dp, was done according to Rolston and Mol­drup (2002).MODELS FOR SOIL­GAS DIFFUSIVITYSoil­Type Independent ModelsBuckingham (1904) suggested that the soil­gas diŠu­sion coe‹cient 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,Dp0.66vaDo(2)Call (1957) modiˆed the Penman model by assuming10z of the total soil volume consisted of isolated (inac­tive) air­ˆlled pores. This model successfully describedthe diŠusion of ethylene dibromide in a sandy loam soil.The Call (1957) Dp/Do model is given as,Dp0.66(va|0.1)DoDp (va)2Do 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 »vaDpF2DoF2{3b(7)where the expression, F2, is a reference gas diŠusivity 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 diŠusivity 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»vaDpF2DoF(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 TØ 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 diŠusivi­ty model, we consider a linear so­called Penman­Calltype Dp(va)/Do model (Moldrup et al., 2005a),DpC(va|va, th)Doif vaÆva, th(11a)Dp0Doif vaºva, th(11b)where C is the slope of the linear Dp(va)/Do model, andFig. 2. Plot of the soil­gas diŠusivity against soil­air content forTsumagoi and Nishi­Tokyo volcanic ash soils. A linear ˆt 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 soil­gasdiŠusivity becomes negligible (ceases due to the inactiveor remote air­ˆlled pore space created by inter­connectedwater ˆlms). 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.,va–Dp/Do coordinates) on the prediction line are su‹cientto derive the model parameters (slope C and interceptva, th). In order to deˆne the prediction line, it is necessaryto estimate the gas diŠusivities 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 0–5 cm, 15–20 cm and 55–60 cm depths atsoil­water matric potentials of pF 3 and 6 (air­dry, as ˆlled out symbols). The Buckingham (1904) Dp/Do power­law model ˆtted 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 ˆtted 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)Cwhere 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, thva, 4.1 1|Fig. 4. Model concept for the two­retention­point (2RP) soil­gasdiŠusivity 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 X2.3 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 air­ˆlled pore spacelikely occurs because voids between aggregates are almostcompletely drained eliminating the inter­connected waterˆlms between water­ˆlled aggregates resulting in a mini­mum water blocking eŠect (and, therefore, minimum Xvalue). This is in agreement with the Dp/Do data of Mol­drup et al. (2005b) for 44 diŠerently 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 ˆeld 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 ˆeld 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 theˆtted 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 air­ˆlled pores less than 0.2 mm that con­stitutes the threshold soil­air content for soil­gas diŠu­sion.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 ˆeldcapacity. The ˆeld 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 aŠects 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 eŠect of hystere­sis on the conˆguration of the air­ˆlled pore connectivityis outside the scope of this paper and should be furtherstudied.Statistical AnalysesTo compare the diŠerent predictive Dp/Do models, theroot mean square error (RMSE, Eq. (14)) was used forthe best overall ˆt compared to measured data.RMSE1nnS (d )i1i2(14)where di is the diŠerence 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 overestimated TWO SOIL­WATER RETENTION POINTS IN UNSATURATED VOLCANIC ASH SOILS403Fig. 5. Scatterplot comparison of predicted and measured gas diŠusivities (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 diŠusivity 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) withX2(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)Modiˆed Buckingham(1) with(this study)X2.3Two­Retention­Point, 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 diŠusivi­ties (Fig. 5(e)).The original Buckingham Dp(va)/Do model, Eq. (1),performed surprisingly well in predicting Dp/Do values(RMSE0.060, Fig. 5(a) and Table 2). When X was mo­diˆed to 2.3, signiˆcant 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 X2.3, became com­parable to the performance of the SWC­based Dp(va)/Domodels (BBC with RMSE0.056, the va, 100­dependentmodel with RMSE0.052, and TPM with RMSE0.058; 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 (RMSE0.026, Fig. 5(i) and Table 2). In contrastto the non­linear, SWC­based Dp/Do models, no large 404RESURRECCION ET AL.Fig. 6. Plot of gas diŠusivity against soil­air content for individual undisturbed samples from (a) Tsumagoi, (b) Fukushima 0–5 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 diŠusionin the remote air­ˆlled pore space within the soil ag­gregates when soil samples were drained past pF 3.EŠects of Soil Compaction on Gas DiŠusivityThree individual undisturbed volcanic ash soils fromTsumagoi, Fukushima, and Nishi­Tokyo shown in Fig.6(a)–(c) diŠer in bulk density and porosity due to diŠer­ent 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 air­ˆlled 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 eŠectsbetween aggregates at wet conditions, giving low valuesof slope C and va, th at high bulk density, in agreementwith data for the three diŠerently compacted soils in Fig.6(a)–(c).To illustrate the eŠect 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. EŠect of uniaxial compaction on soil­gas diŠusivity at pF 6(air­dry). The compaction was assumed to aŠect only the macropores, va, 2, between aggregatesF1|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 re‰ected only on the reduction of larger inter­aggregate pores, va, 2. Further, since the intra­aggregatepores are not likely aŠected by soil compaction, thediŠerences between va, 4.1 and va, 2 and between va, 6 (air­ˆlled porosity at pF 6) and va, 4.1 were kept constant andassumed equal to 0.2 m3 m|3 (i.e., from the initial diŠer­ence 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. 7 TWO SOIL­WATER RETENTION POINTS IN UNSATURATED VOLCANIC ASH SOILS405Fig. 8. Plot of gas diŠusivity 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 diŠusivity increasedwith a decrease in bulk density. This is in agreement withCurrie (1984) and further supported by the ˆndings 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 diŠerent 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 diŠusivities across moisture condi­tions (from wet to dry) in both non­compacted and com­pacted volcanic ash soils.CONCLUSIONSIn this study, we developed an easily applicable, linearsoil­gas diŠusivity 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 diŠusivitymeasurements, soil compaction has a large eŠect on gasdiŠusivity 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 diŠusivity and calculation of gasdiŠusive transport in volcanic ash soils, especially underdry moisture conditions where the 2RP model is sig­niˆcantly more accurate than previous models while req­uiring the same or less data input.ACKNOWLEDGEMENTThis study was made possible by the Grant­In­Aid forScientiˆc 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 GasDiŠusivity 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 ˆne sand and a ˆne sandy loam duringin­situ drainage, South African J. Plant and Soil, 4, 151–158 (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. O‹ce,Washington, DC.3) Burdine, N. T. (1953): Relative permeability calculations frompore­size distribution data, Trans. AIME, 198, 71–78.4) Call, F. (1957): Soil fumigation: V, DiŠusion of ethylene dibromidethrough soils, J. Sci. Food Agric., 8, 143–150.5) Campbell, G. S. 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(2005b): Predictive­descriptive models for gas and solutediŠusion coe‹cients in variably saturated porous media coupled topore­size distribution: II, Gas diŠusivity in undisturbed soil, SoilSci., 170, 854–866.Osozawa, S. (1998): Bulletin of National Institute for Agro­En­vironmental Sciences, (15), Natl. Inst. of Agro­Environmental Sci.,Ibaraki, Japan.Penman, H. L. (1940): Gas and vapor movements in soil: The diŠu­sion of vapors through porous solids, J. Agric. Sci., 30, 437–462.Petersen, L. W., El­Farhan, Y. H., Moldrup, P., Rolston, D. E.and Yamaguchi, T. (1996): Transient diŠusion, adsorption, andemission of volatile organic vapors in soils with ‰uctuating lowwater contents, J. Environ. Qual., 25, 1054–1063.Poulsen, T., Moldrup, P., Yoshikawa, S. and Komatsu, T. (2006):Bimodal probability law model for uniˆed description of waterretention, air and water permeability, and gas diŠusivity in variablysaturated soil, Vadose Zone J., 5, 1119–1128.Resurreccion, A. C., Kawamoto, K., Komatsu, T., Moldrup, P.,Ozaki, N. and Rolston, D. E. (2007a): Gas transport parametersalong ˆeld transects of a volcanic ash soil, Soil Sci., 172, 3–16.Resurreccion, A. C., Kawamoto, K., Komatsu, T., Moldrup, P.,Sato, K. and Rolston, D. E. (2007b): Gas diŠusivity and airpermeability in a volcanic ash soil proˆle: EŠects of organic matterand water retention, Soil Sci., 172, 432–443.Rolston, D. E. and Moldrup, P. (2002): Gas DiŠusivity, in: Dane,J. H. and Topp, G. C. (eds.). Methods of Soil Analysis, Part 4,SSSA Book Ser. 5, ASA and SSSA, Madison, WI, 1113–1139.Schjønning, P. (1985): A laboratory method for the determinationof gas diŠusion in soil, Rep. S1773, Danish Institute of AgriculturalSciences, Jyndevad, Denmark (in Danish with English summary).Shoji, S., Nanzyo, M. and Dahlgren, R. (1993): Volcanic ash soils:Genesis, properties and utilization, Developments in Soil Science,21, Elsevier, Amsterdam.So, E. K. (1998): Statistical correlation between Allophane contentand index properties for volcanic cohesive soil, Soils and Founda­tions, 38(4), 85–94.Takahashi, T. and Shoji, S.(2002): Distribution and classiˆcationof volcanic ash soils, Global Environmental Research, 6, 83–97.Troeh, F. R., Jabro, J. D. and Kirkham, D. (1982): Gaseous diŠu­sion equations for porous materials, Geoderma, 27, 239–253.Wada, K. (1986): Ando Soils in Japan, Kyushu University Press,Japan, 168–203.
  • 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
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 407–417, 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 eŠects of cations contained inwaste leachates, this study investigated the eŠects 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 diŠerences 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 0.1–0.5 M. However, GCLs with granularbentonite may be di‹cult to homogeneously prehydrate and exhibit an unstable hydraulic conductivity, which variesfrom k2.9~10|9 cm/s to k1.5~10|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 eŠects of geologi­cal and hydrological conditions in actual sites on the per­formance of the GCLs.Prehydration is one factor that aŠects 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 eŠective 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 landˆlls.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 (tkatsumi—mbox.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.407 408KATSUMI 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 eŠective 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 eŠects 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 insu‹cient 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 conˆne bentonites with a highereŠective 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 40–100z 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 diŠers from the actual process that GCLs absorbmoisture from the unsaturated base layers; they usedˆlter papers instead of the base layers. Hence, it shouldbe clariˆed how prehydration eŠects induced in actualsites in‰uence 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 thesu‹ciently swelled parts included in the heterogeneouslyprehydrated bentonite material can exhibit the lowhydraulic conductivity, the insu‹ciently 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 eŠects 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 eŠects 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 needlepunchingˆbers were used. One had powdered bentonite (BentoˆxNPS 4900–1), while the other had granular bentonite(Bentoˆx NPS 4900–2). The mass per unit area of eachGCL was 4.73 kg/m2 (the data provided by the manufac­ 409PREHYDRATION 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|928.0—59.6518.297.150.412.023.140.462.600.130.016.1562.5320.524.550.161.202.430.522.380.050.005.66turer), and the initial thickness was 6.0–7.0 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 eŠects 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 0151–2000, ``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 aconˆning 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 coe‹cient of variation, dcov, were eval­uated as follows:wavewstd1nnSwi11nwstdwavedcov(1)inS (w |wi1iave)2(2)(3)where n is the number of the sampling species (n16 inthis study). The average water content distribution, wave,indicates the prehydration water content, and thecoe‹cient 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 distribution2000Àmm2000–75 mm75–5 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|57.930.020.00100.000.000.0015.6469.0612.692.6294.042.780.580.240.160.111.420.320.010.010.33——————————1.00Fig. 2[z][z][z][z][z][z][z][z][z][z][z][z][z][z][z]Water retention curves of base layer soilsHydraulic Conductivity TestTwenty­ˆve specimens of the GCLs prepared in theabove prehydration tests were used for the hydraulic con­ductivity test in order to discuss the prehydration eŠecton the barrier performance of GCLs against the permea­tion of chemical solutions. Calcium chloride solutionswith a molar concentration of 0.1–0.5 M were used as thepermeant liquids to clarify the prehydration eŠects on thehydraulic conductivity of GCLs: this concentration levelhas an in‰uence 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 20–30 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 ˆlter 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 20–30 kPa by ˆll­ing 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 eŠects: (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 aŠects the prehydration eŠects. But, this studydoes not evaluate the eŠects of the heterogeneity in the 411PREHYDRATION 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 aŠect the prehydration eŠect. In thisstudy, however, the eŠect 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 eŠects of the water supplyfrom the water table like groundwater on the water con­ 412KATSUMI ET AL.Fig. 3.Fig. 4.Division of prehydrated GCLApparatus for hydraulic conductivity testtent distribution after prehydration. A diŠerence 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 aŠect the prehydration eŠect.Figures 5(c) and (d) show the water content distribu­tion of GCLs that contains powdered bentonite andgranular bentonite, respectively. The bentonite form sig­niˆcantly aŠects the average and the coe‹cient 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 eŠectivelyimproves 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 signiˆcantchange appears in the water content distribution of theGCL with granular bentonite. The prehydration watercontent increased from 82.9z to 141.3z, while thecoe‹cient of variation decreased from 0.38 to 0.13.Figures 6 and 7 show the eŠects of the curing period onthe prehydration water content and the heterogeneity ofits distribution, respectively. These ˆgures 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 signiˆcantchange 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 signiˆcantchange in either the prehydration water content orheterogeneity.Hence, it is concluded that prolonging the curingperiod and employing GCLs with the powder bentoniteare eŠective 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 eŠect 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 eŠect 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 water PREHYDRATION EFFECT ON GCLS413Fig. 5. Distribution of prehydration water content of GCLs; where Powd.Bpowdered bentonite GCL, Gran.Bgranular bentonite GCL,DGSdecomposed granite soil, TSToyoura sand, and WLwater levelFig. 6.EŠect 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. EŠect 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 then 414KATSUMI 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 withtime—52.3120.5200.6—80.182.983.2106.5119.5136.2147.8—98.8109.7126.5155.8162.9177.1188.8192.1—138.4138.5266.1—5.34.413.9—10.431.330.621.229.118.819.3—3.711.06.215.811.49.419.922.6—8.813.943.8—0.100.040.07—0.130.380.370.200.240.140.13—0.040.100.050.100.070.050.110.12—0.060.100.16Time[year]PVF[—]pH[—]EC[S/m]k[cm/s]º1º2º2º1º1º2º2º2º2º2º2º2º1º2º2º2º2º2º2º2º2º1º1º1º112.2253.0943.4478.659.4530.8182.6918.9225.0157.3014.3183.8610.6093.6943.9639.85123.8892.7491.2579.1824.8023.7232.4119.2619.698.197.067.316.53———6.69—————6.89—6.80—6.686.556.56—6.576.786.816.7217.8118.0016.6016.98———38.80—————39.60—38.70—39.7040.9038.00—66.0076.5065.7073.501.83~10|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 ˆrst 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 eŒuent 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 in‰uent andeŒuent should fall within 0.9–1.1 according to ASTM D6766 ``Standard Test Method for Evaluation of Hydraul­ic Properties of Geosynthetic Clay Liners Permeated withPotentially Incompatible Liquids''.Figure 9 shows the eŠects of the prehydration watercontent on the hydraulic conductivity of prehydratedGCLs against 0.1–0.5 M CaCl2 solutions. When the watercontent was À50z, the prehydration water content bare­ly in‰uenced 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 signiˆcantly aŠects 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 that PREHYDRATION EFFECT ON GCLSFig. 9.415EŠects of the prehydration water content on the hydraulic conductivity of GCLsFig. 10. EŠects 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 su‹cientlyswelled parts included in the heterogeneously prehydrat­ed GCL can exhibit the low hydraulic conductivity, theinsu‹ciently 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 eŠects 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 (thecoe‹cient 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 eŠects 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, theeŠect 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 k2.8~10|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 diŠerence appears in the hydraulicconductivity between the nonprehydrated GCL and the 416KATSUMI ET AL.Fig. 11. Comparison between non­prehydrated GCLs and prehydrat­ed GCLs in the hydraulic conductivityprehydrated GCL. It is concluded that prehydrationeŠectively 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 eŠects 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 eŠective method for improving barrier performanceagainst chemical attack.(2) The curing period for prehydration in‰uences 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 coe‹cient of variation, which is aparameter that indicates the heterogeneity of the watercontent distribution, decreases. However, the change inthe water content and its coe‹cient 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 insu‹cientlyswelled 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 eŠectsof geological and hydrological conditions such as notonly retention characteristics, groundwater level but alsophysical heterogeneity of base layer soils (the physicalheterogeneity eŠects 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. 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  • 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
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 419–432, 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 puriˆcation 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 diŠusion in gas phase of soil, we investigatedmulti­component diŠusion systems in gas phase of soil. Numerical modeling for multi­component diŠusion is useful tothe prediction of the movement of components. A dusty gas model for multi­component diŠusion 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 diŠusion in a multi­component gas system; and the study showed that the diŠer­ence between molecular weights of gas phase components in‰uenced the movement of components in the gas system.Key words: dusty gas model, ˆnite element method, multi­component diŠusion, 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 diŠusion 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 diŠusioncoe‹cient [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 maydiŠuse in a multi­component gas system in most cases,but there are a few cases in which the components diŠusein a binary gas system. The application of Fick's law isrestricted to systems that exhibit binary gas diŠusion. Ad­vection of chemical components is signiˆcantly in themulti­component gas system and has been solved formass transfer in groundwater. However, multi­compo­nent diŠusion in gas phase of soil has not been investigat­ed except for Fick's law. Accordingly, we investigatemulti­component diŠusion in this study.A diŠusion coe‹cient which considers molecular diŠu­sion in a multi­component gas system can be employed inplace of the binary diŠusion coe‹cient in Eq. (1) as longas each component is present in low concentrations. Inthis case, the molecular diŠusion coe‹cient 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(hibiy—ccmfs.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.419 420HIBIeach component is very low.1XjSDJ1ijDim(2)nIn the equation, Dim is a molecular diŠusion coe‹cient[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 ;cnJ1J» iijjijii(3)Equation (3) represents the diŠusion of components inmulti­component systems with accuracy, and can be ap­plied to molecular diŠusion in multi­component gas sys­tems even if the concentration of each component is high.The diŠusion in Eq. (3) occurs when molecules collidewith each other, as shown in Fig. 1.Baehr and Bruell (1990) carried out experiments on theadvective­diŠusion 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 advec­tive­diŠusion 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 diŠusion ‰ux and viscous ‰ux. Knud­sen diŠusion 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 deˆned 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 DiŠerence Method (FDM). This study attempts tosolve the dusty gas model equations by FEM, and severaldiŠerent gas systems will be simulated by the numericalmodel developed in this study. The results will demon­strate the diŠerence between the diŠusion coe‹cient cal­culated by Eq. (2) and the diŠusion coe‹cient calculatedby the dusty gas model in a binary gas system, and thediŠerence 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 diŠusion equations with diŠusion‰ux and viscous ‰ux depending on temperature from adusty gas model, and Cunningham and Williams (1980)explained the process of induction for Stefan­Maxwellequations and multi­component diŠusion equations, add­ing a term for the Knudsen diŠusion to the Stefan­Max­well equations. Knudsen diŠusion is a phenomenonwherein molecules of gas diŠuse by colliding with the sur­Schemata of Molecular diŠusion and Knudsen diŠusion 421FORMULATION OF A DUSTY GAS MODELfaces of soil particles. Reinecke and Sleep (2002) demon­strated a relationship between the Knudsen coe‹cient,soil permeability, and the Klinkenberg parameter(Klinkenberg, 1941), and Thostenson and Pollock (1989)investigated the in‰uence of Knudsen diŠusion ‰ux onmulti­component diŠusion in the soil gas phase.The dusty gas model equation without viscous ‰ux un­der constant temperature is,XiNj|XjNi Nj| ;cjSDijDii1»nidiŠusion coe‹cient without soil particles (Millingtion,* and D *BA take account of tortuosity t1959). The D AB[dimensionless], which in‰uences 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 diŠusivity [L2/T] ofcomponent A in component B or B in A, and DA and DBare the Knudsen diŠusivities [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), moleculardiŠusion coe‹cients in Eq. (1) correspond with the D *AB* deˆned from Eq. (7). Because particles of soiland D BAresist molecular diŠusion in the soil gas phase, themolecular diŠusion coe‹cient with soil particles presentin the system is generally smaller than the molecularØ »XB MBtDAB MAjwhere Di is the Knudsen coe‹cient [L2/T], and the sec­ondary term of the left side indicates Knudsen diŠusion.Ø »XA MAtDAB MB11/2XB1{{tDAB DA11/2XA1{{tDAB DB(8a)(8b)A molecular diŠusion 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 diŠusion coe‹cient 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 diŠusion coe‹cientis consistent with the binary diŠusion coe‹cient 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 KnudsendiŠusion coe‹cient is almost equal to the binary diŠusioncoe‹cient of Eq. (9). If XB is below 1.0 and KnudsendiŠusion is taken account of, Eq. (10) is inconsistent withthe binary diŠusion coe‹cient of Eq. (9).Therefore Eq. (10) has the limitation when the equa­tion is applied to the binary diŠusion coe‹cient. 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 DiŠusion Coe‹cients inthe Binary Gas SystemMolecular diŠusion coe‹cients 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 diŠusion coe‹cient 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 thediŠusing gas is dilute. 422HIBIFig. 2. DiŠusion coe‹cients for binary gas system consisting ofmethane gas and air in the gas phase of soil. Circles in case of adiŠerence between molecular weights, and triangles in case of equalmolecular weightsFig. 3. DiŠusion coe‹cients for binary gas system consisting oftrichloroethylene and air in the gas phase of soil. Circles in case of adiŠerence between molecular weights, and triangles in case of equalmolecular weightsTable 2. Parameters for calculation of molecular diŠusion coe‹cientsfor binary gas systemParameterTortuosity, tComponent A : air Molecular weight, MAComponent B: methane Molecular weight, MBTCE Molecular weight, MBMolecular diŠusion coe‹cient between air andmethane, DABMolecular diŠusion coe‹cient 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 diŠusion coe‹cient calculated by Eq.(8a) or Eq. (10) in a binary diŠusion system consisting ofair and methane. This situation implies that methane, oflower density than air, inˆltrates through the air­gas sys­tem by molecular diŠusion. Figure 2 shows the relation­ship between the molar fraction of methane in an air­methane system and the relative diŠusion coe‹cientwhich divides the diŠusion coe‹cient of Eq. (8a) or Eq.(10) by the diŠusion coe‹cient of Eq. (9).Relative diŠusion coe‹cients 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 diŠusion coe‹cients calculat­ed by Eqs. (8a) and (10) that the relative diŠusioncoe‹cient given by Eq. (10) is larger than that given byEq. (8a). Actually, the relative diŠusion coe‹cient givenby Eq. (10) should become 1.0 for the case of a moleculardiŠusion coe‹cient in a binary gas system without Knud­sen diŠusion and a diŠerence in the molecular weight.The relative diŠusion coe‹cient 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 diŠusion coe‹cient given by Eq. (10) isnot equal to the binary molecular diŠusion coe‹cient forhigh concentrations of methane. Equation (10) must notbe employed under conditions of high concentrationcomponents diŠusing in a gas system. The moleculardiŠusion coe‹cient given by Eq. (8a) or Eq. (8b) shouldbe equal to the diŠusion coe‹cient in Eq. (9) if themolecular weight of component A is consistent with thatof component B and Knudsen diŠusion does not occur ingas system. The diŠusion coe‹cient given by Eq. (8a)diŠers from the diŠusion coe‹cient in Eq. (9) by reasonof the ( XA/tDAB)( MA/MB)1/2 term included in the numer­ator of Eq. (8a). The relative diŠusion coe‹cient 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 diŠusion coe‹cient is highly in­‰uenced by the diŠerence in the molecular weight, andthe binary diŠusion coe‹cient of Eq. (9) can not be usedwhen simulating a system of gases that are of signiˆcantlydiŠerent molecular weights.Figure 3 shows the relationship between the molarfraction of trichloroethylene (TCE) and a relative diŠu­sion coe‹cient 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 diŠusion coe‹cient 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 diŠusion only if the concentra­tion of TCE is su‹ciently low. On the other hand, the rel­ative diŠusion coe‹cient calculated by Eq. (8a) does notexceed 1.0, and decreases with increasing TCE molarfraction. The relative diŠusion coe‹cient 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 diŠusion coe‹cient given by Eq. (8a) may becomesmaller than that in Eq. (9) if the molecular weight of thegas diŠusing 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 diŠusion only if theconcentration of gas diŠusing into the system is very di­lute, and that Eqs. (8a) and (8b) must be used for simula­tions of systems with gas phase components that diŠer inmolecular weight. The total molar diŠusion ‰ux NT is de­ˆned as the sum of the molar diŠusion gas ‰ux ND [mol/L2T], given by Eq. (9) representing Fick's law, and a none­ 423FORMULATION OF A DUSTY GAS MODELquimolar diŠusion gas ‰ux NT [mol/L2T] (Thorstensonand Pollock, 1989, Cunnigham and William, 1980),which occurs by reason of the diŠerence in gas molecularweight. The diŠerence between the diŠusion coe‹cientsgiven by Eq. (8a) and the binary diŠusion coe‹cient inEq. (9) is a reason for the nonequimolar diŠusion.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 diŠusion coe‹cient[L2/T] of component B in component C or C in B, DAC isa binary molecular diŠusion coe‹cient [L2/T] of compo­nent A in component C or C in A and DC is the KnudsendiŠusion coe‹cient [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 diŠerencebetween molecular weights is very important, and Eq.(10) must be used when the concentration of the compo­nents diŠusing 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 signiˆcantfor multi­component diŠusion 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 deˆned as follows:1D A*XC1XB{{tDAB tDAC DAØ1D *BXAXC1{{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 *CXBNA|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 gas­ˆlled porosity.A diŠerential equation like Eq. (15) can generally besolved approximately by means of the Finite ElementMethod (FEM) or Finite DiŠerence method (FDM). FEMhas an advantage that any shape of element can be usedfor discretization of the analytical domain. On the other 424HIBIhand, 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 veriˆed 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.npugS Fiugi1npckS Ficki1(16a)ifor k Component A, B, Ci(16b)npD k*S FiD *k for kComponent A, B, C(16c)XkS FiXkfor kComponent A, B, C(16d)NkS FiN*k for kComponent A, B, C(16e)ii1npi1npi1iiIn 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.f˜u F dVc {SfD˜ * ;F ¥;F dVc1D˜ *X˜˜uF dVc {S;F ¥F dVNf DDt fD˜ *X˜{S{;F ¥F dVNf DfF q ¥ndV1DtVt{Dt, mgVt{Dt, m{1Aiit{Dt, mgnpAj1tAiit{Dt, mnpj1npj1t{Dt, mAAt{Dt, mt{Dt, mit{Dt, m{1Ajjt{Dt, miABViACVAVt{Dt, mCjijt{Dt, mBjt{Dti AVffD˜ * ;F ¥;F dVc1D˜ *X˜˜uF dVc {S;F ¥F dVNf DDt fD˜ *X˜{S{;F ¥F dVNf DfF q ¥ndV1DtnpVt{Dt, m{1˜ugt{Dt, mFidVc Bi{Sj1Vt{Dt, mgnpBj1tBiit{Dt, mnpj1t{Dt, mBBt{Dt, mt{Dt, mit{Dt, mBt{Dt, mCjjijt{Dt, mAjt{Dti BVffD˜ * ;F ¥;F dVc1D˜ *X˜˜uF dVc {S;F ¥F dVNf DDt fD˜ *X˜{S{;F ¥F dVNf DfF q ¥ndV1DtnpVt{Dt, m{1˜ugt{Dt, mFidVc Ci{Sj1Vt{Dt, mgnpj1CVtCiit{Dt, mBCnpj1t{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 molar‰uxes [mol/L2T] of components A, B, and C at theVfor i1¿np(17b)t{Dt, m{1CjjACVit{Dt, m(17a)t{Dt, m{1BjjABViBCVBVfor i1¿npjt{Dti Ct{Dt, mAjfor i1¿np(17c)boundaries, respectively, and are deˆned as follows:D *AXAD *AXANB|NCtDABtDAC(18a)D *BXBD *BXBNA|NCtDABtDBC(18b)D C*XCD *CXCNA|NBtDACtDBC(18c)qAD A*;cA|qBD *B;cB|qCD *C;cC|The coe‹cients D *A, D B*, and D C* can be calculated from 425FORMULATION 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.Xkck/c, for kcomponent 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 (i1¿np)( M /M )1|X˜F F dVNS f{ tDtD }( M /M )11111{Sf{Ø tD |tD »X˜ {Ø tD |tD »X˜ {tD {D }F F dVN|SfF ;F dVc (i1¿np)npSj1BAABVnpj1npj11/2BCC1/2AABVBABC1/2ACVBCnpj1Bnpj1VAijt{Dt, mC1/2ACVt{Dt, mBBCABt{Dt, mBijt{Dt, mCit{Dt, mABCt{Dt, m{1CjjBCiBjnpj1Vit{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 ˆnalvalues 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 speciˆed maximum time.VALUATION OF THE DEVELOPED NUMERICALMODEL FOR THE MULTI­COMPONENT GASSYSTEM IN GAS PHASE OF SOILIn this section we illustrate diŠerences between the nu­merical model developed in this study (the DG Model)and the numerical model with a diŠusion coe‹cient cal­culated by Eq. (2) which can be used when the concentra­tions of components diŠusing into gas phase of soil arevery low. It has been described for the binary gas systemin this study that a diŠerence between molecular weightsof components in‰uences the diŠusion in multi­compo­nent gas system, and that the diŠusion coe‹cient 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 the 426HIBITable 3. Parameters for simulations of multi­component gas systemsif the molecular weight of gas diŠusing 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 soileŠort 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 veriˆed that the DG model developed in thisstudy is useful for multi­component gases in the gasphase of soil.The constituted equations with diŠusion coe‹cient 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 modiˆed Fick's law model (theMF model) thereafter.The Case of Gas with Lower Molecular Weight than theSurrounding GasesA simulation of methane diŠusing into a region full ofoxygen and nitrogen was carried out in this study becauseit illustrates the diŠerence 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 diŠusion coe‹cient between oxygenand nitrogen, DABMolecular diŠusion coe‹cient between oxygenand methane, DABMolecular diŠusion coe‹cient 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 speciˆed 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 X0 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 speciˆed at X0 m during the simulations. Theconcentrations of oxygen, nitrogen, and methane werespeciˆed 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 speciˆed 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. DiŠusioncoe‹cients 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 atX0 m. As shown in Fig. 5, no diŠerence 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 conˆrmed in Fig. 6 which il­lustrates the distributions of the concentrations of oxygenand nitrogen when the molar fraction of methane is 0.10at X0 m, but the diŠerence between the concentrations FORMULATION 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 ˆlled 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 ˆlled circles the case of MF modelgiven by the two models for methane is not distinct be­cause this diŠerence becomes 0.08 mol/m3 at X10 m.Figure 7 shows distributions of each concentrationwhen the molar fraction of methane is set to 0.20 at X0m, and Fig. 8 shows concentration distributions for amethane molar fraction of 0.50. As shown in Fig. 7, thediŠerences between the concentrations given by the DGand MF models are more obvious than those shown inFig. 6, and the diŠerence between concentrations ofmethane given by each numerical model becomes 0.35mol/m3. A larger diŠerence 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 conˆrmthat the diŠerences between the concentrations of oxygenand nitrogen given by the DG model and MF model in­crease with the molar fraction of methane at X0 m.Therefore the diŠusion coe‹cient 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 diŠusing component has a lighter molecular weightthan those of the components ˆlling 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 diŠerence 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 diŠusing through a domain of highermolecular weight gases. Applicability of these models willbe examined for the condition of a diŠusing component 428HIBIFig. 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 ˆlled 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 ˆlled 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 thediŠusing gas. The molecular weight of TCE is approxi­mately four times that of oxygen and nitrogen as shownin Table 4, and the diŠusion coe‹cient 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 X0 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 diŠusing 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 diŠusion coe‹cient between oxygenand nitrogen, DABMolecular diŠusion coe‹cient between oxygenand TCE, DABMolecular diŠusion coe‹cient 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 diŠerences 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 the FORMULATION 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 ˆlled 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 ˆlled 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 X10 m as shown in Fig. 10, while thatgiven by the MF model is 1.99 mol/m3 at X10 m, adiŠerence of 0.23 mol/m3, just as shown in Fig. 10. ThediŠerence between both concentrations is 5.5 percent ofthe boundary value concentration of 4.16 mol/m3 speci­ˆed and X0 m. The oxygen and nitrogen diŠerences 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. ThesediŠerences in regard to oxygen, nitrogen, and TCEbecome greater as the concentration of TCE at X0 mincreases, as can be seen by comparing Figs. 10 and 11.When the molar fraction of TCE is 0.50 at X0 m, thediŠerence between the TCE concentrations given by theDG model and MF model is 6.37 mol/m3, the diŠerencebetween the concentrations for oxygen is 3.3 mol/m3, andthe diŠerence between the concentrations for nitrogen is3.1 mol/m3, as shown in Fig. 12.Therefore the concentration calculated for the compo­nent diŠusing into the domain is diŠerent depending onthe type of numerical method used, even if the molarfraction of TCE is very low (0.05) at X0 m, when themolecular weight of the diŠusing 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 X0 m; however diŠer­ences between the concentrations simulated by the twomodels for TCE, oxygen, and nitrogen at X10 m in­crease with increasing molar fraction of TCE at the inletof the diŠusing component.Consequently, the diŠusion coe‹cient calculated byEq. (2) for a diŠusing component of higher molecular 430HIBIFig. 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 ˆlled 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 ˆlled circles the case of MF modeweight than those of the surrounding components mustnot be used in the case that the concentration of thediŠusing 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 diŠusion coe‹cient 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 oŠ 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 diŠusion coe‹cient calcu­lated by Eq. (2) which is applied for gas phase diŠusion ofa component with very low concentration has often beenused instead of the diŠusion coe‹cient in Fick's law.Complexity of the calculation can be avoided by em­ploying Eq. (2), reducing the eŠort of computation.CONCLUSIONBy comparison between a Fick's law of diŠusioncoe‹cient for a binary gas system and a diŠusioncoe‹cient derived by means of the dusty gas model andGraham's law for the binary gas system with a very dilutediŠusing gas, it became obvious that the diŠusioncoe‹cient given by means of the dusty gas model andGraham's law could be used only if the concentration ofthe diŠusing gas is considerably dilute. Furthermore, itwas found in this study that the diŠerence in componentmolecular weights in‰uences the diŠusion coe‹cient in abinary gas system when the diŠusion coe‹cient is given FORMULATION 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 diŠusing 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 diŠerent thanthose simulated by the MF model, and it has been con­ˆrmed that the DG model developed in this study must beapplied for modeling multi­component diŠusion in thesoil gas phase.Only diŠusion 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 diŠusion­ad­vection or dispersion­advection equations by means ofthe numerical model developed in this study.NOTATIONcciDiDijDimtotal concentration [mol/L3]molar concentration [mol/L3] of component iKnudsen coe‹cient [L2/T]binary molecular diŠusion coe‹cient [L2/T] betweencomponent i and component jmolecular diŠusion coe‹cient [L2/T] in the multi­component gas system»/Ø»/Ø»/Ø/Ø Ø »/Ø Ø »D *A1XC1XB{{tDAB tDAC DAD *B1XC1XA{{tDAB tDBC DBD *C1XAXB1{{tDAC tDBC DCD *AB1XA M AtDAB MB1/2D *BA1XB 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 diŠusion gas ‰ux [mol/L2T]NN nonequimolar diŠusion gas ‰ux [mol/L2T]NT total molar diŠusion ‰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 gas­ˆlled porosity˜ug average of the respective values of ug within each ele­mentttortuosity [dimensionless]V boundary of an analytical domainREFERENCES1) Abriola, L. and Pinder, G. F. (1985): A multiphase approach to themodeling of porous media contamination by organic compounds 1Equation development, Water Resources Research, 21(1), 11–18.2) Abriola, L. and Pinder, G. F. (1985): A multiphase approach to themodeling of porous media contamination by organic compounds 2Numerical simulation, Water Resources Research, 21(1), 19–26.3) Baehr, A. L. and Corapciglu, M. Y. (1987): A compositional mul­tiphase model for groundwater contamination by petroleumproducts 2 Numerical solution, Water Resources Research, 23(1),2001–2132.4) Baehr, A. L. and Bruell, C. J. (1990): Application of the Stefan­Maxwell equations to determine limitations of Fick's low whenmodeling organic vapor transport in sand columns, WaterResources Research, 26(6), 1155–1163.5) Celia, M. and Bouloutas, E. T. (1990): A General mass­conserva­tive numerical solution for the unsaturated ‰ow equation, WaterResources Research, 26(7), 1483–1496.6) Corapciglu, M. Y. and Baehr, A. L. (1987): A compositional mul­tiphase model for groundwater contamination by petroleumproducts 1 Theoretical considerations, Water Resources Research,23(1), 191–200.7) Costanza­Robison, M. S. and Brusseau, M. L. (2002): Gas phaseadvection and dispersion in unsaturated porous media, WaterResources Research, 38(4), 7–1–7–10.8) Cunnigham, R. E. and Williams, R. J. J. (1980): DiŠusion Gasesand Porous Media, Plenum Press, 1–80.9) Curtiss, C. F. and Hirschfelder, J. O. (1949): Transport propertiesof multicomponent gas mixtures, Journal of Chemical Physics, 17,550–555.10) Fischer, U., Schulin, R., Keller, M. and StauŠer, F. (1996): Ex­perimental and numerical investigation of soil vapor extraction,Water Resources Research, 32(12), 3413–3427.11) Hoeg, S., Scholer, H. F. and Warnatz, J. (2004): Assessment of in­terfacial mass transfer in water­unsaturated soils during vapor ex­traction, Journal of Contaminant Hydrology, 74, 163–193.12) Jellali, S., Benremita, H., Muntzer, P., Razakarisoa, O. andSchader, G. (2003): A large­scale experiment on mass transfer oftrichloroethylene from the unsaturated zone of a sandy aquifer toits interfaces, Journal of Contaminant Hydrology, 60, 31–53.13) Klinkenberge, L. J. (1941): The permeability of porous media toliquids and gases, Drilling and Production Practice, 200–213.14) Knesfsey, T. J. and Hunt, J. R. (2004): Non­aqueous phase liquidspreading during soil vapor extraction, Journal of ContaminantHydrology, 68, 143–164.15) Lenhard, R. J., Oostrom, M., Simmons, C. S. and White, M. D.(1995): Investigation of density­dependent gas advection oftrichloroethylene: Experiment and a model validation exercise, 432HIBIJournal Contaminant Hydrology, 19, 47–67.16) Mason, E. A. (1967): Flow and diŠusion of gases in porous media,Journal of Chemical Physics, 46, 3199–3216.17) Mason, E. A. and Malinauskas, A. P. (1983): Gas Transport inPorous Media the Dusty Gas Model, Elsevier, 30–49.18) Massmann, J. and Farrier, D. F. (1992): EŠects of atmosphericpressures on gas transport in the vapor zone, Water ResourcesResearch, 28(3), 777–791.19) Mendoza, A. and Frind, E. O. (1990): Advective­Dispersion trans­port of dense organic vapor in unsaturated zone 1. Model develop­ment, Water Resources Research, 26(3), 379–387.20) Mendoza, A. and Frind, E. O. (1990): Advective­Dispersion trans­port of dense organic vapor in unsaturated zone 2. Sensitivity anal­ysis, Water Resources Research, 26(3), 388–398.21) Millingtion, R. J. (1959): Gas diŠusion in porous media, Science,130, 100–102.22) Milly, P. C. D. (1985): A mass­conservative procedure for time­stepping in models of unsaturated ‰ow, Advance Water Resources,23(8), 32–36.23) Poling, B. E., Prausnitz, J. M. and O'Connell, J. P. (2001): Theproperties of gases and liquids, McGraw­Hill, 11.19–11.20.24) Reinecke, S. A. and Sleep, B. E. (2002): Knudsen diŠusion, gaspermeability, and water content in an unconsolidated porous medi­um, Water Resource Research, 38(12), 16–1–16–15.25) Shan, C., Falta, R. W. and Javandel, I. (1992): Analytical solutionfor steady state gas ‰ow to a soil vapor extraction well, WaterResources Research, 28, 1105–1120.26) Sleep, B. E. and Sykes, J. F. (1989): Modeling the transport ofvolatile organics in variably saturated media, Water ResourcesResearch, 25(1), 81–92.27) Sleep, B. E. and Sykes, J. F. (1993): Compositional simulation ofgroundwater contamination by organic compounds 1. Model de­velopment and veriˆcation, Water Resources Research, 29(6),1697–1708.28) Sleep, B. E. and Sykes, J. F. (1993): Compositional simulation ofgroundwater contamination by organic compounds 2. Model appli­cations, Water Resources Research, 29(6), 1709–1718.29) Thorstenson, D. C. and Pollock, D. W. (1989): Gas transport inunsaturated zones: Multicomponent systems and the adequacy ofFick's Laws, Water Resources Research, 25(3), 477–507.
  • 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
  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 433–445, 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 stiŠ 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 ˆrst derived using a solution from a proposed upper bound analysis based on observations from centrifuge testsand then modiˆed, taking on the basis of an equivalent ˆnite 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, ˆnite element, improved berm, upper bound (IGC: E6/H2)INTRODUCTIONIn an excavation in soft ground with a signiˆcant thick­ness of soft soil below the ˆnal excavation level, the maxi­mum de‰ection 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 de‰ection through jetgrouting or deep mixing to form an improved soil raft.The eŠectiveness 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) classiˆed 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 (cvetants—nus.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.433 434ZHANG ET AL.Fig. 2. Bearing capacity components of an improved soil berm in anexcavationwall from moving inwards to the excavated side. Theprincipal diŠerence 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 aŠect 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 modi­ˆed using results from ˆnite 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 ˆnite element analysesare used to improve the estimation of the end bearingcapacity factor and provide further clariˆcation on themechanism that was used in the limit analysis. The ana­lytically developed upper bound solution is then modiˆedby back­analyzing the results from FE analyses. In thepresent study, the ˆnite 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 aŠects the capacity. Such a ``feel'' isdi‹cult 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:QuQb{QsAbqb{(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:gBNg2qbcuNc{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 Nq1 and Ng0.In such a case, Eq. (2a) becomes:qbcuNc{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 Nq1 for an undrained case. The valueof Nc is ˆrst 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 aV1V0;VvV1 cos atan 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 bV12V1 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:EqbDV0|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:WcucuDCV1{2cuV2{cu( D tan a)V12cos acos (909|b)D V0CV0{2cucos a sin acos (909|b) tan a sin b 436ZHANG ET AL.Ø1tan a tan b{cu( D tan a)V0 1|»(4)By equating E and W, the resulting upper­bound solutionobtained is:qb2Ccucu{{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:&qb0&aFig. 5.Bearing capacity factor for the upper bound mechanism&qband0&bIn the present form, it is di‹cult to solve for the two opti­mum angles directly. However the upper bound solutionof Eq. (5) could be re­arranged into:qbcu1{tan2 aC 1{tan2 b{2cutan aD tan a tan2 bØC 1cu{{gD{cu tan a|D 2tan b»(6)using the relations:sin a1tan a; and cos a.21{tan a(1{tan2 a)Fig. 6.Let stan a, ttan b and mC/D, where the ratio mcould be thought of as an embedment ratio for an embed­ded improved soil berm. Then Eq. (6) could be simpliˆedas:«qbcu 2s{» $ØØ12m112m{1{ 2 |{gD m{stt2»(7)The upper­bound solution could now be obtained withrespect to variables s and t as follows:&qb&qb0 and0&s&tA system of two equations is then obtained:2m1{2m{ 2t2|0s24m 1{ 0st 3 t 2|t2 |m{16m21{2mby:ØqbNc1cu{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)WhereNc11{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 1809barctan Ø»p1{2maarctanSolving 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 m0, Nc should be 2 (qb2cu{gD(C/D{1/2)), implying that the soil surrounding theend of the berm is in a passive state of failure. If the over­ 437IMPROVED 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 modiˆcation is needed for Eq. (13) in thecase of very small m (the deˆnition 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 V1V2 and V120, which leads to:b909|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 2aqbcu2uuIt is obvious that the optimum solution for this failuremechanism is when a459. In this case, the corre­sponding upper bound solution is:ØqbNc2cu{gD m{Nc22{4m2{4»1, where2CD(18)1|1{16m,2m1for mÆ ; and41{NcNc22{4m,for 0ÃmÃ14qbNccu{gDØ DC { 12 »(19)This process also helps to clarify the deˆnition 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 m0.25, in other word with acover one­quarter of the berm thickness. Variation of Ncwith m, as deˆned 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 m0 and increases linearlywith m. The variation of Nc2 with m is also presented inFig. 5. The point of intersection between Nc1 and Nc2 is m1/4, 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 modiˆ­cation, 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:NcNc1Fig. 7. A collapse­in upper bound failure mechanism for a planestrain tunnel (after Davis et al., 1980)N4Ø DC { 12 »C 1{D 4with tan atan b2(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 smalldiŠerence re‰ects the slightly diŠerent 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, ˆnite 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 stressTotalNetØqbNccu{gD m{ØqbnetNccu{gD m{1212»»(1|k0)qmØqmnetqm|k0gD m{12»FINITE ELEMENT ANALYSISPotts (2003) summarized the solution requirements sa­tisˆed 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 besatisˆed. 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 ˆnite element and ˆnitediŠerence 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 ˆnite element analysis. All the four re­quirements stated above are met, and the geometry andboundary conditions of a speciˆc problem can be ac­curately modeled. The ˆnite element method has beenwidely used to evaluate various stability problems such asslope stability (GriŠths and Lane, 1999), bearing capacity(Potts, 2003; GriŠths, 1982; Zdravkovic et al., 2003) andbasal stability of an excavation (Faheem et al., 2003;Hashash and Whittle, 1996). Gri‹ths (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 diŠerent consoli­dation ratios using the ˆnite element method, whichwould be di‹cult to evaluate by other traditional analyti­cal methods. This clearly demonstrated the ‰exibility andversatility of the ˆnite 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 di‹cult 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 eŠect 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.Veriˆcation ProblemA traditional plane strain bearing capacity problem fora strip foundation with diŠerent 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/B4. The meshes IMPROVED 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 reˆned 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 ˆrst. However as the eŠect 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 di‹cult 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 in‰uence from the endof the berm that is in contact with the retaining wall. Infact, the length of the berm needs to exceed the passive in­‰uence zone to behave eŠectively (Thanadol, 2002).Figure 11 shows two meshes for the cases of mC/D0and mC/D4. 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 the 440ZHANG ET AL.improved soil berm.The computed Nc is presented in Fig. 12 which showsthat Nc starts from 2.037 for m0 and reaches a maxi­mum of 8 for mÆ8. For m0, 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 ˆnding 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 coe‹cients 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, usingcu0 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 Nq1 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 Nq1. 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 diŠerent 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 modiˆed. This modiˆcation was implemented throughthe introduction of a mobilisation factor l to modify theFig. 14.End bearing capacity factors from diŠerent solutions 441IMPROVED 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 modiˆed 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:WcuD V0CV0{2lcucos a sin acos (909|b) tan a sin bØ1tan a tan b{cu (D tan a)V0 1|»Nc1|1{16lm2lm1{Obviously, Nc from the modiˆed solution is equal tothat in Eq. (13) if l1. 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 ˆgure shows thatthe relationship between l and m can be divided intothree zones. The ˆrst 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 themodiˆed upper bound isCcucu{2l{cu tan acos a sin aD tan a sin2 bqbØcuC1|{{gDD 2tan b»(27)Following the same working procedure, Nc for the modi­ˆed upper bound becomes:Fig. 16.(28)Fig. 15.Relationship between l and mDisplacement contours at diŠerent values of m 442ZHANG 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 modi­ˆed 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 aŠect the cal­culated Nc values signiˆcantly, as discussed later. In theregion of 0ÃmÃ0.25, the value of l is set to 1. The ˆttedrelation is also presented in Fig. 15. With this ˆtted rela­tion, the complete description of the modiˆed upperbound solution is given by Eq. (20) with the value of Nc asfollows:11|1{16lm, for ºmÃ8; (29a)2lm4NcNc1 1{NcNc22{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 m8 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 modiˆed 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 modiˆed upper bound solutionof Eqs. (20), (29) and (30) lies in not only providing asemi­analytical solution in determining the end bearingcapacity but also oŠering 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 thediŠerence 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 ˆnallyequals 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 eŠect of the improved soil berm.It should be also noted that the end bearing capacityprovided in Eq. (20) together with the modiˆed 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:ØqbnetNccu{gD m{»1(1|K0)2(32)where K0 is the coe‹cient of total earth pressure at rest.To provide a feel for the modiˆed upper bound solu­tion developed, the results of a centrifuge test will bepresented. In this test, the embedment depth C before IMPROVED SOIL BERM IN AN EXCAVATION443end bearing through increasing the total contact stress be­tween berm and soil. It is precisely this combined eŠect 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 modiˆed 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 eŠect 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 conˆningstresses 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 (qbNccu{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 modiˆed 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 conˆrmed 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 the 444ZHANG 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 eŠect 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 ˆnite elements for limit analysis, G áeotechnique, 34(2),199–210.3) 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), 397–416.6) Faheem, H., Cai, F. and Hagiwara, T. (2003): Two­dimensionalbase stability of excavations in soft soils using FEM, Computersand Geotechnics, 30(2), 141–163.7) Gri‹ths, D. (1982): Computation of bearing capacity factors usingˆnite elements, G áeotechnique, 32(3), 195–202.8) GriŠths, D. and Lane, P. A. (1999): Slope stability analysis by ˆniteelement, G áeotechnique, 49(3), 387–403.9) Hashash, Y. and Whittle, A. J. (1996): Ground movement predic­tion for deep excavations in soft clay, Journal of Geotechnical En­gineering, 122(6), 474–486.10) 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), 146–157.11) 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),933–948.12) Meyerhof, G. G. (1951): The ultimate bearing capacity of founda­tions, G áeotechnique, 2(4), 301–332.13) Meyerhof, G. G. (1973): Uplift resistance of inclined anchors andpiles, Proc. 8th ICSMFE, Moscow, USSR, 2.1, 167–172.14) 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), 387–409.15) 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, 41–62.16) 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), 709–715.17) Page, R. J., Ong, J. C. W. and Osborne, N. (2006): Jet grouting forexcavations in soft clay–design and construction issues, Interna­tional Conference on Deep Excavations, 28–30 June, Singapore.18) Potts, D. M. (2003): Numerical analysis: a virtual dream or practi­cal reality?, G áeotechnique, 53(6), 535–573.19) Skepmton, A. W. (1951): The bearing capacity of clays, Proc. Con­ference on Settlement of Structures, Pentech press, London, 1,180–189.20) Sloan, S. W. and Randolph, M. F. (1982): Numerical prediction ofcollapse loads using ˆnite element methods, International Journalfor Numerical and Analytical Methods in Geomechanics, 6(1),47–76.21) Tanaka, H. (1993): Behavior of braced excavations stabilized bydeep mixing method, Soils and Foundations, 33(2), 105–115.22) 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), 738–755. 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), 619–631.26) Zdravkovic, L., Potts, D. M. and Jackson, C. (2003): Numericalstudy of the eŠect of preloading on undrained bearing capacity, In­ternational Journal of Geomechanics, 3(1), 1–10.27) 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), 17–28.28) Zhang, Y. D. (2004): An embedded improved soil berm in an ex­cavation–Mechanisms and capacity, PhD Thesis, Department ofCivil Engineering, National University of Singapore.
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  • Rate-dependent Response of Dense Sand in Cyclic Triaxial Tests
  • 著者
  • L. A. Salvati・L. Q. AnhDan
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  • Soils and Foundations
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  • 447〜451
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  • 2008/06/15
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  • SOILS AND FOUNDATIONSJapanese Geotechnical SocietyVol. 48, No. 3, 447–451, 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 eŠect 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 conˆning pressures, cyclic shear stresses, and peak shear stresses.Under certain loading conditions, the frequency of loading did have a noticeable eŠect on the response of the sand;larger axial strains were measured in the samples that were subjected to the lower frequency of loading. This diŠerencein response measured at the two loading frequencies occurred mainly in the ˆrst few cycles of loading, when the diŠer­ence 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 diŠerence 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 diŠerent but constant strain rates in Matsushita etal. (1999). While there was little diŠerence in response be­tween the tests performed at constant strain rates, thestiŠness 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 in‰uence on the response, but some tests on granularmaterials have shown diŠerences in response betweentests performed at diŠerent constant strain rates. San­tucci de Magistris et al. (1999) noted that the strain rateaŠected the stiŠness of a silty sand at strains less than0.001z, although the change in strain rate had more in­‰uence 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 eŠect that the loadingrate has on the cyclic response of granular materials.Therefore, cyclic triaxial tests were performed on drysands at diŠerent loading frequencies under a range ofconditions. These tests and their results, which will bediscussed in subsequent sections, will contribute to theINTRODUCTIONTra‹c 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 eŠective 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 in‰uences the soil stiŠness and deformationunder monotonic and cyclic loading is needed, especiallyfor sand, since rate eŠects 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 (aile—ellisassoc.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.447 448SALVATI AND ANHDANTable 1.Properties of Monterey No. 0/30 and Sacramento River Sand2SandeminemaxGsCuD60/D10CcD30/(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 eŠects (e.g., DiBenedetto et al., 2002; Tatsuoka et al., 2002), which canlead to improved predictions of deformations at diŠerentrates 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 diŠerent particle angularities. The Mon­terey No. 0/30 Sand is a highly uniform, subroundedbeach sand, and it was modiˆed slightly by removing theparticles with diameters less than 0.075 mm. TheSacramento River Sand is a subangular to subroundedsand, and it was modiˆed 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 Dr86z to 89z for the MontereyNo. 0/30 Sand and Dr87z to 90z for the SacramentoRiver Sand. Dense samples were used to minimize theeŠects of non­uniformity between diŠerent 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 eŠects 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 theeŠect of loading frequency on the response of sand, it isdesirable to minimize the diŠerences 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.Deˆnition of terms and symbols used with a typical testTEST RESULTSA series of triaxial tests with varying cyclic shear stress­es (qcyclic), conˆning pressures (s3), and peak stresses(qpeak) were performed to in order to investigate theresponse of the sands at the diŠerent loading frequencies.The conˆning pressures used in the tests ranged from 65kPa to 200 kPa. As an example of the eŠect of conˆningpressure, Fig. 2(a) shows the results from tests performedon Monterey Sand with qpeak300 kPa and qcyclic150 kPa. The conˆning pressures for the tests were s365 kPa, s3100 kPa, and s3150 kPa, which cor­respond to peak stress levels of 5.6, 4 and 3, respectively.For the tests performed at s3150 kPa, the axial strainsafter 100 cycles are nearly identical for the two frequen­cies of loading. However, in the tests performed at s3100 kPa and s365 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 withs365 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 s3100 kPa,qpeak300 kPa, and qcyclic150 kPa, 100 kPa, and 50kPa. With increasing cyclic stresses, an increasing diŠer­ence 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 diŠerence 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 diŠerence be­tween the axial strains measured at the two loading fre­ 449DENSE SAND IN CYCLIC TRIAXIAL TESTSquencies increased with increasing qcyclic/s3 for bothsands.served rate eŠects 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 s3100kPa and varying qcyclicFig. 2. Cyclic triaxial tests of Monterey No. 0/30 Sand with qpeak300kPa and varying s3: a) axial strain measured from qmean and b)deviator stress vs. axial strain for s365 kPaTable 2.aFig. 4. Cyclic triaxial tests of Monterey No. 0/30 Sand with s3200kPa 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|4DiŠerence in finalea valuesa (z)Monterey300300300300300600600600150150150100503001003001501501502002503005003006510015010010020020015043.78.50.54.305.91.375.339.210.40.51.114.41.875.311.811.10.61.41.56.93.427.6Sacramento300300300300300600600150150150100501003001501501502002505003006510015010010020020017.96.40.93.90.56.28.517.96.40.94.10.68.99.37.69.73.56.81.29.311.5DiŠerence in ˆnal ea values (z)[(ea(100 cycles)f0.1 Hz|ea(100 cycles)f1.5 Hz)/ea(100 cycles)f0.1 Hz]~100 450SALVATI AND ANHDANFig. 6. Results from a two phase cyclic triaxial test with qcyclic increas­ingFig. 5. In‰uence of qcyclic/s3 for cyclic triaxial tests with diŠerentloading 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 conˆning pressure. Next, the conˆning pressure isincreased for base/subbase soils or decreased for sub­grade soils, and the cyclic shear stresses are increasedagain. To investigate the in‰uence 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 diŠerent value of s3 orqcyclic.Sacramento River Sand was subjected to 100 cycles ofloading with s3100 kPa, qmean250 kPa, and qcyclic50kPa. Then the soil was subjected to 100 cycles of loadingwith qcyclic100 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 ˆrst phase for comparison. In theˆrst 100 cycles of loading there was a small but noticeablediŠerence in the recorded axial strain at the two diŠerentloading frequencies. However, even though the cyclicshear stresses in the second phase were larger, there wasvery little diŠerence in the axial strains measured at thetwo diŠerent frequencies of loading.The eŠect of varying conˆning pressure in the secondphase was also investigated. The Sacramento River Sandwas subjected to a 100 cycles of loading with qmean150kPa, qcyclic150 kPa, and s3150 kPa. Then, in the sec­ond phase, s3 was dropped to 100 kPa and the samplewas subjected to 100 cycles of loading with qmean150kPa and qcyclic150 kPa. There was a small diŠerence inthe axial strains measured at the two loading frequenciesin the ˆrst phase, but in the second phase there wasFig. 7.Results for a two phase cyclic triaxial test with s3 decreasingalmost no diŠerence, as shown in Fig. 7. A test in whichthe conˆning pressure was increased in the second phasewas also performed. Although the test results are notshown, little axial strain and almost no diŠerence be­tween the axial strains were measured at the diŠerentloading 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 ˆrst few cycles of loading the rateof strain for the higher loading frequency dropped sig­niˆcantly. After the ˆrst ˆve to twenty cycles, the strainrates for the diŠerent loading frequencies were very simi­lar, as seen in Fig. 8. Correspondingly, the greatest diŠer­ence in response between tests run at the two loading fre­quencies occurred during the ˆrst ˆve to twenty cycles,which can be seen in Figs. 2 through 4. In the ˆrst few cy­cles, the sample subjected to the slower rate of loading ex­ DENSE SAND IN CYCLIC TRIAXIAL TESTS451two loading frequencies as shown in Fig. 9. When therate of loading aŠected the results, the diŠerence inresponse occurred mostly in the ˆrst ˆve to twenty cycles,when the diŠerence in strain rate was the greatest. In thetwo­phase tests performed, the rate­dependent responsewas observed in the ˆrst 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. EŠect of loading frequency in cyclic triaxial tests with increas­ing axial strainperienced more axial strain. However after the ˆrst ˆve totwenty cycles of loading, the diŠerence 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 diŠerence 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 eŠect; the stiŠness of the sam­ples subjected to a higher frequency of loading was higherthan the stiŠness of the samples loaded at a lower fre­quency. Larger diŠerences 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 in‰uence the rate­dependentresponse. Overall, in the tests presented in this paper,loading conditions that resulted in higher levels of strainresulted in greater diŠerence 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. FHWA­RD–96–176,Federal Highway Administration, Washington, DC.2) Di Benedetto, H. and Tatsuoka, F. (1997): Small strain behavior ofgeomaterials modelling of strain rate eŠects, Soils and Founda­tions, 37(2), 127–138.3) Di Benedetto, H., Tatsuoka, F. and Ishihara, K. (2002): Time­dependent shear deformation characteristics of sand and their con­stitutive modelling, Soils and Foundations, 42(2), 1–22.4) Di Benedetto, H. (2007): Small strain behaviour and viscous eŠectson sands and san­clay mixtures, Proc. Stress­Strain Behaviour:Measurement, Modeling and Analysis, Springer,159–190.5) Lade, P. V. (1994): Creep eŠects and cyclic instability of granularsoils, Journal of Geotechnical Engineering, 120(2), 404–419.6) Lade, P. V., Yamamuro, J. A. and Bopp, P. A. (1997): In‰uenceof time eŠects on instability of granular materials, Computers andGeotechnics, 20(3/4), 179–193.7) Matsushita, M., Tatsuoka, F., Koseki, J., Cazacliu, B., Benedetto,H. and Yasin, S. J. M. (1999): Time eŠects on the pre­peak defor­mation properties of sands, Proc. 2nd International Symposium onPre­failure Deformation Characteristics of Geomaterials, Balkema,1, 681–689.8) 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, 44–60.9) 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, 17–61.10) Tatsuoka, F., Santucci de Magistris, F., Hayano, K., Momoya, Y.and Koseki, J. (2000): Some new aspects of time eŠects on thestress­strain behaviour of stiŠ geomaterials, Proc. 2nd Internation­al Conference on Hard Soils and Soft Rock, Balkema, 2,1285–1371.11) Tatsuoka, F., Uchimura, T., Hayano, K., Di Benedetto, H.,Koseki, J. and Siddiquee, M. S. A. (2001): Time­dependent defor­mation characteristics of stiŠ geomaterials in engineering practice,Proc. 2nd International Symposium on Pre­failure DeformationCharacteristics of Geomaterials, Balkema, 1, 1161–1262.12) 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),103–129.13) Tatsuoka, F. (2007): Inelastic deformation chracteristics of geo­material, Proc. Stress­Strain Behaviour: Measurement, Modelingand Analysis, Springer, 1–108.
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  • 発行
  • 2008/06/15
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