Department of Civil Engineering Sydney NSW 2006 AUSTRALIA http://www.civil.usyd.edu.au Centre for Geotechnical Research Research Report No R814 A Structured Cam Clay Model By Martin D Liu BE MPhil PhD John P Carter BE PhD FIEAust MASCE March 2002 Department of Civil Engineering Centre for Geotechnical Research http://www.civil.usyd.edu.au/ A Structured Cam Clay Model Research Report No R814 Martin D Liu, BE, MPhil, PhD John P Carter, BE, PhD, FIEAust, MASCE ABSTRACT Atheoreticalstudyofthebehaviourofstructuredsoilispresented.Anew model, which is referred to as the Structured Cam Clay model, is formulated by introducingtheinfluenceofsoilstructureintoModifiedCamClay.The proposed model is hierarchical, i.e., it is identical to the Modified Cam Clay soil model if a soil has no structure or if its structure is removed by loading.Three newparametersdescribingtheeffectsofsoilstructureareintroducedandthe results of a parametric study are also presented.The proposed model has been usedtopredictthebehaviourofstructuredsoilsinbothcompressionand shearingtests.Bymakingcomparisonsofpredictionswithexperimentaldata andbyconductingtheparametricstudyitisdemonstratedthatthenewmodel providessatisfactoryqualitativeandquantitativemodellingofmanyimportant features of the behaviour of structured soils. Keywords: calcareous soils, clays, fabric, structure, constitutive relations, plasticity. A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 2 Copyright Notice Department of Civil Engineering, Research Report R814 A Structured Cam Clay Model 2002 MD Liu and JP Carter m.liu@civil.usyd.edu.au;j.carter@civil.usyd.edu.au Thispublicationmayberedistributedfreelyinitsentiretyandinitsoriginal form without the consent of the copyright owner. Use of material contained in this publication in any other published works must beappropriatelyreferenced,and,ifnecessary,permissionsoughtfromthe author. Published by: Department of Civil Engineering The University of Sydney Sydney NSW 2006 AUSTRALIA March 2002 http://www.civil.usyd.edu.au A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 3 Contents 1.Introduction......................................................................................................................5 2.Generalisation of Modified Cam Clay.............................................................................6 2.1Influence of soil structure on virgin isotropic compression .........................................8 2.2Yield surface for structured clay ..................................................................................9 2.3Volumetric deformation for virgin yielding along general stress paths .......................9 2.4Flow rule.....................................................................................................................13 2.5Additional assumptions ..............................................................................................14 3.Stress-Strain Relationships ............................................................................................15 3.1Elastic deformation.....................................................................................................15 3.2Virgin yielding............................................................................................................15 3.3Softening.....................................................................................................................15 4.Parameter Determination ...............................................................................................17 5.Features of the Model ....................................................................................................20 5.1Parameter b.................................................................................................................21 5.2Parameter py,i.............................................................................................................23 5.3Parameter ................................................................................................................24 6.Model Evaluation...........................................................................................................25 6.1Background.................................................................................................................25 6.2Compression behaviour of three clays........................................................................27 6.2.1Leda Clay.............................................................................................................27 6.2.2Bangkok Clay.......................................................................................................28 6.2.3Artificially Cemented Clay..................................................................................29 6.3Behaviour of a natural calcarenite..............................................................................31 6.4Behaviour of Corinth marl..........................................................................................37 6.5Behaviour of La Biche clayshale................................................................................38 7.Conclusion .....................................................................................................................40 8.Acknowledgements........................................................................................................41 9.References......................................................................................................................41 A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 4 A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 5 1.Introduction Soilsinsituusuallypossessnaturalstructure,whichenablesthemtobehave differently from the same material in a reconstituted state (e.g., Burland, 1990; LeroueilandVaughan,1990;CuccovilloandCoop;1999).Recently,there havebeenimportantdevelopmentsinformulatingconstitutivemodels incorporatingtheinfluenceofsoilstructure,suchasthoseproposedbyGens andNova(1993),Whittle(1993),Wheeler(1997),RouainiaandMuirWood (2000),andKavvadasandAmorosi(2000).Inthispaperanewconstitutive modelforstructuredclaysisproposed.Themainobjectiveofthisnew formulationistoprovideaconstitutivemodelsuitableforthesolutionof boundaryvalueproblemsencounteredingeotechnicalengineeringpractice.It is intended therefore, that the new model should be relatively simple and should havefewparameters,eachofwhichhasaclearphysicalmeaningandcanbe conveniently identified.The model should also be relatively easy to understand and apply. TheModifiedCamClaymodel(RoscoeandBurland,1968)iswidely referencedandhasbeenwidelyusedinsolvingboundaryvalueproblemsin geotechnicalengineeringpractice(e.g.,GensandPotts,1988;Yu,1998;Potts andZdravkovic,1999),althoughitwasdevelopedoriginallyforreconstituted clays.Becauseofsomefamiliaritywiththemodelbythegeotechnical profession and because it captures well the essential behaviour of reconstituted soil,theModifiedCamClaymodelwaschosenasthebasisforthecurrent research.A new model has been formulated by introducing the influence of soil structureintoModifiedCamClay.Aparametricstudydemonstratingthe capabilities and limitations of this new model is presented.The model has also been used to predict the behaviour of a variety of structured natural soils in both compressionandshearingtests,allowingareasonablycomprehensive evaluationofittobeundertaken.Itisdemonstratedthattheproposednew A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 6 model is suitable for describing the behaviour of a variety of natural clays and cemented soils. 2.Generalisation of Modified Cam Clay TheModifiedCamClaymodelwasproposedbyRoscoeandBurland(1968) and a description and systematic study of the model can be found in the text by MuirWood(1990).Formulationsofthismodelsuitableforuseinfinite element analysis can also be found in various texts (e.g., Britto and Gun, 1987; PottsandZdravkovic,1999).Inthispaper,theModifiedCamClaymodelis employedasabasisforformulatingahierarchicalmodelforstructuredclays, which is referred to as the Structured Cam Clay model. It is assumed that the behaviour of soil in a reconstituted state can be described adequately by the Modified Cam Clay model.The term soil structure is used heretomeanthearrangementandbondingofthesoilconstituents,andfor simplicityitencompassesallfeaturesofasoilthataredifferentfromthoseof thecorrespondingreconstitutedsoil.FollowingthesuggestionofBurland (1990),thepropertiesofareconstitutedsoilarecalledtheintrinsicproperties, and are denoted by the symbol * attached to the relevant mathematical symbols.Hence,underallstressconditions,theinfluenceofsoilstructurecanbe measured by comparing its behaviour with the intrinsic behaviour. Theformationanddevelopmentofsoilstructureoftenproducesanisotropyin themechanicalresponseofsoiltochangesinstress.Destructuringusually leads to the reduction of anisotropy.In order to concentrate on introducing the physicalconceptsoftheframeworkandtoavoidunnecessarycomplexityof mathematicaldetail,onlytheisotropiceffectsofsoilstructureareincludedin theproposedtheoreticalframework.Theextensionrequiredtoincludethe influence of soil anisotropy shall be a future research topic, however it is noted thatothershavepreviouslyconsideredthisfeatureofsoilbehaviour,e.g., Dafalias(1987),WhittleandKavvadas(1994),Wheeler(1997)andRouainia A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 7 andMuirWood(2000).Itshouldalsobenotedthatcoaxialitybetweenthe principalaxesofplasticstrainincrementandthoseofstressisassumedinthe proposed framework. Thestressandstrainquantitiesusedinthepresentformulationaredefinedas follows.ij and ij are the cartesian components of effective stress and of strain respectively.Thesimplifiedformsforstressandstrainconditionsin conventional triaxial tests are also listed, where 1 (or 1) and 3 (or 3) are the axial effective stress (strain), and the radial effective stress (strain) respectively.The mean effective stress p, deviatoric stress q and stress ratio are given by ( )( ) tests, triaxial al convention for 231313 133 22 11 + + + p(1) ( ) ( ) ( ) ( ) [ ]( ) tests, triaxial al convention for6213 131 23 12211 33233 22222 112 2 2 + + + + + q(2) pq .(3) The corresponding (work-conjugate) volumetric strain increment, dv,, and deviatoric strain increment, dd, are defined by tests triaxial al convention for 23 133 22 11 d dd d d dv+ + + (4) and A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 8 ( ) ( ) ( ) [ ]( ) . tests triaxial al convention for32) ( 6323 131 23 12211 33233 22222 112 2 2 d dd d d d d d d d d dd + + + + + (5) 2.1Influence of soil structure on virgin isotropic compression TheworkbyLiuandCarter(1999and2000)isemployedhereasastarting pointforincludingtheeffectsofsoilstructureinthemodel.Thematerial idealisationoftheisotropiccompressionbehaviourofstructuredclayis illustratedinFig.1.Inthisfigureerepresentsthevoidsratioforastructured clay,e*isthevoidsratioforthecorrespondingreconstitutedsoilatthesame stressstateduringvirginyielding,py,iisthemeaneffectivestressatwhich virgin yielding of the structured soil begins, and e, the additional voids ratio, is thedifferenceinvoidsratiobetweenastructuredsoilandthecorresponding reconstitutedsoilatthesamestressstate.Hence,thevirginisotropic compressionbehaviourofastructuredsoilcanbeexpressedbythefollowing equation, e e e +*.(6) The following equation was proposed by Liu and Carter (2000) to describe the volumetric behaviour of natural clays during virgin isotropic compression, bi yippe e e((,\,,(j + ,* .(7) eiistheadditionalvoidsratioatp = py,i,wherevirginyieldingofthe structuredsoilbegins(Fig.1).bisaparameterquantifyingtherateof destructuring and it is referred to here as the destructuring index.The value of b depends on soil type and structure and generally b 1 for soft structured clays and b < 1 for stiff clays.For the thirty different clays studied by Liu and Carter A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 9 (1999,2000),itwasfoundthatgenerally0 b 30.Forclaysamplesofa given mineralogy and with similar geological stress history but different depths below the surface, it is found that b depends mainly on the liquidity index. 2.2Yield surface for structured clay In the Modified Cam Clay model, the behaviour of a clay is divided into virgin yieldingbehaviourandelasticbehaviourbyitscurrentellipticalyieldsurface.Thesize oftheyieldsurfacecanbeidentified uniquelyaccordingtothe stress stateandthevoidsratioandisafunctionofstresshistory.Intheproposed StructuredCamClaymodel,thebehaviourofclayisalsodividedintovirgin yieldingbehaviourandelasticbehaviourbyitscurrentyieldsurface,whichis dependentonsoilstructureaswellasstresshistory.Hence,thecurrentyield surface of a structured clay, named as the structural yield surface, is defined by itscurrent stress state,voidsratio, stress history,and soil structure. Similar to theoriginalproposalbyRoscoeandBurland(1968),theyieldsurfaceofa structuredsoilinp-qspaceisassumedtobeellipticalinshapeanditpasses throughtheoriginofthestresscoordinates(Fig.2).Theaspectratioforthe structural yield surface is *, the critical state strength of the reconstituted soil.Oneaxisoftheellipsecoincideswiththepaxis.ps,thevalueofthep coordinate where the ellipse again intersects the axis, represents the size of the yield surface.The yield surface is thus given by the yield function f, where 0 15 . 05 . 0* 5 . 02 2 ((,\,,(j +((,\,,(j

ssspp ppqf .(8) 2.3Volumetric deformation for virgin yielding along general stress paths AsillustratedinFig.1,virginyieldingandelasticbehaviourofreconstituted clay,i.e.,aclaywherestructureiscompletelyremoved,arebothlinearine - lnpspace,withgradients*and*respectively.Theisotropicvirgin compression line for the reconstituted soil, i.e., ICL*, is given by A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 10 p e eIC ln * * * (9) wheree*ICisthevoidsratioofthereconstitutedsoilwhenp = 1 kPaduring virgin isotropic compression.We seek now to generalise equation (9) for a soil that possesses structure. Considerloadingwherethecurrentstressstatestaysontheyieldsurface,and thesizeofthecurrentyieldsurfaceisdenotedasps.Formonotonicloading, virgin yielding occurs if ps py,i. Undertheassumption thatthe hardening of structured soil isdependent on the plastic volumetric deformation, the yield surface for a structured soil is defined byallstressstatesthathavethesameaccumulationofabsoluteplastic volumetricstrain.Insuchamodeltheplasticvolumetricdeformationis dependentonthechangeinsizeoftheyieldsurfaceonly.Iftheelastic deformationforastructuredsoilisassumedtobethesameasthatofthe reconstitutedsoil,anychangeintheadditionalvoidsratiosustainedbysoil structuremustalsobeassociatedwithplasticvolumetricdeformation,and therefore isalso dependent onthesizeoftheyield surface.Consequently,the variable p in formula (7) may be written in terms of the size of the current yield surfaceps.Onsubstitutingequation(9)intoequation(7),thefollowing expression for the variation of the voids ratio is obtained i y sbsi yi ICp p pppe e e,,for ln * * ((,\,,(j + .(10) py,iisthevalueofthemeaneffectivestressattheinitialyieldpointforan isotropicstressstate,andisnumericallyequaltothesizeoftheinitialyield surface associated with the initial soil structure. AccordingtoCriticalStateSoilMechanics(SchofieldandWroth,1968),for compression along a general stress path the volumetric deformation defined by A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 11 *ln p,whichisassociatedwithintrinsicsoilproperties,canbedividedinto twoparts.Theelasticpartisdefinedby*ln p,whichisdependentonthe currentmeaneffectivestress,andtheplasticpartisgivenby(*-*)ln ps, whichisdependentonthesizeoftheyieldsurface.Thevoidsratiofora structuredsoilduringvirgincompressionalongageneralstresspathisthus obtained as follows: ( ) p pppe e esbsi yi IC ((,\,,(j +ln * ln * * *, .(11) Thegeneralcompressionequation(11)statesthatvoidsratioforastructured soilduringvirgincompressionisdependentontwoparts,viz.theelasticpart whichisdependentonthecurrentmeaneffectivestress,andtheplasticpart which is dependent on the size of the current yield surface.The plastic part is againsubdividedintotwoparts,viz.thepartassociatedwiththeintrinsic properties of the soil and that associated with soil structure. Differentiatingequation(11)andnotingequations(6)and(7),thetotal volumetricstrainincrementforcompressionalongageneralstresspathis obtained as follows ( )( ) ( ) ( )p ep dp ep de bp ep ddssssv ++ + + + 1*1 1* * .(12) The last part of the expression for the total volumetric strain, i.e., the last term ontherighthandsideofequation(12),isassociatedwithelasticdeformation.Hence ( )p ep ddev +

1* (13) and A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 12 ( )( ) ( )ssss pvp ep de bp ep dd + + + 1 1* * .(14) The plastic volumetric strain is therefore made up of two parts.The first part is dependent on the intrinsic soil properties and has been described already by the Modified Cam Clay model.The second part is dependent on soil structure and isresponsibleforthereductionoftheadditionalvoidsratiosustainedbysoil structure.Hence,thispartrepresentstheeffectofstructureanddestructuring.Itmaybeseenfromequation(14)aswellasequation(11)thattheplastic volumetricdeformationassociatedwithdestructuringisalsodependentonthe change in size of the yield surface, irrespective of the magnitude of the current shearstress.Consideringthemechanismofshearing,itisrationaltoassume thatdestructuringandtheassociatedplasticvolumetricdeformationshouldbe dependent on both the change in size of the yield surface and the magnitude of the current shear stress.Therefore, a modification of equation (14) is made so that the effect of shear stress on destructuring is also considered, i.e., ( )( ) ( )ssss pvp ep de bp ep dd +((,\,,(j + + + 1 *11* * (15) whereistheshearstressratiodefinedinequation(3).Itmaybeseenfrom equation (15) that the effect of destructuring, which is described as the reduction of the additional voids ratio, increases with the value of the current stress ratio. Alternatively, equation (15) can be rewritten as ( )( ) ( )ssss pvp ep de bp ep dd +((,\,,(j + + 1 **1* * .(16) Because of the modification made to equation (12), the new hardening rule for a structuredsoilisnolongerdependentonlyontheplasticvolumetric deformation.It also depends on the shear stress ratio, . A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 13 Insummary,structuredclayisidealisedhereasanisotropichardeningand destructuring material with elastic and virgin yielding behaviour.It is assumed that during virgin yielding the yield surface includes the current stress state and expands isotropically causing destructuring of the material. 2.4Flow rule In the Modified Cam Clay model, associated plastic flow is assumed.Thus, the yield surface is also the plastic potential and the flow rule is given as 2 2*2

pvpddd .(17) Thestructureofsoilalsohasinfluenceontheflowrule.Itisobservedthata structuredclaywithpositiveegenerallyhasalowervalueforthestrain incrementratiodpd/dpvthanthecorrespondingreconstitutedsoilatthesame virgin yielding stress state (e.g., Olson, 1962; Graham and Li, 1985; Cotecchia andChandler,1997).Thefollowingequationisthereforeproposedasaflow rule for structured clay, ( )2 2*1 2

eddpvpd .(18) isanewmodel parameterwhichdescribes the influenceof soil structureon the flow rule.The modifier should not be negative otherwise the plastic strain increment vector will always be directed inside the yield surface.Hence, based ontheneedtomeetthisconditionatalltimes,includingthestartofvirgin yielding, the following constraint is imposed: 1 1 0 0,virginyieldingoccurs.Basedontheplasticvolumetricdeformation,i.e.,equation(16),theflowrule givenbyequation(18)andconsideringtheelasticdeformation,thefollowing stress and strain relationships for virgin yielding are obtained ( )( )( ) ( )ssssvp ep de bp ep dp ep dd +((,\,,(j + + + +

1 **1* *1* ,(23) ( )( )( )( )( )( )ssdp ep de bepdqed +]]],,((,\,,(j + +(,\,(j+ +

1 *** **1 21** 2 1 9* 1 22 2 .(24) 3.3Softening Soil is regarded as an elastic material for loading inside the virgin yield surface.Whenthecurrentstressstatereachesthevirginyieldsurfaceatapointwith A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 16 dps > 0virginyieldingoccurs.Ifthesoilreachestheyieldsurfacewith > *,softeningoccursiftheboundaryconditionsallowappropriate adjustment of the stress state.Otherwise, catastrophic failure will be predicted.During the softening process, soil structure will be broken down, and the yield surfaceshrinkswiththecurrentstressstatealwaysremainingonit.Insuch casestheyieldsurfacecontractsuntilthesoilreachesacriticalstateof deformationwherethestructureof thesoiliscompletelyremoved. Itfollows, therefore,thatthesofteningbehaviourofasoilshouldbedescribedbyvirgin yielding equations.Consequently, the plastic volumetric strain increment given byequation(16)shouldalsobevalidforthesofteningprocess.Itmaybe noticedthatbecausetheyieldsurfaceshrinksthevolumetricdeformation associatedwithintrinsicsoilpropertiesisnegative,i.e.,expansive.However, thevolumetricdeformationassociatedwiththedestructuringisdeterminedby e, because both the terms (*-) and dps are negative.If e is positive, this partoftheoverallvolumetricdeformationispositive.Ifeisnegative,the structuralpartofthevolumetricdeformationisnegative.Thisisrational because destructuring occurs during the softening process, and consequently the additionalvoidsratiosustainedbysoilstructurenecessarilydecreases.Asa result,softeningofstructuredclayscanbeaccompaniedbyeitheroverall volumetricexpansion(negativeporepressureforundrainedtests),oroverall volumetriccompression(positiveporepressureforundrainedtests).This tendency can be seen in test data for both natural soils and artificially structured soilsreportedbyseveralresearchers,includingLo(1972),Nambiaretal. (1985), Burland et al. (1996), and Carter et al. (2000). The plastic deviatoric strain increment during softening is proposed as follows, ( ) ( )( ) ( )ss pdp ep de b e d + ]]],,((,\,,(j 1 * **1 22 2* * .(25) A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 17 Comparedwithequation(24),itcanbeseenthatonlythesignoftheplastic deviatoricstrainassociatedwithdestructuringischanged,sothatthestrain increment vector will point outside the yield surface. The elastic part of the deformation can be calculated by equations (21) and (22).Thetotalstrainincrementsduringsofteningarethusfullydetermined.As softeningisastrained-controlledprocess,thechangeinthestressstatecanbe decidedfromthesizeofthecurrentstructuralyieldsurface.Whencondition = *isreached,thestructureofsoilisusuallycompletelydestroyedwith e = 0,andtherefore,thestructuredclayhasreachedthecriticalstateof deformation. It may be noticed that for both virgin yielding and softening behaviour the soil may reach a state with = * but with e 0.A specific example is the case where a soil reaches critical state by loading entirely inside the yield surface.In thiscasevirginyieldingcommencesoncetheyieldsurfaceisreachedand, according to equations (23)and(24), thesoilisalso in astatewhere itcan be distorted continuously at constant volume (dvp = 0 and dvp ).Hence, the proposedmodelpredictsthatunderspecialstresspathsasoilmayreacha criticalstateofdeformationwithitsstructurehavingnotbeenremoved completely.Consequently, in such cases the soil state will not be on the critical state line defined in e - p space.If there is evidence that the structure of a soil isdestroyedcompletelyafterthesoilreachesthecriticalstateofdeformation then destructuring could be described by the plastic distortional strain instead of the current stress ratio.However, this possibility has not been pursued here. 4.Parameter Determination Eight parameters define the proposed model, and they are *, e*IC, *,*, *, b, py,i, and .The first five parameters, denoted by the symbol *, are intrinsic soilpropertiesandareindependentofsoilstructure.Thesefiveintrinsic A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 18 parametersarethesameasthoseadoptedintheModifiedCamClaymodel (RoscoeandBurland,1968).Theinfluenceoftheseparameterswillnotbe investigatedinthispapersincestudiesofthemarewelldocumented(e.g.,see Muir Wood, 1990). Threenewparameters,viz.,b,py,iand,areintroducedtodescribethe influenceofsoilstructureonitsmechanicalbehaviour.Thevalueofthe destructuringindex,b,indicatestherateofthedestructuringduringvirgin yielding(Fig.1),andpy,irepresentsthesizeoftheinitialyieldsurfacefora structured soil (Fig. 5).The values of these two parameters can be determined directlyfromanisotropiccompressiontestonanintact(undisturbed)soil specimen.Parameterwasintroducedtodescribetheinfluenceofsoil structureontheflowrule(e.g.,seeequation(18)),anditsvaluecanbe determined by applying the flow rule to the strains measured in a shearing test on an intact specimen provided that the elastic properties of the soil are known. Valuesoffiveofthemodelparameters,viz.,e*IC,*,*,b,andpy,icanbe determined from isotropic compression tests.The values of parameters * and *andbcan bedetermineddirectlyfromanycompression testswithconstant ,whereasthevaluesofe*ICandpy,icanonlybedetermineddirectlyfrom isotropic tests.In geotechnical engineering practice oedometer tests on soils are muchmorewidespreadthanisotropiccompressiontests.Therefore approximate methods for obtaining soil parameters e*IC and py,i from oedometer tests, as well as any constant tests, are also proposed. Thebehaviourofreconstitutedclayisassumedtofollowtheassumptionsof CriticalStateSoilMechanics(e.g.,detailsseeMuirWood,1990).Fora reconstituted soil with a given mineralogy, the compression lines with different stressratioarethereforeassumedparallel(Fig.4).Thedifferenceinvoids ratiobetweene*ICande*,thevoidsratioatp = 1 kPaforacompressiontest with constant , can therefore be expressed as A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 19 ( )((,\,,(j + ppe eoICln * * * * .(26) The size of a yield surface po and the mean effective stress for a stress state on the yield surface with stress ratio are related as follows, 2 22** +

opp .(27) Based on equations (26) and (27), the size of the initial yield surface py,i can be computedifthevalueofthemeaneffectivestressatthevirginyieldpointis measured from a compression test with constant , and the soil parameter e*IC can therefore be computed from the measured value of e*. Foroedometertests,anapproximationismadebasedonJackysempirical equation(Jacky,1944),inwhichthehorizontaleffectivestressvandthe vertical effective stress h for a soil during one dimensional virgin compression is expressed as csvhsin 1 (28) wherecsisthecriticalstatefrictionanglemeasuredfromatriaxial compression test.The critical state strength parameter * can be expressed in terms of cs as cscssin 3sin 6* .(29) Therelationshipbetweenvandpforone-dimensionalcompressioncanbe obtained as csvp sin 2 33

.(30) A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 20 Thus the stress ratio for a one-dimensional compression test can be expressed as cscssin 2 3sin 3

.(31) Consequently,thefollowingequation can be derivedfor estimatingthe size of theinitialyield surfacebasedon the initial verticalyieldstressmeasuredfrom an oedometer test, i vycscscs i yp,2,sin 4 6sin 31 sin321 ]]]],,,((,\,,(j+(,\,(j .(32) e*ICcanberelatedtothevalueofe*obtainedfromanoedometertestbythe following equation, ( )]]]],,,((,\,,(j+(,\,(j + 2sin 4 6sin 31 sin321 ln * * * *cscscs ICe e .(33) Itshouldbepointedoutthattheproposedmethods,basedontheresultsof oedometer tests, are approximate and should be used only when more accurate methods for deriving the soil parameters are not available. 5.Features of the Model Theinfluenceofthethreenewparametersb,py,iand,andsomefeaturesof thenewStructuredCamClaymodelaredescribedinthissection.Example calculations have been made using the new model and the values of the intrinsic soil properties adopted are listed in Table 1.Based on these values, it is found that e*cs = 2.1, where e*cs is the well known parameter defining the position of the critical state line in e p space. A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 21 Table 1Model parameters Parameter***e*IC* Value1.200.160.052.1760.25 5.1Parameter b Theinfluenceofthedestructuringindexbisdemonstratedbythesimulations shown in Figs 5 and 6.The following values of parameters for the soil structure were employed in these calculations: py,i = 100 kPa and = 1.Eight different valuesofbwereassumedandtheyare0,0.25,0.5,1,2,5,10and100.The initialstressstatewasp =100 kPaandq = 0,andtheinitialvalueofthe additional voids ratio was ei = 0.8. Itcanbeseenthatthedestructuringindexbhasthefollowingeffectsonthe simulated isotropic compression behaviour (Fig. 5). Thecompressionbehaviourofstructuredsoilisasymptotictothatofthe corresponding reconstituted soil for situations with b > 0. Therateofreductionintheadditionalvoidsratiomaintainedbysoilstructure increases with the magnitude of b.For situations with b 100, there is almost an immediate collapse of soil structure when the initial yield stress is surpassed. Forb = 0,thevirgincompressionlineforastructuredsoilandthatforits corresponding reconstituted soil are parallel in the e lnp space.Theoretically, inthiscasenodestructuringtakesplaceduringthevirginyieldingande remains unchanged. Thesimulatedshearingbehaviourofastructuredsoilwithdifferentvaluesof thedestructuringindexbisshowninFig.6.Theeffectivestresspaths A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 22 simulatedfollowthoseinaconventional drained triaxialtest byincreasingthe axial loading only.The following features of soil behaviour are simulated. Exceptfor the unlikelysituationwithb = 0,the finalstatefor astructured soil undermonotonicshearingisindependentofsoilstructureandisatthecritical stateofdeformation.Atthisstatethestructureofsoilhasbeencompletely removed.Forthesimulatedcaseswheretheinitialstressstateand voidsratio and the loading path are the exactly the same, the final states for all seven cases fall onto the same point on the critical state line (Fig 6a), and the final values of thedeviatoricstressandthevolumetricstrainarethesame(Figs6band6c).Thereforeparameterbhasnoinfluenceonthefinalstateofthesoilunder monotonic shearing if b > 0. As has been discussed previously, there is no destructuring for the situation with b = 0. The final state of the soil does not fall onto the critical state line (Fig. 6a).The structure of the soil remains intact even when the soil is sheared to failure, i.e.,wherethesoilhasnoresistancetofurtherdistortionaldeformation.This particularsituationismostlikelyahypotheticallimitstateoftheresistanceof soilstructure.Whetherthestructureofrealgeotechnicalmaterialsunder extreme situations may respond to shearing in a manner similar to that described by b = 0 is probably unlikely but needs further investigation. It can be seen from the stress path in the e-lnp coordinates (Fig. 6a) that the rate ofdestructuringincreaseswiththevalueofb.Forthesituationwithb = 100 soilstructureisdestroyedalmostimmediately,wherethereisasharpdropin voids ratio when shearing commences.After the structure of the soil has been removed,thereductioninthevoidswithloadingismuchslowerandthe behaviour of the original structured soil is the same as that of the corresponding reconstitutedsoil.Thisconclusionisconfirmedbythedeviatoricand volumetricstrainrelationship(Fig.6b).Thefinalvolumetricstrainforallthe casessimulatedisthesame,howeverthedeviatoricstrainatwhichthesoil reaches its final volumetric strain decreases with the increase of b. A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 23 Forsmallstrains,sayd < 1%,theshearstiffnessdecreaseswithb.For relativelylargedeformation,tosaywithd > 1%,theshearstiffnessismore complicated and the change of shear stiffness with b is not monotonic. 5.2Parameter p y,i To illustrate the influence of the size of the initial yield surface defined by py,i, thesoilparameterslistedinTable1,togetherwithb = 1and = 1,were adopted.Six different values of py,i were assumed and they are 100, 150, 200, 334, 500and 1,000 kPa.The influenceofparameter py,i onthesimulationsis showninFig.7.Theeffectivestresspathssimulatedfollowthoseina conventionaldrainedtriaxialtestinwhichtheaxialloadingonlyisincreased.The initial stress state for all six cases is the same, with p =100 kPa and q = 0, and the initial voids ratio was ei = 1.439.For this initial soil state and the given intrinsicsoilproperties,theinitialyieldsurfaceforthecorresponding reconstitutedsoilispo = 100 kPa.Therefore,fortheparticularsituationwith py,i = 100 kPa the soil is in a reconstituted state and has no structure.The soil is structuredforsituationswithpy,i > 100 kPa.Thus,thissetofcomputations simulatesthedevelopmentofstructureforsoilatconstantvoidsratioandthe same stress state.The following features are simulated. Asindicatedinthepreviousparagraphs,thefinalstateforastructuredsoil undermonotonicshearingwithb > 0isthecriticalstateofdeformation.Becausethefinaldeviatoricstressforallsixcasesisthesame(Fig.7a),their finalstatesarethesame,i.e.,thesamecriticalstateofdeformationwiththe samestressstateandvoidsratio.Hence,thefinalstateofastructuredsoil under monotonic shearing is independent of the size of the initial yield surface. For soil of a given mineralogy in a given initial condition, i.e., stress state and voids ratio, and tested under a given stress path, a peak strength may or may not be mobilised, depending on the size of the initial yield surface.Consequently, a structuredsoilmaybeabletoresistamuchhighershearstressthanthe A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 24 correspondingreconstitutedsoilatthesameinitialstressstateandthesame voids ratio. Duringthesofteningprocessthehigherthepeakstrength,thequickerthe reduction in the soil strength with the respect to the deviatoric strain.Hence, if softeningoccursthepeakstrengthofastructuredsoilreducestothecritical state strength more rapidly than the corresponding reconstituted soil. Theresponsepatternusuallylabelleddrybehaviour(SchofieldandWroth, 1968) may not be observed for a structured soil, i.e., volumetric expansion may notoccurwhenthesofteningprocessstarts.Itisseenthatforthecasewith py,i = 500 kPa there is a continuous volumetric compression accompanying the softeningprocess.Forthesimulationwithpy,i = 1000 kPa,volumetric expansion,althoughobserved,startsonlyafteraconsiderableamountof softening has occurred. Aninterestingphenomenonisobservedinthesimulationwithpy,i = 334 kPa.Thesoilbehavesentirelyelasticallybeforethestressstatereachestheyield surface.Whenthestressstatereachesthepointontheyieldsurfacewiththe criticalstatestressratio,virginyieldingalsostarts(seetheinsetinFig.7a).Becauseofthespecialfeatureofthisstressstate,thestructuredsoilhasno furtherresistancetosheardeformation.However,thevolumetricstrain increases continuously with the deviatoric strain after this stress state is reached indicating thatthesoilhas notyetreachedthecriticalstate ofdeformation.It reaches a critical state of deformation after the additional voids ratio due to the initial structure is completely diminished. 5.3Parameter To illustrate the influence of parameter , the soil parameters listed in Table 1 were adopted, together with b = 1 and py,i = 100 kPa.The initial stress state is definedasp =100 kPaandq = 0,andtheinitialvalueoftheadditionalvoids A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 25 ratioisei = 0.8.Fivedifferentvaluesofwereassumed,i.e., = 0,0.313, 0.625,0.938and1.25(thecorrespondingvaluesofeiare0,0.25,0.5,0.75 and 1 respectively).The influence of parameter on the simulated behaviour is showninFig.8.Theeffectivestresspathssimulatedfollowthoseina conventionaldrainedtriaxialtestinwhichtheaxialloadingonlyisincreased.As can be seen from the volumetric deformation, equation (23), parameter has no influence on the volumetric strain.In the figure showing the deviatoric and volumetricstrainrelationship,thevariationinthisrelationshipisattributed entirely to the influence of on the deviatoric strain.The higher is the value of the stiffer is the shear deformation. Basedonthestudyofthethreeparametersdescribingsoilstructure,itcanbe concludedthatthefinalstateofastructuredsoilundermonotonicshearing, predicted by the proposed model for situations with b > 0, is the critical state of deformation.Atsuchastate,thestructureofthesoiliscompletelyremoved.Thusthefinalstateofastructuredsoilisindependentofsoilstructureand consequentlyisnotinfluencedbythethreenewparameters,whichdescribe onlytheinfluenceofsoilstructureonsoildeformation.Theexistenceofthe criticalstateofdeformationforgeo-materialsandtheimplicationthatthe associatedmechanicalpropertiesareindependentofmaterialstructurehave been widely observed features of soil behaviour (e.g., Been and Jefferies, 1985; Ishihara, 1993; Novello et al, 1995; Carter et al, 2000). 6.Model Evaluation 6.1Background Theproposedmodelwasalsousedtosimulatethebehaviourofsoilswith structure,andthemodelwasevaluatedbasedoncomparisonsbetweenthe model performance and the corresponding experimental data.The compression behaviour of three different clays is considered first, and they are natural Leda clay, weathered Bangkok clay, and an artificially cemented clay.The shearing A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 26 behaviourofthreeotherstructuredsoilswasalsoconsidered,andtheyarea natural calcarenite, natural Corinth marl and a natural clay shale. Twodifferenttypesofcomputationweremadeusingtheproposedmodel: simulations and predictions.If the model is used to describe the behaviour of a soilinaparticulartestorasetoftestsandthesameexperimentaldatahave beenemployedpreviouslyinthedeterminationofthemodelparameters,this typeofcomputation is definedhereasa simulation.If the modelisused to describethebehaviourofasoilinaparticulartestorasetoftestsandallthe model parameters have been determined independently of that test or that set of tests, this type of computation is defined as a prediction. The following methods were used in the determination of model parameters: (a) values were measured directly from a test and have a physical meaning, (b) use wasofempiricalequations,(c)someparametersweredeterminedbycurve fitting,and(d)otherswerebasedonassumedvalues.Forthelastmethod, selectionofthevalueofaparameterisusuallybasedonexperiencein geotechnicalengineeringpractice.Itisproposedthatifnoexperimentaldata are available the value of parameter is determined by the following equation, 5 . 0 1 ie .(34) Itmaybeseenthatthisassumptionimpliesamid-rangevalue,basedonthe constraint conditions imposed on parameter , i.e., equation (19). In all computations the stress units adopted are kPa.In presenting the results of thecomputations,experimentaldataforstructuredsoilsarerepresentedinthe figures by solid circles or squares, which in some cases are linked by thin lines.Data for reconstituted soils are represented by open circles, which in some cases arelinkedbythinlines.Themodelsimulationsarerepresentedbysolidlines and those for reconstituted soils by broken lines. A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 27 6.2Compression behaviour of three clays Threesetsofcompressiontestsondifferentsoilsaresimulatedandforthese tests only the volumetric deformation has been computed.As can be seen from equation(23),thevolumetricdeformationisnotinfluencedbythevaluesof parameters * and .Hence, there is no need to determine or specify values for these parameters. 6.2.1Leda Clay The first group of test data includes five compression tests on natural soft Leda clay performed by Yong and Nagaraji (1977) and Walker and Raymond (1969).The two oedometer tests on the natural and reconstituted Leda clay reported by YongandNagaraji(1977)wereusedtoidentifiedsoilparameters,andtheir values are listed in Table 2. The values of parameters * and * and b and vy,i were obtained directly from the experimental data.The critical state strength of LedaclaywasreportedbyWalkerandRaymond(1969)as* = 1.2.The intrinsicsoilpropertye*ICwasestimatedaccordingtoequation(33).Itwas foundfromtheexperimentaldata(Fig.9)thate*forone-dimensional compression is equal to 2.353, which gives e*IC = 2.338. The initial state of the structured soil is v = 20 kPa and e = 1.96.As shown in Fig. 9, the compression behaviour of Leda clay is well simulated by the model. Table 2Model parameters for Leda clay Parameter***e*ICbvy,i (kPa) Value1.20.2230.032.3381168.6 ThreetestsperformedbyWalkerandRaymond(1969)wereusedtoevaluate themodelspredictions.AlthoughallthespecimenstestedbybothYongand Nagaraji(1977)andWalkerandRaymond(1969)wereLedaclay,theywere obtainedfromdifferentlocationsinthesamearea.Itisassumedthatthese specimens differed only in the size of the initial yield surface, i.e., the different A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 28 Leda clay samples possessed the same mineralogy and type of structure but may havehaddifferentmagnitudesofstructure.Thethreecompressiontestswere with = 0,0.63and1respectively.Theexperimentaldataforthetestwith = 0were usedtoidentifythesizeof theyieldsurface,anditwasfound that py,i = 265 kPa.The predicted compression behaviour of the Leda clay is shown inFig.10.Forcomparison,thevirginisotropiccompressionlineforthe reconstituted Leda clay is also represented in the figure by a broken line.It may be observed that the initial voids ratios of the samples for the tests with = 0.63 and1areessentiallythesameatthesamemeaneffectivestressintheelastic region, but different from that for the test with = 0.This indicates that some difference in py,i may exist between the first two samples and the third sample.Itisseenthattheproposedmodelgivesanapproximatebutreasonable description of the compression behaviour of natural Leda clay. 6.2.2Bangkok Clay The second groupoftestdataincludes theresults offivecompressiontests on weatheredBangkokclayperformedbyBalasubramanianandHwang(1980).Thestressratiosfor the five testsare 0,0.16, 0.43,0.6and 0.75.Theauthors wereunabletoobtaininformationonthebehaviourofreconstitutedBangkok clay.However,theliquidlimitvaluefortheclaywas123%,andsotheone-dimensional compression curve for the reconstituted soil type was estimated by theempiricalmethodsuggestedbyBurland(1990).Basedontheestimated one-dimensionalcompressioncurve,valuesofparameters*ande*forone-dimensionalcompressionwereobtained.Theisotropictestontheweathered clay was used to identify soil parameters b and py,i.The critical state strength for the clay was reported by Balasubramanian and Hwang (1980) as * = 0.9.Theintrinsicsoilpropertye*ICwasestimatedbasedonequation(33).The values of these soil parameters are listed in Table 3.The simulated behaviour of BangkokclayisshowninFig.11.Itmaybenoticedthatthecompression behaviour of the Bangkok clay is well simulated in this case. A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 29 Table 3Model parameters for weathered Bangkok clay Parameter***e*ICbvy,i (kPa) Value0.90.40.13.820.5535 The predicted compression behaviour of Bangkok clay with = 0.16, 0.43, 0.6 and0.75isshowninFig.12.AsmaybeseenintheinsetinFig.11,some differences in the initial soil structure exist among the samples used for the five tests.The test specimens were obtained from the field and some variation in the specimenswouldnormallybeexpected.Itmaybeseenthattheinitialsoil states for the five specimens may be divided into three groups, i.e., the test with = 0,thetestwith = 0.16,andtestswith = 0.43and0.6and0.75.Itis assumed in the simulations that the differences in the initial states of the soil can be represented adequately by the differences in the sizes of the initial structural yield surfaces.It may be seen from the compression curve that the initial stress state for the test with = 0.16 is on the yield surface, i.e., py,i = 67.6 kPa.The size of the initial yield surface for the other three specimens is 45 kPa (the test with = 0.43 is used to identify the value of this parameter).Overall, it is seen thattheproposedmodelgivesareasonablygoodapproximationofthe compression behaviour of weathered Bangkok clay. 6.2.3Artificially Cemented Clay The third group of test data includes the results of five compression tests on an artificially cemented clay performed by Burghignoli et al (1998).The soil was composedofanaturalAvezzanoclay,commercialbentonite,ordinary425 Portlandcement,anddistilledwater.Homogeneousandfullysaturated artificiallycementedspecimensweremade(fordetailsofthesample preparation see the report by Burghignoli et al, 1998).Based on two oedometer testsonthereconstitutedclayandthestructuredclay,modelparameterswere identifiedandtheyarelistedinTable4.Theauthorswerenotabletoobtain data for the critical state strength and a value of * = 1.2 was assumed, which corresponds to a critical state friction angle of 30.e*IC was estimated based on A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 30 theproposedequation(33).Thebehaviouroftheclaywithstructureandina reconstitutedstateundercyclicoedometertestswassimulatedandtheresults areshowninFig.13.Thecycliccompressionbehaviouroftheartificially cemented clay in the oedometer test is well simulated. Table 4Model parameters for an artificially cemented clay Parameter***e*ICbvy,i (kPa) Value1.200.5050.025.3830.7430 Burghignolietalalsoperformedthreesetsofcompressiontestsinorderto investigatetheanisotropicpropertiesofthestructuredclaygeneratedby anisotropiccompression.Inonesetofthesetests,isotropicsampleswere created.Three of these tests were chosen for prediction.Because at this stage ofdevelopmenttheproposedmodelonlytakesaccountoftheisotropic propertiesofasoilwithandwithoutstructure,itwouldnotbemeaningfulto examinetheperformanceofthemodelindescribingtheanisotropicbehaviour of soil.ThethreeidenticalsampleswereloadedisotropicallyfromstressstateA (Fig. 14) with p = 25 kPa and ei = 3.5 to state B with p = 300 kPa.They were unloadedisotropicallytostateCwithp = 140 kPa.Subsequently,thefirst samplewasloadedagainisotropically.Thesecondsamplewasshearedwith constantmeaneffectivestresstoastateDwithp = 140 kPaandq = 75 kPa.This sample was then loaded at constant , i.e., = 0.5.The third sample was shearedwithconstantmeaneffectivestresstoastateEwithp = 140 kPaand q = 140 kPa.This sample was then loaded at constant , i.e., = 1.The stress paths for the three tests are shown schematically in the inset to Fig. 14. Thesizeoftheinitialyieldsurface,identifiedfromtheisotropictest,is py,i = 212 kPa.The value ofpy,iforthis setoftests ismuchsmaller than that obtainedfromtheoedometertest,butitshouldbenotedthatthesamplesin A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 31 these two sets of tests were different.It was observed that the yield surface for the structuredclayafterthe initial virgin loading totheisotropicstress state B withp = 300 kPa,plussubsequentisotropicunloadingandreloadingalong stresspathBCB,is340 kPa,avaluelargerthanthemaximumyieldstressthe soilhaseverexperienced.Thisphenomenonhasbeenconfirmedby Burghignolietal(1998)asamaterialpropertyforthisartificiallystructured clayanditishighlylikelythatitisassociatedwiththedevelopmentofsoil structure during the duration of the test, perhaps due to the ageing effect of the cement.In the prediction, this development of soil structure was considered by choosing py,i = 340 kPa for the clay for reloading after point C. Thesimulationoftheisotropictestandthepredictionsforthetwotestswith constantshearstressratioareshowninFig.14.Itisseenthattheproposed modelgivesanapproximatebutreasonabledescriptionofthecompression behaviour of the artificially structured clay. Inthissection,descriptionsofhowthemodelwasemployedtosimulateand predictthecompressionbehaviourofstructuredsoilshavebeenpresented.Overall,itmaybeconcludedthattheproposedmodelprovidesagood qualitativedescriptionofthesoilbehaviour,butthequantitativedescriptionis onlyapproximate.Intheselectionofexperimentaldataformodelevaluation, onlytestsperformedonstructuredsoilwithisotropicmechanicalproperties wereselectedbecausethecurrentversionofthemodeldoesnotallowfor anisotropic behaviour of the soil. 6.3Behaviour of a natural calcarenite Results of the experimental work carried out by Lagioia and Nova (1995) on a naturalcalcarenitehavebeencomparedwiththemodelpredictionsand simulations.The naturalcalcarenitewas formedbymarinedeposition.It is a coarse-grainedmaterialwithahighdegreeofuniformityandcalcareousinter-particle cement.An isotropic compression test on the soil was used to identify A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 32 soil parameters and their values are listed in Table 5.The isotropic compression behaviour of the calcarenite and its simulation are shown in Fig. 15. Table 5Model parameters for a natural calcarenite Parameter***e*IC*b py,i (kPa) Value1.450.2080.01652.570.25303.332400 Thevaluesofparameterse*ICand*and*andbandpy,iwereobtained directly from the experimental data.The value of Poissons ratio was assumed.ThecriticalstatestrengthforthenaturalclacarenitewasreportedbyLagioia andNova(1995)as* = 1.45.Theinitialstateforthestructuredsoilis defined by p = 147 kPa and e = 1.148.Thus, the initial value of the additional voidsratiosustained bythe soil structure isfoundasei = 0.15.The valueof parameter was estimated using equation (34). By using the values of the model parameters listed in Table 5, the behaviour of thenaturalcalcareniteunderconventionaldrainedtriaxialtestswaspredicted.Thereareeighttestsintotalandthestresspathsforthepredictionsareas follows.Firstly,thesoilwasloadedorunloadedisotropicallyfromtheinitial isotropic state with p = 147 kPa and e = 1.148 to the chosen state, i.e., p = 25, 200, 400, 600, 900, 1,100, 2,000 and 3,500 kPa.The confining pressure 3 was thenkeptconstantandtheaxialloadingwasincreaseduntilfailureofthe sample was observed.The test results and the predictions are shown in Figs 16 to24.Forthetestwith3 = 3,500 kPa,theinitialstressstateismuchlarger thanthesizeoftheinitialstructuralyieldsurface.Accordingtotheproposed model,thestructureofthesoilat3 = 3,500 kPaisactuallycompletely destroyed since the soil has a very high destructuring index, i.e., b = 30.Thus, thesoilinthistestbehavesasareconstitutedmaterialthroughoutthistest.DestructuringofthissamplewasconfirmedbyLagioiaandNova(1995).Considering the wide range of initial stresses, it is seen that the proposed model A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 33 givesasuccessfulpredictionofthebehaviourofthisnaturalandhighly structured calcarenite. Simulationsofthebehaviourofthecalcarenitehavealsobeenmade,wherea partofthetestdatawasemployedtodeterminethemodelparameters.The valuesofthemodelparametersusedforthesimulations(asopposedto predictions)arelistedinTable6.ComparisonwithvalueslistedinTable5 revealsthatthevaluesforthefollowingparametersaredifferent:e*IC,*(or K*),*,andpy,i.Inthepreviouspredictionsthevaluesforparameters* andwereassumed.Inthesesimulations,thevaluefor*suggestedby Lagioia and Nova (1995) was adopted, while the value for was obtaining by curve fitting.In Table 6, a value of Youngs modulus E* is given, instead of a value for *.It was observed by Lagioia and Nova (1995) that the pre-yielding behaviourofthecalcarenite,althoughelastic,isnotlinearinthee-lnp coordinates.Hence,aconstantparameter*overthefullrangeofstress explored is inappropriate for this material, and so Lagioia and Nova suggested a constant Youngs modulus, i.e., E* = 76,923 kPa.Based on the definition of the Youngs modulus and that for parameter *, the following relationship between E* and * is obtained ( )( )** 2 1 1 3*Ep e +

.(35) Because the mean effective stress p generally varies during a test and E* is now consideredasamaterialconstant,*isactuallyavariable,ratherthana constant.However,thebasicequationsoftheproposedmodel,suchasthose givenbyequations(15),(23)and(24),werederivedbasedontheassumption that both the virgin yielding behaviour and the elastic behaviour of a soil under isotropicloadingarelinearinthee - lnpcoordinates.Therefore,inorderto employ the equations of the Structured Cam Claymodel for these simulations, differentvaluesoftheconstantparameterweredeterminedforeach A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 34 individualtest,accordingtoequation(35).Itisnecessarytomakesuchan approximation in order to retain use of this relatively simple constitutive model.Itisobviousthattheconstitutiveequationsoftheproposedmodelcanbe reformulated so that the linear elastic behaviour of soil in the e p space can be modelled accurately.A method for such formulation can be found from a paper byLiuandCarter(2001).Thereformulationisnotintroducedinthispaper. Theaboveapproximatemethodissuggestedinstead.Theideaforthis approximationiswidelyusedingeotechnicalengineering,andisconsistent with the method of stress path analysis (Lambe, 1964; Wood, 1984). In order to determine the constant value of * for a particular test, a particular value of p must be selected for substitution into equation (35).The value of the initialmeaneffectivestressisanobviousandalsothesimplestchoice.However,anaveragevalueofthemeaneffectivestressmaybemore appropriate,butthisselectionwouldcausedifficultyinmanyapplications because the stress paths of soil elements are usually not known a priori.In the simulations considered here, the stress paths of the tests are known.Hence, the average value of p for the stress path from the initial stress state to the state at the yield surface was used to compute * for each individual test. Arevisedvalueofparametere*ICwasdeterminedbasedonacomparison between the predictions and the experimental data in the e-lnp coordinates (Fig. 25).Itisseenthatthemeasuredfinalstateofthesoilduringmonotonic shearingdoesnotfallontothecriticalstatelinepredictedbythemodel,but rather falls onto a line below and parallel to the predicted critical state line.The difference between the two lines in the vertical direction can be measured from thefigureanditisfoundthate = 0.187.Therefore,thevaluefore*ICwas modified as e*IC = 2.57 - 0.187 = 2.383 for the simulations. Theinitialyieldsurfaceforthecalcareniteadoptedinthepredictionsisan ellipse with the aspect ratio being * and the size defined by py,i = 2,400 kPa, A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 35 as identified from the isotropic compression test.The actual initial yield points forthesoilmeasuredbyLagioiaandNova(1995)areshowninFig.26.Itis foundthattheinitialyieldpointsconstituteapproximatelyanellipse,withan aspect ratio being 1.12, different from that of the critical state strength.In the simulationsthelattervalueoftheaspectratiowasadoptedonlyfor determination of the initial yield points. Table 6Revised values of model parameters for a natural calcarenite Parameter** E* (kPa) e*IC*B py,i (kPa) Value1.450.20876,9232.3830.133032,400 kPa; the aspect ratio of the yield surface = 1.12. Comparisons between the theoretical simulations and the experimental data are also shown in Figs 16 to 24.The simulations are represented by broken lines.The range of the variation of the mean effective stress simulated for this series oftestsisfrom25 kPato3,500 kPaandthestructureofthesoilvariesfrom intacttocompletelydestructured.Itcanbeseenthatthebehaviourofthe naturalcalcarenitehasbeensimulatedsatisfactorilywithonesetofrevised modelparameters(giventhat*variesfromtesttotestwhileE*isheld constant). Aqualitativedifferenceisobservedbetweentheexperimentaldataandthe predictionsduringthesofteninganddestructuringofthecalcarenite(e.g.,see Figs 16, 17 and 18).It is observed in the experiments that after softening starts thestrengthofthecalcareniteimmediatelydropstoa verylowvalue, near the finalcriticalstatestrength.Afterthisreductionofthesoilstrengththe deviatoricstressandstrainrelationshipisbasicallyflat.AccordingtoLagioia andNovasexplanation(LagioiaandNova,1995),theimmediatedropofsoil strength is attributed to the fact that the structure of the calcarenite is not stable.LagioiaandNova(1995)explainedthatevenduringanisotropiccompression test the structure ofthis soil isremovedimmediatelyandcompletelywhenthe A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 36 soilisloadedtoavirginyieldstressstate.Theyobservedthatduring destructuring the mean effective stress was actually reduced by a small amount inthestrain-controlledtest.Thatistosay,thisparticularstructureofthe calcarenite cannot sustain the initial yield stress without destructuring when the soil is loaded to that stress state.However, for the shearing tests shown in Figs. 16and17and18,thedataindicatethatthecapacityofthestructuredsoilto sustain additional voids ratio is not diminished in step with the shear strength of thesoil.Itmayalsobeobservedthatthereisnogreatamountofvolumetric deformationduringthewholesofteningprocess.Whythecapacitytosustain additionalvoidsratioassociatedwithsoilstructuredoesnotdiminishinstep with the reduction in soil strength appears to need further investigation. In the predictions, destructuring occurs as the material softens.Because of the highlysensitivenatureofthesoilstructure,thedeformationofthesoilatthe beginning ofthe softeningisdominated bydestructuringand thedestructuring is completed within a small decrease of stress, or shrinkage of the yield surface.Consequently,itispredictedthatthereisbasicallyaflatdeviatoricstressand strain curve after the occurrence of softening.After the structure of the soil is removed,somesofteningcontinuesandthereductionofsoilstrengthfromthe peak strength to the critical state strength is achieved mainly during this period of deformation.The model predicts consistently that the additional voids ratio sustainedbysoilstructureisreducedtozeroinaccordancewiththe destructuring. Aconclusionmaybedrawnaboutthequalitativedifferencebetweenthe experimentaldataandthepredictionsofdestructuringduringsoftening.The proposed model is suitable to describe the destructuring of soil resulting from a variationofstress,butnottheinstabilityofsoilstructure,i.e.,catastrophic collapse of structure the moment the soil reaches a virgin yield stress state. The authorshavestudiedthedestructuringofoverfiftydifferentnaturallyand artificially structured soils from over a dozen of countries, and found almost all A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 37 thesoilstructuresarerelativelystableandarecapableofsustainingtheinitial yieldstressunderisotropicandone-dimensionalcompression(LiuandCarter 1999,2000;Liuetal.2000).Fromtheseobservationsitisdeducedthatthe mechanism of destructuring proposed in the model is valid for most soils found in situ. 6.4Behaviour of Corinth marl ResultsoftheexperimentalworkperformedbyAnagnostopoulosetal(1991) onanaturalCorinthmarlhavebeencomparedwiththemodelsimulations.Twosetsoftestswerereported:asetofthreeisotropiccompressiontestson bothnaturalandreconstitutedCorinthmarl,andaset offiveshearingtests on theintactandpartiallydestructuredsoil.Fromthefirstsetoftests,thesoil parameterse*IC,*,*,bandpy,ihavebeenidentified,andtheirvaluesare listed in Table 7.The measured and simulated behaviour of the soil in isotropic compressionisshowninFig.27.Twoisotropiccompressiontestson reconstitutedCorinthmarlarereported,andsomesmalldiscrepanciesonthe isotropiccompressionlineareobservedbetweenthetwotestsamples,which wereassumedtobeidentical.Formostnaturalsoils,i.e.,notartificially manufacturedsamples,somediscrepancyinthestressandstrainbehaviouris expectedduetomaterialvariance.Theisotropictestwhichgavethebetter simulationoftheshearingbehaviouroftheCorinthmarlwasselectedfor identifying the model parameters. Theinitialvalueoftheadditionalvoidsratio,i.e.,ei,wasfoundtobe0.102.The value of parameter was estimated based on equation (34).The value of Poissonsratiowasassumedas0.25.Thecriticalstatestrength*was determinedbasedonthesecondsetoftests,i.e.,thefinalstrengthofthesoil reachedundermonotonicshearing.Thevalueof*istheonlyparameter determinedfromthedatafromtheshearingtests.Thebehaviouroftheintact and partially destructured soil during conventional drained triaxial compression A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 38 tests was simulated, based on the values of model parameters listed in Table 7.Both the simulations and the experimental data are shown in Fig. 28. Table 7Model parameters for natural Corinth marl Parameter** * e*IC*b py,i (kPa) Value1.380.040.0080.7750.250.44.93,800 kPa For all five compression tests, the confining pressures were kept constant at 98, 294, 903, 1,500 and 4,000 kPa respectively, and the axial loading was increased untilthespecimensfailed.Theinitialstateofthesoilwasobtainedfromthe isotropictestreportedbyAnagnostopoulosetal(1991),asshowninFig.27, with p = 34.6 kPa and e = 0.585.The initial states of the specimens for the four testswerecalculated basedon theproposedmodel.Theyare:p = 98 kPaand e = 0.577,p = 294 kPaande = 0.568,p = 903 kPaande = 0.559, p = 1,500 kPaande = 0.555andp = 4,000 kPaande = 0.543.Forthefirst four tests, the initial stress state of the soil was within the initial structural yield surface,definedbypy,i = 3,800 kPa,andthereforethesoilsamplesforthese tests are assumed to be intact.For the fifth test, the initial stress state of the soil exceedstheinitialstructuralyieldsurfaceandthesoilsamplehasexperienced partialdestructuring.Itisseenthattheproposedmodelgivesareasonable representation of the behaviour of the highly structured, stiff Corinth marl. 6.5Behaviour of La Biche clayshale ResultsoftheexperimentalworkperformedbyWong(1980)onanatural clayshalehavebeencomparedwiththemodelsimulations.Theclayshale specimenswereobtainedbycoresampling.Thesoilisahighlyover-consolidated,compactedshale.Thewatercontentforthenaturalshalewas between11.5%and12.4%withanaveragewatercontentof12.1%.Three conventionaldrainedtriaxialtestsonthenaturalclayshaleweresimulatedin order to demonstrate the capability of the proposed model.The values of model A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 39 parametersemployedforthesimulationarelistedinTable8.Acomparison between the simulations and the experimental data is shown in Fig. 29.For all thetests,theconfiningpressureswerekeptconstantat50,250and500 kPa respectively. Table 8Model parameters for a natural clayshale Parameter** E* (kPa) e*IC*b py,i (kPa) Value1.450.0673,0000.6680.250.243,800 kPa Thevaluesofparameters*andpy,iandE*wereobtainedfromthe experimental data.It can be observed from Fig. 29(a), that the shear behaviour of the clayshale before the peak strength is reached is essentially independent of the initial confining pressure.Consequently, the behaviour of the soil before the peakstrengthcanbeinterpretedaselasticandtheelasticshearmodulusis constant.Thevalue ofPoissonsratiowasassumedto be0.25.Based onthe elastic shear modulus of the clayshale and the value of *, the Young modulus for the soil was found as E* = 73,000 kPa.The values of *, e*IC, b and were determined by best fitting. Theinitialwatercontentfortheclayshaleatp = 50 kPawasassumedtobe 12.1%,theaveragewatercontentofthesoilatnaturalstate,andsotheinitial sate is given by p = 50 kPa and e = 0.327.Thus the initial voids ratio sustained by the soil structure can be calculated as ei = 0.076.The initial states for the soilintheothertwotestswerecalculatedtobep = 250 kPa,e = 0.322,and p = 500 kPa, e = 0.317. As explained previously, adopting a constant value of E* overall implies a value of*thatvariesbetweentests.Thefollowingvalueswereusedhere: * = 0.005forthetestwith3 = 50 kPa,* = 0.012forthetestwith 3 = 250 kPa, and * = 0.02 for the test with 3 = 500 kPa. A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 40 It is seen from Fig. 29 that the proposed model has the capability of modelling thebehaviourofthisstructuredclayshale.Fortheclayshaleinthetestwith 3 = 500 kPa, the volumetric deformation remains compressive even though the shear strength of the soilsoftensfromapeak of 2,600 kPato 1,800 kPa.This typeofbehaviourhasbeenwidelyobservedinstructuredclaysandclayshales (e.g.,Bishopetal,1965;Lo,1972;Georgiannouetal,1993;Robinetetal, 1999; Carter et al, 2000). 7.Conclusion TheModifiedCamClaymodelhasbeengeneralisedsothattheisotropic variationofthemechanicalpropertiesresultingfromthepresenceofsoil structurecanbedescribed.Anewhierarchalmodel,referredtoasthe StructuredCamClaymodel,wasproposed.Besidestheoriginalfive parameters introduced in the Modified Cam Claymodel, three new parameters have been introduced.They are: b, the destructuring index, py,i, the size of the initialstructuralyieldsurface,and,aparameterdescribingtheeffectofsoil structureontheplasticflowrule.Valuesofthefirsttwoparameterscanbe determined from an isotropic compression test or an oedometer test.The third parametercanbedeterminedfromthevolumetricstrainanddeviatoricstrain curve obtained from a shearing test. Overall, the proposed model has been used to predict both the compression and shearingbehaviourofsixstructuredsoils.Thecomputationscoverawide rangeofstress,initialvoidsratioandsoilstructure,bothnaturallyand artificially formed.It has been demonstrated that the proposed model describes successfullymanyimportantfeaturesofthebehaviourofstructuredsoilsand hasimprovedsignificantlytheperformanceoftheModifiedCamClaymodel byquantifyingtheimportantinfluenceofsoilstructure.Inparticular,thefact thatthenewmodelisabletopredictsimultaneousmaterialsofteningand A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 41 compressivevolumetricstrainisconsideredtobeadistinctadvantageofthe new model over Modified Cam Clay. Because the Modified Cam Clay model is the basis of the new model, obviously thenewmodelissuitableonlyforthosesoilsforwhichthebehaviourofthe reconstitutedmaterialscanbedescribedadequatelybyModifiedCamClay.Anisotropic features of soil behaviour, either due to the reconstituted parent soil or due to the presence of soil structure, were not studied in this paper, but will be the topics of future research. Thispaperhasconcentratedonintroducingthenewmodelanditsbasic features, and therefore only the behaviour of soil under fully drained conditions hasbeenconsidered.Theauthorsalsoplanafutureinvestigationofthe performanceofthemodelforundrainedconditionsandasystematicstudyon theidentificationofmodelparametersfromtestscommonlycarriedoutby engineers in geotechnical practice. 8.Acknowledgements Someoftheworkdescribedhereformspartoftheresearchprogramofthe SpecialResearchCentreforOffshoreFoundationSystems,establishedand supported under the AustralianResearch CouncilsResearch CentresProgram.Inaddition,aLargeGrantfromtheAustralianResearchCouncilinpartial support of this work is also gratefully acknowledged. 9.References AnagnostopoulosA.G.,KalteziotisN.,TsiambaosG.K.,andKavvadasM.(1991), GeotechnicalpropertiesoftheCorinthCanalmarls,GeotechnicalandGeological Engineering, Vol. 9(1), pp.1-26. ArcesM.,NocillaN.,AversaS.andCiceroG.L.(1998),Geologicalandgeotechnical featuresoftheCalcarenitediMarsala,TheGeotechnicsofHardSoils-SoftRocks, Evangelista and Picarelli (eds), pp.15-25. BalasubramaniamA.S.andHwangZ.M.(1980),YieldingofweatheredBankokclay, Soils and Foundations, Vol. 20(2), pp.1-15. Been K. and Jefferies M. G. (1985), A state parameter for sands, Gotechnique, Vol. 35(1), pp.99-112. A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 42 BishopA.W.,WebbD.L.,andLewinP.I.(1965),UndisturbedsamplesofLondonclay fromtheAshfordCommonshaft:strength-effectivestressrelationship,Gotechnique, Vol. 15(1), pp.1-13. BrittoA.M.andGunnM.J.(1987),CriticalStateSoilMechanicsviaFiniteElements, Chichester: Ellis Horwood Ltd. BurlandJ.B.(1990),Onthecompressibilityandshearstrengthofnaturalsoils, Gotechnique, Vol. 40(3), pp.329-378. Burland J. B., Rampello S., Georgiannou V. N., and Calabresi G. (1996), A laboratory study of the strength of four stiff clays, Gotechnique, Vol. 46(3), pp.491-514. Burghignoli A., Milizaano S., and Soccodato F.M. (1998), Theeffect of bond degradation incementedclayeysoils,TheGeotechnicsofHardSoils-SoftRocks,Evangelistaand Picarelli (eds), pp.465-472. Carter J. P., Airey D. W. and Fahey M. (2000), A review of laboratory testing of calcareous soils, Engineering for Calcareous Sediments, Al-Shafei (ed), Vol. 2, pp.401-431. CotecchiaF.andChandlerR.J.(1997),Theinfluenceofstructureonthepre-failure behaviour of a natural clay, Gotechnique, Vol. 47(3), pp.523-544. CuccovilloT.andCoopM.R.(1999),Onthemechanicsofstructuredsands, Gotechnique, Vol. 49(6), pp.741-760. DafaliasY.F.(1987),Ananisotropiccriticalstateclayplasticitymodel,Proc.2ndInt. Conf.OnConstitutiveLawsforEngineeringMaterials,Tucson,Arizona,Vol.1,pp.513-521. GensA.andPottsD.M.(1988),Criticalstatemodelsincomputationalgeomechanics, Engineering Computation, Vol. 5, pp.178-197. Gens A. and Nova R. (1993), Conceptual bases for a constitutive model for bonded soils and weak rocks, Geotechnical Engineering of Hard Soils Soft Rocks, Anagnostopoulos et al (ed), Vol. 1, pp.485-494. Georgiannou V. N., Burland J. B., Hight D. W. (1993), The behaviour of two hard clays in direct shear, Geotechnical Engineering of Hard Soils Soft Rocks, Anagnostopoulos et al (ed), Vol. 1, pp.501-507. GrahamJ.andLiC.C.(1985),Comparisonofnaturalandremouldedplasticclay,J. Geotechnical Engineering, ASCE, Vol. 111(7), pp.865-881. IshiharaK.(1993),Liquefactionandflowfailureduringearthquakes,Gotechnique,Vol. 43(3), pp.351-415. JackyJ.(1944),Thecoefficientofearthpressureatrest,J.oftheSocietyofHungarian Engineers and Architects, Budapest, pp.355-358. KavvadasM.andAmorosiA.(2000),Aconstitutivemodelforstructuredsoils, Gotechnique, Vol. 50(3), pp.263-273. Lagioia R. and Nova R. (1995), An experimental and theoretical study of the behaviour of a calcarenite in triaxial compression, Gotechnique, Vol. 45(4), pp.633-648. LambeT.W.(1964),Methodofestimatingsettlement,J.GeotechnicalEngineering, ASCE, Vol. 90, pp.43-67. LeroueilS.andVaughanP.R.(1990),Thegeneralandcongruenteffectsofstructurein natural soils and weak rocks, Gotechnique, Vol. 40(3), pp.467-488. LiuM.D.andCarterJ.P.(1999),Virgincompressionofstructuredsoils,Gotechnique, Vol. 49(1), pp.43-57. LiuM.D.andCarterJ.P.(2000),Modellingthedestructuringofsoilsduringvirgin compression, Gotechnique, Vol. 50(4), pp.479-483. LiuM.D.,CarterJ.P.,DesaiC.S.andXuK.J.(2000),Analysisofthecompressionof structuredsoilsusingthedisturbedstateconcept,Int.J.forNumericalandAnalytical Methods in Geomechanics. Vol. 24, pp.723-735. LiuM.D.andCarterJ.P.(2001),Aconceptualframeworkformodellingthemechanical behaviourofstructuredsoils,ComputerMethodsandAdvancesinGeomechanics,edts Desai, Kundu, Harpalani, Contractor & Kemeny, Vol. 1, pp.347-354. A Structured Cam Clay ModelMarch 2002 Department of Civil Engineering Research Report No. R814 43 LiuM.D.andCarterJ.P.(2002),AstructuredCamClayModel,ResearchReport, University of Sydney. LoK.Y.(1972),Anapproachtotheproblemofprogressivefailure,Canadian Geotechnical. J., Vol. 9(4), pp.407-429. Muir-WoodD.(1990),SoilBehaviourandCriticalStateSoilMechanics,Cambridge University Press. NambiarM.R.M.,RaoG.V.,andGulhatiS.K.(1985),Thenatureandengineering behaviouroffine-grainedcarbonatesoilfromoffthewestcoastofIndia,Marine Geotechnology,Vol.6(2),pp.145-171.NovelloE.andJohnstonI.W.(1995),Geotechnical materials and the critical state, Gotechnique, Vol. 45(2), pp.223-235. NovelloE.andJohnstonI.W.(1995),Geotechnicalmaterialsandthecriticalstate, Gotechnique, Vol. 45(2), pp.223-235. OlsonR.E.(1962),Theshearstrengthpropertiesofcalciumillite,Gotechnique,Vol. 12(1), pp.23-43. Potts D. M. and Zdravkovic L. (1999), Finite Element Analysis in Geotechnical Engineering: Theory, London, Thomas Telford. Robinet J. C., Pakzad M., Jullien A., and Plas F. (1999), A general modelling of expansive and non-expansive clays, Int. J. Numerical and Analytical Method in Geomechanics, Vol. 23, pp.1319-1335. Roscoe K. H. and BurlandJ. B. (1968), On the generalised stress-strain behaviour of wet clay , Engineering Plasticity, Heyman and Leckie (ed), pp.535-609. Rouainia M. and Muir Wood D. (2000), A kinematic hardening model for natural clays with loss of structure, Gotechnique, Vol. 50(2), pp.153-164. SchofieldA.N.andWrothC.P.(1968),CriticalStateSoilMechanics,MacGraw-Hill, London. WalkerL.K.andRaymondG.P.(1969),Thepredictionofconsolidationratesina cemented clay, Canadian Geotechnical J., Vol. 6(4), pp.193-216. Wheeler S. J. (1997), A rotational hardening elasto-plastic model for clays, Proc. 14thInt. Conference Soil Mechanics and Foundation Engineering, Vol. 1, pp.431-434. WhittleA.J.(1993),Evaluationofaconstitutivemodelforoverconsolidatedclays, Gotechnique, Vol. 43(2), pp.289-314. WhittleA.J.andKavvadasM.J.(1994),FormulationofMIT-E3constitutivemodelfor overconsolidatedclays,JournalofGeotechnicalEngineering,ASCE,Vol.120(1),pp. 199-224. WongR.C.K.(1980),SwellingandsofteningbehaviourofLaBicheshale,Canadian Geotechnical J., Vol. 35, pp.206-221.Yong R. N. and Nagaraj T. S. (1977), Investigation of fabricandcompressibilityofasensitiveclay,Proc.Int.SymposiumonSoftClay,Asian Institute of Technology, pp.327-333. WoodD.M.(1984),Choiceofmodelsforgeotechnicalpredictions,Mechanicsof Engineering Materials, Desai & Gallagher (ed), pp.633-654. YuH.S.(1998),CASM:aunifiedstateparametermodelforclayandsand,Int.J. Numerical Analytical Method in Geomechanics, Vol. 22(8), pp.621-653. Fig. 1 Idealization of the isotropic compression behaviour of reconstituted and structured soilsqp'M*p'sFig. 2 The yield surface forstructured soilsMean effective stress lnp'Voids ratio eStructured soil:e= e * + eReconstituted soil: e * e * ee ei p'y,ip'Fig. 3 Compression behaviour of reconstituted clay based on Critical State Soil Mechanicsp'eIsotropic compression lineCompression line with constant e *ICe * p'= 1 kPa0.61.11.62.110 100 1000 10000Mean effective stress p'Voids ratio eFig. 4 Influence of parameter b on isotropic compression behaviourb =0b =0.25b =5b =2b =1b=0.5b =100b =10ICL*11.31.61.92.2100 1000Mean effective stress p'(kPa)Voids ratio eb =0b =0.25b =0.5b =1b =2b =5b =10b =100CSLp'qCSL3Stress path of the testsp'y,iFig. 5 Influence of destructuring index b on the shearing behaviour of soil in the e-p'space00.20.40 0.25 0.5 0.75Deviatoric strain dVolumetric strain v01002000 0.25 0.5Deviatoric strain dDeviatoric stress q (kPa)b =100b =10 b =5b =0.25b =0.5b =1b =2b =0b =0b =0.25b =0.5b =1b =2b =5b =100b =10(a) Stress and strain relationship0501001500 0.01 0.02Deviatoric strain dDeviatoric stress q (kPa) b =2b =5b =0b =0.25b =0.5b =1b =100b =1001002000 1 2 3Deviatoric strain dDeviatoric stress q (kPa)Fig. 6 Influence of destructuring index b on the shearing behaviour of soil (b) Deviatoric stress and strain relationship at different scalesFig. 7 Influence of the size of the initial yield surface on simulated soil behaviour 01503004506000 0.25 0.5Deviatoric strain dDeviatoric stress q (kPa)p'y,i=1000 kPap'y,i=500 kPap'y,i=334 kPap'y,i=150 kPap'y,i=100 kPap'y,i=200 kPa(a) Deviatoric stress and strain(b) Deviatoric and volumetric strains00.0250.050.0750 0.25 0.5Deviatoric strain dVolumetric strain vp'y,i=200 kPap'y,i=500 kPa p'y,i=100 kPap'y,i=150 kPap'y,i=334 kPap'y,i=1000 kPap'qCSLp'y,i=1000 kPa500 kPa334 kPaStress path of the tests200 kPa150 kPa0501001502000 0.2 0.4 0.6 0.8Deviatoric strain dDeviatoric stress q (kPa)00.10.20.30.40 0.2 0.4 0.6 0.8Deviatoric strain dVolumetric strain v ei=0 ei=0.25 ei=0.5 ei=0.75 ei=1 ei=0 ei=0.25 ei=0.5 ei=0.75 ei=1(b) Deviatoric and volumetric strainsFig. 8 The Influence of parameter on soil behaviour simulated(a) Deviatoric stress and strain0.71.11.51.910 100 1000 10000Vertical effective stress 'v (kPa)Voids ratio eFig. 9 Behaviour of Leda clay in an oedometer test (Test data after Yong ang Nagaraji, 1977)Fig. 10 Compression behaviour of Leda clay with different values of (Test data after Walker and Raymond, 1969)0.81.21.6210 100 1000Mean effective stress p'(kPa)Voids ratio e4=0 =0=0.63 =0.63=1 =179ICL* (estimated) =0 =0.63 =1ExperimentPrediction1.522.533.510 100 1000Mean effective stress p'(kPa)Voids ratio e1.41.92.42.93.43.910 100 1000Mean effective stress p'(kPa)Voids ratio e=0.16 =0.16=0.43 =0.43=0.6 =0.6=0.75 =0.75Fig. 11Isotropic compression behaviour of weathered Bankok clay (Test data after Balasubramanian and Hwang, 1980)ICL*(estimated)Fig. 12Compression behaviour of weathered Bankok clay (Test data after Balasubramanian and Hwang, 1980) =0.6 =0.75 =0.16 =0.43lnp'eComparison of soil initial states =0 =0.43, 0.6 0.75 =0.16Fig. 13 Oedometer tests on an artificially cemented clay (Test data after Burghignoli et al , 1998)1.62.12.63.13.610 100 1000Mean effective stress p'(kPa)Voids ratio e0123410 100 1000 10000Vertical effective stress 'v (kPa)Voids ratio eFig. 14 Compression behaviour of an artificially cemented clay (Test data after Burghignoli et al , 1998) =0 =0.5 =1ICL*(estimated)A BCDE =0 =0.5 =1p'qStress pathsFig. 15 Isotropic compression test on a calcarenite (Test data after Lagioia and Nova, 1995)0.750.951.15100 1000 10000Mean effective stress p'Voids ratio eExp. dataSimulationReconstituted soilStructured soil-0.2-0.100.10 0.1 0.2 0.3 0.4 0.5Deviatoric strain dVolumetric strain vExp. dataPredictionSimulationFig. 16 Shearing behaviour of a calcarenite at '3= 25 kPa (Test data after Lagioia and Nova, 1995)(b) Volumetric strain and deviatoric strain relationship0400800120016000 0.1 0.2 0.3 0.4 0.5Deviatoric strain dDeviatoric stress q (kPa)Exp. dataPredictionSimulation(a) Deviatoric stress and strain relationship-0.0500.050.10.150 0.1 0.2 0.3 0.4 0.5Deviatoric strain dVolumetric strain vExp. dataPredictionSimulationFig. 17 Shearing behaviour of a calcarenite at '3= 200 kPa (Test data after Lagioia and Nova, 1995)(b) Volumetric strain and deviatoric strain relationship05001000150020000 0.1 0.2 0.3 0.4 0.5Deviatoric strain dDeviatoric stress q (kPa)Exp. dataPredictionSimulation(a) Deviatoric stress and strain relationship00.050.10.150 0.25 0.5 0.75 1Deviatoric strain dVolumetric strain vExp. dataPredictionSimulationFig. 18 Shearing behaviour of a calcarenite at '3= 400 kPa (Test data after Lagioia and Nova, 1995)(b) Volumetric strain and deviatoric strain relationship0400800120016000 0.25 0.5 0.75Deviatoric strain dDeviatoric stress q (kPa)Exp. dataPredictionSimulation(a) Deviatoric stress and strain relationship00.050.10.150.20 0.1 0.2 0.3 0.4 0.5Deviatoric strain dVolumetric strain vExp. dataPredictionSimulationFig. 19 Shearing behaviour of a calcarenite at '3= 600 kPa (Test data after Lagioia and Nova, 1995)(b) Volumetric strain and deviatoric strain relationship05001000150020000 0.1 0.2 0.3 0.4 0.5Deviatoric strain dDeviatoric stress q (kPa)Exp. dataPredictionSimulation(a) Deviatoric stress and strain relationship00.050.10.150.20 0.1 0.2 0.3 0.4 0.5Deviatoric strain dVolumetric strain vExp. dataPredictionSimulation(b) Volumetric strain and deviatoric strain relationshipFig. 20 Shearing behaviour of a calcarenite at '3= 900 kPa (Test data after Lagioia and Nova, 1995)060012001800240030000 0.1 0.2 0.3 0.4 0.5Deviatroic strain dDeviatoric stress q (kPa)Exp. dataPredictionSimulation(a) Deviatoric stress and strain relationship00.050.10.150.20.250 0.1 0.2 0.3 0.4 0.5Deviatoric strain dVolumetric strain vExp. dataPredictionSimulation(b) Volumetric strain and deviatoric strain relationshipFig. 21 Shearing behaviour of a calcarenite at '3= 1100 kPa (Test data after Lagioia and Nova, 1995)08001600240032000 0.1 0.2 0.3 0.4 0.5Deviatoric strain dDeviatoric stress q (kPa)Exp. dataPredictionSimulation(a) Deviatoric stress and strain relationship00.050.10.150.20.250 0.1 0.2 0.3 0.4 0.5Deviatoric strain dVolumetric strain vExp. dataPredictionSimulationFig. 22 Shearing behaviour of a calcarenite at '3= 1300 kPa (Test data after Lagioia and Nova, 1995)(b) Volumetric strain and deviatoric strain relationship010002000300040000 0.1 0.2 0.3 0.4 0.5Deviatoric strain dDeviatoric stress q (kPa)Exp. dataPredictionSimulation(a) Deviatoric stress and strain relationship00.060.120.180.240.30 0.1 0.2 0.3 0.4 0.5Deviatoric strain dVolumetric strain vExp. dataPredictionSimulation(b) Volumetric strain and deviatoric strain relationshipFig. 23 Shearing behaviour of a calcarenite at '3= 2000 kPa (Test data after Lagioia and Nova, 1995)015003000450060000 0.1 0.2 0.3 0.4 0.5Deviatoric strain dDeviatoric stress q (kPa)Exp.dataPredictionSimulation(a) Deviatoric stress and strain relationship0300060009000120000 0.1 0.2 0.3 0.4 0.5Deviatoric strain dDeviatoric stress q (kPa)Exp. dataPredictionSimulation(a) Deviatoric stress and strain relationship00.050.10.150.20 0.1 0.2 0.3 0.4 0.5Deviatoric strain dVolumetric strain vExp. dataPredictionSimulationFig. 24 Shearing behaviour of a calcarenite at '3= 3500 kPa (Test data after Lagioia and Nova, 1995)(b) Volumetric strain and deviatoric strain relationship05001000150020000 500 1000 1500 2000 2500Mean effective stress p'(kPa)Deviatoric stress q (kPa)Aspect ratio = 1.12Aspect ratio =1.45Fig. 26 The initial yield points for a natural calcarenite (Test data after Lagioia and Nova, 1995)0.40.60.811.2100 1000 10000Mean effective stress p'(kPa)Voids ratio eICL200 kPa1100 kPa2000 kPa3500 kPaFig. 25 Stress paths in the e -lnp'space fortests on a natural calcarenite (Test data after Lagioia and Nova, 1995)CSL assumedCSL predictedICL*Prediction '3=2000kPa '3=3500kPaPrediction '3=200 kPa '3=11000kPaFig. 27 Isotropic compression behaviour of Corinth marl (Test data after Anagnostopoulos et al , 1991)0.450.50.550.610 100 1000 10000Mean effective stress p'(kPa)Voids ratio eData (structured)Data (reconstituted)Data (reconstituted)SimulationNatural Corinth marlReconstituted Corinth marlelastic behaviour(a)Deviatoric stress and strain relationship0250050007500100000 0.05 0.1 0.15 0.2Deviatoric strain dDeviatoric stress q (kPa) '3=294 kPa '3=1500 kPa '3=4000 kPa '3=903 kPa '3=98 kPa-0.0350.0050.0450.0850 0.05 0.1 0.15 0.2Deviatoric strain dVolumetric strain v(b)Volumetric and deviatoric strain relationshipFig. 28 Behaviour of natural Corinth marl (Test data after Anagnostopoulos et al , 1991) '3=98 kPa '3=294 kPa '3=903 kPa '3=1500 kPa '3=4000 kPa060012001800240030000 0.05 0.1 0.15 0.2Deviatoric strain dDeviatoric stress q (kPa)(a) Deviatoric stress and strain relationship '3=250 kPa '3=500 kPa '3=50 kPa-0.1-0.0500.050 0.05 0.1 0.15 0.2Deviatoric strain dVolumetric strain v(b) Volumetric strain and deviatoric strain relationshipFig. 29 Shearing behaviour of a clayshale (Test data after Wong, 1980) '3=50 kPa '3=250 kPa '3=500 kPa