��Fundamentals of Soil Behavior��\63027_11a

CHAPTER11StrengthandDeformationBehavior11.1INTRODUCTIONInreality,theshearingresistanceofasoildependsonmanyfactors,andacompleteequationmightbeofAllaspectsofsoilstability—bearingcapacity,slopetheformstability,thesupportingcapacityofdeepfoundations,andpenetrationresistance,tonameafew—dependonShearingresistanceϭF(e,c,,,C,H,T,,˙,S)soilstrength.Thestress–deformationandstress–deformation–timebehaviorofsoilsareimportantin(11.3)anyproblemwheregroundmovementsareofinterest.Mostrelationshipsforthecharacterizationoftheinwhicheisthevoidratio,Cisthecomposition,Hstress–deformationandstrengthpropertiesofsoilsareisthestresshistory,Tisthetemperature,isthestrain,empiricalandbasedonphenomenologicaldescriptions˙isthestrainrate,andSisthestructure.Allparam-ofsoilbehavior.TheMohr–Coulombequationisbyetersintheseequationsmaynotbeindependent,andfarthemostwidelyusedforstrength.Itstatesthatthefunctionalformsofallofthemarenotknown.Consequently,theshearresistancevalues(includingcand)aredeterminedusingspecifiedtesttype(i.e.,ϭcϩtan(11.1)directshear,triaxialcompression,simpleshear),drain-ffffageconditions,rateofloading,rangeofconfiningϭϩffcfftan(11.2)pressures,andstresshistory.Asaresult,differentfric-tionanglesandcohesionvalueshavebeendefined,in-cludingparametersfortotalstress,effectivestress,whereffisshearstressatfailureonthefailureplane,drained,undrained,peakstrength,andresidualcisacohesionintercept,ffisthenormalstressonthestrength.Theshearresistancevaluesapplicableinfailureplane,andisafrictionangle.Equation(11.1)practicedependonfactorssuchaswhetherornottheappliesforffdefinedasatotalstress,andcandareproblemisoneofloadingorunloading,whetherornotreferredtoastotalstressCopyrightedparameters.Equation(11.2)short-termMaterialorlong-termstabilityisofinterest,andappliesforffdefinedasaneffectivestress,andcandstressorientations.areeffectivestressparameters.Astheshearresis-Emphasisinthischapterisonthefundamentalfac-tanceofsoiloriginatesmainlyfromactionsatinter-torscontrollingthestrengthandstress–deformationparticlecontacts,thesecondequationisthemorebehaviorofsoils.Followingareviewofthegeneralfundamental.characteristicsofstrengthanddeformation,somere-369Copyright©2005JohnWiley&SonsRetrievedfrom:www.knovel.com37011STRENGTHANDDEFORMATIONBEHAVIORϪϭϩlationshipsamongfabric,structure,andstrengthare(1ff3ff)(1ff3ff)sin(11.5)examined.Thefundamentalsofbonding,friction,par-ticulatebehavior,andcohesionaretreatedinsomede-wheretheprimesdesignateeffectivestressestailinordertorelatethemtosoilstrengthproperties.1ffand3ffarethemajorandminorprincipalMicromechanicalinteractionsofparticlesinanassem-effectivestressesatfailure,respectively.blageandtherelationshipsbetweeninterparticlefric-2.Thebasiccontributionstosoilstrengtharefric-tionandmacroscopicfrictionangleareexaminedfromtionalresistancebetweensoilparticlesincon-discreteparticlesimulations.Typicalvaluesofstrengthtactandinternalkinematicconstraintsofsoilparametersarelisted.Theconceptofyieldingisintro-particlesassociatedwithchangesinthesoilfab-duced,andthedeformationbehaviorinboththepre-ric.Themagnitudeofthesecontributionsde-yield(includingsmallstrainstiffness)andpost-yieldpendsontheeffectivestressandthevolumeregionsissummarized.Time-dependentdeformationschangetendenciesofthesoil.ForsuchmaterialsandagingeffectsarediscussedseparatelyinChapterthestress–straincurvefromashearingtestis12.ThedetailsofstrengthdeterminationbymeansoftypicallyoftheformshowninFig.11.1a.Thelaboratoryandinsitutestsandthedetailedconstitutivemaximumorpeakstrengthofasoil(pointb)modelingofsoildeformationandstrengthforuseinmaybegreaterthanthecriticalstatestrength,numericalanalysesareoutsidethescopeofthisbook.inwhichthesoildeformsundersustainedload-ingatconstantvolume(pointc).Forsomesoils,theparticlesalignalongalocalizedfailureplane11.2GENERALCHARACTERISTICSOFafterlargeshearstrainorsheardisplacement,STRENGTHANDDEFORMATIONandthestrengthdecreasesevenfurthertotheresidualstrength(pointd).ThecorrespondingStrengththreefailureenvelopescanbedefinedasshown1.IntheabsenceofchemicalcementationbetweeninFig.11.1b,withpeak,critical,andresidualgrains,thestrength(stressstateatfailureorthefrictionangles(orstates)asindicated.ultimatestressstate)ofsandandclayisap-3.Peakfailureenvelopesareusuallycurvedintheproximatedbyalinearrelationshipwithstress:mannershowninFig.4.16andschematicallyinFig.11.1b.Thisbehavioriscausedbydilatancyϭfffftan(11.4)suppressionandgraincrushingathigherstresses.Curvedfailureenvelopesarealsoob-orservedformanyclaysatresidualstate.WhenShearτSecantPeakStressStrengthEnvelopeorStressτ/σRatioPeakbShearTangentPeakCriticalstateStressτStrengthEnvelopeStrengthEnvelopeφPeakStrengthpeakcAtLargeStrainsφb,ccriticalstateCriticalStatebResidualStrengthEnvelopedcφResidualresidualdadStrainaaNormaleffectivestressσDenseorLooseorNormallyCopyrightedOverconsolidatedMaterialConsolidated(a)(b)Figure11.1Peak,critical,andresidualstrengthandassociatedfrictionangle:(a)atypicalstress–straincurveand(b)stressstates.Copyright©2005JohnWiley&SonsRetrievedfrom:www.knovel.comGENERALCHARACTERISTICSOFSTRENGTHANDDEFORMATION371expressedintermsoftheshearstrengthnor-4.Thepeakstrengthofcohesionlesssoilsisinflu-malizedbytheeffectivenormalstressasafunc-encedmostbydensity,effectiveconfiningtionofeffectivenormalstress,curvesofthepressures,testtype,andsamplepreparationtypeshowninFig.11.2fortwoclaysareob-methods.Fordensesand,thesecantpeakfric-tained.tionangle(pointbinFig.11.1b)consistsinpartCopyrightedMaterialFigure11.2Variationofresidualstrengthwithstresslevel(afterBishopetal.,1971):(a)BrownLondonclayand(b)Wealdclay.Copyright©2005JohnWiley&SonsRetrievedfrom:www.knovel.com37211STRENGTHANDDEFORMATIONBEHAVIORofinternalrollingandslidingfrictionbetweenresistancedependsonlyoncompositionandef-grainsandinpartofinterlockingofparticlesfectivestress.Thebasicconceptofthecritical(Taylor,1948).Theinterlockingnecessitatesstateisthatundersustaineduniformshearingateithervolumeexpansion(dilatancy)orgrainfailure,thereexistsauniquecombinationoffractureand/orcrushingifthereistobevoidratioe,meanpressurep,anddeviatordeformation.Forloosesand,thepeakfrictionstressq.1Thecriticalstatesofreconstitutedangle(pointbinFig.11.1b)normallycoincidesWealdclayandToyourasandareshowninFig.withthecritical-statefrictionangle(pointc),11.4.Thecriticalstatelineonthep–qplaneisandthereisnopeakinthestress–straincurve.linear,2whereasthatonane-lnp(ore-logp)5.Thepeakstrengthofsaturatedclayisinfluencedplanetendstobelinearforclaysandnonlinearmostbyoverconsolidationratio,drainagecon-forsands.ditions,effectiveconfiningpressures,original7.Atfailure,densesandsandheavilyoverconsol-structure,disturbance(whichcausesachangeinidatedclayshaveagreatervolumeafterdrainedeffectivestressandalossofcementation),andshearorahighereffectivestressafterundrainedcreepordeformationrateeffects.Overconsoli-shearthanatthestartofdeformation.Thisisdatedclaysusuallyhavehigherpeakstrengthatduetoitsdilativetendencyuponshearing.Atagiveneffectivestressthannormallyconsoli-failure,loosesandsandnormallyconsolidateddatedclays,asshowninFig.11.3.Thediffer-tomoderatelyoverconsolidatedclays(OCRupencesinstrengthresultfromboththedifferenttoabout4)haveasmallervolumeafterdrainedstresshistoriesandthedifferentwatercontentsshearoralowereffectivestressafterundrainedatpeak.Forcomparisonsatthesamewatercon-shearthantheyhadinitially.Thisisduetoitstentbutdifferenteffectivestress,asforpointscontractivetendencyuponshearing.AandA,theHvorslevstrengthparametersce8.Underfurtherdeformation,platyclayparticlesandeareobtained(Hvorslev,1937,1960).begintoalignalongthefailureplaneandtheFurtherdetailsaregiveninSection11.9.shearresistancemayfurtherdecreasefromthe6.Duringcriticalstatedeformationasoiliscom-criticalstatecondition.Theangleofshearre-pletelydestructured.AsillustratedinFig.11.1b,sistanceatthisconditioniscalledtheresidualthecriticalstatefrictionanglevaluesareinde-frictionangle,asillustratedinFig.11.1b.Thependentofstresshistoryandoriginalstructure;postpeakshearingdisplacementrequiredtoforagivensetoftestingconditionstheshearingcauseareductioninfrictionanglefromthecrit-icalstatevaluetotheresidualvaluevarieswiththesoiltype,normalstressontheshearplane,andtestconditions.Forexample,forshalemy-wNormallyConsolidatedlonite3incontactwithsmoothsteelorotherpol-ishedhardsurfaces,ashearingdisplacementofVirginCompressiononly1or2mmissufficienttogiveresidualstrength.4Forsoilagainstsoil,aslipalongtheVoidRatioeWaterContentAAeffRebound1ϭOverconsolidatedInthree-dimensionalstressspace(xyz,,,xy,yz,zx)ortheequivalentprincipalstresses(123,,),themeaneffectiveσσstressp,andthedeviatorstressqisdefinedasffeτϭϩϩϭϩϩp(xyz)/3(123)/3τPeakStrengthEnvelopeφqϭ(1/͙2)crit͙Ϫ222222ϩϪϩϪϩϩϩOverconsolidated(xy)(yz)(zx)6xyyzzx66φϭ͙͙Ϫ222ϩϪϩϪAe(1/2)(12)(23)(31)ShearStressCopyrightedAMaterialϾϭϭϩcHvorslevEnvelopeFortriaxialcompressioncondition(123),p(1eϭϪ2212)/3,qNormallyConsolidated2Thecriticalstatefailureslopeonp–qplaneisrelatedtofriction0σangle,asdescribedinSection11.10.ffσNormalEffectiveStress3Arockthathasundergonedifferentialmovementsathightemper-atureandpressureinwhichthemineralgrainsarecrushedagainstFigure11.3Effectofoverconsolidationoneffectivestressoneanother.Therockshowsaseriesoflaminationplanes.strengthenvelope.4D.U.Deere,personalcommunication(1974).Copyright©2005JohnWiley&SonsRetrievedfrom:www.knovel.comGENERALCHARACTERISTICSOFSTRENGTHANDDEFORMATION3735004CriticalStateLineCriticalStateLine40033002200Overconsolidated1100NormallyConsolidatedDeviatorStressq(kPa)DeviatorStressq(MPa)00010020030040050060001234MeanPressurep(kPa)MeanPressurep(MPa)(a-1)pversusq(b-1)pversusq0.7CriticalStateLineCriticalStateLineInitialState0.95IsotropicNormal0.6CompressionLine0.900.50.85VoidratioeVoidratioe0.800.4Overconsolidated0.750.3NormallyConsolidated1002003004005000.020.050.10.515MeanPressurep(kPa)MeanPressurep(MPa)(b-2)eversuslogp(a-2)eversuslnp(a)(b)Figure11.4Criticalstatesofclayandsand:(a)CriticalstateofWealdclayobtainedbydrainedtriaxialcompressiontestsofnormallyconsolidated(⅙)andoverconsolidated(●)specimens:(a-1)q–pplaneand(a-2)e–lnpplane(afterRoscoeetal.,1958).(b)CriticalstateofToyourasandobtainedbyundrainedtriaxialcompressiontestsoflooseanddensespecimensconsolidatedinitiallyatdifferenteffectivestresses,(b-1)q–pplaneand(b-2)e–logpplane(afterVerdugoandIshihara,1996).shearplaneofseveraltensofmillimetersmayoftwosamplesofthesamesoilatthesamevoidberequired,asshownbyFig.11.5.However,ratiobutwithdifferentfabricsareaccountablesignificantsofteningCopyrightedcanbecausedbystraininMaterialtermsofdifferenteffectivestressesasdis-localizationanddevelopmentofshearbands,cussedinChapter8.especiallyfordensesamplesunderlowconfine-10.Undrainedstrengthintriaxialcompressionmayment.differsignificantlyfromthestrengthintriaxial9.Strengthanisotropymayresultfrombothstressextension.However,theinfluenceoftypeoftestandfabricanisotropy.Intheabsenceofchemi-(triaxialcompressionversusextension)onthecalcementation,thedifferencesinthestrengtheffectivestressparameterscandisrelativelyCopyright©2005JohnWiley&SonsRetrievedfrom:www.knovel.com37411STRENGTHANDDEFORMATIONBEHAVIORFigure11.5Developmentofresidualstrengthwithincreasingsheardisplacement(afterBishopetal.,1971).small.Effectivestressfrictionanglesmeasuredinplanestrainaretypicallyabout10percentgreaterthanthosedeterminedbytriaxialcom-pression.11.Achangeintemperaturecauseseitherachangeinvoidratioorachangeineffectivestress(oracombinationofboth)insaturatedclay,asdis-cussedinChapter10.Thus,achangeintem-peraturecancauseastrengthincreaseorastrengthdecrease,dependingonthecircum-stances,asillustratedbyFig.11.6.ForthetestsonkaoliniteshowninFig.11.6,allsampleswerepreparedbyisotropictriaxialconsolidationat75F.Then,withnofurtherdrainageallowed,temperatureswereincreasedtothevaluesindi-cated,andthesamplesweretestedinuncon-finedcompression.Substantialreductionsinstrengthaccompaniedtheincreasesintemper-ature.Stress–StrainBehaviorCopyrightedMaterial1.Stress–strainbehaviorrangesfromverybrittleforsomequickclays,cementedsoils,heavilyoverconsolidatedclays,anddensesandstoduc-Figure11.6Effectoftemperatureonundrainedstrengthoftileforinsensitiveandremoldedclaysandloosekaoliniteinunconfinedcompression(afterSherifandBur-sands,asillustratedbyFig.11.7.Anincreaseinrous,1969).Copyright©2005JohnWiley&SonsRetrievedfrom:www.knovel.comGENERALCHARACTERISTICSOFSTRENGTHANDDEFORMATION375(a)TypicalStrainRangesintheFieldRetainingWallsFoundationsTunnelsGorELinearElasticNonlinearElasticStiffnessPreyieldPlasticFullPlastic10-410-310-210-1100101Figure11.7Typesofstress–strainbehavior.Strain%DynamicMethodsLocalGaugesconfiningpressurecausesanincreaseinthede-ConventionalSoilTestingformationmodulusaswellasanincreaseinstrength,asshownbyFig.11.8.(b)TypicalStrainRangesforLaboratoryTests2.Stress–strainrelationshipsareusuallynonlin-Figure11.9Stiffnessdegradationcurve:stiffnessplottedear;soilstiffness(oftenexpressedintermsofagainstlogarithmofstrains.Alsoshownare(a)thestraintangentorsecantmodulus)generallydecreaseslevelsobservedduringconstructionoftypicalgeotechnicalwithincreasingshearstrainorstressleveluptostructures(afterMair,1993)and(b)thestrainlevelsthatcanpeakfailurestress.Figure11.9showsatypicalbemeasuredbyvarioustechniques(afterAtkinson,2000).stiffnessdegradationcurve,intermsofshearmodulusGandYoung’smodulusE,alongwithtypicalstrainlevelsdevelopedingeotechnicalconstruction(Mair,1993)andasassociatedwithfourzones:(1)linearelasticzone,(2)nonlineardifferentlaboratorytestingtechniquesusedtoelasticzone,(3)pre-yieldplasticzone,and(4)measurethestiffness(Atkinson,2000).Forex-fullplasticzone.ample,Fig.11.10showsthestiffnessdegrada-3.Inthelinearelasticzone,soilparticlesdonottionofsandsandclaysubjectedtoincreaseinsliderelativetoeachotherunderasmallstressshearstrain.AsillustratedinFig.11.9,thestiff-increment,andthestiffnessisatitsmaximum.nessdegradationcurvecanbeseparatedintoThesoilstiffnessdependsoncontactinterac-tions,particlepackingarrangement,andelasticstiffnessofthesolids.Lowstrainstiffnessval-uescanbedeterminedusingelasticwaveveloc-itymeasurements,resonantcolumntesting,orlocalstraintransducermeasurements.Themag-nitudesofthesmallstrainshearmodulus(Gmax)andYoung’smodulus(Emax)dependonappliedconfiningpressureandthepackingconditionsofsoilparticles.Thefollowingempiricalequa-tionsareoftenemployedtoexpressthesede-pendencies:ϭnGGmaxAFGG(e)p(11.6)EϭAF(e)nE(11.7)CopyrightedMateriali(max)EEiwhereFG(e)andFE(e)arefunctionsofvoidratio,pisthemeaneffectiveconfiningpres-Figure11.8Effectofconfiningpressureontheconsoli-sure,iistheeffectivestressintheidirection,dated-drainedstress–strainbehaviorofsoils.andtheotherparametersarematerialconstants.Copyright©2005JohnWiley&SonsRetrievedfrom:www.knovel.com37611STRENGTHANDDEFORMATIONBEHAVIORConfiningTCPSCPressureConfiningPressures140ToyouraSand78.4kPa12049kPaσTicinoSandc=400kPa(MPa)120(MPa)GG100σ100c=200kPa8080σc=100kPa6060σ4040c=30kPa2020SecantShearModulusSecantShearModulus10-410-310-210-110010-510-410-310-210-1100ShearStrain(%)ShearStrain(%)(a)(b)Figure11.10Stiffnessdegradationcurveatdifferentconfiningpressures:(a)ToyouraandTicinosands(TC:triaxialcompressiontests,PSC:plainstraincompressiontests)(afterTatsuokaetal.,1997)and(b)reconstitutedKaolinclay(afterSogaetal.,1996).Figure11.11showsexamplesofthefittingofplasticsoilsatlowconfiningpressureconditionstheaboveequationstoexperimentaldata.togreaterthan5ϫ10Ϫ2percentathighconfin-4.Thestiffnessbeginstodecreasefromthelinearingpressureorinsoilswithhighplasticity(San-elasticvalueastheappliedstrainsorstressestamarinaetal.,2001).increase,andthedeformationmovesintothe5.Irrecoverablestrainsdevelopinthepre-yieldnonlinearelasticzone.However,acompletecy-plasticzone.Theinitiationofplasticstrainscancleofloading,unloading,andreloadingwithinbedeterminedbyexaminingtheonsetofper-thiszoneshowsfullrecoveryofstrains.Themanentvolumetricstrainindrainedconditionsstrainattheonsetofthenonlinearelasticzoneorresidualexcessporepressuresinundrainedrangesfromlessthan5ϫ10Ϫ4percentfornon-conditionsafterunloading.Availableexperi-Ateachverticaleffectivestress,UndisturbedσЈhorizontaleffectivestressh(kPa)104Remoldedwasvariedbetween98kPaandRemoldedwithCaCO3500196kPaMPan=0.13103G450maxG)(MPa)400n=0.49eE102n=0.65(GE350n=0.63/FGx1ma10v300EShearModulus,100VerticalYoung'sModulus250100101102103104100150200250300Confiningpressure,pЈ(kPa)VerticalEffectiveStress,σЈ(kPa)CopyrightedMaterialv(a)(b)Figure11.11Smallstrainstiffnessversusconfiningpressure:(a)ShearmodulusGmaxofcementedsiltysandmeasuredbyresonantcolumntests(fromStokoeetal.1995)and(b)verticalYoung’smodulusofsandsmeasuredbytriaxialtests(afterTatsuokaandKohata,1995).Copyright©2005JohnWiley&SonsRetrievedfrom:www.knovel.comGENERALCHARACTERISTICSOFSTRENGTHANDDEFORMATION377mentaldatasuggestthatthestrainlevelthatin-changeswhendrainageisallowedorchangesinitiatesplasticstrainsrangesbetween7ϫ10Ϫ3porewaterpressureandeffectivestresswhenand7ϫ10Ϫ2percent,withthelowerlimitfordrainageisprevented.ThegeneralnatureofthisuncementednormallyconsolidatedsandsandbehaviorisshowninFigs.11.13aand11.13btheupperlimitforhighplasticityclaysandce-fordrainedandundrainedconditions,respec-mentedsands.tively.Thevolumeandporewaterpressure6.Adistinctivekinkinthestress–strainrelation-changesdependoninteractionsbetweenfabricshipdefinesyielding,beyondwhichfullplasticandstressstateandtheeasewithwhichshearstrainsaregenerated.Alocusofstressstatesdeformationscandevelopwithoutoverallthatinitiateyieldingdefinestheyieldenvelope.changesinvolumeortransferofnormalstressTypicalyieldenvelopesforsandandnaturalfromthesoilstructuretotheporewater.clayareshowninFig.11.12.Theyieldenvelope8.Thestress–strainrelationofclaysdependsexpands,shrinks,androtatesasplasticstrainslargelyonoverconsolidationratio,effectivedevelop.Itisusuallyconsideredthatexpansionconfiningpressures,anddrainageconditions.isrelatedtoplasticvolumetricstrains;thesur-Figure11.14showstriaxialcompressionbehav-faceexpandswhenthesoilcompressesandiorofclayspecimensthatarefirstnormallycon-shrinkswhenthesoildilates.Thetwoinneren-solidatedandthenisotropicallyunloadedtovelopesshowninFig.11.12bdefinethebound-differentoverconsolidationratiosbeforeshear-ariesbetweenlinearelastic,nonlinearelastic,ing.Thespecimensareconsolidatedatthesameandpre-yieldzones.Whenthestressstateconfiningpressurep0,buthavedifferentvoidmovesinthepre-yieldzone,theinnerenvelopesratiosduetothedifferentstresshistory(Fig.movewiththestressstate.Thismultienvelope11.14a).Drainedtestsonnormallyconsolidatedconceptallowsmodelingofcomplexdeforma-claysandlightlyoverconsolidatedclaysshowtionsobservedfordifferentstresspaths(Mroz,ductilebehaviorwithvolumecontraction(Fig.1967;Pre´vost,1977;DafaliasandHerrman,11.14b).Heavilyoverconsolidatedclaysexhibit1982;Atkinsonetal.,1990;Jardine,1992).astiffresponseinitiallyuntilthestressstate7.Plasticirrecoverablesheardeformationsofreachestheyieldenvelopegivingthepeaksaturatedsoilsareaccompaniedbyvolumestrengthandvolumedilation.ThestateoftheYieldStateInitialConditionPre-yieldStateσЈσЈσЈσЈq=a-rYieldStateq=a-rInitialStateSurroundedbyMPaLinearElasticBoundaryStressPathMPa0.8FailureLine0.6YieldEnvelopeYieldEnvelope0.60.40.4PreyieldBoundary0.20.2LinearElasticMPaBoundaryMPa0.00.00.20.40.60.81.00.20.40.6p=(σa+2σr)/3p=(σa+2σr)/3-0.2-0.2-0.4CopyrightedFailureLineMaterial(a)(b)Figure11.12Yieldenvelopes:(a)Aoisand(Yasufukuetal.,1991)and(b)Bothkennarclay(fromSmithetal.,1992).Copyright©2005JohnWiley&SonsRetrievedfrom:www.knovel.com37811STRENGTHANDDEFORMATIONBEHAVIORSameInitialConfiningPressureSameInitialConfiningPressureDenseSoilCriticalStateDenseSoilMetastableFabricDeviatorDeviatorCavitationStressStressCriticalStateLooseSoilLooseSoilCriticalStateMetastableFabricAxialorDeviatorStrainAxialorDeviatorStrainDenseSoilDenseSoilΔΔCavitation+V/V0-u00LooseSoilLoosesoilΔΔ-V/V0+uMetastableFabricMetastableFabric(a)(b)Figure11.13Volumeandporepressurechangesduringshear:(a)drainedconditionsand(b)undrainedconditions.3HeavilyOverconsolidated3HeavilyOverconsolidatedInitialStateDeviatorDeviatorFailureatCriticalStateStress2LightlyStressU3(D:Dr