Abaqus之岩土专题讲座

IntroductionTestingRequirementsOverviewofConstitutiveModelsMohr-CoulombModel JointedMaterialModel InfiniteDomainsPoreFluidSurfaceInteractionsGeostaticStatesofStressElementAdditionandRemoval SaturatedProblems AppendixA AppendixBAnalysisofGeotechnicalTheinformationinthisdocumentissubjecttochaABAQUS,Inc.,assumesnoresponsiThesoftwaredescribedinthisdocumentisfurnonlyinaccordancewiththetermsofsuchlicense.NopartofthisdocumentmaybereproducedinanyformordistributedinaCopyright◎ABAQUS,Inc.,2003.ThefollowingaretrademarksofABAQUS,Inc.:Allotherbrandorproductnamesaretrademarksorregisteredtrademarksoftheirrespective•Lecture4:AnalysisofPorousMedia•AppendixB:BibliographyofGeotechnical•ClassicalandMod•SomeCasesforNumer3/033/03(finiteelement)analysisforgeotechnicalprLecture2dealswithexperimentaltestingancalibrationofconstitutivemodelsforgeotechnicalmaterialmaterialsarepresentedinLecture3.Theirusage,calibratioimplementation,andlimitationsareInLecture4weoutlinethetreatmentofporousmediainABdiscussthecouplingbetweenfluidfloSeveralmodelingissuesrelatin3/03IntheclassicalapproachtwobasictypesofcalculationestimatesanddeformFailureestimatesarebasedonrigidperfectlyplasticconstantshearstrengthatfailureconstantshearstrengthatfailureZeroelasticstrainsbeforefailureγSlopestabilityτ3/03BearingcapacityoffoundationRetainingwallstab(designcode).3/03properties:σσEεsettlement,w=pbf,pisbearingpressurebiswidthoffoundationfisshapefactor(basedonsmallscaletests)3/03Inthemodernapproach,failureandobtainedfromthesεε3ε1σ1-σ3andthenumericalsolutionofaboundaryvalueproblem.3/03PPuσVuσσσσσεεεεεNumerical(finiteelement)analysiscanhandlearbitrarygeometries.3/03Caseswhenselfweightofsoilplaysanimportantrole,suchasslopeWaccuratelybecausecollapsestressesonthefailureplaneareproptotheweightofthesoilandindependentofthedetailedsoilbehavior.Modernnumericalanalysisisnecessaryforcalculationofdeformations.3/03Caseswhendetailedsoilbbuildingofearthdamandsubsequentfillingofreservoir:reservoirreservoirfillupphrconstructionhamperfunctionalityofstructure.Thesequenceofevents(construction,fillingofreservoir,andlongtermconsolidation)mustbeconsideredusingnumericalanalysis.CaseswhentheinitialstateThevirginstateofstresscausedbytheweightofthesoilandtectonicsequenceoftheexcavationprocess.Itispossibletocontrolthestoftheexcavationbydesigningtheexcavausingaidssuchaslinersandrockbolts).3/033/03ConstitutivemodelSmallorlargescaletestiComparisonofmodelpredictio3/03Themeasurementsrequiredinthesimplelaboratorytestsdproposedconstitutivemodel.Theconbasedonsimpleexperimentalobservations.LaboratorytTheconstitutivemodelmusttocapturethemajorfeaturesofmaterialbehaviorwhileminorfeaturesmaybeignoredinthemodel.Calibration(orquantitativechoice)ofthemodelparametersfollows.Calibrationshouldnotavailable(andrepeThefiniteelementmodelmustcaptureimportantfeaturesofthephysicaliscriticalalthoughsimplificationsareoftenjustifiable.Smallorlargescaletestingusuallyrequiressomeknowledgephysicalbehaviorbeingmodeled.DetailsofthephysicaltestsandfiniteelementmodelsmustbecompatibleformeaningfUltimately,designrequiresengineeringjudgmentandagooddealof3/03Realisticconstitutivemodelsshouldhelpustotheunderstandingofthemicromechanicalbehaviorofthematerial,translatedtoamacromodelsimpleenoughtouseinnumercalculations,thuscreatingatoolforraRealisticconstitutivemodelsmustbethree-dimensionalanalyses).Realisticmodelsmustbebasedonexperimeasytoobtain.Theymustthencannotbereproducedwithlaboratorytest•TestingRequirements3/033/03Geotechnicalmaterialsaregenofthehydrostaticpressurestress,soitisimportanttotestthematerialsovertherangeofhydrostaticpressureofinterest.Mostlaboratorytestingfacilitiesarecapableofperformingstandard-Hydrostatic(orisotrop3/03ApracticalconstitutivemodelshouldrequireinformationgeneratedbythesestMoresophisticatedlaboratorytestscanlimitednumberoftestingfacilities.Trulytriaxialtestsrequirecubicaldevicesthatareveryexpendirecttensiletestisdifficulttoperformsinceitrequiresavery“stiff”machine(thesameappliestocompressiontestsinbrittlematerisoftensignificantlyincompression).models,assumptionsaremaderegardingthetensileaswelltriaxialbehaviorofthematerialbecausethetestsrequiredforcalibrationThediversityofgeotechnicalmaterialsmeansthatawiderangeofbehaviorsispossib3/033/03σ3=σ21σσ113/03221envelope__ε1+3/03((1eewhichcontinuedsheardeformationcanocceffectivestressandvolume(voidratio)ofthem3/03-Isotropiccompressiσσ13/033323hydrostaticstressxxxxxxxxxxxxxxxxxxxxxxdeviatoricstressdeviatoricplanexxxxxxx1xxsEssentialaspectsofbehaviorofvoidedfrictionalmaterials:+Nonlinearstress-strain+Influenceofhydrostaticpressurestresson“strength”+Influenceofhydrostaticpressureonstress-strainbehavior+Influenceofintermediateprincipalstresson“strength”+Influenceofhydrostaticpressurestressonvolumechanges+Hardening/softeningrelatedto+Effectsofsmall–Effectsoflargestressreversals(hysteres–Degradationofelasticstiffne–Notincludedinmostmodels3/033/03Basicrequirementsforlaboratorytestingofgeotechnicalmaterials:anaveragematerialbehaviorspecimens).rangeofstresses,drainageconditionsanddensityofthematerial(fordeepminingcasesthismaybedifficult).-Allstressesandstrainsmustbemestress-strainresponsetoallowcompletecharacterizationofthe3/03Laboratorytestingshouldbeguidedbyaconstitutivemodel.Understandingofthismodelisnecessaryforcorrectinterpretationoflaboratorytests.ModelparametersshouldbephysicalandmeasurableinpractThefollowingisalistoflaboratorytecomponentsoftheconstitutivemodelthattheyhelpcalibrate:-Isotropiccompressiontestoroedometertest.tocalibratehydrostaticbcalibratetheelasticpartofthisbehavior.requiredtocalibratetheshearbehavioranditpressuredependence.Oneunloading(ineachtest)isnecessarytocalibratetheelasticpartofthisbehavior.tocalibratetheintermediateprincipalstressdependenceofthe-Directtensiontest.Onetestisrequiredbehaviorofcohesivematerials(rocksorsoilswithcohesion).3/03-Trulytriaxial(cubical)t-Shearboxtestsandindirecttbeusefultocalibratethecohesivepropertiesofthematerial.-Multipleunloading-reloadingcyclesinanyofanecessarytocalibrateefhysteresisandelastic3/033/03Stressinthreedimensions:tσ11σ33y,σ11σ33σ22σ21σ23σ12σ32σ31σ13x,1z,3Symmetryofstresste3/03σσ1σ3σ2zero.3/03τ12)12)3/03σ=S–pI.pressurestress,ptrace 3/03tbatba1-sothatt=q/Kintriaxialtension(r=q)andt=qintriaxialcompression(r=–q).IfK=1,t=q.(t=constantisa“rounded”SS33/03σ3σ2=σ3σ2σ3σ2=σ3σ2σ1h3/03p3/03–Porous,isotropic(nonlinear)–Damaged,orthotropic(nonlinear;usedinconcrete,jointed–Opensurface,pressureindepend–Multisurface(jointedmate3/033/03–Continuumdamagetheories†–Endochronictheories†Noneoftheavailablemodels(withthepossibleexceptionofthejointedmaterialmodel)iscapableofaccuratelyhandlinglargestressreversals3/03plasticitymodelsdescribedinthefollowingPorouselasticityisanonlinear,isotropic,pressurestressvariesasanexponentialfunctionowhereJel–1isthenominalvolumetricstrain.3/03ThroughoutthesenotesJ=dV/dV°istheratioofcurrentvolumetoreferencevolume,soεvol=ln(J)andJ=exp(εvol),whereεvolisthelogarithmicmeasureofvolumetricstrain.ThismodelallowsazeroS=2Geel,dependentonthepredS=2deel,elpressurestress,ande0istheinitiel3/030__εelvolptpelεvolhasanarbitraryorigin,definedsothatp=p0elεvol3/03TheMohr-Coulombplasticitymodelisintendedformaterialssuchassoilsundermonotoniconsiderratedepende–Thereisaregimeofpurelylinearelasticresponse,afterwhichsomeofthematerialdefobeidealizedasbeingplastic.–Thematerialisinitiallyisotconsequencesofthisisthatthematerialbecomesstrongerasthe–Theyieldbehaviormaybeinfluencedbythemagnitudeofthe3/03–Thematerialmayhardenorsoftenisotropi–Theinelasticbehaviorwillgenerallybeaccompani–Theplasticflowpotentialissmoothan–Itdoesnotconsiderrate-dependentmaterial3/03LinearisotropicelasticitymustbeusedwiththeMoTheMohr-CoulombyieldfunctioF=Rmcq–ptanφ–c=0,plane,φistheslopeoftheMohr-Coulombyield3/03cisthecohesionofthematerial;andofthematerial’scohesion,c.Thecohesioncanbedefinedasafunctionofplasticstrain,temperature,orfieldvariables.3/03MohrMohr-CoulombφTrescacpDrucker-PragermeridionalstressplaneandthesmoothellipticfunctionproposedTheinitialcohesionofthematerial,c0=c(εpl=0.0);thedilation3/033/03potentialtendstoastraightlineimeridionaleccentricitytendstozero).dεplRmwq3/03.Thedeviatoriceccentricdeviatoricsectionintermsoftheratiobetweentheshearstressalongthemeridian(Θ=π/3).ThedefaultvalueofthedeviatoriceccentricityiscalculatedbythebehavioroftheclassicalMohr-Coulombmodelintriaxial3/03Mohr-CoulombmodelonlyintriaxPlasticflowinthedevia3/03The*ELASTIC,TYPE=IS–TheECCENTRICITYparameMohr-Coulombmodelonlyintriax3/03The*MOHR-COULOMBoptionmustalwaysbeaccompaniedby*MOHR-COULOMBHARDENINGmaterialoption,whereevolutionofthecohesion,c,oftheasafunctionoftemperatureandpredefinedfieldvariables.unsymmetricsolver(*STEP,UNSYMM=YES)materialhasMohr-Coulombplastic3/03plottedinthemeridionalplanetoprovideanestimateofthefrictiontheplasticdeformationmatchesthatseenexper–Ifthematerialisgoingtohardenthetriaxialtestsshouldbeusedtoprovidethehard3/03potential,itdoesnotalwaysprovidethesamclassical(associated)Mohr-potential.matchclassicalMohr-Coulombbehaviomodelforplanestraindeformat3/03Thissetofmodelsisintendedtosimulatematerialresponseunderessentiallymonotonicloading,Thebasiccharacteristicsofthissetofmodelsare:–Thereisaregimeofpurelyelasticresponse,afterwhichsomeofthematerialdeformationisnotrecoverable–Thematerialisinitiallyisotconsequencesofthisisthatthematerialbecomesstrongerastheconfiningpressureincreases.Thematerialmayharhydrostaticpressuredependenceisintrod3/03–Theinelasticbehaviorwillgenerallybeaccompani–Theyieldbehaviormaybeinfluencedbythemagnitudeofthe–Thematerialmaybesensitivetotherateofstraining.EitherlinearelasticityornonlineaElasticity(p.L3.12),canbeusedwiththesAchoiceofthreedifferentyieldcriteriaisprovidbasedontheshapeoftheyieldsurfaceinthemeridionalplane:alinearThechoiceofmodeltobeuseddependslargelyonthekindofmaterial,ontheexperimentaldataavailableforcalibratparameters,andontherangeofpressurestressvaluesthatthematerialis3/033/03TheyieldsurfaceofthelinearmodeliswrittenasF=t–ptanβ–d=0.Thecohesion,d,isredtanβ)σcifhardeningisdefinedbyuniaxialcompression,σc;dtifhardeningisdefinedbyuniaxialtension,σt;andd=difhardeningisdefinedbyshear(cohesion),d.asthe(isotropic)hardeningparameter,whichis3/03Themeasureofdeviatoricstress,t,allowsmatchingvaluesintensionandcompMohr-Coulombsurface.1-CurveK0.8ba3/03Weassumea(possibly)nonassociatedflowrule,wherethedirecdεpl=dεlinuniaxialcompression,dεpl=dεinuniaxialtension,anddplinpureshear.ψisthedilationangleinthep–tplane.Thisflowruledefinitionbealimitationforrealmateria3/03Flowisassociatedinthedeviatoricplanebutnonassociatedinthep–tβββdp3/03ThehyperbolicyieldcriterionisacontinuouscombinationofthemaximumtensilestressconditionofRankine(tensilecut-off)andthelinearDrucker-Pragerconditwhered,isthehardeningparameterthatisrelatedtothehardeningindtanβifhardeningisdefinedbyuniaxialdtanβifhardeningisdefinedbyuniaxialtension,σt;difhardeningisdefinedbyshear(cohesion),d.3/03l0=d,0–pt0sketch).pt0istheinitialhydrostatictensionstrengthofthematerial,d,0istheinitialvalueofd,,andβistpressure.3/03pKparameterisnotavailableforthismodel.)3/03Thegeneralexponentformprovidesthemosavailableinthisclassofmodels.TheyieldfunctF=aqb–p–pt=0,whereaandbarematerialparametersindependentodeformationandptisthehardeningparameterthatrepresentsthept=aifhardeningisdefinedbyuniaxialcompression,σc;pt=aifhardeningisdefinedbyuniaxialtension,σt;andpt=adbifhardeningisdefinedbyshear(cohesion),d.3/03ppKparameterisnotavailableforthismodel.)Thematerialparametersa,b,andptcanbewilldeterminethematerialparametersfromthetriaxialtestdatausingtendstozero).Thisflowpotential,whichiscontinuousandThefunctionapproachestheasymptoticallyathighconfiningpressurestressandpotentialfortheDrucker-Pragermodelsoverthewhichhasavertexonthehydrosta3/033/03q0p3/03Inthegeneralexponentmodelmeridionalplane.Thwiderangeofconfiningpressurestressvalues.Increasingthevalueoftheeccentricityprovidesmorecurvaturetotheflowpotential,implyingthatthedilationangleincreasesmtheconfiningpressuredecreases.Valuesoftheeccentricityldefaultvaluemayleadtoconvergenceproblemsifthematerialsubjectedtolowconfiningpressuresbecauseoftheverytightoftheflowpotentialnearitsintersectionwiththep-axis.3/03CRITERIONparameterissettoLINEAR,The*DRUCKERPRAGERopti*DRUCKERPRAGERHARDENINevolutionoftheyieldstressinuniaxialcompressionpureshear(TYPE=SHEAR).Itispossibletomaketheyieldfunctionratedependentfunctionoftheplasticstrainrate.Aratedependencyisrarelyusedforgeotechnicalmaterials,butthesesameyieldmodelintroducingratedependenc3/03Theelasticityisdefinedwiththe*ELASTICmateroflinearelasticityorwiththe*POROUSELASTICoptionifporousAllofthematerialparameterscanbeenteredasfunctionsoftemperaturevoidsratio(porosity)ofthematerialifporouselasticityisused.AnalysesusinganonassociatedflowversionofthemodelmayrequiretheuseoftheUNSYMM=YESparameteronthe*STEPoptionbecauseoftheresultingunsymmetricplasticityequations.IfUNSYMM=YESisnotusedwhenthefl3/03AtleasttwoexperimentsarerequiredtocalibratethesimplestversionoftheDrucker-Pragerplasticitymodel(linearmodel,rtemperatureindependent,andyieldingindependentofthethirdstressForgeotechnicalmaterialsthemostcommonexperimethispurposeareuniaxialcompression(forcohesiveTheuniaxialcompressiontworigidplatens.Theloadanddisplacementinthedirectionofloadingarerecorded.Thelateraldisplacementsshouldthecorrectvolumechangescanbe3/03thedirectionofloadingarerecorded,togetherwiththelateralstrain,sothatthecorrectvolumechangescanbecaliσ3ε33/03additionalcompressionstressissuperThetriaxialresultscan,thus,beplottedintheq–pplane.3/03stressatonsetofinelasticbehaviorortheultimateyieldstress)proonedatapointforcalibratingtheyieldsurfacemaofconfinement.Thesedatapointsdefinetheshapeandpositionoftheyieldsurfaceinthemeridionalppq3/03Definingtheshapeandpositionoftheyieldsurfaceisadequatetodefithemodelifitistobeusedasafailuresurface.Toincorporateisotropichardening,onethetriaxialtestscanbeusedthatrepresentshardeningmostaccuratelyoverawiderangeofloadingconditionsshouldbeselecUnloadingmeasurementsinthesetestsareusefultocalibratetheelasticity,particularlyincaFittingthebeststraightlinethroughtheresultsprovidestcqdt3/033/03TriaxialtensiontestdataarealsoneededtodefineK.Undertriaxialonedirectionisreduced.InthiscasetKcan,thus,befoundbyplottingthesetestresultsasqversuspandagainfittingthebeststraightline.TheratioofvaluesofqfortriaxialtensionandcompressionatthesamevalueofpthengivesK.Thedilationangleψmustthevolumechangesduringyieldingisobtaine3/03FittingthebeststraightlinethroughthetriaxialcompressionresuInaddition,hydrostatictensiondata,pt,arerequiredtocompletethed'd'__d'/tanβ__ptpb)Hyperbolic:F=√(d'|0__pt|0tanβ)2+q2__ptanβ__d'=0βq3/03a,b,andptrequiredfortheexponentmodelfromtriaxialdata,whisdoneonthebasisofa“bestfit”ofthetriaxialtestdataatdifferentlevelsofconfiningstresppq3/03Thedatapointsobtainedfromtriaxialtestsaresprequiredonthe*DRUCKERThecapabilityallowsallthreeoftheparametersareknown,tocalibrateonlytheunknownparameters.3/03parametersofthelinearDrucker-PragermodeltoprovideareasonablematchtotheMohr-Coulombpar3/03atfailureintheplaneofthemaximumandminimumprincipalstresses.__σ__σ3__σ3_σ1σ3_cφ_σ__σ1__σ12323/03ishalfofthedifferencebetweenthemaximumandminimumprincipalstresses(andis,thereistheaverageofthemaximumandminimumprincipalstresses.(p,q)planeinthelinearDrucker-Pragermodel.3/03ofthevalueoftheintermediateprincipalstress.TheDrucker-Pragermodeldoesnot.Thefailureoftypicalgranulargeotechnicalmaterialsgenerallyincludesonlysmalldependenceontheintermediatepristress,sotheMohr-Coulombmodelisgenerallymorere3/03PlanestrainproblemsareoftenencounteredinTherefore,theconstitutivemodelparamprovidethesameflowandK=1.Usingtheplanestrainconstraint,wecande =.3/033/03Thedifferencebetweenassuincreaseswiththefrictionangle,butfortypicalfrid/cd/c46.2°TheresultsobtainedforafoundationprobDrucker-Pragermatc(p.L6.3)ofthesenotes.3/03AnalternativeapproachtomatchinDrucker-Pragermodelparameterthesamefailuredefinitioninapproachyieldsthefollowin3/03ThevalueofKintheDrucker-PragermodelisrestrictedtoK≥0.778