土的本构模型

UniversityofArizona

DepartmentofCivilEngineering&EngineeringMechanics

CE544–SpecialTopicsinGeotechnicalEngineering

FIELDINSTRUMENTATIONANDMONITORING

Instructor:MuniramBudhu

Date:Apeil14,2003MBMarch10,2002ModelTworequirementsforagoodmodel1:Itmustaccuratelydescribealargeclassofobservationswithfewarbitrarilyelements.2:Itmustmakedefinitepredictionsabouttheresultsoffutureobservations.

(extractedfromStephenHawking‘Ábriefhistoryoftime,’BantamBooks)

MBMarch10,2002TypesofModels(CE544)ELASTICLINEARNON-LINEARPLASTICITYNON-LINEARCAM-CLAYFAMILYElasto-plasticMBMarch10,2002NON-LINEARITYGEOMETRIC–changeofshape,size,etc.MATERIAL–changeofpropertiesCAUSES:stressstate.Historyofloading,changeinstiffness,physicalconditions,insitustress,watercontent,voidsratioMBMarch10,2002ELASTICMODELSLINEAR–magnitudeofresponseproportionaltoexcitationNon-LINEAR–magnitudeofresponsenotproportionaltoexcitationstressstrainLinearNon-linearMBMarch10,2002CONSTITUTIVELAWSSETOFEQUATIONSTHATRELATESTRESSESTOSTRAINS.F(stress,stressrate,strain,strainrate)=0Homogeneityoftime.MBMarch10,2002CONSTITUTIVEEQUATIONSStiffnessmatrixCompliancematrixMBMarch10,2002ELASTICMODELSElasticmaterials:Stateofstressisafunctionofthecurrentstateofdeformation;nohistoryeffectsCauchy–stressisafunctionofstrain(infinitesimalstrain,firstorder)Green–basedonstrainenergyfunction(Hyper-elastic)MBMarch10,2002Hooke’slaw–simplecaseSimpleonedimensionalcase:E=Young’smodulus(Elasticmodulus)MBMarch10,2002Hooke’slaw–GeneralstateMBMarch10,2002ShearstressesandstrainsGistheshearmodulus.OnlyGorEanduarerequiredtosolvelinearelasticproblemsMBMarch10,2002TypicalvaluesofEandG*TheseareaveragesecantelasticmodulifordrainedconditionMBMarch10,2002PrincipalstressesMBMarch10,2002AXISMMETRICCONDITIONMBMarch10,2002PLANESTRAINCONDITIONMBMarch10,2002Hooke’slawusingstressinvariantspismeanstress,Kisbulkmodulus;theprimedenoteseffectiveMBMarch10,2002Constitutiveelasticmodel–stressinvariantsDecoupling-Meaneffectivestresscausesvolumetricstrain;deviatoricstress(shearstress)causesdeviatoricstrainMBMarch10,2002Lame’sconstantMBMarch10,2002Poisson’’sratioalsoThenMBMarch10,2002Green’selasticmodelTheworkdonebyexternalforcesinalteringtheconfigurationofabodyfromitsnaturalstateisequaltothesumofthekineticenergyandthestrainenergyStraintensor-symmetricalStraintensor––skewsymmetricalMBMarch10,2002ANISOTROPICELASTICITYAnisotropicmaterialshavedifferentelasticparametersindifferentdirections.Structuralanisotropyortransverseanisotropy–mannerinwhichsoilisdeposited.Stressinducedanisotropy–differencesinnormalstressesindifferentdirections.MBMarch10,2002Transverseanisotropy-mostprevalentinsoilsMBMarch10,2002ELASTICITYANDPLASTICITYTheoryofelasticity:uniqueness–behaviorofthematerialexpressedbyasetofequationsTheoryofplasticity:discontinuityinstress-strainrelationship(involvesdiscontinuitiesandinequalities);dealswithinitialstressproblems,stateofstructureatcollapse,atpost-yield.MBMarch10,2002THEORYOFPLASTICITYTOADEQUATELYDESCRIBETHEPLASTICDEFORMATIONOFSOILSTOUSERELATIONSHIPSDEVELOPEDTOPREDICTFAILURELOADSANDSETTLEMENT.MBMarch10,2002PLASTICRESPONSESstressstressstressstrainstrainstrainRigid–perfectlyplasticElastic-perfectlyplasticElastic-plasticstrainhardeningMBMarch10,2002FULLPLASTICSTATE(COLLAPSE)GuessaplasticcollapsemechanismForsmalldeformationofthismechanism,integratetheworkconsumedinplasticdeformationoverthewholebodyEquatethistotheworksuppliedtofindthecollapseload(ref:Calladine,C.R.“Engineeringplasticity”,PergamonPress,London)MBMarch10,2002PLASTICITYTHEOREMSLOWERBOUND–IFANYSTRESSDISTRIBUTIONTHROUGOUTTHESTRUCTURECANBEFOUNDWHICHISEVERYWHEREINEQUILIBRIUMINTERNALLYANDBALANCESCERTAINEXTERNALLOADSANDATTHESAMETIMEDOESNOTVIOLATETHEYIELDCONDITION,THESELOADSWILLBECARRIEDSAFELYBYTHESTRUCTURE.UPPERBOUND–IFANESTIMATEOFTHEPLASTICCOLLAPS