經(jīng)典土力學教材DavidMuirWoodGeotechnicalmodellingandcriticalstatesoilmechanics

Geotechnicalmodellingandcriticalstatesoilmechanics

Naples,May2007DavidMuirWoodUniversityofBristol13.Designermodels:additionofextrafeatures(GM2,3,EM,GeoF)Designermodels:additionofextrafeatures

Kinematicyielding2.Camclay3.Mohr-Coulombshearstressmeanstresselastic-stiffplastic–lessstiffshearstressshearstrainclassicalelastic-plasticmodellingofsoilforexample,Camclay(1963,1968)stressyield?straintypicalactualresponsevoidratioverticalstress(logscale)preconsolidationpressureclassicalidentificationofyieldfromstress:strainresponsegeometricalconstructionforestimationofpreconsolidationpressureCamclayprovidinginspiration:searchfor‘Camclaylike’yieldlociegkaolin(Al-Tabbaa,1984)yieldlocifornaturalclayscollectedbyGrahametal(1988)typicalexperimentalobservation:

stiffnessfallssteadilywithmonotonicstraining:

isthereanelasticregion?shearstiffnessdegradationdataforQuiousandfromresonantcolumnandtorsionalsheartests(afterLoPrestietal,1997)limitofelasticresponse??howdoweobjectivelyidentifyyielding?

occurrenceofirrecoverablestrain?

dissipationofenergyinloading/unloadingcycles?

changeinslopeofstress:strainresponse?stressstraina.stressstrainb.yieldingofBothkennarclay:boundariesdeducedfrominspectionofstress:strainresponseY1approximatelycentredoninsitustressstateY3reflectsnaturalstructure–damagedbyanyirrecoverablestrain-evanescentafterSmithetal(1992)kaolinrevisited:

isotropicconsolidationhistoriesdatafromAl-Tabbaa(1987)kaolinrevisited:

one-dimensionalconsolidationhistoriesdatafromAl-Tabbaa(1987)qkPaqkPaqkPaqkPap'kPap'kPap'kPap'kPaplasticstrainincrements:approximatenormalitytokinematicyieldlocikaolin:

Al-Tabbaa,1987Deviatoricstressresponseenvelopesdistortionalstressproberosettesconstantmeanstresscrossanisotropy?Ev

>Ehεd=0.05,0.2,0.4,0.6,0.8,1,1.2%σxσyσzσxσyσzA:isotropiccompressionHostunsandSadek,2006distortionalprobingconstantmeanstressnon-monotonicstresspathsstressproberosettes

ABC…probeAB…probeσzσxσxσyσyσzSadek,2006distortionalstrain0.05%:historyrecalled1%:history‘forgotten’radialshearingABtwocornersABCStressresponseenvelopes:Hostunsand:small-mediumstrainεd=0.05,0.2,0.4,0.6,0.8,1,1.2%Sadek,2006comparisonof0.05%strainresponseenvelopesforhistoriesA,AB,ABC

stressresponseenvelopessmall/mediumstrainstiffnesskinematichardeningcentreasindicatorofcurrentfabric

butstraintoolargeSadek,2006Designermodels:additionofextrafeatures

Kinematicyielding2.Camclay3.Mohr-CoulombCamclayelastic-hardeningplasticmodelvolumetrichardeningassociatedflow–normalityCamclayresponseindrainedtriaxialcompressiontestswithconstantp'asymptoticapproachtocriticalstateeffectofoverconsolidationratiosharpdivisionbetweenelasticandplasticresponsecompareresponseofsoilonnonmonotonicloadingwithcapabilityofsingleyieldsurfacemodelextensiontosimplemodels

usingkinematichardeningandboundingsurfaceplasticitycompareresponseofsoilonnonmonotonicloadingwithcapabilityofsingleyieldsurfacemodelelastic-hardeningplasticmodelexpectselasticbehaviouronreversal,suddendropinstiffnessatyieldsoilstypicallyshowhystereticbehaviouronunload-reloadcycles,steadychangeinincrementalstiffnesskinematichardeningextensionyieldlocuscarriedaroundwithstressstate–'bubble'–stronglyinfluencedbyrecenthistorystiffnessfallsasyield'bubble'approachesboundingsurface–controlledbydistancebwhenloadingwith'bubble'incontactwithboundingsurfacemodelisidenticaltoCamclayassumerelativesizeRof'bubble'assumerulefortranslationof'bubble'assumeinterpolationrulelinkingplasticstiffnesswithb…otherwiseidenticaltoCamclaykaolinconstantp'cycleshysteresisbuildupofvolumetricstrainexperimentsimulationvolumetricstraindistortionalstrainηηηηmigrationof'bubble'duringconstantp'unloadingafterone-dimensionalnormalcompressionhardeningof'bubble'andboundingsurfaceqkPap'kPaexperimentsimulationconstantqcyclesafterone-dimensionalnormalcompressionaddfurthereffectsinasimilarlyhierarchicalwaycementationandstructure:extensionto'bubble'modelnaturalsoilsoftencontainstructure:bondingbetweenparticles:destroyedwithmechanicalorchemicaldamagedesignmodelinwhichyieldsurfacehasincreasedsizeasaresultofthebondingwithplasticstraining(orchemicalweathering)theyieldsurfacegraduallyshrinkstotheyieldsurface,forremoulded,structurelessmaterialextensionof'bubble'kinematicextensionofCamclayallfeaturesof'bubble'modelretainedratioofsizesofstructuresurfaceandreferencesurfacegivesindicationofcurrentdegreeofstructureaddmeasureofstructureorbonding:singlescalarparameterr'bounding'surfacenowcalled'structure'surface:sizertimeslargerthanareferencesurfacestructurelostwheneverplasticstrainsoccurdamagelaw:damageplasticstrainincrementδεdpcombinesplasticvolumetricandplasticdistortionalstrainincrements: –additionalparametertocontroltheirrelativeimportancestructureprogressivelydisappears:r

1asplasticdeformationincreaseslogical:structurelesssoilisonewhichhasbeensomechanicallypummelledthatithasnoremainingbondsbetweenparticlesparticularformsoflaboratorytesting(triaxialtesting,forexample)maynotbeabletoprovidesufficientdamageevolutionlawanddefinitionofdamagestrainmayneedtoincludesomemoresubtlereferencetothenatureofthestrainpathshearingwithrotationofprincipalaxesislikelytobeespeciallydamagingfeasibletointroduceotherevolutionlawswhichrelatechange(increaseordecrease)ofscalarmeasureofstructurertochemicalenvironmentortimeortemperatureeffectsCamclaycanberegainedbysettingr=1,R=1hierarchicalextensionof'bubble'modeltoincludeeffectsofstructureotherevolutionlaws:relatechange(increaseordecrease)ofscalarmeasureofstructurertochemicalenvironmentortimeortemperatureeffectsCamclaycanberegainedbysettingr=1,R=1Norrk?pingclay–calibrationtestsRouainia&MuirWood(2000)Norrk?pingclay–parametricvariationRouainia&MuirWood(2000)Norrk?pingclay–undrained–isotropicconsolidationRouainia&MuirWood(2000)Norrk?pingclay–undrained–anisotropicconsolidationRouainia&MuirWood(2000)Norrk?pingclay–undrained–isotropicoverconsolidationRouainia&MuirWood(2000)simulation

experimentBothkennarclayresultsnormalisedbyHvorslevequivalentconsolidationpressurep'eforstructurelesssoilGajo&MuirWood,2001HierarchicalextensionsofCamclayitisrelativelystraightforwardtoaddextrafeaturestoasoilmodeladvantageinusingwellknownmodelasbasis–checkimplementation–acceptabilityextrafeaturesimplyadditionalsoilparametersandadditionalcalibrationtestsseekadequatecomplexityinmodelling–matchcomplexityofmodeltoavailabilityofdataandneedsofapplicationDesignermodels:additionofextrafeatures

Kinematicyielding2.Camclay3.Mohr-Coulombstandardelastic-perfectlyplasticMohr-Coulombmodelnon-associatedplasticflowsimplicitysharpstiffnesschangestangentstiffnesseitherelasticorzerocontinuingvolumechangestandardelastic-perfectlyplasticMohr-Coulombmodelavailableinallnumericalanalysisprogramssubjectivityinselectingvaluesofsoilparameters–stiffness,strength,dilatancyelastic-hardeningplasticMohr-Coulombmodelnon-associatedflowsteadyfallinstiffnesscontinuingvolumechangeispost-peaksofteningimportant?designamodeltoincludesofteningMohr-Coulombfamilypost-peaksofteningtocriticalstatethreeregimesofresponseadaptationofhardeningMohr-Coulombmodelforη<ηpresponseiselastic:η<ηp,ηy=ηp

δεqp=0afterpeak,linearfallinyieldstressratiowithstrain0<εqp<b:(distortional'hardening'law)eventualperfectlyplasticcriticalstate:εqp

b,ηy=Mnon-associatedflowruleasbeforeconventionaltriaxialdrainedcompressiontestelasticpost-peaksofteningcriticalstatetriaxialundrainedcompressiontesteffectivestresspathelastic(isotropic:δp'=0)post-peaksofteningcriticalstatelimitedmodelconcentrationonsingleaspectofresponseMohr-CoulombmodelwithstrengthdependentonstatevariableSevern-TrentsandinfluenceofdensitysofteningdilatancysimplicitybuildonMohr-Coulombmodeldescribejourneyfrominitialelasticresponsetoultimatecriticalstateincludenonlinearity,peakstrengthandsofteningsimplicity?adequatecomplexity?Severn-TrentsandBeen&Jefferiesstateparameterψ=volumedistancefromcriticalstatelinefunctionofdensityandstresslevelmoreusefulthanvoidratioalone–indicatingeffectofdensityandstress

'dense''loose'ψcriticalstatelinemeanstressspecificvolumeSevern-Trentsand:strengthwhatispeakstrength?dataconfirmlinkbetweenstrengthandstateparameterψMohr-Coulombmodelwithcurrentstrengthdependentoncurrentstateparameter

Been&JefferiespeakstrengthSevern-Trentsand:strength'dense''loose'ψmeanstresscriticalstatelinespecificvolumestateparameterψwhatispeakstrength?propertyofthesoilwhichchangeswithstresslevel,densitydataconfirmlinkbetweenstrengthandstateparameterψMohr-Coulombmodelwithcurrentstrengthdependentoncurrentstateparameter

Been&JefferiespeakstrengthSevern-Trentsand:strength'dense''loose'ψmeanstressspecificvolumestateparameterψSevern-Trentsand:dilatancyBenahmeddilatancy:volumechangeduringshearing'dense'sandexpands'loose'sandcontractsdilatancydependsondensity

dilatancyvariesduringtestwhatdowemeanby

'dense'

and

'loose'?volumestrainshearstraindataconfirmlinkbetweendilatancyandstateparameterψifsoilisnotatcriticalstatewhenitisbeingsheared(ψ

0):thenvolumechangesoccurtowardsthecriticalstate:dilatancy'loose':ψ>0:contraction

'dense':ψ<0:dilation'loose''dense'stateparameterψBeen&Jefferiesdilatancy'dense''loose'ψcriticalstatelinemeanstressspecificvolumeSevern-Trentsand:dilatancymobilisedstrength'mobshearstraincurrentlymobilisedstrengthcurrentlyavailablestrengthmonotonicrelationship1ratioavailablestrength':varieswithstateparameterdistortionalhardeningmonotonicincreaseofratioofmobilisedtoavailablestrength(η/ηp)withdistortionalstrainεqphyperbolichardeninglaw:simpleMohr-Coulombmodelwithstrengthdependentonstatevariablevolumechangeaccompaniesshearinghencechangeinstatevariablehencechangeinavailablestrengthmodelautomaticallyhomesinoncriticalstatesofteningemergeswithoutbeingdescribedmathematicallypeakstrengthismovingtargetreachedatinfinitedistortionalstrain–thenidenticalwithcriticalstatestrengthconventionaldrainedtriaxialcompressiontestsdifferentinitialdensity(statevariable)currentpeakstrengthcharacterisationofvariationoftangentstiffnesssoilresponse

perfectlyplasticmodelnonlinearityandreversedplasticityobservedwhendirectionofloadingisreversedelastic-hardeningplasticmodel:behaviourpurelyelasticforstressratioslowerthanthepr