工程土的本构关系讲义讲稿

AdvancedsoilmechanicsConstitutivelawofsoilMicrostructureofsoilStrengthofsoilConsolidationandrheologySlopestabilityConstitutiveLawofSoilYinZong-ze1.AboutStress-strainRelationship(1)Whatisconstitutivelaw?Stress-strainrelationshipStress-strain-strengthrelationshipStress-strain-timerelationshipStress-strain-temperaturerelationshipstrainstressstrength(2)Conventionalcomputationofstress-strainrelationshipofsoilsSimplestressconditionSettlementofbuilding——onedimensionalproblemConfinedcompressiontest,(oedometertest)pshepaCoefficientofcompressionlinearnonlineareepCompressionindexComplicatedstressstateEarthdam,undergroundstructure,harbor,excavation,etc.ExtensiveHooke’slaw（linearassumption）expandcompress(3)Stress-straintestsConventionaltriaxialtestFirst—cellpressureThen—deviatorstressStraincomponentspistonorganicglassbasecylindricalcellrubbermembranecapthroughwatertoapplythroughpistontoapplyPlanestraintestSampleisenclosedinarubbermembrane,andisputinthecylindricalcell.Cellpressure——Axialstress——Dike,dam,retainingwall,nodeformationinlongitudinaldirection—TruetriaxialtestApplyMeasureHollowedtorsionalsheartestMTakehalfofringasisolatebody----fromMd1d22.DeformationCharacteristicsofSoils(1)Non-linearandnon-elasticmetalsoilPlasticstrain——irrecoverablestrain,duetoadjustmentofpositionofgrains.Oneparticlemayslipoveranotherparticle,maydropintoporespace,andtherelativepositionbetweenthetwoparticlescannotberecovered.Deformationcannotberecovered(2)Plasticvolumetricstrainmetal——noplasticvolumetricstrainsoil—obviousplasticvolumetricstraininducedbyploadingpunloadingMacroscopic—compressMicroscopic——slipbetweengrainsinducedbyShearstressPerformtriaxialtestwithp=constantincrease,butdecreasep=constantp=constantShearcompressionSheardilationp—averagenormalstress,orglobalstressSheardilationDilation———densesand,overconsolidatedclayCompression———loosesand,normalconsolidatedclaySheardilativeShearcompressive(3)PlasticshearstrainExpressionofshearstrainShearstressandstrainonagivenplaneandComplicatestressstateOctahedralshearstressOctahedralnormalstressOctahedralshearstrainExtensiveshearstressExtensiveshearstrainIf,thenenergyofshapedeformationShearstraininducedbyglobalstresspTriaxialtestSimultaneouslyreduce,andkeepconstantq=constant,pdecreases.Mohrcirclegoesleft.WhentheMohrcircletangenttothefailureline,thedeviatorstrainisverylarge.Thedeviatorstrainisinducedbypchange.isduetoexistenceofinitialshearstress.Effectofintersectioninstress-strainmatrix—reflectsheardilation—reflectaveragenormalstressinducingshearstrainElasticmodel—=0=0Plasticmodelcanreflecttheseeffects(4)SofteningandhardeningSofteninghardeningdirectsheartesttriaxialsheartestresiduestrengthresiduestrength(5)influenceofstresspath&stresshistoryStressspace—thespaceconsistsofstresscomponentaxes·MPrincipalstressspacep—qplaneApointinstressspacerepresentsastressstateatapointinsoilbodypqFailurelineqf—pStresspath—thelocusofmovingpointinstressspace.Pointrepresentsstressstate.Stresspathrepresentsthevariationofstressstate,thatistheloadingmannerNMAstresspathconsistsofseveralsections.Eachsectionrepresentsaloadingincrement.thedirectionofthesectionreflectstheproportionofstresscomponents··StresspathinfluencesthestrainstatesignificantlyqpqfACBBC’C’CUn-draineddraineddrainedStresshistory—thestressstateinhistoryorthestresspathinhistoryPlasticstrainisirrecoverable.Thehistoricalstrainwasstoredandaccumulated.Stresshistoryinfluencestrain.Thesamestressstate,differentstraindifferentmodulus(6)InfluenceofmeannormalstressExpressionofvariationofmeannormalstressLodeparameterLodeangleM·plane·MXYOctahedralplaneInstressspaceIngeometryspaceInspaceParameterbStateb11000.5-1-0Influenceofmeannormalstressstrengthb—Triaxialtest,axialsymmetric,b=0,σ2=σ3a—Planestraintest,nostraininσ2direction,b=0.3~0.4,σ2>σ3abbaForthesameσ1andthesameσ3shapeofstress-straincurveb=0b=1.0b=0.5(7)Influenceofconsolidationstress(surroundingstress,confiningpressure)Strength···Largegrainisbrokenintosmallgrains1000.010.11100.001d（mm）p（%）BeforetestAftertestGradationcurveSheardilationInlowconfiningpressure,——sheardilationInhighconfiningpressure,——shearcompressionSoftening&hardeningInlowconfiningpressure,——softeningInhighconfiningpressure,——hardeninglowconfiningpressurehighconfiningpressure(8)AnisotropyvirginanisotropyanisotropyinducedbystresstransverseverticalsedimentationRemoldingsoil———isotropicRemoldingsoilappliedisotropicstresses——isotropicRemoldingsoilappliedanisotropicstresses——anisotropicundisturbedsoilABAB≠≠——unsymmetric——unsymmetricTruetriaxialtest——dilative——compressiveσ3=100kPa,σ2=150kPa

σ3=100kPa,σ2=200kPa

σ3=200kPa,σ2=300kPa

σ3=100kPa,σ2=250kPa

σ3=100kPa,σ2=300kPa

ε2(%)

ε1(%)

ε3(%)

ε1(%)

increaseΔε(％)Δ（σ1－σ3）（kPa）-3.00-2.00-1.000.001.002.0040.0080.00120.00160.00试验邓肯模型各向异性Δε1Δε2

Δε3Δε(％)Δσ2（kPa）200.00-1.000.001.002.000150.00试验邓肯模型Δε1Δε2

Δε3图2增增加σ1的试验结果和和邓肯模型与与各向异性模模型计算结果果图3增增加σ2的试验与邓肯肯模型计算结果果Δσ3（kPa）-0.4-0.20.00.0040.0080.00120.00Δε(％)试验邓肯模型Δε1Δε2

Δε3图4增增加σ3的试验与邓肯肯模型计算结果3.NonlinearelasticmodelExtensiveHooke’’slowSoftnessmatrixHardnessmatrixshearmodulusbulkmodulus,volumetricmodulusNonlinearelasticmodelDeterminationofparametersofHooke’slawUnconfinedcompressiontesttangentmodulussecantmodulusTriaxialtest-ControlstresspathtriaxialtestSolvesimultaneousequationstogetPlanestraintestDeterminationofK&G（2）HyperbolicmodelTangentYoung’smodulus················ab—theultimatedeviatorstressasymptoteofthecurve—deviatorstressatfailurecLetThen····n——atmosphericpressureS—stresslevel,reflectingmobilizedextentofstrengthTangentPoisson’sratio········AsymptoticvalueofInterpolatebetweenandlinearlywithstresslevelS····BulkmodulusK（B））=constant·····hyperbola～～Unloading&reloadingmodulusloadingreloadingunloading···CriterionofunloadingIntestsample,decreaseofInrealsoilmass,complicateUnloadingofconfiningstressUnconfinedcompression——maxinhistoryparameters——effectivestrengthparametersK——initialtangentmoduluswhen50～2000Kur———initialtangentmoduluswhen（1.2～～3.0））Kn——index,whichreflectsvariationofEiwith0～1.0Rf———failureratio0.5～0.95lessKn－smallerRfn－greaterF——parameterwhichreflectsvariationofwithG——initialtangentPoisson’sratiowhenD——inverseofasymptoteofofhyperboliccurve～0.2～0.60.0～0.250.0～20.0GDFDiscussionSuitability。Constantconfinedstress=constant。Straininducedonlybydeviatorstress。StraininducedonlybydeviatorstressMerits。beingabletoreflectmaindeformationcharacteristics:nonlinear,stresshistory,stresspath。simple,andeasytobeexceptedbyengineers。easytodetermineparameters,andengineershaveexperiencesforparametersShortcomings。cannotreflectsheardilation,softness,andanisotropy。hasnotgivetheparametersforconfinedstressreduction4.Elasto-plasticmodel——recoverablestrain,elastic——irrecoverablestrain,plasticPlasticstrain。failurecriterion,yieldcriterion。hardeninglaw。flueruleFailurecriterionelasticfailureFailuresurface——locusofthepointsinstressspacewhicharrivefailure（1）failurecriterion——failurefunctionvariablesarestresscomponentsTrascacriterionHexagonalcolumnSaturatedsoil,undrainedMisescriterionCircularcolumnsurfaceExtensiveMisescriterionDrucker-PragerGeotecnicalmaterial——firststressinvariant——seconddeviatorstressinvariantCircularconesurfaceCambridgeuniversityMohr-CoulombcriterionHexagonalconewithequaledgesbutunequalanglesMisesMohr-CoulunbTrascaLade-Duncancriterion（2）yieldcriterionsimplestresselasticplastic,yieldcomplicatestresselasticplastic,yieldtheoreticalmaterial,yield=failuregeotechnicalmaterial,yieldfailureConceptofyield—yieldfunction,correspondingtoyieldsurfaceinstressspaceyieldsurface—locusofthepointsinstressspacewhichreachyieldifkchanges,yieldsurfacemovesYieldsurfaceVariationofyieldsurfaceLoadingandunloadingCurrentstressstate—onyieldsurface,Anewstressincrementisapplied.*unloading*loading*neutralloadinglimitofelasticplasticelastic2vectorsmultiplyYieldsurfaceforgeo-materialIndependentoncoordinatesConetypeCaptype2yieldsurfacekincreases—hardeningkdecreases—softeningkconstant—theoretical（3）hardeninglawAfteryield,kchanges,H—hardeningparameter,aphysicalvariantwhichcourseskchangeForagivenvalueofH,yieldsurfaceisdefined.Howdoeskchange?Whichfactorcauseskchange?（4）flueruleHowtheplasticstraindevelopsamongthestraincomponents?Howtodeterminetheproportionofthestraincomponents?—plasticstrainincrementDirectionofdetermineseachcomponentoftheplasticstrainincrement.FluerulegivesdirectionofConceiveaplasticpotentialfunctionStrainspaceisoverlappedwithstressspace.PlasticstrainincrementisperpendiculartoplasticpotentialsurfaceAssociatedflueruleDrucker’spostulation—anelementexitsinitialstressstate,loadingslowly,andthenunloading,duringloading,workdonebyexternalagencyispositive.Andduringloadingandunloading,workdonebyexternalagencyisnotnegative.··Ifonyieldsurface,··derivation*Allthepointswhichrepresentthestressmustbeontheothersideoftheplaneperpendiculartoyieldsurfacefmustbeconvex.····ifconcave*isperpendiculartoyieldsurfacef··ifnot,Non-associatedfluerule·softening(5)Elasto-plasticMatrixElasticPlastic(a)(b)(c)softnessmatrix:(6)Cambridgemodel－－1.StateboundarysurfaceAnexampleofElasto-plasticmodelDrainedsheartestUndrainedshearteste~effectivestressp&qarethesameforbothdrainedandundrainedtests.q=0q=MpVirgincompressioncurvefailurecurve31,onyieldsurfaceNB,onstateboundarysurface（1）——q—reduce,p—constant,e—constant.ND—verticalline（2）——,onlypreducesBD,unloadingcurveongroundLineNBprojecttoq—pplane,yieldlocus;projecttoe—pplane,unloadingcurve.NB,intersectionlineofverticalcolumnsurfaceBDNandhorizontalsurfaceNN´B´BStateboundarysurfaceisthelocusofmovingcurveNB.VerticalcolumnsurfaceBDNiscalled‘elasticwall’.Onlyelasticdeformationinthewall.Gooverthetopofthewall—plasticdeformation.2.Mathexpressionofstateboundarysurface⑴N’B