DevelopmentandapplicationsofhypoplasticconstitutivemodelsAdissertationsubmittedforhabilitationDavidMasnDecember2009CharlesUniversityinPragueInstituteofHydrogeology,EngineeringGeologyandAppliedGeophysicsContents1 Introduction 32 Basichypoplasticmodel forclaysanditsevaluation 42.1 Ahypoplasticmodelforclays[21] . . . . . . . . . . . . . . . . . . . . . . . 42.2 Stateboundarysurface[28] . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Graphicalrepresentationofthemodel[9] . . . . . . . . . . . . . . . . . . . 72.4 Evaluationofpredictivecapabilitiesofthemodel . . . . . . . . . . . . . . . 82.4.1 Directionalresponse[31] . . . . . . . . . . . . . . . . . . . . . . . . . 82.4.2 Theinuenceofoverconsolidationratio[10] . . . . . . . . . . . . . . 102.5 Improvementforundrainedconditions[29]. . . . . . . . . . . . . . . . . . . 113 Modicationsofthemodeltopredictthebehaviourofnonstandardma-terials 133.1 Modelforstructured/cementedclays . . . . . . . . . . . . . . . . . . . . . . 133.1.1 Basicmodelforstructuredclays[22] . . . . . . . . . . . . . . . . . 133.1.2 Evaluationofthemodelforstructuredclays[24] . . . . . . . . . . . 143.1.3 Modelforthesmall-strainshearstinessbehaviour[45] . . . . . . . 153.2 Modelforunsaturatedsoils . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2.1 Hypoplasticmodel forthemechanical responseofunsaturatedsoils[30] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2.2 Modelforthehydraulicresponse[25] . . . . . . . . . . . . . . . . . . 203.3 Modelfordoubleporositymaterials[32] . . . . . . . . . . . . . . . . . . . . 224 Clayhypoplasticityinpractical applications 244.1 Finiteelementimplementationandthesoilmodels.infoproject[8] . . . . . . 244.2 Heathrowexpresstrialtunnel[23] . . . . . . . . . . . . . . . . . . . . . . . 251CONTENTS CONTENTS4.3 Dobrovskehotunnelandexploratoryadits[42] . . . . . . . . . . . . . . . . 274.4 ModellingNATMtunnelsin2D[43] . . . . . . . . . . . . . . . . . . . . . . 304.5 Embankmentsondoubleporositysoils[32] . . . . . . . . . . . . . . . . . . 315 Summaryandconclusions 342Chapter1IntroductionThis thesis is asummaryof the researchbythe author andcoworkers onhypoplasticconstitutive models, undertaken in the period between years 2004 and 2009. By the time theresearchstarted, hypoplasticitywasusedmainlyforpredictingthebehaviourofgranularmaterials, such as sands or gravels. The most notable model is the one by von Wolerdor[47], which may be seen as a basic outcome of the research work carried out at the UniversityinKarlsruheduring80sand90s. Inadditiontothemodelsforgranularsoils, severalmodications topredict the behaviour of ne grainedsoils were available [11, 33] andtheoretical aspects of hypoplasticity were understood into a great detail (see Niemunis [34]for asummary). Theauthor of this thesis proposedaconceptuallysimplehypoplasticmodelforclaysthatwasaimedtobeeasytouseinpracticalapplications. Insubsequentresearch, thepredictivecapabilitiesof themodel wereextendedtoanumberof dierentspecialmaterials. Themodelwasimplementedintoanumberofniteelementcodesandappliedforsolvingpracticalproblems.ThisHabilitationthesisissubdividedintotwomainparts. Therstisanoverviewpart,inwhichtheresearchisbrieyoutlinedintheformof shortsummarisingchapters. TheoverviewpartofthethesisisfollowedbyanAppendixpart,withfulltextsofselectedkeypublications. Notall papersdiscussedintheoverviewpartarepresentintheAppendixpart,however. TheoverviewpartoftheHabilitationthesisissubdividedintothreemainchapters. Chapter 2 describes the basic hypoplastic model for clays and its evaluation withrespect to experimental data. Chapter 3 presents modications of the model to predict thebehaviourofdierentspecialmaterials. Finally,severalexamplesoftheuseofthemodelinpracticalapplicationsaredescribedinChapter4.The research described in the thesis was carried out by the author himself [21, 22, 24, 25, 23],in cooperation with his colleagues and coworkers[28, 9, 31, 29, 30, 8] and,importantly,bytheMScandPhDstudentssupervisedorco-supervisedbytheauthor[10,45,32,42,43].EspeciallytheresearcheortbythePhDthestudentsfromourresearchgroupatCharlesUniversity, namely V. H ajek [10], J. Najser [32], T. Svoboda [42, 43], R. Suchomel [40] andJ. Trhlkova [45] is greatly appreciated. The research would not have started and continuedwithouthelpandsupportbyDr. JanBohacandProf. IvoHerle.3Chapter2Basichypoplasticmodelforclaysanditsevaluation2.1 Ahypoplasticmodelforclays[21]Development of a new constitutive model is described step-by-step in Reference [21]. First,shortcomings of the hypoplastic model for soils with low friction angles by Herle and Kolym-bas[11] areoutlined. Itisthenproposedtoimprovethismodel bytakingintoaccountgeneralisedhypoplasticityprinciplesbyNiemunis[34]. ThegeneralrateformulationoftheproposedmodelreadsT = fsL : D+fsfdND (2.1)whereT is an objective stress rate,D is the Eulers stretching tensor, L andN are fourth-andsecond-orderconstitutivetensors, fsandfdareso-calledbarotropyandpyknotropyfactorsrespectively. ThetensorNiscalculatedbyN = L :_Ymm_(2.2)Degreeof nonlinearityY andthetensormmaybeseenashypoplasticequivalentsof ayieldsurfaceandaowrule. Theparticularcomponentsofthemodel(namelyY , m,fs,fdandL)arederivedinsuchawaythatthemodelhasthefollowingproperties:1. Y ischosensuchthatthelimitstatelocusinthestressspace(denedbyT=0)corresponds with the formulation by Matsuoka-Nakai [20], with critical state frictionanglecasamodelparameter.2. mimpliesthatthecritical stateispredictedforT=0atthecritical statevoidratiothemodelpredictszerovolumetricstrains(tr D = 0).3. fsischosensuchthatforthegivenvalueoffdthemodelispositivelyhomogeneousofdegree1inT, i.e. soilbehaviourmaybenormalisedbythemeanstressp. Con-sequently, normal compressionlinesarelinearinthelnpvs. ln(1 + e)plane. The42.2.Stateboundarysurface[28] Chapter2.Clayhypoplasticityisotropicnormalcompressionlineisdenedbyln(1 +e) = N lnppr(2.3)with the reference stress pr= 1 kPa and parameters Nand that control its positionandslope,respectively.4. The pyknotropyfactor fdcontrols the inuence of overconsolidationratio. It isdenedinthewayensuringthatthecriticalstatelineinthelnpvs. ln(1 +e)spacereadsln(1 +e) = N ln2 lnppr(2.4)and the slope of the isotropic unloading line from the isotropic normally consolidatedstateisinthelnpvs. ln(1 +e)planedenedbytheparameter.5. Thehypoelastictensor Limplies that theshear stiness is controlledbythelastmodelparameter,r. Italsoensuresthatacorrectinitialshearstinessispredictedwhenthemodelisusedtogetherwiththeintergranularstrainconcept[36].Insummary, themodel requiresveconstitutiveparameters, namelyc, N, , andr. TheseparameterscorrespondtotheparametersoftheModiedCamclaymodel and,inprinciple,onlytwoexperimentsarerequiredfortheircalibrationanisotropicloadingandunloadingtestforN,andandatriaxialsheartestforcandr.Themodel isevaluatedwithrespecttoexperimental dataonLondonclay. Itisdemon-strated that although the proposed model requires smaller number of parameters than thereferencemodel,itspredictionsaremoreaccurate. MoredetailedevaluationofpredictivecapabilitiesofthemodelisgiveninSection2.4.2.2 Stateboundarysurface[28]Anatural componentof manyelasto-plasticmodelsisso-calledstateboundarysurface,ahypersurfaceinthestressvs. voidratiospacethatboundsall admissiblestates. Thissurface, experimentally well conrmed, is not incorporated explicitly in hypoplastic models.Thepredictionofthissurfacebytheproposedmodelhasbeenstudiedinref. [28].Thankstothefactthatforthegivenfdtheproposedmodelispositivelyhomogeneousofdegree 1 inT,its behaviour may be normalised by the Hvorslev equivalent pressure at theisotropicnormalcompressionlinepedenedbype= pr exp_N ln(1 +e)_(2.5)TakingintoaccountEq. (2.5),rateofthenormalisedstressTn= T/peisgivenbyTn=fspe(L : D+fdND) +Ttr Dpe(2.6)52.2.Stateboundarysurface[28] Chapter2.ClayhypoplasticityLimitsurfaceinthestressvs. voidratiospace,namedswept-out-memory(SOM)surface,denedbyTn=0, maybefoundbysolvingEq. (2.6)forunknownsDandfd. Asthemodelispositivelyhomogeneousofdegree1inD(i.e.,rateindependent), Dmaytakeanarbitrarypositivevalue, forsimplicity D=1. Itwasshownthatattheswept-out-memorysurfacethepyknotropyfactorfdreadsfd= fsA1: N1(2.7)withthecorrespondingdirectionofstretching

D = A1: NA1: N(2.8)wherethefourth-ordertensorAreadsA = fsL+1T1 (2.9)Eqs. (2.7-2.9)allowustoplottheshapeof theSOMsurface. Forreasonablevaluesofthematerial parameters(namely, asdiscussedin[28], for