Loading-Conditions-in-the-Brazilian-Test-Simulatio

1.INTRODUCTIONWhenexcavatingahardandhealthyrockmassinthedeepunderground,crackpropagationmayoccurwiththepassageoftime.Thisphenomenonwillcausethefailureofthesurroundingrockmass.Therefore,itisimportanttoevaluatethelong-termsafetyofrockmassstructures.TheParticleFlowCode(PFC),asimulationcodebasedonthedistinctelementmethod(DEM),isaneffectivenumericaltoolforsimulatingthefailureprocessofhardrock[1].Byintroducingthecontact-andparallel-bondandclumpedparticlemodel[2],thecodehasbecomebetterabletoexpressthebrittlefailureofhardrock[3].Ontheotherhand,aproblemhasarisen,namely,thatPFCsimulationswiththeclumpedparticlemodelcannotreproducerapidstrain-softeningbehaviorinBraziliantensiletests[4,5].Inaddition,thecracksgeneratedinthespecimensaremuchmorewidelydistributedinthesimulationthanintheexperiments,aswillbediscussedlaterindetail.ThisproblemwiththeBraziliantestsimulationshouldbeovercomebeforehandlingactualexcavationproblems,firstlybecausethestressfieldgeneratedaroundrealundergroundcavitiesmaybemuchmorecomplicatedthanthatunderBraziliantensileconditionsandsecondlybecauseBraziliantestsanduniaxialcompressiontestsarethemostcommonlyusedelementteststocalibratetheinputparametersofPFCsimulations.IfBraziliantestsarenotsimulatedwithadequateaccuracy,reliableinputparameterscannotbeobtainedtomodelthetargetedrock.AsapossiblereasonwhyBraziliantestsarenotsuccessfullysimulatedbyPFCwiththeclumpedparticlemodel,thisstudyconsiderstheloadingconfigurationinthesimulation.Consideringtheidealizedlineloading(pointloadingintwodimensions)andstriploading(lineloadingintwodimensions),aBraziliantestsimulationwascarriedoutwithPFC2D(ParticleFlowCodeintwodimensions)targetingLacduBonnetgranite,anditsfailureprocessandcrackpropagationwerecompared.2.PROBLEMSINBRAZILIANTESTSIMULATIONSUSINGPFCWITHCLUMPEDPARTICLEMODELTable1showstheinputparametersinthePFCsimulationwiththeclumpedparticlemodel.Theyincludethephysicalandmechanicalpropertiesofparticlesandmicro-bonding,asillustratedinFigure1.Theseparametersaredeterminedtoreproducethemechanicalpropertiesofatargetedrock,suchasthecompressivestrength,thetensilestrength,Young'smodulus,Poisson'sratioandsoon,byiteratingelementtestsimulations.ARMA13-515LoadingconditionsintheBraziliantestsimulationbyDEMNakashima,S.,Taguchi,K.,Moritoshi,A.andShimizu,N.YamaguchiUniversity,Ube,Yamaguchi,JapanFunatsu,T.AdvancedIndustrialScienceandTechnology,Tsukuba,Ibaraki,JapanCopyright2013ARMA,AmericanRockMechanicsAssociationThispaperwaspreparedforpresentationatthe47thUSRockMechanics/GeomechanicsSymposiumheldinSanFrancisco,CA,USA,23-26June2013.ThispaperwasselectedforpresentationatthesymposiumbyanARMATechnicalProgramCommitteebasedonatechnicalandcriticalreviewofthepaperbyaminimumoftwotechnicalreviewers.Thematerial,aspresented,doesnotnecessarilyreflectanypositionofARMA,itsofficers,ormembers.Electronicreproduction,distribution,orstorageofanypartofthispaperforcommercialpurposeswithoutthewrittenconsentofARMAisprohibited.Permissiontoreproduceinprintisrestrictedtoanabstractofnotmorethan200words;illustrationsmaynotbecopied.Theabstractmustcontainconspicuousacknowledgementofwhereandbywhomthepaperwaspresented.ABSTRACT:TheParticleFlowCode(PFC),asimulationcodebasedonthedistinctelementmethod(DEM),isaneffectivenumericaltoolforsimulatingthefailureprocessofhardrock.Byintroducingcontact-andparallel-bondandclumplogic,thecodehasbecomebetterabletoexpresstheratioofuniaxialcompressivestrengthtotensilestrengthofhardrock.Ontheotherhand,aproblemhasarisen,namely,thatPFCsimulationswiththeclumpedparticlemodelcannotreproducerapidstrain-softeningbehaviorinBraziliantensiletests.Inaddition,crackspropagatetoowidelyinthespecimens;thisdiffersfromtheexperimentalfacts.Attributingtheaboveproblemstotheloadingconfiguration,sometwo-dimensionalPFCsimulationsofBraziliantestswereconductedinthisstudyunderseveralloadingconditions.Striploading(lineloadingintwodimensions)andlineloading(pointloadingintwodimensions)weretakenintoconsideration.Fromthesimulationresults,pointloadingwasfoundtobeeffectiveforexpressingrapidstrain-softeningbehaviorandcrackpropagationinBraziliantensiletests.Table1.InputparametersforPFCsimulationusingclumpmodelDescriptionParameterMinimumballradiusRmin[mm]BallsizeratioRmax/RminBalldensity[kg/m3]ContactmodulusEc[GPa]Normal/shearstiffnessratiokn/ksFrictioncoefficientParallel-bondmodulusE―c[GPa]Parallelbondstiffnessratiok―n/k―sParallel-bondradiusmultiplier―Parallel-bondnormalstrength―c[MPa]Parallel-bondshearstrength―c[MPa]ClumpradiusRc[mm]RmaxNormalstiffnessRbond(=Rmin)RminknknFnFnParallelbondBondresistballrotationBondresistshearingBondstiffnessContactstiffnessFcsFcnFsfricTensionShearCompressionBondbreaksBondbreaksksknOverlapFci:Bondstrengthkn:ContactstiffnessUi:DisplacementUn(Us)RminRmaxShearstiffnessksFsFsksContactstiffnessBondstiffnessBondstiffnessContactstiffnessFig.1.Micro-parametersandillustrationofyieldingprocessformicro-bonding[2].Figure2illustratestheclumpmodel.Aclumpisagroupofparticles.Itactsasarigidbody.Itcanmodeltheirregularshapeofgraininrock.Introducingclumplogicen