A mesoscale model based on MonteCarlo method for concrete fracture behavior study.docx

A mesoscale model based on MonteCarlo method for concrete fracture behavior study.docx

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AmesoscalemodelbasedonMonteCarlomethodforconcretefracturebehaviorstudy

外文参考资料：

AmesoscalemodelbasedonMonte-Carlomethodforconcretefracturebehaviorstudy

ZHANGNaiLong1,2,GUOXiaoMing1,2*,ZHUBiBo3&GUOLi1,2

1.DepartmentofEngineeringMechanics,SchoolofCivilEngineering,SoutheastUniversity,Nanjing210096,China;

2.JiangsuKeyLaboratoryofEngineeringMechanics,SoutheastUniversity,Nanjing210096,China;

2.DayaBayNuclearPowerOperationsandManagementCompany,Shenzhen518110,China

AnaggregategenerationandpackingalgorithmbasedonMonte-Carlomethodisdevelopedtoexpresstheaggregaterandomdistributionincementconcrete.Amesoscalemodelisproposedonthebasisofthealgorithm.Inthismodel,theconcretecon-sistsofthreeparts,namelycoarseaggregate,cementmatrixandtheinterfacialtransitionzone（ITZ）betweenthem.Toverifytheproposedmodel,athree-pointbendingbeamtestwasperformedandaseriesoftwo-dimensionalmesoscaleconcretemod-elsweregeneratedforcrackbehaviorinvestigation.Theresultsindicatethatthenumericalmodelproposedinthisstudyishelpfulinmodelingcrackbehaviorofconcrete,andthattreatingconcreteasheterogeneousmaterialisveryimportantinfrac-turemodeling.

cementconcrete,fracture,Monte-Carlomethod,aggregategenerationandpackingalgorithm,mesoscalemodels

1Introduction

Concretematerialiswidelyusedinbuilding,highway,bridge,dam,airportandmanyotherkindsofinfrastructuralfacilitiesduetoitscharacteristicssuchashighstrength,convenientconstruction,highplasticproperty,goodfire-proofandcorrosionresistance.Withtheincreaseofmagni-tudeofconcretematerialininfrastructuralfacilitiesinre-centyears,anumberofcasesonstructurefailureintheirearlierdesignlifeandserviceexterminationcanbeeasilyfoundinconcreteconstructions.Asoneofthemostcom-mondistresses,cracksdirectlyreducetheconcretestructureservicecapacityandlowerthemechanicalperformance.Crackingphenomenaposeaseverechallengetoapplicationanddesignofconcretestructures.Understandingthefun-damentalmechanismsbehindtheinitiationandthepropaga-tionofcracksinsideconcreteindifferentcasesisacriticalsteptostudytheconcretematerialperformanceforfurtherdesign.

Itiswellknownthatconcreteisaheterogeneouscompo-sitematerialcomposedofcoarseandfineaggregates,ce-mentpastematrix,interfacialtransitionzone（ITZ）betweentheaggregateandcementpastematrixandvoidsatmesoscale.Thesizeofparticlesinsideconcretecanberangingfromafewmicrons（cementparticles）totensofmillimeters（coarseaggregates）.Aggregatesusuallycoverabout85%ofthevolumeofconcreteindifferentsizes,ir-regularshapesandrandomlocations.Mechanicalpropertiesofeverycomponentinconcretearedifferentobviously.Forexample,thecementpastematrixisatypicalporousmate-rialwhileitsmechanicalperformancesareverysensitivetothecementwaterratio,cementhydrationdegree,curingcondition,porosityandsoon.Themechanicalpropertiesofconcretearesignificantlyaffectedbymicrostructuraldetailsandcementcontent,aggregatetype,gradationofaggregateparticles,distributionandevenorientationofaggregates,thevoidratioandsoon.Whereasinamacroscalemodelofconcrete,theheterogeneousnatureofconcreteisignoredandananalyticalmodelingcanbeperformedbasedonthelinearelasticity.Theinitiationandpropagationofacrackinanelastichomogeneousmediumleadstothedevelopmentofsingularstressfieldaroundcracktipandthusdisturbsthestressdistributionintheregion.However,thesingularstressfieldfinallyresultsinafinitestressreachingthetensilestrengthoftheweakestcomponent.Therefore,theeffectsofdifferentcomponentsonthelocationofcrackinitiationandthetrajectoryofcrackpropagationinconcreteareignored.Thecomplexfracturebehaviourofconcreteatmacroscaleisamanifestationofvariousinterlinkedmechanismsoccur-ringatlengthscalesmuchsmallerthanthecontinuumlengthscale.Analyticalmodelingofsuchsystemsisdiffi-culttoreproducetheeffectsofdifferentcomponentsonthelocationofcrackinitiationandthetrajectoryofcrackprop-agation.Continuummodelslikecrackbandmodel,twopa-rameterfracturemodel,andfictitiouscrackmodelhavebeenproposedinthepastbuttheydonotaccountforheter-ogeneity.

Therefore,itisnecessarytoconstructamesomechanicalmodelcontaininginformationofcomponentsandmicro-structuresforsimulatingthecrackingbehaviorsofconcretemoreaccurately.SadoukiandWittmannwerethefirsttounderlinetheimportanceofstudyingthematerialatvaryinglengthscales[1].Inrecentyears,alotofexperimentalandnumericalinvestigationsoncrackpropagationinconcretehavebeenperformed.Someresearchers,suchasDeSouzaetal.[2],KimandButtlar[3]andLopezetal.[4],haveattachedtheirattentiontothemicrostructureeffectsinthefractureofcompositematerial.Simoneetal.appliedme-so-modeltoafourpointbendingconcretebeamtostudythefracturingoftheheterogeneousspecimen[5].Xiaoetal.[6]developedarandomaggregatemodelofrecycledaggregateconcretetosimulatethemeso-structuraldamageofrecycledaggregateconcreteunderuniaxialcompressioninalatticemodel.TejchmanandSkarzynski[7]investigatedfractureprocesszones（FPZ）atmeso-scaleinnotchedconcretebeamssubjecttoquasi-staticthree-pointbending.Nguyenetal.[8]developedameso-modeltoinvestigatethetransitionfromdiffusedamagetolocalizeddamageofconcrete.Themodelshowedinterestingresultsonthetransitionfromdif-fusetolocalizeddamageandwasabletoreproducedila-tancyincompression.Lietal.[9]employedameso-scalelatticemodeltopredicttheprimarymechanicalpropertiesandthecrackpathsofthedesignedcementitiousmaterial.Themodelingwasdonebasedonthemeso-structureofconcretecapturedthroughamicro-CT.GrasslandJirasek[10]proposedameso-scalemodeltostudythefractureprocesszoneofconcretesubjecttouniaxialtension.Themeso-structureofconcretewasidealisedasstiffaggregatesembeddedinasoftmatrixandseparatedbyweakinterfacesinthemodel.Moetal.presented2Dand3Dmeso-levelmechanicalmodelsfornumericalanalysisofravelingre-sistanceofporousasphaltconcrete（PAC）[11–21].Manyinvestigatorshavedevelopedsomeothermesoscalemodelsintheirworks.

WithaggregategenerationandpackingalgorithmbasedonstochasticMonte-Carlomethod,amesoscalemodelframeworkwasproposedinthisworkandappliedtothecrackinitiationandpropagationstudy.Aseriesoftestsandnumericalsimulationsonthethree-pointbendingofconcretebeamwereperformedtoevaluatethemesoscalemodel.

2Mesoscaleheterogeneousmodelframe

Inthepresentmesoscaleheterogeneousmodel,thewholecementmixturesolidisdividedintothreegroupsofregions,thatis,theregionsoftheaggregates,theregionofthece-mentmatrixandtheregionsbetweenaggregatesandcementmatrix,alsocalledITZ.Therefore,cementconcretehereconsistsofthreecomponents.WiththeaggregategenerationbystochasticMonte-Carlomethodandpackingalgorithm,amesoscalemodelwasdevelopedandusedtoinvestigatetheeffectsofmicrostructureonconcretecrackingbehaviorandcapturethetrajectoryofcrackpropagation.

2.1Simplificationofaggregategradation

Ingeneralhydraulicconcrete,thefineaggregateisdefinedasparticle,whosemassexceeds85%passesofa5mmsieve,whilethecoarseaggregateisdefinedasthatwhosemassexceeds85%retainsona5mmsieve.Itisnotedthatthevolumefractionoffineaggregatesislow,buttheiramountisthousandsoftimesthatofcoarseaggregatesorevenmore.Thelargenumberoffineaggregateswouldgreatlyincreasetheelementnumberandgoagainstthecomputationalefficiency,soitisrealistictoconstructasimplifiedmesoscalemodelofcementconcretewithcon-tinuousgradation.Animportantissueinthissimplificationmethodistodeterminethecut-offsizebetweenfineaggre-gateandcoarseaggregate.Thenthefineaggregateisclassi-fiedintocementmatrixwhilecoarseaggregateiscatego-rizedintodifferentlevelsbyparticlesize.Bydoingso,thedifficultyasmentionedpreviouslyinmodelingwillbealle-viated.Ifweconsider5mmasthecut-offsizeinthisstudy,theprocedureofaggregategradationsimplificationiscom-pleted.ThissimplifiedaggregategradationfulfillsFuller’scurve,fromwhichtheWalraven’sformulaisdeduced:

（1）

wherePcistheprobabilityofaggregatewhoseparticlesizefulfillsD

（2）

whereSiisthetotalareaoccupiedbytheithlevelaggregates;niisthenumberoftheithlevelaggregatesandDiistheequivalentdiameteroftheithlevelaggregates.Asanexample,thesimplifiedaggregategradationisshowninTable1.

Table1Simplifiedaggregategradation：

Aggregateparticlesizelevel（mm）

Masscontent（%）

25

4

20

6

15

32

10

32

5

26

2.2Aggregategenerationandpacking

Oncethenumberofaggregatesofeveryparticlesizeleveliscalculatedbythemethoddescribedpreviously,thenextissueistogenerateaggregatesandpacktheminapre-scribedregion.Consideringtherandomnessoftheaggre-gatedistribution,Monte-Carlomethodisemployedinag-grega