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USINGPLANESTRESSMETHODTOSIMULATETHEINTERFACIALBONDBETWEENSTEELFIBERANDCONCRETEABSTRACTINTERFACIALBONDBETWEENSTEELFIBERANDCONCRETEIMPACTSDIRECTLYONTHEREINFORCINGANDTOUGHENINGFORTHEFIBERSTOTHECONCRETEALLALONG,MOSTINTERFACIALBONDRESULTSBETWEENTHETWOWEREBASEDONTHETESTITISDIFFICULTTOSIMULATETHEDESTRUCTIONOFTHEINTERFACEBYTHENUMERICALFINITEELEMENTMETHODDUETOTHELACKOFBONDSTRESSVERSUSSLIPRELATIONSHIPINLOCALTHISPAPERIMPROVESTHECALCULATINGMETHODONBONDSTRESSVERSUSSLIPRELATIONSHIPINLOCALOFSTRAIGHTSTEELFIBERPULLEDOUTFROMTHECONCRETE,ANDADOPTSANEWMODELINGMETHODUSINGPLANESTRESSMETHODTOSIMULATETHEPROCESSOFTHESHEARSTAIGHTSTEELFIBERPULLEDOUTFROMTHECONCRETEFINITEELEMENTRESULTSANDTESTRESULTSAREINGOODAGREEMENTSOTHECALCULATINGMETHODINTHISPAPERONBONDSTRESSVERSUSSLIPRELATIONSHIPINLOCALANDPLANESTRESSMETHODAREREASONABLEKEYWORDSSTEELFIBERREINFORCEDCONCRETESFRCINTERFACIALBONDINGPLANESTRESSFINITEELEMENT1INSTRUCTIONTHEDESTRUCTIONOFSTEELFIBERREINFORCEDCONCRETESFRCISGENERALLYSTARTWITHTHECONCRETEMATRIXCRACKINGALARGENUMBEROFMICROCRACKSINCONCRETEMATRIXCONTINUOUSEXPANSIONUNDERTHEFORCEBRIDGINGFIBERBLENDINGINCONCRETEWILLPLAYABLOCKINGROLE,WHILETHESIZEOFWHICHWILLULTIMATELYDEPENDONINTERFACEBONDINGSTRENGTHBETWEENSFANDCONCRETETHEREFORE,INTERFACEISSUEHASBECOMETHEBASISRESEARCHSUBJECTSUNREMITTINGWITHTHEDEVELOPMENTOFCOMPUTERTECHNOLOGYANDTHEMODERNCOMPUTINGMETHODS,MOREANDMOREDOMESTICANDFOREIGNRESEARCHERSUSEFEMTOSIMULATETHEPROCESSTHATSTEELFIBERPULLEDOUTFROMTHEMATRIX,THISPROCESSUSUALLYBESIMPLIFIEDAXISYMMETRICALTWODIMENSIONALMODEL2HOWEVER,THISSIMPLIFICATIONCANONLYBESIMULATEDTHEPROCESSOFSTRAIGHTFIBERSPULLEDOUTFROMTHEMATRIXWITH0DEGREEANGLERATHERTHANNON0DEGREEANDITCANNOTBESIMULATEDTHEPROCESSOFDEFORMEDFIBERSPULLEDOUTFROMTHEMATRIXWHENMODELING,WENEEDTOBONDSTRESSVERSUSSLIPRELATIONSHIPINLOCALOFINTERFACEBETWEENSFANDCONCRETEBUTDUETOTHEDISTRIBUTIONOFINTERFACESHEARSTRESSISCOMPLEXANDSTEELFIBERISSMALLERINSIZE,ITISDIFFICULTTOOBTAINEFROMTHEEXPERIMENTDIRECTLY2,ANDTHEFORMULAWITCHUSEDTOCALCULATEISFEWATTHEPRESENTTIME,THECONSTITUTIVERELATIONOBTAINEDMAINLYBYTHEFOWLINGMETHODSTHATITERATIVECOMPUTATIONANDPILOTCALCULATIONFORTHEFORMERWEMUSTWORKOUTCOMPUTERITERATIVEPROGRAMANDFORTHELATTERITMAYTAKETIMEANDHARDWORKSOTHISPAPERIMPROVESTHECOMPUTATIONMETHODOFTHEBONDSTRESSVERSUSSLIPRELATIONSHIPFORSFPULLEDOUTFROMTHECONCRETE,WHICHISSUITABLEFORFINITEELEMENTMETHODATTHESAMETIME,ANEWMODELLINGMETHODISADOPTEDA1USINGPLANESTRESSMETHODTOSIMULATETHEPROCESSOFTHESHEARSTAIGHTSFPULLOUTEDOUTFROMTHECONCRETE2TEXT21BONDSTRESSVERSUSSLIPRELATIONSHIPBONDSTRESSVERSUSSLIPRELATIONSHIPCANBEAPPROXIMATECALCULATEDBYLOADDISPLACEMENTCURVEINTESTFORTHESTEELFIBERPULLEDOUTFROMTHECONCRETEACCORDINGTOTHELOADDISPLACEMENTCURVEWITHANEVIDENTTRANSITIONBEFORETHEPEAKLOADORNOT,BONDSTRESSVERSUSSLIPRELATIONSHIPCANBESIMPLIFIEDFOURLINEARMODELFIGORTRILINEARMODELFIGCALCULATIONASSUMPTIONS1SUPPOSETHATSHEARSTRESSONINTERFACEISINUNIFORMDISTRIBUTION,THATISAVERAGEBONDSTRENGTHASBONDSTRENGTH2SUPPOSETHATSHEARSTRESSONSFISINEQUIVALENTDISTRIBUTIONTHEVALUEOFCANBETAKENTHEFOLLOWINGFORMULATOAPPROXIMATECALCULATE1F1/UFLFMAXFMAX/UFLF2F2/UFLF3F3/UFLFFFLUF11A2FFLUFMAXMAXA2FFLUF22A2FFLUF33WHEREUFISCIRCUMFERENCEOFSFCROSSSECTIONMM,LFISEMBEDMENTLENGTHOFSFSMM,ANDF1A3FMAXA3F2A3F3ARETHECORRESPONDINGPULLOUTLOADOFTHELOADA0DISPLACEMENTCUVENIFTHEREAREMORETHANONESTEELFIBERSPULLEDOUT,TAKETHEAVERAGEWHEREFMAXISTHEPEAKLOAD,F1ISTHELOADOFTHEEVIDENTTRANSITIONBEFOREFMAX,F2ISTHELOADOFTHEEVIDENTTRANSITIONAFTERFMAXANDF3ISTHELOADOFTHECUVESENDA41A5AA6A42A5AA6FORTHETWOMODELSABOVEISIMPORTANTTODEFINE1U,WHICHCANBESEENASSLIPPAGEPERUNITLENGTHWEMUSTCONDERITASFOLLOWA7STEELFIBERANDCONCRETEDEFORMTOGETHERWHENTHEPULLOUTLOADISSMALLERA8WITHTHEINCREASINGOFTHEPULLOUTLOAD,THESTEELFIBERANDTHECONCRETEDEBONDINLOCALTHESLIPPAGEBETWEENTHEMOFTHEDEBONDINGSEGMENTISTHEDEFORMATIONDIFFERENCEOFTHETWO,THATISLSCAFACF,WHEREFAISMEANTENSILESTRAINOFSTEELFIBERINLLENGTH,CAISMEANSHEARSTRAINOFCONCRETEINLLENGTHANDLISTHELENGTHOFTHEDEBONDINGSEGMENTA9INPERUNITLENGTH,THEDEFORMATIONDIFFERENCEOFTHEDEBONDINGSEGMENTBETWEENSTEELFIBERANDCONCRETECANBESIMPLIFIEDAPPROXIMATELYASCAFASA10A11SPRINGELEMENTSWHICHARESIMULATEDTHEINTERFACEMUSTBEADDEDONTHECOINCIDENCENODESOFSTEELFIBERELEMENTSANDCONCRETEELEMENTSINTHEORY,STEELFIBERANDCONCRETEDEFORMTOGETHERBEFOREDEBONDINGWHICHEQUIVALENTOFSPRINGNOTSTRETCH,BUTTHESPRINGELEMENTSUSEDARENOTALLOWEDTOTHISSUITATIONTHATTHEFORCEINCRASESANDTHEDEFORMATIONDOESTINCRASESO,1UCANBEWRITTENINTHEFOLLOWINGMANNERXFFSU1,WHEREXFFISTHETENSILESTRAINOFSTEELFIBERWITHPULLOUTLOADXFFORQUADRILATERALFORMMODELXFTAKE1FANDTRILINEARMODELTAKEMAXF2UA123UINMODELANDMAXFUINFOURLINEARMODELTAKETHEMEANVAULEINPERLENGTHCORRESPONDINGTHESLIPPAGEOF2FA123FA12MAXFATTHEPULLOUTLOADDISPLACEMENTCURVE22MATERIALPROPERTIESTAKINGINTOACCOUNTTHESHEARSTRAIGHTSTEELFIBERMAYINLARGEDEFORMATIONORPULLEDOFFWHENPULLEDOUTSOTHEMATERIALPROPERTYOFITADOPTINGPERFECTELASTICPLASTICANDHARDENINGMODELFIG2A132ACTUALLYCONCRETECONSTITUTIVEMODELSHAVEDECLINEDSECTIONWHICHCANLEADTOUNCONVERGENCEWHENUSEDTOCALCULATESOMETIMESA14WESHOULDAVOIDTHEDECLINE3INTHISPAPER,THEMODELOFCONCRETECONSTITUTIVEPROPOSEDBYRA15SCHISADOPTEDCUBECRUSHINGSTRENGTHOFCONCRETEOBTAINEDINTESTCOMEFROM4THEYARETHEMATRIX12859MPATHEMATRIX24104MPATENSILESTRENGTHISCACULATEDBY32260CUTFF23UINGPLANESTRESSMETHODTOSIMULATETHEPROCESSOFTHESHEARSTAIGHTSFPULLOUTEDOUTALONGTHEAXISFROMTHECONCRETE231THEFINITEELEMENTMODELELEMENTPLANE82ISADOPTEDTOSIMULATESTEELFIBERANDCONCRETEANDELEMENTCOMBIN39WHICHISNONLINEARSPRINGTOSIMULATETHEINTERFACEOFTHETWOSPRINGSAREADDEDONTHEINTERMEDIATECOINCIDENCENODESOFSTEELFIBERELEMENTANDCONCRETEELEMENTINTERFACIALBONDINGSTRENGTHISCONSIDEREDONLYALONGTHEFIBERAXISASTHEPULLEDOUTMODELINTESTHASSYMMETRY,THEREFORE,THEPULLEDOUTPROCESSOFONLYONESTEELFIBERISSIMULATEDBYPLANESTRESSMETHODTHEDIMENSIONSOFTHEFIBERSCROSSSECTIONINFINITEELEMENTMODELCANBECONVERTEDBYEQ221LLSF2WHEREFSISTHEORIGINALCROSSSECTIONALAREAOFFIBER,1LISTHEWIDTHOFTHEFIBERSCROSSSECTIONINMODELAND2LISTHEHEIGHTEQ3ALSONEEDEDTOSATISFIED,FUL223WHEREFUISCIRCUMFERENCEOFTHESTEELFIBERTHEFINITEELEMENTMODELESTABLISHEDASSHOWNFIG3A163232SELECTIONOFTHEMODELPARAMETERSINTHISPAPER,1L054MM,2L16956MMANDFL1674MM,WHEREFLISTHEEMBEDDEDLENGTHSINONECONCRETEBLOCKTHESIZEOFTHECONCRETEBLOCKIS5076MM2214MM16956MMBECAUSETHEMODELISINPLANE,SO16956WHICHISNOTDIRECTLYINVOLVEDINTHEGEOMETRICMODELLINGISUSEDASREALCONSTANTSOFTHICKNESSFOURLINEARMODELISUSEDASBONDSTRESSVERSUSSLIPRELATIONSHIPA17A18A19A20A21A22INTHISPAPERANDUVALUECALCULATEDBYTHEABOVEMETHODASSHOWNINTABLE1A231UA24A25A23TABLE1TABLEOFUVALULATIONTYPEPARAMETER1U/MM1/MPAMAXFU/MMMAXF/MPA2U/MM2/MPA3U/MM3/MPAJ1J20000809000084225662830125009002730323030002180070115755700600003710437J1A26SHEARSTAIGHTSTEELFIBERPULLEDOUTFROMTHETHEMATRIX1J2A26SHEARSTAIGHTSTEELFIBERPULLEDOUTFROMTHETHEMATRIX2THEFORCESOFSPRINGELEMENTALONGTHEFIBERSAXISCANBEWRITTENINTHEFOLLOWINGMANNER2LLFEE4WHEREELISTHEMESHINGLENGTHOFTHEELEMENTS,TAKING054MMASTHEVALUEOFTHEBONDSTRENGTHISSMALLERANDSHORTERBETWEENTHEFIBERENDSANDTHEMATRIX,TAKING079MPASUPPOSINGTHESTIFFNESSOFTHESPRING0K260N/MM,SOTHEFORCESOFTHESPRINGELEMENTSARESHOWNASPI2FRF0542079PI0723N,WHERERFISTHEEQUIVALENTRADIUSOFTHEFIBERTHUSTHEELONGATIONOFTHESPRINGSISSHOWNAS0KF0003MMANDAFTERTHENITBECOMES0233THENUMERICALRESULTSCOMPAREDWITHTHEEXPERIMENTALRESULTSFIG4PRESENTSTHATANEXCELLENTCONCORDANCEHASBEENOBTAINEDBETWEENTHETWOCURVESOFTHEEXPERIMENTALRESULTSANDTHENUMERICALRESULTS,BUTTHECHANGEINDISPLAMENTOFTHENUMERICALCURVESARENOTVERYCLEARBEFOREDEBONDINGCOMPLETELYTHECURVESOFSMALLDISPLACEMENTFORJ1A27J2AREILLUSTRATEDINFIG5A28A29A28A30A28A31A28A32A28A33A28A28A33A29A28A33A30A28A33A31A28A33A32A28A29A28A28A28A34A31A35A33A29A36A37A38A39A40A41A42A43A44A43A45A46A47A44A44A48PULLOUTLOADNEXPERIMENTALRESULTOFJ1NUMERICALRESULTOFJ1EXPERIMENTALRESULTOFJ2NUMERICALRESULTOFJ2A49A50A49A51A49A52A49A53A49A54A49A49A54A50A49A54A51A49A54A52A49A54A53A49A50A49A49A49A49A55A49A49A56A49A55A49A54A49A55A49A54A56A49A55A49A50A57A58A59A60A61A62A63A64A65A64A66A67A68A65A65A69A70A71A72A72A73A71A74A72A73A75A76A77A78A79A80A81A82A83A84A80A81A82A83A85A864A865ASCANBESEENFROMFIG5THELOADDISPLACEMENTCURVESBEFOREDEBONDINGCOMPLETELYAREDIVIDEDINTOTWOSTAGES,THATISELASTICSTAGEANDLOCALDEBONDINGSTAGEATTHEFORMERSTAGE,THELOADANDTHEDISPLACEMENTAREALMOSTBYLINEARGROWTHWHENTHETWOCURVESREACHTHESTAGEOFDEBONDINGCOMPLETELY,THELOADSCOMPLYWITHTHELAWTHATINCREASEATFIRST,THENDECREASEWITHANARROWRANGEANDTHENINCREASEAGAINTHISISENTIRELYCONSISTENTWITHTHECONDITIONSFROMTHESTAGEOFDEBONDINGCOMPLETELYTOOFTHEPEAKLOADTHENUMERICALRESULTSCOMPAREDWITHTHEEXPERIMENTALRESULTSOFTHEINTERFACIALBONDOFSFRCSHOWNINTABLE2TABLE2BONDSHEARSTRENGTHOFNUMBERIALRESULTSANDEXPER
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