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NUMERICALSIMULATIONOFHYDRO-THERMO-MECHANICALBEHAVIOR OFCONCRETESTRUCTURESEXPOSEDTOELEVATEDTEMPERATURES By JAEHYEONCHUNG ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHE REQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2003 Copyright2003 By JaeHyeonChung ACKNOWLEDGEMENTS PraisebetoGodwhoendowedmewithcircumstancestobeginandendthis work. Iwouldliketothanktomyadviser.Dr.GaryR.Consolazioforhissincere guidanceduringthecourseofthiswork.Withouthisconscientiousadviceandhearty help,completionofthisworkwouldnothavebeenaccomplished.Mostofall,Isincerely appreciatehismentorshipandfriendshipthatenabledmetostandupthroughoutevery difficultmomentofthelastfiveyears. Also,Iwouldliketoexpressmygratitudetothemembersofthesupervisory committee;Dr.KurtisR.Gurleyforhischeerfulencouragement,Dr.MichaelC.McVay forhisacademicadviceandsuggestions,Dr.MarcI.Hoitforhisfriendlyassistance,and Dr.LocVu-Quocforhiscreativesuggestions. TheassistanceandguidanceofDr.JosephW.Tedescoaresincerelyappreciated. OthersdeservingofthanksareMr.AnthonyJ.MurphyandMr.WilliamA. Yanko.Theirconstantfriendshipandencouragementhelpedinaidingthesuccessful completionofthisresearchfrommanyaspects. Finally,Iwouldliketodedicatethisdissertationtomymotherforherpatience, moralsupport,andendlesslovewithoutwhichthisworkwouldnothavebeensuccessful. iii TABLEOFCONTENTS Page ACKNOWLEDGEMENTS iii ABSTRACT vii CHAPTER 1INTRODUCTION 1 1.1MaterialResponseofConcretetoHeating 3 1.2FailureMechanismsofConcreteatElevatedTemperatures 4 1.3TwoHypothesesinAnalysisofSpalling 5 1.4MoistureClogSpalling 7 1.5OverviewoftheDissertation 8 2LITERATUREREVIEW 11 2.1RelevantFlowParameters 12 2.2MaterialCharacteristicsofHighStrengthvs.NormalStrengthConcrete 16 2.3MaterialPropertiesofHeatedConcrete 18 2.4HeatandMassTransportPhenomenainHeatedConcrete 19 2.5StressAnalysisofConcreteExposedtoFire 20 3.MACROSCOPICDESCRIPTIONOFTRANSPORTPHENOMENAINHEATED CONCRETE 21 3.1ConcreteasaPorousMedium 21 3.2AveragingPrinciples 23 3.2.1Volumeaveragingprocess 24 3.2.2ThesizeofanREV 26 3.2.3Mathematicalrepresentationoftheaveragedporosity 29 3.3BalanceLawsforContinua 31 3.3.1Governingdifferentialequationsformicroscopicconservedquantities...33 3.3.2Governingdifferentialequationsformulti-phasecontinua 36 3.4MacroscopicMassBalanceLawforaMultiphaseMixture 38 3.4.1Themassbalancelawforthesolidphase 38 3.4.2Themassbalancelawforthefluidphases 39 3.4.4Speciesmassbalanceinthegaseousphase 40 IV 3.5MacroscopicLinearMomentumBalanceLawforaMultiphaseMixture 43 3.5.1Thelinearmomentumbalancelawforthesolidphase 43 3.5.2Thelinearmomentumbalancelawforthefluidphases 44 3.5.3Thelinearmomentumbalancelawforthemultiphasemedium 45 3.6MacroscopicEnergyBalanceLawforaMultiphaseMixture 46 3.7ConstitutiveEquations 48 3.7.1Flowequationsinporousmedia 50 3.7.2DeviationfromDarcy’law 51 3.7.3Liquidpermeability 53 3.7.4Multi-fluidflowequation 55 3.7.5Massdensityofwater 57 3.7.6Theidealgaslaw 58 3.7.7Fick’slawfordiffusion 59 3.7.8Fourier’slaw 61 3.7.9Sorptionisotherms 61 3.7.10Totalstressandeffectivestressinthesolidphase 63 3.8PhysicalApproximationsandFieldEquations 64 3.8.1Continuityequationforthefluidphases 64 3.8.2Enthalpybalanceequationforthemultiphasemedium 69 3.9InitialandBoundaryConditions 73 4.NUMERICALMODELINGOFTRANSPORTPHENOMENAINREINFORCED CONCRETEEXPOSEDTOELEVATEDTEMPERATURES 77 4.1Overview 77 4.2GoverningEquations 79 4.3DiscretizationofIntegratedFiniteDifferenceMethod 82 4.4KeyParametersofFluidandHeatFlowinConcrete 85 4.4.1Relativepermeabilityofconcrete 85 4.4.2Slipflowconstantofconcrete 91 4.4.3Volume-averagedquantitiesforthermalpropertiesofconcrete 93 4.5CalculationofInitialConditions 95 4.6ComparisonofNumericalResultswithExperimentalData 97 4.7FiniteDifferenceSimulation 101 4.7.1Modelingboundaryconditions 101 4.7.22-Dsimulationresults 102 4.7.3Comparisonof2-Dsimulationsmodeledbyvariousfireconditions 105 4.7.43-Dsimulationresults 107 v 5.FINITEELEMENTSTRESSANAYSISOFAREINFORCEDHIGH-STRENGTH CONCRETECOLUMNINSEVEREFIRES 113 5.1GoalsandScope 113 5.2GoverningDifferentialEquationsfortheMassandEnergyBalance 115 5.3TheCoupledHeatConductionEquation 116 5.4ThePrincipleofStressSuperposition 117 5.52-DAxisymmetricFiniteElementStressAnalysis 121 5.5.1Initialandboundaryconditions 121 5.5.2Axisymmetricfiniteelementmodeling 122 5.5.3Simulationresults 125 5.63-DFiniteDisplacement/TemperatureMixedFormulations 127 5.7DiscretizationoftheTransientHeatConductionEquation 134 5.827/8FiniteElement 139 5.9SolutionApproach 141 5.103-DFiniteElementThermoelasticStressAnalysis 145 5.10.1Modeldescription 145 5.10.2Modelingofthetransientthermalloadingcondition 148 5.10.3Simulationresults 149 5.10.4Summary 156 6.CONTRIBUTIONOFPOREPRESSUREANDTHERMALGRADIENTSTRESS TOSPALLING 163 6.1FactorsInfluencingSpallingatEarlyStagesofHeating 163 6.2ContributionofPorePressureataLaterStageofHeating 165 7.CONCLUSION 171 7.1ThermalSpallingofConcrete 172 7.2FutureResearchWork 175 LISTOFREFERENCES 177 BIOGRAPHICALSKETCH 185 vi AbstractofDissertationPresentedtotheGraduateSchool OftheUniversityofFloridainPartialFulfillmentofthe RequirementsfortheDegreeofDoctorofPhilosophy NUMERICALSIMULATIONOFHYDRO-THERMO-MECHANICALBEHAVIOR OFCONCRETESTRUCTURESEXPOSEDTOELEVATEDTEMPERATURES By JaeHyeonChung August2003 Chair:Dr.GaryR.Consolazio Cochair:Dr.KurtisR.Gurley MajorDepartment:CivilandCoastalEngineering Inthisstudy,thermalspallingofhigh-strengthconcretestructuralelementshas beeninvestigatedbydevelopingnumericalmodelscapableofanalyzingthecombined effectsofmassandheattransferphenomenaonthermallyinducedstresses.Throughthe useoffinitedifferencesimulations,thisstudyinvestigatesmoistureeffectson thermodynamicstatesofconcreteatelevatedtemperaturesandtheinfluenceofpore pressureondevelopmentofthermalstressinducedbytemperaturegradients.Afinite elementstressanalysismodeliscombinedwithfinitedifferencesimulationstopredict stressstatescapableofinducingspallingofthetypethathasbeenobservedbothinthe fieldandinlaboratoryfiretestingofconcretestructuralelements.Thecombinedhydro- thermo-mechanicalanalysisprocedurepresentedheremayeventuallyserveasacritical vii componentofstressanalysisusedforevaluatingthefireresistanceofhigh-strength concretestructuralsystems. Themodelofconcreteexposedtofirethatisdevelopedhereininvolvesmassand heattransportphenomenainamulti-phasecontinuum.Simultaneousflowofmultiple fluidphases(i.e.,liquidandgaseous)ismodeledusingnewlyproposedconstitutive relationshipsthatareconsideredmoreaccuratethanthosepreviouslyavailableinterms ofassessmentofthermodynamicstatevariablesofconcretesystem.Inaddition, numericalsimulationsareusedtoexploretheeffectsthatsteelreinforcingbarshaveon internaltemperatureandpressurewithinconcretemembers. Porepressureandtemperaturetimehistoriesfromhydro-thermalfinitedifference simulationsarepresentedanddiscussed.Resultsfromthesimulationsyieldanimproved understandingofthethermodynamicstatevariablessuchasporepressure,temperature, anddegreeofliquidwatersaturation.Selectionofconstitutivemodelstodescribethe flowcharacteristicsofconcreteandtheproceduresimplementedforthecreationofthe concretemodelsarealsodiscussed.Modelingaspectssuchasmeshingtechniques, selectionofinitialconditions,anddefinitionofboundaryconditionsarediscussed.The modelingtechniquesusedtorepresentradiantheatfluxboundaryconditionsandvolume- averagingprocessesareexplainedindetail. Finally,atheoryofstresssuperpositionisdevelopedandsubsequentlyusedto evaluatestressstatessoastodeterminethecontrollingcontributortothermalspallingof Vlll high-strengthconcrete,e.g.,hydrostaticpore-pressuresandthermalgradientstresses, underextremethermalloadingconditions. IX CHAPTER 1 INTRODUCTION Thethermo-mechanicalbehaviorofconcretestructuresexposedtohightemperature environmentshasbecomeveryimportantformanyengineeringproblemsinrecentyears. Assessmentofthefireresistanceofbuildings,bridgesandtunnels,andassessmentoffire damageinstructuresrepresentafewexamplesituations.Intheseareas,manyengineers considerunderstandingthefireresistantcharacteristicsofconcretetobeacritical componentofaccuratestructuralanalysisandthussafeyeteconomicaldesigns. Economically,concretehasbetterfire-resistantpropertiesthanotherbuilding materialsandthus,itprovideseffectiveshieldingtomaterialssuchassteelagainst seriousdamageduringfires. However,inanextremelyrapidheatingconditionresulting fromanelevatedtemperatureenvironment,suddenexplosivematerialfailureofconcrete, i.e.,spalling,mayoccur,renderingitincapableofprotectingsteelreinforcementand structurallyunabletocarryload. Ifareinforcedconcretecolumninanextremefireenvironmentundergoesspalling atitssurface,thenthesteelreinforcementcanbedirectlyexposedtofire.Strengthofthe steelathighertemperatureswillbeprogressivelyreduced.Suddenlossofgrosssectional areaintheconcretecolumnduetospallingcanalsoresultinareductionofcolumn stiffness.Asspallingprogressesintodeeperregionsofthestructuralmember’score,the concretecolumnmaybecomeincapableofcarryingtheactingloadsasseverelossof strengthoccurs. 1

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197 Pages·2003·7.6 MB·English

by Chung, Jae Hyeon

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