Citation
Investigation of Normal Strength and Ultra-High Performance Concrete Cylinder Failure Behavior under Impact

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Title:
Investigation of Normal Strength and Ultra-High Performance Concrete Cylinder Failure Behavior under Impact
Creator:
Stone, Michael A
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
Publication Date:
Language:
english
Physical Description:
1 online resource (126 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Civil Engineering
Civil and Coastal Engineering
Committee Chair:
KRAUTHAMMER,THEODOR
Committee Co-Chair:
CONSOLAZIO,GARY R
Committee Members:
FERRARO,CHRISTOPHER CHARLES
SUBHASH,GHATU
FOUST,BRADLEY W

Subjects

Subjects / Keywords:
concrete -- impact -- nsc -- uhpc -- uhpfrc
Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Civil Engineering thesis, Ph.D.

Notes

Abstract:
Increases in terrorism have led to more interest in protective structures and hardening current facilities. To aid this, new materials have been developed that are much stronger than conventional building materials such as ultra-high performance concrete (UHPC) and ultra-high performance fiber-reinforced concrete (UHPFRC). These materials differ from normal strength concretes (NSC) by combining advanced mix design with steel fibers for increased ductility. The result is a material that is much stronger and much more ductile than NSC. Structural response of these materials can differ significantly from simple strength based parameters derived from standard laboratory tests. Parameters such as size of the structure and loading rate can drastically affect the performance of the material. These parameters are typically only considered implicitly, and these parameters might be coupled in ways that are not currently well understood. Research into dissipation mechanisms of impact energy can yield insights into behavior that is useful for structural engineers. This research covers the impact testing of NSC, UHPC, and UHPFRC cylinders to investigate the coupling of these failure mechanisms and the response using linear elastic fracture mechanics (LEFM) and analysis of energy dissipation mechanisms via energy balance. Energy flow and distribution through the cylinder is documented to examine the fracture behavior and material response to impact loading. Static compression results indicate that both UHPC and UHPFRC have similar energy capacities. Dynamic results, however indicate that the UHPFRC is capable of absorbing and dissipating six times as much energy as the reference UHPC mix. The mechanism for this increased capacity is explained primarily by the large amounts of steel fibers which greatly enhance the energy absorption capacity. ( en )
General Note:
In the series University of Florida Digital Collections.
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Includes vita.
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Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2017.
Local:
Adviser: KRAUTHAMMER,THEODOR.
Local:
Co-adviser: CONSOLAZIO,GARY R.
Statement of Responsibility:
by Michael A Stone.

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UFRGP
Rights Management:
Applicable rights reserved.
Classification:
LD1780 2017 ( lcc )

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INVESTIGATIONOFNORMALSTRENGTHANDULTRA-HIGHPERFORMANCECONCRETECYLINDERFAILUREBEHAVIORUNDERIMPACTByMICHAELSTONEADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2017

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c2017MichaelStone

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Idedicatethistomyfamily,inpartiuclarJaime,fortheirconstantloveandsupport.

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ACKNOWLEDGMENTSThankstosupportfromUSACE-ERDCforthematerialsupportinbothmaterialsanddata.FurtherthanksaregiventotheIsraeliMoDforfundingtheinitialresearchintosize-eect.ThanksaregiventocommitteememebersDr.Krauthammer,Dr.Ferraro,Dr.Subhash,Dr.Consolazio,andDr.Foustfortheirinputandwisdom. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS ................................... 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 11 CHAPTER 1INTRODUCTION ................................... 13 1.1ProblemStatement ............................... 13 1.2Hypothesis .................................... 13 1.3ResearchSignicance .............................. 14 1.4ObjectiveandScope ............................... 15 2LITERATUREREVIEW ................................ 16 2.1Introduction ................................... 16 2.2FractureMechanics ............................... 16 2.2.1LinearElasticFractureMechanics .................... 17 2.2.2Non-LinearFractureMechanics ..................... 20 2.3SizeEectinNSC ................................ 24 2.4RateEectsinNSC ............................... 26 2.5CombinedSize-RateInvestigations ....................... 28 2.6EnergyFlowEects ............................... 30 2.7UltraHighPerformanceConcrete ........................ 31 2.7.1RateEectinUHPC ........................... 32 2.7.2SizeEectinUHPC ........................... 33 2.7.3COR-TUF ................................ 33 2.7.3.1Staticstrength ......................... 34 2.7.3.2Dynamicstrength ....................... 35 2.8Summary ..................................... 35 3METHODOLOGY ................................... 40 3.1Introduction ................................... 40 3.2ExperimentalProcedure ............................. 40 3.2.1LargeDropHammer ........................... 41 3.2.2VariableMassDropHammer ....................... 42 3.2.3DataAcquisition ............................. 42 3.2.4Instrumentation .............................. 44 3.2.5PhysicalTestMatrix ........................... 44 3.3DataProcessingandPhysicalTestAnalysis ................... 46 5

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3.4EnergyBalanceApproachandLEFMAnalysis ................. 47 3.4.1KineticEnergy .............................. 48 3.4.2StrainEnergy ............................... 49 3.4.3PlasticStrainEnergy ........................... 52 3.4.4CrushingEnergy ............................. 52 3.4.5FiberPull-outEnergy .......................... 53 3.4.6ExternalFrictionWork .......................... 54 3.4.7FractureEnergy ............................. 54 3.4.8EnergyDistribution ............................ 55 4RESULTSANDDISCUSSION ............................. 67 4.1PhysicalTesting ................................. 67 4.1.1StaticTesting .............................. 67 4.1.2DynamicTesting ............................. 68 4.1.2.1NSC-6-D-1 ........................... 68 4.1.2.2NSC-6-D-3 ........................... 69 4.1.2.3CT2-6-D-5 ........................... 69 4.1.2.4CT2-6-D-7 ........................... 70 4.1.2.5CT1-6-D-8 ........................... 70 4.1.2.6CT1-6-D-9 ........................... 71 4.2EnergyBalanceAnalysis ............................. 72 4.3Discussion .................................... 72 4.4Summary ..................................... 74 5CONCLUSIONANDRECOMMENDATIONS ..................... 116 5.1Conclusion .................................... 116 5.2AssumptionsandLimitations .......................... 118 5.3Implications ................................... 119 5.4RecommendationsforFutureResearch ..................... 119 REFERENCES ........................................ 121 BIOGRAPHICALSKETCH ................................. 126 6

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LISTOFTABLES Table page 2-1MixPropertiesofCOR-TUF .............................. 36 2-2StaticMaterialPropertiesofSAM35andCOR-TUF1/2 ............... 36 2-3ImpacttestresultsonUHPFRCbeams. ........................ 38 3-1PhysicalTestVariables ................................ 57 3-2LowpassFilterParameters ............................... 57 3-3ExampleEnergyAnalysisofUHPCCylinder ..................... 58 4-1StaticCylinderTestResults .............................. 76 4-2DynamicNSCTestResults .............................. 76 4-3DynamicUHPCTestResults ............................. 76 4-4DynamicUHPFRCTestResults ............................ 77 4-5EnergyDistributionSummary ............................. 77 7

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LISTOFFIGURES Figure page 2-1Stressininniteplatewithellipticalcrack ...................... 37 2-2Linearelasticmaterialresponse ............................ 37 2-3Center-crackedplate .................................. 37 2-4Non-linearmaterialresponse .............................. 38 2-5Cohesivecracklinestress ............................... 38 2-6Crack-bandstress-strain ................................ 38 2-7Energytankanalogyforstructuralresponse ...................... 39 3-1LargeDropHammer .................................. 59 3-2Variablemassdrophammer .............................. 60 3-3Straingagemap. .................................... 61 3-4StaticStress-Strainfor100mmUHPCCylinders. ................... 61 3-5SmallImpactHammerCrosshead ........................... 62 3-6StandReinforcingDetail ................................ 63 3-7DynamicStress-Strainfor150mmUHPCCylinder .................. 63 3-8CrossSectionofUHPFRC. .............................. 64 3-9MagniedCrossSectionofUHPFRC. ......................... 64 3-10CT2-6-D-5FractureAreaonMat ........................... 65 3-11EnergyDistributionofCT2-6-D-5 ........................... 66 4-1NSCStressvsStrain .................................. 78 4-2UHPCStressvsStrain ................................. 78 4-3UHPFRCStressvsStrain ............................... 79 4-4NSC-6-D-1StressvsTime ............................... 79 4-5NSC-6-D-1AxialStrainvsTime ........................... 80 4-6NSC-6-D-1VolumetricStrainvsTime ........................ 80 4-7NSC-6-D-1DynamicStressvsStrain ......................... 81 8

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4-8NSC-6-D-1Pre-Test .................................. 82 4-9NSC-6-D-1Post-Test ................................. 83 4-10NSC-6-D-1Fragments ................................. 84 4-11NSC-6-D-1FragmentsandFractureArea ....................... 85 4-12NSC-6-D-3StressvsTime ............................... 86 4-13NSC-6-D-3AxialStrainvsTime ........................... 86 4-14NSC-6-D-3VolumetricStrainvsTime ........................ 87 4-15NSC-6-D-3DynamicStressvsStrain ......................... 87 4-16NSC-6-D-3Pre-Test .................................. 88 4-17NSC-6-D-3Post-Test ................................. 89 4-18NSC-6-D-3FragmentsandFractureArea ....................... 90 4-19CT2-6-D-5StressvsTime ............................... 91 4-20CT2-6-D-5AxialStrainvsTime ............................ 91 4-21CT2-6-D-5VolumetricStrainvsTime ........................ 92 4-22CT2-6-D-5DynamicStressvsStrain ......................... 92 4-23CT2-6-D-5Pre-Test .................................. 93 4-24CT2-6-D-5Post-Test ................................. 94 4-25CT2-6-D-5FragmentsandFractureArea ....................... 95 4-26CT2-6-D-7StressvsTime ............................... 96 4-27CT2-6-D-7AxialStrainvsTime ............................ 96 4-28CT2-6-D-7VolumetricStrainvsTime ........................ 97 4-29CT2-6-D-7DynamicStressvsStrain ......................... 97 4-30CT2-6-D-7Pre-Test .................................. 98 4-31CT2-6-D-7Post-Test ................................. 99 4-32CT2-6-D-7FragmentsandFractureArea ....................... 100 4-33CT1-6-D-8StressvsTime ............................... 101 4-34CT1-6-D-8AxialStrainvsTime ............................ 101 9

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4-35CT1-6-D-8VolumetricStrainvsTime ........................ 102 4-36CT1-6-D-8DynamicStressvsStrain ......................... 102 4-37CT1-6-D-8Pre-Test .................................. 103 4-38CT1-6-D-8Post-Test ................................. 104 4-39CT1-6-D-8Fragments ................................. 104 4-40CT1-6-D-8FragmentsandFractureArea ....................... 105 4-41CT1-6-D-9StressvsTime ............................... 106 4-42CT1-6-D-9AxialStrainvsTime ............................ 106 4-43CT1-6-D-9VolumetricStrainvsTime ........................ 107 4-44CT1-6-D-9DynamicStressvsStrain ......................... 107 4-45CT1-6-D-9Pre-Test .................................. 108 4-46CT1-6-D-9Post-Test ................................. 109 4-47CT1-6-D-9Fragments ................................. 110 4-48CT1-6-D-9FragmentsandFractureArea ....................... 111 4-49NSC-6-D-1EnergyDistribution ............................ 112 4-50NSC-6-D-3EnergyDistribution ............................ 112 4-51CT2-6-D-5EnergyDistribution ............................ 113 4-52CT2-6-D-7EnergyDistribution ............................ 113 4-53CT2-6-D-7FragmentFracturePattern ........................ 114 4-54CT1-6-D-8EnergyDistribution ............................ 114 4-55CT1-6-D-9EnergyDistribution ............................ 115 10

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyINVESTIGATIONOFNORMALSTRENGTHANDULTRA-HIGHPERFORMANCECONCRETECYLINDERFAILUREBEHAVIORUNDERIMPACTByMichaelStoneDecember2017Chair:TheodorKrauthammerMajor:CivilEngineeringIncreasesinterrorismhaveledtomoreinterestinprotectivestructuresandhardeningcurrentfacilities.Toaidthis,newmaterialshavebeendevelopedthataremuchstrongerthanconventionalbuildingmaterialssuchasultra-highperformanceconcrete(UHPC)andultra-highperformanceber-reinforcedconcrete(UHPFRC).Thesematerialsdierfromnormalstrengthconcretes(NSC)bycombiningadvancedmixdesignwithsteelbersforincreasedductility.TheresultisamaterialthatismuchstrongerandmuchmoreductilethanNSC.Structuralresponseofthesematerialscandiersignicantlyfromsimplestrengthbasedparametersderivedfromstandardlaboratorytests.Parameterssuchassizeofthestructureandloadingratecandrasticallyaecttheperformanceofthematerial.Theseparametersaretypicallyonlyconsideredimplicitly,andtheseparametersmightbecoupledinwaysthatarenotcurrentlywellunderstood.Researchintodissipationmechanismsofimpactenergycanyieldinsightsintobehaviorthatisusefulforstructuralengineers.ThisresearchcoverstheimpacttestingofNSC,UHPC,andUHPFRCcylinderstoinvestigatethecouplingofthesefailuremechanismsandtheresponseusinglinearelasticfracturemechanics(LEFM)andanalysisofenergydissipationmechanismsviaenergybalance.Energyowanddistributionthroughthecylinderisdocumentedtoexaminethefracturebehaviorandmaterialresponsetoimpactloading.StaticcompressionresultsindicatethatbothUHPCandUHPFRChavesimilarenergycapacities.Dynamicresults,howeverindicatethattheUHPFRCiscapableofabsorbinganddissipatingsixtimesasmuchenergyasthereferenceUHPCmix.Themechanismforthisincreasedcapacity 11

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isexplainedprimarilybythelargeamountsofsteelberswhichgreatlyenhancetheenergyabsorptioncapacity. 12

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CHAPTER1INTRODUCTION 1.1ProblemStatementStructuraldesignhaslongbeendominatedbystress-basedlimitstates.Theuseoffracturecriteriaforstructuraldesignisarelativelyrecentphenomenon,andwasoriginallydevelopedformetallicandcrystallinestructures.Theuseofenergy-basedfracturecriteriaforcementitiousmaterialsisrelativelyrareduetothedicultyofcharacterizingtheirfailureprocesses.Previousresearchhasshownthatconcretestructurescanfailatlowerthanpredictedloadsduetophenomenasuchassizeeectswhicharepredominatelyenergybased.Additionalenergyparameterssuchasloadingratecanalsoaectthefailurecriteriaforthesematerials.Researchonthesendingshaveshownthepossibilitythatthesefactorsarelinked,howeverthemechanismsandamountofcouplingareunknown.Experimentsonnormalstrengthconcrete(NSC)andultra-highperformanceconcrete(UHPC)specimenssubjectedtocompressiveimpactloadshaveshowndierentfailuremechanismsthatappeartobelinkedtospecimensize,strength,andloadingrate.Furthermore,therearerecentstudiesthatdemonstratealinkbetweenstructuralfailuremechanismsandenergyowthroughthestructureasfailureprogresses( TsaiandKrauthammer 2016 ; Wilkes 2016 ).ExistingresearchonsizeeectinUHPCisextremelylimitedandsomeresultsarecontradictory.ThecombinationofsizeandrateeectsinNSCandUHPCunderimpactisthereforeunknownandposesacriticalproblemforstructuralengineersinvolvedwithhardenedprotectivefacilities.Understandingtheunderlyingphenomenathatdeterminebothsizeandrateeectsisessentialfordevelopingarationalapproachforusingsuchmaterialsinprotectivedesign. 1.2HypothesisItishypothesizedthatthechangeindynamicstrengthsforthesematerialscanbeexplainedviadistributionofenergyandenergyowduringthefailureprocess.Totestthis,calibrateddynamictestingwillbeperformeduntilafailurewithminimalkineticenergyoccurs. 13

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Thesetestresultswillthenbeanalyzedusingforensicmethodsincludinganenergybalancetoexplorethedistributionofenergyduringthefailureprocess. 1.3ResearchSignicanceConcretestructuresaretypicallydesignedbasedonstrengthparametersderivedfromlaboratorytestsonstandardsizedspecimens.Whilethesetestscangiveconsistentdata,theyarenotrepresentativeofthetruestructuralcapacity.Forcriticalprotectivestructures,orlargestructureswherenon-lineareectshaveagreaterroleinstructuralresponse,thetruecapacityisofparamountconcern.Whilethisistypicallyhandledthroughmagnicationofpredictedstructuralloads,newmaterialsinuseforprotectivefacilitiesareextremelyexpensivecomparedtotypicalmaterials.Assuch,characterizingtheabilityofthesematerialstoperformunderhighlyenergeticloadsshouldbeundertaken.Secondly,thereisgrowingunderstandingoftherelationshipbetweenenergyowthroughstructuresandfailure.Workdoneonprogressivecollapseofsteelframedstructureshasshownalinkbetweenenergyowthroughthestructureandglobalfailuremodes.Previousworkonnormalstrengthandhighstrengthcylindersunderimpacthaveshownarelationshipbetweenimpactrate,specimensize,andfailuremode.Thiscorrelationappearstobesimilartoacouplingofthesizeandrateeectsonstructuralresponse;howeveritisnotwellcharacterized.Additionally,thesenewmaterialshavedierentsensitivitiestostrainrateeectsthannormalconcretes.However,thecouplingofsizeandrateeectsinevennormalconcreteisnotwellunderstood,anddataforUHPCarealmostnon-existant.Acomprehensivestudyofthesematerialsinthecompressivedomaincanleadtoafurtherunderstandingoftheresponseofthesematerialsandallowforimprovedanalysisanddesigncapabilities.Characterizationoftherelationshipbetweenenergydistributionandowduringthefailureprocesswillhelpunderstandhowthesematerialsaectstructuralbehaviorandfurthertheirproperuseinprotectivedesign,particularlyinenergydissipationduringdynamicloading. 14

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1.4ObjectiveandScopeTheobjectiveofthisresearchistocharacterizetheresponseofnormal-strengthandultra-highperformanceconcreteundercompressiveimpactloadings.Frompreviousdynamiccylindertests,atleastsixglobalfailuremodesforcylindersunderdynamicimpacthavebeenobserved( Elfahaletal. 2005 ).Severalfailuremodesresemblestaticfailuremodes,whileothershavevaryingamountsofobservedejectaandexcesskineticenergy.Thesefailuremodesvarydependingontheseverityofloadimpulseandspecimensize.Characterizationoftherelationshipbetweenfailuremodeandenergydistributionandowwillprovidenewmethodsofanalysisandunderstandingforstructuralfailureduringdynamicevents.Itisproposedtotestthreematerialsunderimpactloading.Fromthesetests,asinglefailuremodefromeachmaterialwillbeanalyzedviauseofstraingages,loadcells,andvisualinspectionincludingmicroscopyandhigh-speedvideoanalysis.Datawillbeusedtoformulateabreakdownofenergycomponentsduringthefailureprocess.Thedataextractedwillbesubjectedtoaforensicanalysisusingenergybalancemethodstodeterminewhatparametersmightcontributetothisparticularfailuremode:boundaryconditions,loadrate,ormicromechanicaldamage.Theproposedworkwillbedoneinthreesteps:staticphysicaltesting,dynamicphysicaltesting,andanalysisusingforensicsandprinciplesofenergymethods.First,statictestingwillbeperformedoncylinderstodeterminethemechanicalandstructuralpropertiesofthematerials.Second,dynamictestingwillbeperformedoncylindersusingadrophammer.Finally,datafromthedynamictestswillbeusedtodeterminethedistributionofenergyduringthefailureprocess,andexaminetherelationshipbetweentheenergydistributionandthefailuremethod.AreviewofexistingliteratureisprovidedinChapter 2 .ResearchapproachandmethodologyarediscussedinChapter 3 .ResultsanddiscussionarepresentedinChapter 4 .ConclusionsandrecommendationsarepresentedinChapter 5 15

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CHAPTER2LITERATUREREVIEW 2.1IntroductionFailureofcementitiousmaterialsinthedynamicregimeisamajorconcernforstructuralandprotectiveengineering.Dynamicfailurecanbesuddenandwithlittlewarning,whichrequiresafundamentalunderstandingofnotonlythemodesoffailurebuttheunderlyingcauseforeachtypeoffailure.Researchhasbeenfocusedonthefailuremechanisms,buttypicallybasedonstress-straincriteria.Energyanalysisforfailureofconcretehastypicallybeenlimitedtoinvestigationofstructuralcomponents,butnotaddressingallenergyforms(suchasstrain,kinetic,fracture,etc.).Criticaltoanyfractureenergyapproachtostructuralresponseisthetoughnessorfractureenergyofthematerial.Multiplemethodshavebeendevelopedtoinvestigatethetoughnessofconcreteandothermaterials.Additionally,newtypesofconcretehavebeendevelopedforbetterprotectionofcriticalstructures.Thissectiondetailsthebackgroundliteratureonfailuremechanisms,researchmethods,andnewtypesofconcreteunderdevelopmentandusageinprotectivestructures. 2.2FractureMechanicsFracturemechanicsisthestudyofmaterialandstructuralfailurethroughcrackpropagationandotherfailuremechanics.Itdiersfromstrengthbaseddesignproceduresinthatthefailureofthestructureisderivedbyenergyprinciplessuchaspropagationoffailureplanesandnotthematerialstrengthitself.Fracturemechanicscanbesubdividedintotwoareasofstudy:linearelasticfracturemechanics(LEFM)andnon-linearfracturemechanics(NLFM).LEFMisrestrictedtothestudyofmaterialsthatareperfectlylinearelasticuntilfailure,whileNLFMexaminesallmaterialsthatdisplayotherbehaviorssuchasplasticbehavior,hardening,softening,etc.Crackpropagationcanbeclassiedasoneofthreeseparatemodes:ModeI,opening;ModeII,sliding;andModeIII,tearing.ModeIfractureiswherethefailureplanepropagates 16

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normaltothedrivingforce,andistypicaltotensilestress.ModeIIisasheartypeslidingfailurethattravelsparalleltothedrivingforce.ModeIIIisasheartearingfailureassociatedwithtorsionalforces,wherethefailureplaneisparalleltoboththeforcesandthecrackfront.ModesIandIIarethemostcommonformoffailureformostconcretestructures. 2.2.1LinearElasticFractureMechanicsLinearelasticmechanicsassumethatthematerialstress-strainrelationshipispurelylinearuntilthefailurestressisreached.Inthepresenceofadefectsuchasacrack,stressesconcentrateandcanbeshowntobeafunctionofthegeometryofthedefectandthefar-eldstresses. Inglis ( 1913 )showedthatthemaximumstressatthetipofadefectisthefree-eldnormalstressmultipliedbyaconcentrationfactorktthatisdependentonlyonstructuralgeometry.Forexample,thestressatthetipofanellipticalholeasseeninFigure 2-1 is: tip=1+2a b(2{1)whichcanbeapproximatedby tip=2p a==kt(2{2)wherektistheconcentrationfactorandisthecurvatureofthecracktip.Foraninnitelynarrowtip,thestressconcentrationapproachesinnity.Foramaterialwithalinearelasticmaterialresponseuntilfailure,asshowninFigure 2-2 ,oncethetipstressreachesthefailurestress,theentirestructurewillfailcatastrophically.Thisindicatesthatthestressbasedfailurecriterionisnotapplicabletopurelylinearmaterials,asanyappliedloadatasharptipwillresultinaninnitestress.Asaresult, Grith ( 1920 )developedanenergybasedfailurecriterionbasedontheenergyrequiredtoextendaunitwidthcrack.ForasmallcrackinaninniteplateasseeninFigure 2-3 ,thechangeinenergyduetocrackextensioncanbecalculatedas: U)]TJ /F4 11.9552 Tf 11.955 0 Td[(U0=)]TJ /F4 11.9552 Tf 10.494 8.088 Td[(2a2 E+4as(2{3) 17

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wheresistheelasticsurfaceenergy,amaterialproperty.BytakingthepartialderivativeofUwithrespecttocracklengthandsettingequaltozero,thefailurestresscanbecalculatedas: =r 2Es a(2{4)NotethatforGrithcracktheory,the2ndderivativeofpotentialenergyisnegativeforappliedtensilestress,whichimpliesthattheequilibriumisunstableandthecrackwillalwaysgrow.Theenergyreleaserateisaconceptderivedfromstabilityconceptsandderivativesofpotentialenergy.Ifthestructureisstable(nochangeinpotentialenergy),thentherstderivativeofenergywithrespecttocracklengthwillbeequaltozero(Equation 2{5 ).Anychangeinstrainenergyofthestructure(U)orexternalwork(F)willbeequaltothechangeinenergyforcrackformation(W).ThecriticalenergyreleaserateistermedGc.IfG=Gc,thenthecrackcanpropagate. @ @a=@ @a(F)]TJ /F4 11.9552 Tf 11.955 0 Td[(U+W)=0(2{5)TypicalmethodstoevaluateGinvolvecalculationofeitherstrainenergyorcomplementarystrainenergyataconstantloadPorconstantdisplacementu.ForalinearelasticmaterialwithacompliancefunctionC( Shahetal. 1995 ),Gcanbeexpressedas: G=)]TJ /F6 11.9552 Tf 10.494 8.088 Td[(1 t@U(a;P) @aP=P2 2t@C @a(2{6)AsGistheenergyrequiredtoopenacrackaunitdistance,itisequaltothesameenergytoclosethecrackunderatractionstressy,whichisafunctionofcrackshape,specimengeometry,andloadingcondition. 18

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Westergaard( Shahetal. 1995 )derivedthestressanddisplacementeldsforfractureasafunctionofdistanceandorientationtothetipofthecrack: y=K p 2rcos 21+sin 2sin3 2 (2{7a)x=K p 2rcos 21)]TJ /F6 11.9552 Tf 11.956 0 Td[(sin 2sin3 2 (2{7b)xy=K p 2rsin 2cos 2cos3 2 (2{7c)whereKisastressintensityfactorthatdependsonthegeometryofthecrackandthespecimenaswellastheappliedloadandstresslevel.Forexample,itcanbeshownthatfortheellipticalcrackinaninniteplate,KIandKIIcanbeshowntobe: KI=p a (2{8a)KII=p a (2{8b)ormoregenerally, K=p ag1a b(2{9)whereg1isageometriccompliancespecictothestructureandloadingcondition.Kcontainsmoreinformationaboutthecurrentloadandgeometrythanthestressconcentrationfactorktalone.SinceKhasinformationaboutstresslevelsatthecracktip,itcanbeusedincalculationsforG.Aftercalculatingthestressintensity,thecrackgeometryandmouthopeningdisplacment(CMOD)canbedeterminedbasedonstructuralgeometry: CMOD=4a Eg2a b(2{10)whereg2isanadditionalgeometriccompliancefunction.Basedonthesetwoparametersthecrackopeningdisplacement(COD)canbecalculatedforeachgeometryandloadcase.UsingthepreviousobservationthatGcanbecalculatedbasedonthestressclosingacrack, Irwin ( 1957 )showedthatGIisrelatedtoKIviatherelationshipinEquation 2{11 .Similar 19

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relationshipsexistforGII-KIIandGIIIandKIII. GI=2 aZa01 2ywdx=KI2 E(2{11)TheuseofKforcalculationsofGistypicallyeasiersinceKisadditivefordierentloadingandboundaries.Additionally,sincethereismoreinformationcomparedtostressconcentrationalone,Kcanbeusedtoguidestructuraldesign.IfKiisequaltoacriticalthresholdvalueKic,thenthecrackpropagates.InthismannerKandGarethesamecriteriondenedwithdierentparameters.Forasharpcracktipinarealmaterial,therecannotexistaninnitestressasimpliedbyEquation 2{1 wherebapproacheszero.Assuch,theremustbeacertainamountofinelasticdeformationaheadofthecracktip.TwoapproachesareusedinLEFM:theGrith-Irwinequivalentcrackmethod,andtheDugdalectitiouscrackmethod.Therstmethodassumesalargercrackthantheactualcrack,andthedierenceinsizeiscalculatedviaforcebalance.Thectitiouscrackiscalculatedbyassumingalongerstripwiththematerialyieldstressactingontheadditionalcracklength,wherethectitiouscrackstripiscalculatedusingstressthematerialstressintensityfactorK.Inbothapproaches,thesizeofthefractureprocesszoneisassumedtobesmallcomparedtothesizeofthecrack.Forquasi-brittlematerials,thereisnodenedyieldlimitandtheprocesszonecanbeasizeappreciabletothecracksize.Forthatreason,non-linearfracturemechanics(NLFM)mustbeusedwithquasi-brittlematerialssuchasconcrete. 2.2.2Non-LinearFractureMechanicsNon-linearmaterialsincludeallmaterialswithstress-strainrelationshipsoutsideofpureelasticbehavior,suchasshowninFigure 2-4 .Asseen,concretesareclassiedasquasi-brittlematerials.Fornon-linearmaterials,thecrackbehavioroncetherequiredenergyisreachedmaybeunstable,stable,orstationary.Crackstabilitycanbedeterminedbyevaluatingthepotentialenergyfunctionforstabilitybytakingthesecondderivativeofwithrespecttocracklength.Forastableorstationarycrack,therateofenergyreleaserate(@Gq)willbelessthanorequaltotherateofthefractureresistance@R.Fornon-linearmaterials,theenergyreleaserateGq 20

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asourceoffractureenergy,andthefractureresistanceRisasink,analogoustoGandGcinLEFM.ThetotalfractureenergyGqcanthenbeassumedtobeacombinationoftheLEFMenergydissipationmechanismandtheenergyrequiredtoovercomethecohesivestressesinthefractureprocesszone,seeninEquation 2{12 Gq=GIc+Zwt0(w)dw(2{12)TheuseofNLFMforquasi-brittlematerialsisdemonstratedbyexperimentsonsize-similarspecimens( HigginsandBailey 1976 ).AccordingtoLEFM,thecriticalstressintensityfactorshouldbesizeindependent,sincethesquareofKiislinearlyproportionaltoGrith'ssurfaceenergyasamaterialproperty.However,resultsshowedthatthemeasuredKiissizedependent.TwomethodsaretypicallyusedforNLFMofquasi-brittlematerialsdependingonhowtheenergyEquation 2{12 ishandled.Thegeneralmethodistoassumethatoneofthetwotermsisequaltozero.IfGIcissettozero,theenergyisassumedtodissipatethroughacracklinejustaheadofthecracktip,alsoknownasthectitiouscrackapproach.If(w)isassumedtobezero,thentheenergydissipationisconcentratedinthecracktip,alsoknownastheeectiveelasticcrackapproach.Two-energymethodshavealsobeensuggested( CoxandMarshall 1994 )butarenottypicallyused.Inthectitiouscrackapproach,theLEFMenergydissipationtermfromEquation 2{12 issettozero,andenergydisspationischaracterizedbythepostpeakstressrelationship(w).Allfractureenergyisassumedtobedissipatedthroughacracklineoflengthwt,wherethecohseivestress(w)overthecracklengthbalancestheenergyproducedbytheappliedload,andisrepresentedinEquation 2{13 .Ifwtisnotlocatedatthecracktip,whichcanoccurafterpeakload,thentheintegralisevaluateduntil(w)equalszero,denotedwc.Whentheprincipletensilestressreachesthematerialstrengthftthecrackpropagateswithasoftening 21

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curvecontrollingthecracktipopening,asseeninFigure 2-5 Gq=Zwt0(w)dw(2{13)Thisapproachwasrstproposedby Hillerborgetal. ( 1976 )usingconcreteplatessubjectedtouniformtension.Bymountinggagesoverthelengthofthespecimenandrecordingthestrainsovercrackedanduncrackedsections,thestress-strainresponsecanbedividedintotwoparts:pre-peaktensileresponse,andpostpeaksoftening.ThefractureenergyGFisequaltotheareaunderthepostpeaksofteningcurve.Thespecicsofthecurvearedeterminedbythreeparameters:criticalenergyreleaserate,tensilestrengthft,andshapeofthecurve.Accurateshapeofthecurvemustbedeterminedthroughextensivematerialtesting,andmanydierentshapessuchaslinear( Hillerborgetal. 1976 ),bilinear( RoelfestraandWittmann 1986 ),andexponential( GopalaratnamandShah 1985 )havebeenproposedanddocumented.Typicallythecurveshapeisdeterminedthroughtestingspecimenssuchasthree-pointbendspecimens,howeverdirecttensiletestinghasbeenattemptedwithlimitedsuccess.Acriticalassumptionofthemodelisthatcrackedfacesareincontactduringstablecrackpropagation.ThisconstraintimpliesthatGFforpeakloadequalstheinputloadenergyGqonlyforstructuresofinnitesize.ObservedvaluesofGFaretypicallylowerthantheoreticalpredictions,indicatingasize-eectrelationship.Anothermethodistoassumethatauniformlydistributedbandofmicrocracksofconstantwidthexistsjustaheadofthecracktip,asproposedby BazantandOh ( 1984 ).Asthecrackpropagates,asimplestressstrainrelationshipasseeninFigure 2-6 describestheprogressionofmicrocrackswithinthisband,andthecrackopeningiscalculatedbythestrainandcrackbandwidth.Thetotalenergyrateconsumed,Gf,isthereforetheareaofthestress-straincurvemultipliedbythewidthofthecrackbandhc.Totalenergyconsumptioncanthereforebecalculatedviaalgebraas: Gf=hc1+E Etf2t 2E(2{14) 22

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Empiricaltestinghasestablishedthatthecrackbandwidthhcisafunctionofmaterialpropertiessuchasmaximumaggregateorgrainsizedaandaconstantna.Foratensileplatesubjectedtoacentercrackofdimension2a,thecriticalstresscanbeapproximatedviastrainenergymethodstobe: Nc=Bft p 1+b=b0(2{15)whereBftisarearrangmentof 2{14 andb0isageometriccompliancefunctiondependentonspecimenshape,na,andda.Intheeectiveelasticcrackapproachallenergyisdissipatedbyaequivalentelasticcrackwithnocohesionstress(w).ThecrackistreatedusingLEFMprinciples,butwithmodel-specicparameterstotiethebehaviortoactualcrackbehavior.Thesemodicationsextendthecracktipanitedistancetoaccountfortheenergydissipationatthecracktip.Forquasi-brittlematerials,theextensionofacrackfromanexistingawextendsinastablemannerbeforecriticalextensionatpeakload.Thiscriticalextensionisthefailurepointofthestructure.LEFMcanbeusedforpostcriticalbehavior,buttheinitialenergyconsumptionrequiresmoreinformationbasedonmaterialbehaviorandstructuralgeometry.Twopossibleparametersusedforthisapproacharethecriticalcracktipopeningdisplacement,CTODc,andthecriticalcrackextensioncfforaninnitelylargestructure.Three-pointbendingtestswreconductedby JenqandShah ( 1985 )onconcretespecimensandtheplasticandelasticcrackmouthopeningdisplacements(CMOD)weremeasuredatpeakspecimenload.Thesevalueswerethenusedtocalculatethecracktipopeningdisplacement(CTOD)bygeometricfunctions( Tadaetal. 2000 ).BasedontheseparametersalongwiththesolutionsforLEFMthecrackbehaviorandcriticalfractureloadofquasi-brittlestructurescanbepredicted. KarihalooandNallathambi ( 1989 )proposedusingthepeakloadofthree-pointbendingtestsandsecantcompliancewithLEFMtocalculatethecriticalelasticstressintensityfactorKeIc. SwartzandRefai ( 1988 )measuredcrackextensionandcriticalloadsofbeamsundercyclicloadingtocalculatethestressintensityfactorforvariousbeams. 23

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Additionally,BazantandKazemiexaminedgeometricallysimilarstructuressubjectedtosimilarloads.Examiningstructureswithconstantratioofcracksizea0tocharacteristicdimension,D,theywereabletoshowthatthecriticalcrackextensioncfandcriticalenergyreleaserateGfforaninnitelylargestructurecanbeusedtocalculatethenomianlcriticalstress,Ncforanitestructure.Insummary,mostapproachesformodelingconcreteusingfracturemechanicsuseaLEFMapproach,withmodicationstoincludeknownnon-linearfracturemechanicssuchaspost-peakstresssofteningandcrackbridging.LEFMismoreapplicableforbrittlefracturebutissimplertoevaluate,whileNLFMmodelsductileresponsemoreaccuratelybutrequiresamuchmoreinvolvedanalysismethod.Bymodelingthenon-linearresponseinasimpliedmanner,theproblemcanbeanalyzedusingaLEFMapproach. 2.3SizeEectinNSCThebasisofmuchofcivilandstructuralengineeringisstrengthbasedapproaches,wherethepeakstrengthisamaterialparameterindependentofstructuralsizeandloadingcondition.However,throughmanyyearsofobservationsandtests,ithasbecomeapparentthatstructuresoflargersizetendtohavecriticalfailureloadsandstressesthatarelowerthanthosepredictedbysimplestrengthbasedapproaches. Gonnerman ( 1925 )observedalmost100yearsagothatconcretecylindersofdierentsizeswiththesameshapefactorhaddecreasingstrengthwithincreaseinsize.Duringthe1960sand1970s,multipleresearchersobservedevidenceofsizeeectonstructuresofdierentgeometriesandloadingconditions.TheformaldenitionofsizeeectisbasedongeometricallysimilarstructuresofdierentsizeandtheirnominalstressNatpeakloadPu.IfNcanbeshowntobedependentonstructuralsizethenasizeeectissaidtoexist.Dierentapproacheshavebeenproposedtoexplainthisphenomena,includinghydrationandchemicalreactionphenomena,boundarylayereects,stochasticeects,andenergydissipationduetofracturemechanics( BazantandPlanas 1998 ).InitiallyitwasbelievedthatlowerstrengthwasduetostatisticaleectsusingWeibull'sweakestlinktheory.Thetheory 24

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isbasedonthatofachain,inwhichthetotalloadcapacityisdependentontheweakestlink.Thelargerthechain,themoreprobabilityaweakerlinkwillbepresent.However,thispredictionisonlyvalidforstructureswherefailureisinitiatedatmacroscopiccrackgrowthofmicroscopiccracks,suchasmetallicstructuresandlongbarsundertension,andisnotwellsuitedforconcrete,whichfailsthroughstablecrackzonegrowth.Additionaleortshavebeenmadetostudysize-eectincompressionfailureofcementitiousmaterials,especiallyasrelatedtoboreholesandtunnelingoperations.Ithasbeenshownthatcertainfracturebehaviors(suchasamacroscopicverticalsplittingcrack)ofcompressionmembersdonotresultinaglobalenergyreleasethataectstheglobalstresseld,andthereforesizeeectisonlypresentforcertaintypesoffailuremodes( BazantandOzbolt 1992 ).Ifthefailuremechanisminvolvesformationandsidewaysgrowthofaxialsplittingcracks,thenasizeeectcanbepredictedviaLEFM.Experimentsperformedonrectangularstubcolumnsundercompressiveloadsprovedasize-eectlawforcolumnsthatexperiencethiscrackbandfailure( BazantandPlanas 1998 ).Thiscriteriondependsontheprinciplestressescausedbyaneccentricloadingandthegeometryofthecrackandcolumncross-section.Ingeneral,thefailurecriterionalongthecrackbandcanbeexpressedasafunctionofthesizeofthestressreliefzone(k),thesizeofthecrack(bothdepthandheight,andh),theassumedwidthofthemicrocracksinthecrackzone(s),thematerialfractureenergy(Gf),andtheappliedload(P): F(k;;h;s;Gf;P)=0(2{16)wheretosolveforPtherstvevariablesmustbeknown.Ofthesevariables,Gfandharematerialpropertieswhilekisdeterminedfromelasticity.Sincethecrackisapropertyofthetotalcracklengthwhilesisthedepthofeachmicro-slab,thecriticalloadPthatwillcausebucklingofthecrackmicro-slabsisthereforedependentons.BydierentiatingFwithrespect 25

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tosandsettingequaltozero,thefailurecriterionsolutioncanbeobtained. @F @s=)]TJ /F6 11.9552 Tf 9.299 0 Td[(2k22+2)]TJ /F4 11.9552 Tf 5.48 -9.684 Td[(k3)]TJ /F6 11.9552 Tf 11.861 2.657 Td[(h2+h3+3h3Gf 22s3D=0(2{17)Usingtheseequations,thevaluesofNuandDcanbedetermined.However,ifthecolumnisstockyandthereisnoeccentricitytotheappliedload,theLEFMequationscanbesimpliedto: Nu=2:76E3G2f (2ka+h)21=5(2{18)asnotedin( BazantandPlanas 1998 ). 2.4RateEectsinNSCItiswellknownthroughexperimentationthatresponseofstructuralsystemsisdependentontheloadingrate.Duringdynamicloading,astresswaveinitiatesinthematerialatthepointofloadandthenpropagatesthroughthematerialatthematerialwavespeed,whichcanbecalculatedbycontinuummechanicsasdetailedin( Tedescoetal. 1999 ; Malvern 1969 ).Asthestresswavetravelsthroughthemedium,itinteractswithanymediuminterfacessuchasfreeendsorboundaries,whichcausewavereection.Theintensityandsign(i.e.whetherthestresswaveistensileorcompressive)ofthereectedstresswaveisdeterminedbytheboundingmedium'sdensityandmaterialproperties,andiscalculatedbytheratiobetweenthematerialpropertiesandgeometryoneithersideoftheboundary.Interferencebetweenthestresswavecancauseeitherenhancmentornegationofstresses.Formulaforderivingthewavepropertiesaredevelopedin( Tedescoetal. 1999 ; Krauthammer 2008 ).Rateeectisdenedastheapparentstrengthofthematerialhavingasensitivitytostrain-rate.Forconcretesandcementitiousmaterials,themechanicsandoriginoftherateeecthavebeenlinkedtoviscoelasticityofthecementpaste,thermallyactivatedcrackgrowth,mechanicallimitationsofcrackgrowthvelocity,andinertialeects( ACICommittee466 2004 ).Strain-ratesensitivityistypicallystudiedthroughseveraltestingmechanisms(Charpyimpacttests,drophammertests,andSplit-HopkinsonPressureBar)listedbelow. 26

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Charpyimpacttestsarecharacterizedbyhorizontalimpactofspecimensusingapendulumtypemechanism.Thespecimenisplacedintothetestingapparatusatthebaseofthemachine,andapendulumwithaweightedimpactorisliftedandreleased.Atrelease,thependulumswingsandimpactsthespecimenwithaconstantparallelvelocity.Drophammersareavariantofthecharpyimpacthammer.Insteadofusingapendulum,themassisraiseddirectlyabovethespecimenonrailsandreleased.Advanceddrophammershavefeaturestopreventmultipleimpacts,measureimpactenergy,impactload,andotherparameters.TheSplit-HopkinsonPressureBar(SHPB)isanadvancedmachinefortestingspecimensunderextremelyhighstrainrates,typically10s)]TJ /F8 7.9701 Tf 6.587 0 Td[(1to102s)]TJ /F8 7.9701 Tf 6.586 0 Td[(1.Thetestingapparatusiscomposedoftwosteelbarswithaspecimenplacedinbetween.Ablowisdeliveredtotherstbar,termedtheincidentbar,andaloadpulsetravelsdownthebartothespecimen.Whenthewavereachesthespecimen,partwillbereectedbackintotheincidentbarwherestrainismeasured.Thestrainwavetravelsthroughthespecimentowardsthesecondbar,termedthetransmitterbar.Attheboundary,asecondpartialreectionoccursandtravelsbackintothespecimen.Theremainingstrainwaveismeasuredviaastraingageinthetransmitterbar.Bymeasuringthestrainsandstressesthefailurestress/strainofthematerialcanbedeterminedwithveryhighstrainrates.Bychangingtheboundaryconditionsandloadingpointofthetwobars,eithertensionorcompressionwavescanbemeasuredonthesample.ComprehensivereviewsofSHPBtestingonconcrete( BischoandPerry 1991 )showedthatnotonlyisthereasignicantincreaseinstrengthduetoloadrates,butthattheincreasecanbedistinguishedintotwoseparatemodes.Therstmodeoccursatratesbetweenquasi-static(10)]TJ /F8 7.9701 Tf 6.586 0 Td[(6s)]TJ /F8 7.9701 Tf 6.586 0 Td[(1)anddynamic(10s)]TJ /F8 7.9701 Tf 6.586 0 Td[(1),wherethedynamicincreasefactorisapproximately1.5.Theprimarycauseforthisdomainissuspectedtobeacombinationofmaterialviscosityandcrackingoflargeaggregateinthethematerial( ChandraandKrauthammer 1995b )Thesecondmode,whichoccursatstrainrateshigherthan10s)]TJ /F8 7.9701 Tf 6.587 0 Td[(1,hashigherDIFswhichareduetoinertialeects( Weerhejim 1992 ; ChandraandKrauthammer 1995a ). 27

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Inertialeectscanbeclassiedintotwotypes:structuralinertiaandfailurecriteriainertia.Structuralinertiaisinertialforcesoftheentirestructureresistingdynamicmotion,whichaddtotheabilityofthestructuretoresistexternalforces(F=mu+ku).Whencombinedwithamaximumstrainfailurecriterion,thisresultsinanapparentstrengthincreaseforthestructure.Thisphenomenawasinvestigatedinreferencetothree-pointbeamsunderbending( ChandraandKrauthammer 1995b )wherethestressatthebottomberreachespeaktensilestressatahigherloadthenthestaticcriticalloadduetonegativeinertialforces.InertialeectsalsoaectthecrackgrowthandthefailurecriteriaforLEFMmaterials.ForaLEFMmaterial,thestressintensityfactorhasbeenshowntodecreaseastheloadrateincreases( ParkandKrauthammer 2009 ).IntitalmodelsassumedadynamicreductionfactorthatdecreasedtozeroasthecracktipvelocityapproachestheRayleighwavevelocity,wherethematerialaroundthecracksurfacecannotrespondtoactualcracksize.Testingonsingleedgednotchedbeamswithspecialgagesthattrackedload,strain,andcrackextensionovertimewithvaryingloadratesrevealedthatcrackgrowthandthefractureprocesszonepriortopeakloadwasstrainratedependent,anddecreasedasloadrateincreased.Resultsindicatedthatcrackgrowthprimarilypropagatesatpeakload,andthatLEFMmightbevalidforhighloadratesforsizeandrateeects.Additionalinvestigationshavefocusedoncrackvelocityandhowitrelatestostructuralbehavior.Crackedthree-pointbeamshavebeenanalyzedusingTimoshenkobeamtheory( Kishimotoetal. 1984 ; Tadaetal. 2000 )andequivalentmass-springmodels( Marur 1996 )forrelationshipbetweencrackvelocity,andstrengthgainduetoinertialforces.Thesestudiesyieldedasingledegreeoffreedom(SDOF)structuralmodelfornotchedthree-pointbeamsunderdynamicloadingbasedonenergyprinciples. 2.5CombinedSize-RateInvestigationsImpacttestingofconcretecylindersofdierentsizesunderdierentloadingconditionsrevealedapotentialcouplingofsizeandrateeectsforNSCandHSC( Elfahaletal. 2005 ).Fourdierentsizesofgeometricallysimilarcylindersweresubjectedtostaticloadingaswell 28

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asimpactloadsbya2600kgmassateither5m/sor7m/s.Testswerealsoconductedwithandwithoutrubberpadsontopofthespecimentoinvestigateimpactspikes.Whiletheresearchwasoriginallylimitedinscopetoinvestigationofsize-eectpresenceduringdynamicloading,itwasfoundthattheimpactrateandthesizeofthespecimenhadaneectonthefractureprocessandmechanicsofthecylinders.Severaldierenttypesoffailurebehaviorwereobservedandarediscussedbelow.Failuremodesweredividedintoseveraldierenttypes,andareshownin( Elfahaletal. 2005 ).Thetypesarecategorizedasfollows: VerticalSplitting,wherethecylindersplitverticallythroughtwoormoreverticalplanes.Thistypeofbehaviorwasassociatedwithhigherrecordedstrengthmeasurements. Cone-shapedShear,whichwassimilartotypicalstaticfailure,wherethecylindersfailedatthesidesleavingtwoconesforminganhourglassshape. DiagonalShear,whichischaracterizedbyadiagonalfailureplane. Bucklingfailure,whichwascharacterizedbyinationofthecylinderfromeitherthetoporbottomandbulgingofmaterialinthecenter. Compressivebellyfailure,wherethecenterofthecylinderbulgedout,sometimescombinedwithshell-burstingfailure. Shell-corefailure,wheretheshellofthecylinderburstleavingacentralcoretoresisttheload.Thistypeoffailurewasalsoassociatedwithadoublepeakintheload-timehistory. Progressivecollapsefailurewithgradualgrowthoffailurecracksfromthetopofthecylinderdownwardwhilethehammerprogressivelypusheddownintothespecimen.IngeneralitwasobservedthatlargerHSCspecimenstendedtofailinmorebrittlefailuremodescomparedtotheNSCandsmallersizedspecimens.Numericalanalysisofcombinedsize-rateeects:Furtherinvestigationwasperformedanalyticallyby ParkandKrauthammer ( 2009 )toinvestigatecouplingofsize-ratephenomena.AdynamiccrackcriterionwasdevelopedbasedonLEFMandisexpressedas: _UE=_Us+_Uk+2B_a(2{19)whereUE,Us,andUkaretheexternalwork,strainenergy,andkineticenergyratesrespectively,Bisthespecimenwidth,andisthespecicsurfaceenergyperunitarea.Ofcriticalnote 29

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hereisthatisamaterialpropertyandshouldnotbemodiedtosuitdierentstructuralgeometry.Usingthisprincipleequationtoinvestigateasingledegreeoffreedom(SDOF)system,thecriterionwascombinedwiththeequationofmotiontobeexpressedas: 2=1 B)]TJ /F6 11.9552 Tf 10.494 8.088 Td[(1 2dK dau2+1 2dM da_u2(2{20)whereKisthespringconstant,Misthemass,anduisthevelocityoftheSDOFsystem.Byrequiringakineticenergyterm(M_u2),thedynamiccrackcriterionisapparenttobedependentnotonlyonsizeofthesystembuttheenergyrateaswell.Usingthismodel,thekineticenergytermallowsforanincreaseinstrainenergybeforecrackpropagation.Additinally,thekineticenergytermisnotlinearlycoupledtothesizeeectterm,andthereforethetotalcontributionofbothsizeandrateeectsshouldnotbetreatedasmultiplicationoftwostrengthfactors. 2.6EnergyFlowEectsDuringanydynamicevent,theconservationofenergyrequiresthattheinputenergybeequaltotheoutputenergy.Energyofthetotalsystemmaybevisualizedasauidstoragetank( CloughandPenzien 1985 ).Inputenergyisvisualizedasowintoasystemofwatertanks,withowexitsandbucketsrepresentingplasticenergydissipationanddampeningmechanisms,asseeninFigure 2-7 .Energyisinputintothestructuralsystem,isstoredinthekineticenergyandstrainenergyprimarytank,withareleasethroughdampeningandfrictionmechanisms.Iftheenergylevelaccumulates,overowisreleasedintotheplasticenergydissipationtank.Iftheplastictanklls,thenthestructurereachesfailure,whicharepredenedcriteriathatmightbeadamagelimitsuchasdisplacementorsupportrotation.Additionalworkondynamicowofthisenergyhasbeendonetoextendstudiestoprogressivecollapse( Wilkes 2016 ; SzyniszewskiandKrauthammer 2012 )andmodicationofP-Idiagrams( TsaiandKrauthammer 2016 ).Progressivecollapsethroughstructureshasbeenshowntodependontheenergyowthroughthestructureandtheresponsemechanismshavingachancetodissipatetheenergyaccumulation. 30

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Furtherworkhasbeendoneondistributionofenergyduringfractureandfragmentationofglassbarsimpactedbysteelballs( Jannottietal. 2015 ).Impactorposition,crackpropagation,andfragmentpositionandvelocityweretrackedusinghigh-speedphotography.Measurementswereusedalongwithanenergybalancetoequatetheinputkineticenergyfromtheimpactortovariousenergydissipationmechanismssuchaselasticstrainenergy,kineticenergyofthebarandfragments,frictionenergy,fragmentationenergy,andrigidbodymotion.Useoftheenergybalanceallowedforcomparisonofstrengthenedandnon-strengthedglassandfurtherunderstandingofenergydissipationmechanismsduringimpact. 2.7UltraHighPerformanceConcreteDevelopmentofhighperformanceconcretemixesbeganinthe1940swithresearchintotherelationshipbetweenporosityandcompressivestrength( PowersandBrownyard 1946 ).Laterresearchwasdonetoreduceporesizeandincreaseparticlepackingdensityofcementpastes.Earlyexperimentswereabletoincreasecompressivestrengthbeyond200MPaupto655MPathroughuseofexoticaggregates( Brunaueretal. 1970 ; RoyandGouda 1973 ).Furtherresearchintoadditivessuchassilicafumeandsuperplasticizersresultedinmaterialswithporositybelow2%andextremelyhighcompressivestrengths( Buitelaar 2004 ).Increasingcompressivestrengthinsuchmannerhasamajordrawback,however:theresulingmaterialisextremelybrittleandanyinitialfracturetypicallyresultsincatastrophicfailure.Separately,researchintoadditionofberstoincreaseconcreteductilitybeganinthe1960s( RomualdiandMandel 1964 )butwasnotcombinedwithultrahighcompressivestrengthconcretesuntilthe1990s( RichardandCheyrezy 1995 ).ThecombinationhasresultedinanewclassofconcretestermedUltra-HighPerformanceFiberReinforcedConcrete(UHPFRC),whichdierentiatefromUltra-HighPerformanceConcrete(UHPC)throughtheuseofberstoenhanceductilitybeyondtheextremestrengthcapacityofUHPC.UHPFRCischaracterizedbythefollowingproperties: Lowwater-to-cementratiotoincreasestrengthofcementmixture. Nocoarseaggregatestoensurehomogeneousmixproperties. 31

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Increasedpackingdensitythroughoptimumselectionofaggregateandpackingadditivessuchassilicafume,silicaour,and/oryash. Useofsteelberstoenhanceductilityandpost-peakmaterialresponse. Useofheatand/orpressureduringcuringprocesstoenhanceperformance.ThelinearrangefortheUHPCstress-strainrelationshiphasalsobeencomparedtoNSC( Graybeal 2007 )bycomparingthesecantmodulus(E0)atpeakstresstothemodulusofelasticity(E)establishedbyASTMC469.Thetransitiontonon-linearbehaviorwasinvestigatedbyexaminingwherethesecantmodulusdeviatedfromtheelasticmodulusby1,3,and5%.Forsteam-curedUHPC,the5%deviationwasreachedatstresslevelsbetween80-90%ofpeakstress.Theratiobetweensecantmodulusandmodulusatpeakstresswasalsoexamined.ForNSC,theratioE=E0variesfrom3.5for7MPaNSCto1.25for70MPaconcrete.TheratioforUHPFRCinvestigatedvariedfrom1.1to1.2. 2.7.1RateEectinUHPCDuetoitshighstrengthUHPChasimplicationsforuseinstructureswheredynamicandshockloadingsareexpected,particularlyinprotectivestructures,andhasshownrate-sensitiveloadingresponse.InitialprovisionsbyAFGC( AssociationFrancaisedeGenieCivil 2002 )recommendedincreasingthecompressiveandtensilestrengthsby1.5and2,resepectively,forstrainratesbetween10)]TJ /F8 7.9701 Tf 6.587 0 Td[(1and1_".Parantstudied11%berbyvolumeUHPFRCbeamsandslabsunderfour-pointbendingandhighrateimpacttestsusingagasgun( Parantetal. 2007 ).Peaktensilestressincreasedbyafactorof1:5MPa=log10_,whilethesamemixwithoutbershadanincreaseof0:67MPa=log10_. Ngoetal. ( 2007 )tested50mmdiameterreactivepowderconcrete(RPC)cylindersundercompressiveloadratesbetween3x10)]TJ /F8 7.9701 Tf 6.586 0 Td[(5s)]TJ /F8 7.9701 Tf 6.586 0 Td[(1and267:4s)]TJ /F8 7.9701 Tf 6.586 0 Td[(1.TheRPCcylindershad28-daycompressivestrenghtsof160MPa.TheRPCcylindershadadynamicincreasefactor(DIF)lessthanthatofNSCforsimilarstrainrates.AmodelforUHPFRCDIFwasproposedas: DIF=f0cd f0cs=_" _"s1:026(2{21) 32

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forstrainratesbelowacriticalmaterial-specicstrainrate_"1,whileforhigherloadingratestheDIFshouldbecalculatedas: DIF=f0cd f0cs=A1ln(_"))]TJ /F4 11.9552 Tf 11.955 0 Td[(A2(2{22)whereA1andA2arematerialconstantsderivedthroughexperimentaltestdata. 2.7.2SizeEectinUHPCTodate,studiesperformedonbeamsandslabshaveshownlimitedsize-eectrelationshiptopre-peak-loadandpre-crackbehavior,butsizeindependenceofpost-crackbeams( ChuangandUlm 2004 ),orthatsizeeectwasnon-existent( Mahmudetal. 2013 ).Additionalstudies,however,haveshownacompletesizeeectthatwasdependentonbercontentandductility( Nguyenetal. 2014 ).Theseresultsarecontradictoryandlimited,andthereisnofurtherinformationavailableonsize-eectofUHPCspecimens. 2.7.3COR-TUFCOR-TUFwasdevelopedattheGeotechnicalandStructuresLaboratoryattheUSArmyERDC( Williamsetal. 2009 ).Itbelongstoafamilyofultra-highperformanceconcretesknownasreactivepowderconcretessinceitdoesnotcontainanycoarseaggregatessuchasgravel.Itiscomposedofnesilicasandwithamaximumsizeof0.6mm,silicaour,andsilicafume.COR-TUFhasaverylowwater-to-cementratioof0.21,whichistypicalforUHPCmixes.Superplasticizerisaddedtoreducewaterdemandandincreasetheworkabilityofthemixtureduringpreparation.TypicalmixproportionsforCOR-TUF1(i.e.,COR-TUFwithbers)areshowninTable 2-1 .AcomparativemixtureknownasCOR-TUF2wasalsodeveloped,andconsistsofthesamemixproportionsbutwithoutsteelbers.DramixZP305bersfromBekaertareusedintheproductionofCOR-TUF1.Thebersare30mmlongwithhookedendstoimprovebondingwiththeconcrete,andtheyhaveadiameterof0.55mmandatensilestrengthof1100MPa.Theyarebundledtogetherwithawater-solubleglue,addedtothemixtureafter 33

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thewaterandcementhavebeenfreshlymixed,andarethenmixedforseveralmoreminutes.ThebercontentofCOR-TUF1is3.6%byvolume.Bothmixtureshavethesamecastingandcuringprocedure: 1. Drymaterialsaremixedinstandmixerfor5minutes. 2. Wetmaterialsaregraduallyaddedandmixedforapproximately15minutes. 3. COR-TUF1:Steelbersareaddedoverthecourseof10minutes.COR-TUF2:Furthermixedfor10minutes. 4. Materialiscastintoformworkandvibratedtoremoveairvoids. 5. Freshspecimensarecuredat22Cand100%humidityfor7days. 6. Specimensareplacedina85Cwaterbathfor4days. 7. Specimensaredriedinanovenat85Cfor2days. 2.7.3.1StaticstrengthMaterialpropertiesofCOR-TUFhavebeenobtainedfromtestson75mmx150mmcylinders,100mmx200mmcylinders,and3and4-pointbendingtests( Williamsetal. 2009 ; Rothetal. 2010 ).Additionaltestsonnotched3-pointbeamswereperformedonUHPCbeamsinaccordancewithASTME399( Lietal. 2009 ).Staticpropertiessuchascompressivestrengthandbehavior,Young'smodulus,andpoissonratiowereobtained.ForCOR-TUF1,28-daycompressivestrengthrangedbetween216-244MPa,whilethe28-daycompressivestrengthofCOR-TUF2rangedbetween190-228MPa.Young'smoduluswasalsoobtainedviaunconnedcompressivetests,andpoisson'sratiowasdeterminedthroughtheuseofvarioustriaxialtests.Flexuralstrengthwasalsoevaluatedviatheuseof1000mmlongbeams.Fiberpull-outtestswereconductedonCOR-TUF1specimens( Lietal. 2009 ).Fibersweretestedatdierentlevelsofembedmentandpulledoutindividually,aswellasdirect-pulltestsondog-bonespecimens.Resultsindicatedapull-outenergyof22J=m2pereachhookedber.ResultsandsummaryareshowninTable 2-2 alongwithacomparisontoareferenceNSCknownasSAM35developedbyERDC. 34

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2.7.3.2DynamicstrengthAdditionalmaterialpropertiesofCOR-TUFhavebeenobtainedfromdynamictestingofbothbeams,cylinders,anddirectshearspecimens( Kochetal. 2013 ; Stoneetal. 2013 ; Frenchetal. 2017 ).Dynamicimpacttestswereperformedon2743mmspanbeamswithdropmassesbetween250-408kg.Dierentreinforcementratiosandvaryingshearreinforcementlevelsweretested.Peakandresidualmid-spanandquarter-spandeectionswerecomparedtoNSCbeams,andaresummarizedinTable 2-3 .ResultsshowedlowerdeectionsandincreasingstinessfortheUHPC,UHPFRC,thenUHPFRCwithoutshearreinforcement.Impactexperimentson100mmx200mmUHPCandUHPFRCcylindersindicatedlowerthanexpectedDIFsforUHPFRCandinconsistentdataforUHPCcylinders( Friedrichetal. 2013 ).DirectshearresultsindicatedthattheUHPFRChasashearcapacitythatismuchhigherthanfullyreinforcedNSCspecimens,andthatthereissignicantshearcapacitywithoutanyreinforcement. 2.8SummaryAsshownabove,thereisalargebodyofknowledgeonNSC,UHPC,andUHPFRCrelatingtofracturemechanics,sizeeects,rateeects,anddynamicsimulationsindividually.However,therelationshipbetweenallthesefactorsandunderstandingthefractureandbehaviorofthesematerialsisnotwellcharacterized.Therelationshipbetweensizeandrateeectsisstillnotwelldeveloped.TheeectsofrateonUHPCandUHPFRCareunderstood,butthesize-eectisnotwelldened.Modelingtechniquesforthesenewmaterialsarehighlyvariable,andareprimarilyrestrictedtopost-testsimulationwithcurvettingofmaterialparameterstolimitedmaterialmodels.Acomprehensiveexperimentalstudyofthesematerialsundercompressiveimpactloading,alongwithaforensicinvestigationintothefracturebehaviorwillallowforunderstandingofpossiblesize-ratecouplingmechanisms.Additionally,itwouldprovideinsightintotherelationshipbetweenenergyowthroughstructuresandthefracturebehavior,whichwouldprovideguidanceforengineeringprotectivestructurestoresisttheeectsofblast,impact,and 35

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progressivecollapse.Aproposedmethodologyforstudyingtheserelationshipsisdiscussedinthenextchapter. Table2-1. MixPropertiesofCOR-TUF MaterialProductProportionbyWeight CementLafarge,ClassH,Joppa,MO1.00SandUSSilica,F55,Ottawa,IL0.967SilicaFlourUSSilica,SilcoSil75,BerkeleySprings,WV0.277SilicaFumeElkem,ES900W0.389SuperplasticizerW.R.Grace,ADVA1700.0171WatertapVicksburg,MSMunicipalWater0.208SteelFibersBekaert,DramixZP3050.310 Table2-2. StaticMaterialPropertiesofSAM35andCOR-TUF1/2 MaterialPropertySAM35(NSC)COR-TUF1(UHPFRC)COR-TUF2(UHPC) WetDensity(kg/m3)216325572328WaterContent(%)3.392.733.24Young'sModulus(GPa)31.240.937.5Poisson'sRatio()0.210.230.22ShearModulus(GPa)5.716.715.3BulkModulus(GPa)8.925.222.7CompressiveStrength(MPa)34237210TensileStrength(MPa)3.675.588.88FlexuralStrength(MPa)N/A25.016.0SplittingStrength(MPa)N/A25.69.8FractureToughness(MPap m)N/AN/A1.17 36

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2a 2b y x tip Figure2-1. Stressesininniteplatewithanellipticalcrack. Figure2-2. Linearelasticmaterialresponse. 2a Figure2-3. Center-crackedplatesubjecttotension. 37

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Table2-3. ImpacttestresultsonUHPFRCbeams. MaterialMeanPmax(kN)Pmax=max(kN/mm) NSC1152.614.08UHPC1451.718.88UHPFRC1889.028.78UHPFRC(Noshearreinforcing)2072.338.71 (a) (b) Figure2-4. Non-linearmaterialresponse:(a)Elastic-Plastic,(b)Quasi-brittle. =0 =(w) w=0 ft w Figure2-5. Cohesivestressalongcrackline. Strain Stress ft Gf Figure2-6. Stress-strainrelationshipforCrack-bandmodel. 38

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Einput(ExternalWork) Eout(damping) Eplastic Eelastic,Ekinetic Figure2-7. Energytankanalogyforstructuralresponse. 39

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CHAPTER3METHODOLOGY 3.1IntroductionFractureofconcretespecimenscanbeanalyzedintwomethods:viastressbasedanalysisorviaenergybasedanalysis.AnalysisofNSC,UHPC,andUHPFRCcylindersunderimpactloadsusinganenergybalancemethodwillyieldabetterunderstandingoffailurebehaviorofthematerialsunderdynamicloadingconditions.Researchisdividedintothreephases:statictesting,dynamictesting,andanalysisoftestedspecimensviaenergybalance.Therelationshipbetweenmaterials,rate-eects,andimpactbehaviordevelopedinSection 2.5 wasexaminedviaenergybalanceanddistributionfromphysicaltesting.First,statictestingofeachmaterialwasperformedtodeterminebaselinematerialpropertiesandcharacteristics.Secondly,impacttestingwithinstrumentationtocaptureimpactload,specimenstrain,andhammerandfragmentspeedwasperformedtoisolateafailuremodethatminimizeskineticenergyejecta.Finally,1-2specimensofeachmaterialthatexhibitedthesefailureswereexaminedviatestdata,highspeedphotography,andpost-testvisualinspection.Itishypothesizedthatthedynamicfailurestrengthandmodeoffailureislinkedtotheenergyowanddistributionofenergyterms.Totestthishypothesis,specimenswereidentiedandsortedbythetypeoffailuremode,andthenexaminedtocharacterizethefailureorigin,type,andpropagation.Failuremodeswereclassiedandsortedbyglobalresponseandlocalorigin.Acalculationofenergytermsduringthefailureprocesswasperformed,andcomparedtotheinputenergyviaanenergybalance.Thisinformationwasusedtoanalyzedistributionofenergyandenergyowasitrelatestothefailureprocessforeachmaterialandenergydissipationmechanismsasdetailedbelow. 3.2ExperimentalProcedureStaticphysicaltestswereconductedateithertheUniversityofFloridaorFloridaDepartmentofTransportationMaterialsTestingLab.Twosamplesizesweretested:100mmby200mmand150mmby300mmspecimens.Specimenswereloadedataconstant 40

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loadratewithagoalofreachingthepreviouslydocumentedstaticstrengthcapacitywithinveminutes.DynamicphysicaltestingwasperformedusingtheCIPPSDropHammerslocatedinPowellLabattheUniversityofFlorida.Thereweretwodrophammersfortesting:onehigh-mass(2700kg)forlargespecimensandonevariablemass(100-500kg)forsmallersizedspecimens.Bothhammerswereequippedwithsensorstorecordimpactvelocity,impactforce,andpneumaticreboundbrakestolimitspecimenstoasingleimpactevent.TestdatawererecordedviaaDataAcquisition(DAQ)systemsamplingupto2millionsamplespersecond(2MHz).DatacollectedwasanalyzedusingMATLABsoftwareandprocessedusingavarietyoftechniquestorevealinsightsintomaterialbehaviorandresponseunderdynamicresponse.Theprocedureforexperimentationisexplainedasfollows: 1. Performstatictestingonthreecylindersofeachsizeandmaterialtype.Collectloadandstraindatatocharacterizestress-strainrelationship. 2. Calculatetheoreticalenergyrequirementtofracturecylinderbasedonstress-strainrelationship,anddetermineestimateddropheightandmassrequiredforcompletefailureofthespecimen. 3. Performintitaltestoneachspecimentypeusingtheappropriatedrophammer,withprogressivelyhigherdropheightsuntilthedesiredfracturebehaviorisobtained. 4. Performatleastthreetestsoneachspecimentype/sizeusingthedrophammertorecordstrainandenergydata.Beforeeachtest,measurethemassofthecompletecylinder.Afterexperiment,locateandcataloguepositionofalllargefragments.Measuremassoffragmentsforkineticenergycalculations. 5. Evaluatestrainenergiesofthecylinderduringthetestprocess. 6. PerformaLEFManalysisusingthedatacollected(inputenergy,load-timehistory,straindata)andthencalculatetheenergydissipationmechanismsusingenergybalance. 7. Comparefractureresponseandenergydissipationmechanismsofeachmaterial. 3.2.1LargeDropHammerThelargedrophammeratCIPPSisa2700kgdrophammerwithpneumaticreboundbrakesandisshowninFigure 3-1 .Thehammerisdesignedfordropheightsupto6metersontospecimensofvarioussizes.Thedrophammeriscomposedofarailmountedcrosshead, 41

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whichisconnectedtotherail-mountedloadcartviamagneticandphysicallatches.Thecrossheadisliftedbya5-tonhoisttosetthedropheight.Whentriggered,thelatchesdisenageandtheloadcartdropsundergravitytoimpactthespecimen.ThedrophammerhastwophotoeyeswhichdetectthemotionofthehammerimmediatelybeforeimpactandareusedtotriggertheDAQ,highspeedcamera,pneumaticreboundbrakes,andrecordimpactvelocitydata. 3.2.2VariableMassDropHammerThevariablemassdrophammeratCIPPSisasmallerhammerwiththeabilitytochangethedropmassbetween100and500kg.Thehammeriscomposedofasteelframestructurethathousestworailsthatthecombinedrailcarttravelson,andisshowninFigure 3-2 .Therailcartiscomposedoftwopieces:acrossheadthatisattachedtothehammerframeviaawinchandhousesthereleasemechanism,andtheloadcartthathousestheadjustablemassplatesabovethestrikerandimpactloadcell.Themaximumdropheightdependsonthespecimengeometryandmasschosen.Thedrophammeralsofeaturestwoadjustablepneumaticreboundbrakes,whicharecomposedofapneumaticactuatorandalargeviscoelasticdamper.Thesebrakesaretriggeredbyanadjustablephoto-eyethatdetectsimpactofthehammeronthespecimen.Afterthestrikerimpactsthespecimen,itwillremainincontactforaperiodoftimebeforebouncing(rebounding).Thebrakesaretimedtoreafterthisreboundoccurs,andextendupwardstocatchtheloadcartandpreventasecondimpactfromoccuring.Thisallowsformorepreciseimpacttestsforevaluationofmaterialresponse. 3.2.3DataAcquisitionManychallengesexistwhenselectingadataacquisitionsystemfordynamictests.Sucientdatamustbecollectedforproperconditioningataproperprecisiontoprovidemeaningfulresults.Assuch,thesamplingrateandsignalconditioningsystemmustbecarefullyselectedtoensurenoeventsaremissedandtopreventaliasing.Fordynamicexperiments,thisdependsonthematerialpropertiesandthegeometryofthespecimen.Forconcrete,wavespeedscanvarydependingonthematerialpropertiesandwavetypebeingstudied(Rayleigh, 42

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P-,orS-wave)( Linetal. 1997 ).Thehighestwavespeedfortheexperimentsdetailedwouldbethelongitudinalwave,whichcanbeestimatedusingEquation 3{1 c=s E(1)]TJ /F4 11.9552 Tf 11.955 0 Td[() (1+)(1+2)(3{1)TheaxialP-wavevelocityofCOR-TUF1andCOR-TUF2havebeenmeasuredas5040and5050m/s,respectively( Williamsetal. 2009 ).Forthestraingagesused,thetimeforapulsetotravelthelengthofthegageis3.8s.TheDAQusedsampleddataat1MS/s,andthereforehadahighfactorofsafetyforcapturingalldata.Samplingat1MHzdeliveredatleast57samplesofdataduringthetimeittakestheloadpulsetotravelthelengthofthecylinder,withatleast5samplesperstraingagelocationasthestrainwavetraversesthelengthofthegageandavoidsaliasing.Previousimpactexperimentsandsimulationsonsimilarhavetotaltesttimeintherangeof10-50ms.Asamplerateof1MHzallowsenoughsamplepointstopreventaliasingandcaptureanytransientresponseofthespecimensortestequipment,aswellaswavereectionsfromthestrikerorbaseatthecylinder.Thedataacquisitionsystem(DAQ)usedatCIPPSiscomposedofseveralpartsandaredetailedasfollows.HammercontrolsandsignalsarecontrolledbyacentralcomputerrunningaNationalInstrumentsNI-6225DAQ( Stoneetal. 2013 ).ThisDAQreceivessignalsfromthehammerimmediatelybeforeimpactbyuseofphoto-detectorsplacedabovethespecimen.Whenthecomputersensesthehammerabouttoimpact,triggersarethensenttothehigh-speedcameraaswellastheWin600DAQ( ZineddinandKrauthammer 2002 ).SensorsarepoweredandampliiedbyanEndevco4990Arackmountsignalconditioner.Theconditionerhas12cards:10Endevco436DCAmplierswhichprovidethreechannelsof5-15VDCwithagainof0-1000,andtwoEndveco482Bconstantcurrentampliers.The436DCampliershaveabandwidthof200KHz.Forconstantcurrentsensorssuchasaccelerometers,two8-channelEndevco482Bampliersareused.Thesehaveaprogrammablegainbetween0-100andabandwidthof100KHz.Sensoroutputissentfromthesignal 43

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conditionertotheWin600,a64-channelDAQcapableofsamplingupto2MHzsimultaneouslywithasweeplengthof8millionpoints. 3.2.4InstrumentationMultipletypesofdatawerecollectedbyvarioussensorsandinstrumentation:loaddata,straindata,accelerationdata,impactvelocitydata,andfragmentvelocitydata.Loaddatawascollectedusingeithera3114kN(700kip)ora8896kN(2000kip)loadcelldependingonthematerialtype.Normalstrengthspecimensweretestedunderthesmallhammerwiththe3114kNloadcell,andallotherspecimensweretestedusingthelargehammerandthe8896kNloadcell.Straindatawascollectedatseverallocationsonthespecimenusing20mmstraingagesfortheUHPC/UHPFRC,and50mmstraingagesfortheNSC,asindicatedinFigure 3-3 .Axialstrainwasmeasuredusingninestraingagesinsetsofthreeequallyspacedaroundthecylinder.Volumetricstrainwasmeasuredusingthreegageslocatedatthemid-heightofthecylinder.Ahighspeedcamera(PhantomV5.2)recordedeachtest.Thecameraiscapableofobjecttrackingandcalculatingpositionandvelocitymeasurementsofobjectsintheframe.Testswerelmedat19000framespersecond.Alaser( Frenchetal. 2017 )wasusedtomeasuretheimpactvelocityofthehammer.Endevco20,000gaccelerometersweremountedonthestrikerofthehammerformeasurementofsuddenshockassociatedwithhardimpacts. 3.2.5PhysicalTestMatrixThreeprimaryvariableswereexamined.Thesevariableswere:material,testrate,andboundarycondition.Atotalof36specimenswerecast,representingalmostallpossiblecombinationsofthesevariables.Thepossiblevariablesarethreematerials,twotestrates,andtwoboundaryconditions.Threematerialsweretested:acontrol35MPaNSCknownasSAM-35,aUHPFRCknownasCOR-TUF1,andaUHPCknownasCOR-TUF2.MaterialpropertiesforeachtypeofconcretearedescribedinSection 2.7.3 .Statictestingconsistedof100mmby200mm(4inby8in)aswellas150mmby300mm(6inby12in)specimens.Dynamictestingconsistedof150mmby300mm(6inby12 44

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in)specimens.ThestatictestswereconductedattheFloridaDepartmentofTransportationMaterialsTestingLablocatedinGainesville,Florida.Testdataincludedloaddatafromaloadcellabovethespecimen,andstraindatafromlocationsalongthespecimen.Datacollectedwereusedtogeneratestaticstress-strainrelationshipsforeachmaterialtype.Basedonthestatictestingresults,specimensweretestedundereitherthevariablemassorthehighmassdrophammer.Forthedynamictesting,onetothreespecimenswereusedtocalibratethedropheightatareferencemasstodeterminetheenergyinputrequiredtocompletelyfracturethespecimenwithminimalkineticejecta.Forreference,astatictestwasperformedonthree100mmUHPCspecimens,andthestress-strainrelationshipisshowninFigure 3-4 .Integratingthecurvesgivesanaveragespecicenergy(u0)of451.3kJ=m3.Multiplyingbythevolumeofacylindergivesanestimateoftheenergyrequiredforfractureofthecylinder.Ifthevolumeusedisforthe150mmcylinders,thetotalenergycapacityofthe150mmby300mmcylinderis: U0=u0volume=451:3kJ m3(150mm)2 4300mm=2:509kJ(3{2)Takingthisvaluethendividingbythedropmassandgravitywillthenyieldaninitialestimatefortheheightofthedrophammer.Forexample,ifthemassissetat2700kg,thenthetheoreticaldropheightrequiredis: height=U0 massg=2:509kJ 2700kg9:81m=s2=0:095m(3{3)BasedonpreviousexperimentsatCIPPSonNSC,UHPC,andUHPFRCspecimens,theboundariesofthespecimenswereadjusted.Referenceconditionwasthespecimencontactingthestrikerplatedirectly,whileavariableconditionwasinclusionofrubberdampeningpadsandendcapstoensureequalcontacttorestrictlateralexpansionattheboundaries,asthesecapsaretypicallyusedinstatictestingofconcretecylinders.AsummaryofthetestvariablesisshowninTable 3-1 .Cylinderswerenotedusingthefollowingformat:Material-Diameter-Static/Dynamic-SampleNumber-TestNumber-ExtraInfo.Materialtypes 45

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wereeitherNSC,CT1(UHPFRC),orCT2(UHPC).Specimensizeswererepresentedininches.Forexample,thethirddynamictestsampleof150mmdiameterUHPFRC,rstimpactwasidentiedbyCT1-6-D-3-1. 3.3DataProcessingandPhysicalTestAnalysisDataprocessingwasperformedinMATLAB( Mathworks 2015 )andpresentedusingDPLOT( HydeSoft 2014 ).Datawereprocessedinthetimedomain.DatawasrstlteredusingMATLABtoeliminatenoiseinthesignal.Thersttypeoflterappliedwasahigh-orderbutterworthlter.Thepass-bandwaschoseninitiallybasedonthetestequipment:200kHzforDCsensorspoweredbythe436signalamplier,and100kHzfortheconstantcurrentsensorspoweredbythesignalconditioner.Abutterworthlterwaschosenforitslowrippleandatresponseinthepassbandregion.ParametersarelistedinTable 3-2 .Filteringwasperformedusingtheltltcommandtoelimnatephase-shiftingofthesignal.Afterthedatawereltered,thestresswascalculatedusingtheloadcelldatadividedbythegrossareaofthecylinder.Thesestressdatawerethencomparedtothestrainalongthelengthofthecylindertocalculatethestress-strainresponseofeachheightofthecylinder.Usingthiscurve,theintegralwastakeninordertocalculatethestrainenergydensity,andthenmultipliedbythesub-volumetocalculatethetotalenergyforeachsectionofthecylinder.Strainenergydatawerethencomparedtemporallytothehigh-speedphotographytoidentifypointsofinterestbasedoncrackandfracturepattern.Inaddition,thetotalkineticenergyofthesystemwascalculatedbytrackingthevelocityoffragmentsofthespecimenwiththehigh-speedvideo.Bycollecting,labeling,andweighingfragmentsaftereachexperiment,thekineticenergyofeachmajorfragmentwascalculatedusingthevideodata.FracturebehaviorwasalsoanalyzedandclassiedaccordingtothenotedtypesasshowninSection 2.5 .Collecteddataconsistsof: Impactload; Impactstress; Impactandreboundvelocity; 46

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Inputenergyfromimpact; Cylinderaxialstrain(top,middle,bottom); Cylindervolumetricstrain; Cylinderstrainenergy(top,middle,bottom); Cylinderandfragmentkineticenergy;and Cylinderfracturetype(ascharacterizedinSection 2.5 ). 3.4EnergyBalanceApproachandLEFMAnalysisUsingthedatafromthetests,ananalysisofenergyandstressesinthecylinderisperformedusinganenergybalanceapproachandLEFM.Theenergyforfracturecanbederviedusinganenergybalance,whereenergiesandexternalworkaresummedupandsubtractedfromthetotalenergyavailable.Duetotheconservationofenergy,anyinputenergymustbeeitherconsumedorusedduringthefailureprocessbyothereventssuchaselasticdeformation,kineticresponse,fractureprocesses,plasticdeformation,externalworksuchasfrictionordampening,andothermechanismssuchasheat,sound,etc.Allresultswereanalyzedfortotalenergyduetowork,strainenergy(elasticandplastic),andfractureenergy.Thesevalueswereusedintheenergybalancetodeterminefractureenergyparametersforthematerialsaccordingtothefracturebehavior.Theglobalenergybalanceisdrivenbytheconservationofenergy.Theenergydistributionduringthefailureprocessmustequaltheinitialinputenergyofthesystem,andcanberepresentedasfollows: Einput=Eoutput(3{4)whereEinputistheinputenergy,whichiscalculatedasthechangeinkineticenergyofthehammer: Einput=KEhammer(3{5) 47

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wheretheKEhammerrepresentsthechangeinkineticenergyofthehammer.Thechangeinkineticenergyisdenedas: KEhammer=1 2masshammer(v2impact)]TJ /F4 11.9552 Tf 11.955 0 Td[(v2rebound)(3{6)wheremasshammeristhemassoftheimpacthammer,vimpactisthevelocityofthehammeratthetimeofimpact,andvreboundisthevelocityofthehammerasitreboundsawayfromthespecimen.Theoutputenergyisthesumofallenergytermsfordissipation: Eoutput=KEspecimen+SEspecimen+SEstand+SEhammer+PEspecimen+Efiber+fracture+Wext(3{7)WhereKEiskineticenergy,SEiselasticstrainenergyofeachitem,PEisplasticstraindeformationenergy,Efiberisberpull-outenergy,fractureisthefractureenergy,andWextisexternalworkduetofriction.Otherenergiessuchassound,heat,andlightareconsideredtobeminimalandwerenotcalculated.Derivationandexplainationofenergytermsarediscussedbelow.Testspecimensthatdisplayedidealcrackgrowthwithminimalexcesskineticenergywereidentied.Usingthestrainandstressdata,ananalysisoftheenergytotalsandfailurecriteriawasperformedandcomparedtotheoreticalpredictionsinaforensicmanner.Anydierencesinenergyamountswerenoted.Forexample,usingdatafromanexperimentonaUHPC150mmspecimen(CT2-6-D-5),thetotalenergyavailableforfracturewascalculatedas530.3J,asdetailedinTable 3-3 .Theenergybalanceapproachtogettothisvalueisexplainedbelow. 3.4.1KineticEnergyKineticenergyistheenergyassociatedwithmovementofamass,andcanbecalculatedas: KE=1 2mv2(3{8)wheremisthemass,andvisthevelocityoftheobject.Kineticenergiesofthehammer,collectedfragments,andbodiesbefore,during,andaftertheimpacteventwerevitalfor 48

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calculatingtheenergydistribution.Kineticenergyofthehammerwasusedtocalculatetheinputenergy.Thiswasdonebymeasuringtheimpactvelocityandthereboundvelocityofthehammer.Thedierenceintermsyieldsthetotalenergyinputintothesystem.Thevelocitywasdeterminedviaoneoftwomethods:ahigh-speedlaserthattracksthepositionofthecrossheadorthehigh-speedvideooftheimpactevent.Theimpactandreboundvelocitywascomputedbyexaminingthevelocitiesatthebeginningandendofloaddata.KineticenergyofthehammerwascalculatedasderivedinEquation 3{6 .Fortheexamplegiven,theimpactvelocitywasdeterminedtobe1.9m/s,thereboundvelocityis-1.3m/s,themassofthehammeris2700kg,andtheresultingchangeinkineticenergywas2592J.Additionalkineticenergytermsincludedtheenergyinanyfragments.Althoughspecimenswereselectedthathaveminimalejecta,evenasmallnumberoffragmentscanhaveanappreciableamountofkineticenergystoredinthem.Forlargefragments,theejectavelocitywasrecordedusingthehigh-speedcameraandcalculatedviapost-processing.Collectedfragmentswereweighedpost-testtocalculatethetotalkineticenergyimpartedtothefragment.Analysisoffragmentswaslimitedtothosethatcouldbeindividuallyidentiedandtrackedusingthehigh-speedvideo. 3.4.2StrainEnergyElasticstrainenergyisdistributedintothreecomponents:energyoftheconcretespecimen,energyofthestand,andenergyofthehammeritself.Strainenergyofthespecimenwascomputedviauseofthestrainandtheconstitutiverelationshipsdevelopedfromstatictestingandthemethodofcomplementarystrainenergy.Theenergyistheareaunderthestress-straincurveatanytime,andthecomplementaryenergycanalsobecalculatedas: U=U=Z"d=E"2 2(3{9)where"isthestrain,isthestressinthestress-straincurve,Eisthemodulusofelasticity,Uisthestrainenergyunderthestress-straincurve,andU*isthecomplementarystrainenergy.Thestraindataforeachsectionofthecylinder(top,middle,andbottom)wasusedto 49

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calculatethestrainenergyatthepointoffracture(whentheloaddropssuddenly)andtheneachwasmultipliedbyone-thirdthevolumeofthecylinder.Thesevalueswerethensummedtogiveavalueofstrainenergyforthesystem.TheelasticstrainenergyofCT2-6-D-5wascalculatedas922.4J.Otherelasticstrainenergytermsincludethehammeritselfaswellasthereinforcedstand.ThestrainenergyofthesecomponentswerecalculatedusingaSDOFapproximation,usingtherecordedloaddataasaninput.Theequivalentstinessofthehammerandthebeamwerecalculatedusingbasicstructuralengineeringprinciples.Forthelargehammer,thedropmassisconstructedoutofa50mmsteelplatesformingahollowbox939.8mm(37in)highby355.6mm(14in)deepby3677mm(12feet-0.75in)wide.Themomentofinertiaofthebeamwascalculatedusingahollowboxcrosssectionwiththesedimensionsandatotalmassof2700kg.Themomentofinertiawasfoundtobe944.2x106mm4.Assumingthedisplacedshapeofthebeamisaxed-xedbeamwithacentralpointload,thestinesswascalculatedas: k=192EsIbeam Lbeam3=945:5106N=m(3{10)wherekistheequivalentstinessofthehammer,Esisthemodulusofelasticityforsteel,Ibeamisthemomentofinertia,andLbeamisthelengthofthebeam.Usingthestinessandassuminglinearbehavior,thedisplacementcanbecalculatedbyintegratingtheforce-timehistoryasacentralloadingfunctionappliedtothehammer.Assuming5%damping,thenaturalfrequencyofthehammerwascalculatedandthedisplacementwassolvedforusingdirectintegrationoftheappliedloadusingtheDuhamelmethod.Thesmallhammerisconstructedofamixtureofasteelstrikerandloadcell,andanaluminumrailcartcomposedofamixtureofhorizontalandverticalI-beamswithaluminumplatesforstability.ApictureofthecrossheadisshowninFigure 3-5 .TheequivalentstinesswascalculatedbymodelingthehammerinSolidWorkstodeterminesectionalpropertiesforeachmember,andaVisualAnalysismodelwasthenconstructedusingbeamandtrusselementswiththesectionalproperties.Aunitloadwasappliedtothecenterofthemassplate,andthe 50

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deectionatthemidpointofthetophorizontalspanwasthencalculatedundertheappliedload,andtheequivalentstinesswascalculated.Theequivalentstinessforthesmallhammerwascalculatedas489106N/m.ThedisplacementoftheequivalentspringwasthensolvedforusingdirectintegrationoftheappliedloadusingDuhamelintegration.ThestandisconstructedofaUHPFRCstubcolumnreinforcedwithrebarandverticalhollowbars.Thecrosssectionfeaturesfour31.75mm(1.25in)hollowsteelbarstoallowforall-threadrodtoattachtothebaseofthehammerorstrongoor.ThemainreinforcingiscomposedoffourUSnumber9rebarswithnumber3shearreinforcement.ThereinforcingdetailisshowninFigure 3-6 .Thecrosssectionwasanalyzedasastubcolumninpurecompressionwithnobendingmoment.ThematerialpropertiesfortheUHPCstress-strainwereobtainedfromChapter 2 ,andthesteelusedwas60ksiwithayieldstrainof0.2%.Theequivalentstinesswasobtainedbyenforcingstraincompatibilityandassumingthatbothmaterialsremainedinthelinearelasticrange.Usingthegeometryofthestand,theequivalentstinesswascalculatedas24.85x106N/m.Thestrainenergyofeachtermcanbecalculatedby: SEstand=1 2kstandx2max;stand(3{11)and SEhammer=1 2khammerx2max;hammer(3{12)wherekistheequivalentSDOFstinessofthestandandhammer,respectively,andxmaxisthemaximumdisplacementofx(t)calculatedviastructuraldynamicsandequationsofequilibrium.ForCT2-6-D-5,thestandstrainenergywascalculatedas75.6J,whilethehammerstrainenergywascalculatedas304.9J.Analsinkofstrainenergywaselasticwaveenergydissipatedbyimpactintothebaseandground.Theamountofinputkineticenergydissipatedbyreboundwasusedby Jannotti 51

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etal. ( 2015 ).Thefractionalenergydissipatedisgivenby: =7:267 2C30(1+2)1)]TJ /F4 11.9552 Tf 11.955 0 Td[(22 1+22)]TJ /F8 7.9701 Tf 6.586 0 Td[(1=5K6=5V3=5(3{13)whereC0isthewavevelocityofthereboundsurface(concrete),Vistheimpactvelocity,andarethedensitiesandPoisson'sratiosofthematerials,isadimensionlessquantitycalculatedbasedonthetargetPoisson'sratio,andKisaparametercalculatedusingthetargetandimpactorPoisson'sratiosandModulusofElasticity.FortheUHPCspecimenunderexamination,thefractionalenergyratiowasfoundtobe0.052forCT2-6-D-5,and0.054forCT2-6-D-7.FortheNSCspecimens,thevalueswerefoundtovarybetween0.072and0.073.FortheUHPFRCspecimens,thevalueswerebetween0.078and0.079.Multiplyingbytheimpactkineticenergy,theelasticwaveenergyforCT2-6-D-5wascomputedas253.4J. 3.4.3PlasticStrainEnergyPlasticstraindissipationiscalculatedusingthedynamicstraindatarecorded.Asthestrainpassestheelasticlimitdenedfromstatictesting,energyisdissipatedthroughplasticdeformationofthematerial.Plasticstraincanbecalculatedviathedynamicstress-straincurve,asshowninFigure 4-22 .Theplasticdeformationiscalculatedvianumericalintegrationofthestress-strainfromthepointofimpactuntiltheloadisremoved.Bycalculatingtheareaunderthestress-straincurve,aboundontheenergydissipatedviaplasticdeformationoftheremainingfragmentscancalculated.Plasticenergyalsoaccountsforcrushingofthematerial,andcanbecalculatedusingthechangeinmassofthecollectedspecimensandthestaticstress-strainrelationship.ForCT2-6-D-5,theplasticstrainenergywascalculatedas247.4J. 3.4.4CrushingEnergyAftertheexperiment,allmassesofthespecimenweretaken.Duringthetests,specimensrecordedalossofmass.Thiswasassumedtobecausedbycrushingofmaterialduringtheimpactevent.Theinitialvolumeofthecrushedmasswascalculatedusingthedensityofthe 52

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materialsasrecordedinChapter 2 andthefollowingequation: Volumedust=mdust concrete(3{14)wheremdustisthemasslossandconcreteistherecordeddensityoftherespectiveconcrete.ForCT2-6-D-5,themasslostwas0.530kg,andthespecimendensitywas2328kg/m3.Thetotalenergythenrequiredtocrushthisvolumeistheareaunderthestaticstress-straincurve,asdetailedabove.Theenergydissipationcanthenbecalulatedas: Udust=Volumedustu0(3{15)whereu0isthespecicenergyofthematerialcalculatedabove,andUdustisthetotalenergyconsumedbycrushing.ForCT2-6-D-5thecrushingenergywascalculatedas102.7J. 3.4.5FiberPull-outEnergyFiberpull-outoftheUHPFRCwasestimatedviathefollowingmethod:energyperberpull-outtimesbersperunitareatimestotalareaoffracturesurface.Theberpull-outenergyperunitareawithasemi-randomberdistribution(Jfiber)fortheUHPFRCstudiedis22J/m2( Lietal. 2009 ).Thismodelcanalsobeusedtocalculatetheenergyrequiredtopull-outasingleber.Thetotalberenergycanbemeasuredas: Efiber=efibernfibersAfracture(3{16)Whereefiberistheenergyperber,nfiberisthenumberofbersperunitarea,andAfractureistheareaofthefractureplanewherebersexperiencepull-outanddislocation.Additionally,anon-randomberorientationfordierentlysizedspecimenswillhaveaneectonthefailuremode.Threeuntested150mmspecimenswerecutintocross-sectionsandinspectedatERDCtodeterminetheradialdistributionofbersandorientationtodeterminewhatinuencethismayhaveontheenergydissipationmechanism.Thiscutoutindicatedthatapproximately90%ofbersweredistributedinaatmanner,andwereprimarilyorientedtoresistverticalcracks.Thebersshoweddistributedbandsthatindicatedapropensitytowardsconicalfailure 53

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mechanisms,andwerenottrulyrandomasseeninFigure 3-8 .Therewereapproximately11berspercm2,asseeninFigure 3-9 3.4.6ExternalFrictionWorkTheexternalfrictionworkwasestimatedbycalculatingthefrictionalforcesworkinguponthehammerasitmovesupanddowntherailsduringtheimpactevent.Bymeasuringtherecordedimpactvelocityandcomparingittothetheoreticalimpactvelocity,theaveragefrictionalforcesofthehammer-railinterfacecanbederived.Bythenmultiplyingthisvaluebythedistancethehammertraversesduringtheimpacteventthetotalexternalworkdonebyfrictioncanbeestimated. KEtheoretical=KEacutal)]TJ /F4 11.9552 Tf 11.955 0 Td[(Wfriction(3{17) Ffriction=KEtheoretical)]TJ /F4 11.9552 Tf 11.956 0 Td[(KEactual h(3{18) Wext=Ffrictionxhammer(3{19)WhereFfrictionistheaveragefrictionalforce,andxhammeristhedistancetraveledbythehammerduringthefailureprocessasmeasuredbyeitherlaserdisplacementsensorsorhigh-speedphotography.FrictionalworkofCT2-6-D-5wasapproximately101J. 3.4.7FractureEnergyThemodeIfracturecriteriaoftheUHPCandUHPFRChasbeenestimatedas1.07MPap m,or21J/m2.Aboundonfractureenergycanbeestimatedbyapproximatingtheareaoffractureandmultiplyingbythefractureenergyofthematerial: fracture=2GIAfracture(3{20)wherefractureisthetotalfractureenergy,GIisthespecicmodefractureenergyreleaserate,andAfractureistheareaofthefracturesurface.Thisfractureenergywasthencomparedtoonecalculatedbasedonthesurfaceareaofthecracksandfragmentscollectedfromthetest.Forinstance,verticalsplittingofthecylinderisapureModeIfailure,whileashearplanewith 54

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slipisacombinationofModeIandModeII.Thefractureenergyreleaserateswereeitherobtainedfromtheliteratureasdenedabove,orfromtheGrithsEnergyCriterionandtherelationship: GI=K2I E(3{21)whereKIistheenergycriterionandEisthemodulusofelasticity.FortheUHPC,GIwascalculatedas21.05J=m2basedonresultsfrom Lietal. ( 2009 ).ThecriticalreleaseratefortheUHPFRCwas22J=m2,andfortheNSCitwascalculatedas89J=m2.Thespecicgeometryofthefractureplaneswasbasedonphysicaltestobservations.Remainsfromthespecimenswereplacedonagriddedmatandphotosweretaken.Areasoffractureweremeasuredusingthematforreference,anddepthofcracksweremeasuredusinga0.5mmthicksteelber.Observabledepthsweremeasuredusingastandardtapemeasure.Forexample,byplacingtheUHPCspecimenonamatasshowninFigure 3-10 ,theareaofCT2-6-D-5wasestimatedasapproximately0.08m2,resultinginafractureenergyof3.3J. 3.4.8EnergyDistributionThesumsoftheoutputenergiesforeachmaterialwerethencomparedtotheinputenergytoanalyzethedistributionofenergyduringthefailureprocess.Theratioofeachtermintheoutputenergywasbecomparedtothetotalinputenergyaswellastheotherenergyterms.Thisallowedforcomparisonofenergydissipationmechanismsbetweenthematerialtypes,andisdetailedinChapter 4 .AgraphicalrepresentationoftheenergydistributionisshowninFigure 3-11 .Thetotalinputenergywas2592J.Strainofthecylinderabsorbedapproximately35.59%oftheenergy,with11.74%beingkineticenergyofthecylinderandfragments.Thehammerandstandwerecalculatedtodissipate17.06%and3.03%oftheenergy,whileelasticwavesintothebaseaccountedforafurther9.78%.Frictionbetweenthehammerandtherailsaccountedfor3.9%oftheenergydissipation.Plasticstrainenergyofthespecimenwasapproximately9.54%oftheinputenergy,andvolumetriccrushingaccountedfor3.96%oftheenergy.Examinationofthespecimenfractureareasandthespecicenergy 55

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releaseratefortheUHPCunderinvestigationrevealedthatfractureaccountedfor0.13%oftheobservedenergydissipation. 56

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Table3-1. PhysicalTestVariables ParameterPossibilities Material3LoadRate2(Static,Dynamic)StaticSamples/Case3DynamicSamples/Case9TotalRequired36(9Static,27Dynamic) Table3-2. LowpassFilterParameters ParameterValue TypeButterworthFrequencyResponseLow-passImpulseResponseIIRPassband(kHz)190Stopband(kHz)210PassbandRipple(dB)1StopbandAttenuation(dB)60 57

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Table3-3. ExampleEnergyAnalysisofUHPCCylinder ParameterValue MaterialUHPCDiameter150mm(6inches)StaticEnergyCapacity2509JDropMass2700kgDropHeight0.241m(9.5in)RecordedImpactVelocity1.9m/sRecordedReboundVelocity1.3m/sInputEnergy2592JCylinderKineticEnergy304.3JCylinderStrainEnergyatFracture922.4JCylinderPlasticStrainEnergy(Dissipated)247.4JDissipatedStrainEnergybyDustFormation102.7JElasticWaveEnergy253.4JEnergyStoredinStand78.6JEnergyStoredinHammer442.1JFrictionWorkonHammer101JRemainingEnergy136.6J 58

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Figure3-1. LargedrophammeratCIPPS.Dropmasshighlightedinwhitesquare. 59

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Figure3-2. VariableMassDropHammeratCIPPS. 60

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Figure3-3. Straingagemapfortestcylinders. Figure3-4. StaticStress-Strainforthree100mmUHPCCylinders. 61

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Figure3-5. Smallhammercrosshead.Steelsectionsarelocatedinbottomarea,aluminumintoparea. 62

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Figure3-6. DetailofsteelreinforcementforUHPFRCstand. Figure3-7. DynamicStress-Strainfor150mmUHPCCylinderCT2-6-D-5. 63

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Figure3-8. UHPFRCcrosssectiondisplayingberorientation. Figure3-9. MagniedviewofUHPFRCcrosssection. 64

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Figure3-10. CT2-6-D-5onmattomeasurefracturearea. 65

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Figure3-11. EnergydistributionofCT2-6-D-5. 66

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CHAPTER4RESULTSANDDISCUSSIONResultsanddiscussionfrommethodologydiscussedinChapter 3 arepresentedbelow.Physicaltestresultsarepresentedrst,followedbyresultsfromtheenergybalancemethodpresentedearlier.Comparisonofresultsforeachmaterialanddiscussionofmaterialdierencesareattheend.AnexampleofmethodologywasdemonstratedforaUHPCcylinderinthepreviouschapter. 4.1PhysicalTesting 4.1.1StaticTestingStatictestingwasconductedatFDOTMaterialsResearchLabandtheUniversityofFloridaStructuresLab.Threecylindersofeachmaterialandtwosizes(100mmby200mmand150mmby300mmcylinders)wereinstrumentedforaxialandvolumetricstrain,andtheloadwasrecordedduringtesting.Averagepeakloadforallserieswererecorded.Fromthisdata,stressvsstraincurveswereobtainedandusedtoevaluatethestaticmodulusofelasticityaswellasthestaticspecicenergyofeachmaterialandspecimensize.ResultsareshowninTable 4-1 .MaterialstressstraincurvesforNSC,UHPFRC,andUHPCareshowninFigures 4-1 4-2 ,and 4-3 .Datafromtheexperimentsareusedtoguessattheinitialdropheightforthehammer,aswellascalculationofthecomplementaryenergyasdescribedaboveinEquation 3{9 .TheNSCspecimenshadanaveragecompressivestrengthof36.4MPaand36.1MPaforthe100mmand150mmspecimens;theUHPCspecimenshadaveragecompressivestrengthsof227.8MPaand190.8MPa;andtheUHPFRCspecimenshadaveragecompressivestrengthsof184.0MPaand190.9MPaforthe100mmand150mmspecimens.Allspecimensweretestedtocompletefailureexceptforthe150mmUHPCandUHPFRCspecimens,whichwereunabletobeloadedtofailureduetolimitationsofthetestingmachine.Thespecicstrainenergycapacitywascalculatedusingthe100mmspecimens.Integratingtheareasunderthestaticstress-straincurvesyieldedspecicstrainenergydensitiesof46.4kJ=m3,451.3kJ=m3,and351.4kJ=m3fortheNSC,UHPC,andUHPFRCrespectively. 67

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4.1.2DynamicTestingDynamictestingwasconductedon150mmNSC,UHPC,andUHPFRCspecimens.UHPCandUHPFRCspecimensweretestedusingthe2700kgdrophammer.NSCspecimensweretestedusingthe250kgdrophammer.Inititaldropheightswereestimatedusingtheenergycapacityderivedfromthestaticstress-strainrelationship.Testswerecarriedoutfromprogressivelyhigherdropheightsuntiladropwithminimalfragmentationandkineticenergyofthespecimenwasacheived.Criteriaforselectingspecimensincluded: Specimenhadobservablecracksindicativeofafailure; Specimenandfragmentsdidnotleavethesurfaceoftheteststandduetokineticejection; Specimenwasnotpulverized,orhadthreeorfewermajorfragments.ResultsaresummarizedbelowinTables 4-2 4-3 ,and 4-4 .ResultsincludecylinderID,dropheight,andfractureresponse.Usingthetestdata,thefollowingspecimenswereselectedforanalysis:NSC-6-D-1,NSC-6-D-3,CT2-6-D-5,CT2-6-D-7,andCT1-6-D-8,CT1-6-D-9.Resultsforeachspecimenarediscussedbelow. 4.1.2.1NSC-6-D-1SpecimenNSC-6-D-1wastestedunderthesmalldrophammerwithadropmassof250kg.Thedropheightwas812.8mm.Pre-testmasswas12.281kg.Theimpactvelocitywasrecordedas3.3m/s,andthereboundvelocitywasrecordedas1.15m/s,resultinginaninputenergyof1162.3J.Thepeakstressrecordedwas38.2MPa.Duringtheimpactevent,minorfragmentschippedofromthebaseofthespecimen.Themainfragmentweighed12.036kg,whilesecondaryfragmentsweighed0.160kg.Fragmentvelocitieswererecordedas0.9m/sand0.5m/s.Theremaingmassofdustlossduetocrushingwas0.085kg.Posttest,thespecimendisplayedminorcrackingalongtheheightofthecylinderfromthepeakofthesespots.StressandaxialstraindataareshowninFigure 4-4 andFigure 4-5 .VolumetricstraindataisshowninFigure 4-6 .Adynamicstress-straincurveisshowninFigure 4-7 .Apre-testphotoisshowninFigure 4-8 ,andapost-testphotoisshownin 68

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Figure 4-9 .Acapturefromhigh-speedvideoshowingadiagonalcrackwithsmalldustfragmentsbeingejectedisshowninFigure 4-10 .Fractureareawasmeasuredas0.02m2.ApictureofthefractureareaisshowninFigure 4-11 4.1.2.2NSC-6-D-3SpecimenNSC-6-D-3wastestedunderthesmalldrophammerwithadropmassof250kg.Thedropheightwas812.8mm.Pre-testmasswas12.338kg.Theimpactvelocitywasrecordedas3.3m/s,andthereboundvelocitywasrecordedas0.82m/s.Thepeakstressrecordedwas39.0MPa.Duringtheimpactevent,fragmentschippedofromthebaseofthespecimen.Themainfragmentweighed11.983kg,whilesecondaryfragmentsweighed0.056kgandtertiaryfragmentsweighed0.035kg.Fragmentvelocitieswererecordedas1.5m/s,1.4m/s.,and0.5m/s.Theremaingmassofdustlossduetocrushingwas0.264kg.Posttest,thespecimendisplayedcrackingalongtheheightofthecylinderfromthepeakofthesespots.StressandaxialstraindataareshowninFigure 4-12 andFigure 4-13 .VolumetricstraindataisshowninFigure 4-14 .Adynamicstress-straincurveisshowninFigure 4-15 .Apre-testphotoisshowninFigure 4-16 ,andapost-testphotoisshowninFigure 4-17 .Fractureareawasmeasuredas0.03m2.ApictureofthefractureareaisshowninFigure 4-18 4.1.2.3CT2-6-D-5SpecimenCT2-6-D-5wastestedunderthelargedrophammerwithadropmassof2700kg.Thedropheightwas241.3mm.Pre-testmasswas13.243kg.Theimpactvelocitywasrecordedas1.9m/s,andthereboundvelocitywasrecordedas1.3m/s.Thepeakstressrecordedwas112.4MPa.Duringthetest,alargeverticalcracksplitfromthetopdown,cleavingthecylinderintoatleastthreepieces.Themainmasswas10.833kg,whilethesecondarycloudwasrecordedas1.88kg.Fragmentvelocitieswererecordedas3.4m/sand16.1m/s.Dustmasswascalculatedas0.530kg.StressandaxialstraindataareshowninFigure 4-19 andFigure 4-20 .VolumetricstraindataisshowninFigure 4-21 .Adynamicstress-straincurveisshowninFigure 4-22 .Apre-test 69

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photoisshowninFigure 4-23 ,andapost-testphotoisshowninFigure 4-24 .Fractureareawasmeasuredas0.08m2.ApictureofthefractureareaisshowninFigure 4-25 4.1.2.4CT2-6-D-7SpecimenCT2-6-D-7wastestedunderthelargedrophammerwithadropmassof2700kg.Thedropheightwas241.3mm.Pre-testmasswasrecordedas13.320kg.Theimpactvelocitywasrecordedas2.0m/s,andthereboundvelocitywasrecordedas1.2m/s.Thepeakstressrecordedwas115.9MPa.Duringthetest,thehammermadecontacttwicewiththespecimenduetoadelayedactivationofthereboundbrakes.Ontherstimpact,therewasminordamageandsignicantreboundofthebodyofthespecimen.Onthesecondimpact,severallargefragmentsviolentlybrokeawayfromthespecimen.Thefragmentmasseswererecordedas6.359kg,4.361kg,and1.879kg.Theejectionvelocitieswererecordedas3.25m/s,14.9m/s,and1.8m/s.Dustmasswascalculatedas0.451kg.Posttest,thespecimendisplayedseverallargefractureareasonthemainbodypiecealongwithseveralsmallfragments.StressandaxialstraindataareshowninFigure 4-26 andFigure 4-27 .VolumetricstraindataisshowninFigure 4-28 .Adynamicstress-straincurveisshowninFigure 4-29 .Apre-testphotoisshowninFigure 4-30 ,andapost-testphotoisshowninFigure 4-31 .Fractureareawasmeasuredas0.11m2.ApictureofthefractureareaisshowninFigure 4-32 4.1.2.5CT1-6-D-8SpecimenCT1-6-D-8wastestedunderthelargedrophammerwithadropmassof2700kg.Thedropheightwas812.8mm.Pre-testmasswasrecordedas14.444kg.Theimpactvelocitywasrecordedas3.67m/s,andthereboundvelocitywasrecordedas1.12m/s.Thepeakstressrecordedwas204.3MPa.Duringthetest,thesurfaceofthespecimenunderwentsigncantspalling.Themainbodyofthespecimenreboundedfromthestandwithkineticenergy,butnomajorfragments.Themainbodymasswasrecordedas14.146kg.Recoveredfragmentswereweighedandfoundtobe0.069kg.Bodyandejectavelocitieswererecordedas1.8m/sand1.9m/s.Dustmasswascalculatedas0.229kg. 70

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Posttest,thespecimendisplayedcrackingalongtheheightofthecylinderfrombase.StressandaxialstraindataareshowninFigure 4-33 andFigure 4-34 .VolumetricstraindataisshowninFigure 4-35 .Adynamicstress-straincurveisshowninFigure 4-36 .Apre-testphotoisshowninFigure 4-37 ,andapost-testphotoisshowninFigure 4-38 .Acapturefromhigh-speedvideoshowingadiagonalcrackwithsmalldustfragmentsbeingejectedisshowninFigure 4-39 .Fractureareawasmeasuredas0.019m2.ApictureofthefractureareaisshowninFigure 4-40 4.1.2.6CT1-6-D-9SpecimenCT1-6-D-9wastestedunderthelargedrophammerwithadropmassof2700kg.Thedropheightwas838.2mm.Pre-testmasswasrecordedas14.143kg.Theimpactvelocitywasrecordedas3.81m/s,andthereboundvelocitywasrecordedas0.94m/s.Thepeakstressrecordedwas231.2MPa.Duringthetest,thespecimendisplayedadiagonalshearresponsewithminimalkineticenergyandfragmentswherethetopportionofthespecimensliddownrelativetothebottomportionofthespecimenalongadiagonalcrack.Thebasedisplayedseveralfragmentssplittingawayfromthespecimen.Mainfragmentmasswasrecordedas13.783kg,whilethefragmentswererecordedas0.175kg.Ejectavelocitieswereobservedat0.8m/sand2.4m/s.Massofdustlostduetocrushingwascalculatedas0.185kg.Posttest,thespecimendisplayedalargecrackfromthebasesimilartothesmush-typefailuredisplayedbyotherspecimensindicativeofacupandconetypefailure.StressandaxialstraindataareshowninFigure 4-41 andFigure 4-42 .VolumetricstraindataisshowninFigure 4-43 .Adynamicstress-straincurveisshowninFigure 4-44 .Apre-testphotoisshowninFigure 4-45 ,andapost-testphotoisshowninFigure 4-46 .Acapturefromhigh-speedvideoshowingadiagonalcrackwithsmalldustfragmentsbeingejectedisshowninFigure 4-47 .Fractureareawasmeasuredas0.023m2.ApictureofthefractureareaisshowninFigure 4-48 71

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4.2EnergyBalanceAnalysisAnenergybalanceanalysisofallspecimenswasperformed.ResultsareshowninTable 4-5 .EnergytermswerecalculatedasdescribedinChapter 3 .Inputkineticenergieswerecalculatedanddemonstratedawiderangebetweenthedierentmaterialsrequiredforfracture.Frictionenergywascalculatedusingthedierencebetweenthepredictedimpactvelocityandtherecordedvelocity.Kineticenergyofcylinderandfragmentswererecordedusinghigh-speeddataandpost-testcollection.Cylinderelasticandplasticstrainenergieswerecalculatedusingstraindatarecorded.StandandhammerstrainenergieswerecalculatedusingasimpliedSDOFsystemwiththerecordedloadappliedtotheelement.Fractureenergywascalculatedbyestimatingthefractureplaneareaofrecoveredspecimenfragments,andmultipliedbytheenergyreleaserateforeachmaterial.FortheUHPFRC,theberpull-outenergywascalculatedbyestimatingthenumberofbersfromthefracturearea,andmultiplyingbytheberpull-outenergy.Fiberswereestimatedat11berspercm2basedonphotographicanalysis.Anyremainingenergywasmarkedasremainderorunaccountedenergy. 4.3DiscussionStatictestresultsforthe100mmand150mmspecimensagreedwithpreviousresultsfromtheliteratureforthesamematerials.Thepeakstrengthsforthe150mmUHPCandUHPFRCspecimenswereunabletoberecordedtoreachingtheloadlimitofthetestingframe.Young'smodulusforeachmaterialandsizewererecorded.Basedonpreviousresearch,the5%deviationforthemodulusofelasticitywascalculatedtodeterminethelimitofmateriallinearity.Forthe100mmUHPC,the5%deviationoccuredat84.5%ofthepeakstress.The5%deviationforthe100mmUHPFRCoccuredat91.2%ofthepeakstress.Thenormalstrengthspecimensrequiredtheleastinputenergyasexpected,whiletheUHPCspecimensrequiredsignicantlylessenergythantheUHPFRCspecimens.FortheNSCspecimens,kineticenergyconsumedbetween0.42%and1.09%oftheinputenergy,whiledissipatingbetween36.2%and46.8%ofenergyaselasticstrainenergy.Plasticstrainenergyaccountedfor1.32%and1.45%oftheenergyconsumption.Crushingenergyaccountedfor 72

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0.54%and0.55%oftheinputenergy.Elasticenergyintothebaseaccountedfor7.69%to8.34%oftheinputenergy.Strainenergyofthestandandhammeraccountedfor23.33%and25.16%oftheinputenergies.Frictionalenergyconsumptionwas1.12%and1.27%.Fractureenergyconsumptionaccountedfor0.34%and0.46%basedonobservablesurfaceareasofthespecimens.EnergydistributionsforthetwospecimensanalyzedareshowninFigures 4-49 and 4-49 .Thevastmajorityoftheenergywasconsumedbystrainofthehammerandthestand.TheUHPCspecimensrequiredmoreinputenergythantheNSCspecimens,butmuchlessthantheUHPFRCspecimens.ThepeakdynamicstressesforalltheUHPCspecimenswereapproximatelyhalfthestaticfailurestressofthesamematerial.AllUHPCspecimenswereobservedtohaveabrittlefracturefailuremode,withnoarrestingofcrackpropagationoncefailureinitiated.Itisbelievedthatthelowerdynamicstrengthsareduetothisbrittlefailuremechanism.FortheUHPCspecimens,kineticenergyconsumedbetween11.74%and16.13%oftheinputenergy,whiledissipatingbetween33.68%and35.59%ofenergyascylinderstrainenergy.Plasticstrainenergyaccountedfor8.28%and9.54%oftheenergyconsumption.Crushingenergyaccountedfor2.53%and3.96%oftheinputenergy.Elasticenergyintothebaseaccountedfor8.44%to9.78%oftheinputenergy.Strainenergyofthestandandhammeraccountedfor16.71%and20.09%oftheinputenergies.Frictionalenergyconsumptionwas1.42%and3.90%.Fractureenergyconsumptionaccountedfor0.13%and0.14%basedonobservablesurfaceareasofthespecimens.EnergydistributionsforthetwospecimensanalyzedareshowninFigures 4-51 and 4-52 .AnexampleoftheviolentfractureisshowninFigureTheUHPFRCspecimensrequiredmoreinputenergythantheNSCandUHPFRCspecimens.AllUHPFRCspecimenswereobservedtohavefewerfragments,andthecracksthatdidformhadlargeamountsofbersbridgingthesecracks.Asignifcantportionoftheinputenergywasconsumedbythesteelbers.FortheUHPFRCspecimens,kineticenergyconsumedbetween0.04%and0.14%oftheinputenergyduetolackoffragmentationof 73

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thespecimen,whileelasticstrainenergydissipatedbetween9.81%and10.11%ofinputenergy.Plasticstrainenergyaccountedfor2.73%and3.54%oftheenergyconsumption.Crushingenergyaccountedfor0.14%and0.19%oftheinputenergy.Duetothelackoffragmentationandlossofmass,internalcrushingcouldnotbemeasured.Elasticenergyintothebaseaccountedfor8.42%to8.60%oftheinputenergy.Strainenergyofthestandandhammeraccountedfor13.98%and14.41%oftheinputenergies.Frictionalenergyconsumptionwas0.31%and0.43%.Fractureenergyconsumptionaccountedfor0.05%forbothspecimensbasedonobservablesurfaceareasofthespecimens.Fiberpull-outenergyaccountedfor17.34%and18.90%oftheenergydissipation.EnergydistributionsforthetwospecimensanalyzedareshowninFigures 4-54 and 4-55 .Theabsolutevaluesoftheenergyterms,however,aresimilarinmagnitudetotheUHPC.Asdisplayed,theremainingenergyaccountsforasignicantportionoftheenergydistribution.Duringthetestprocess,largeamountsofvibrationandmovementofthestandandhammerframeswereobserved.Asignicantportionoftheenergywasdissipatedintotheframeandbuilding.Theremainingenergyisunaccountedforusingtheenergydistributiontermsforthecylinderandtheequivalentspringstinessesofthestandandhammer.Thislargeportionisduetoinabilitytomeasureinternalenergydissipationmechanismssuchasfracture,micro-cracking,crushing,andberpull-outmechanisms.Othermechanismsincludebouncingofthestandandmotionofthehammer,andvibrationandstrainoftheframeandoorofthestructureduetoenergytransferthroughthespecimen. 4.4SummaryPhysicaltestingwascarriedoutonanumberofNSC,UHPC,andUHPFRCspecimens.Thephysicaldataandobservationsdisplayeddistinctfracturemodesforthedierentmaterialsatdierentloadratesandinputenergies.Normalstrengthspecimensabsorbedapproximately35%oftheimpactenergyaselasticstrainenergy,whiletherestwasdissipatedviafractureandkineticmechanisms.TheUHPCspecimensdisplayedbrittlefailureswithhighlykineticejectaaccoutingfor11%to16%ofinputenergy.TheUHPFRCspecimenswereabletoabsorb 74

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themostenergyofallspecimens,withasignicantportion(17%to19%)beingdissipatedbyberpull-outmechanisms.Quantitiesofnon-berenergytermsforUHPCandUHPFRCweresimilarinnmagnitude.Changesinrelative(%)termswasmainlyduetothelargedierenceininputenergyvalues(17kJforUHPFRCvs3kJforUHPC).Thelargeamountofremainingenergywasduetointernalprocessesalongwithenergydissipationbybaseandframethatwasunaccountedforbyinstrumentationonthedrophammerandbase. 75

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Table4-1. Statictestresultsoncylinders. MaterialSize(mm)AveragePeakStress(MPa)ModulusofElasticity(GPa)EnergyCapacity(kJ=m3) NSC10036.433.555.6NSC15036.129.146.4UHPC100227.854.8451.3UHPC150190.550.9365.7UHPFRC100184.055.9351.4UHPFRC150190.953.4261.3 Table4-2. DynamictestresultsonNSCcylinders. SpecimenDropHeight(mm)FractureResponse NSC-6-D-1812.8SmallspallingandchippingfrombaseNSC-6-D-2838.2DoubleshearfailurewithminimalKENSC-6-D-3812.8SmallspallingandchippingfrombaseNSC-6-D-4825.5Largeshearconeatbase,fragmentsonfrontandsideNSC-6-D-5819.2Majorfragmentsfromfrontandside Table4-3. DynamictestresultsonUHPCcylinders. SpecimenDropHeight(mm)FractureResponse CT2-6-D-1254BucklingfrombaseCT2-6-D-2203.2VerticalsplittingCT2-6-D-3203.2VerticalsplittingCT2-6-D-4-2228.6ChippingCT2-6-D-4-3228.6ChippingCT2-6-D-4-4228.6ChippingCT2-6-D-4-5254FragmentationfrombottomCT2-6-D-5241.3VerticalsplittingwithKECT2-6-D-6241.3BrittlefailurefrombottomCT2-6-D-7241.3Verticalcrack,minimalKEandfragments 76

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Table4-4. DynamictestresultsonUHPFRCcylinders. SpecimenDropHeight(mm)FractureResponse CT1-6-D-1-1-A685.8Nodamage-RubberPadCT1-6-D-1-2-A685.8ChippingattopCT1-6-D-1-3-A685.8Diagonalsheardamage,spallingCT1-6-D-2-1-A762DiagonalshearspallingCT1-6-D-2-2-A762ProgressivecollapseCT1-6-D-3-A838.2Buckling-burstingfrombottomCT1-6-D-4-A838.2DiagonalshearCT1-6-D-5-A838.2Shell-coreburstingCT1-6-D-6-A838.2Diagonalshear,shell-coreburstingCT1-6-D-7838.2Diagonalshear,verticalsplittingCT1-6-D-8812.8Slightcracking,surfacechippingCT1-6-D-9838.2DiagonalCrackband,surfacespallingCT1-6-D-10838.2Bottomcupandcone,highKEfragments Table4-5. Energydistributionsummary(%)fromdynamictesting. ParameterNSC-6-D-1NSC-6-D-3CT2-6-D-5CT2-6-D-7CT1-6-D-8CT1-6-D-9 InputEnergy(kJ)1162.31242.2259234561647018344Wfriction1.271.123.901.420.430.31KEfragments0.421.0911.747.760.130.02SEcylinder46.836.235.5933.6810.119.81PEcylinder1.321.459.548.282.733.54Ecrushing0.540.553.962.530.190.14EElasticWaves8.347.699.788.448.608.42SEstand1.501.433.032.662.061.87SEhammer23.6621.9017.0614.0511.9212.54Efibern/an/an/an/a17.3418.90fracture0.340.460.130.140.050.05Eremaining15.8028.125.2721.0546.4444.39 77

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Figure4-1. StaticNSCstressvsstrain. Figure4-2. StaticUHPCstressvsstrain. 78

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Figure4-3. StaticUHPFRCstressvsstrain. Figure4-4. NSC-6-D-1stressvstime. 79

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Figure4-5. NSC-6-D-1axialstrainvstime. Figure4-6. NSC-6-D-1volumetricstrainvstime. 80

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Figure4-7. NSC-6-D-1dynamicstressvsstrain. 81

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Figure4-8. NSC-6-D-1beforetesting. 82

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Figure4-9. NSC-6-D-1aftertesting. 83

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Figure4-10. NSC-6-D-1fragmentscapturedbyhigh-speedvideo. 84

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Figure4-11. NSC-6-D-1fragmentsandfracturearea. 85

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Figure4-12. NSC-6-D-3stressvstime. Figure4-13. NSC-6-D-3axialstrainvstime. 86

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Figure4-14. NSC-6-D-3volumetricstrainvstime. Figure4-15. NSC-6-D-3dynamicstressvsstrain. 87

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Figure4-16. NSC-6-D-3beforetesting. 88

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Figure4-17. NSC-6-D-3aftertesting. 89

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Figure4-18. NSC-6-D-3fragmentsandfracturearea. 90

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Figure4-19. CT2-6-D-5stressvstime. Figure4-20. CT2-6-D-5axialstrainvstime. 91

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Figure4-21. CT2-6-D-5volumetricstrainvstime. Figure4-22. CT2-6-D-5dynamicstressvsstrain. 92

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Figure4-23. CT2-6-D-5beforetesting. 93

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Figure4-24. CT2-6-D-5aftertesting. 94

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Figure4-25. CT2-6-D-5fragmentsandfracturearea. 95

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Figure4-26. CT2-6-D-7stressvstime. Figure4-27. CT2-6-D-7axialstrainvstime. 96

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Figure4-28. CT2-6-D-7volumetricstrainvstime. Figure4-29. CT2-6-D-7dynamicstressvsstrain. 97

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Figure4-30. CT2-6-D-7beforetesting. 98

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Figure4-31. CT2-6-D-7aftertesting. 99

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Figure4-32. CT2-6-D-7fragmentsandfracturearea. 100

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Figure4-33. CT1-6-D-8stressvstime. Figure4-34. CT1-6-D-8axialstrainvstime. 101

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Figure4-35. CT1-6-D-8volumetricstrainvstime. Figure4-36. CT1-6-D-8dynamicstressvsstrain. 102

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Figure4-37. CT1-6-D-8beforetesting. 103

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Figure4-38. CT1-6-D-8aftertesting. Figure4-39. CT1-6-D-8fragmentscapturedbyhigh-speedvideo. 104

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Figure4-40. CT1-6-D-8fragmentsandfracturearea. 105

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Figure4-41. CT1-6-D-9stressvstime. Figure4-42. CT1-6-D-9axialstrainvstime. 106

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Figure4-43. CT1-6-D-9volumetricstrainvstime. Figure4-44. CT1-6-D-9dynamicstressvsstrain. 107

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Figure4-45. CT1-6-D-9beforetesting. 108

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Figure4-46. CT1-6-D-9aftertesting. 109

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Figure4-47. CT1-6-D-9fragmentscapturedbyhigh-speedvideo. 110

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Figure4-48. CT1-6-D-9fragmentsandfracturearea. 111

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Figure4-49. NSC-6-D-1energydistribution. Figure4-50. NSC-6-D-3energydistribution. 112

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Figure4-51. CT2-6-D-5energydistribution. Figure4-52. CT2-6-D-7energydistribution. 113

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Figure4-53. FragmentfracturepatternofCT2-6-D-5. Figure4-54. CT1-6-D-8energydistribution. 114

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Figure4-55. CT1-6-D-9energydistribution. 115

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CHAPTER5CONCLUSIONANDRECOMMENDATIONS 5.1ConclusionThisstudydemonstratedanapproachtoinvestigatethefailurebehaviorofNSC,UHPC,andUHPFRCcylindricalspecimensunderimpactloadingbyuseoflinearelasticfracturemechanicsandanenergybalance.Aprocedurefortestingspecimensusingadvanceddrophammerswasdetailed,andmethodstoobserveandcalculatevariousenergiesduringthetestprocedureusingloadcells,straingages,andhighspeedvideowasdemonstrated.Experimentswereperformedonspecimensandtestresultswithminimalkineticfailuremodeswereusedtoexaminetheenergydissipationviavariousmechanismssuchaselasticstrain,plasticstrain,crushing,fracture,berpull-out,andkineticenergyoffragments.PreviousresearchonimpactofNSC,UHPC,andUHPFRCspecimenshavefocusedpurelyontotalstrengthofthespecimenscomparedtostaticstrengthcapacities.Experimentsvalidatedthedynamicstrengthcapacitiesanddemonstratedsimilarresponsesofthematerialstopreviousresearch.Furtherresultsdemonstratedthattherearesignicantlydierentenergydissipationmechansimsbetweenthethreematerials.TheinputenergiesoftheUHPFRCtestswassignicantlyhigherthantheUHPCorNSCspecimens(16470and18344J,versus2592and3456JfortheUHPCand1162and1242JfortheNSC).Allmaterialsdisplayedasigncantamountofenergystorageaselasticstrainenergyduringtheimpactloadingprocess.TheNSCspecimensdisplayedhighamountsofstrainenergystorageduringtheimpactevent,rangingfrom36.2-46.8%comparedtotheUHPCandUHPFRCspecimens(33.7-35.6%,and9.81-10.1%,respectively).TheUHPCspecimensdisplayedalargeamountofenergydissipationviakineticenergyterms(11-16%,comparedto0.05%fortheUHPFRCand1.27%fortheNSCspecimens).ThefracturemechanismforUHPFRCdisplayedmuchlessfragmentationandspallingcomparedtoboththeUHPCandNSCspecimenswithasignicantreductioninobservedkineticenergy.TheUHPFRCspecimensdisplayedalargeamountofenergydissipationvia 116

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berpull-out.Additionofthebersallowedfor477%-707%increasesintotalinputenergycomparedtotheUHPC.Additionally,theUHPFRCspecimensdisplayedmuchlessrelativeelasticstrainenergycomparedtotheUHPCorNSCspecimens,howeverinabsolutetermsitwassimilar(1665-1800JfortheUHPFRCcomparedto922-1164JfortheUHPFRC).ItistheorizedthatthebermatrixoftheUHPFRCspecimenspreventedbrittlefractureandseparationofthespecimen,andthereforeenergytoowthroughthespecimenintothestandandintothebaseofthehammer.Similarly,theplasticstrainenergyvaluesfortheUHPFRCcomparedtotheUHPCweresimilarinrawvalues(450-650JfortheUHPFRCvs247-286JfortheUHPC)butsignicantlydierentinpercentage.ItwasobservedthatfortheUHPFRCspecimenstherewasasignicantamountofenergytransmittedthroughthespecimenintothebaseofthesupportstructureforboththestandandhammer.Thehammerframewasobservedtoshakeaftertests,andgroundvibrationscouldbefeltapproximately10metersawayfromthetestlocation.ThehigherkineticenergiesoftheUHPCspecimensmatchobservationsofthebrittlefracturecomparedtotheNSCandUHPFRCspecimens.Duringthefailureprocess,strainenergywasconvertedtokineticenergyforthefailureoftheUHPCspecimens.FortheUHPFRCspecimens,asignicantamountofenergywasabsorbedbythepull-outofthebersacrossobservablefailureplanes.FortheUHPFRCspecimens,asignicantamountofenergyremainsunaccountedforcomparedtotheNSCandUHPCspecimens.Itistheorizedthatthisisduetoacombinationofinternaldissipationprocessesinsidespecimensduringtheimpacteventandtransferofenergyintothebasestructure.Itisnotedthatofallthematerials,theUHPFRCspecimenshadthefewestfragmentsandleastamountofkineticenergy,whileabsorbingthehighestinputenergy.However,themagnitudeofenergyterms(excludingberenergyterms)fortheUHPFRCandUHPCweresimilarinmagnitude.CombinedwiththefewerfragmentsoftheUHPFRCspecimens,thisindicatesthattheexcessenergywasconsumedbyeithertransferintothebaseorbyinternalfailureprocessesandberenergy. 117

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5.2AssumptionsandLimitationsSeveralassumptionsandlimitationsareidentiedinthecurrentmethodology.First,thestressandstrainvaluesarelimitedtolocationofinstrumentation.Strainvaluesarelimitedtosurfacevaluesanddonotaccountforinternalcrackingandnon-linearbehaviorofthematerial.Thecurrentmethodassumesthatthestrainsmeasuredforeachareaofthecylinder(top,middle,bottom)aredistributedequallyacrosstheareaofthecylinder.Otherlimitationsincludetheobservationandmeasurementoffailuresurfaces.Surfacesweremeasuredusingvisualinspectionandmechanicalprobingusingawire.Fractureprocesses,however,canbemicroscopicinnatureandextremelysmall.Thetotalareameasuredshouldbeconsideredaminimumofnewsurfaceareacreatedbyfracture.Thisalsoaectstheberdissipationenergy.Internalfailureandpull-outofbersthatarenotvisiblecouldbealargesourceofenergydissipation.Internalcrackingwasnotabletobemeasuredusingthecurrentmethodology.Althoughtheberswereassumedtohavearandomorientationwithuniformdistribution,previousexperimentsandresearchhaveshownthatUHPFRCberstohaveorientationdependingonthecastingmethodandproximitytoformwork.OtherUHPFRCspecimensthatexhibitedmorekineticfailuredisplayedfailuresurfacesthathadfewerbersthanexpectedbasedonthecross-sectionalanalysis.Finally,thevisualanalysiswaslimitedbymethodsused.Fracturesurfaceareawaslimitedtophotographicanalysis,andvideoevidencewaslimitedtoasinglecamerawhichlimitedthefragmenttrackingtospecimensthatdisplayedspecicfailurepatterns.Second,thematerialisassumedtobehavelinearelasticuntilfailure.WhileUHPCandUHPFRCstress-strainrelationshipsaremuchmorelinearthanNSC,thetotalbehaviorisnottruelinearelastic.However,duetolimitedtestdataandlackoffullstress-straindataforthe150mmcylinders,thematerialwasassumedtobelinearelasticuntilcatastrophicfailure.Additionalenergytermsthatmighthavehadanimpactontheenergydissipationincludefrictionalenergybetweenthespecimenandthecontactsurfaces,whichwereassumedtobenegligiblecomparedtotheoverallinputenergy. 118

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5.3ImplicationsThemethodsandresultspresentedheredemonstrateamethodtocomparethefailureofNSC,UHPC,andUHPFRCcylindersusingenergybalanceanddistributionmechanisms.FortheNSCandUHPCspecimens,theenergydistributionwasusedtoobservethedissipationmechanismsduringfailureofthespecimensunderimpact.FortheUHPFRCspecimens,thesamemethodsyieldedenergytermsthatweresimilarinmagnitudetotheUHPCspecimens,butquitedierentinrelativepercentageofinputenergy.TheonlydierencebetweentheUHPCandtheUHPFRCwastheadditionofsteelberstothemixdesign,resultinginalargeincreaseinenergyrequiredforcylinderfailure.Furthermore,theUHPFRCspecimenshadfewfragmentscomparedtotheUHPCspecimens.AdditionofthebersthusgreatlyincreasedtheenergycapacityofthecylindersinthedynamicdomaincomparedtotheUHPCcylinders,eventhoughthestatictestingindicatedsimilarenergycapacities. 5.4RecommendationsforFutureResearchBasedontheresultsobtainedinthepresentresearch,thefollowingrecommendationsforfurtherresearchareproposed: Thedrophammers,stands,andsupportstructuresshouldbeinstrumentedwithaccelerometers,straingages,oracombinationofthetwoinordertoproperlygageenergyowthroughtheframeworkandawayfromthetestspecimens. Specimensofdierentsizesshouldbeexamined.Previousresearchhasdemonstratedasize-eectinconcretecylindersunderimpactloading,andthestaticresultsinthecurrentresearchvalidatedthosendings.Researchonspecimensofthesameaspectratiobutwithdierentsizescouldyieldinsightsintotheenergydissipationmechanismsforlargerspecimenswhichcouldhaveaectsonfull-scalestructuralresponsetodynamicloads. Specimensofdierentshapesshouldbeexamined.Mostofthepreviousenergyrateresearchhasbeenperformedonlyonsquareorrectangularspecimens,andmostmaterialparametersforenergyreleaseratearederivedfromspecimenswiththosesizesandaspectratios.Dynamictestingofstandardfractureenergyspecimenswoulddemonstrateadirectlinkbetweenstaticanddynamicenergyreleaseratesforthematerialsunderinvestigation. EnergydissipationmechanismsinstructuralsystemsutilizingUHPFRCunderdynamicloadsshouldbeinvestigatedandcomparedtothecurrentresultsforenergydistribution, 119

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particularlyregardingtheplasticdissipationmechanismsandberpull-outmechanisms.Otherresearchintoenergydissipationratesonstructuralsystemsusingreinforcedconcreteshouldbeexpandedtoincludeberpull-outeects. Investigationandanalysisofinternalfractureplanesshouldbeconsidered.UHPCandUHPFRCspecimenscouldbeanalyzedusingacombinationofpre-andpost-testmicro-tomographyscans.Computeranalysisofthedierencesbetweenthescanscouldyieldinsightsintopossibleinternaldamageandfracture. Applicationofnumericalanalysesthatcanbeusedtotrackenergyowinsuchspecimensshouldbeconsideredtoassistinbetterunderstandingtheobservationsfromthetestsperformed. 120

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BIOGRAPHICALSKETCHMichaelStoneattendedFloridaInternationalUniversityforundergraduatestudiesandreceivedaBachelorofScienceinCivilEngineeringwithaconcentrationinStructures.HebeganhisMasterofScienceinCivilEngineeringatUniversityofFloridain2011,andreceivedhisDoctorofPhilosophyinCivilEngineeringin2017.Hisresearchhasincludedtopicssuchasreinforcedconcreteunderimpact,structuralresponsetoimpulsiveloads,andsimpliedcomputationalmodelsfordynamicloading. 126