NCAT Report 09-XX EFFECTS OF LOADING RATE AND MIX...

NCATReport09-XX

EVALUATION OF MIXTURE PERFORMANCE AND

STRUCTURAL CAPACITY OF PAVEMENTS UTILIZING

SHELL THIOPAVE®

PhaseI:

MixDesign,LaboratoryPerformanceEvaluationandStructuralPavement

AnalysisandDesign

By

DavidTimm

AdamTaylor

NamTran

MaryRobbins

NCATReport17-09

EFFECTSOFLOADINGRATEANDMIXREHEATINGONINDIRECTTENSILENFLEX

FACTORANDSEMI-CIRCULARBENDJ-INTEGRALTESTRESULTSTOASSESSTHE

CRACKINGRESISTANCEOFASPHALTMIXTURES

FanYinRandyWestZhaoxingXieAdamTaylorGrantJulian

December2017

Yin,West,Xie,Taylor,andJulian

ii

EffectsofLoadingRateandMixReheatingonIndirectTensileNflexFactorandSemi-CircularBendJ-integralTestResultstoAssesstheCrackingResistanceofAsphaltMixtures

NCATReport17-09by

FanYin,Ph.D.PostdoctoralResearcher

RandyC.West,Ph.D.,P.E.

Director&ResearchProfessor

ZhaoxingXieGraduateResearchAssistant

AdamTaylor,P.E.

AssistantResearchEngineer

GrantJulianAssistantResearchEngineer

NationalCenterforAsphaltTechnologyAuburnUniversity,Auburn,Alabama

SponsoredbyFederalHighwayAdministration

December2017


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ACKNOWLEDGEMENTS

ThisprojectwasfundedbytheFederalHighwayAdministration(FHWA).Theauthorswouldliketothankthemanypersonnelwhocontributedtothecoordinationandaccomplishmentoftheworkpresentedherein.

DISCLAIMER

Thecontentsof this reportreflect theviewsof theauthorswhoareresponsible for the factsandaccuracyofthedatapresentedherein.Thecontentsdonotnecessarilyreflecttheofficialviews or policies of the sponsor(s), the National Center for Asphalt Technology, or AuburnUniversity.This reportdoesnotconstituteastandard,specification,or regulation.Commentscontained in this paper related to specific testing equipment and materials should not beconsidered an endorsement of any commercial product or service; no such endorsement isintendedorimplied.


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TABLEOFCONTENTS

1.Introduction...............................................................................................................................62.Objective....................................................................................................................................63.ExperimentalDesign...................................................................................................................63.1ResearchMethodology........................................................................................................63.2MaterialsandSpecimenFabrication....................................................................................73.3PreliminaryFieldPerformance...........................................................................................103.4LaboratoryTests.................................................................................................................123.4.1IndirectTensile(IDT)NflexFactorTest.........................................................................123.4.2Semi-circularBend(SCB)J-integralTest......................................................................14

4.TestResultsandDataAnalysis.................................................................................................154.1IDTNflexFactorTestResults................................................................................................164.1.1EffectofMixReheating...............................................................................................184.1.2EffectofLoadingRate.................................................................................................194.1.3ComparisonofDifferentMixtures...............................................................................23

4.2SCBJ-integralTestResults..................................................................................................254.2.1EffectofMixReheating...............................................................................................274.2.2EffectofLoadingRate.................................................................................................284.2.3ComparisonofDifferentMixtures...............................................................................29

4.3CorrelationofIDTNflexFactorandSCBJ-integralTestResults...........................................315.ConclusionsandRecommendations........................................................................................326.References................................................................................................................................34Appendix......................................................................................................................................35


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LISTOFFIGURES

Figure1.ResearchMethodology...................................................................................................7Figure2.AL1ProjectFieldPerformanceMonitoring...................................................................11Figure3.AL2ProjectFieldPerformanceMonitoring...................................................................11Figure4.TNProjectFieldPerformanceMonitoring....................................................................12Figure5.IDTTestSetupandSpecimenConfiguration.................................................................12Figure6.DeterminationofIDTNflexFactor..................................................................................13Figure7.SCBTestSetupandSpecimenConfiguration................................................................15Figure8.SCBNotchDepthversusStrainEnergyPlot..................................................................15Figure9.ExampleoftheLoad-DisplacementCurvesfromtheIDTTest(ReheatedSpecimens;LoadingRateof50mm/min)........................................................................................................16Figure10.FracturedIDTTestSpecimens.....................................................................................18Figure11.EffectofMixReheatingonIDTNflexFactor.................................................................19Figure12.EffectofLoadingRateonIDTNflexFactor....................................................................20Figure13.EffectofLoadingRateonIDTToughness....................................................................21Figure14.EffectofLoadingRateonIDTPost-PeakSlope...........................................................22Figure15.ComparisonofIDTNflexFactorResultsforAL1Mixes.................................................24Figure16.ComparisonofIDTNflexFactorResultsforAL2Mixes.................................................25Figure17.ComparisonofIDTNflexFactorResultsforTNMixes...................................................25Figure18.ExampleoftheLoad-DisplacementCurvesfromtheSCBTest(ReheatedSpecimens;LoadingRateof0.5mm/min;25.4mmNotchDepth)..................................................................26Figure19.EffectofMixReheatingonSCBJ-integral...................................................................27Figure20.EffectofLoadingRateonSCBJ-integral......................................................................28Figure21.ComparisonofSCBJ-integralTestResultsforAL1Mixes...........................................29Figure22.ComparisonofSCBJ-integralTestResultsforAL2Mixes...........................................31Figure23.ComparisonofSCBJ-integralTestResultsforTNMixes.............................................31Figure24.CorrelationofIDTNflexFactorandSCBJ-integralTestResults....................................32LISTOFTABLES

Table1.MixtureComponentsandVolumetricParametersofAL1Mixes.....................................8Table2.MixtureComponentsandVolumetricParametersofAL2Mixes.....................................9Table3.MixtureComponentsandVolumetricParametersofTNMixes.......................................9Table4.SummaryofAverageAirVoidsResultsofHotProductionandReheatedSpecimens....10Table5.AL1ProjectFieldCrackingInspectionResults................................................................11Table6.SummaryofIDTNflexFactorResults...............................................................................17Table7.IDTToughnessandPost-PeakSlopeRatioResults.........................................................23Table8.StatisticalComparisonofIDTNflexFactorTestResults...................................................24Table9.SummaryofSCBJ-integralResults.................................................................................26Table10.StatisticalComparisonofSCBJ-integralTestResults...................................................30Table11.DetailedStatisticalComparisonofSCBJ-integralTestResultsforAL1Mixes..............35Table12.DetailedStatisticalComparisonofSCBJ-integralTestResultsforAL2Mixes..............35Table13.DetailedStatisticalComparisonofSCBJ-integralTestResultsforTNMixes...............36


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1.INTRODUCTION

Implementation of the Superpavemix designmethod began over 20 years ago. Although itsinitial visionwas to includemixture performance tests for higher risk projects, the cost andcomplexityoftherecommendedperformancetestsweretoomuchforuseinroutinepractice.Therefore, the Superpave mix design method relied upon improved asphalt bindercharacterizationandaggregatecriteriabasedonspecific trafficandclimaterequirementsbutcontinuedtheuseofvolumetricpropertiestodeterminetheoptimumasphaltbindercontent.Overthepasttwodecades,severalrefinementshavebeenmadetotheSuperpavestandards,and individual stateDepartments of Transportation (DOTs) havemade additional changes tothemethod and criteria. Still, someaspects of the Superpavemix designmethod arewidelyquestioned and the resulting designed mixtures in many states are viewed to be lackingdurability. Recently, several highway agencies began to explore the use of mixture crackingtestsandcriteriaforsomemixcategories.

TherearecurrentlyoveradozendifferentasphaltmixturecrackingtestsavailableinAmericanAssociationofStateHighwayandTransportationOfficials (AASHTO)andAmericanSociety forTesting and Materials (ASTM) standards or as draft procedures developed by differentresearchers. Some of these tests are better suited for routine use inmix design and qualityassurancetesting,whileothersarebettersuitedforuseinmodelingpavementresponsesandmayultimatelyprovideameansforpredictingcrackingovertime.However,mostofthesetestsarenotreadyforimplementationintoroutinepracticeduetocomplexity.Therefore,thisstudywas undertaken to explore two relatively simple laboratory tests, indirect tensile (IDT) NflexFactortestandsemi-circularbend(SCB)J-integraltest,forevaluatingthecrackingresistanceofasphaltmixturesformixdesignandqualityassurance.

2.OBJECTIVE

TheobjectiveofthisstudywastoevaluatetheeffectsofmixreheatingandloadingrateontheresultsofIDTNflexFactortestandSCBJ-integraltest.Analysiswasalsoperformedtoassesstheeffects of asphalt mixtures with different components and production parameters on theresultsofthesetwotests.

3.EXPERIMENTALDESIGN

3.1ResearchMethodology

Figure 1 presents the researchmethodology employed in this study. Seven asphaltmixturesfrom three field projects were tested in the IDT Nflex Factor and SCB J-integral tests tocharacterizetheircrackingresistance.Foreachproject,theloosemixwassampledduringplantproduction andwas used to fabricate on-site specimens and off-site specimens. The on-sitespecimens were compacted at the plant without reheating the loosemix, while the off-sitespecimenswerefabricatedbycompactingtheloosemixaftersignificantreheating.Forthesakeofexpeditingimplementationofthesetestsduringmixdesignandqualityassurance,bothon-siteandoff-sitespecimenswerecompactedtoNdesigninsteadoftothetargetairvoidcontents.Testing of existingNdesign specimens fabricated for volumetricmeasurements greatly reducesthesamplepreparationtime,andthereforemakesthecrackingtestseasiertoimplement.Forboth cracking tests, two different loading rates of 0.5 and 50mm/minwere investigated to


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determinewhethertheywouldyielddifferenttestresults.Finally,theIDTNflexFactorandSCBJ-integral resultswereanalyzed todiscriminate thecrackingpotentialof asphaltmixtureswithdifferent combinationsof reclaimedasphaltpavement (RAP), recycledasphalt shingles (RAS),rejuvenators,andwarmmixasphalt(WMA)technologies.

Figure1.ResearchMethodology

3.2MaterialsandSpecimenFabrication

Materials evaluated in this studywereobtained from two fieldprojects inAlabamaandoneprojectinTennessee.ThefirstprojectinAlabama(AL1),locatedonU.S.Highway31inAutaugaCounty,includedthreeasphaltmixtureswithvariousRAPandRAScontents.Allthreemixtureswerepavedasa2-inchoverlayoveranexistingasphaltpavement.Rejuvenatorswereusedintwoof thesemixtures,whichhad25%RAPand5%RAS.Theothermixturehad20%RAP,noRAS,andnorejuvenators;thus,itwasconsideredasthecontrolmix.Thejobmixformula(JMF)for all three mixtures consisted of a 12.5 mm nominal maximum aggregate size (NMAS)SuperpavemixturewithanNdesignof60gyrations.APG67-22virginbinderwasusedinthemixdesignasthebasebinder.ThetworejuvenatorsevaluatedinthisprojectarereferredtoasRA1andRA2.Thedosageoftherejuvenatorswasdeterminedbasedontherecommendationsfromthecontractorandthesuppliers.Table1summarizesthemixturecomponentsandvolumetricparametersofthethreeAL1mixtures.

The second field project in Alabama (AL2), located on U.S. Highway 84 in Coffee County,includedaWMAmixtureandahotmixasphalt(HMA)controlmixture.Bothmixturescontained15%RAPand5%RASandusedaPG67-22virginbinder.TheWMAmixturewasproducedbyaGencorplant foamerusing1.5%foamingwatercontentbyweightof thebinder.TheJMFforbothmixturesconsistedofa12.5mmNMASSuperpavemixturewithanNdesignof60gyrations.Thetotalbindercontentwas5.1%,with3.4%contributedfromthevirginbinderand1.7%fromthe recycled materials. A liquid anti-stripping additive manufactured by ArrMaz CustomChemicals was included in both mixtures at 0.5% by weight of the total binder. The two


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mixtureswereusedasthesurfaceliftofanewconstructionpavementwithatargetthicknessof1.5 inches.Table2summarizesthemixturecomponentsandvolumetricparametersofthetwoAL2mixtures.

ThefieldprojectinTennessee(TN),locatedonRaccoonValleyDrive(SR170)inAndersonandRoane Counties, also included a WMA mixture and a HMA control mixture. Both mixturescontained 10% RAP and 3% RAS and used a PG 64-22 virgin binder. For theWMAmixture,Evotherm3Gwasaddedata rateof0.5%byweightof the totalasphaltbinder.The JMF forbothmixtures consisted of a 12.5mm NMASMarshall mixture with 75 blows. During plantproduction, a correlation was established between Marshall 75 blows and Superpave 25gyrationstoyieldspecimenswithsimilarairvoidscontents,andthus,anNdesignof25gyrationswas selected. For both mixtures, a liquid anti-stripping additive manufactured by ArrMazCustomChemicalswas added at 0.5%byweight of the total binder. The twomixtureswerepavedasa1.5-inchoverlayoveranexistingasphaltpavement.Table3summarizesthemixturecomponentsandvolumetricparametersofthetwoTNmixtures.

Table1.MixtureComponentsandVolumetricParametersofAL1Mixes

MixtureComponentsandVolumetricParameters ControlMix RA1Mix RA2Mix

#78LMS,% 20 25 25#8910LMS,% 10 5 5CoarseSand,% 15 15 15ShotGravel,% 17 17 17

CrushedGravel,% 17 7 7BaghouseFine,% 1 1 1

RAP/RAS,% 20/0 25/5 25/5Rejuvenator,%* - 4.5 8

WMA,%* - 0.3(Evotherm3G) -VirginBinder(PG67-22),% 4.1 2.95 2.95

ACfromRAP,% 1.0 1.25 1.25ACfromRAS,% 0 0.9 0.9TotalAC,% 5.1 5.1 5.1

MixExtractedBinderPG 88-10 94-10 94-10Ndesign 60 60 60

AirVoids,% 4.3 2.0 2.4Gmm 2.470 2.447 2.461

VMA,% 15.9 15.5 15.1D/ARatio 0.91 0.95 0.97

CompactionTemperature,°F 275 240 240Note:*byweightofthetotalbinder


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Table2.MixtureComponentsandVolumetricParametersofAL2Mixes

MixtureComponentsandVolumetricParameters HMAMix WMAMixCRGravel,% 39 39

ShortGravel,% 11 11#78LMS,% 7 7

LMSSCRN’s,% 7 7NaturalSand,% 15 15RAP/RAS,% 15/5 15/5WMA,%* - 1.5%(Foaming)

Anti-Stripping,%* 0.5 0.5VirginBinder(PG67-22),% 3.4 3.4

ACfromRAP,% 0.7 0.7ACfromRAS,% 1.0 1.0TotalAC,% 5.1 5.1

MixExtractedBinderPG 88-10 88-10Ndesign 60 60

AirVoids,% 3.0 2.5Gmm 2.480 2.476

VMA,% 13.3 13.3D/ARatio 1.05 1.16

CompactionTemperature,°F 305 280Note:*byweightofthetotalbinder

Table3.MixtureComponentsandVolumetricParametersofTNMixes

MixtureComponentsandVolumetricParameters HMAMix WMAMixHardLMS,% 42 42CoarseSlag,% 20 20SoftLMS#10,% 20 20NaturalSand,% 25 25RAP/RAS,% 10/3 10/3WMA,%* - 0.5(Evotherm3G)

Anti-Stripping,%* 0.5 0.5VirginAC(PG64-22),% 4.4 4.4

ACfromRAP,% 0.65 0.65ACfromRAS,% 0.65 0.65TotalAC,% 5.7 5.7

MixExtractedBinderPG 82-10 76-16Ndesign 25 25

AirVoids,% 6.2 5.3Gmm 2.596 2.570

VMA,% 16.1 16.7D/ARatio 1.26 1.03

CompactionTemperature,°F 290 240Note:*byweightofthetotalbinder


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For all three projects, during production loosemix samples were taken from the end-dumptrucks before leaving the plant. For each of the mixtures sampled, a set of specimens wascompacted on-site in the National Center for Asphalt Technology (NCAT) mobile laboratorywithout significant reheating. The loose mix was placed in an oven for approximately 30minutes to account for the temperature loss that occurred between sampling and splitting.Oncethedesiredcompactiontemperaturewasachievedandstabilized,themixwascompactedtoNdesignintheSuperpavegyratorycompactor(SGC).Allspecimenscompactedon-sitewithoutreheatingintheNCATmobilelaboratoryarehereinreferredtoashotproductionspecimens.

IntheNCATmainlaboratory,off-sitespecimenswerefabricatedusingthereheatedloosemixsampled from the plant, referred to as reheated specimens in this study. For the reheatingprocess, the bucket with loose mix was first placed in an oven at the desired compactiontemperature for approximately two hours. The loose mix was then batched into individualsamplesizesusingthequarteringmethoddescribedinAASHTOR76-16andwasplacedbackinthe oven for further reheating. A dial thermometer was used to continuously monitor thetemperatureofthemix.Oncethedesiredcompactiontemperaturewasachieved,theloosemixwascompactedintheSGCtoNdesign.Thetotalreheatingprocesstookapproximatelyfourhours.Table 4 summarizes the air voids results of both hot production and reheated specimens. Inmostcases,thedifferenceintheaverageairvoidsbetweenthetwosetsofspecimenswasnogreaterthan0.5%,whichwasconsideredpracticallyinsignificant.

Table4.SummaryofAverageAirVoidsResultsofHotProductionandReheatedSpecimens

MixTypeIDTSpecimens(AV%) SCBSpecimens(AV%)

HotProduction Reheated HotProduction ReheatedAL1ControlMix2 4.5 4.1 5.0 4.6

AL1RA1Mix 2.6 3.6 2.7 3.1AL1RA2Mix 2.1 2.6 2.7 4.2AL2HMA 2.6 2.2 3.1 3.2AL2WMA 2.3 2.1 2.6 2.9TNHMA 5.9 5.4 6.1 6.0TNWMA 5.2 4.7 5.5 5.3

3.3PreliminaryFieldPerformance

A field performance evaluation was conducted for the AL1 project in August 2016,approximately two years after construction. Pavement cracking was inspected and rated inaccordancewith theAlabamaDepartment of Transportation (ALDOT) ConditionAssessmentsDataCollectionManual(ALDOT2015).Table5summarizesthefieldcrackinginspectionresultsof the three test sections. In general, the control mixture showed the best crackingperformance,followedbytheRA1mixtureandthentheRA2mixture,respectively.Only37feetof low-severity longitudinal crackingwasobserved for thecontrolmixture,buta significantlygreater amountof alligator and longitudinal crackswasobserved for theother twomixturescontainingRAS and rejuvenators. Considering that the conditionof theunderlyingpavementbefore resurfacing was similar for the three sections, the difference in their crackingperformancewasprimarilyduetothecrackingpotentialoftheoverlaymixtures.


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Table5.AL1ProjectFieldCrackingInspectionResults

TestSections

AlligatorCracking(ft2) LongitudinalCracking(ft.) TransverseCracking(crackcount)

Level1 Level2 Hairto1/8” 1/8”to1/4" Hairto1/8” 1/8”to1/4"Control 0 0 37 0 0 0RA1 985 10 12 0 2 0RA2 560 0 723 16 9 1

(a)ControlSection (b)RA1Section (c)RA2Section

Figure2.AL1ProjectFieldPerformanceMonitoring

FortheAL2project,fieldperformancemonitoringwasconductedonNovember19,2015andNovember16,2016afterapproximately17and29monthsoftraffichadbeenappliedtothepavementsections,respectively.AsshowninFigure3,bothsectionshaveperformedwellinthefirstcoupleofyearswithoutanycrackingobservedduringeitherinspection.

(a)HMASection (b)WMASection

Figure3.AL2ProjectFieldPerformanceMonitoring

FieldperformanceoftheTNprojectwasevaluatedonNovember11,2015andNovember11,2016afterapproximately13and25monthsoftraffic,respectively.Nocrackingwasobservedforeithertestsectionduringthefirstinspection.Atthetimeofthe25-monthinspection,onelow-severity transverse crack was observed in the WMA section; however, it was notdetermined whether the crack was a thermal crack or a reflective crack. Figure 4 showsphotographsoftheTNproject.Ingeneral,bothsectionshaveperformedwellthroughthefirst


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twoyears;nodifferenceincrackingperformancewasobservedfortheHMAversustheWMAsections.

(a)HMASection (b)WMASection

Figure4.TNProjectFieldPerformanceMonitoring

3.4LaboratoryTests

3.4.1IndirectTensile(IDT)NflexFactorTestThe IDT test was originally developed in Japan (Akazawa 1953) and Brazil (Carniero andBarcellos1953)fordeterminingthestrengthofconcrete.TheIDTloadingarrangementisnowwell known in the asphalt pavement industry for use in evaluating moisture damagesusceptibilityofasphaltmixturesperAASHTOT283.Severalotherstandardtestsusethesameloading arrangement with variations in loading rates, test temperatures, and specimendimensions.Forthisstudy,loadingratesof0.5and50mm/minwereappliedbyasimpleloadframethatdigitallycaptured loadandverticaldeformationdataduringthetest.Thetestwasperformed at 25°C using approximately 50mm thick specimens thatwere cut from150-mmdiameterSGCsamples.Figure5presentstheIDTtestsetupandspecimenconfiguration.

Figure5.IDTTestSetupandSpecimenConfiguration


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For data analysis, a new parameter termed Nflex Factor was used to evaluate the crackingresistanceofdifferentasphaltmixtures(Westetal.2017).ThedeterminationofNflexFactorwasinspired by a similarmethod used in the flexibility index test developed at theUniversity ofIllinois (Al-Qadietal.2015).Asexpressed inEquations1 to4andschematically illustrated inFigure6,NflexFactorwascalculatedasthespecimentoughnessdividedbytheslopeofthepostpeak stress-strain curve at the inflection point. For data analysis, a sixth-degree polynomialfunctionwas used to fit the stress-estimated strain data, and the critical point on the curvewhere thesecondderivativeof thepolynomial functionequaledzerowasdeterminedas theinflectionpoint.Sincenostraingaugewasusedduringthetest,theIDTstrainofthespecimenwasestimatedbymultiplying theverticaldeformationbyanassumedPoisson’s ratioof0.35anddividingbythespecimendiameter.AhighNflexFactorvalueisconsideredtoindicatebettercrackingresistance.

Figure6.DeterminationofIDTNflexFactor

tDP

ps 2000= (1)

whereσ= IDTstress(kPa);P= verticalload(N);t = specimenthickness(mm);andD= specimendiameter(mm).

neDD

= (2)


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whereε= estimatedIDTstrain(%);ν= Poisson’sratio,assumedtobe0.35at25°C;andD= verticaldeformation(mm).

ò=nfi

dTe

es0

inf )( (3)

whereTinf= toughnessuptotheinflectionpointonthepostpeakstress-straincurve(kPa).

sT

FactorN flexinf= (4)

where|s|= slopeofthepostpeakstress-straincurveattheinflectionpoint(kPa).

3.4.2Semi-circularBend(SCB)J-integralTestTheSCBtestwasoriginallydevelopedtocharacterizethefracturemechanismsofrocks(Chongand Kuruppu 1988) and has recently been used to characterize the fracture and fatiguepropertiesofasphaltmixtures(LiandMarasteanu2004;ArabaniandFerdowsi2009;Huangetal.2009;Kimetal.2012).TheSCBtestwasconductedinaccordancewithASTMD8044-16inmost regards. This method has been championed by the Louisiana Transportation ResearchCenter. The test utilized notched half-moon shaped specimens cut from SGC cylinders withthreenotchdepthsof25.4,31.8,and38.1mm.Figure7showsSCBtestsetupandspecimenconfiguration.Duringthetest,aSCBspecimenissupportedbytwobarsonaflatsurfaceandamonotonicloadisappliedtothecurvedsurfaceabovethenotch.TheASTMstandardspecifiesaverticaldisplacementrateof0.5mm/min.Forthisstudy,testswereconductedwithtworatesof0.5and50mm/min.Fordataanalysis,strainenergytofailurewasfirstcalculatedforeachnotchdepthastheareaundertheloadversusdisplacementdata,andalinearregressionwasdetermined based on the strain energy versus notch depth results (Figure 8). Finally, thecrackingparameterJ-integral(Jc)wascalculatedbydividingtheslopeoftheregressionlinebythespecimenthickness,asexpressedinEquation5.AsphaltmixtureswithhigherJcvaluesareexpectedtohavebetterresistancetointermediatetemperaturecrackingthanthosewithlowerJcvalues. It shouldbenotedthat there isanotherSCBtestavailable termed IllinoisFlexibilityIndex (I-FIT) test that takes into consideration both the fracture energy and post-peak load-displacement behavior of the mixture under loading. Although the I-FIT test had also beenfoundpromising for evaluating the cracking resistanceof asphaltmixtures duringmixdesignandqualityassurance(Al-Qadietal,2015),itwasnotincludedintheexperimentaltestplanofthisstudy.

dadU

bJc

1-= (5)


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whereb= specimenthickness(m);a= notchdepth(m);andU= strainenergytofailure(kJ).

Figure7.SCBTestSetupandSpecimenConfiguration

Figure8.SCBNotchDepthversusStrainEnergyPlot

4.TESTRESULTSANDDATAANALYSIS

ThissectionpresentstheIDTNflexFactorandSCBJ-integralresultsobtainedinthisstudy.DataanalysiswasperformedtoidentifytheeffectsofmixreheatingandloadingrateontheIDTandSCB test results. In addition, the cracking resistance of asphalt mixtures with variouscombinationsofRAP,RAS,rejuvenator,andWMAtechnologieswascompared.


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4.1IDTNflexFactorTestResults

Figure 9 presents an example of the load-displacement curves obtained from the IDT NflexFactor test using a loading rate of 50 mm/min. As illustrated, the mixtures with differentcomponents showed significantly different behaviors during the test. In general, the two TNmixtureshad lowerpeak loadsandhigherdisplacementsascomparedto theothermixtures,indicatingamoreductilebehavior.AscomparedtotheAL1controlmixture,thetwomixtureswithrejuvenatorsshowedhigherpeakloads,whichwaslikelyduetotheinclusionofahighercontentofrecycledmaterials,especiallytheRASwithheavilyagedandverystiffasphaltbinder.

Table6summarizestheIDTNflexFactortestresults;areasonablygoodrepeatabilityisobservedwithanaveragecoefficientof variation (COV)ofapproximately13%. It shouldbenoted thatnotenoughhotproductionspecimenswereavailablefromtheAL2projecttoconducttheIDTNflexFactortest.

Figure9.ExampleoftheLoad-DisplacementCurvesfromtheIDTTest(ReheatedSpecimens;

LoadingRateof50mm/min)

Duringthe IDTtest, itwasobservedthatcrackinggenerallydevelopedfromtwo locations:1)neartheloadingstripsand2)nearthecenterofthespecimen,asshowninFigure10.Failureinitiatingfromthecenterofthespecimenisthedesiredlocation,asthisiswherethemaximumindirecttensilestressoccursbasedonprinciplesofmechanics,whereascrackinginitiatingneartheloadingstripsisprimarilyduetolocalizedshearstress(HudsonandKennedy1968).Duetothelimitedtestresults,thetwofailuremodesobservedintheIDTtestwerenotinvestigatedinthisstudybutneedtobeaddressedbyfutureresearch.


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Table6.SummaryofIDTNflexFactorResults

SpecimenType LoadingRate MixIDNflexFactor(4replicates)

Average Stdev COV

HotProductionSpecimens

0.5mm/min

AL1Control 0.573 0.044 8%AL1RA1 0.483 0.040 8%AL1RA2 0.432 0.082 19%AL2HMA n/aAL2WMA n/aTNHMA 0.941 0.088 9%TNWMA 1.300 0.108 8%

50mm/min

AL1Control 0.545 0.065 12%AL1RA1 0.513 0.076 15%AL1RA2 0.517 0.044 9%AL2HMA n/aAL2WMA n/aTNHMA 1.037 0.103 10%TNWMA 1.386 0.202 15%

ReheatedSpecimens

0.5mm/min

AL1Control 0.556 0.049 9%AL1RA1 0.257 0.069 27%AL1RA2 0.112 0.015 13%AL2HMA 0.181 0.016 9%AL2WMA 0.312 0.043 14%TNHMA 0.765 0.055 7%TNWMA 1.493 0.016 1%

50mm/min

AL1Control 0.453 0.055 12%AL1RA1 0.389 0.099 25%AL1RA2 0.220 0.048 22%AL2HMA 0.168 0.039 23%AL2WMA 0.237 0.023 10%TNHMA 0.841 0.121 14%TNWMA 1.112 0.097 9%


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(a)AL1Mixes

(b)AL2Mixes

(c)TNMixes

Figure10.FracturedIDTTestSpecimens

4.1.1EffectofMixReheatingFigure11presentsthecomparisonoftheNflexFactorresultsforreheatedversushotproductionspecimens of AL1 and TN mixtures. The test was not performed on the hot-productionspecimensforAL2mixturesduetolackofavailablematerial.AsshowninFigure11,formostofthemixtures, the reheatedspecimensexhibited lowerNflex Factorvaluesas compared to thehotproductionspecimens, indicatingreducedcrackingresistance.TheonlyexceptionwastheTNWMAmixture,whichshowedahigherNflexFactorvaluewithaloadingrateof0.5mm/minafter mix reheating. As compared to the AL1 control mixture, the two mixtures withrejuvenators(especiallytheRA2mixture)showedmoresubstantialreductionsinNflexFactorforreheatedversushotproductionspecimens.Toconsiderthetestvariabilityindiscriminatingtheproperties of reheated versus hot production specimens, the analysis of variance (ANOVA)generalizedlinearmodel(GLM)wasusedtoanalyzetheNflexFactorandthecorrespondingCOVresults.TheANOVAtestwasselectedoverthetwo-samplet-testbecauseitwasabletoaccountfor the two-way interactionbetween the two factors of ‘SpecimenType’ and ‘LoadingRate’.ANOVAGLManalysisshowedthatthefactorof‘SpecimenType’hadap-valueof0.026forthe


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Nflex Factor results and a p-value of 0.329 for the corresponding COV results. These resultsindicatedthatmixreheatinghadastatisticallysignificanteffectonthe IDTNflexFactorresultsbuthadnoeffectonthevariabilityoftestresults.

(a)LoadingRateof0.5mm/min

(b)LoadingRateof50mm/min

Figure11.EffectofMixReheatingonIDTNflexFactor

4.1.2EffectofLoadingRateFigure12presentsthecomparisonofIDTNflexFactorresultsfortwodifferentloadingratesof0.5and50mm/min.Overall,noconsistenttrendwasobserved;somemixturesshowedhigherNflexFactorvaluesatahigher loadingratewhileothersshowedtheoppositetrend.However,thedifferencesmightnotbesignificantconsideringthetestvariabilityasdenotedbytheerrorwhiskers.Figure13andFigure14presentthe IDTtoughnessandpost-peaksloperesultsthatwereusedtodeterminetheNflexFactor.Asillustrated,allmixturesexhibitedsignificantlyhighertoughnessandpost-peakslopeswhentestedwiththehigherloadingrateof50mm/minthantheslowerrateof0.5mm/min.Furtherinvestigationsindicatedthattheeffectofloadingrate


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onIDTtoughnesswasproportionaltothatofpost-peakslopes.AsshowninTable7,theratiosofbothIDTparametersat50mm/minoverthoseat0.5mm/minwereintherangeof2.0to3.0formostofthemixtures.SinceIDTNflexFactorwasdeterminedasspecimentoughnessdividedbythepost-peakslope(Equation4),theeffectofloadingrateonNflexFactorwascancelledout.The samestatisticalanalysismethod introducedpreviouslywasused to identify theeffectofloadingrateontheIDTNflexFactorresultsaswellasthetestvariability.TheresultsconfirmedthattheeffectofloadingrateonIDTNflexFactorwasnotstatisticallysignificant,asindicatedbyap-valueof0.476fortheNflexFactorresultsandap-valueof0.249forthecorrespondingCOV.Consideringthatashortertestingtimeisdesiredduringmixdesignandqualityassurance,thefaster loading rateof50mm/min is recommended for implementation in the IDTNflexFactortesttoassessthecrackingperformanceofasphaltmixtures.

(a)HotProductionSpecimens

(b)ReheatedSpecimens

Figure12.EffectofLoadingRateonIDTNflexFactor


21



Figure13.EffectofLoadingRateonIDTToughness


22



Figure14.EffectofLoadingRateonIDTPost-PeakSlope


23

Table7.IDTToughnessandPost-PeakSlopeRatioResults

SpecimenType MixID ToughnessRatio(50mm/min/0.5mm/min)

Post-PeakSlopeRatio(50mm/min/0.5mm/min)


AL1Control 2.19 2.30AL1RA1 2.46 2.35AL1RA2 2.55 2.10AL2HMA

n/aAL2WMATNHMA 2.65 2.43TNWMA 2.73 2.59

ReheatedSpecimens

AL1Control 2.14 2.65AL1RA1 2.44 1.62AL1RA2 2.31 1.17AL2HMA 2.58 2.55AL2WMA 2.95 3.88TNHMA 2.75 2.54TNWMA 2.40 3.24

4.1.3ComparisonofDifferentMixturesFigure 15 presents the comparison of IDT Nflex Factor results for the AL1mixtures. The hotproductionspecimensofallthreemixturesshowedsimilarNflexFactorvaluesregardlessoftheloadingrate.ConsideringthatthetworejuvenatedmixtureshadahigherRAPcontentplusRASthan the control mixture, the rejuvenators seemed effective in restoring the properties ofrecycled materials. However, after mix reheating, the Nflex Factor of both the RA1 and RA2mixturesdecreasedsubstantially.TheseresultsareconsistentwithfindingsbyYinetal.(2017),which showed that the effectiveness of rejuvenators on the properties of recycledmaterialsreducedwithaging.Inaddition,theANOVAresultsinTable8indicatedthat,forthereheatedspecimens,thecontrolmixturehadthehighestIDTNflexFactorvalueandthus,thebestcrackingresistance, followed by the RA1mixture and RA2mixture, respectively. These results are inagreement with the ranking of these mixtures based on their two-year pavement crackingperformance(Table5).


24

Figure15.ComparisonofIDTNflexFactorResultsforAL1Mixes

Table8.StatisticalComparisonofIDTNflexFactorTestResultsFieldProject MixtureType HotProductionSpecimen ReheatedSpecimen

AL1*Control A ARA1 A BRA2 A C

AL2#HMA

N/A WMA>HMAWMA

TN#HMA

WMA>HMA WMA>HMAWMA

Notes *comparisonsmadebasedonANOVAandTukey’sHSDtest#comparisonsmadebasedontwo-samplet-test

Figure16presents thecomparisonof IDTNflex Factor results for theAL2mixtures.TheWMAmixturehadhigherNflexFactorvaluesthantheHMAmixtureforbothloadingratesevaluatedinthis study. The better cracking resistance of the WMA mixture was likely due to greaterflexibility resulting from the lower temperature (280°F versus305°F) duringplantproductionandlaboratoryreheatingprocess.Thetwo-samplet-testresultsinTable8alsoconfirmedthattheWMAmixturehadsignificantlybettercrackingresistancethantheHMAmixtureintheIDTNflexFactortest.AsimilartrendwasalsoobservedfortheIDTNflexFactorresultsofTNmixtures(Figure17),wheretheWMAmixturehadstatisticallyhigherNflexFactorvaluesthantheHMAmixtureforbothhotproductionandreheatedspecimens.


25

Figure16.ComparisonofIDTNflexFactorResultsforAL2Mixes

Figure17.ComparisonofIDTNflexFactorResultsforTNMixes

4.2SCBJ-integralTestResults

Figure 18 presents an example of the load-displacement curves obtained from the SCB J-integral testwitha loadingrateof0.5mm/min. Ingeneral, the trendsobserved fordifferentasphaltmixtureswereconsistentwith thoseshown in the IDTNflex Factor test (Figure9).Forexample,theTNmixturesshowedamoreductilebehaviorascomparedtoothermixtures,asindicated by lower peak loads, less steep post-peak load-displacement curves, and higherdisplacements.Inaddition,thetwoAL1mixtureswithrejuvenatorsandahigherRAPandRAScontent weremore brittle than the corresponding controlmixturewithout rejuvenator. TheSCBJ-integralresultsaresummarizedinTable9.


26

Figure18.ExampleoftheLoad-DisplacementCurvesfromtheSCBTest(ReheatedSpecimens;

LoadingRateof0.5mm/min;25.4mmNotchDepth)

Table9.SummaryofSCBJ-integralResults

SpecimenType LoadingRate MixID dU/da J-integral(KJ/mm2)


0.5mm/min

AL1Control -0.044 0.771AL1RA1 -0.031 0.544AL1RA2 -0.031 0.556AL2HMA -0.031 0.554AL2WMA -0.049 0.881TNHMA -0.030 0.538TNWMA -0.025 0.451

50mm/min


ReheatedSpecimens

0.5mm/min


50mm/min



27

4.2.1EffectofMixReheatingFigure19presentsthecomparisonofSCBJ-integralresultsforreheatedversushotproductionspecimens.AsillustratedinFigure19(a),whenthetestwasconductedwithaloadingrateof0.5mm/min,thereheatedandhotproductionspecimensshowedsimilarJ-integralvaluesinmostcases.However,thereweresubstantialdifferencesinJ-integralresultsforreheatedversushotproduction specimenswhen the testwasperformedat ahigher loading rateof 50mm/min.Considering the SCB test provides a single J-integral value (no replication of the result),evaluationofthetestvariabilitywasnotavailable.TheANOVAGLManalysisshowedthatthep-value for the factor ‘SpecimenType’washigher than the specified significance level of 0.05,indicatinganinsignificanteffectfrommixreheatingontheSCBJ-integralresults.



Figure19.EffectofMixReheatingonSCBJ-integral


28

4.2.2EffectofLoadingRateFigure20presentsthecomparisonofSCBJ-integralresultsforthetwodifferentloadingratesof0.5and50mm/min.Inmostcases,thehigherloadingrateresultedinahigherJ-integral.ThetrendwasconfirmedbytheANOVAGLSanalysisresults;thefactorof ‘LoadingRate’hadap-valueof0.001,whichwaswellbelowthesignificancelevelof0.05.Therefore,loadingratehada significanteffecton theSCB test results; specifically,mixtures testedwithahigher loadingrateof50mm/minshowedhigherJ-integralvaluesthanthosetestedwithalowerrateof0.5mm/min.



Figure20.EffectofLoadingRateonSCBJ-integral


29

4.2.3ComparisonofDifferentMixturesFigure21presentsthecomparisonofSCBJ-integralresultsfortheAL1mixtures.Whentestedataloadingrateof0.5mm/min,thethreemixturesexhibitedsimilarJ-integralvaluesforbothhotproductionand reheated specimens.However,noconsistent trendwasobserved for thehigherloadingrateof50mm/min.Forthehotproductionspecimens,theRA1mixturehadthehighest J-integral value followed by the RA2 mixture and then the control mixture; for thereheated specimens, the controlmixturehadahigher J-integral value than the twomixtureswithrejuvenators.

Figure21.ComparisonofSCBJ-integralTestResultsforAL1Mixes

Aspreviouslydiscussed,sinceonlyoneSCBJ-integralvaluewasdeterminedforeachmixture,statisticalanalysis forcomparing the test resultswasnotavailable.Toovercomethis issue,apractical comparison method developed by Moore (2016) was used to discriminate the J-integralresultsofdifferentmixtures.Forthismethod,thebuilt-inregressionfunctioninExcelwasfirstusedtocalculatethemeandU/daslopebasedonthestrainenergyversusnotchdepthresults and the sum of squared residuals (SSResid) of the regression model. The standarddeviationofthemeandU/daslopewasthencalculatedbyfollowingEquations6through8.

2Re22-

=»nSSS sid

ees (6)

whereσe= standarddeviationofregressionmodelpopulationtotalerror;Se = estimatedstandarddeviationofregressionmodeltotalerror;

SSResid= sumofsquaredresiduals;andn= samplesize.


30

( )å å-=

n

xxS iixx

22 (7)

whereSxx= sumofsquareddifferencesbetweennotchdepths;andxi = ithvalueofnotchdepth.

xx

es

SS

S = (8)

whereSs = estimatedstandarddeviationofthedU/daslopeoftheregressionmodel.

Finally,the95%confidenceintervalsofthedU/daslopeforeachmixturetypeweredeterminedusing Equation 9 andwere used to statistically compare the cracking resistance of differentmixtures.

sStSlopeCI *±= (9)

whereCI = 95%confidenceintervalofthedU/daslopeoftheregressionmodel.

If the confidence intervals of twomixtures did not overlap, the resultswould be consideredstatisticallydifferent. It shouldbenoted that the statistical comparisondescribedhereinwasonlyperformedonthesignificantfactorof‘LoadingRate’asidentifiedintheprevioussection.Table10summarizesthestatisticalcomparisonresults;moredetailedoutputsarepresentedintheAppendixinTables10-12.Asshown,nostatisticallysignificantdifferencewasobservedfortheSCB J-integral test resultsamong the threemixtures forboth loading ratesof0.5and50mm/min.

Table10.StatisticalComparisonofSCBJ-integralTestResults

FieldProject MixtureType LoadingRate0.5mm/min

LoadingRate50mm/min

AL1Control

Control=RA1=RA2 Control=RA1=RA2RA1RA2

AL2HMA

WMA=HMA WMA=HMAWMA

TNHMA

WMA=HMA WMA=HMAWMA

Figure 22 presents the comparison of SCB J-integral results for the AL2mixtures. TheWMAmixturehadhigherorsimilarSCBJ-integralvaluesthantheHMAmixture,indicatingbetterorequivalent cracking resistance. However, the difference was found to be statistically


31

insignificant,asshowninTable10.AsimilartrendwasobservedfortheSCBJ-integralresultsofTNmixturesinFigure23.

Figure22.ComparisonofSCBJ-integralTestResultsforAL2Mixes

Figure23.ComparisonofSCBJ-integralTestResultsforTNMixes

4.3CorrelationofIDTNflexFactorandSCBJ-integralTestResults

Figure24presentsthecorrelationofIDTandSCBtestresultsforallmixturesevaluatedinthisstudy.Eachofthedatapointsrepresentsonemixturewithaspecificcombinationofspecimentype(i.e.,hotproductionandreheatedspecimens)andloadingrate(i.e.,0.5and50mm/min);thex-axiscoordinatereferstotheIDTNflexFactorvalue,andthey-axiscoordinaterepresentsthe corresponding SCB J-integral value. The dashed line is the best fitting linear regressionrelationship determined based on the least squares method. In general, no correlation wasobservedbetweentheIDTandSCBtestresults(i.e.,R2valuesof0.0503and0.0669).


32



Figure24.CorrelationofIDTNflexFactorandSCBJ-integralTestResults

5.CONCLUSIONSANDRECOMMENDATIONS

ThisstudyevaluatedtheIDTNflexFactorandSCBJ-integralaspotentialparametersforassessingthe cracking potential of asphalt mixtures for mix design and quality assurance. Theexperimentalplanwasdesignedtoinvestigatetheeffectsofmixreheatingandloadingrateonthe results of these two tests. In addition, test results were analyzed to discriminate thecrackingresistanceofasphaltmixtureswithdifferentcombinationsofRAP,RAS,rejuvenators,andWMAtechnologies.Basedon the results fromthis study, the followingconclusionswereobtained:

• Mix reheating showed a significant effect on the IDT Nflex Factor results; reheatedspecimensexhibited lowerNflex Factor values compared tohotproduction specimens.This suggests that the IDTNflex Factor is sensitive to changes inmixture stiffness andembrittlementresultingfromthereheatingprocess.


33

• TheeffectofloadingrateontheIDTNflexFactorresultswasnotstatisticallysignificant.Thefasterrateof50mm/minisrecommendedforuseduetotheshortertestingtimeandthebroadavailabilityofsimpleloadframestoapplythisrate.

• MixreheatingdidnotshowaneffectontheSCBJ-integralresultsfortestsconductedatthe standard loading rate of 0.5 mm/min. However, results of reheated versus hotproductionmixturesweredifferent for the loading rateof50mm/min,but therewasnot a consistent trend. Some reheated specimens had higher J-integral results thancompanionhotproductionspecimens;othermixtureshadlowerJ-integralresultsafterreheating.

• LoadingrateshowedasignificanteffectontheSCBJ-integralresults;inmostcases,thehigherloadingrateresultedinahigherJ-integralvalue.

• The two rejuvenators used in the AL1 project seemed effective in restoring thepropertiesofrecycledmaterials,buttheireffectivenesswassubstantiallyreducedwithmix reheating (aging).The IDTNflex Factor resultsof reheatedspecimensmatched thetwo-yearpavementcrackingperformance.

• WMAmixturesfromAL2andTNprojectsexhibitedbettercrackingresistancethanthecorresponding HMAmixtures in both IDTNflex Factor and SCB J-integral tests, but nodifferenceinthepavementcrackingperformancehasbeenobserved.

• NorelationshipwasfoundbetweentheIDTNflexFactorandSCBJ-integralresults.

Further research is needed tomonitor the field cracking performance of the projects over alongerperiodoftime.Inaddition,thetwomodesoffailureobservedfortheIDTtestshouldbefurther explored. Finally, ruggedness and inter-laboratory evaluations are recommended forbothcrackingtestspriortobeingconsideredforimplementationintoroutinepractice.


34

6.REFERENCES

Akazawa,T.TensionTestMethodforConcrete.BulletinNo.16,InternationalAssociationofTestingandResearchLaboratoriesforMaterialsandStructures,1953,pp.11-23.

ConditionAssessmentsDataCollectionManual.AlabamaDepartmentofTransportation,2015.Al-Qadi,I.,H.Ozer,J.Lambros,A.ElKhatib,P.Singhvi,T.Khan,J.RiveraPérez,andB.Doll.

TestingProtocolstoEnsurePerformanceofHighAsphaltBinderReplacementMixesusingRAPandRAS.IllinoisCenterforTransportationSeriesNo.15-017,IllinoisCenterforTransportation,UniversityofIllinoisatUrbana-Champaign,2015.

Arabani,M.,andB.Ferdowsi.EvaluatingtheSemi-CircularBendingTestforHMAMixtures.InternationalJournalofEngineering,TransactionsA:Basics,Vol.22,No.1.2009,pp.47-58.

Carniero,F.L.,andA.Barcellos.ConcreteTensileStrength.BulletinNo.13,InternationalAssociationofTestingandResearchLaboratoriesforMaterialsandStructures,1953,pp.97-127.

Chong,K.P.,andM.D.Kuruppu.NewSpecimensforMixedModeFractureInvestigationsofGeomaterials.EngineeringFractureMechanics,Vol.30,No.5,1988,pp.701-712.

Huang,L.,K.Cao,andM.Zeng.EvaluationofSemicircularBendingTestforDeterminingTensileStrengthandStiffnessModulusofAsphaltMixtures.ASTM:JournalofTestingandEvaluation,Vol.37,No.2,2009,pp.1-7.

Hudson,W.R.,andT.W.Kennedy.AnIndirectTensileTestforStabilizedMaterials.ResearchReportNumber98-1,CenterforHighwayResearch,TheUniversityofTexasatAustin,1968.

Kim,M.,L.N.Mohammad,andM.A.Elsefi.CharacterizationofFracturePropertiesofAsphaltMixturesasMeasuredbySemicircularBendTestandIndirectTensionTest.TransportationResearchRecord:JournaloftheTransportationResearchBoard,No.2296,TransportationResearchBoardoftheNationalAcademies,Washington,D.C.,2012,pp.115-124.

Li,X.,andM.Marasteanu.EvaluationoftheLowTemperatureFractureResistanceofAsphaltMixturesUsingtheSemiCircularBendTest.JournaloftheAssociationofAsphaltPavingTechnologists,Vol.73,2004,pp.401-426.

Moore,N.D.EvaluationofLaboratoryCrackingTestsRelatedtoTop-DownCrackinginAsphaltPavements.MSThesis.AuburnUniversity,Auburn,Ala.,2016.

West,R.RelationshipsbetweenSimpleAsphaltMixtureCrackingTestsUsingNdesignSpecimensandFatigueCrackingatFHWA’sAcceleratedLoadingFacility.SubmittedforpublicationatJournaloftheAssociationofAsphaltPavingTechnologists,2017.

Yin,F.,F.Kaseer,E.Arámbula-Mercado,andA.EppsMartin.CharacterizingtheLong-TermRejuvenatingEffectivenessofRecyclingAgentsonAsphaltBlendsandMixtureswithHighRAPandRASContents.RoadMaterialsandPavementDesign,2017,pp.1-20.


35

APPENDIX

Table11.DetailedStatisticalComparisonofSCBJ-integralTestResultsforAL1Mixes

Loading

RateMixID

dU/da

SlopeIntercept

Jc

(KJ/mm2)

Absolute

valueof

estimateof

slopeβ(b)

Estimateof

total

model

variance

σ2(se2)

Estimateof

total

model

deviationσ

(se)

Estimateof

deviation

inslope

only(ss)

df

95%

confidence

intervalof

slope

(lower)

95%

confidence

intervalof

slope

(upper)

0.5

Control -0.039 1.826 0.678 0.039 0.007 0.081 0.004 16 0.031 0.047

RA1 -0.031 1.503 0.541 0.031 0.004 0.064 0.003 16 0.024 0.037

RA2 -0.030 1.475 0.532 0.030 0.004 0.062 0.003 16 0.024 0.036

50

Control -0.048 2.475 0.829 0.048 0.103 0.320 0.015 16 0.017 0.079

RA1 -0.070 2.959 1.222 0.070 0.147 0.383 0.018 16 0.032 0.107

RA2 -0.045 2.077 0.785 0.045 0.139 0.372 0.017 16 0.009 0.081

Table12.DetailedStatisticalComparisonofSCBJ-integralTestResultsforAL2Mixes

Loading

RateMixID

dU/da

SlopeIntercept

Jc

(KJ/mm2)

Absolute

valueof

estimateof

slopeβ(b)

Estimateof

total

model

variance

σ2(se2)

Estimateof

total

model

deviationσ

(se)

Estimateof

deviation

inslope

only(ss)

df

95%

confidence

intervalof

slope

(lower)

95%

confidence

intervalof

slope

(upper)

0.5HMA -0.035 1.630 0.618 0.035 0.003 0.059 0.003 16 0.029 0.040

WMA -0.044 2.001 0.794 0.044 0.006 0.079 0.004 16 0.037 0.052

50HMA -0.080 3.790 1.418 0.080 0.054 0.232 0.011 16 0.057 0.102

WMA -0.093 4.414 1.663 0.093 0.053 0.230 0.011 16 0.070 0.115


36

Table13.DetailedStatisticalComparisonofSCBJ-integralTestResultsforTNMixes

Loading

RateMixID

dU/da

SlopeIntercept

Jc

(KJ/mm2)

Absolute

valueof

estimateof

slopeβ(b)

Estimateof

total

model

variance

σ2(se2)

Estimateof

total

model

deviationσ

(se)

Estimateof

deviation

inslope

only(ss)

df

95%

confidence

intervalof

slope

(lower)

95%

confidence

intervalof

slope

(upper)

0.5HMA -0.032 1.749 0.568 0.032 0.011 0.106 0.005 16.000 0.022 0.042

WMA -0.037 1.967 0.666 0.037 0.044 0.210 0.010 16.000 0.017 0.058

50HMA -0.057 2.977 1.000 0.057 0.104 0.322 0.015 16.000 0.025 0.088

WMA -0.104 4.689 1.824 0.104 0.173 0.417 0.020 12.000 0.060 0.147

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