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Estimating the Strength of Concrete Using Surface 省略Parameters of Concrete Material
EstimatingtheStrengthofConcreteUsingSurfaceReboundValueandDesignParametersofConcreteMaterialJenCheiLiu,MouLinSueandChangHuanKouDepartmentofCivilEngineeringandEngineeringInformatics,ChungHuaUniversity,HsinChu,Taiwan300,R.O.C.AbstractThisstudyestimatesthestrengthofconcrete,anattemptisalsomadetoincreasetheaccuracyofCalculatingthestrength,usingthenondestructivetestNDTsurfacehardnessreboundvalue,materialdesignparametersandregressionanalysis.Thestrengthoftheconcretespecimenswas130c45480kgf/cm2,andtheirageswere7c4538days.Intotal,166standardspecimensofconcreteweregroupedinto146trainingexamplesand20testexamplestoestimateconcretecompressivestrength.Regressionanalysiswasperformedtoestablishamathematicalformula.Studyresultsindicatethatthecorrelationcoefficientmayreach0.9622,indicatingthattheproposedmethodhasreferentialvalue.Therefore,engineersmayusethiscomprehensiveapproachtodevelopNDTstodetermineconcretestrength.KeyWordsStrengthofConcrete,ReboundValue,DesignParameters,RegressionAnalysis1.IntroductionConcretehassignificantlyinfluencedthenatureofengineeringprojects.Concrete,asacompositematerial,isgenerallycomposedofcement,sand,aggregate,water,mineraladmixturesandchemicaladmixtures.Considerableworkhasbeenconductedtodeveloprapid,nondestructivetestsNDTsthatprovideareproduciblemeasureofconcretequalityinastructure1.Unfortunately,asisusuallythecaseinconcretetesting,alltheseNDTgenerateresultsthatareaffectedbyvariousparameterssuchasaggregatetypeandsize,age,moisturecontent,andmixproportions1.Therefore,thecorrelationbetweenmeasuredpropertiesandstrengthdiffersforvariousconcretesandmustbelimitedtotheconcreteinquestion.However,theNDTsarealsoconvenientandhavebeenusedformanyyearsinqualitymanagementofengineeringmaterials.Thesetestsareusefulindeterminingthedifferencesinconcretequalityfromonepartofastructuretoanother.DevelopedinGermanyin1930,thereboundhammertestRHT,basedonASTMC805andBS4408Part4,canbeutilizedfortestingconcretesurfacehardness1,2.In1948,SchmidtdevelopedtheSchmidtreboundhammertest3,4.Thisdeviceisuniversallyusedbecauseofahardenedsteelhammerimpactedontheconcretebyaspring.TheRHTisaconvenientNDT.Thesurfaceofhardenedconcreteisstruckwiththehammer,andconcretecompressivestrengthisestimatedviathesurfacehardnessreboundvalue.In1979,theASTMlistedthereboundhammertestingmethodASTMC80579asastandardtestingmethod,explainingthatthismethodcanbeusedtoestimatetheuniformityofconcreteanddetectareasofinferiorqualitywithinaconcretestructurehowever,itisnotasubstituteforconcretestrengthtestingmethods.ThegeneralviewheldbymanyusersoftheSchmidtreboundhammeristhatitisusefulinassessingconcreteuniformityandincomparingoneconcreteagainstanother,butcanonlybeusedasaroughindicationofconcretestrengthinabsoluteterms1.WhentheRHTisperformed,kineticenergyfromtheTamkangJournalofScienceandEngineering,Vol.12,No.1,pp.1cCorrespondingauthor.Emailchkouchu.edu.twimpactandamountoflostkineticenergyaffectthereboundvalue.Typically,theamountofenergylostduringcontactbetweenthepoleandconcretemustbedeterminedviathestressstrainrelationshipoftheconcretetherefore,reboundenergyiscorrelatedwiththeconcretestrengthandrigidity.However,theaccuracyofRHTneedtobeimprovedinrealapplicationswhenestimatingconcretestrengthusingthesurfacereboundvalue.Lowstrengthconcretewillhavealowreboundvalue.However,whentwoconcretespecimenshavethesamestrengthanddifferentrigidities,theresultingreboundvaluesmaynotequaleachother5.Theamountofenergylostwithlowrigidityconcreteisgreaterthanthatlostwithhighrigidityconcrete.Thereasonforthisdifferencemaybeassociatedwithmaterialparameters.Forinstance,theamountofcoarseaggregateandhowaggregateismixedinaconcretemixtureaffecttheconcreterigidity,thusaffectingthereboundvalue.Thus,thisstudyanalyzestheproportionsinconcretemixtures.Designparametersareusedasinputdatatocreateareboundmodel,toenhancetheaccuracyofdeterminingconcretestrength.Intheconventionalmaterialmodelingprocess,regressionanalysisisanimportanttoolforconstructingamodel.Inthisstudy,sevendesignparameters,i.e.amountsofcement,coarseaggregate,fineaggregate,slag,flyash,chemicaladmixture,watertobinderratioX17andreboundvalueofconcrete,wereusedtobuildtheregressionformula.2.ExperimentalWorkFigure1presentstheresearchflowchart.Thecompressivestrengthofconcreteisestimatedusingthestatisticalregressionanalysismodel.Additionally,therootmeansquareoferrorRMSEandcoefficientofdeterminationareusedtodeterminemodelreliability.Theresearchmethodisasfollows1Thereboundvaluewithconcretedesignparameters,usingstatisticalregressiontofindthecompressivestrength.Statisticalregressionisusedtoidentifycompressivestrengthbasedonthereboundvalueandconcretedesignparameters.Intotal,146specimenswithdifferentmixtureproportionsaremadeinthisstudy.DifferentmethodsfortheHRTofstandardcylindersc61c24215cm,L30cmarecategorizedasfollows.1Measure20distributedtestpointsandcalculatetheaverage.2Take5points,perform4measurementsateachpoint,andcalculatetheaverage.3Forasinglepoint,performHRT20timesandcalculatetheaverage.Thelargestmeanreboundvalueinthisstudyisthereboundvalueusedasinputdata.Thelargestreboundvalueobtainedusingmethod320testsaremadeatthesamepointandcalculatetheaverage.Inthismodel,146concretespecimenswithdifferentmixtureproportionsareusedasrawdata.RegressionanalysisisappliedtothevariablesTable1.Table1liststherangesofvaluesforappliedparameters.Regressionanalysiswasutilizedtoconstructamodelforestimatingtheconcretestrength.2ModelConfirmationWhenthemodelwascompleted,20setsoftestdataareusedtodeterminetheaccuracyofregressionesti2JenCheiLiuetal.Figure1.Researchflowchart.mates.Theabsolutedeviationvaluesandpercentagesareutilizedforcomparisonswithtruevalues.Astheabsolutedeviationvaluesandpercentagesdecreases,thedegreeofdifferencebetweenthepredictedcompressivestrengthandtruecompressivestrengthdecreases,andmodelaccuracyincreases.Thus,theaccuracyofthemodelisconfirmed.3.FindingsandAnalysisInputparametersemployedinthisstudyincludemoisturecontent.Theinfluenceofmoisturecontentonreboundvalueis99c4550average24.ThedifferentmethodsfortheRHTappliedtostandardcylinders15c242cm,L30cmareasfollows.Foronepoint,applytheRHT20timesandcalculatetheaverage.Testresultsindicatethatreboundvalueincreasesby20c4570whenmultipletestsaremadeonthesamepoint,withmethod320testsonthesamepoint.Appliedtoalldatacollectedforthe146concretesamples,theresultingregressionequationofSinglePointestimationisasfollowsy23.085xcwhereyiscompressivestrength,xisthereboundvalue,andthecorrelationcoefficientis0.916.Withmethod320testsonthesamepoint,concretecompressivestrengthvaluesdirectlydeducedfromthesinglereboundingpointdeviateby1c4553average11strengtherror,27.26kgf/cm2.Thereboundvaluewithdesignedparametersandstatisticalregressionareusedtoestimatethecompressivestrengthofconcrete.Inthismodel,statisticalregressionanalysisisappliedtoalldatacollectedforthe146concretesamples.TheresultingregressionisasfollowsY.695X1–0.292X2–0.501X3–0.530X4–1.117X51.013X6–606.478X73.673X8–30.994X912.887X102whereYisconcretecompressivestrengthandX1isamountofcementTable1presentsX2c4510.Byemployingtheregressionequationformulatedinthisstudy,whichincorporatesmaterialdesignparameterssuchasageandmoisturecontent,errorsofestimatedandactualvaluesofconcretecompressivestrength.Obtainedfromtheregressionanalysisreasoningformulaandtheaccuracyarehigh.Totesttheresultsoftheregressionanalysis,thisexaminestheRMSEasacriterionforevaluatingtheextentofdataerrorinregressionanalysis.TheRMSEformulais3whereTijthetestoutputvalueofthejthorderontheithsampleOijtheobjectiveoutputvalueofthejthorderontheithsamplensamplenumberNnumberofoutputvariablesEstimatingtheStrengthofConcreteUsingSurfaceReboundvalueandDesignParametersofConcreteMaterial3Table1.RegressionanalysisoutputandinputvariablesThelowerandupperboundsofeachcomponentVariableComponentRangeofvaluesInputvariableX1Cementkg/mInputvariableX2Coarseaggregatekg/mInputvariableX3Fineaggregatekg/m379c45910InputvariableX4Slagkg/mInputvariableX5Flyashkg/mInputvariableX6Chemicaladmixturekg/m31.7c458.6.InputvariableX7Watertobinderratio0.45c450.62InputvariableX8Agedays07c4538InputvariableX9Moisturecontent0.015c450.060InputvariableX10Reboundvaluen12c4530OutputvariableYCompressivestrengthkgf/cm213c45480
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