外文翻译时间变化的钢筋混凝土阻力分析（英文）.pdf

Vol.17No.4JournalofWuhanUniversityofTechnology-Mater.Sci.Ed.Dec.2002RandomTimeDependentResistanceAnalysisonReinforcedConcreteStructures3GUANChang2sheng1)WULing2)1)WuhanUniversityofTechnology2)WuhanUniversityofScienceandTechnology(Received:Aug.20,2001)Abstract:Theanalysismethodonrandomtimedependenceofreinforcedconcretematerialisintroduced,theeffectmechanismonreinforcedconcretearediscussed,andtherandomtimedependenceresistanceofreinforcedconcreteisstudied.Furthermore,thecorrosionofsteelbarinreinforcedconcretestructuresisanalyzed.Apracticalstatisticalmethodofevaluatingtherandomtimedependentresistance,whichincludesmaterial,structuralsizeandcalculationinfluence,isalsoestablished.Inaddition,anexampleofpredictingrandomtimedependentresistanceofreinforcedconcretestructuralelementisgiven.Keywords:randomanalysis；timedependentresistance；reinforcedconcreteGUANChang2sheng(管昌生):Bornin1957；Prof.；InstituteofArchitectureandCivilEngineering,WuhanUniversityofTechnol2ogy,Wuhan430070,China3FundedbyHubeiProvinceConstructionBureau(G200219)1IntroductionReinforcedconcreteisoneofthemostusefulmateri2alsincivilengineeringforitssuitabilityandinexpensiveprice.Therefore,alargenumberofthiskindmaterialisused.However,intraditionaldesignofconstructionstructureandmaterialresearchofreinforcedconcrete,litteattentiontothetimedependentstrengthofreinforcedconcreteispaid,especiallytherandompropertiesofthevariouseffectsonthematerialsarehardlystudied1,2.Untilrecentyearthereareafewresearchesthatmentiontheproblemabouttherandomtimedependenceofrein2forcedconcreteinengineeringstructures.LiandMelch2ers3havestudiedthefailureprobabilityofreinforcedconcretecolumnsunderstochasticloads,andgivenatech2niquetocalculatethetime2variantfailureprobability.LiandLiu4havestudiedthedurabilityofconcretestructureconsideringtheeffectofreinforcedcorrosion.Leng5etalhavediscussedthestatusandproblemofstudyonthestresscorrosionofconcrete.AlsoLu6etalhavedis2cussedthestateofreinforcementcorrosion.Generallyspeaking,reinforcedconcreteresistanceobviouslyde2crease,whichdependsondifferentfactors7.Toevaluatethesafetyofconcretestructure,abasictheoryforanalyz2ingdurabilityofreinforcedconcreteshouldbeproposed.Itisnecessorytostudyrandomtimedependentpropertiesofreinforcedconcretestructures.2TimeDependentEffectMechanismsofReinforcedConcreteTherearemanyfactorsaffectingtheresistanceofre2inforcedconcrete.Morethan50kindsofchemicalcorro2sionfactorsexistonlyintheareaofwaterbasin,waterworksandwaterconditioning.Thepracticalmethodtoob2tainatimedependentmodelofreinforcedconcreteisamulti2factorcomprehensiontechnique.Ingeneral,forsin2gle2factor,manyresultshavebeenshownthatifonlycon2cretecarbonizationisconsidered,aformulaofpredictingcarbonizationthickcanbewrittenas:D(t)=Kt(1)whereD(t),Kandtarethick,speedcoefficientandtimeofcarbonization,respectively.Uptonowmanypredictingmodelsareusedinsteelcorrosion,fatiguedamage,andchemicalerosion,butnocommonrecognizedresultsunanimouslyexist.Generallyspeaking,thedecreasingresistancefunctionofreinforcedconcreteincludessomevariablesthatcanexpressassteelbar,concrete,geometricsize,environmentconditionnear2by,andpropertiesofrandomandtimedependenceofre2sistance1,5.Obviously,reinforcedconcreteresistanceisafunctionofrandomprocessorvariableofseriesofmate2rialsandstructures.Reinforcedconcretecarbonizationinairiscalledneutralization,whichisacomplexandslowneutralizationprocessofCO2intheairandalkalinemate2rialinreinforcedconcrete.Inairitwilltakeseveraldecadestocompletelycarbonizetheprotectivecoatingofsteelbarindenseconcrete,butonlytakeafewyearsinnon2denseconcrete.Iffinenessofcarbonizedmaterialsishigher,itsstrengthislowerandcarbonizationprocessisfasterindecreasingcrosssectionofstructure.Carboniza2tionmakesalkalinitylowerandsteelbarcorrosion2.Steelbarcorrosionisaprocessthatironinsteelbarsur2facelosseselectroncontinuallyanddissolvesinwaterun2dertheconditionofoxygenandwaterinteraction.There2fore,thevolumeoferodedmaterialsisexpendedseveraltimes,whichcanmaketheprotectivecoatingofreinforcedconcretecrack,drop,andcohesiondamagebetweensteelbarandconcretealongsteelbardirectionsothatrein2forcedconcretestructurelossesbearingcapability.Recentresearchesshowthatthesteelbargetsintoaseriouscor2rosionstatewhennon2carbonizedprotectivecoatingisonly15mmthick.Ontheotherhand,thestarttimeofcorro2sionmaybeinadvanceduetoincompletecoatingandcrackinconcrete,alsocorrosionvelocitymayincreasegreatly.Whensteelstressislessthanyieldingpoint,thecorrosionvelocityisstable,butincreasesseveraltimesifthecorrosionvelocitypassesovertheyieldingpoint.Thelatteriscalledstresscorrosion,whichisofbrittlenessandmoredangerous.Steelcorrosioncanmakebearingareaofsteelbardecrease,cohesiondamage,andlosestructureeffectiveness.Erosionairandliquidallhavestrongeffectonreinforcedconcrete,whichcanmakereinforcedcon2creteerosion,decreaseprotectivecoatingofconcrete,andfinallyacceleratesteelcorrosion.Whenbearingdynamicload,reinforcedconcretestructurecanundergofatiguedamage,leadingstrengthandrigiditytodecreasing,form2ingcrackandexpansion.Usuallyfatiguedamagecanbedividedintodetermineandrandommodels,theformerdealswithdetermineperiodloading,andthelatterisrel2ativetotherandomofmaterialandload.Besidesallmentionedabove,therearemanyotherfactors,suchastemperature(includinghighorlow,andcyclictemperature,freezingdamage),humidity,(includingcyclicofdryandhumid),andtheamplitudeofloading,whichcanresultinresistancedecreasingofreinforcedconcretestructure.3RandomTimeDependenceAnalysisUndertheconditionthateveryrandomvariableofstructureisindependentoneachother,andconsideringtimedependencecharacteristicofmaterial,therandomtimedependentfunctionofreinforcedconcretematerialcharacteristiccanbewrittenas8:KM(t)=k-10K0(t)Kf(2)whereK0(t)isarandomvariableindicatingpropertydif2ferenceofstructuralmaterialandtestingmaterial；k0isacoefficientofpropertydifferenceofstructuralandtestingmaterial,andKfisarandomvariableoftestingmaterial.Asstatisticstheory,themeanvalueandstandarddeviationcoefficientofKM(t)areasfollowsrespectively:KM(t)=k-10k0(t)Kf(3)KM(t)=2KKM0(t)+2Kf(4)wherek0(t)andKKM0(t)respectivelyaremeanvalueandstandarddeviationcoefficientofrandomprocess.K0(t),KfandKfarethemeanvalueandstandarddevia2tioncoefficientoftestingmaterialpropertyandrandomvariableKf,respectively.Bythesamewaythesimilarrandomanalyticalmodelmaybesetupforstudyingtherandomnessandtimede2pendencetogeometricparametersandcalculationmethodsofreinforcedconcretestructure.Theresistanceofreinforcedconcretecanbeex2pressedbyresistancefunctionR(x1,x2,xn),inwhichxidenotestheparametersofmaterials,geometryandcalculationprocedureofstructuralmaterial.Ifrandomandtimedependenceareappliedsimultaneouslytoresis2tanceandrelativevariables,xicanbedealtwithasaran2domprocess.Moreover,consideringfatiguemechanics,calculationmodelandinitialconditions,timedependentresistancemodelcanbewrittenas:R(R0,t)=R0KpR(x1,x2,xn)(5)whereR(R0,t)isresistancerandomprocess,R0isini2tialresistance,isarandomprocessoffatiguedamage,andKpisanundeterminableparameterofcalculationmodel,xidenotesarandomprocessofmaterialparame2ters.Manyexperimentsonsteelcorrosionindicatethatsteelerosionprocessaccordswithnormalrandomprocess.Byseparationprocedure,randomtimedependentresis2tanceR(R0,t)cansimplybeexpressedas:R(R0,t)=R(t)R0(6)whereR(t)isadeterminingtimedependentfunction,andR0israndominitialresistance.Inaddition,someotherundeterminedconditionsshouldbeemployed,suchasundeterminedresistanceofactualmaterial,geometricsizeandcalculationmodel.Astoasimplestructure,resistancefunctionofrandompro2cessalsocanbesimplifiedas:R(t)=g(t)Kp(y)Rp(t)(7)whereg(t)istimedependentfunction,Kp(t)isunde2terminableparameterofcalculationmodel,andRp(t)isstructureresistancedeterminedbycalculatingmodel.Toasinglestructuralelementequation(7)canbewrittenas:R(t)=Kp(t)KM(t)KA(t)RK(t)(8)whereKp(t),KM(t),andKA(t)arerespectivelytimedependentparameterofcalculation,geometryandmaterialcharacteristicofreinforcedconcretestructuralelement.RK(t)isstandardvalueofmaterialresistance.Themeanvalueandstandarddeviationofequation(8)arerespectivelyasfollows:R(t)=KP(t)KM(t)KA(t)RK(t)(9)R(t)=2KP(t)+2KM(t)+2KA(t)1/2(10)Inengineeringapplication,decreasingfunctionrandomprocessofconcretestructuralresistancecanbeexpressedby:R(t)=(t)(11)whereR(t)israndomprocessofconcretestructuralre2sistance,isrelativerandomvariable,and(t)istimedependentdeterminingfunction.Basedondurabilitygrade95Vol.17No.4GUANChang2shengetal:RandomTimeDependentResistanceAnalysison.ofdesignedconcretestructure,equation(11)canbees2tablishedas:cu(t)=cu(1-1t)(12)cu(t)=cu(13)y(t)=y(1-2t)(14)y(t)=y(15)wherecu(t)andy(t)arerespectivelyresistancemeanvalueofconcreteandsteelbarwhenreinforcedconcreteisuseduptotimet；cu(t)andy(t)arestandarddevia2tioncoefficientsofconcreteandsteelbarofreinforcedconcreteattimetrespectively；cu,y,cu,yareinitialvaluesofvariousvariables；1and2areresistancede2creasecoefficientsofconcreteandsteelrespectively,whichrelatetostructuralmaterialandcanbeobtainedfrommaterialexperiment.4EngineeringApplicationAstructuralelementofreinforcedconcretebearingaxialpressureistested,somestatisticaldataofstructuralresistanceiscalculated.Considerinitialvalues:C30con2crete,themeanvaluecu=1.41andstandarddeviationcu=0.19；20MnSisteelbar,meanvaluey=1.14andstandarddeviationy=0.07；initialsectionsizeis1m2.Thereare0.02variationoneachsideofthestructuralel2ement.ResistancedecreasecoefficientsofconcreteandsteelobtainedfromRef.4arerespectively1=810-7and2=2.210-6.Undertheseconditionstherandomtimedependentresistanceofthereinforcedcon2cretestructurebearingaxialloadcanbeobtained.Accordingtodesigntheoryofreinforcedconcretestructures,resistancefunctioncanbeformedbyR=AcuRcu+AyRy,inwhichRcuandRyareinitialresistanceofconcreteandsteelbarrespectively,andthenusingthetheorysuggestedinthispaper,therandomtimedepen2dentresistancecanbecalculated.SomestatisticaldataarelistedinTable1.Fromtheresultsitisseenthattheresistancechangeofreinforcedconcreteisobvious(de2creasingwithtime).Thisphenomenonissignificantandnottobeignoredforevaluatingthesafetyofreinforcedconcrete.Table1RandomTimeDependentResistanceofReinforcedConcreteStructuralElementBearingAxialLoadt/year01020304050Meanvalue/KN7625.207323.957136.566885.756517.445987.32Standarddeviation/KN1248.631193.801164.731129.491080.281011.05Variationcoefficient0.16370.16290.16320.16400.16570.16885ConclusionsThecharacteristicofreinforcedconcretestructuresisimportantforresearch,designandconstructionofcivilen2gineering.Thestudyofrandomandtimedependenceofreinforcedconcretematerialisnecessaryforstructuraltesting,maintainingandsafetyevaluationofreinforcedconcretestructures.Forstructuralreliabilitydesign,apracticalrandomandtimedependentresistanceshouldbeestablished.Inthispaperrandomtimedependentcharac2teristicsofreinforcedconcretemate