岩土工程可靠度关于强度参数分布函数概型的敏感度分析

18118(1):363919992ChineseJournalofRockMechanicsandEngineeringFeb.,1999(400045)(FOSM),Mohr2Coulombc,,,,,,,TU4511,c,,,,[1,2],Mohr2Coulombc,,[3,4][5]FOSMu=ming(T(…u))=0(…uT…u)1/2(1):…uu3M=g[T(…u)]M-…uT…(2):……uT…=-¨…ug|¨…ug||…u=u3(3)[6]FOSMdd=u3||5T-15(4):(u)=12exp(-u22)(5)T()T-1()[7]FOSM,,,,Mohr2Coulomb,2T-1(X,u,)=-1[F(X,u,)](6):F()(4)dd=u3||1()5F(x3,u,)5(7),,199769,199791:,33,,1988,,©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.,dd,u3||5F(x3,u,)5,,,,,(7),5F(x3,u,)5dddd2.1Fx(x)=(lnx-uLL)(8):,uLL(8)5Fx(x3)5=lnx3-uLL]5lnx3-uLL5(9):5lnx3-uLL=(5=2L(2+u2)(L-u3)=2L(2+u2)(ln(2x+1)-u3)(10):,u2,L,5Fx(x3)/5(ln(2x+1)-u3)1dd,1,uu3L,xi,d/duu3L,xi,Mohr2Coulomb,c,,c,,d/d,2.2Fx(x)=exp{-exp[-a(x-b)]}XR(11):a,b1Fig.1Thesensitivityforlognormaldistribution(11),d/d5Fx(x3)5=-exp{-exp[-a(x3-a)]}exp[-a(x3-b)]5[-a(x3-b)]5(12)5[-a(x3-b)]5=56(x3-u)-0.5572i5(13)x-u=0(14)m,m=b-ln(ln2)/a=u-0.164(15),mxu,,d/dxm,,d/du3=0.17722.3WeibullWeibull,Fx(x)=1-exp[-(xk)b]x0(16)73181.©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=k(1+1b)(17)=k(1+2b)-2(1+1b)(18)m=k(ln2)1b(19):(),u,kb,5Fx(x3)5,vx=u,3vx0.166xc(vx)x3mvx0.1660x3xc(vx),d/dvx0.166xc(vx)x3mvx0.1660x3xc(vx),d/d,,:(1),,,(2),,,3WeibullFig.3ThesensitivityfortheWeibulldistribution3Mohr2Coulombc,Mohr2Coulombc,,Mohr2Coulomb12:f(x)=1(1+sin)-2(1-sin)-2ccos=0c,,,c,c,Mohr2Coulomb,c,Mohr2Coulombc,,,,,831999©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.,€c=30.68MPaVar(c)=(112.15MPa)2…=34.52Var()=(19.973)2,12,0.2,€1=100MPa€2=30MPaMohr2Coulomb,1,2,c,Weibull,[1],11Mohr2CoulombTable1TheresultofsensitivityandreliabilityofMohr2CoulombcriterionE(c)(c)E()()d/d30.6810.5934.524.451.7119-0.06728.9510.2934.234.451.60390.05628.8810.1233.764.271.57470.657Weibull28.1910.7733.294.311.4581-0.432:1,c,,20%30%,c,Weibull,,c,4(1),c,Weibull,20%30%(2),(3),1HarrME.MechanicsofParticulateMediaaProbabilityApproach.Washington:McGraw2HillInc.,19772..,19943YanChunfeng,ZhangJianhui.TheuseofBayesmethodtoinferdis2tributionofmechanicalparameters.In:ProccedingsofRockMechan2icsandEnviromentalGeotechnology,EMRG97.Chongqing:ChongqingUniversityPress,1997,61664,.Bayes.,1997,19(2):65715..:,19936DalsgaardJ,EnevodsenI.Sensitivityweaknessesinapplicationofsomestatisticaldistributionsinfirstorderreliabilitymethods.Struc2turalSafety,1993,12:3153257,,.FOSM.,1997,16(1):4350THESUSCEPTIBILITYANALYSISOFRELIABILITYFORTHEPROBABILITYDISTRIBUTIONTYPESOFPARAMETERSINSTRENGTHCRITERIONYanChunfengLiuDongyanZhangJianhuiZhuKeshan(ChongqingJianzhuUniversity,Chongqing400045)AbstractSomemethodsareintroducedtoestimatethereliabilityindex.Thesusceptibilityofseveralfunctionsofprobabilitydistributiontypestoreliabilityindexisanalyzed.BasedonMohr2Coulombstrengthcriterion,thesusceptibilitytoreliabilityforprobabilitydistributiontypesofparametersisanalyzed.Threeconclusionsarepro2posed.Ausefulsuggestionisgivenforgeotechnicalengineers.Keywordsgeotechnicalengineering,reliability,probabilitydistribution,susceptibility,strengthcriterion93181.©1994-2008ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.