关于有限元边坡稳定性分析中安全系数的定义问题

2413Vol.24No.1320057ChineseJournalofRockMechanicsandEngineeringJuly20052004021120040605(1964)[e-mail]12222(1.4300712.443002)31233132323O242.21A10006915(2005)13222506ONDEFINITIONSOFSAFETYFACTOROFSLOPESTABILITYANALYSISWITHFINITEELEMENTMETHODZHENGHong12TIANBin2LIUDe-fu2FENGQiang2(1.InstituteofRockandSoilMechanicsChineseAcademyofSciencesWuhan430071China)2.CollegeofCivilandHydroelectricEngineeringChinaThreeGorgesUniversityYichang443002China)AbstractThereexistthreedefinitionsofsafetyfactorinslopestabilityanalysesbylimitequilibriummethods(LEM).Definition1definesthesafetyfactorastheratiooftheshearstrengthofsoiltotheshearstressrequiredforequilibrium.Definition2definesthemarginofsafetyfactorasthefactorofthestrengthreductionbywhichtheshearstrengthofthesoilwouldhavetobedividedtobringtheslopeintoastateofcriticalequilibrium.Definition3definesthesafetyfactorastheratiooftheresistantshearforcetothedrivingshearforcealongacertainslipsurface.ThisstudydiscussestherelationbetweenDefinition1and3.AunifiedalgorithmisgivenwhichisusedtolocatethecriticalsliplinescorrespondingtoDefinition3andDefinition2respectively.ItisalsoprovedwhilethefiniteelementmethodisusedtoanalyzeslopestabilityboththesafetyfactorandthepotentialslipsurfacebasedonDefinition3aredifferentfromthoseonDefinition2.SomeirrationalresultsmightbeobtainedifDefinition3isusedinfiniteelementslopestabilityanalysis.Keywordsnumericalanalysisslopestabilityanalysissafetyfactorfiniteelementmethod(FEM)1[116][1]1996•2226•200525a323323[7]7[117]ττ][1=F(1)τ][τMohr-Coulombϕστtan][−=c(2)cϕσ(1)1[1]12F2F22[18]2)tan(12ϕNclF+lN11F[1921]FF1F[1]1FF[1]∫∫=ssssF3dd][ττ(3)s3Fellienius3F[22][23]1F3F1F13FF=(1)ττ1][F=(4)(5)s∫∫=sssFs1dd][ττ(5)τs[24]sξ∫∫=sssFsF11ddττξ(6)1ξF1Fsξ(3)(6)13ξFF=(7)3F1Fss(7)332413.•2227•1F3F[52526]3F1F3F2F(3F)(2F)2[16]2F[216][26]4323Fxxlττ][)(=lxF(8)Mohr-Coulomblx1σ−π±24ϕ)(lxF(7))(lxFx222s′s==iilylxββsinddcosdd(9)dls′iβdl−π±=24ϕαβi(10)α1σx2(8)3FNN(8)2N3F3F[26]2F(9)ϕsϕ=sϕ−21tantanFϕ51212[27][11]•2228•20051Fig.1Sectionforcomputation1Table1Parametersofrocksγ/(kNm3)c/kPaϕ/()E/MPaµ24.034.02621040.3525.039.03551040.302Fig.2Meshandboundaryconditions3232Fν[6])48.1(33=FF)58.1(22=FF6.3%3F(3)2F(2)[17]Fellenius5%20%42FellieniusBishop232323Fig.3SafetyfactorsandpotentialslipsurfacesbasedonDefinitions2and3respectivelyusingFEM4Fig.4Contourlinesofequivalentplasticstraininthecriticalstate2Table2Safetyfactorsoftwoslipsurface3()2()Fellenius1.3931.344LEMBishop1.5421.5361.480FEM1.580Fellienius2()233(3)(1.580)Bishop2(1.536)2.8%26.3%28.8m3.4m4m10m1.3m15m10m24m2m∇5.00mF3=1.48F2=1.589.070.072413.•2229•6(3)3F2F3FBishopSpencer(References)[1]DuncanJM.Stateoftheartlimitequilibriumandfinite-elementanalysisofslopes[J].JournalofGeotechnicalandGeoenvironmentalEngineeringASCE1996122(7)577596.[2].[J].200123(4)406411.(LianZhenyingHanGuochengKongXianjing.StabilityanalysisofexcavationbystrengthreductionFEM[J].ChineseJournalofGeotechnicalEngineering200123(4)406411.(inChinese))[3].[J].199719(1)17.(SongErxiang.Finiteelementanalysisofsafetyfactorforsoilstructures[J].ChineseJournalofGeotechnicalEngineering199719(1)17.(inChinese))[4]GriffithsDVLanePA.Slopestabilityanalysisbyfiniteelements[J].Géotechnique199949(3)387403.[5]ZouJZWilliamsDJ.Searchforcriticalslipsurfacebasedonfiniteelementmethod[J].CanadianGeotechnicalJournal199532(1)233246.[6].[J].200224(5)626628.(ZhengHongLiChunguangLeeChaofengetal.Finiteelementmethodforsolvingthefactorofsafety[J].ChineseJournalofGeotechnicalEngineering200224(5)626628.(inChinese))[7].[J].200021(2)152155.(ShiHengtongWangChenghua.Someproblemsinfiniteelementanalysisofslopestability[J].RockandSoilMechanics200021(2)152155.(inChinese))[8].[J].20024(1)5761.(ZhengYingrenZhaoShangyiZhangLuyu.SlopestabilityanalysisbystrengthreductionFEM[J].EngineeringScience20024(1)5761.(inChinese))[9]MatsuiTSanKC.Finiteelementslopestabilityanalysisbyshearstrengthreductiontechnique[J].SoilsandFoundations199232(1)5970.[10]DawsonEMRothWHDrescherA.Slopestabilityanalysisbystrengthreduction[J].Géotechnique199949(6)835840.[11]DawsonEMotamedFNesarajahSetal.Geotechnicalstabilityanalysisbystrengthreduction[A].InGriffithsDVed.GeotechnicalSpecialPublicationSlopeStability2000ProceedingsofSessionsofGeo-Denver2000[C].[s.l.][s.n.]2000.99113.[12]LechmanJBGriffithsDV.Analysisoftheprogressionoffailureofearthslopesbyfiniteelements[A].InGriffithsDVed.GeotechnicalSpecialPublicationSlopeStability2000ProceedingsofSessionsofGeo-Denver2000[C].[s.l.][s.n.]2000.250265.[13]DawsonEYouKParkY.Strength-reductionstabilityanalysisofrockslopesusingtheHoek-Brownfailurecriterion[A].InLabuzJFed.GeotechnicalSpecialPublicationTrendsinRockMechanics[C].[s.l.][s.n.]2000.6577.[14]JeremićB.Finiteelementmethodsfor3Dslopestabilityanalysis[A].InGriffithsDVed.SlopeStability2000ProceedingsofSessionsofGeo-Denver2000[C].[s.l.][s.n.]2000.224239.[15].3#[J].200325(4)389394.(GeXiurunRenJianxiLiChunguangetal.3DFEManalysisofdeepslidingstabilityof3#damfoundationofleftpowerhouseoftheThreeGorgesproject[J].ChineseJournalofGeotechnical