黏性土桩间土拱效应计算与桩间距分析

273Vol.27No.320063RockandSoilMechani[e-mail]10007598(2006)030445061121.6100592.610031cφ-TU443AAnalysisofsoilarchingeffectbetweenadjacentpilesandtheirspacingincohesivesoilsJIANGLiang-wei1,HUANGRun-qiu1,JIANGZhong-xin21.CollegeofEnvironmental&CivilEngineering,ChengduUniversityofTechnology,Chengdu610059,China;2.TheNo.2RailwaySurveyingandDesigningInstitute,Chengdu610031,ChinaAbstract:Soilarchingeffectisanimportantpreconditionofadjacentpertainingoranti-slidingpilesworkingsafelyandcost-efficiently.Incohesivesoils,thespacingbetweenadjacentpilesisrelatedtoarchingeffect.Bymeansoftheanalysisofmechanicalconcepts,takinggeometricalcharacteristicofarchlineandthefracturingfacedirectionangleofMohr-Coulombfailuretoaccount,theforce-balancingconditionandstrengthconditionareintegratedandsimplifiedtoauniformexpression,whichisonlypresentedbythenormalstressonthecrosssectionplaneofarchfoot.BasedonMohr-Coulombfailurecriterion,theleasthandysoilstrengthparameterswhichonlyincludingcohesioncandinternalfrictionangleφ,accordingtotherelationshipbetweenthenormalstressandarrow-spanratio,thearchlineandspacingbetweenpilesareobtained.Furthermore,thedepthstableconditionofsoilarchisdiscussed,pilespacingcanbeemendedmorerationally.Theapplicationconsistswithpracticeprojectstoacertainextent.Aconciseestimatemethodtosoilarcheffectmaybeputforward.Keywords:cohesivesoil;soilarchingeffect;pilespacing;arrow-spanratioofarch1[1,2]()()[3~8]2006[3,4][5][6][7][911]()kφ[10,11](cφ)2[10]()123[4,7]()224/yfxl=0x2/l1lf()xy1()1Fig.1Theanalysissketchofforcealongthearchline1C2/8qlfqxN422(64)/8Nqlxff=+2q11228tantan(/8)qxfxqlflα−−⎡⎤⎛⎞′===⎜⎟⎢⎥⎝⎠⎣⎦1tan(d/d)yx−N2NxA22(16)/8qllff+B2/8qlf3(2)[5~7]12b′θB′34-2NyxAl/2αql2ql28fql28fCqxα’fB44632Fig.2Theanalysissketchofforceinarchfoot2cosBbθ′′=cos2cosBbδθ′=14tan()flα−=3bδ[57]xyστ2xy22(sincos)/8sincosqlbbqlfbbτθσθσθτθ′′=+⎫⎪⎬′′=−⎪⎭42(4tan)cos/4qlflBfσθθ′=+52(4tan)cos/4qlflBfτθθ′=−6AC20σ22016cos4cosqllfNbBfθσδ+==′7222016coscoscos4qllfBfθδσσδ+==′822016cossinsincos4qllfBfθδτσδδ+==′9tan4/flα=2δ=90θα+−D22sin(4sincos)/16fllfδθθ=−+1022cos(4cossin)/16fllfδθθ=++115869756(3)3Fig.3TheMohr-Coulombfailurecriterion3CBB0σ4-45/2φ+D[12]45/2δφ=+D135θ=+D/2φα−704tan(45/2)cos(45/2)4cos(45/2)qlflBfφφσφ⎡⎤−−−⎣⎦=′+DDD12φ0σl12l0/0lσ∂∂=0σ12tan(45/2)flφ=−D13sin(45/2)cos(45/2)φφ−=+DD13120/2zqlBσ′=202cos(45/2)02cos(45/2)qlBfσφφ∂−=−′∂+DD0zσ0max0/2zqlBσσ′==14-(3)44720060max0max()sin22tancσσφφ=+150max2cos1sincφσφ=−16c1416max4cos(1sin)Bclqφφ′=−17B′cqφ1/(1sin)φ−φlmax120σf/1/[2tan(45/2)]flφ−D0σfl120max/qlBσ′′=max2cos(1sin)Bclqφφ′′=−18maxl′18175[5]()()()Rankine(4)40()tan(45/2)ffhzφ=+−−D19hzff04Fig.4Thecollapseareainfrontofthesoilarch[13]()Rankine20tan(45/2)qqzφγ=+−D20q0γ0σfqqfzz0σ0/zσ∂∂01920120ll=z30020020020cos(45/2)4tan(45/2)4cos(45/2)tan(45/2)()tan(45/2)tan(45/2)[tan(45/2)][()tan(45/2)]lzBlfhzlqzfhzσφγφφγφφφφγφ∂−⎧=−−⎨′∂+⎩−−+−−⎫−+−⎬+−−⎭DDDDDDDD21zz=h0f018tan(45/2)8tan(45/2)lφγφ+⋅−−DD22220000[16tan(45/2)16]llhqlγγφγ+−+D22A′44832012162002002cos[tan(45/2)](1sin)BcAllqhAlφγφγφγ′′−=+−−′+D230l0lmaxl(maxl′,maxl)0l(maxl′,maxl)(maxl′,0l)66.11c=30kPaφ=25°B′=1.2mh=5mRankineq=40kPa(00q=)γ=20kN/m3[4]171823maxl=5.65mmaxl′=2.83m0l=6.89m()4.036.85m5.5m6m6.22c=80kPaφ=30°B′=2mh=8m560kN/m[5]0560/8q==70kPaRankineγ=20kN/m320tan(45/2)qqhφγ=+−=D123.33kPa171823maxl=8.99mmaxl′=4.50m0l=7.84m6.509.84m8.1m[5]6.9m6.1m1.56m6.5m[5]6.3320m95m110m502m×3m17m7m950kN36m[14]γ=20kN/m33m14m()0202[(9511020cos5020)(sin50cos50tan)951109503110/6]cos50/(11014)837.3720.9tan4.36tan(45/2)2014837.3720.9tan4.36280tan(45/2)qccqqcφφφφφ=×××××−⋅−××−××××=−−=+−××=−−+−DDDDDDmaxl=5mB′=2m172cos/(1sin)523.3450.6tan2.73175tan(45/2)ccφφφφ−=−−+−Dφ=40°c=38kPaφ=35°c=55kPaφ=30°c=72kPac,φ7m[14]70σc,φ1213-1718449200623[1],,.[J].,1994,9(1):17.YANGXue-qiang,HEShi-xiu,ZHUANGXin-shan.Onarcheffectincivilengineering[J].JournalofHubeiInstituteofTechnology,1994,9(1):17.[2],,.[J].,1995,(2):1519.WUZi-shu,ZHANGLi-min,HUDing.Studiesonthemechanismofarchingactioninloess[J].JournalofChengduUniversityofScienceandTechnology,1995,(2):1519.[3],,.[J].,2001,19(6):556559.WANGCheng-hua,CHENYong-bo,LINLi-xiang.Soilarchmechanicalcharacterandsuitablespacebetweenoneanotheranti-slidingpile[J].JournalofMountainScience,2001,19(6):556559.[4],,.[J].,2003,24(6):7981.FENGJun,LUHe-lin,WANGCheng-hua.ApplicationofM.M.Promojiyfakonovtheorytosolutionofdistancebetweenanti-slidepiles[J].ChinaRailwayScience,2003,24(6):7981.[5],,.[J].,2002,21(5):745748.YEXiao-ming,MENGFan-tao,XUNian-chun.Formationconditionofhorizontalunloadingarchinsoillayer[J].ChineseJournalofRockMechanicsandEngineering,2002,21(5):745748.[6],,.[J].,2004,26(1):132135.ZHOUDe-pei,XIAOShi-guo,XIAXiong.Discussiononrationalspacingbetweenadjacentanti-slidepilesinsomecuttingslopeprojects[J].ChineseJournalofGeotech-nicalEngineering,2004,26(1):132135.[7].[A].()[C].:,1998,7378.CHANGBao-ping,Astudyonsoilarchbetweenstabilizingpilesandcriticalspan[A].Proceedingsoflandslides(Volumethirteen)[C].Beijing:ChinaRailwayPress,1998,7378.[8],,.[J].,2004,25(2):17