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©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[]20090715[](200612)[](1971),,,,,1,2,2,2(1.,410008;2.,410075)[],,,:,,,[];;;;;;[]TU432[]A[]16740610(2010)01001305GeneralFormulasforPredictingtheEarthPressureActingonBackofReinforcedRetainingWallUsingLimitEquilibriumMethodHUANGXiangjing1,2,LIUZhezhe2,YANGGuolin2(1.DepartmentofCivilandArchitecturalEngineering,CentralSouthUniversity,Changsha,Hunan410075,China;2.HunanProvincialCommunicationsPlanningSurvey&DesignInstituteChangsha,Hunan410008,China)[Abstract]Basedonlimitequilibriummethod,generalformulaswerededucedforpredictingthenonlineardistributedactiveearthpressureactingonbackofreinforcedretainingwallwithanybackfill,anyinclinationofback,aswellasanysingleslopeoffillingsurface.Expressionsofresultantforceandheightofactionpointoftheresultantforcewereobtained.Comparativeanalysiswasconductedbetweenmeasuredvaluesandcalculatedvaluesofactiveearthpressureofreinforcedretainingwallwithshalyredsandstonefilling.TheanalysisresultsindicatethatthegeneralformulaswhichwidentheapplicationrangeofRankinesearthpressuretheoryandCoulombsearthpressuretheoryarereasonableandcanbeusedinengineeringdesign.[Keywords]soilmechanics;limitanalysis;reinforcedretainingwall;activeearthpressure;rein2forcementtension;generalformula;comparativeanalysis,,(W.J.M.Rankine)(1978Schlosser)(Segretin.P)(1977Osman.M.A)(1981)[1]:,,[2]1776,,,H/3,©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[3][4],[57],,,,,p,,,1,,,,,,,[8],,1.11,:,,1Figure1Retainingwall,rupturewedgeanddifferentialelement()()cct,1.21ABC,ACdefg(2),3(H=0),(V=0),gd(M=0)2Figure2Differentialelement:-1a0,:p=m1x-a-m2x-m3(1)a0,a=0,:p=n1hcos(-)cos+q0-blnx+n2c-n3c-n4t(2)41©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:a-1,a=-1,:p=n1q0x+bhH-(H-h)cos(-)coslnx+n2c-n3c-n4t(3):m1=n1cos(-)cosH1+a+ba+q0,m2=n1cos(-)cosH1+,m3=n1ba-n2c-n3c-n4tx=1-hH(0x1)a=1-n1cos(+)cos(+)sin(+++)cos(+)b=2coscos(-)sin(+-)c-coscos(+)sin(++)c+sin(+)cos(-)sin(+-)tsin(+)sin(++--)+cos(+++)sinn1=cos(+)cos(+)2sinsin+sin(-)cossin(++--)+cos(+++)sinn2=cos(++-)+sin(++)sinsin(++--)+cos(+++)sinn3=cos(-)cos(+)coscossin(++--)+cos(+++)sinn4=1cos(+)sin(+)+cos(-)cossin(++--)+cos(+++)sinE:-1a0,E=Hcosm11-a-m22-m3(4)a=0,E=Hcosn1Hcos(-)2cos+n1b+n1q0+n2c-n3c-n4t(5)a=-1,E=Hcosn1Hcos(-)4cos+12n1b+12n1q0+n2c-n3c-n4t(6)m1,m2,m3,n1,n2,n3,n4a,b,:E=12H2cos(-)cosKa+q0HKa-cHK-cHK-tHKt(7):Ka=sin(+)cos(+)coscos(+)sin(+++)K=coscos(-)coscos(+)sin(+++)K=cos(++)cossin(+++)Kt=sin(+)cos(-)coscos(+)sin(+++):z0=H0pzdhcosH0pdhcosa0a-1,:z0=H31-a2-a6m1-2(2-a)m2-3(2-a)m32m1-(1-a)m2-2(1-a)m3a=0a=-1,c=0,c=0,q0=0,t=0,:z0=H3(a=0)()z0=49H(a=-1)()1.3(7),3251©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=0,:Ecos(+)-cABsin-Rcos(+)+cBCsin+tBC=0(8)V=0,:Esin(+)-cABcos-Rsin(+)+cBCcos-W-q0AC=0(9):E=12H2sin(+)cos(-)cos(+)cos2cos(+)sin(+++)+q0Hsin(+)cos(+)coscos(+)sin(+++)-cHcoscos(-)coscos(+)sin(+++)-cHcos(++)cossin(+++)-tHsin(+)cos(-)coscos(+)sin(+++)(10)(10)(7),,,,,,,,,1.4200,,,,,,,VB,44Figure4RunninginterfaceofVBprogram212(),,=-11,=0,=19.0kN/m3,c=3.0kPa,c=2.0kPa,,=28k124+3402008916,6.5m,;2008928,1m,,t=2kN/mt=3kN/m(-01003-0.005)H,,,5ct,,,,33.1c,,c,,6(a)(b),c,,61©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:5Figure5Earthpressureactingonbackofwall,,3.2,,6(c),,,,,4,,,,,,,,0.3H,c,.,[9],6c,,tFigure6Influenceofc,,tvalueonearthpressure,,,,,,,[10]:,![][1],,,.[J].,2009,30(1):206-210.[2][].L.,.J.,JR,(55)71©1994-2010ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:4(0.5)3,(),,,,,,[][1].[M].:,1990.[2],,.[M].:,1992.[3].[M].:,2004.[4].[M].:,1999.[5],.[M].:,1994.[6],.[M].:,1998.[7],,.[J],,2004,(3).[8].[J].,(3).[9].[J].,1997,13(4).[10].[M].:,1988.[11].[R].:,1983.[12].[J].,2000.[13].[J].(),2003.[14].[M]:.,1982.[15].[J].,2007,(2).(17),,,.[M].:,2007.[3],.[J].,1998,24(4):20-23.[4],.[J].,2008,33(5):61-64.[5],.[J].,2008,11(8):88-89.[6],,.[J].,2009,35(5):5-6.[7],,.[J].,2007,7(36):31-32.[8].[M]..,2006.[9],,.[J].,2001,20(1):1079-1082.[10],.[M]..,1996.(44)[3]Garib,A.,A.E.RadwanandH.Al2Deek.EstimatingMa2gnitudeandDurationofIncidentDelays[J].JournalofTransportationEngineering.1997,(6):459-466.[4]Ozbay,KaanandPushkinKachroo.IncidentManagementinIntelligentTransportation[Z].Boston,MA:ArtechHouse,1999.[5]Breiman,Leo,JeromeH.Friedman,RichardA.OlshenandCharlesJ.Stone.ClassificationandRegressionTrees[Z].PacificGrove,CA:Wadsworth,1984.[6]Nam,DooheeandFredMannering.AnxploratoryHazard2BasedAnalysisofHighwayIncidentDuration.[J]Trans2portationResearch2A.2000,(2):85-102.[7]Khattak,AsadJ.,JosephL.SchoferandMu2HamWang.ASimpleTimeSequentialProcedureforPredictingFreewayIncidentDuration.[J]IVHSJournal.1995,(2):113-138.[8]Golob,ThomasF.,WilfredW.ReckerandJohnD.Leon2ard.AnAnalysisoftheSeverityan