极限平衡法边坡稳定性分析课件

极限平衡法边坡稳定性分析俞翔

4/12/2024二目录ONTENTSSlopestability-whatdoesthecodessay?一CGeneralLimitEquilibriumFormulation三LEMforSlopestabilityanalysis!四How

to

use?Slopestability-whatdoesthecodessay?《建筑地基基础设计规范》（GB50007-2011）5.4.1圆弧滑动面

–Simplified

Bishop6.4.3折线滑动面-传递系数法（显式解）什么是传递系数法？放大自重下滑分力Slopestability-whatdoesthecodessay?《建筑边坡工程技术规范》GB50330-20135.2.2计算方法选择Slopestability-whatdoesthecodessay?《建筑边坡工程技术规范》GB50330-2013A.0.1圆弧滑动面

–Simplified

BishopIgnoredtheintersliceshearforces;Satisfiesonlymomentequilibrium.Slopestability-whatdoesthecodessay?《建筑边坡工程技术规范》GB50330-2013A.0.2

平面滑动面

Whatifthere’snoleakingatthetoe?Slopestability-whatdoesthecodessay?《建筑边坡工程技术规范》GB50330-2013A.0.3折线滑动面-传递系数法（隐式解）显式法

VS隐式法折减抗滑力Slopestability-whatdoesthecodessay?《建筑边坡工程技术规范》GB50330-2013显式法

VS隐式法显式法：尚可写出Fs的公式

Slopestability-whatdoesthecodessay?《建筑边坡工程技术规范》GB50330-2013显式法

VS隐式法隐式法：更符合力学规律

GeneralLimitEquilibriumFormulationGeneralLimitEquilibrium(GLE)FredlundandKrahn1977;Fredlundetal.1981Twofactorofsafetyequations:momentequilibrium,Fmhorizontalforceequilibrium,FfAllowsforarangeofintersliceshearandnormalforceassumptionsX=Elf(x)where,f(x)isafunction

isthepercentageofthefunctionusedEistheinterslicenormalforceandXistheintersliceshearforceGeneralLimitEquilibriumFormulationGeneralLimitEquilibrium(GLE)NNNNNcosa+(N-ub)tanf’sina/F+cbsina/F-W+XR-XL=0bDFredlundandKrahn1977XR-XLHowisintersliceshearforcerelatedwithnormalforce?Andhowshouldthenormalforce,Ei,besolved?更进一步的推导！GeneralLimitEquilibriumFormulationGeneralLimitEquilibrium(GLE)X=Elf(x)LEMforSlopestabilityanalysis!OrdinaryorFelleniusmethodAllintersliceforcesignored;SummationofmomentsaboutapointusedtocomputeFos;Fosisthetotalavailableshearstrengthalongtheslipsurfacedividedbythesummationofthegravitationaldrivingforces(mobilizedshear).LEMforSlopestabilityanalysis!OrdinaryorFelleniusmethodAllintersliceforcesignoredNointersliceshearornormalforceExtremelypoorforcepolygonclosureSlicesnotinforceequilibrium

UnrealisticFosShearattheslicebaseisthemobilizedshear,

i.e.,R/Fos!LEMforSlopestabilityanalysis!Bishop’ssimplifiedmethodIncludedinterslicenormalforces;Ignoredintersliceshearforces;Satisfiesverticalforceequilibriumforeachslice&Overallmomentequilibriumaboutthecenterofthecirculartrialsurface;LEMforSlopestabilityanalysis!Bishop’ssimplifiedmethod

Fosappearsonbothsides;iterativeprocedurerequired.LEMforSlopestabilityanalysis!Bishop’ssimplifiedmethodinterslicenormalforcesconsideredShearattheslicebaseisthemobilizedshear,

i.e.,R/Fos!FairlygoodforcepolygonclosurewiththeadditionoftheinterslicenormalforcesLEMforSlopestabilityanalysis!Bishop’ssimplifiedmethodX=Elf(x)=0 i.e.,l=0;Momentequilibrium.LEMforSlopestabilityanalysis!Janbu’ssimplifiedmethodIncludedinterslicenormalforces;Ignoredintersliceshearforces;Satisfiesverticalforceequilibriumforeachslice;Satisfiesonlyoverallhorizontalforceequilibrium,butnotoverallmomentequilibrium;Canbeusedforbothcircularandnon-circularfailuresurfacesLEMforSlopestabilityanalysis!Janbu’ssimplifiedmethod

LEMforSlopestabilityanalysis!Janbu’ssimplifiedmethodinterslicenormalforcesconsideredShearattheslicebaseisthemobilizedshear,

i.e.,R/Fos!BetterforcepolygonclosurethanBishop’sSimplifiedmethod.LEMforSlopestabilityanalysis!Janbu’ssimplifiedmethodX=Elf(x)=0 i.e.,l=0;Horizontalforceequilibrium.LEMforSlopestabilityanalysis!SpencermethodConsiderbothforceandmomentequilibrium;Constantintersliceshearandnormalforcesrelationship,i.e.,constantintersliceresultantforceangle;Canbeusedforbothcircularandnon-circularfailuresurfacesLEMforSlopestabilityanalysis!Spencermethod–derivation1

LEMforSlopestabilityanalysis!Spencermethod–derivation2

KnowingthatTistheactual/mobilizedshearresistancealongtheslope:

①②③

④Equilibriumsalong(x)andnormal(y)totheslope:

LEMforSlopestabilityanalysis!Spencermethod–derivation2SlopeStability:TheSpencerMethodofSlices|GOverallmomentequilibriumIftheoverallmomentwithrespecttothecenterofrotationiszero,thenthemomentoftheinternalintersliceforcesQmustalsobezero:

Inacircularfailuresurface,allradiiareequal,equation⑥canbesimplifiedas:⑤⑥

⑦

Afunctionofq,W,l,ai,candf.LEMforSlopestabilityanalysis!Spencermethod–derivation2SlopeStability:TheSpencerMethodofSlices|GOverallforceequilibriumThesumoftheinternalforcesoftheentireslidingmassintheverticalandthehorizontaldirectionmustbezero.Hence,twomoreequationsemerge:

SincetheinclinationofQisconstant,theabovetwoequationsareidenticalandbothyield:⑧⑨⑩

Afunctionofq,W,l,ai,candf.LEMforSlopestabilityanalysis!Spencermethod–derivation2

LEMfor