《FREDLUND边坡稳定的未来.ppt》由会员分享，可在线阅读，更多相关《FREDLUND边坡稳定的未来.ppt（91页珍藏版）》请在taowenge.com淘文阁网|工程机械CAD图纸|机械工程制图|CAD装配图下载|SolidWorks_CaTia_CAD_UG_PROE_设计图分享下载上搜索。
1、What is the Future for Slope Stability Analysis?(Are We Approaching the Limits of Limit Equilibrium Analyses?)Dr.Delwyn G.FredlundUniversity of Saskatchewan,CanadaUniversity of Saskatchewan,CanadaSecond Symposium and Short Course on Second Symposium and Short Course on Unsaturated Soils and Environm
2、ental GeotechnicsUnsaturated Soils and Environmental GeotechnicsBudapest,HungaryBudapest,HungaryNovember 4-5,2003November 4-5,2003Introduction qqLimit Equilibrium methods of slices have been“Good”for the geotechnical engineering profession since the methods have produced financial benefit qqEngineer
3、s are often surprised at the results they are able to obtain from Limit Equilibrium methodsSo Why Change?There are Fundamental Limitations with Limit Equilibrium Methods of Slices?The boundaries for a FREE BODY DIAGRAM are not known-The SHAPE for the slip surface must be assumed-The LOCATION of the
4、critical slip surface must be found by TRIAL and ERRORSHAPE and LOCATION are the driving force for a paradigm shiftObjectives of this Presentation:qqTo show the gradual change that is emerging in the way that slope stability analyses can be undertakenqqTo illustrate the benefits associated with impr
5、oved procedures for the assessment of stresses in a slopeOutline of PresentationqqProvide a brief Summary of common Limit Equilibrium methods along with their limitations(2-D&3-D)qqTake the FIRST step forward through use of an independent stress analysisqqTake the SECOND step forward through use of
6、Optimization TechniquesIs a Limit Equilibrium Analysis an Upper Bound or Lower Bound Solution?qqLimit Equilibrium Methods primarily satisfy the requirements of an upper bound type of solutionReason:the shape of slip surface is selected by the analyst and thereby a displacement boundary condition is
7、imposedLimit Equilibrium and Finite Element Based Methods of AnalysesWWWWWWWWNLimit EquilibriumMethod of AnalysisSm=t ta dldls sndlFinite Element Based Method of Analysisldt ta dlQUESTION:How can the Normal Stress at the base of a slice be most accurately computed?Consider the Free Body Diagrams use
8、d to calculate the Normal Stress?Assumption for all Limit Equilibrium AnalysisqqSoils behave as Mohr-Coulomb materials(i.e.,friction,(i.e.,friction,and cohesion,c),and cohesion,c)qqFactor of safety,Fs,for the cohesive component is equal to the factor of safety for the frictional componentqqFactor of
9、 safety is the same for all slices()msnsSFuFc=-+b b s sb btanSummary of Available Equations Associated with a Limit Equilibrium AnalysisqqEquations(knowns):Quantityl lMoment equilibriumnl lVertical force equilibriumnl lHorizontal force equilibriumnl lMohr-Coulomb failure criterionn4nqqUnknowns:Unkno
10、wns:Quantity Quantityl lTotal normal force at base of slice Total normal force at base of slice n nl lShear force at the base of slice,Shear force at the base of slice,S Smmn nl lIntersliceInterslice normal force,E normal force,En-1n-1l lIntersliceInterslice shear force,X shear force,Xn-1n-1l lPoint
11、 of application of Point of application of intersliceinterslice force,E force,E n-1n-1l lPoint of application of normal forcePoint of application of normal forcen nl lFactor of safety,FFactor of safety,Fs s1 1 6n-26n-2Summary of Unknowns Associated with a Limit Equilibrium AnalysisOne FOne Fs s per
12、sliding mass per sliding massForces Acting on Each SliceFocus on SmbyxSmXREREXLSlip surfaceGround Ground surfacesurfaceWhRN=s snb bb bfNLPhreatic linePhreatic lineMobilized Shear Force,Sm forSaturated-Unsaturated Soils()()swasansmFuuFuFcSb b b b s sb bbtantan-+-+=Only new variable required for solvi
13、ng saturated-unsaturated soils problems is the shear force mobilized b b =Friction angle with respect to matric suction=Friction angle with respect to matric suctionu ua a=Pore-air pressure=Pore-air pressureu uww =Pore-water pressure=Pore-water pressure qqMoment equilibrium,Fm:qqForce equilibrium,Ff
14、:-+=NfWxtanRtantanuNR cFbwm b bb b -+=a aa a b ba ab bsincostantantancosNuNcFbwfPore-air pressures are assumed to be zero gaugeqqNormal force at base of slice:qqLimit Equilibrium methods differ in terms of how(XR-XL)is computed and overall statics satisfiedqqLimit Equilibrium problem is indeterminat
15、e:l lCan apply an assumption Can apply an assumption(Historical solution)(Historical solution)l lCan utilize additional physics Can utilize additional physics(Future solution)Future solution)()FFuFcXXWNbwLRtansincostansinsin a aa a a ab ba ab b+-=s sxbaArea=Interslice normal force(E)width of slice,b
16、 bs sxt txys syDistance(m)Elevation(m)t txybaArea=Interslice shear force(X)Vertical sliceDistance(m)Elevation(m)=baxydyXt t=baxdyEs sStresses on the Boundary Between SlicesMorgenstern&Price,1965Summary of Limit Equilibrium Methods and AssumptionsMethod Equilibrium Satisfied Assumptions Ordinary Mome
17、nt,to base E and X=0 Bishops Simplified Vertical,Moment E is horizontal,X=0 Janbus Simplified Vertical,Horizontal E is horizontal,X=0,empirical correction factor,f0,accounts for interslice shear forces Janbus Generalized Vertical,Horizontal E is located by an assumed line of thrust Spencer Vertical,
18、Horizontal,Moment Resultant of E and X are of constant slope Forces Acting on One Slice in Ordinary or Conventional MethodhWbb ba aN=s bN=s b nN NSmForces Acting on One Slice in Bishops Simplified and Janbus Simplified Methods hWbb ba aN=s bN=s b nN NSmERELSummary of Limit Equilibrium Methods and As
19、sumptionsDirection of Direction of X X and and E E is the is the average of the ground surface average of the ground surface slope and the slope at the base of slope and the slope at the base of a slicea sliceVerticalVerticalHorizontalHorizontalLowe and Lowe and KarafiathKarafiathDirection of Direct
20、ion of X X and and E E is parallel to is parallel to the groundthe groundVerticalVerticalHorizontalHorizontalCorps of Corps of EngineersEngineersDirection of Direction of E E and and X X is defined by is defined by an arbitrary function.Percent of an arbitrary function.Percent of the function requir
21、ed to satisfy the function required to satisfy moment and force equilibrium is moment and force equilibrium is called called VerticalVerticalHorizontalHorizontalMomentMomentMorgenstern-Morgenstern-Price,GLEPrice,GLEAssumptionsAssumptionsEquilibriumEquilibriumSatisfiedSatisfiedMethodMethod Forces Act
22、ing on One Slice in Spencers,Morgenstern-Price,andGLE Methods hWbb ba aN=s bN=s b nN NSmERELXRXLVarious Interslice Force FunctionsProposed byMorgenstern&Price(1965)SpencersWilson and Fredlund(1983)Used a finite element stress analysis(with gravity switched on)to determine a shape for the Interslice
23、Force FunctionInterslice Force Function Interslice Force Function for a Deep-seated Slip for a Deep-seated Slip Surface Through a 1:2 Surface Through a 1:2 SlopeSlopeX=E f(x)Definition of Dimensionless Distance f(x)is largest at mid-pointInflection points near crest&toeGeneralizedGeneralizedFunction
24、alFunctionalShapeShapewhere:K=magnitude of function at mid-slopee =base of natural logC=variable to define inflection pointn=variable to define steepness=dimensionless x-position()2/)(nnCKexfw w-=Wilson and Fredlund,1983X=E f(x)Dimensionless DistanceDimensionless DistanceUnique function of“slope ang
25、le”for all slip surfaces“C”coefficient versus slope angleUnique function of“slope angle”for all slip surfaces“n”coefficient versus tangent of slope angleComparison of Factors of Safety Circular Slip Surface00.20.40.61.801.851.901.952.002.052.102.152.202.25l lJanbus GeneralizedSimplified BishopSpence
26、rMorgenstern-Pricef(x)=constantOrdinary=1.928FfFmFredlund and Krahn1975Factor of safetyMoment and Force Limit Equilibrium Factors of SafetyFor a Circular typeslip surfaceMoment limit equilibrium analysisForce limit equilibrium analysisFredlund and Krahn,1975Lambda,l l Factor of safetyForce and Momen
27、tLimit equilibriumFactors of Safety for a planar toe slip surfaceForce limit equilibrium analysisMoment limit equilibrium analysisLambda,l l Factor of safetyKrahn 2003Force and MomentLimit equilibrium Factors of Safety for a composite slip surfaceMoment limit equilibrium analysisForce limit equilibr
28、ium analysisLambda,l l Factor of safetyFredlund and Krahn 1975Force and MomentLimit equilibrium Factors of Safety for a“Sliding Block”type slip surfaceMoment limit equilibrium analysisForce limit equilibrium analysisLambda,l l Factor of safetyKrahn 2003Extensions of Methods of Slices toThree-dimensi
29、onal Methods of ColumnsqqHovland(1977)3-D of OrdinaryqqChen and Chameau(1982)3-D of Spencer qqCavounidis(1987)3-D Fs 2-D FsqqHungr(1987)3-D of Bishop SimplifiedqqLam and Fredlund(1993)3-D with f(x)on all 3 planes;3-D of GLEShape and Location Become Even More Difficult to Define in 3-DTwo Perpendicul
30、ar Sections Through a 3-D Sliding MassSection Parallel to MovementSection Perpendicular to MovementFree Body Diagram of a Column with All Interslice ForcesParallelPerpendicularBaseInterslice Force Functions for Two of the DirectionsX/EV/PFirst Step ForwardQuestion:qIs the Normal Stress at the base o
31、f each slice as accurate as can be obtained?qIs the Normal Stress only dependent upon the forces on a vertical slice?Improvement of Normal Stress ComputationsFredlund and Scoular1999Limit equilibrium and finite element normal stresses for a toe slip surfaceFrom limit equilibrium analysisFrom finite
32、element analysisLimit equilibrium and finite element normal stresses for a deep-seated slip surfaceFrom finite element analysisFrom limit equilibrium analysisLimit equilibrium and finite element normal stresses for an anchored slopeFrom finite element analysisFrom limit equilibrium analysisqqTo illu
33、strate procedures for combining a finite element stress analysis with concepts of limiting equilibrium.(i.e.,finite element method of slope stability analysis)qqTo compare results of a finite element slope stability analysis and conventional limit equilibrium methods Using Limit Equilibrium Concepts
34、 in a Finite Element Slope Stability AnalysisObjective:qqThe complete stress state from a finite element analysis can be“imported”into a limit equilibrium framework where the normal stress and the actuating shear stress are computed for any selected slip surface HypothesisAssumption:The stresses com
35、puted from“switching-on”gravity are more reasonable than the stresses computed on a vertical sliceManner of“Importing Stresses”from a Finite Element Analysis into a Limit Equilibrium Analysis s snFinite Element Analysis for StressesLimit Equilibrium Analysiss snt tmMohr Circlet tmIMPORT:Acting Norma
36、l StressActuating Shear StressLimit Equilibrium AnalysisFinite Element Analysis for StressesqqBishop(1952)-stresses from Limit Equilibrium methods do not agree with actual soil stresses qqClough and Woodward(1967)-“meaningful stability analysis can be made only if the stress distribution within the
37、structure can be predicted reliably”qqKulhawy(1969)-used normal and shear stresses from a linear elastic analysis to compute factor of safety“Enhanced Limit Strength Method”Background to Using Stress Analyses in Slope StabilityStress LevelRezendiz 1972Zienkiewicz et al 1975Strength&Stress LevelAdika
38、ri and Cummins 1985Enhanced limit methods(finite element analysiswith a limit equilibriumFinite Element Slope Stability MethodsDirect methods(finite element analysis only)Strength LevelKulhawy 1969F -Z=1313 D DD DLLfs ss ss ss s F=(c +tan)-c +tanA 1313 s s s ss ss ss ss s D D D DL Lf*F=(c +tan )K s
39、s t tD D D DLLDefinition of Factor of SafetyLoad increaseto failureStrength decreaseto failureanalysis)Differences and Similarities Between the Finite Element Slope Stability and Conventional Limit Equilibrium qqDifferencesl lSolution is determinatel lFactor of safety equation is linearqqSimilaritie
40、sl lStill necessary to assume the shape of the slip surface and search by trial and error to locate the critical slip surfaceWhy hasnt Finite Element Slope Stability Method been extensively used?qqDifficulties and perceptions related to the stress analysisqqInability to transfer large amounts of dat
41、a and find needed information Now:Microcomputer have dramatically changed our ability to combine Finite Element and Limit Equilibrium analysesDefinition of Factor of Safety qqKulhawy(1969)qqwhere:l lSr=resisting shear strength or l lSm=mobilized shear force =mrFEMSSFb b s stan)u(cSwnr-+=Actuating Sh
42、earActuating ShearNormal StressNormal StressAnalysis Study Undertaken by Fredlund and Scoular(1999)qqAdopted the Adopted the KulhawyKulhawy(1969)(1969)procedure procedureqqUsed Sigma/W and Slope/W Used Sigma/W and Slope/W qqPoissons ratio range=0.33 to 0.48Poissons ratio range=0.33 to 0.48qqElastic
43、modulus,E=20,000 to 200,000 Elastic modulus,E=20,000 to 200,000 kPakPaqqCohesion,c=10 to 40 Cohesion,c=10 to 40 kPakPaqqFriction,Friction,=10 to 30 degrees=10 to 30 degreesqqCompared Compared conventional Limit Equilibrium conventional Limit Equilibrium results with Finite Element slope stability re
44、sults with Finite Element slope stability results results Location of Center of a Section along the Slip Surface within a Finite Element Analysisxyx-Coordinatey-CoordinateSlip SurfaceFinite Element(r,s)srFictitious slice defined withthe Limit Equilibrium analysisCenter of the base of a slice(x,y)Pre
45、sentation of Finite Element Slope Stability Results qqConditions Analyzed:l l Dry slopel l Piezometric line at 3/4 height,exiting at toel l Dry slope,partially submergedl l Piezometric line at 1/2 height and submerged to mid-heightSelected 2:1 Free-Standing Slope with a Piezometric Line Exiting at t
46、he Toe of the Slope20406080100120204060800CrestPiezometric LineToe21x-Coordinate (m)Note:Dry slope with&without piezometric liney-Coordinate (m)Selected 2:1 Partially Submerged Slope with a Horizontal Piezometric Line at Mid-Slope20406080100120204060800CrestToe21x -Coordinate (m)WaterPiezometric Lin
47、ey -Coordinate (m)Note:Dry slope with&without piezometric line050100150200250300203040506070 x-Coordinate(m)Acting and restricting shear stress(kPa)CrestToeShear StrengthShear ForcePoisson Ratio,m m=0.33Shear Strength and Shear Force for a 2:1 Dry Slope Calculated Using the Finite Element Slope Stab
48、ility MethodLocal and Global Factors of Safety for a 2:1 Dry Slope012345672025303540455055606570 x-CoordinateFactor of SafetyCrestToeLocal F(m mLocal F(m m=0.33)Bishop Method,F=2.360=2.173Global Factors of SafetyBishop 2.360Janbu 2.173GLE(F.E.function)2.356Fs(m m=0.33 )2.342Fs(m m=0.48 )2.339Ordinar
49、y 2.226sJanbu Method,FsssFs=2.342Fs=2.339=0.48)Factors of Safety Versus Stability Number for a 2:1 Dry Slope as a Function of c 0.00.51.01.52.02.50510152025Stability Number,g g Htan /c Factor of Safetyc =20kPac =10kPac=40kPaFs(m m =0.33)Fs(m m =0.48)Fs(GLE)2:1 Dry Slope Factor of Safety Versus Stabi
50、lity Coefficient for a 2:1 Dry Slope as a Function of 0.00.51.01.52.02.50.000.020.040.060.080.100.12Stability Coefficient,c /g g H Factor of Safety =30 =10 =202:1 Dry SlopesFs(m m =0.33)F(m m =0.48)Fs(GLE)sFactor of Safety Versus Stability Coefficient as a Function of for 2:1 Slope with a Piezometri