FREDLUND边坡稳定的未来.pptVIP

What is the Future for Slope Stability Analysis? (Are We Approaching the Limits of Limit Equilibrium Analyses?) Dr. Delwyn G. Fredlund University of Saskatchewan, Canada Second Symposium and Short Course on Unsaturated Soils and Environmental Geotechnics Budapest, Hungary November 4-5, 2003 Introduction qLimit Equilibrium methods of slices have been “Good” for the geotechnical engineering profession since the methods have produced financial benefit qEngineers are often surprised at the results they are able to obtain from Limit Equilibrium methods So 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 critical slip surface must be found by TRIAL and ERROR SHAPE and LOCATION are the driving force for a paradigm shift Objectives of this Presentation: qTo show the gradual change that is emerging in the way that slope stability analyses can be undertaken qTo illustrate the benefits associated with improved procedures for the assessment of stresses in a slope Outline of Presentation qProvide a brief Summary of common Limit Equilibrium methods along with their limitations (2-D 3-D of GLE Shape and Location Become Even More Difficult to Define in 3-D Two Perpendicular Sections Through a 3-D Sliding Mass Section Parallel to MovementSection Perpendicular to Movement Free Body Diagram of a Column with All Interslice Forces Parallel Perpendicular Base Interslice Force Functions for Two of the Directions X/EV/P First Step Forward Question: qIs the Normal Stress at the base of 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 Computations Fredlund and Scoular 1999 Limit equilibrium and finite element normal stresses for a toe slip surface From limit equilibrium analysis From finite element analysis Limit equilibrium and finite element normal stresses for a deep-seated slip surface From finite element analysis From limit equilibrium analysis Limit equilibrium and finite element normal stresses for an anchored slope From finite element analysis From limit equilibrium analysis qTo illustrate procedures for combining a finite element stress analysis with concepts of limiting equilibrium. (i.e., finite element method of slope stability analysis) qTo compare results of a finite element slope stability analysis and conventional limit equilibrium methods Using Limit Equilibrium Concepts in a Finite Element Slope Stability Analysis Objective: qThe 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 Hypothesis Assumption: The stresses computed from “switching-on” gravity are more reasonable than the stresses computed on a vertical slice Manner of “Importing Stresses” from a Finite Element Analysis into a Limit Equilibrium Analysis s n Finite Element Analysis for Stresses Limit Equilibrium Analysis s n tm Mohr Circle tm IMPORT: Acting Normal Stress Actuating Shear Stress Limit Equilibrium Analysis Finite Element Analysis for Stresses qBishop (1952) - stresses from Limit Equilibrium methods do not agree with actual soil stresses qClough and Woodward (1967) - “meaningful stability analysis can be made only if the stress distribution within the structure can be predicted reliably” qKulhawy (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 Stability Stress Level Rezendiz 1972 Zienkiewicz et al 1975 Strength G stage “i+1“stage “i“ lij lij f t tfij ij j s ij t ij q k ij s ij t Element (ij) Element (ij) R = Resisting Shear Strength: S = Actuating Shear Stress Fs = ( Shear Strength) / (Actuating Shear Stress) Difficult to Difficult to minimize !minimize ! = D-= n i iisfi LFG 1 )(tt dLFG s B A f )(tt-= = -= n i isi SFRG 1 )( Actuating Shear Forces and Resisting Shear S = Actuating Shear Stress R = Resisting Shear Strength = =D= ne ij ijij ne ij ijiii l S L S 11 tt = =D= ne ij ijf ne ij ij i fi lRLR iji 11 tt ij b ijwaijaij ne ij iji luuucRtan)(tan)( 1 s-+-+= = Definition of “Optimal Function“ : Minimum Value of “Return Function“ = the optimal function obtained at point k of stage i+1, = the optimal function obtained at point j in stage i, and = the return function calculated when passing from the state point j in stage i to the state point k in stage i+1. where: Introduce an “optimal function”, H = Optimal Function G = Return Function = -= n i isi SFRGG 1 min )(minmin )( jH i ),()()( 1 kjGjHkH iii += + )( 1 kH i+ )(jHi ),( kjG i Boundary Conditions of “Optimal Function“ At the initial stage, (i=1) : At the final stage, ( i = n+1) : where: = the number of state points in the final stage H = Optimal Function 0)( 1 =jH 1 .1 NP j = ),()()( 1 kjGjHkH nnn += + = + -= n i isimn SFRGkH 1 1 ).()(.1= n+1 NPk 1+n NP The Minimum (or Optimal) Travelling Time Problem DYNAMIC PROGRAMMING SOLUTION 1 1 6 48 7 511 114 12 1 H1 (1) = 0 9 2 7 4 7 H1(1) =13 A H (2)= 8 123 10 B 5674 STAGE NUMBER 1234567 d=(4, 2) 3 G (1,2) = 3 3 10 52 43 25 2 8 2 7 22441 55 32 BA THE MINIMUM TRAVELLING TIME PROBLEM Analytical Scheme of the Dynamic Programming Method Entry point “1“ “Initial A B point“ Y “State point“ .i i+1.XB B “n+1“X .Stage No. “Exit point“ Si “Grid element“ boundary“ “Searching ii+1 k Searching grid j Ri “Final point“j k Kinematical Restriction 5 S6 R S R 3 S R5 4 4 R S2 2 3 B R6 S R S1 1 A X Y R1 1 S R 22 S i SiR R n S n . . Kinematical Restriction Ri ii+1 k j Si Eliminated = 0.33 DYNPROG = 1.02 Enhanced = 1.13 Bishop; M-P = 1.17 Distance, m Elevation, m Example of a Homogeneous Slope Example of a Homogeneous Slope = 0.33 DYNPROG = 1.02 Bishop; M-P = 1.17 Enhanced = 1.13 Example of a Homogeneous Slope = 0.33 Factor of SafetyFactor of Safety Stability Coefficient, C/Stability Coefficient, C/g g H H = 0.48 Factor of SafetyFactor of Safety Stability Coefficient, C/Stability Coefficient, C/g g H H Example of a Homogeneous Slope Example of a Homogeneous Slope = 0.33 = 0.48 Factor of Safety,Factor of Safety, DYNPROGDYNPROG Factor of Safety,Factor of Safety, Morgenstern-PriceMorgenstern-Price = 0.33 Distance, m Elevation, m Bishop; M-P = 1.64 Enhanced = 1.62 DYNPROG = 1.49 Example of a Partially Submerged Slope Example of a Partially Submerged Slope = 0.33 Enhanced = 1.62 Bishop; M-P = 1.64 DYNPROG = 1.49 Example of a Multilayered Slope Enhanced = 1.10 M-P = 1.14 DYNPROG = 0.96 Distance, m Elevation, m The Re-Analysis of the Lodalen Slide = 0.48 DYNPROG = 0.975 Bishop = 1.00 Actual Actual Enhanced = 0.997 The Re-Analysis of the Lodalen Slide = 0.38 Enhanced = 1.02 Bishop = 1.00 DYNPROG = 0.997 Actual Distance, m Elevation, m Actual DYNPROG = 1.18 Distance, m Elevation, m Example Problem Involving the Search for a Convex Critical Slip Surface Along a Weak Clay Layer Solution of the Concave Slip Surface Problem Using Slope/W Once the Critical Slip Surface has been Defined Elevation, m Distance, m Slope / W = 1.196 Conclusions from Step 2 Forward qThe Shape of the critical slip surface can be made part of the solution qThe critical slip surface can be irregular in shape but must be kinematically admissible qNo assumptions is required regarding the Location of the critical slip surface which is defined