A method for locating critical slip surfaces in slope stability analysis: Discussion

Discussion 770 I have read this paper with interest since its subject matter pertains to our work in embankment dam engineering. As indicated in the paper, there are several procedures devised to locate a shear surface with the lowest factor of safety, and the author has presented one more and compared the results of his procedure with those of others; all based on the limit equilibrium method of slope stability analysis. The new results are about the same as the results previously reported by others. In an attempt to see how the results from a continuummechanics-based procedure will compare with those included in the paper, I made a quick analysis of the six problems using a commercially available computer program, FLAC (Itasca 1995). Also, I made an analysis of the problems using the limit-equilibrium-based slope stability analysis procedure SSTAB2 (Chugh 1992). Results of these analyses form the basis of this discussion. For Example 3, the values of effective internal friction angle, φ′, given in Table 1 of the paper are different from the values in the 1996 Greco paper; in fact they are a repeat of the numbers in the unit weight, γ, column. The values given in the 1996 Greco paper were used for results included in this discussion. For the Case 2 problem, Fig. 15 of the paper was scaled to obtain the data necessary for the analysis. In limit-equilibrium-based numerical procedures, the effectiveness of an automated search procedure depends on the successful performance of a nonlinear equation solver used to adjust trial values of factor of safety, F, and interslice force inclination, θ, to achieve a match between the computed and known values of boundary parameters at the other end of a shear surface. However, there is no assurance that the solution details associated with the critical shear surface thus found will necessarily be reasonable. These solution details are in terms of normal and shear forces at the base of slices, and interslice forces; their inclination and locations. Thus a search procedure which does not involve a criterion for an acceptable solution leaves the task of final selection of critical shear surface up to the user. There is no uniqueness in criteria for an acceptable solution to a slope problem by limit equilibrium procedures. For the location of interslice forces, some engineers prefer the middle third of the interslice boundary on the basis of linear distribution of normal stress, while others accept a solution in which interslice forces remain within the slide mass on the basis of nonlinear distribution of normal stress. Simi larly, when a soil has cohesive strength, some engineers are willing to accept a solution with tensile stresses that are con sistent with the magnitude of the cohesion value, while others consider the tensile strength of the soil to be zero and introduce a crack at the upper end of a shear surface. Inclination of interslice forces affects interslice shear forces. Some computer programs check for interslice shear failures, while others do not. Relying on a computed factor of safety without checking on the acceptability of the associated solution details is a mistake and should be discouraged. It would be helpful to know the criteria the author used in his work. Also, in limit equilibrium slope stability analysis, a search for critical shear surface should be preceded by analysis of shear surfaces of the engineers’ choosing. Such practices sharpen engineers’ skills to judge the path along which a sliding failure is likely, if one were to occur. Some of the shear surfaces included in the paper, especially those with long-drawn reverse curvatures at their exits, must be numerical constructs, as those geometries are unlikely to occur even in an ideal environment where the numerical model conditions could be duplicated, much less in nature. Thus, all of the slip surfaces attempted in the problems included in the paper must not have acceptable solution details. This should affect the final selection of an acceptable critical shear sur face. It would be helpful to know what nonlinear procedure the author used; the slope stability computer program in which he implemented his search procedure; his experiences with their use; and if he checked the computed solutions by examining the details for each shear surface obtained and what he found. Use of eq. [9] does not necessarily preclude occurrence of an unacceptable solution to a slope stability problem in general. Figures D1–D6 show the results of the problems using the continuum mechanics program FLAC. There are three parts to each figure: (a) shows the problem as modeled, (b) the convergence of trial factors of safety, and (c) the material

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