Slope Stability Analysis: Generalized Approach

Abstract

Limit equilibrium analysis of slope stability is comprised of two coupled problems: kinematical (i.e., find the critical slip surface) and statical (i.e., assure the existence of global equilibrium at the defined limit state). Determination of the general‐shaped critical slip surface can be attained by available optimization techniques where the minimal factor of safety is sought. However, since the problem is statically indeterminate, assumptions are necessary. The available general methods suggests the wide variety of possible statical assumptions. Consequently, there might be a question whether the critical results are indeed critical. The presented method, which is a generalization of Baker and Garber's approach, attempts to avoid statical assumptions by using a variational technique to minimize the safety factor. The variational analysis results in an ordinary differential equation that describes the normal stress distribution over a slip surface. Solving this equation numerically, and substituting the resulting stress into the global limiting equilibrium equations for the sliding body, one can determine the factor of safety corresponding to the user's specified slip surface. The general‐shaped slip surface is left to be varied, as done in other rigorous limit equilibrium methods, until a feasible surface that renders the absolute minimum factor of safety is located. To enable the application of the presented generalized method, a numerical scheme is proposed. The solutions to three example problems, involving complex slopes, soil profiles, and total and effective stress analyses, are presented in detail. These examples provide insight as to the method's performance.