A New Limit Equilibrium Analysis of Slope Stability Based on Lower-Bound Theorem

Abstract

This paper develops a new numerical procedure for the slope stability analysis, by combining the slice method in the limit equilibrium method with the lower-bound approach in the limit analysis method. The procedure provides an appropriate lower-bound solution subject to the collapse mechanism represented by a potential slip surface. First, the safety factor for the shear strength is calculated for the case in which the position of the slip surface is known beforehand. The problem is formulated as an optimization problem for finding a stress field which minimizes the safety factor within the limitations of satisfying the lower-bound conditions. The formulated problem is solved numerically by the mathematical programming technique. The obtained stress field appears physically reasonable. Several case studies have shown that the simplified Janbu method based on the critical slip surface tends to underestimate the safety factor on the safety side, compared with the lower-bound solution by the proposed procedure. Subsequently, the assumption used in each of the representative slice methods, which are necessary to render the stability problem to a statically determinate, is verified by the use of the stress field determined by the proposed procedure. Finally, a procedure for locating the critical noncircular slip surface which minimizes the safety factor within the lower-bound conditions is developed. Many important properties in the slope stability analysis are clarified through the development of this procedure.