Determination of Critical Slope Failure Surfaces

The analysis of the stability of slopes using limit equilibrium methods usually requires the determination of the critical failure surface having the minimal factor of safety. This paper presents an optimization technique, adapted from operations research, to determine both the minimal factor of safety and the associated critical failure surface. The technique treats the factor of safety as an optimal function of the N geometrical coordinates defining potential admissible failure surfaces, and searches for the optimum by a reflection algorithm through an N‐dimensional space defined by these geometrical coordinates. Application of the technique, as illustrated by examples, revealed that in comparison with the popularly known grid search method, the technique yields lower values of the minimal factor of safety for fewer computations, and is suitable for virtually all types of failure surfaces.