A perturbation method for upper bound analysis of stability of slopes based on rigid translational/rotational moving elements

Abstract

Collapse mechanisms consisting of translational or rotational rigid blocks are widely used as the basis for computing the upper bound on the factor of safety in slope stability problems. Constructing admissible velocities for these blocks mechanism often relies on experience, and optimizing these blocks can be cumbersome work, especially for layered slopes containing both hard and soft layers. In this paper, we present a numerical technique for evaluating and optimizing mechanisms composed of an arbitrary number of spline rigid translational/rotational moving elements, assuming plane strain material obeys the Mohr-Coulomb yield condition. In the proposed method, coordinates defining the nodes of the blocks are treated as unknowns, and the optimal geometry is found by successively perturbing node coordinates and block velocities, starting initially from a user-specified structured mesh. Two different definitions of the factor of safety are considered and the corresponding analysis procedures are introduced. The proposed method is applied to four examples related to slope stability analysis, and these examples illustrate that the proposed method is an efficient and reasonable way to analyze the stability of slopes.