Probabilistic stability analysis of block toppling failure in rock slopes

Abstract A probabilistic model for the analysis of the block toppling failure in rock slopes is described in the present paper. The 2-D limit equilibrium analysis of rock blocks, resting on a stepped failure surface is carried out including both a Monte-Carlo simulation procedure and Markov Chains theory. Accounting for the variability of selected input parameters describing the joints in a rock mass, a number of possible failure paths are generated. For each path, the statistical distribution of the interaction forces is calculated. In both cases, use is made of a Monte-Carlo simulation. Then, by concepts of Markov Chains theory, the probability of failure of one or more rock blocks is assessed. Two examples are discussed. The first is intended to show an idealized slope design problem; the second is a practical application to an open-cast operation, where the stability conditions needed to be assessed. It is shown how the probabilistic model can also be used as an aid in deciding on stabilization procedures.