System reliability approach to rock slope stability

A systematic quantitative methodology for the reliability analysis of stability of rock slopes is presented. A sliding mass resting on an inclined plane and composed of two blocks separated by a vertical tension crack is considered, and a disjoint cut-set system formulation is proposed, with each cut-set corresponding to a different failure mode of the slope. Methods for the evaluation of the system reliability problem are discussed and applied to solve an example problem. Monte Carlo simulation method may be used to obtain the “exact” solution, at the expense of a higher computational cost, while methods based on first order approximations are found to be computationally efficient and to provide information of interest for the design process, but they are also shown not to be particularly accurate in some cases. The results also show that reliability bounds based on linear programming provide a flexible way of estimating the range of possible failure probabilities, and that accurate estimations of the probability of failure are obtained when sufficient information is considered.