Rock Wedge Stability Analysis Using System Reliability Methods

Summary We present a system reliability approach to rock wedge stability analysis. Different failure modes are considered, and a disjoint cut-set formulation is employed – with each cut-set corresponding to a different failure mode – to explore the system aspects of the problem, so that the reliability of the system is assessed by computing the probability of failure of the slope under each failure mode. An example case is used to demonstrate different approaches to compute the reliability of the slope design. Our results show that an approximation to the “exact” probability of failure – given by Monte Carlo simulation results – may be obtained using a first order approximation to the failure domain, and that linear programming techniques may be used to obtain bounds of the probability of failure. Furthermore, we identify the most likely failure mode, and we explore the sensitivity of the computed probabilities to changes in the random variables considered. The results indicate that the reliability results are quite sensitive to the geometry of the wedge. Changes in water conditions are also found to have a significant impact on the computed probabilities, while changes in unit weight of the rock have a considerably smaller effect on the reliability.