ROCKTOPPLE: A spreadsheet-based program for probabilistic block-toppling analysis

Uncertainty and variability are inherent in the input parameters required for rock slope stability analyses. Since in the 1970s, probabilistic methods have been applied to slope stability analyses as a means of incorporating and evaluating the impact of uncertainty. Since then, methods of probabilistic analysis for planar and wedge sliding failures have become well established in the literature and are now widely used in practice. Analysis of toppling failure, however, has received relatively little attention. This paper introduces a Monte Carlo simulation procedure for the probabilistic analysis of block-toppling and describes its implementation into a spreadsheet-based program (ROCKTOPPLE). The analysis procedure considers both kinematic and kinetic probabilities of failure. These probabilities are evaluated separately and multiplied to give the total probability of block toppling. To demonstrate the use of ROCKTOPPLE, it is first verified against a published deterministic result, and then applied to a practical example with uncertain input parameters. Results obtained with the probabilistic approach are compared to those of an equivalent deterministic analysis in which mean values of input parameters are considered.