Factor of safety of tetrahedral wedges: A probabilistic study

An investigation of the effect of variability of strength and orientation on the factor of safety of tetrahedral wedges with two free surfaces is presented. The study was limited to potential sliding along the line of intersection of the two joint planes. An analytical procedure which combines a deterministic analytical method and the Monte Carlo simulation technique was used to perform the study. Variability of orientations of the joint planes was modeled by the Fisher distributions. Shear strength of the joint planes was modeled by the Mohr Coulomb criterion. Variability of shear strength parameters of the joint planes was modeled by the bivariate normal distributions. The effect of variability of orientation was found to be more pronounced than the effect of variability of strength on the factor of safety. Variability of the factor of safety increased with decreasing correlation between the strength parameters, cohesion, c, and Internal friction angle, o. The effect of variability of c was found to be more pronounced than the effect of variability of o on the factor of safety. The propagated variabilities of the factor of safety due to the combination of orientation and strength variabilities were found to be very significant. The study clearly shows the importance of making allowances for these variabilities in rock slope design.