Minimum rock bolt force and minimum static acceleration in tetrahedral wedge stability: A probabilistic study

An investigation of effect of variability of strength and orientation on stability of tetrahedral wedges with two free surfaces is presented. Study was limited to potential sliding along the line of intersection of the two joint planes. Minimum rock bolt force and minimum static acceleration were Considered as output stability parameters in this study. An analytical procedure which combines a deterministic analytical method and Monte-Carlo simulation technique was used to perform this study. Variability of orientations of the joint planes was modeled by the hemispherical normal distribution. Shear strength of the joint planes was modeled by the Mohr Coulomb criterion. Varability of shear strength parameters of the joint planes was modeled by the bivariate normal distributions. Effect of variability of orientation was found to be more pronounced than the effect of variability of strength on both output parameters. Variability of the magnitudes of the output parameters increased with decreasing correlation between the strength parameters of the Mohr Coulomb model. Effect of variability of cohesion was found to be more pronounced than the effect of variability of friction angle on the magnitude of both output parameters. The variabilities of the two output parameters were found to be significant in comparison to the introduced input parameter variabilities. The study shows clearly the importance of making allowances for these variabilities in rock slope design.