Mining Publication: Applications of the Point Estimation Method for Stochastic Rock Slope Engineering
The point estimation method can be applied to the safety factor (SF) equation for any specified rock slope failure mode (such as plane shear, step path, or wedge) to obtain reliable estimates of the mean and standard deviation of the SF probability distribution. A gamma probability density function is recommended for modeling this probability distribution, because it allows only for positive values and is flexible enough to provide symmetrical shapes and right-skewed, exponential-type shapes for the SF distribution. The mean and standard deviation define this distribution, which then can be integrated numerically from 0 to 1 to obtain the probability of sliding, PS (portion of the SF distribution where SF < 1.0). The overall probability of failure, PF, for the potential slope failure mass is the joint probability that the rock discontinuities are long enough to allow kinematic failure (PL) and that sliding occurs along the rock discontinuities (PS); that is, PF = PSPL. This method for estimating the probability of sliding is extremely efficient computationally, and thus, expedites slope stability simulation routines used by NIOSH software to stochastically describe rock slope behavior and assist the engineer in designing catch benches for large rock slopes. Enhanced bench design translates into increased operational efficiency and safer working conditions in open pit mines and quarries.