Probabilistic Analysis of Step-Shaped Slopes Using Random Field Models

AbstractStep-shaped slopes are often found in mines. The reliability of step-shaped slopes was investigated based on random field models. The factor of safety of slopes was derived by the horizontal and vertical integration methods. Meanwhile, the cohesion and friction angle along the discontinuity failure surface were treated as random variables that were assumed to follow Gaussian random distribution. The effects of spatial correlation and cross-correlation between parameters on the stability of step-shaped slopes were taken into consideration. A closed-form solution for the probability of failure (Pf) of step-shaped slopes was finally derived. It was found that the derived Pf was greatly affected by the input spatial correlation length of geomechanical parameters. The effectiveness of the proposed method was validated using Monte Carlo simulations.