Probability analysis of rock slope with nonlinear plane failure

Abstract

Abstract The reliability of a rock slope is a main focus in the slope design to avoid landslide that is a significant threat to lives, architecture, and roads. Traditionally, the nonlinear shear strength of the majority of geotechnical materials has been neglected in favor of using the linear Mohr-Coulomb strength criterion to assess the reliability of a rock slope. The paper proposes an improved probability method to estimate the reliability of rock slopes. A novel analytical method to determine the safety factor of slopes with plane failure is derived based on the nonlinear strength criterion. Furthermore, an analytical method based on two-dimensional random field theory is proposed to determine the local mean value of a random variable on the failure surface, which can consider the spatial variability of shear strength, avoiding the random field simulation. The mean-value first-order second-moment method is adopted in combination with the proposed analytical methods to quantify the failure probability of rock slopes. To quickly search the minimum reliability index βmin, a dichotomy search method is proposed. The validity of the proposed method is demonstrated in two cases.