An analytical solution for reliability assessment of pseudo-static stability of rock slopes using jointly distributed random variables method

Abstract

Reliability analysis of rock slope stability has received considerable attention in the literature. It has been used as an effective tool to evaluate uncertainty so prevalent in variables. In this research the application of the jointly distributed random variables method for probabilistic analysis and reliability assessment of rock slope stability with plane sliding is investigated. In a recently published paper, the authors showed the dependency of the numerator and denominator of the safety factor relationship and argued that, as a result of this dependency, the method could not assess the reliability correctly. In the current research the authors present a new approach to solve this problem. In this approach, using the basic relations in this method, the safety factor relationship is obtained directly without separation of its numerator and denominator. Furthermore, in addition to friction angle of sliding surface, apparent cohesion, depth of water in tension crack, and earthquake acceleration ratio, in the present work the unit weight of rock is also considered as a stochastic parameter. The results are compared with the Monte Carlo simulation. Comparison of the results indicates good performance of the proposed approach for assessment of reliability. The new results of parametric analysis using the jointly distributed random variables method show that the friction angle of sliding surface is the most effective parameter in rock slope stability with plane sliding.