An analytical probabilistic analysis of slopes based on limit equilibrium methods

Probabilistic analysis of slopes has been used as an effective tool to evaluate uncertainty that is so prevalent in variables. In this paper, the jointly distributed random variables (JDRV) method is used as an analytical method to compare the reliability of four widely used limit equilibrium methods for slope stability analysis. These methods include the simplified Bishop, simplified Janbu, Morgenstern–Price, and Spencer’s methods. The selected stochastic parameters are angle of shearing resistance (φ), cohesion intercept (c), and unit weight (γ) of soil, which are modeled using a truncated normal probability distribution function. Geometric parameters such as height and angle of the slope relative to the horizontal are regarded as constant parameters. For reliability assessment, the reliability indices of the limit equilibrium methods for the critical surface with minimum factor of safety are determined by the particle swarm optimization (PSO) technique. It is shown that, among the assessed methods, the Janbu and Bishop methods are those with upper and lower probabilities of failure, respectively, in two conditions with and without considering cross correlation between c and φ.