Analytical stochastic analysis of rock wedge stability using a JDRV method considering the residual factor as a random variable

摘要

The stability of a rock wedge is one of the main failure models of rock slopes. Although the strength parameters of the discontinuity planes are commonly deemed to be between the peak and residual strengths, the effect of a residual factor on the stability of a rock wedge still has not been considered. This paper presents an analytical stochastic method, considering the residual factor as a random variable, for determining the stability of a rock wedge. First, based on the Hoek–Bray method, this paper derives the formulas for evaluating the wedge stability in terms of the residual factor, and then, based on a jointly distributed random variables (JDRV) method, the calculation formulas for the probability distribution function of the safety factor is established. In the analytical method, the friction angle and cohesion are selected to satisfy the truncated normal distribution, and the residual factor is assumed to obey the generalized beta distribution. The study of a typical rock wedge shows that the results of the analytical method and the Monte Carlo simulation are almost consistent. Besides, it is also shown that the residual factor has a substantial influence on the estimation accuracy of the failure probability of the wedge.