An analytical solution in probabilistic rock slope stability assessment based on random fields

An analytical solution for calculating the probability of failure of rock slopes against planar sliding is proposed. The method in based on the theory of random fields accounting for the influence of spatial variability on slope reliability. In this framework, both the cohesion and friction coefficient along a discontinuity are treated as Gaussian random fields which are fully described by their mean values (μc,μtanφ), standard deviations (σc,σtanφ), spatial correlation lengths (θc,θtanφ), and the parameters (ρc−tanφ,θc−tanφ) which account for the cross-correlation between cohesion and coefficient of friction. As shown by the examples presented herein, the spatial correlation of shear strength can have an important influence on slope performance expressed by the probability of failure. This is a significant observation, since ignoring the influence of spatial correlation in design may lead to unconservative estimations of slope reliability.