Probabilistic Slope Stability Analysis Based on the Upper Bound Theorem

This paper presents a probabilistic numerical approach for stability analysis of soil and rock slopes. The slope is divided into a family of inclined slices, and according to the upper bound theorem in plasticity theory, a work-energy balance equation is constructed for each soil/rock slice. Geotechnical parameters such as the cohesion, the friction angle and the pore pressure ratio etc. are modelled as random variables, and the factor of safety is treated as a functional of these random parameters. By using Winner´s polynomial chaos expansion, the random safety factor is solved through a stochastic optimization process. Comparing to conventional deterministic limit equilibrium methods, the proposed probabilistic approach has the advantage of accurately estimating not only the safety factor and the critical failure surface but also the failure probability of the slope.