Element Failure Probability of Soil Slope under Consideration of Random Groundwater Level

Abstract

The instability of soil slopes is directly related to the shear parameters of the soil material and groundwater, which usually causes some uncertainty. In this study, a novel method, the element failure probability method (EFP), will be proposed to analyze the failure of soil slopes. Based on upper bound theory, finite element discretization, and stochastic programming theory, an upper bound stochastic programming model will be established by simultaneously considering the randomness of the shear parameters and groundwater level to analyze the reliability of slopes. The model will be solved using the Monte Carlo method based on the random shear parameters and groundwater levels. Finally, a formula will be derived for the EFP based on the safety factors and velocity fields of the upper bound method. The probability of a slope failure can be calculated using the safety factor, and the distribution of failure regions in space can be determined using the location information of the element. The proposed method will be validated using a classic example. This study could have theoretical value for further research that attempts to advance the application of plastic limit analysis to analyze slope reliability.