Quantification of the model uncertainty of limit equilibrium and finite element methods for undrained slopes

Abstract

Throughout history, many cases of failure in natural or man-made slopes have been reported. The possible instability of a slope is a major geologic hazard which necessitates the need for accurate slope stability methods. Published work on the reliability of slopes is geared towards modeling the impact of spatial variability of soil properties while neglecting the contribution of model uncertainty to the probability of failure. Model uncertainty is the uncertainty associated with the inability of a geotechnical model to fully represent the true physical behavior of a geotechnical system. It arises from unavoidable idealizations in analytical or numerical models for predicting engineering behavior. The main objective of this thesis is to quantify the model uncertainty of Limit Equilibrium Methods (Bishop, Ordinary Method of Slices, Janbu, and Spencer) and Finite Element Methods used for stability analysis of undrained slopes. To achieve this objective, 50 published historical failure cases of undrained slopes were compiled and modeled using Limit Equilibrium Methods and Finite Element Methods to assess the predictive performance of these models in estimating the factor of safety of the failed slopes. To investigate the effect of uncertainty due to spatial variability on the model predictions, the 50 failure cases were also modeled using random fields. This probabilistic analysis allowed for separating the effects of model uncertainty from those of spatial variability and allowed for quantifying for the first time the statistics that describe the uncertainty in predictions of Limit Equilibrium and Finite Element models for undrained slopes. The database of the historical cases was also used to investigate the existence of a lower-bound factor of safety and its effect on the probability of failure of slopes. Finally, design factors of safety are recommended to attain acceptable probabilities of failure for undrained slopes by combining the effect of the model uncertainty and spatial variability in a reliability-base