Simplified risk assessment for a spatially variable undrained long slope

This paper develops a novel method for predicting the failure probability (p(t)) of a spatially variable undrained long slope. The method can also predict the length (b(e)) and volume (V-a) of the sliding mass of the undrained long slope. The proposed novel method adopts a revised Vanmarcke's method to obtain preliminary solutions, and regression equations are applied to correct the biases of the preliminary solutions to obtain the corrected solutions. It is found that the corrected (p(r), b(e), V-r) solutions are close to the reference solutions computed by a more rigorous method. The effectiveness of the proposed novel method is demonstrated through numerical examples and a real case study.