Multiple response surfaces for slope reliability analysis

This paper develops a multiple response surfaces approach to approximate the limit state function for slope failure by second-order polynomial functions, to incorporate the variation of the most probable slip surfaces, and to evaluate the slope failure probability p(f). The proposed methodology was illustrated through a cohesive soil slope example. It is shown that the p(f) values estimated from multiple response surfaces agree well with those p(f) values that have been obtained by searching a large number of potential slip surfaces in each Monte Carlo simulation (MCS) sample. The variation of number of the most probable slip surfaces is studied at different scale of fluctuation () values. It is found that when full correlation assumed for each of random fields (i.e., spatial variability is ignored), the number of the most probable slip surfaces is equal to the number of random fields (in this study, it is 3). When the spatial variability grows significantly, the number of the most probable slip surfaces or number of multiple response surfaces firstly increases evidently to a higher value and then varies slightly. In addition, the contribution of a specific most probable slip surface varies dramatically at different spatial variability level, and therefore, the variation of the most probable slip surfaces should be accounted for in the reliability analysis. The multiple response surfaces approach developed in this paper provides a limit equilibrium method and MCS-based means to incorporate such a variation of the most probable slip surfaces in slope reliability analysis. Copyright (c) 2014 John Wiley & Sons, Ltd.