Abstract: The commonly used approximation for evaluating the correlation coefficients between failure modes has a certain degree of error. This paper uses Pearson correlation coefficient to characterize the correlation between different slope failure mechanisms. Based on the correlation coefficients calculated from two different methods, this paper studies the effect of soil spatial variability on correlation coefficients between failure modes, the number of failure modes of a slope and the bimodal bounds of system failure probability. A brief introduction to risk aggregation method aiming at selecting representative slip surfaces, and Ditlevsen’s formulas for calculating bimodal bounds of system failure probability is presented. A single-layered and a two-layered slopes are studied to evaluate applicability of the approximation correlation coefficients. The results show that the commonly used approximation correlation coefficients cannot reflect the effect of soil spatial variability on correlation between failure modes, whereas the Pearson correlation coefficients can. When the spatial variability of soil properties is weak, there is large discrepancy between approximation correlation coefficients and Pearson correlation coefficients. Too many representative slip surfaces are selected and the representative failure modes cannot be reflected effectively based on approximate correlation coefficients. Furthermore, the upper-bound limit of system failure probability calculated by approximation correlation coefficients is probably greater than 1, and the bimodal bounds of system failure probability are too wide, all of these make system failure probability become meaningless. By contrast, the calculated bimodal bounds of system failure probability based on Pearson correlation coefficients are narrower, showing the changes of system failure probability effectively.

Key words: slope, spatial variability, correlation coefficient, failure mode, system failure probability