Fuzzy-random reliability analysis of slope stability in anisotropic random fields

Spatial variability is the essential characteristic of the soil properties, which performs remarkable difference between the horizontal and vertical directions. In order to improve the traditional fuzzy-random reliability analysis methods which cannot deal with the spatial variability, a new method for slope fuzzy-random reliability analysis with reasonable consideration of the spatial variability is proposed. Firstly, the mean values of cohesion and friction angle are described by the normal fuzzy numbers and then randomly combined via cut set theory at different levels. Secondly, the corresponding reliability index of each parameter combination is calculated by the cooperation of finite element method and Monte-Carlo simulation under the anisotropic random fields of soil properties. And then, the total reliability index at each cut set level is obatined through a mathematical method. Finally, the fuzzy-random reliability index of the slope is achieved by the weighted average method. The illustration results show that the vertical-direction spatial variability has a more significant influence on fuzzy-random reliability of the slope, and ignoring the sptial variability of soil properties may also underestimate the probability of failure when the cohesion and the friction angle have great coefficients of variations. Moreover, the effect tendency of the correlation between the cohesion and the friction angle to failure probability is insensitive to the spatial variation of soil properties.