Reliability analysis of slope with cross-correlated spatially variable soil properties using AFOSM

Efficient approaches for slope reliability computation with spatially variable soil properties are of great interest. In this paper, an advanced first-order second-moment method (AFOSM) combined with the limit equilibrium method (LEM) is adopted for efficient slope reliability analysis considering cross-correlated random fields of shear strength parameters. In the slope reliability analysis, random fields of the soil shear strengths are locally discretized along the slip surface. A systematic framework is presented for constructing a full correlation matrix incorporating both autocorrelation and cross correlation for the shear strength parameters in multiple soil layers, which could be useful for multi-layered slope reliability analysis involving cross-correlated spatially variable soil properties. A single-layered c–φ slope and a two-layered c–φ slope are investigated to illustrate and validate the proposed approach. As regards the examples, parametric studies show that slope reliability decreases with an increase in the autocorrelation distance and the cross-correlation coefficient between c and φ. Moreover, the effect of the vertical autocorrelation distance on the slope reliability is much more significant than that of the horizontal autocorrelation distance. The directly searched minimum reliability indices are all smaller than those computed with the deterministic critical slip surface. The slope reliability indices are affected by the number of slices, however, if a sufficient number of slices are used to represent the random field, increasing the number of slices does not significantly affect the reliability indices. The AFOSM is quite efficient for slope reliability analysis with spatially variable soil properties and its accuracy is satisfactory compared to the MCS. Although only a two-layered slope is considered in the illustrative example for convenient demonstration and easy understanding, the AFOSM is generally applicable to slopes with multiple soil layers.