Cross-Correlation Analysis of the Stability of Heterogeneous Slopes

Geologic material properties of hillslopes are inherently heterogeneous, with complex layering structures due to geological deposition processes. Lacking detailed sampling of the properties’ spatial distribution has led to the stochastic representation of the properties to address uncertainty in the hillslope stability evaluation. This study treats the spatial distributions of the shear strength parameters, the cohesion (c), and the internal friction angle (φ), in a synthetic two-dimensional slope as stochastic random fields characterized by their means, variances, and correlation scales. This study then evaluates the cross-correlation between these parameters and the factor of safety (FS) using unconditional Monte Carlo simulation (MCS). Different from classical sensitivity analyses, the cross-correlation analysis of FS and the stochastic parameter fields stresses the importance of the orientation of the large-scale geological layering, the correlation between the geological media’s cohesion, and the internal friction angle at the local scale on the probability and uncertainty of failure of the heterogeneous hillslope. The analysis further guides the field sampling strategy to reduce uncertainty in the slope stability analysis due to unknown heterogeneity. More importantly, it suggests the location of stability reinforcement measures. The results of this study provide cost-effective tools for geoengineers to deal with field slope stability analysis under uncertainty.