Influence of cross correlation between soil parameters on probability of failure of simple cohesive and c-φ slopes

This paper focuses on the calculation of probability of failure of simple unreinforced slopes and the influence of the magnitude of cross correlation between soil parameters on numerical outcomes. A general closed-form solution for cohesive slopes with cross correlation between cohesion and unit weight was investigated and results compared with cases without cross correlation. Negative cross correlations between cohesion and friction angle and positive cross correlations between cohesion and unit weight, and friction angle and unit weight were considered in the current study. The factors of safety and probabilities of failure for the slopes with uncorrelated soil properties were obtained using probabilistic slope stability design charts previously reported by the writers. Results for cohesive soil slopes and positive cross correlation between cohesion and unit weight are shown to decrease probability of failure. Probability of failure also decreased for increasing negative cross correlation between cohesion and friction angle, and increasing positive correlation between cohesion and unit weight, and friction angle and unit weight. Probabilistic slope stability design charts presented by the writers in an earlier publication are extended to include cohesive-frictional (c-phi) soil slopes with and without cross correlation between soil input parameters. An important outcome of the work presented here is that cross correlation between random values of soil properties can reduce the probability of failure for simple slope cases. Hence, previous probabilistic design charts by the writers for simple soil slopes with uncorrelated soil properties are conservative (safe) for design. This study also provides one explanation why slope stability analyses using uncorrelated soil properties can predict unreasonably high probabilities of failure when conventional estimates of factor of safety suggest a stable slope.