Modeling dependence between shear strength parameters using Copulas and its effect on slope reliability

The influence of Copulas for modeling dependence between shear strength parameters on slope reliability is investigated. Firstly, four data sets of shear strength parameters in hydropower projects are collected. Then, the Akaike information criterion is adopted for identifying the best-fit Copula underlying the collected shear strength parameters. The formulae for probability of failure of an infinite slope using the direct integration are derived. Finally, an example of reliability analysis for the infinite slope is presented to demonstrate the influence of Copulas on the probability of slope failure. The results indicate that the Copulas have a significant influence on the probability of slope failure. The probabilities of slope failure produced by different Copulas may differ considerably. Such difference increases with increasing slope factor of safety (or decreasing probability of slope failure), increasing negative dependence between cohesion and internal friction angle and decreasing coefficient of variation of shear strength parameters. In addition, the Gaussian Copula is not the best-fit one for modeling the dependence structure underlying the shear strength parameters. If the Gaussian Copula is adopted, the probability of slope failure will be underestimated significantly. It is emphasized that the Gaussian Copula should not be adopted out of expedience without proper validation to model the dependence between the shear strength parameters.