Copula-based approaches for evaluating slope reliability under incomplete probability information

• Slope reliability under incomplete probability information is highlighted.
• Three copula-based approaches are proposed to evaluate slope reliability.
• Probabilities of slope failure produced by different copulas differ considerably.
• Global and local dispersion factors increase with decreasing probability of failure.
• Copula-based approaches can effectively reduce dispersion in probability of failure.

Slope reliability under incomplete probability information is a challenging problem. In this study, three copula-based approaches are proposed to evaluate slope reliability under incomplete probability information. The Nataf distribution and copula models for characterizing the bivariate distribution of shear strength parameters are briefly introduced. Then, both global and local dispersion factors are defined to characterize the dispersion in probability of slope failure. Two illustrative examples are presented to demonstrate the validity of the proposed approaches. The results indicate that the probabilities of slope failure associated with different copulas differ considerably. The commonly used Nataf distribution or Gaussian copula produces only one of the various possible solutions of probability of slope failure. The probability of slope failure under incomplete probability information exhibits large dispersion. Both global and local dispersion factors increase with decreasing probability of slope failure, especially for small coefficients of variation and strongly negative correlations underlying shear strength parameters. The proposed three copula-based approaches can effectively reduce the dispersion in probability of slope failure and significantly improve the estimate of probability of slope failure. In comparison with the Nataf distribution, the copula-based approaches result in a more reasonable estimate of slope reliability.