Dynamic Reliability Analysis of the Stability of the 3D Slope of a Rockfill Dam Based on the Copula Function and Generalized Probability Density Evolution Method

Rockfill strength parameters are important indicators of the stability of a rockfill dam slope. Therefore, a rational representation of the distribution characteristics of these parameters is extremely important to accurately assess the stability of the dynamic response and reliability of the three-dimensional (3D) slope of a rockfill dam. A joint distribution model of the rockfill strength parameters is constructed in this study using the copula function. In addition, a dynamic reliability analysis method for slope stability is proposed using a number-theoretical method and the generalized probability density evolution method (GPDEM). First, the method is validated by comparing the results for a numerical example with those obtained by Monte Carlo simulation (MCS). Second, the traditional and proposed joint distribution models are comparatively analyzed in terms of the dynamic response and reliability. Finally, the effect of the type of copula function on the dynamic reliability of the slope is investigated. The results show that the copula theory, the number-theoretical method, and the GPDEM provide an effective approach to analyze the dynamic response and reliability of slope stability. The randomness of rockfill strength parameters is sensitive to the safety factor of the slope stability of rockfill dams. The reliability analysis method can reasonably characterize the influence of strength parameter uncertainty on dam slope stability, which makes up for the deficiency of using a single safety measurement standard in the deterministic analysis method. The copula function can reasonably characterize the nonnormal distribution characteristics of rockfill strength parameters, improve the calculation accuracy of the slope stability reliability of rockfill dams, and provide an important scientific basis for the accurate safety assessment of dam slope stability. The type of copula function has an important impact on the dynamic reliability results for slope stability. Thus, it is extremely important to build a joint distribution model of rockfill strength parameters based on a rational selection of the optimal copula function.