Direct Probability Integral Method for Seismic Performance Assessment of Earth Dam Subjected to Stochastic Mainshock–Aftershock Sequences

Abstract

Studying the impact of mainshock–aftershock sequences on dam reliability is crucial for effective disaster prevention measures. With this purpose in mind, a new method for stochastic dynamic response analyses and reliability assessments of dams during seismic sequences has been proposed. Firstly, a simulation method of stochastic seismic sequences is described, considering the dependence between mainshock and aftershock based on Copula function. Then, a novel practical framework for stochastic dynamic analysis is established, combined with the improved point selection strategy and the direct probability integration method (DPIM). The DPIM is employed on a nonlinear system with one degree of freedom and compared with Monte Carlo simulation (MCS). The findings reveal that the method boasts exceptional precision and efficiency. Finally, the seismic performance of a practical dam was evaluated based on the above method, which not only accurately estimates the response probability distribution and dynamic reliability of the dam, but also greatly reduces the required calculations. Furthermore, the impact of aftershocks on dam seismic performance is initially evaluated through a probability approach in this research. It is found that seismic sequences will significantly increase the probability of earth dam failure compared with sequences of only mainshocks. In addition, the influence of aftershocks on reliability will further increase when the limit state is more stringent. Specifically, the novel analysis method proposed in this paper provides more abundant and objective evaluation indices, providing a dynamic reliability assessment for dams that is more effective than traditional evaluation methods.