Probability density evolution method for seismic displacement-based assessment of earth retaining structures

Earthquakes have damaged many earth-retaining structures worldwide, causing much loss of life and property as well as disrupting traffic. To assess the seismic performance of earth-retaining structures in earthquake-prone areas, a new probabilistic methodology is proposed, namely the probability density evolution method (PDEM). As a novel dynamic reliability method based on random vibration theory, PDEM combines stochastic dynamic analysis with current advanced deterministic methods. Not only does PDEM give the dynamic reliability of the global system of a structure, it also gives the probability density function and its evolution characteristics of the seismic response of interest. A tie-back wall is chosen as the type of earth retaining structures with which to show the feasibility of the method. After stochastic ground motions are generated by stochastic ground motion model, a series of deterministic seismic responses of the tie-back wall are obtained by the finite-element method. The PDEM is then used to obtain the stochastic seismic responses and the dynamic reliability of the system. Finally, the seismic performance of the tie-back wall is assessed using performance indices and displacement-based criteria selected from standards and the literature. High efficiency and accuracy of the PDEM is verified by comparing its results with those from Monte Carlo simulations. Not only can this novel method give more objective indices than can traditional evaluation methods, it can also provide a reference for the performance-based seismic analysis and design of geotechnical engineering structures.