Shaking Table Test-Based Verification of PDEM for Random Seismic Response of Anchored Rock Slopes

This study systematically verified the applicability and accuracy of the Probability Density Evolution Method (PDEM) in the probabilistic modeling of the dynamic response of anchored rock slopes under random seismic action through large-scale shaking table model tests. Across 144 sets of non-stationary random ground motions and 7 sets of white noise excitations, key response data such as acceleration, displacement, and changes in anchor axial force were collected. The PDEM was used to model the instantaneous probability density function (PDF) and cumulative distribution function (CDF), which were then compared with the results of normal distribution, Gumbel distribution, and direct sample statistics from multiple dimensions. The results show that the PDEM does not require a preset distribution form and can accurately reproduce the non-Gaussian, multi-modal, and time evolution characteristics of the response; in the reliability assessment of peak responses, its prediction deviation is much smaller than that of traditional parametric models; the three-dimensional probability density evolution cloud map further reveals the law governing the entire process of the response PDF from “narrow and high” in the early stage of the earthquake, “wide and flat” in the main shock stage, to “re-convergence” after the earthquake. The study confirms that the PDEM has significant advantages and engineering application value in the analysis of random seismic responses and the dynamic reliability assessment of anchored slopes.