Stochastic ground motion simulation considering fully non-stationary non-Gaussian characteristics and its applications in slope reliability assessment

With respect to evolutionary non-stationary processes, the underlying evolutionary power spectral density (EPSD) cannot be accurately calculated from the autocorrelation function (ACF). Efficient and accurate characterization of the non-Gaussianity and fully non-stationarity of ground motions is a difficult problem to be solved, and the stochastic response analysis of strongly nonlinear structures such as slopes under non-stationary non-Gaussian earthquakes does not provide clarity. In this paper, an efficient non-iterative approach for estimating the EPSD of the underlying Gaussian process built upon the unified Hermite polynomial Model (UHPM) is proposed. The proposed method eliminates the need for iterative procedures and avoids the need to solve integral equations, thereby improving computational efficiency, and the accuracy is validated through a typical case study. Proper orthogonal decomposition (POD) and Fast Fourier Transform (FFT) techniques are introduced, and efficient and accurate modelling of fully non-stationary and non-Gaussian random earthquakes is achieved. The Congress Street cut slope is employed as a numerical illustration and the slope stochastic dynamic stability assessment is conducted via the direct probability integral method (DPIM). The impact of the non-Gaussianity and non-stationarity of earthquakes on slope dynamic stability is studied for the first time. The analysis indicates that neglecting the non-Gaussian characteristics of earthquakes can cause an undervaluation of seismic slope stability, whereas the non-stationary characteristics can reduce seismic slope stability.