Dimension-reduction representation of stochastic ground motion fields based on wavenumber-frequency spectrum for engineering purposes

Abstract

It is of great necessity to achieve the efficient and accurate representation of ground motion fields considering the spatial variation of which possess paramount importance to the seismic safety and reliability evaluation of lifeline systems. To circumvent the difficulties caused by the decomposition of cross power spectral density (PSD) matrix and the interpolation between discretized spatial points in the spectral representation method (SRM) for uni-dimensional multi-variate (1D-nV) stochastic vector process (regarded as discrete stochastic field), a wavenumber-frequency SRM (WSRM) for simulating multi-dimensional uni-variate (mD-1V) spatial-temporal stochastic field (regarded as continuous stochastic field) has been developed for years. In this paper, an updated WSRM (UWSRM), which can reduce the number of elementary random variables, is proposed for simulating the 2D-1V stochastic ground motion fields. Compared with the conventional WSRM (CWSRM) which belongs to the Monte Carlo simulation schemes, merely two elementary random variables are required to realize the precise modeling of ground motion fields. For the sake of facilitating the calculation, the UWSRM embedded in the Fast Fourier Transform (FFT) technique is applied to simulate the stochastic ground motion fields. Numerical results including the comparison of the accuracy and efficiency with the CWSRM verify the effectiveness of the UWSRM. Moreover, to illustrate the application prospect of the UWSRM, the refined random seismic response analysis of a buried pipeline network is implemented by combining with the probability density evolution method (PDEM). The analysis results preliminarily demonstrate the applicability of the UWSRM in lifeline systems.