Source-Based Stochastic Response Analyses of Structures Using a Seismological Fourier Amplitude Spectral Model

Most existing power spectral models used in structural stochastic response analyses only account for site effects through parameters such as fundamental period and damping ratio. However, these site-based models lack an explicit consideration of seismic source and path characteristics, which are inherently critical factors. With the accumulation of knowledge and advancements in seismic exploration technologies in recent decades, detailed seismic source information has become increasingly accessible, making it now both desirable and feasible to conduct stochastic response analyses that integrate not only site conditions but also source and path effects. Therefore, this study proposes an end-to-end analytical framework that simultaneously accounts for source, path, and site effects to efficiently compute the structural stochastic responses, thereby achieving direct prediction from specific seismic source conditions to structural responses. The proposed framework employs a source-based Fourier amplitude spectrum (FAS) model coupled with a ground motion duration model to represent the entire seismic wave propagation process, which has been thoroughly investigated and validated using real seismic records. The FAS parameters can be adjusted to simulate specific seismic sources of interest in earthquake engineering. Then, analytical formulations are derived for the stochastic response analyses of widely used multiple-degree-of-freedom structural systems in the frequency domain, which also supports time-domain stochastic response analysis by converting FAS into time series. Finally, the proposed method is applied to a series of numerical examples for reliability analysis, and the results are validated against time-domain analyses, demonstrating the applicability and accuracy of the method under varying seismic source conditions.