Vulnerability-Based Economic Loss Rate Assessment of a Frame Structure Under Stochastic Sequence Ground Motions - Zheng Zhang; Yunmu Jiang; Zixin Liu (Buildings)
Modeling mainshock–aftershock ground motions is essential for seismic risk assessment, especially in regions experiencing frequent earthquakes. Recent studies have often employed Copula-based joint distributions or machine learning techniques to simulate the statistical dependency between mainshock and aftershock parameters. While effective at capturing nonlinear correlations, these methods are typically black box in nature, data-dependent, and difficult to generalize across tectonic settings. More importantly, they tend to focus solely on marginal or joint parameter correlations, which implicitly treat mainshocks and aftershocks as independent stochastic processes, thereby overlooking their inherent spectral interaction. To address these limitations, this study proposes an explicit and parameterized modeling framework based on the evolutionary power spectral density (EPSD) of random ground motions. Using the magnitude difference between a mainshock and an aftershock as the control variable, we derive attenuation relationships for the amplitude, frequency content, and duration. A coherence function model is further developed from real seismic records, treating the mainshock–aftershock pair as a vector-valued stochastic process and thus enabling a more accurate representation of their spectral dependence. Coherence analysis shows that the function remains relatively stable between 0.3 and 0.6 across the 0–30 Rad/s frequency range. Validation results indicate that the simulated response spectra align closely with recorded spectra, achieving R2 values exceeding 0.90 and 0.91. To demonstrate the model’s applicability, a case study is conducted on a representative frame structure to evaluate seismic vulnerability and economic loss. As the mainshock PGA increases from 0.2 g to 1.2 g, the structure progresses from slight damage to complete collapse, with loss rates saturating near 1.0 g. These findings underscore the engineering importance of incorporating mainshock–aftershock spectral interaction in seismic damage and risk modeling, offering a transparent and transferable tool for future seismic resilience assessments.