Vulnerability-Based Economic Loss Rate Assessment of a Frame Structure Under Stochastic Sequence Ground Motions
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...
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MDPI AG
2025-07-01
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| author | Zheng Zhang Yunmu Jiang Zixin Liu |
| author_facet | Zheng Zhang Yunmu Jiang Zixin Liu |
| author_sort | Zheng Zhang |
| collection | DOAJ |
| description | 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 R<sup>2</sup> 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. |
| format | Article |
| id | doaj-art-120bfa82907a481c8b07cdfb89a2914d |
| institution | Kabale University |
| issn | 2075-5309 |
| language | English |
| publishDate | 2025-07-01 |
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| spelling | doaj-art-120bfa82907a481c8b07cdfb89a2914d2025-08-20T03:36:03ZengMDPI AGBuildings2075-53092025-07-011515258410.3390/buildings15152584Vulnerability-Based Economic Loss Rate Assessment of a Frame Structure Under Stochastic Sequence Ground MotionsZheng Zhang0Yunmu Jiang1Zixin Liu2Heilongjiang Institute of Technology, School of Economics and Management, Hongqi Avenue, Harbin 150050, ChinaState Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116000, ChinaKey Laboratory of Building Collapse Mechanism and Disaster Prevention, Institute of Disaster Prevention, China Earthquake Administration, Sanhe 065201, ChinaModeling 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 R<sup>2</sup> 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.https://www.mdpi.com/2075-5309/15/15/2584mainshock–aftershock ground motionsattenuation relationshipspectral coherenceeconomic loss assessmentvulnerability analysis |
| spellingShingle | Zheng Zhang Yunmu Jiang Zixin Liu Vulnerability-Based Economic Loss Rate Assessment of a Frame Structure Under Stochastic Sequence Ground Motions Buildings mainshock–aftershock ground motions attenuation relationship spectral coherence economic loss assessment vulnerability analysis |
| title | Vulnerability-Based Economic Loss Rate Assessment of a Frame Structure Under Stochastic Sequence Ground Motions |
| title_full | Vulnerability-Based Economic Loss Rate Assessment of a Frame Structure Under Stochastic Sequence Ground Motions |
| title_fullStr | Vulnerability-Based Economic Loss Rate Assessment of a Frame Structure Under Stochastic Sequence Ground Motions |
| title_full_unstemmed | Vulnerability-Based Economic Loss Rate Assessment of a Frame Structure Under Stochastic Sequence Ground Motions |
| title_short | Vulnerability-Based Economic Loss Rate Assessment of a Frame Structure Under Stochastic Sequence Ground Motions |
| title_sort | vulnerability based economic loss rate assessment of a frame structure under stochastic sequence ground motions |
| topic | mainshock–aftershock ground motions attenuation relationship spectral coherence economic loss assessment vulnerability analysis |
| url | https://www.mdpi.com/2075-5309/15/15/2584 |
| work_keys_str_mv | AT zhengzhang vulnerabilitybasedeconomiclossrateassessmentofaframestructureunderstochasticsequencegroundmotions AT yunmujiang vulnerabilitybasedeconomiclossrateassessmentofaframestructureunderstochasticsequencegroundmotions AT zixinliu vulnerabilitybasedeconomiclossrateassessmentofaframestructureunderstochasticsequencegroundmotions |