Multivariate Distribution Models for Design Spectral Accelerations on Uniform Hazard Spectra

De-Yi Zhang(1*), Shun-Hao Ni(2), Hong-Yu Jia(3), Wei-Chau Xie(4), Mahesh D. Pandey(5)

(1) Department of Civil Engineering, University of Waterloo, Canada
(2) Department of Civil and Environmental Engineering, University of Waterloo, Canada
(3) Department of Civil Engineering, Southwest Jiaotong University, China
(4) Department of Civil and Environmental Engineering, University of Waterloo, Canada
(5) Department of Civil and Environmental Engineering, University of Waterloo, Canada
(*) Corresponding author


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Abstract


Uniform Hazard Spectra (UHS), a product derived from the scalar Probabilistic Seismic Hazard Analysis (PSHA), have many advantages over other spectra and have been widely used as design ground motions in the standard. However, it is often criticized that a UHS fails to represent a design spectrum induced by a single earthquake, and it is unable to provide any knowledge regarding the simultaneous exceedence of spectral accelerations at multiple vibration periods. Thus it is difficult to apply UHS directly in probabilistic seismic risk analysis and reliability-based seismic design of structures. To overcome this problem, a multivariate probability distribution model, which can represent the joint probability of exceedence of spectral accelerations on UHS, is derived and validated in this paper. Through analytical and numerical illustrations, it is observed that the multivariate lognormal distribution can be reasonably selected to model the joint distribution of spectral accelerations on UHS.
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Keywords


Probabilistic Seismic Hazard Analysis; Uniform Hazard Spectra; Multivariate Probability Distribution; Spectral Acceleration; Reliability-Based Seismic Design

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