Probabilistic assessment of response spectra for multiple damping levels in seismic hazard analysis

The response spectra for specific recurrence periods are typically constructed for a 5 % damping ratio based on probabilistic seismic hazard analysis (PSHA). Nevertheless, practical structures exhibit a range of damping characteristics, requiring response spectra at various damping levels. Commonly, a damping modification factor (DMF) is applied to adjust the 5 %-damped spectra derived from PSHA to other damping levels. Most DMF formulations, however, are developed solely through the regression analysis of seismic records, overlooking the consistency of the recurrence period of the response spectra before and after adjustment. A direct probabilistic analysis of the response spectra across different damping ratios provides a more reasonable solution, although it typically needs multiple ground motion prediction equations (GMPEs) for each damping level or, alternatively, the application of a DMF to adjust the 5 %-damped GMPE. However, many recent studies have highlighted the difficulty of directly constraining the scaling of the response spectra within GMPEs via seismological theory. To address this issue, this study proposes a new framework for conducting a probabilistic analysis of the response spectra across multiple damping ratios. The framework estimates site-specific response spectra for various damping ratios using a single GMPE for the Fourier amplitude spectrum (FAS) combined with a ground-motion duration model. Because the FAS is more closely related to the physics of wave propagation, its scaling within GMPEs is easier to constrain using seismological theory. Furthermore, the moment method, in conjunction with Latin hypercube sampling, is applied to calculate the exceedance probability for response spectra with any damping ratio, thereby obtaining the corresponding seismic hazard curves. The proposed framework was verified and compared with traditional approaches using a numerical example. The proposed framework enables the acquisition of response spectra for distinct recurrence periods at any desired damping ratio while eliminating the need to construct multiple GMPEs for various damping ratios or to develop DMF models.