Damping modification factor for the vertical seismic response spectrum: A study based on Japanese earthquake records

Abstract

This paper aims to establish a regional (Japanese) damping modification model for scaling the 5%-damped vertical seismic response spectra to other damping ratios. In doing so, 3198 strong vertical ground motion (VGM) records are selected from the Japanese seismic database, and their linear elastic response spectra are computed by the Newmark-β algorithm. Taking the 5%-damped vertical response spectra as benchmarks, the vertical spectral damping modification factors (DMFV) for ζ (damping ratio) = 0.5%, 1%, 2%, 3%, 4%, 6%, 7%, 8%, 9%, 10%, 12.5%, 15%, 17.5%, 20%, 25%, 30%, 35% and 40% are calculated. For structural design purpose, the DMFVs of both the vertical pseudo acceleration response spectra and the vertical absolute acceleration response spectra are calculated. The DMFV spectra have their peaks (for ζ < 5%) or valleys (for ζ > 5%) at T = 0.12 s (here T indicates spectral period), and their values get farther away from unity as earthquake magnitude or VGM epicenter distance increases. The effect of earthquake hypocenter depth, local site condition (represented by Vs30) and peak ground acceleration on DMFV generally shows no pattern. For each ζ, the mean DMFV-lgT curves are simulated by highly accurate piecewise functions. Moreover, it is revealed that the normal distribution model is feasible for representing the probabilistic properties of DMFV, especially in the short-to-medium period region where the skewness of the DMFV distribution is not quite pronounced. The standard deviations of DMFV are modeled by piecewise functions as well, yet it is emphasized that the variation of a damping-scaled spectral ordinate is jointly controlled by the probabilistic properties of DMFV and the uncertainties of the 5%-damped spectral ordinates.