A Damping Modification Factor Prediction Model for Horizontal Displacement Spectrum from Subduction Slab Earthquakes in Japan Accounting for Site Conditions

Abstract

ABSTRACT A damping modification factor (DMF) model without source and path parameters is presented in this article for subduction slab earthquakes in Japan, using a similar dataset in the Zhao, Jiang, et al. (2016) study. Site classes based on site periods were used as the site-effect proxy. DMF models were derived from spectra of 13 damping ratios and 34 spectral periods, and the DMF can be calculated for any damping ratio between 1% and 30% and at any spectral period between 0.03 and 5.0 s. A simple fourth-order polynomial for the logarithm of the spectral periods and a simple quadratic function of the logarithm of damping ratios were used to model the effects of spectral periods and damping ratios, respectively. The model satisfies boundary conditions that require the DMF values equal to 1.0 at very short spectral periods; at long spectral periods, the DMFs for different damping ratios appear to converge to 1.0 to satisfy the constant displacement spectrum at long periods. Model standard deviations are smaller than those for the ground-motion prediction equations. All standard deviations vary linearly with the increasing logarithm of damping ratios. The DMFs presented in this study combined with the spectrum from the Zhao, Jiang, et al. (2016) study produce smoothed displacement spectrum that may be used for engineering designs. In a spectral period range of 0.2–3.0 s, the DMF values from this study are close to those by Daneshvar et al. (2016), but, at short periods, the difference is significant. The residual distribution suggests that DMFs also depend on earthquake source and path parameters. The model presented in this article does not include the effect of source and path variables so that this model can be used to scale a 5% damped spectrum without a known magnitude and a source distance.