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

This article presents a damping modification factor (DMF) model without source and path parameters for subduction interface earthquakes in Japan using a similar dataset as the one used in the Zhao, Liang, et al. (2016) study. Site effect was modeled by site classes based on site periods. DMF models were constructed using the spectra for 13 damping ratios at 34 spectral periods. The DMF values can be calculated in a damping ratio range of 1%–30% and in a spectral period range of 0.03–5.0 s. The effect of damping ratios was modeled by a simple quadratic function of the damping ratios in the logarithm scale, and the effect of the spectral period was modeled by a simple fourth‐order polynomial of the spectral period also in the logarithm scale. The DMF value is 1.0 at a spectral period of $≤0.02s$ . At long periods $>5.0s$⁠, the DMFs for different damping ratios appear to converge to 1.0, satisfying the condition of constant displacement spectrum at long periods. For an extrapolation to $>5.0s$ for a damping ratio $<5%$⁠, $DMF=1.0$ can be selected when $DMF<1.0$⁠; for a damping ratio $>5%$⁠, $DMF=1.0$ can be selected when $DMF>1.0$⁠. For a damping ratio $<5%$⁠, all standard deviations decrease linearly with increasing damping ratios in the logarithm scale; for a damping ratio $>5%$⁠, all standard deviations increase linearly with increasing damping ratios in the logarithm scale. A smoothed displacement spectrum useful for engineering designs can be obtained by scaling the spectrum from Zhao, Liang, et al. (2016). The DMF values from this study are close to those of the published models at some spectral periods. The residual distribution suggests that DMFs are functions of earthquake source and path parameters.