A Damping Modification Factor Prediction Model for Horizontal Displacement Spectrum from Shallow Crustal and Upper-Mantle Earthquakes in Japan Accounting for Site Conditions

This article presents damping modification factors (DMFs) for the horizontal component of the strong-motion records generated by the shallow crustal and upper-mantle earthquakes in Japan. This model can be used to scale a 5% damped design spectrum that does not associate with a known magnitude and rupture distance to obtain a design spectrum with the desirable damping ratios. Our previous study suggested that the site effect on DMF was significant, and we used site class as the site-effect parameter. We used a quadratic function of damping ratio in a natural logarithm scale to model the effect of damping ratios and we used fourth-order polynomials of the natural logarithm spectral period to present the effect of the spectral period when the spectral period is over 0.06 s. The between-event, betweensite, and within-site standard deviations can be described by the linear function of the damping ratio in a natural logarithm scale. The between-event standard deviations are smaller than the within-event standard deviations and the between-site standard deviations are less than the within-site ones at many spectral periods. Reasonable displacement spectra can be obtained by using the DMF model from this study to scale the 5% damped displacement spectra. The differences in the DMF values from the three types of earthquakes are moderate at many spectral periods and the predicted DMF values from this study are similar to those from other studies at some spectral periods, but the differences are considerable at the other spectral periods. The variation trend of the DMF values suggests that the predicted DMF values may reach the theoretic value of 1.0 at some spectral periods over 5.0 s. Residual distribution analysis suggested that the bilinear function of magnitude and fault-top depth can be used in a model for scenario earthquakes.