| Ground-motion prediction equations(GMPEs)for displacement response spectrum play an important role in determining the deterministic displacement design spectrum and a probabilistic seismic hazard analysis.The displacement spectrum in many design codes and the spectrum from existing GMPEs are usually based on a damping ratio of 5%.However,many types of structures have a damping ration larger than 5%,because of either added damping devices or nonlinear structural response.Other types of structures such as the cables in the cable-stayed bridges have very small damping ratios.In the design for these structures,damping correction factors derived from strong-motion records are used to scale the 5% damped spectrum to obtain the design spectrum for an appropriate damping ratio.The use of empirical functions for damping correction factors brings more uncertainties.Therefore,it is important to develop GMPEs for displacement response spectra with different damping ratios.In this study,5,595 ground motion records from the shallow crustal and upper mantle earthquakes obtained by the Ki K-net and K-NET strong-motion networks in Japan were used.Based on these records,GMPEs for displacement response spectrum with 14 damping ratios in a range of 1-30% were developed for 36 spectral periods in a range of 0.01 to 5.0s,accounting for nonlinear site effect.A random effects regression method was used together with residual analyses and statistical tests.The GMPEs contain two magnitude terms,geometric and anelastic attenuation rates,the volcanic path attenuation rate,the style-of faulting,et ct.The results of statistical analyses suggest that only the magnitude term for events with an MW≤7.1,geometric and anelastic attenuation rates,and site terms vary with damping ratios whereas the coefficients of the other terms,including the focal mechanisms,magnitude terms for events with MW>7.1,and depth terms are independent of the damping ratios.Following conclusions can be reached.(1)At a very short period up to 0.04 s,all model coefficients,including the magnitude terms,distance attenuation rates and site terms are the same for all damping ratios,consistent with theoretical results,i.e.the response of a stiff structure does not depend on damping ratios;(2)At short spectral periods up to 0.16 s,the effect of damping ratios on the magnitude term is small.At spectral periods over 0.16 s,the coefficients for the magnitude term decrease with increasing damping ratios and the reduction rates increase with increasing spectral periods;(3)The effect of damping ratios on attenuation rates:(a)at the period range over 0.04 s,the absoulte values of geometric spreading rate increase with increasing damping ratio;(b)in the spectral period range of 0.04-0.6s,the attenuation rates vary with damping ratios considerably.The absolute values for the anelastic attenuation rates and volcanic distance anelastic attenuation rates decrease with increasing damping ratios,at spectral periods over 0.6s,the effect of damping ratios is not large.(4)The effect of damping ratios on site class terms:(a)in the spectral period range for SC I sites,the site class terms for SC II,III,and IV sites have a trough and the coefficients decrease with decreasing damping ratios.(b)At the spectral period ranges close to the site period ranges for SC II,III,and IV sites,the site terms have peak values that increase with decreasing damping ratios;and(c)at spectral periods over the average site period,the coefficients for the site terms increase with increasing damping ratios by a small amount;(5)Using random effects models,residuals were separated in between-and within-event parts and the within-event residual were separated into between-and within-site parts.The results show that:(a)the total and within-event standard deviations decrease with increasing damping ratios,(b)at all spectral periods between-event standard deviations are smaller than the within-event standard deviations,suggesting that the modeling of source effect is better than for the path and site effects;(6)Nonlinear response affect the displacement spectrum significantly.For an MW 7.5 event at a source distance of 10 km,the nonlinear response can reduce the elastic site spectrum at a SC IV site by as much as 25% at short spectral periods;(7)Using residual distributions with different model terms,the evaluation of the predicted spectrum for different values of various model variables and comparison with other models,the GMPEs for displacement spectrum presented in this thesis and the model standard deviations are also are reasonable. |
