A Study On The Modelling Of Damping Modification Factors For The Acceleration Spectrum From Subduction Interface Earthquake

China is located at the intersection of two major seismic belts in the world,the Pacific seismic belt,and the Himalayan seismic belt.How to carry out scientific and effective seismic design is an important subject in the civil engineering field.The response spectrum method is widely used in seismic design guidelines.However,most of the response spectrum is usually established based on a damping ratio of 5%,which cannot be used to design a structure with damping ratios other than 5%.The damping modification factor(DMF)can be used to adjusts the response spectrum with a damping ratio of 5%to the response spectrum with the desired damping ratio.The subduction zone is geologically active and produces abundant earthquakes.These earthquakes can be divided into groups according to the hypocenter location.Recent studies suggested that different types of earthquakes in a subduction zone may affect the DMF values and a separate DMF model may be required for each type of subduction earthquakes.In this study.a DMF model will be developed for subduction interface earthquakes.The acceleration response spectra of 3,552 records from 76 earthquakes obtained at the KiK-net and K-NET strong-motion stations in Japan were used.In order to model the site effect on the DMF model,recording stations were divided into four site classes.A fixed effects method and a random effects method were used to build a DMF model.A fixed effects method was used to fit the average of the DMF values in each site class to establish a simple model that has only two variables:a damping ratio and a spectral period.To avoid error propagation from one damping ratio to another,model coefficients were determined in two steps by a fixed effects method,i.e.,the coefficients for damping ratios were derived first and these coefficients for the spectral periods were derived in the second step.The effect of damping ratios was modeled by the third-order polynomials of the logarithm of normalized damping ratios;the fourth-order polynomials of the logarithm of spectral periods to model the effect of periods.These functions met to boundary conditions,i.e.DMF=1.0 when a spectral period is very small and DMF=1.0 when the damping ratio is 5%.The total,between-and within-event residuals,and standard deviations were obtained by using a random effects model;the within-event residuals and standard deviation were further separated into the between-site and the within-site components.The model residuals and standard deviations were evaluated,and the influences of magnitude,fault depth,and source distance on the model were investigated.When the damping ratio is less than 5%,the DMF values increase first and then decrease with increasing spectral periods.When the damping ratio is greater than 5%,the DMF values decrease first and then increase with increasing spectral periods.DMF tends to increase when the damping ratio is high and the damping ratio is long.At short periods,the within-event standard deviations are greater than the between-event standard deviation.The within-event standard deviations are smaller than the between-event standard deviation for long periodsUsing between-event residual analyses,the effects of magnitude and source depth can be examined and the function types for correcting any bias can be determined.The depth influence on the residual distribution for the shallow differs from those of the deep earthquakes.A fixed effects regression method was used to derive the coefficients for the added magnitude and depth terns.Based on the bias of within-site residual distributions,a correction function distance can be designed and coefficients of the geometric attenuation term and the anelastic attenuation term can be derived by a fixed effects regression can be derived.Because the regression analyses were obtained in a step-by-step manner,a constant term was added to correct the errors accumulated in each step of the regression analyses.All coefficients were derived by a fixed effects model for each damping ratio and site periods.These computed values for the source and path terms were then fitted to a model to the functions that are similar to those of the simple model.With these smoothed model coefficients,a function of spectral periods and damping ratios similar to those of the simple model was used to model the effects of damping ratios and spectral periods for the terms for magnitude,fault depth,and source distance.Extensive residual analyses were performed and any biased distributions of residuals were corrected to the best possible level.As expected,the between standard deviations of the full model are much smaller than those of the simple model by as much as 0.4 in the natural logarithm scale,suggesting that the full model is much more accurate than the simple model.The within-site and between-site standard deviations of the full model are similar to those of the simple model at short periods and are smaller than those of the simple model at long spectral periods.A DMF model for the damping modification factor based on the strong-motion records obtained in the subduction zone of Japan was established in this study.In the future,based on this model,A DMF model based on the ground-motion records in China may be established.