Damping Modification Factor For Displacement Spectrum From Subduction Earthquakes In Japan

Damping modification factor(DMF)is the ratio between the response spectrum with an appropriate damping ratio and the 5% damped spectrum,and it is important to estimate the response spectrum for the design of structures with damping ratios other than 5%.The design spectra from many seismic design codes and modern ground-motion prediction equations(GMPEs)are usually based on a damping ratio of 5%.For many structures,the inherent damping ratio differs from 5%,such as seismically isolated structures or structures with additional damping devices.In the design for this type of structure,a damping modification factor(DMF)is usually used to scale the 5% damped spectrum to obtain the design spectrum with an appropriate damping ratio.The form of DMF in seismic design code of China is relatively simple,and that may lead to erroneous estimates for the response of structures with different damping ratios.So,it’s imminent to study DMF.After studying various factors of DMF,the objective of this thesis is to develop DMF models for subduction zone earthquakes.This thesis can be divided into three parts as follows:Part I: Effects of the earthquake source,path and site condition on DMFThis study investigated the effects of earthquake categories,source parameters,source distance,and site conditions on DMFs for the displacement response spectra of the horizontal components of the records from Japan.This study used a total of 14713 strong-motion records from the Ki K-Net and K-net to compare the DMFs from different earthquake category groups,namely shallow crustal and upper mantle(SCU),subduction interface(INT),and subduction slab(SLAB)earthquakes.The smallest magnitude is 4.94 and the largest distance is 300 km.Statistical tests were carried out to determine whether the DMFs from these three groups of earthquakes differ significantly from each other.The test results show that the effects of the earthquake category and site conditions on the DMFs are significant.The effects of magnitude,fault depth and source distance are also significant.Therefore,separate DMF models for the response spectrum of the horizontal component should be derived for each type of earthquakes and should account for the effects of site conditions,earthquake source parameters,and source distance.Part II: Simple DMF models for subduction slab and interface earthquakes in Japan accounting for site conditionsSimple DMF models without source and path parameters are presented in this study for subduction slab and interface earthquakes in Japan.Site classes based on site periods were used as the site effect proxy.DMF models were derived from spectra for 13 damping ratios and 34 spectral periods and the DMF can be calculated for any damping ratio between 1% and30% and at any spectral period between 0.01 s and 5.0s.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 to1.0 at very short spectral periods(T≤0.02s).At long spectral periods,the DMFs for different damping ratios appear to converge to 1.0 because of the constant displacement spectrum at long periods.All standard deviations decrease linearly with increasing damping ratios in the logarithm scale when the damping ratio is within 5% and increase linearly with increasing damping ratios in the logarithm scale when the damping ratio is over 5%.The DMFs presented in this study combined with the spectrum from Zhao,Jiang,et al.(2016)and Zhao,Liang,et al.(2016)study produce smoothed displacement spectrum that may be used for engineering designs.The DMF values from this study are close to Daneshvar et al.(2016,2017),and Lin and Change(2004)at some spectral periods.The residual distribution suggests that DMFs also depend on earthquake source and path parameters.Note that the model presented in this thesis 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.Part III: Full DMF models for subduction slab and interface earthquakes in JapanBased on the simple DMF models,the full DMF models are presented in this study for subduction slab and interface earthquakes in Japan,accounting for the effects of earthquake source and path parameters.The model function forms are based on residual analysis of the simple DMF models.A simple quadratic function of the damping ratios in the logarithm scale was also used to model the effects of damping ratios and a simple fourth-order polynomial for the logarithm of the spectral periods to model the effect of spectral periods.All standard deviations vary linearly with the increasing logarithm of damping ratios.The DMF models derived in this study combined with the acceleration spectrum form Zhao,Jiang,et al.(2016)and Zhao,Liang,et al.(2016)produce smoothed displacement spectra.At periods over 0.5s,the total standard deviations of full DMF models were reduced significantly compared with simple DMF models.Compared with the Rezaeian et al.(2014)model,more comprehensive parameters such as fault depth,attenuation rate terms,and site conditions were taken into account in the models of this study.Note that the full DMF models presented in this thesis can be used to scale 5% damped spectrum with a known magnitude and a source distance.The DMF values can be calculated for any damping ratio between 1% and 30% and at any spectral period between 0.01 s and 5.0s.