Study On The Damping Correction Factor Of The Seismic Horizontal Displacement Spectrum In The Subduction Zone Shallow Crust And Upper Mantle

China is one of the earthquake-prone countries and large earthquakes caused significant damage to infrastructure,such as the widespread collapse of buildings and bridges,and heavy human casualties.With newly developed engineering design,seismic isolation and energy dissipation structures have been widely used.The damping ratio of the structure has a great influence on the structural response.At present,the design response spectrum is usually based on the structural damping ratio of 5%.With the increasingly complex architectural design of buildings and bridges,the seismic design of structures with different damping ratios has become a popular research topic in the field of earthquake engineering.To obtain design spectra with a damping ratio different from 5%,a damping modification factor（DMF）can be used.DMF is the ratio between a spectrum with a damping ratio different from 5%and the 5%damped response spectrum.Unfortunately,the code-specified DMF models are often oversimplified and based on the research results over a decade or two ago.A large number of studies show that DMF is related to factors such as spectral period and the characteristics of the ground motion.For the design of many structures,inter-story drift is related to the displacement spectrum.The other structures such as those with seismic isolation and energy dissipation devices are sensitive to displacement and therefore it is more appropriate to use the horizontal displacement spectrum for the seismic design for these types of structures,At present,there are relatively few studies on DMF of displacement spectrum from subduction zones.To design a structure that can withstand large earthquakes,it is of great significance to estimate the displacement design response spectrum for the horizontal ground motions.Based on the 6466 strong-motion records from 76 shallow crustal and 47 upper-mantle earthquakes obtained by the K-NET and Ki K-net networks,A DMF model for the displacement spectrum of the horizontal ground motions from the shallow crustal and upper mantle earthquakes was established,which was derived for the response spectra for 13 damping ratios and 36 spectral periods.In this study,the influencing factors of ground motion separated into the effects of source,path parameters,and site category on DMF were studied and the statistical significance of the difference between DMF model factors from different site categories was investigated by using a Z-test.Two DMF models for the horizontal displacement spectrum were established.The first is the simple DMF model,which only accounts for spectral period,damping ratio,and site conditions.This model can be used to adjust a 5%damped design spectrum that is not associated with a known scenario earthquake,i.e.without a known magnitude,focal depth,and focal distance.The second DMF model accounts for source,path,and site parameters and can be used to scale a 5%damped spectrum for a scenario earthquake with a known set of ground motion parameters,including magnitude,fault-top depth,source distance,and site conditions.The main understanding of this study is as follows:（1）Through decoupling the influencing factors of ground motions,this study found that fault depth,focal distance,and site category have significant effects on DMF model.Z-test shows that it is necessary to distinguish the site category and establish a separated DMF model for each site class.（2）The simple model was the function of site category,spectral period and damping ratio,which was the combination of the quadratic function of the logarithm of damping ratio and the quartic function of the logarithm of the spectral period with 0.06s as the segment point;Through the residual distribution of the simple model,it is necessary to add the magnitude scale rate of the two linear segments hinging at M_W=7.1 and the fault depth term up to 25km to improve the between-event residuals,while to improve the distribution of within-event residuals in each site class,it is necessary to add the geometric and anelastic attenuation terms.（3）All coefficients of the full model were functions of the damping ratio and spectral period and were a combination of the quadratic function of the logarithmic values of the damping ratio and quintic function of the logarithmic value of the spectral period.The modeling of the source,path,and site effects by relatively simple functions leads to improved model predictions and an increase in the goodness-of-fit parameters for the full model.（4）At moment,there are no GMPEs for the 5%damped displacement spectrum from the crustal and upper mantle earthquakes,but an approximate 5%damped displacement spectrum can be obtained from the GMPE for the 5%damped acceleration spectrum and the DMF model in this study can be used to obtain the horizontal displacement design spectrum under different damping ratio.