Study On The Damping Correction Factor Of Vertical Acceleration Spectrum For Intraplate Earthquakes In Subduction Zone

Many earthquake damage investigations show that the vertical seismic action has a significant influence on the damage to buildings,the vertical response spectrum should not be simply derived from the ratio of the vertical to the horizontal response spectra(V/H)and the response spectrum of the horizontal component.The seismic performance of the structure with different damping ratios and failure mechanisms differs significantly different from the conventional structures.With the increase in the use of seismic isolation devices and energy dissipation devices such as additional damping,and the construction of steel structures,long cantilever structures and large-span structures,the seismic design of a structure with different damping ratios becomes a popular and important research topic in the field of earthquake engineering.A damping modification factor(DMF)is expressed as the ratio between the response spectrum with an arbitrary damping ratio to the 5% damped response spectrum for a given same period.By establishing a vertical DMF model,the vertical design response spectrum and vertical ground motion attenuation relationship under multiple damping ratios can be obtained,which can provide a reference for the seismic design.At present,the dependence of DMF on spectral period and seismic characteristic parameters is usually neglected in the many current seismic design codes,and DMFs from different types of earthquakes and different components differ significantly.The establishment of a DMF model requires a large number of high-quality strong-motion records.However,the construction of the strong-motion network in China started relatively recently,and the basic information is seriously missing.This study used 4695 vertical strongmotion records obtained by the K-NET and Ki K-net networks from the subduction slab earthquakes in Japan for building a DMF model.After a series of exploring various model function forms and influencing factors of DMF model,two DMF models were developed: The first one is referred to as the simple model,which only accounts for the damping ratio,spectral period,and the site effect.It is suitable for adjusting the response spectrum with unknown source and distance parameters to obtain a response spectrum with damping ratios different from 5%.The second DMF model is referred to as the full DMF based on the simple model but accounting for the source and path effects,so that response spectra with a damping ratio different from 5%can be obtained from a 5% damped spectrum for a scenario earthquake,leading to improved final design spectrum.The residual and standard deviation of the two DMF models were analyzed by the random effects algorithm,and the standard deviation models were established by the least square method.Then,two types of DMF models were used to provide examples of the vertical acceleration response spectra from subduction slab earthquakes with multiple damping ratios.The main conclusions are as follows:(1)Earthquake category,site conditions,moment magnitude,fault depth,and fault distance affect the DMF significantly;(2)For the simple model,the effect of damping ratios on DMF was be described by a cubic polynomial of ln((?)/0.05),the period effect was be simulated by the fourth-order polynomial of the spectral period in the natural logarithm scale,and the effect of site conditions on DMF was be considered by site classes.Moment magnitude,fault depth,and fault distance affect the distribution of the residual errors significantly.For short and moderate spectral periods,the source effect on the residual distribution is less than the site and path effect.However,for the long period and high damping ratios,the source effect is more significant on the residual distribution than the site and path effect;(3)A comparison with the Zhao2020 model shows that the vertical DMF model cannot be obtained by scaling the DMF mode for the horizontal component by a constant or a simple function.However,the standard deviations of the vertical and horizontal models are similar except for the short periods.A comparison with the XH2019 model shows that for a damping ratio of less than 10%,the prediction by the XH2019 model is close to that of the simple DMF model for SCI sites only,and the standard deviations of the XH2019 model are significantly larger than those of simple DMF model for most spectral period ranges;(4)All parameters of the full DMF parameter model can be fitted by simple functions of the damping ratio and spectral period.The full DMF model used bilinear models for linear and squared magnitude terms and bilinear functions for the fault depth term can correct the biased distribution between-event residual,while the geometric attenuation term and anelastic attenuation term can correct the biased distribution of within-site residual.These simple functions in the full DMF model significantly reduce the between-and within-event and the total standard deviations for moderate and long spectral periods;and(5)With a damping ratio of 5.0% as a boundary,the variation of standard deviations can be described by the bilinear function of the damping ratio in the natural logarithmic scale.