Damping Modification Factor For Vertical Displacement Spectrum From Shallow Crustal And Upper Mantle Earthquake

In the seismic design and analysis of engineering structures,vertical ground motions are generally not considered.Designers usually consider that the safety reserve of the structure may be enough to resist the influence of gravity and vertical seismic force.However,the strongmotion records show that the influence of vertical ground motion can not be ignored,and the combination of vertical and horizontal ground motions can cause severe structural damage.The response spectral analysis is often used in engineering seismic design and the design response spectrum is based on a damping ratio of 5%.However,the damping ratio for many structures is much higher than 5%,for example,structures with a base isolation system,or additional energy dissipation damping devices.In a displacement-based design and evaluation,the design response spectrum with an appropriate damping level must be defined.To obtain a design spectrum with a desired damping ratio from the design response spectrum with a damping ratio of 5%,one of the methods is to use the damping correction factor(DMF)to adjust the 5%design response spectrum.Based on 6466 strong-motion records from 76 shallow crustal and 47 upper mantle earthquakes obtained by K-Net and KiK-net networks in Japan,a DMF model for the vertical ground motions from these two types of earthquakes was established for 13 damping ratios(1%?30%),34 spectral periods(0.03s?5.0s),and four site classes.The first DMF model contains three ground motion parameters:site class,damping ratio,and spectral period referred to as the simple model.The model equation is simple and the parameters are consistent with those in the design spectrum of buildings.The model can be used to adjust the 5%damping ratio design response spectrum without source and path parameters.Then,based on the simple DMF model,the source and path parameters were introduced to obtain the second DMF model referred to as the full model.Using the random effect method,the total residuals from the simple model were decomposed into between-and within-event residuals,and the within-event residuals were further decomposed into between-and within-site residuals.The functional forms for the source parameters were determined by the analysis of between-event residuals and the functional forms for path parameters were determined by the analysis of within-event residuals.The full model consists of a simple model,a linear magnitude term and a magnitude square term for events with a magnitude of less than 7.1,a linear fault depth term for events with a depth of less than 25 km,a geometric attenuation term,and an anelastic attenuation term.Finally,a DMF model with values varying with spectral period smoothly was developed.The results are as follows.(1)The Z-test results show that the DMF mean values of different site types are significantly different,and a separate model should be established for each site class.(2)The variation of all coefficients of the full model can be described by a quadratic function of damping ratio,and the influence of spectral period can be described by a polynomial of logarithm values of spectral periods.(3)For almost all spectral periods,the between-event standard deviations of the full parameter model are less than that of the simple model,and the between-event standard deviation of the two models is significantly less than the within-event standard deviations.(4)Compared with the simple model,the full DMF model is significantly improved the goodness-of-fit,especially the source effect.(5)A linear function of the logarithm of the damping ratio can be used to calculate the standard deviations of the model;A smooth displacement spectrum can be generated by using the DMF model in this study and the spectrum from the Zhao et al(2017)model.(7)The predicted DMF values from the simple model for SC I sites are very similar to those by the Xiang and Huang(2019)model in all damping ratios and spectral periods(except 0.03s).However,the predicted DMF values by the simple model from this study for other site classes differ significantly from those by Xiang and Huang(2019)model;and the predicted DMF values by the full model in this study are generally similar to those by the Rezaeian(2014)model at many spectral periods.The total standard deviation of DMF full parameter model for SC I are very similar,but the model in this paper considers more abundant model parameters such as fault depth,viscous attenuation and site conditions,and the curve is smoother.