| Most of the seismic design codes worldwide usually provide a 5% damped design spectrum and most ground motion prediction equations are based on a damping ratio of 5%.However,the inherent damping ratio of structures differs from 5%,for example,a structure with added damping devices can have a damping ratio much larger than 5% whereas some structures can have a damping ratio much less than 5%.To design a structure with a damping ratio other than 5%,a damping modification factor(DMF),i.e.,the ratio between the response spectrum with the desired damping ratio and the 5% damped spectrum,is usually used to scale the 5% damped spectrum to obtain the spectrum with an appropriate damping ratio.The damping modification factor(DMF)is the ratio between the response spectrum with a given damping ratio and the 5% damped spectrum.At present,China's GB 50011-2010 for design spectrum is based on a 5% damping ratio and also provides a relatively simple DMF model that is based on the shallow crustal earthquakes and may not be appropriate for the subduction earthquakes in Taiwan and the South China Sea.For the research in earthquake engineering,the horizontal ground motions have been considered to be important and until recently there is relatively little research on the vertical ground motions.However,within about 15 km of the earthquake fault,the spectral values at short and moderate spectral periods for the vertical component can be larger than those for the horizontal component.When a structure has large internal spaces with long spans or a long-span bridge,the structural members,structural or non-structural elements,will produce large vertical axial force in the column,shear wall,bridge pillar,or other supporting structural elements.Therefore,it is necessary to estimate the spectra for the vertical ground motions appropriately.To design a structure with different damping ratios for the vertical ground motions,to develop a DMF for the vertical component is overdue.Many earthquakes occur in the subduction zone and these events can be divided into several groups with the ground motion characteristics of one group differing from the others.This study will develop a DMF for the earthquakes that occurred at the interface between the crust or the mantle wedge and the subducting plate,referred to as subduction interface earthquakes.This study is to develop a DMF model for the vertical displacement spectrum for this group of earthquakes with a maximum depth of 50 km.Here is a summary of the research work in this study.1.Dataset compilationAll the strong earthquake records in this study were recorded by densely distributed Ki K-net and K-NET networks in Japan and a large number of high-quality strong-motion records have been collected.The acceleration time histories were filtered and manually screened to eliminate unusable data and determine the maximum useful period.A total of 3,552 strong-motion records from 76 were assembled;2.Analysis of influencing factors of DMFThis part studied the influence of earthquake type,focal parameters,fault distance,and site conditions on the vertical displacement spectrum.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 vertical component should be derived for this type of earthquake,accounting for the effects of site conditions,earthquake source parameters,and source distance;3.Simple DMF model of subduction interface earthquakesA simple DMF model without source and path parameters was established first and this DMF model does not account for the source and path and can be used to scale a 5% damped code design spectrum not associated with a scenario earthquake.However,this model accounts for the effect of damping ratios,as well as spectral period and site conditions for 13 damping ratios and 34 spectral periods.The design spectrum for the desired damping ratio can be obtained by scaling the 5%damped displacement spectrum with the DMF model.The simple model adopts a quartic function of the logarithmic values of the spectral periods and a quadratic function of the logarithmic values of the damping ratio to simulate the effects of spectral periods and damping ratios.Combining the simple model of this study with the displacement spectrum converted from the accelearation spectrum from the Bai and Zhao(2022)study can generate the required displacement spectrum for engineering designs.The distributions of various residuals show that DMF from this study is also affected by source and path effects.When a design spectrum for a scenario earthquake with known source and path parameters,a model accounting for these parameters is required;4.Full DMF models for subduction interface earthquakesBased on the simple DMF model,a full DMF model accounting for the source and path effects was developed.The added model parameters include the magnitude and fault-top depth,geometric and anelastic attenuation,and volcanic path terms.All model coefficients were described by a quadratic function of the logarithmic values of damping ratio,and by a fourth-order polynomial of the logarithmic values of spectral periods.The same function forms for standard deviations of the simple DMF model were used for the full model.Multiplying the displacement spectrum converted from the acceleration spectrum of Bai and Zhao(2022)with the DMF model from this study,a displacement spectrum with the desired damping ratio can be generated.The total standard deviations of the full DMF model are significantly smaller than those of the simple model.Compared with Rezaeian 2014 model,the displacement spectrum from this study varies smoothly with all model parameters.The model from this study can predict the displacement spectrum for a scenario earthquake. |
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