| The design response spectrum plays an important role in guiding the earthquake resistance of buildings.At present,most design codes at home and abroad are generally based on a damping ratio of 5%.For structures with the other damping ratio(such as steel structures,cable structures,and long-span truss structures that usually have a damping ratio of much less than 5%;and the structures with added damping devices or seismic energy dissipation and isolation devices that will have a damping ratio of much larger than 5%),the damping modification factor(DMF)model is usually used to adjust the 5% damped spectrum to obtain the design spectrum with the desired damping ratios.In most design codes,the effect of vertical seismic action is not considered for many structures,or use 2/3 of the horizontal load.However,many real strongmotion records show that within 15 kilometers of the fault rupture surface,the vertical component is often larger than the horizontal ground component,which has a great impact on long-period structures such as long-span space buildings and bridges.Strong vertical seismic action can cause damage or even collapse of such structures.Some studies suggest that due to the significant difference between the vertical and the horizontal ground motion,a simple V/H(Vertical/Horizontal)model cannot accurately describe the characteristics of the response spectrum of the vertical ground motions and the structural safety can not be effectively guaranteed.The vertical response spectra suitable for different damping ratios are in great demand in practical engineering applications.On the other hand,in the displacement-based aseismic design method,reasonably accurate estimates of the displacement response spectrum with an appropriate damping ratio are required.For a damping ratio over 5%,the corresponding displacement spectrum can not be calculated simply by the pseudo-response spectrum relationship and separate displacement spectrum models are of great value in this type of engineering application.Based on these reasons,a DMF model suitable for the vertical seismic displacement spectrum will be developed in this study.Subduction earthquakes can be divided into four groups according to the tectonic locations and focal mechanisms,i.e.,shallow crustal,upper mantle,subduction interface,and subduction slab earthquakes.Slab earthquakes occur within the subducting plate and this type of earthquake tends to generate large short-period ground motions compared with the other three types of events;therefore,a DMF specifically for the vertical displacement spectrum for the subduction slab earthquakes will be developed.Using the vertical components of 4695 records from the subduction slab earthquake obtained by the strong motion networks of K-NET and Ki K-net in Japan,two sets of the DMF models for the vertical displacement spectra with 14 damping ratios(1%?30%)and 36 spectral periods(0.01s?5.0s)were established in this study.The first set of models has only three model parameters,i.e.,damping ratio,spectral period,and site conditions and are referred to as the simple DMF models with all coefficients for model parameters being derived by using a fixed effects method.This set of models can be used to adjust the design response spectrum without known source and distance parameters,such as the earthquake magnitude and source distance.The second set of models are referred to as the full model of DMF,which contains source terms,such as magnitude and fault-top depth terms,and path terms,such as the geometric and anelastic attenuation terms,as well as the model parameters in the simple model.The function form and the necessary terms of the full model were determined by a detailed analysis of the residuals from the simple model.A random effects regression analysis was used to decompose the total residual and the total standard deviations into the between-and within-event parts that were further decomposed into the between-and within-site components to explore the impact of source and path parameters on the model.Starting from the simple DMF model,through a stepby-step analysis,the terms for magnitude,fault depth,geometric attenuation,and anelastic attenuation were added,to derive all coefficients for the full DMF model that can be used to adjust the design response spectrum associated with known ground motion parameters,such as magnitude,fault-top depth,and source distances.The main conclusions of this study are summarized below:(1)The effect of the damping ratio can be described well by a quadratic function of the logarithm of the normalized damping ratio;(2)The Z-test results show that the site conditions have a significant effect on the mean value of DMF and it is necessary to establish different DMF models for different site classes;(3)Based on the residual analysis,adding source effect terms for magnitude and fault-top depth,and path effect terms for geometric,anelastic path attenuation to the full DMF model can effectively improve the model goodness of fit of the full model.In the full DMF model,the quadratic function of the logarithm of the damping ratio and the polynomial function of the spectral period in the logarithm scale were used for regression analysis;(4)For almost all spectral periods in both DMF models,the between-event standard deviations are much smaller than the within-event ones,indicating that the variability for the source effect on DMF is less or is better modelled than that for the path effect.The betweenevent standard deviations for the full model are significantly smaller than those of the simple model because of the added source parameters,suggesting that the modeling of the source effect is important;(5)The displacement spectrum of the full DMF model varies smoothly with all model parameters,including the spectral period and the full DMF model has a better performance than the simple model. |
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