Damping Modificaton Factor For The Vertical Acceleration Response Spectrum Of Shallow Crustal And Upper-mantle Earthquakes

The response spectrum from a ground motion prediction equation(GMPEs)or the design spectrum from a design code is usually based on a damping ratio of 5%.To design a structure with a damping ratio much less than 5%,for example,for a cable structure,or match larger than5%,such a structure with a seismic isolation system or with damping devices,a damping modification factor(DMF)is usually used to determine the seismic load in a design of structures with different damping ratios.Damping modification factor(Damping Modification Factor,DMF)is defined as the response spectral ratio between a response spectrum for a given damping ratio to that with a 5% damping ratio.Simple DMF is available in some design codes and has only one parameter,i.e.,damping ratio.This simple DMF model leads to that the 5% damped spectrum is scaled by the same DMF value for all spectral periods to obtain the response spectrum for a target damping ratio and leads to an inaccurate estimate of the earthquake load for structures with different damping ratios.In many design codes,including the Chinese design code,the vertical seismic load is taken as a 2/3 of the horizontal load or not be considered for many types of structures.However,lessons learned from recent large earthquakes suggest that vertical ground motion can also lead to the destruction of building structures,especially in the near-fault region.The combined actions of the horizontal and the vertical ground motion can accelerate the destruction of building structures.In most design codes,DMF models for the vertical ground motions are not available.For determining an appropriate design spectrum of many types of structures,especially for the building with a large spacing or a bridge with a long span,developing a DMF for the vertical ground motions is necessary.Developing a reliable DMF model requires reliable and a large number of strong-motion records.The subduction zone in Japan is characterized by complex tectonic settings.Since 1996,a large number of strong-motion records obtained by two recording networks are freely available.These earthquakes were classified according to the tectonic locations and focal mechanisms.All recording instruments are high-quality digital devices and many stations have measured shearwave velocity profiles down to bedrock.Therefore,it is possible to develop a DMF model for the vertical ground motion based on the strong-motion records in the subduction zone of Japan.Mainland China does not have shallow subduction zones but Taiwan has very similar tectonic settings to Japan.Event the south-west part of China is not a subduction zone,our research team found that the GMPEs developed for both horizontal and vertical ground motions from the shallow crustal earthquakes fit the strong-motion records from China very well.Therefore we expect that the DMF model derived from this study would fit the records from China very well.In this thesis,two DMF models were developed for the vertical total acceleration from two groups of earthquakes,i.e.,the shallow crustal and the upper mantle earthquakes,for 13 damping ratios(1%?30%)and 34 spectral periods(0.03s?5.0s),using 6466 strong-motion records from76 earthquakes in the shallow crust and 47 earthquakes in the upper mantle obtained by the KNET and KIK-NET networks in Japan.The first group of DMF model is referred to as the simple model,which contains three ground-motion parameters: site conditions,damping ratio,and spectral period.This model can be used to adjust a 5% damped design spectrum that is not related to a particular earthquake.The second DMF model is referred to as the full model.Based on the simple model,the source effect parameters(moment magnitude,fault depth)and path effect parameters(geometric and anelastic attenuation rate)were added to the simple model.This model can be used for a 5% damped spectrum associated with a scenario earthquake with known magnitude,fault depth,and source distance.The main results from this study are as follows:(1)The simple model contains three ground-motion parameters,the damping ratio,spectral period,and site conditions.According to the statistical test(Z-test)method,the geometric mean DMF values from different site classes differ significantly,and therefore site condition must be accounted for;(2)In this study,the simple model was derived by a least-squares regression method and the full model was developed by using a random effects regression method.A third-order polynomial of normalized damping ratio in the logarithm scale was used to describe the effect of damping ratios and a fourth-order polynomial of spectral periods in the logarithm scale was used to describe the effect of spectral periods.The use of a continuous function of damping ratio and spectral period reduced the number of model parameters in the simple model;(3)For the full model.we found that all model coefficients for the source and the path effects can be described very well by similar functions used for the simple model.The number of model coefficients of the full model is greatly reduced;(4)Under most damping ratios,for the simple model,the between-event standard deviations of short and medium spectral periods are smaller than the within-event standard deviations,whereas the between-event standard deviations for long spectral periods are greater than the within-event standard deviations.(5)The between-event standard deviations of the full model are significantly smaller than those of the simple model,indicating that the source effect modelling is the reason for the reduced between-event standard deviations in the full model compared with the simple model.