Empirical Ground Motion Model for Damping Modification Factor for Horizontal Response Spectra in Taiwan

In the Taiwan seismic design code for buildings, damping modification factors (i.e., B values) are provided as a denominator to calculate the elastic design basis response spectra with damping ratios other than 5%. At short periods and at one-second period, the B values are referred to as Bs and B1, respectively. Those values are originally proposed to derive the corresponding design basis response spectra rather than maximum considered ones. According to some observed earthquake records and past relevant studies, it is found that damping modification factors are greatly related to natural periods, at long periods in particular. In addition, some recent studies indicate that damping modification factors, to some extent, are relevant to some ground motion characteristics that are used in ground motion prediction equations, e.g., moment magnitude (MW), rupture distance (Rrup), averaged shear wave velocity in the upper 30 m of sites (Vs30), etc. Therefore, by means of abundant ground motion database recorded in Taiwan, this study aims to develop empirical and localized models for estimating suitable damping modification factors in terms of spectral displacement, velocity, and acceleration. The models are proposed in the form of not only damping ratios and natural periods but also MW, Rrup, duration, and Vs30. Through comparing the damping modification factors obtained from the proposed models with those specified in the current design code, the applicability of the code-specified values is further examined. Moreover, the results obtained from the models determined using the entire ground motion database can satisfactorily reproduce the response spectra of several near-fault pulse-like ground motions with damping ratios different from 5%. It is further implied that the proposed model is robust sufficiently and valid for both far-field and near-fault pulse-like ground motions. The results show that the damping modification factors provided in the current design code are acceptable practically when the damping ratio falls within 2% to 25%, while those may be too conservative when the damping ratio is smaller than 2%.