Effects of magnitude and distance on spectral and pseudospectral acceleration proximities for high damping ratio

The spectral absolute acceleration, Sa, is a useful tool for estimating the inertial force that is of interest in foundation design particularly for buildings with energy dissipation or seismic isolation systems. Nevertheless, seismic codes typically specify only the pseudospectral acceleration, Spa. Many studies have been performed to clarify the relationship between Sa and Spa in order to relate the two spectra. A recent study indicated that this relationship could be affected not only by the structural damping ratio and period but also by seismological parameters such as magnitude and distance. However, how these seismological parameters affect their relationship is not clearly understood. To clarify this issue, an approach that relates the two spectra and includes seismological parameters is proposed herein based on random vibration theory. The proposed approach is verified by comparison with the results of time-series analysis. Furthermore, the effects of moment magnitude and source-to-site distance are explored and explained based on the proposed approach. It is found that although Sa becomes larger than Spa as the structural period and damping ratio increases, this increase becomes smaller with increasing moment magnitude and source-to-site distance due to the increase in the long-period components of earthquake ground motions. Finally, a practical formulation for estimating Sa from Spa considering the seismological effects is constructed and verified using real seismic records.