Estimation of input energy spectrum from pseudo-velocity response spectrum incorporating the influences of magnitude, distance, and site conditions

The input energy spectrum is useful information for determining the hysteretic energy demand in energy-based seismic design. The input energy spectrum commonly expressed in terms of the energy equivalent velocity spectrum, Veq, can be easily established from the code-specified response spectra (RS) based on the relationship between Veq and RS. Several formulations for the Veq-RS relationship have been developed; however, all of them ignore the influences of magnitude, distance, and site conditions. The aim of this study is to propose a practical formulation for the relationship between Veq and the pseudo-velocity response spectrum, RSpv, incorporating the influences of magnitude, distance, and site conditions. Firstly, to explore the influences of magnitude, distance, and site conditions on the Veq-RSpv relationship, an approach for estimating Veq/RSpv is proposed based upon random vibration theory and verified by comparison with the values calculated by traditional time-series analysis. It is found that the magnitude influences Veq/RSpv the most among these parameters by changing the frequency content of the ground motion, and the Veq/RSpv values at long oscillator periods decrease significantly with an increasing magnitude. Then, based on these conclusions, a practical Veq/RSpv formulation incorporating the influences of magnitude, distance, and site conditions was developed using 16,660 real seismic ground motions in Japan.