An analytical model for displacement response spectrum considering the soil-resonance effect

The development of performance-based design methodologies requires a reasonable definition of a displacement response spectrum. Although ground motions are known to be significantly affected by the resonant-like amplification behavior caused by multiple wave reflections within the surface soil, such a soil-resonance effect is seldom explicitly considered in current-displacement spectral models. In this study, an analytical approach is developed for the construction of displacement response spectra by considering the soil-resonance effect. For this purpose, a simple and rational equation is proposed for the response spectral ratio at the site fundamental period (SRTg) to represent the soil-resonance effect based on wave multiple reflection theory. In addition, a bilinear model is adopted to construct the soil displacement-response spectra. The proposed model is verified by comparing its results with those obtained from actual observations and SHAKE analyses. The results show that the proposed model can lead to very good estimations of SRTg for harmonic incident seismic waves and lead to reasonable estimations of SRTg and soil displacement-response spectra for earthquakes with a relatively large magnitude, which are generally considered for seismic design, particularly in high-seismicity regions.