Seismic soil–structure interaction analysis of structure with shallow foundation using response spectrum method

Seismic soil–structure interaction (SSI) of structure with shallow foundation is studied using response spectrum method (RSM). A SSI model is first constructed with the consideration of the coupling of horizontal and rocking motions of structural foundation. In this model, the structure is modelled by finite elements and the soil by the accurate lumped parameter model (LPM) based on rational approximation. The SSI model is a non-classically damped system due to introducing damping of LPM. Complex mode superposition RSM is subsequently applied to solve the non-classically damped SSI system under design response spectrum. Seismic responses of 3-story and 6-story shear structures on two types of sites are finally calculated using the SSI model and RSM. The numerical experiments indicate that RSM can be an effective tool to analyze seismic SSI of structure with shallow foundation, and some conclusions are drawn: (1) the coupling of horizontal and rocking motions of foundation should be considered for relatively high structure on soft soil site, (2) the rational-approximation-based LPM is more accurate than the simple one, (3) the over-damped case can be neglected in the complex mode superposition process although it arises at fundamental frequency, and (4) the quasi spectrum transform relationship can be used to obtain the relative displacement and relative velocity response spectra from the given absolute acceleration design response spectrum.