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.

中文翻译：

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浅层地基地震土-结构相互作用的响应谱分析

利用响应谱法（RSM）研究了浅基础结构的地震土-结构相互作用（SSI）。首先考虑结构基础的水平运动和摇摆运动的耦合来构建SSI模型。在该模型中，结构是通过有限元建模的，土是通过基于有理逼近的精确集总参数模型（LPM）建模的。由于引入了LPM的阻尼，因此SSI模型是非经典阻尼系统。随后将复模叠加RSM用于解决设计响应谱下的非经典阻尼SSI系统。最终使用SSI模型和RSM计算了两种类型的3层和6层剪力结构的地震响应。