An effective procedure for the earthquake analysis of linear structure-foundation systems, idealized as an assemblage of two-dimensional finite elements, is developed. The procedure utilizes a substructure approach. The foundation is analyzed first, independently of the structure, to obtain its frequency dependent compliance characteristics at the connection nodes with the structure. Equations of motion for the structure are then written in the frequency domain incorporating the effect of the foundation. The substructure approach allows a more detailed modeling of the structure, at the same time resulting in a greater flexibility in the selection of the analysis procedure for the foundation and a greater efficiency in numerical computation. The frequency dependent equations of motion for the structure are solved very efficiently by transformation to a generalized coordinate system (Ritz Method), where a few generalized shapes can adequately express the structural response.
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