Direct Method for Generating Floor Response Spectra considering Soil–Structure Interaction

Abstract

A methodology is developed for generating floor response spectra (FRS) considering the effect of dynamic soil–structure interaction (SSI) based on the substructure technique and a recently-developed direct spectra-to-spectra method. Dynamic stiffness matrix of a three-dimensional structure with a rigid foundation subject to three translational and three rotational base excitations is derived, and is expressed in terms of the modal information of the structure. A transfer matrix, depending on the dynamic stiffness matrices of the structure-foundation system and generalized soil springs, is developed to modify the tri-directional response spectra at the foundation level of free-field (FIRS) in soil medium. The modified response spectra, called foundation level input response spectra (FLIRS), are used as the input to the fixed-base structure to generate FRS using the direct spectra-to-spectra method. Numerical examples of a reactor building and a service building in nuclear power plants demonstrate the accuracy and efficiency of the proposed method. FRS with 50% and 84% Non-Exceedance Probability (NEP) given by the proposed method agree well with the FRS obtained from a large number of time history analyses. Furthermore, the effect of SSI on FRS is studied, the physical meaning, and the advantages of the proposed method are highlighted.