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.

KEYWORDS:

• Seismic Analysis
• Floor Response Spectrum
• Direct Method
• Soil-Structure Interaction
• Foundation Level Input Response Spectra

Acknowledgments

The research for this paper was supported, in part, by the Natural Sciences and Engineering Research Council of Canada (NSERC) and University Network of Excellence in Nuclear Engineering (UNENE).