Seismic analysis of underground structures employing extended response spectrum method

Response spectrum method (RSM) has been applied in seismic analysis of underground structures considering linear soil-structure interaction (SSI). However, the RSM has two main shortcomings: it does not account for soil nonlinearity and it is computationally inefficient for processing large soil domains. This paper addresses these shortcomings by extending the RSM to consider soil nonlinearity and by simplifying the modal analysis of SSI systems. The soil nonlinearity is considered by transforming the one-dimensional (1D) frequency-domain equivalent linearization model into a modal damping linear elastic model, in which two explicit formulations of the modal damping ratio are presented. The resulting degraded shear modulus and modal damping ratio are applied to the SSI model to consider soil nonlinearity. In addition, it was found that a small number of natural frequencies and mode shapes of the SSI system are already sufficient to evaluate vibration characteristics in a typical 2D SSI analysis. Accordingly, the first three natural vibration modes of the 1D soil site are used as the loading condition to determine the effective characteristics of the SSI system by iterative static analysis of the SSI system. The effectiveness of the proposed procedure in considering soil nonlinearity and avoiding modal analysis of the SSI system is verified by comparisons with numerical examples. Finally, the extended RSM is applied to the seismic design of three prototype underground structures.