A generalized response spectrum method for seismic response analysis of underground structure combined with viscous-spring artificial boundary

Abstract

Response spectrum analysis (RSA) has been applied to dynamic calculation of underground structure subjected to earthquake excitation. An analysis model composed of the underground structure and the surrounding soil was built to consider the soil-structure interaction (SSI). The seismic free field motion was enforced on the bottom boundary of the calculation model, namely the inertia force acts on the SSI model with fixed bottom to calculate the relative response of system. While the scattered waves propagating from the model into truncated infinite domain, namely the radiation damping effect of infinite domain, was not considered in the SSI model. In this paper, the viscous-spring artificial boundary (VSAB) is used at the bottom boundary of the SSI model to consider the radiation damping effect and to improve the calculation accuracy of the model. The damping of VSAB makes the SSI model being a non-classically damping system. The seismic free field is inputted as the nodal force at VSAB besides the inertia force on SSI model. A generalized response spectrum is defined as the peak value response of a single-degree-of-freedom (SDOF) system subjected to the additional nodal force. Subsequently, the complex modal RSA is generalized to calculate the seismic analysis model with VSAB. Finally, the rationality of the generalized RSA is indicated by applying it to the seismic analysis of a rectangular subway station structure and a circle tunnel in two typical sites.