Longitudinal integral response deformation method for the seismic analysis of a tunnel structure

For the longitudinal seismic response analysis of a tunnel structure under asynchronous earthquake excitations, a longitudinal integral response deformation method classified as a practical approach is proposed in this paper. The determinations of the structural critical moments when maximal deformations and internal forces in the longitudinal direction occur are deduced as well. When applying the proposed method, the static analysis of the free-field computation model subjected to the least favorable free-field deformation at the tunnel buried depth is performed first to calculate the equivalent input seismic loads. Then, the equivalent input seismic loads are imposed on the integral tunnel-foundation computation model to conduct the static calculation. Afterwards, the critical longitudinal seismic responses of the tunnel are obtained. The applicability of the new method is verified by comparing the seismic responses of a shield tunnel structure in Beijing, determined by the proposed procedure and by a dynamic time-history analysis under a series of obliquely incident out-ofplane and in-plane waves. The results show that the proposed method has a clear concept with high accuracy and simple progress. Meanwhile, this method provides a feasible way to determine the critical moments of the longitudinal seismic responses of a tunnel structure. Therefore, the proposed method can be effectively applied to analyze the seismic response of a long-line underground structure subjected to non-uniform excitations.