Three-dimensional numerical analysis for the longitudinal seismic response of tunnels under an asynchronous wave input

The numerical analysis of the longitudinal seismic response of tunnels to the spatial variation of earthquake ground motion is an important issue that cannot be ignored in the design and safety evaluation of tunnel structures. In this paper, numerical modelling techniques for the analysis of the longitudinal response of tunnels under an asynchronous seismic wave are extensively studied. The free field wave motion is calculated using the 1D time-domain finite element method and is then extended to 3D. Based on the theory of wave input, three-dimensional numerical simulation techniques for a site response to an asynchronous earthquake are developed. Then, a 3-D soil–tunnel structure interaction model is established to simulate the longitudinal response of the tunnel when subjected to an asynchronous earthquake. These numerical modelling techniques are discussed in detail, and the analysis results prove their validity. The proposed method is applied to analyse the longitudinal seismic response of a tunnel under the oblique seismic incidence of P, SV and SH waves from a semi-infinite foundation. The influence of the incident angle and incident direction on the longitudinal seismic response is discussed. The study outcome will be beneficial to further research on refined nonlinear numerical analysis and seismic response mechanisms of tunnel structures that experience asynchronous earthquake motion.