Analytical Model of the Dynamic Response of a Long Immersed Tunnel through Various Soil Regions Considering the Traveling Wave Effect

The immersed tunnels of Hong Kong–Zhuhai–Macao Bridge and the Shenzhen–Zhongshan Channel have lengths up to 6–7 km along the longitudinal direction and cross several soil regions. The traveling wave effect is observed in these long immersed tunnels when subjected to seismic waves. Based on the improved response displacement method, a theoretical model of a long immersed tunnel containing 33 tube elements and 32 flexible joints and considering the continuity conditions of flexible joints was developed in this study. The incorporation of the traveling wave effect was achieved by taking into account both the longitudinal propagation distance of the seismic wave within the immersed tunnel and the dynamic variations in seismic wave parameters as the wave traversed through diverse soil regions. An evaluation was developed to assess the traveling wave effect on the response of the long immersed tunnel, and the influences of incidence angles and initial apparent wave velocities of seismic wave were investigated. The results showed that ignoring traveling wave effect for the long immersed tunnel through various soil regions would result in significant underestimations of relative deformations of flexible joints by approximately one order of magnitude, leading to unsafe seismic design.