Semi-analytical solutions for seismic responses of tunnel tube in pier-supported submerged floating tunnel under vertical excitation

The concept of pier-supported submerged floating tunnel (PSFT) is feasible if the water depth is within 100 m. In this study, semi-analytical solutions are proposed for determining the seismic responses of a tunnel tube in a PSFT subjected to vertical excitation. The tunnel tube consisting of tube segments and flexible joints is simplified as beam components connected through bending springs. The supporting system comprising bearings and piers is regarded as a series of discrete Kelvin elements. Seismic action is considered as the inertia force and hydrodynamic pressure is calculated by the Morison equation. The tunnel tube displacement is derived by the modal superposition method. On this basis, the semi-analytical solutions of the displacement and bending moment of the tunnel tube are deduced using the Runge-Kutta method. The finite element method is employed to examine the validity of the proposed solutions. Furthermore, the effects of the fluid, flexible joints, and damping ratio are discussed. The results show that the Froude-Klylov force can significantly reduce the response amplitude, and the hydrodynamic mass force can alter the response frequency under real seismic input motion. Flexible joints can adjust the bending moment distribution in the tunnel tube. With the adoption of flexible joints, the hogging moments at the bearings considerably decrease. The change in damping ratio also have substantial effects on the structural seismic response.