Theoretical analysis for the longitudinal seismic response of shield tunnel by considering axial force and variable stiffness

In order to estimate the seismic response of the tunnel reasonably, the shield tunnel is regarded as a Timoshenko beam upon Pasternak elastic foundation. Considering the axial force and the variable stiffness, the theoretical calculation model under the joint action of longitudinal and transverse strata displacements is proposed and solved by the finite difference method. The theoretical solutions are compared with the numerical simulation results to verify its validity and reliability, then the influences of six key parameters on the longitudinal seismic response were further explored. The increase in shield tunnel stiffness can effectively improve the seismic performance of the tunnel. However, in the vicinity of the stiffness variation, the segments with relatively small tunnel stiffness (regular or degraded segments) may experience higher local deformation under seismic action. Reducing the longitudinal stiffness ratio and shortening the length of reinforcement section, can significantly mitigate the adverse seismic response of tunnel lining caused by variable stiffness. The local deformation at the tunnel is positively correlated with the foundation reaction coefficient, and the local deformation increases and then decreases with the increase of wavelength. Seismic waves with wavelengths between 20 m and 120 m are more likely to lead to larger the opening and dislocation of shield tunnel, on the scenario of higher foundation reaction coefficient. The residual axial force can improve the seismic performance of shield tunnel to a certain extent, especially when the angle of incidence and tunnel stiffness are relatively small. These researches can provide some guidance for the longitudinal seismic design of shield tunnels.