Refined Modeling and Dynamic Response of Tunnel–Soil Interaction System Using the Theory of Coupled Beam on Winkler Foundation

This paper simplifies the tunnel lining section as a straight-curved coupled beam structure, with the tunnel lining and surrounding rock modeled as a straight-curved coupled beam system supported by a soil layer of limited depth to analyze its dynamic response. A refined model of the tunnel–soil coupling system is developed based on Timoshenko curved beam theory, straight beam theory, and the motion equation for an elastic foundation. The finite element method (FEM) is used to validate the numerical solution of the coupled system’s steady-state response, obtained using the transfer matrix method (TMM) and the fourth-order Runge–Kutta method. Through numerical simulations and parameter analysis, the effects of subgrade reaction coefficient, soil thickness, and the tunnel crown’s arc angle on the vibration characteristics of the coupled system are investigated. By applying the symmetry simplification method from structural mechanics, the study demonstrates that this approach is suitable for developing structural dynamic models. The results show that when considering the soil movement around the tunnel, doubling the soil thickness reduces the natural frequency of each order by approximately 15%, while significantly increasing the displacement resonance amplitude. The resonance frequency is most sensitive to the subgrade reaction coefficient in the lower modes, and the overall stiffness of the coupled system decreases as the arc angle at the tunnel crown decreases.