Vibration Characteristics of a Tunnel Structure Based on Soil-Structure Interaction

Abstract

Considering the interaction mechanisms between a subway tunnel’s structure and the surrounding soil, a new theoretical method was established to analyze the vibration characteristics of the tunnel structure. The tunnel structure is assumed to be a moderately thick cylindrical shell that was never previously used, and all following researches were done on this basis. To begin, the vibration equation of the tunnel structure was established based on the moderately thick cylindrical shells theory, which takes into account transverse shear deformation. Then, a motion equation was set up for the soil around the tunnel in the framework of Navier’s wave theory, applicable to a homogeneous, isotropic, linear elastic medium. Based on said analysis and combined with a wave-propagation approach, the vibration control equation of the tunnel structure was established by considering soil-structure dynamic interaction according to the interface conditions. Using the dispersion characteristic equation, the vibration characteristics of the tunnel structure were analyzed. Through the comparison of the analytical results with those obtained based on thin shell theory or the finite element method (FEM), the effectiveness of this research was verified. Finally, the influences of tunnel radius, wall thickness, and length on the vibration characteristics of tunnel structure were analyzed. Some important findings are drawn as follows: (1) The natural frequencies of each order, calculated using the method proposed in this paper, are close to the solutions based on FEM, and the relative error is less than 10%; (2) The natural frequencies of the tunnel structure that were calculated based on this theory are lower than those based on the thin shell theory; (3) Additional stiffness is the main influencing factor of the soil medium on the vibration characteristics of tunnel structure; (4) When the lower order is dominating in one-modal analysis, it would produce a larger error if soil-structure interaction is ignored; and (5) The natural frequency of tunnel structure decreases with the increase of tunnel radius, wall thickness, and length.