Research on Tunnel Structure Vibration and Its Surrounding Vibration Based on Pipe-in-Pipe Theory in Full Space

In this work, the dispersion characteristic equation of cylindrical tunnels in elastic saturated soil is established. We use the pipe-in-pipe model as a frame to model the tunnel lining as a cylindrical shell and the surrounding soil as a saturated porous medium. Based on the Stokes–Helmholtz vector decomposition theorem, the Biot wave equation is successfully decoupled, and parametric analytic expressions of the displacement field and stress field are obtained. Finally, we apply boundary conditions at the interface to determine the dispersion characteristic equation, which controls the tunnel vibration. The effects of tunnel length, wall thickness, and radius on natural vibration frequency are discussed with numerical examples, and the results are compared with those obtained using elastic relations. Finally, the maximum vibration damage of a tunnel lining structure and the surrounding soil under a harmonic load is determined by using a stable natural frequency; this provides a reference for environmental protection.