An analytical model for vibration prediction of a tunnel embedded in a saturated full-space to a harmonic point load

Abstract

The dynamic response of a tunnel embedded in a saturated poroelastic full-space under a vertical harmonic load was investigated by a semi-analytical method. The tunnel was modeled as a thin cylindrical shell surrounded by soil of infinite radial extent. The soil was modeled as a saturated poroelastic full-space. Biot's theory was applied to characterize the soil medium, taking the solid skeleton-pore fluid coupling effects into account. Combined with the boundary conditions at tunnel–soil interface, the coupled equations of the system were solved in the frequency domain with the aid of Fourier decomposition and Fourier transform in the circumferential and longitudinal direction, respectively. Dynamic responses of the tunnel and soil generated by a unit harmonic load applied at the tunnel invert are presented. It is found that the soil permeability and the load frequency have significant influence on the displacements, the stresses and the pore pressure in the saturated soil. In the free field, an increase of the soil permeability leads to a decrease of the soil displacement and pore pressure response. An equivalent single-phase material was used to model the saturated soil and it is found only applicable for soil with lower permeability.