Closed-Form Analytical Solution for Vibrations from a Tunnel Embedded in a Saturated Poroelastic Half-Space

Abstract

A closed-form analytical solution for ground-borne vibrations from a tunnel embedded in a saturated poroelastic half-space is proposed in this paper. The tunnel modeled as an elastic hollow cylinder is surrounded by the water-saturated poroelastic material. The total wave field in the poroelastic half-space with a cylindrical cavity consists of the outgoing cylindrical waves and the down-going plane waves. In addition to the traction-free condition on the ground surface and the continuous conditions of displacement and stress at the tunnel-soil interface, hydraulic boundary conditions on these two scattering surfaces are required to solve this multiple-scattering problem. The transformation properties between the plane and cylindrical wave functions are employed to apply the boundary conditions expressed in both the rectangular and cylindrical coordinate systems. Numerical results for the displacements of the solid on the ground surface and the pore pressure in the saturated soil attributable to a harmonic point load applied at the tunnel invert are presented. The influence of the soil permeability and the hydraulic boundary at the tunnel-soil interface on the free-field responses is investigated. The proposed solution can serve as a benchmark for other computational methods and as an efficient tool for predicting vibrations from a tunnel embedded in a saturated poroelastic half-space.