Dynamic response of a pair of elliptic tunnels embedded in a poroelastic medium

In this paper, a semi-analytical method is developed to solve the dynamic response of a pair of parallel elliptic tunnels embedded in an infinite poroelastic medium. The surrounding poroelastic medium of tunnels is described by Biot's poroelastic theory, while the tunnels are treated as a single-phase elastic medium. By introducing potentials, the governing equations are reduced to Helmholtz equations. The series solutions of the Helmholtz equations are obtained by the wave function expansion method. The surrounding poroelastic medium and the tunnels are coupled together via the stresses and the displacements continuation conditions. Numerical results demonstrate that the dimensionless wavenumber, distance between two tunnels, elliptic ratio and thickness of liner have a considerable influence on the dynamic response of the tunnels and the poroelastic medium.