A Semi-Analytical Solution of a Circular Tunnel Surrounded by a Poroelastic Medium and Subjected to a Moving Load (No. R857)

Abstract

In this study, dynamic response of a circular tunnel embedded in a porous medium and subjected to a moving axisymmetric ring load is investigated. To avoid treating Biot’s dynamic equations directly, two scalar potentials and two vector potentials are introduced to represent the displacements of the solid skeleton and the pore fluid. Based on Biot’s theory and the Fourier transformation, the frequency domain governing equations for the potentials are derived. Performing the Fourier transformation on the axial coordinate, general solutions of the potentials are derived from the governing equations of the potentials. Using the obtained general solutions and boundary conditions along the tunnel surface, the boundary value problem is formulated in the frequencywave-number domain. Solution of the boundary value problem yields the unknown constants of the potentials. The closed form solutions in the frequency-wave-number domain for the displacements, stresses and pore pressure are derived in terms of the obtained potentials. Analytical inversion of the Fourier transformation with respect to the frequency together with the numerical inversion of the Fourier transformation with respect to axial wave number leads to the numerical solutions of the displacements, stresses and pore pressure. For demonstration of our method, some numerical examples and corresponding analysis are given in the paper.