Dynamic Response of a Circular Tunnel Embedded in a Saturated Poroelastic Medium due to a Moving Load

Abstract

Dynamic response of a circular tunnel embedded in a porous medium and subjected to a moving axisymmetric ring load is investigated in this paper. In this study, two scalar potentials and two vectorial potentials are introduced to represent the displacements for the solid skeleton and the pore fluid. Based on Biot’s theory and applying the Fourier transformation on time variable, a set of frequency domain governing equations for the potentials are obtained. Performing the Fourier transformation on the axial coordinate, closed-form general solutions for the potentials with arbitrary constants are obtained. Using the closed-form general solutions and boundary conditions along the tunnel surface, the arbitrary constants involved in the potentials are calculated. Representations for the displacements, the stresses and the pore pressure are derived in terms of the closed-form potentials. Analytical inversion of the Fourier transformation with respect to frequency and numerical inversion of the Fourier transformation with respect to the axial wave number lead to numerical solutions for the displacements, the stresses and the pore pressure in the porous medium. Numerical results demonstrate the soil response due to a high speed load is quite different from those due to a static load or a lower speed load. These differences become more pronounced when the velocity of moving load approaches the velocities of elastic waves of a porous medium.