Effect of imperfect bonding on axisymmetric elastodynamic response of a lined circular tunnel in poroelastic soil due to a moving ring load

A two-dimensional elasticity analysis for steady-state axisymmetric dynamic response of an arbitrarily thick elastic homogeneous hollow cylinder of infinite length, which is imperfectly bonded to the surrounding fluid-saturated permeable formation, subject to an axially moving ring load, is presented. The problem solution is derived by using Biot’s dynamic theory of poroelasticity in conjunction with double Fourier transformation with respect to time (frequency) and axial coordinate (axial wave number). The analytical results are illustrated with numerical examples in which a concrete tunnel lining of uniform wall thickness is imperfectly bonded to a surrounding water-saturated poroelastic formation of soft/stiff frame characteristic. Numerical solutions for the radial shell mid-plane and formation displacements are calculated by analytical (numerical) inversion of the Fourier transformation with respect to the frequency (axial wave number). Primary attention is focused on the influence of bonding condition at the liner/soil interface, formation material type, and load velocity on the system’s dynamic response. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.