Scattering waves generated by cylindrical lining in saturated soil based on nonlocal Biot theory

Based on the Biot theory and the nonlocal elastic theory, the nonlocal Biot governing equations are proposed. The analytical solutions to the scattering wave fields generated by the cylindrical lining structure under incident plane waves are obtained utilizing the wave function expansion method under specific boundary conditions. The solutions are verified by degenerating the two-phase materials into single-phase ones and by comparing with the classical Biot theory as well. It is shown that the dynamic stress concentration factors on the inner and outer surfaces of the lining decrease with the increasing nonlocal factor. The distribution curves of dynamic stress concentration factor on the inner surface of the tunnel increase with the decrease of nonlocal factor. The influences of pore size and porosity dynamics in saturated soils cannot be ignored when the frequency of incident waves is greater than 0.045 MHz. For a certain nonlocal factor, the dynamic stress concentration factor increases with the increase of the ratio of outer radius to inner radius of the lining. The dynamic stress concentration factor may be negative on the inner surface of the lining for a thin lining.