Scattering of plane compressional waves by a variable thickness circular lined tunnel

Abstract

The determination of the dynamic stress concentration factor (DSCF) associated to a circular lined tunnel with variable thickness liner incident upon by compressional P-waves is of particular interest. Due to the lack of symmetry, the treatment of such a problem via the traditional wave-function expansion method is not possible. To circumvent this dilemma it is proposed to employ the dynamic equivalent inclusion method (DEIM). As it will be shown, this method which is based on the notions of the eigenstress and eigenbody-force fields provides an accurate solution for the problem under consideration. In the simple special case where a tunnel with a concentric liner is subjected to plane compressional P-waves the exact wave-function expansion solution given in the literature is recovered. The effect of liner thickness variability on the static and dynamic stress concentration along the interior surface of the liner and along the liner-matrix interface is studied in detail through numerical examples. The maximum value of the DSCF for the concrete and steel liners with positive and negative values of eccentricity is obtained and compared with those of the corresponding concentric cases. It is observed that the eccentricity of the liner results in different behaviors of the stress concentration for the hard (steel) and soft (concrete) liners.