Dynamic Stresses and Displacements in a Buried Tunnel

Abstract

The dynamic response of a cylindrical tunnel embedded in a semiinfinite elastic medium is analyzed. The tunnel is assumed to be infinitely long, noncircular in cross section, and lying parallel to the plane‐free surface of the medium. The problem considered is one of plane strain, in which it is assumed that the waves are propagating perpendicular to the axis of the tunnel. Since this problem cannot be solved exactly except when the tunnel is circular, a numerical technique that combines the finite element method with the eigenfunction expansions is used. Numerical results are presented for the cases in which the tunnel is disturbed by plane longitudinal (P), vertically polarized shear (SV) and Rayleigh (R) waves. It is shown that the dynamic amplifications of the displacements and stresses induced in the tunnel depend crucially on the properties of the surrounding soil, the depth of embedment and the frequency of the incident simple harmonic disturbance.