An analytical solution for sectional estimation of stress and displacement fields around a shallow tunnel

Abstract

In this paper, we present a solution for the sectional estimation of the stress and displacement fields of a liner and a geomaterial near a shallow buried tunnel. The complex variable method and the discrete Fourier transform are employed in the analytical derivation. The initial boundary conditions are the nonexistence of external loads acting on the liner interior and a Fourier curve obtained by fitting the displacement along the liner interior. Stress and displacement are continuous along the excavation line. In the verification, the stress and displacement fields within the excavation line obtained by the analytical solution agree well with the numerical results. Accuracy decreases as the spatial distance between the geomaterial and the excavation line increases, and the 5% error zones are defined. The accuracy of the solution would fall greatly out of these error zones. In another word, the analytical solution is not a general solution for the whole liner–geomaterial entity, but could serve as a quick sectional estimation, and is suitable for a variety of external loads on the ground surface.