Refined explicit solution for the stress field around an elliptical cylindrical tunnel with a moderate depth

Abstract

We consider a horizontal elliptical tunnel buried in a medium under gravity and lateral pressure (perpendicular to the generatrix of the tunnel). The stress field in the medium is generally treated as the superposition of an initial stress field induced by the gravitational body force and lateral pressure before tunnel excavation and the perturbation stress field after the introduction of the tunnel. Closed-form solutions for the perturbation stress field are available if the interaction between the tunnel and the surface of the medium is neglected. The initial stress field is usually assumed to be constant in deriving closed-form solutions for the perturbation stress field since it is often believed that the interaction between the tunnel and the surface of the medium is negligible only for a deep-buried tunnel. However, it is indicated from the literature that the interaction between the tunnel and the surface of the medium is insignificant in determining the stress distribution around the tunnel as long as the distance between them exceeds the diameter of the tunnel’s cross section. Consequently, we are motivated to derive in this paper a refined closed-form solution for the perturbation stress field by admitting a realistic initial stress field that varies linearly in the depth direction. The refined solution may lead to more accurate results in predicting the gravity-triggered stress concentration around a moderate-depth tunnel. The refined solution is compared with the classical solution (obtained by using a constant initial stress field) in calculating the hoop stress around the tunnel via several numerical examples.