Ground Displacements due to the Deformations of Shallow Tunnels with Arbitrary Cross Sections in Soft Ground

Nowadays, a huge number of shield-driven tunnels with noncircular cross sections are constructed in urban areas all around the world. However, the ground displacements associated with tunneling still form a difficult issue, especially for noncircular tunnels. In this study, an analytical solution is derived to estimate the ground displacements induced by the deformations of shallow noncircular tunnels in soft ground. First, a solution for the stresses and displacements around a deep tunnel in a full plane is formulated by imposing a specified convergence pattern over the cavity boundary. Subsequently, this solution is validated using finite element simulations in a case study of an elliptical tunnel with four different convergence patterns. Afterward, the solution in the full plane is extended to a half plane using the virtual image technique to estimate the ground displacements around shallow tunnels. The solution is also validated using finite element simulations.