A Complex Variable Solution for Shallow Rectangular Tunnel in Semi-Infinite Plane

The rectangular pipe jacking method, as a new type of shallow tunnel excavation technology, is increasingly widely used in practical engineering due to its advantages of higher space utilization and fewer impacts on the surrounding environment. The construction process of pipe jacking will cause stress change and deformation of the surrounding soil. In this paper, on the basis of the complex variable elasticity, an analytical solution for a shallow rectangular pipe jacking tunnel under the action of rectangular cavity contraction and inner uniform pressure is proposed. Through the conformal mapping technique, the rectangular cavity in a semi-infinite plane is first transformed as a unit concentric ring. Then, the stress functions for the stress and displacement around the rectangular cavity under two types of boundary conditions are derived, which allows the stress change and deformation of the surrounding soil to be determined. The proposed analytical solutions are verified by comparison with the results of finite-element numerical simulations. Parametric studies are conducted to investigate the influence of the Poisson's ratio effects of soil, tunnel aspect ratio, and tunnel burial depth on the stress and displacement of soil. The proposed analytical solution can be potentially applied to the problem of a rectangular tunnel using pipe jacking.