A Complex Variable Solution for Rectangle Pipe Jacking in Elastic Half-Plane

In mechanics, the solution of soil stresses and displacements field caused by shallow rectangular jacking pipe construction can be simplified as half-plane problem. Both the boundary conditions of the surface and the cavity boundary must be taken into account. It is the essential prerequisite for mechanical analysis of the pipe jacking with the complex variable theory that the mechanical boundary must be transformed from the half-plane with a rectangle cavity to the concentric ring. According to Riemann's existence theorem and basic complex variable theory, a conformal mapping function is established. Both sides of boundary conditions equation are developed into Laurent series, and then the coefficients of complex stress function are solved by power series method. The derived solution is applied to an example and a comparison is made using FEM method to show the accuracy of the methods. The result shows the following: (1) the method presented in this paper is applicable to a shallow-buried rectangular tunnel; (2) the complex function method proposed in this paper is characterized by clear steps, fast convergence, and simple operation.