Generalized complex variable analysis of shallow tunneling through multi-layered ground

Abstract

The mechanical analysis of shallow tunnels crossing multiple ground layers is a common problem in urban underground engineering. Since the tunnel boundary intersects multiple ground layers, the challenges of mixed boundary value problem for composite boundary and the conformal mapping of irregular banding computational domain are faced in solving the multi-boundary problem. For this, a new solution strategy regarding the generalized complex variable method to calculate the mechanical responses of the multi-layered ground is proposed. The research object is divided into two independent objects including the complete multi-layered ground without tunnel and the complete tunnel boundary. Firstly, the mechanical responses of the complete multi-layered ground are solved through the superposition of multiple single-boundary contributions. Subsequently, the virtual boundary circle and its corresponding analytic functions are introduced in analyzing the tunnel boundary contribution. Finally, the solution for the stress and displacement field of the multi-layered ground is modified by superimposing the contribution of the virtual boundary circle, so that all the given boundary conditions are satisfied. The self-consistency and accuracy of the proposed method are validated by several examples. The characteristics of the displacement propagation of typical multi-layered ground patterns are analyzed based on the analytical solution. The proposed method can be used to analyze the mechanical responses of multi-layered ground with arbitrary intersections between the tunnel and ground boundaries.