Complex Function Solution of Stratum Displacements and Stresses in Shallow Rectangular Pipe Jacking Excavation Considering the Convergence Boundary

Abstract

The construction of pipe jacking has little impact on the environment and is usually used to build underground passages with shallow buried depths and short lengths. Compared with circular pipe jacking, rectangular pipe jacking has the advantages of shallow buried depth and high space utilization. Therefore, research on the excavation of rectangular pipe jacking is necessary. This paper establishes a cross-section model of shallow buried rectangular pipe jacking excavation. Taking advantage of complex functions for solving problems involving non-circular tunnels, an analytical solution is obtained using an approximate mapping function and potential functions in series forms for the stress and displacement of the stratum with a displacement condition at the excavation boundary and a stress condition at the ground surface boundary. The finite element simulation results and the engineering-measured data are used for comparisons and verifications. With the analytical solution of the complex function, the influence of selecting control points for the mapping function on the accuracy is calculated and analyzed, as well as the influence of the stratum loss rate, span, buried depth, and stratum unit weight on surface subsidence and major principal stress of the excavation boundary. The proposed analytical solution can be applied to the construction of rectangular pipe jacking tunnels.