Analytical solutions for the displacement and stress of lined circular tunnel subjected to surcharge loadings in semi-infinite ground

Abstract For tunnels located at shallow depths, the adjacent surcharge loadings caused by new building constructions or overloading on the ground surface significantly influence the stability of the tunnel and lining. This study presents a new rigorous analytical solution for the stress and displacement around lined circular tunnels at a shallow depth, fully considering the interaction between the ground and rigid lining, and any distributed surcharge loadings. A new analytical approach is provided, where the original problem is divided into two problems: Problem 1 is a semi-infinite plane subjected to surcharge loads without any holes, and Problem 2 is a tunnel contained in a semi-infinite plane loaded by the prescribed displacements along the tunnel boundary. The solutions, which strictly satisfy all the boundary and compatibility conditions of the original problem, are finally addressed by the superposition of the solutions of Problems 1 and 2 respectively obtained by the modified Flamant's solution and complex variable theory. The good agreement between the analytical and numerical results under the same assumptions verifies the correctness of the proposed analytical solutions. Furthermore, the possible deviation due to the simplification of the analytical solution is also discussed. Based on the obtained analytical solution, a parametric study is carried out to investigate the influence of the key parameters on the stress and displacement of the ground and lining.