Analytical stress and displacement around non-circular tunnels in semi-infinite ground

Abstract The construction of non-circular tunnels at shallow depths is becoming increasingly common to efficiently use excavation space. However, the stress concentration and ground movement are probably much greater around shallow non-circular tunnels than around deep ones; the greater stress and ground movement have significant negative effects on tunnel stability and the safety of nearby structures. This study provides a methodology for obtaining the analytical solutions of ground response induced by non-circular tunnel excavation. The surcharge loadings and gravity induced initial stresses, as well as the internal forces due to liners, are considered in the derivation. Using the Schwartz alternating method combined with complex variable theory, a series of two types of problems on simply connected domain, i.e. , a non-circular hole in an infinite plane and a half-plane without holes, is in turn successfully solved. Convergent and accurate analytical solutions are finally achieved by superposing the solutions in all the alternating iterations. The analytical solutions exhibit a close agreement with the numerical results, except for the horizontal displacement along the line near the ground surface. Finally, a parametric study is performed for the elliptical/square tunnel subjected to infinite surcharge loadings. The proposed analytical solutions have great value for the conceptual understanding of the mechanical behavior of non-circular tunnels and for verifying the numerical models. Moreover, an alternative approach is provided for the preliminary designs of future shallow tunnels excavated in rock or medium/stiff clay.