Approximate analytical solution for elastic stress field of surrounding rock in shallow-buried multi-line non-circular tunnel

Tunnel excavation induces the redistribution of the stress field of surrounding rock, which directly controls its stability. Building upon Flamant’s solution, novel approximate analytical solutions for the elastic stress field around single and multiple holes are derived and validated through photo-elastic experiments and finite element simulations. The analytical method is further applied to stress analysis in multi-line non-circular tunnel surrounding rock to systematically investigate the influence of overload, lateral pressure coefficient, tunnel spacing, and inclined ground surface on stress distribution. The results demonstrate that the theoretical solutions agree well with the photo-elastic test and numerical simulation results. The isochromatic fringes of the centrally square-holed specimen under external loading are symmetrically distributed, whereas the shear stress field exhibits a butterfly-shaped distribution. It is also found that both the location of ground overload and the magnitude of the lateral pressure coefficient have a significant impact on the stress distribution in the tunnel surrounding rock. Moreover, the interaction effect between adjacent tunnels becomes negligible when the tunnel spacing reaches three to four times the maximum excavation dimension. Among the three layout forms, the inclined layout has the greatest influence, followed by the horizontal layout, while the vertical layout has the least. Furthermore, the support method also significantly affects the stress distribution in the surrounding rock. The research findings will provide a theoretical basis for stability assessment and support structure design in tunnel engineering.