Analytical stress and displacement of twin noncircular tunnels in elastic semi-infinite ground

Abstract

In general, twin noncircular tunnels may cause high stress concentrations and large settlements because of the strong interaction between tunnels and their noncircular shape. In this study, new analytical solutions are presented to efficiently predict the elastic stresses and displacements around shallow twin noncircular tunnels in rocks. The key factors, i.e., the real interactions between tunnels, arbitrary tunnel shapes, arrangements and pressures exerted at the internal tunnel boundaries due to liners or water pressures, are fully taken into account.The Schwartz alternating method is used to reduce the twin noncircular tunnels problem to a series of problems where only one noncircular tunnel is contained in the half-plane. Then, the solutions to the problem of a noncircular tunnel in the half-plane are obtained by complex variable theory combined with conformal mapping. Finally, convergent and highly accurate analytical solutions of twin noncircular tunnels are achieved by superposing the solutions of the reduced single tunnel problems. The analytical solutions are verified by the good agreement between the analytical and FEM results under the same assumptions. The proposed analytical solution can help to reveal the mechanical mechanisms of ground responses due to twin tunnelling in an elastic semi-infinite ground.