Analytical Solution of Displacement and Stress Induced by the Sequential Excavation of Shallow Twin Noncircular Tunnels in Viscoelastic Rock

Nowadays, excavation of twin noncircular tunnels is becoming increasingly common. Generally, noncircular tunnels or smaller tunnel spacing would result in stress concentration, posing the underground structures subjected to dangerous conditions. Furthermore, the impact of surcharge loads on the stability of shallow buried tunnels is significant. This study proposes an analytical solution that can efficiently predict the mechanical response of the surrounding rock of shallow twin noncircular tunnels in time-dependent rocks. All key factors are thoroughly considered, including the viscoelastic properties of the rock mass, surcharge loads, arbitrary tunnel shapes and arrangements, excavation sequencing, and the pressures at the internal tunnel boundaries. Combining the complex function method with the conformal transformation technique, an elastic analytical solution for shallow buried noncircular tunnels is obtained. After that, based on the solution of a single tunnel, the elastic analytical solution of shallow twin noncircular tunnels is derived using the Schwartz alternating method. Then, based on the principle of correspondence between elastic and viscoelastic problems, the viscoelastic analytical solution for shallow twin noncircular tunnels is obtained. The comparison between the analytical solution and the finite-element numerical results is very consistent. Parametric analyses are then conducted on the step-by-step excavation of the twin tunnels to examine the effects of surcharge location, tunnel arrangement, and tunnel spacing on displacements and stresses. The analytical solution of this paper helps to reveal the mechanical mechanism of the step-by-step excavation of shallow buried twin noncircular tunnels in viscoelastic semi-infinite rock masses. Additionally, it can be applied to the preliminary design of similar shallow buried tunnels in the future.