Analytical solutions of stresses and displacements for deeply buried twin tunnels in viscoelastic rock

A set of analytical solutions is presented to calculate the stresses and displacements generated when two closely located circular tunnels are sequentially excavated in viscoelastic rock. The solutions are provided for circular tunnels excavated in time dependent rock for any type of linear viscoelastic model, e.g. Burgers and Poyting-Thomson model. In the presented solutions the sequential excavation of the tunnels is also accounted for. The radii of the twin tunnels are time-dependent functions reflecting the excavation process adopted. The solutions are provided as analytical expressions in integral form. These were obtained by extending the principle of correspondence to solid media with time varying boundaries. A comparison of the stresses and displacements predicted by the analytical solutions and FEM analyses for an example case of twin tunnels excavated in a generalized Kelvin medium shows a good agreement between the two methods. Then, a parametric analysis was performed to investigate the influence of the tunnel spacing on displacements and stresses for various excavation processes. Several dimensionless charts summarizing the result of the parametric analysis are provided for the benefit of practitioners.