Analytical study on interaction between existing and new tunnels parallel excavated in semi-infinite viscoelastic ground

A new tunnel is usually excavated in close proximity to existing ones, which leads to significant negative influence on the existing tunnels. Moreover, the rheology of the ground probably induces quite different time-dependent ground deformation if the new tunnel is excavated at different time. This study focuses on the interaction between the existing and the new tunnels which excavated in rheological ground at a shallow depth. Through the strict derivation, a new analytical solution is proposed for ground stress and displacement induced by the interaction of new and existing tunnels. The ground rheology, excavation delay of the new tunnel, tunnel size and various tunnel arrangement, are all taken into account. The complex variable theory combined with the extension of corresponding principle are employed in the derivation. By deriving the potentials in complex variable theory for the problems in all the excavation stages, the time-dependent stresses and displacements are finally addressed for the whole excavation process, where the ground is simulated by any linear viscoelastic models. To verify and validate the analytical solutions, the analytical solution is compared with numerical results under simplified and complex ground conditions, which shows good consistency except the solution for Case 1 (considering gravity gradient). A parametric study is finally preformed to find the influence of excavation time and location of the new tunnel, the tunnel spacing and relative size of the new tunnel, on stresses/displacements around tunnels and surface settlements. The results show that the excavation time of the new tunnel (t(2)) significantly influence the additional displacements around the existing tunnel which is a decrease exponential function of t(2); when the distance from center to center is larger than 2.5R(1) (2.0R(1)), the interaction between two tunnels can be neglected from perspective of displacement (stress).