Analytical solution for the excavation of circular tunnels in a visco-elastic Burger’s material under hydrostatic stress field

By excavating an underground space, the state of stress and displacement are changed in comparison to the initial state. This variation depends on the advance of the tunnel and on the rheological behavior of the hosting rock mass. In this paper, the effect of creep, in the response of the tunnel is discussed. The objective of the paper is to predict time–dependent displacement of the tunnel wall, after stopping the excavation or after installing the support system. The rock mass is assumed to be isotropic and homogenous and incompressible. The tunnel is assumed to be circular and driven in a hydrostatic stress field. The rate of excavation is considered to be infinitely large. The Burger’s body which is able to model the primary and secondary creep regions of the rock mass is applied. In such a condition, an analytical solution for predicting time-dependent deformation of tunnel wall is derived. Thereafter, the application of the proposed solution is illustrated through three examples. The examples are analyzed numerically using the finite difference code FLAC. The results obtained from numerical analyses show proper agreement to the results of proposed solution.