An analytical solution for circular tunnels excavated in rock masses exhibiting viscous elastic-plastic behavior

Investigating time-dependent behavior of tunnels driven in rocks has been the topic of interest for many years. The majority of researches were conducted with the assumption that the behavior of the surrounding rock masses is viscoelastic. In this paper, an analytical solution is proposed for circular tunnels under hydrostatic stress field, whose surrounding rock mass is isotropic, homogenous, obeying viscous elastic-plastic constitutive model. It is assumed that the rate of excavation is infinitely large. Therefore, the solution is proposed for unlined tunnels when the advance of tunnel face is halted, or after lining installation when the tunnel face is far from the studied section. The results were compared with those predicted by finite difference numerical model which exhibited a good agreement for both lined and unlined tunnels, except for large times where numerical model results slightly exceed the values predicted by the proposed solutions for lined tunnels.