Analytical and numerical study of the effect of water pressure on the mechanical response of cylindrical lined tunnels in elastic and elasto-plastic porous media

This paper revisits the classical problem of excavating a deep cylindrical tunnel in a saturated elastic or elasto-plastic porous ground that obeys Terzaghi's effective stress principle. A generalized form of the classical two-dimensional analytical solution by Lamé for the problem of excavating a cylindrical tunnel in elastic medium subject to axi-symmetric loading is presented. The solution considers the long-term (i.e., post-transient) mechanical effect of changes in pore pressure due to drainage of the ground around the opening on the mechanical response of the tunnel. The proposed solution together with the analytical solution for axi-symmetric loading of an annular ring representing a liner are used to explain the fundamental differences in support loading obtained for various hydro-mechanical conditions. These conditions involve excavating the tunnel with a permeable liner, with and without removal of water from the tunnel, excavating the tunnel with an impermeable liner, with subsequent drainage of water in the ground around the tunnel, etc. The results obtained with the analytical solution are compared with results obtained with the hydro-mechanical option in a commercial finite difference code. The finite difference approach is also used to obtain results and explain the behavior of the tunnel under different hydro-mechanical conditions when the ground is assumed to behave elasto-plastically.