Analytical solution of deep tunnels in a strain-hardening elasto-plastic rock mass

Abstract

Excavation of tunnels produces a redistribuition of stresses and induces deformations in the rock mass around the tunnel’s cross section. In the case of elasto-plastic behavior of rock mass, plastic zones may appear. It is important to quantify the influence of this zone on the overall response of the tunnel. In this paper, we deduce a fully analytical solution in terms of displacements and stresses around a circular deep tunnel. The aim here is not to replace a 3D numerical calculation. This kind of analytical calculation are only useful to have a good understanding of the tunnel behavior in the preliminary phases of the project. For example, to perform parametric studies useful to choosing good parameters to introduce in a 3D numerical calculation. A homogeneous and isotropic rock mass is considered. For elasto-plastic behavior, the Tresca’s constitutive model with associate flow rule and Mohr-Coulomb’s constitutive model with non-associate flow rule are considered. For both, the idealized stress-strain curve presents a linear istropic hardening law. A geostatichydrostatic state of initial stresses and infinitesimal strains is assumed. The analytical solutions are compared with the FEM solutions demonstrating excellent agreement.