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 geostatic-hydrostatic state of initial stresses and infinitesimal strains is assumed. The analytical solutions are compared with the FEM solutions demonstrating excellent agreement.
Highlights
During the analysis of a deep tunnel it is essential to understand the behavior of the rock mass after the excavation
The excavation induces a disturbance zone around the tunnel that depends on the properties of the rock mass, the excavation method, in situ stress field, the geometry of the cross section of the tunnel and the type and stiffness of the support and the timing of its installation
This plastic zone is defined as a region in the rock mass where its stiffness parameters have changed due to the process of excavation and support of the tunnel
Summary
During the analysis of a deep tunnel it is essential to understand the behavior of the rock mass after the excavation. Considering different yield criteria (Mohr-Coulomb, Hoek-Brown, Tresca for example), stress-strain behavior (elasto-plastic perfect, hardening/softening or brittle) and strategies for considering volumetric reduction during plastic deformation (such as using a non-associated flow rule). The second case, more complex, considers a Mohr-Coulomb’s constitutive model with linear hardening behavior with non-associated flow rule, in wich post-peak dilatancy occurs at a constant rate with major principal strain. In both cases, an initial geostatic-hydrostatic stress field and infinitesimal deformation is adopted
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