A Numerical Approach for Evaluating the Convergence-Confinement Curve of a Rock Tunnel Considering Hoek-Brown Strength Criterion

The convergence-confinement method is frequently used for the analysis of the behavior of a tunnel and to define the support structures necessary to guarantee its stability. The reasons why it is used extensively, at least in the preliminary study phases of a tunnel are: The fundamental parameters of the problem (the diameter and depth of the tunnel, as well as the mechanical characteristics of the ground in which the tunnel is being excavated) can be considered in the calculation; the stresses and strains in the ground and the displacements of the tunnel wall can be obtained from the results of the calculation; the thickness of the plastic zone around the tunnel can be estimated by the method. The application of this method to rock masses, which are characterized by a non-linear strength criterion, has been limited to a restrictive number of works in the literature. In order to consider non-linear strength criteria, some simplifications are generally introduced in order to be able to obtain a simple expression of the stresses and strains in the rock mass and of the displacements of the tunnel wall. A numerical solution is presented in this study with which it is possible, in a simple way, to precisely describe the convergence-confinement curve of a tunnel excavated in rock masses, without the need of introducing any simplifying hypotheses for the description of the stress-strain relations in a plastic field.