Equivalent Mohr–Coulomb and generalized Hoek–Brown strength parameters for supported axisymmetric tunnels in plastic or brittle rock

The evaluation of equivalent Mohr–Coulomb (M–C) strength parameters to the prototype Hoek–Brown (H–B) ones for tunnels has been tackled in different ways for many years. The extension of the H–B criterion to the generalized one has made the challenge even greater. Most of the latest methods did not account for the effect of the support pressure and none gave formulae for equivalent parameters of supported or brittle rock. Here, an almost exact explicit solution for the evaluation of the critical pressure, of a tunnel in a rock mass satisfying the generalized H–B criterion, is initially investigated. Then, formulae are derived for the evaluation of equivalent parameters, of either elastoplastic or elastic–brittle plastic rock. They are based either on a best fitting procedure of the two envelopes or on the equation of selected responses of the models. Supported tunnels in equivalent M–C rock masses are then validated against those excavated in the prototype H–B rock masses.