A The responses of some lined underground openings under hydrostatic or biaxial stress field are examined numerically for original HB and equivalent MC strength parameters. The rock mass is assumed brittle and the horizontal to vertical stress ratio is varied. Selected tunnel responses of the openings for the original HB rock mass are compared to the responses computed using equivalent MC strength parameters. These include the displacement at the crown and the side walls of the opening, the yielded zone formed around the tunnel and the internal forces within the tunnel lining. Results indicate the cases where deviations in the tunnel performance are computed.


The non-linear Hoek-Brown (HB) strength criterion is widely employed in numerical analysis for tunnel design, as the failure criterion to simulate the triaxial behavior of the rock mass. However, many numerical codes, either of general purpose or specialized for geotechnical design, do not implement the HB criterion, while they may allow for the linear Mohr-Coulomb (MC) criterion. This necessitates the development of procedures for the evaluation of MC parameters from the prototype HB ones, which when used in numerical codes for the simulation of constructions in rock, would evaluate similar responses. Such MC parameters and corresponding rock masses are defined as equivalent to the prototype HB ones, respectively.

Several methods have been developed for the evaluation of equivalent MC strength parameters for given HB ones. Traditionally, they are based on a linearization procedure of the HB strength envelope for a selected range of the minor principal stress. This range is either considered as independent of the in situ stress field (Hoek and Brown, 1997) or depends on it. In the latter case the internal pressure offered by the tunnel support may either be neglected (Hoek et. al., 2002), covering thus a wider range of rock mass responses, or taken into account (Sofianos and Halakatevakis 2002, Sofianos 2003, Sofianos and Nomikos 2006, Jimenez et. al. 2008), aiming to better approximate the final equilibrium condition of the tunnel.

Most of the existing methods are concerned with the case of an elastic-perfectly plastic rock mass. However, rock mass may exhibit a strain-softening behavior after failure. The importance of post-peak behavior of rock mass for rock engineering design has already been recognized (Hoek & Brown 1997, Russo et. al. 1998, Ribacchi 2000) and recently emphasized (Cai et. al., 2007), since it may have a strong influence on the stability of the underground excavations. Sofianos & Nomikos (2006) presented two methods, BFe and EMR, to calculate the equivalent MC rock mass strength parameters for axisymmetric tunnels in plastic or brittle rock. These are shortly described in the following.


Brittle behavior of the rock mass is represented with a sudden drop in its strength parameters after failure, corresponding to the two failure envelopes of Figure 1. For the HB criterion the rock mass strength is defined by two sets of parameters;σci, mb, s and a for the pre-failure behavior and σciR mbR, sR and αR for the post-failure behavior.

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