Although it appears that the Hoek-Brown empirical failure criterion is still the most suitable and realistic criterion for predicting the strength of rocks or rock masses, difficulties have occured in applying the criterion to both laboratory and numerical modelling. It is shown that in three dimensional (3-D) principal stress space, the yield surface of the Hoek-Brown criterion is a combination of the components of six two dimensional parabolic surfaces. After a thorough investigation ?f the nature of the Hoek-Brown and some other yield surfaces, a modified 3-D Hoek-Brown criterion is suggested and tested in association with the finite element method. The proposed criterion has particular advantages in numerical analysis and also in predicting the strength of weak rock masses.


An important phenomenon manifested by rock strata in the vicinity of underground openings is their non-linear response to induced stress. In situ observations and experimental results show that this is caused by a combination of pre-peak non-linear elasticity and post peak behaviour. After failure, a rock mass may exhibit strain softening, perfect plastic or strain hardening behaviour depending on confining pressure, rate of loading and rheologic characteristics of the material (Hudson et al. 1972a,b; Farmer 1983). For the mechanical description of non-linear post failure behaviour of a rock mass, a yield criterion based on the theory of plasticity is usually used.

To determine the conditions which govern the failure or yielding of a rock mass considered as an equivalent continuum, a 3-D strength criterion is generally required. Two of the classical strength criteria in incremental plasticity theory are the Mohr-Coulomb and Drucker-Prager criteria which define the simple yield surfaces of Fig. 1 in 3-D principal stress space.

A suitable shape of yield surfaces for rock materials has been considered to be a curved, pointed 'bullet' with curved cross sections in the octahedral planes, similar to those of Mohr-Coulomb but without sharp intersection points or corners (Serata et al. 1967; Akai and Mori 1970; Franklin 1971; Kim and Lade 1984). Recently, Michelis (1987) interpreted his truly triaxial test data in the meridian and deviatoric planes of yield surfaces and verified most of the above characteristics. Taking into account the practical application of a strength criterion in excavation design, not only the intact rock, but also the rock mass behaviour has to be considered in the development of a criterion(Hoek and Brown 1980). On the other hand, a rock strength criterion is at best only an approximate fit to the observed data, and thus it should be expressed in a simple way and involving the minimum number of parameters for practical excavation design.


Of the classical strength criteria, the Mohr- Coulomb criterion is generally considered the most acceptable for describing rock behaviour. However, through considering the strength criterion in 3-D principal stress space, the main discrepancies between the experimental results and those predicted by the Mohr-Coulomb criterion are the curvature of its yield· surface.

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