The HoekâÂÂBrown failure criterion is an empirical stress surface that is used in rock mechanics to predict the failure of rock. The original version of the HoekâÂÂBrown criterion was developed by Evert Hoek and E. T. Brown in 1980 for the design of underground excavations. In 1988, the criterion was extended for applicability to slope stability and surface excavation problems. An update of the criterion was presented in 2002 that included improvements in the correlation between the model parameters and the geological strength index (GSI).
The basic idea of the HoekâÂÂBrown criterion was to start with the properties intact rock and to add factors to reduce those properties because of the existence of joints in the rock. Although a similar criterion for concrete had been developed in 1936, the significant tool that the HoekâÂÂBrown criterion gave design engineers was a quantification of the relation between the stress state and Bieniawski's rock mass rating (RMR). The HoekâÂÂBrown failure criterion is used widely in mining engineering design.
The HoekâÂÂBrown criterion has the form
where is the effective maximum principal stress, is the effective minimum principal stress, and are materials constants. In terms of the mean normal stress () and maximum shear stress ()
where
We can convert the above relation into a form similar to the MohrâÂÂCoulomb failure criterion by solving for to get
The material constants are related to the unconfined compressive () and tensile strengths () by
If we set in the above equation, we get the pure shear HoekâÂÂBrown criterion:
The two values of are unsymmetric with respect to the axis in the -plane. This feature of the HoekâÂÂBrown criterion appears unphysical and care must be exercised when using this criterion in numerical simulations.