The Hoek-Brown failure criterion is an empirical stress surface used in rock mechanics to predict the failure of rock. It was originally developed by Evert Hoek and E. T. Brown in 1980 for designing underground excavations. The criterion has since been updated and extended to include various applications such as slope stability and surface excavations.
Key components of the Hoek-Brown failure criterion
Basic form
The original Hoek-Brown criterion is given by the equation:
σ1 = σ3 + (Aσ3 + B2)1/2
where σ1 is the maximum principal stress, σ3 is the minimum principal stress, and A and B are material constants related to the unconfined compressive and tensile strengths of the rock (Pariseau, 2007).
Generalized Hoek-Brown Criterion
This version, updated in 2002, includes parameters such as the Geological Strength Index (GSI) and a disturbance factor (D) to better account for the properties of rock masses. It relates the major and minor effective principal stresses (σ1 and σ3) using the equation:
σ’1 = σ’3 + (mbσciσ’3 + sσ2ci)1/2
where mb is a reduced material constant, σci is the uniaxial compressive strength of the intact rock, and s and aa are constants that depend on the rock mass characteristics (Hoek et al., 2002).
The Hoek-Brown criterion is widely used in mining engineering and rock mechanics for predicting rock failure in various conditions, including underground excavations and slope stability analyses. It provides a more accurate estimation of rock strength compared to other criteria like Mohr-Coulomb, especially for tensile strength. The criterion assumes a homogeneous and isotropic rock mass, which may not always be applicable in practice, particularly for structurally controlled failures.
Reference
Hoek, E., Carranza-Torres, C., & Corkum, B. (2002). HOEK-BROWN FAILURE CRITERION – 2002 EDITION. https://www.semanticscholar.org/paper/HOEK-BROWN-FAILURE-CRITERION-2002-EDITION-Hoek-Carranza-Torres/e44829e6d2c1484d25efe6be2db830e16c8f9d89
Pariseau, W. G. (2007). Design analysis in rock mechanics. Taylor & Francis.
