Further Development of the Three-Dimensional Hoek–Brown Yield Criterion

The original Hoek–Brown failure criterion was first introduced in 1980. Since then, it has been further developed and used in different rock mechanics applications. The main advantage of the Hoek–Brown criterion is that its input data are determined from the uniaxial compressive strength, mineralogy and structural properties of the rock. However, its application in the petroleum industry has been limited, partly because it does not take account of the intermediate principal stress in a three-dimensional stress state. In 2005, Priest introduced comprehensive and simplified versions of a new three-dimensional Hoek–Brown yield criterion, which was developed by combining the two-dimensional Hoek–Brown and three-dimensional Drucker–Prager criteria. Until now, direct analytical solutions have not been developed to solve the governing equations and numerical solution strategies have been applied. This paper presents and validates an explicit solution for the comprehensive three-dimensional Hoek–Brown yield criterion, which can be combined with numerical stress modelling codes.