A generalized nonlinear three-dimensional Hoek‒Brown failure criterion

Abstract

To understand the strengths of rocks under complex stress states, a generalized nonlinear three-dimensional (3D) Hoek‒Brown failure (NGHB) criterion was proposed in this study. This criterion shares the same parameters with the generalized HB (GHB) criterion and inherits the parameter advantages of GHB. Two new parameters, β, and n, were introduced into the NGHB criterion that primarily controls the deviatoric plane shape of the NGHB criterion under triaxial tension and compression, respectively. The NGHB criterion can consider the influence of intermediate principal stress (IPS), where the deviatoric plane shape satisfies the smoothness requirements, while the HB criterion not. This criterion can degenerate into the two modified 3D HB criteria, the Priest criterion under triaxial compression condition and the HB criterion under triaxial compression and tension condition. This criterion was verified using true triaxial test data for different parameters, six types of rocks, and two kinds of in situ rock masses. For comparison, three existing 3D HB criteria were selected for performance comparison research. The result showed that the NGHB criterion gave better prediction performance than other criteria. The prediction errors of the strength of six types of rocks and two kinds of in situ rock masses were in the range of 2.0724%–3.5091% and 1.0144%–3.2321%, respectively. The proposed criterion lays a preliminary theoretical foundation for prediction of engineering rock mass strength under complex in situ stress conditions.

Keywords

• Rock mechanics
• Hoek–Brown criterion
• Failure criterion
• Intermediate principal stress
• True triaxial test
• Smoothness and convexity