A Nonlinear Rock Failure Criterion Taking Account of the Intermediate Principal Stress

This paper proposes a new 3-D nonlinear rock failure criterion which is an extension of Hoek-Brown equation to its 3-D form, so that the new criterion employs the same strength parameters appearing in the original 2-D Hoek-Brown criterion, viz. m, s, s_c. The convexity and the smoothness of the new failure surface are ensured for wide range of stress conditions by adopting the Jiang & Pietruszczak (1988)'s octahedral shape function. The new criterion can embody the effect of s₂ and at the same time it preserves the nonlinear characteristics implied in the original Hoek-Brown equation. When depicted in the principal stress space, the new failure surface circumscribes the Hoek-Brown surface with smooth contacts at six corners. Four sets of true triaxial test data collected from the published literature are simulated to demonstrate the performance of the proposed 3-D rock failure criterion. The strength predictions made by the new criterion with the best-fitting parameters are compared with the experimental data in the s₁ -s₂ plane. The best-fitting analysis confirms that the variation of s₁ with s₂ in the prediction is consistent with the trend observed in the test data sets.