A three-dimensional Hoek–Brown failure criterion based on an elliptical Lode dependence

A new three-dimensional (3D) Hoek–Brown (HB) failure criterion based on an elliptical Lode dependence is proposed to describe failure of rocks and concrete under multiaxial stress states. This criterion not only inherits all benefits of the classical HB criterion that is developed for the triaxial compression (TXC) of rocks but also accounts for the effect of the intermediate principal stress. It is capable of representing the strength difference between the triaxial extension (TXE) and TXC with the introduction of an additional coefficient k (0.5 ≤ k ≤ 1.0), which can be derived from TXE tests or taken as 0.53 for rocks in cases where the TXE test data is unavailable. Other two material constants (m_i and σ_ci) involved in this criterion can be obtained from TXC tests. Additionally, the failure surface of this criterion is smooth and convex on the deviatoric stress plane when 0.5 < k ≤ 1.0. The new criterion achieves very good fit to the test data of TXC/TXE, biaxial compression, and polyaxial compression (PXC) on a wide variety of rock materials and concrete, reported in the literature. Comparison of the new criterion with an existing 3D HB criterion based on the same Lode dependence has demonstrated that the new criterion performs better than the latter for test data of rock and concrete under multiaxial stress states except for PXC test data of one rock type. Finally, the influence of values of k on the accuracy of the new criterion is discussed.