A failure criterion for rocks and concrete based on the Hoek-Brown criterion

There have been a number of attempts at developing three-dimensional Hoek-Brown (3D HB) failure criteria with non-circular cross sections to include the effect of the intermediate principal stress for rocks, which is neglected in the classical HB criterion. Those existing 3D HB criteria predict the same strength as the classical HB criterion in triaxial extension (TXE) and triaxial compression (TXC). This paper presents a new failure criterion for rocks and concrete based on a unified expression of the 3D HB failure criteria, which can account for the strength difference between TXE and TXC. The failure cone of the new criterion is convex and smooth everywhere and the deviatoric cross-section of the failure cone can cover various shapes from a curved triangle as the lower bound to a circle as the upper bound. The deviatoric plane locus is controlled by a shape factor k, which can be easily identified from TXE tests. The proposed failure criterion has been validated by biaxial compression tests of concrete, TXC/TXE tests of intact rocks and concrete as well as polyaxial compression (PXC) tests of intact rocks, jointed rock masses and concrete. Results show that the new 3D criterion with an empirical parameter k=−0.99 performs well in characterizing the rock and concrete strength in PXC in the absence of TXE test data. The application of the new criterion to cross-anisotropic rock in PXC is also discussed to show the fabric effect on the rock failure.