A new three-dimensional rock strength criterion based on shape function in deviatoric plane

Rock strength criteria are the theoretical grounding of geotechnical design and stability estimation, the Mohr-Coulomb (MC) and Hoek-Brown (HB) criteria are the widely accepted criteria at present, due to their reasonability and unambiguous concept, however they overlook the effect of intermediate principal stress, and contain six singular corners in pi plane. Aimed at overcoming those limitations, the MC and normal parabolic criterion (NPC) were improved to their 3D versions that lead to smooth and convex for a wide range of strength parameters. The extended 3D strength criteria coincide with corresponding original forms in the triaxial compression and triaxial extension states, which not only take intermediate principal stress into account, but also provide great convenient in numerical calculation. Multigroup of poly-axial strength datasets gathered from the references are used to check the prediction accuracy of the proposed 3D criteria by the least absolute deviation method. Research proved that the 3D NPC criterion has a relatively larger deviation on poly-axial strength data prediction, but the proposed 3D MC criterion can describe peak strength with low misfit for soft or hard rocks. Peak strength sigma 1 increases first and then decreases with the increase of sigma 2, whether increasing or decreasing sigma 2, both will result in rock failure. Moreover, the 3D MC can fit the poly-axial strength data well for lower or higher values of sigma 3, which strongly suggests the proposed 3D MC criterion is adequate. Applicability of the proposed strength criterion will be discussed in further research. The normal parabolic criterion and Mohr-Coulomb criterion are modified to their 3D versions.The established criteria are checked for poly-axial data using the least absolute deviation method.The 3D MC can provide reliable predictions on poly-axial strength for various rock types.The 3D MC can provide reliable predictions on poly-axial strength for various rock types.