A novel three-dimensional nonlinear unified failure criterion for rock materials

To study the failure (strength) regularities of rocks under complex stress states, we propose a novel three-parameter deviatoric function that includes the shape of the failure envelope on the Mohr–Coulomb (MC), Ottosen, Bigoni–Piccolroaz, and Wu–Zhang deviatoric planes. This function realizes the deviatoric plane shape of numerous classic criteria, including the Rankine, Tresca, von Mises, generalized Tresca, MC, Drucker–Prager (DP), Matsuoka–Nakai (MN), Lade–Duncan (LD), and Ottosen. On this basis, taking the nonlinear characteristics of the power function, we establish a novel 3D NUF criterion, namely MCNUF and LDNUF criteria, where the novel parameter γ is based on the basic parameters of two classical criteria, MC and LD, respectively. Based on the triaxial test data of different rocks, the proposed MCNUF and LDNUF criteria are compared with the previous criteria (the generalized nonlinear failure criterion (MNGNF), the DP and MN unified (DPMNu) criterion). Results show that: (1) the internal friction angles predicted by each criterion are equal under the same meridian plane parameters. (2) For four kinds of rock materials, the prediction performance of the proposed criteria is generally better than that of the MNGNF and DPMNu criteria. (3) The proposed criteria describe the hydrostatic stress and IPS and their coupled effect on various rock materials. (4) The 3D graphical visualization of the proposed criteria is carried out systematically, which plays a positive guiding role in enriching and perfecting the strength theory.