A Nonlinear Hoek–Brown Criterion for Bedded Rock with Brittle–Ductile Transition

The conventional Hoek–Brown (H–B) failure criterion does not explicitly account for the combined effects of anisotropy and high confining pressure on rock strength. In bedded rocks, anisotropic mechanical behavior arises from the orientation-dependent weakening induced by bedding planes, which breaks the stress symmetry relative to the loading direction. To address this limitation, this study proposes a modified H–B criterion that incorporates a dip-angle-dependent anisotropy parameter and a high-confinement correction term to describe the brittle–ductile transition of bedded rocks. The proposed criterion was implemented in the discrete element software 3DEC through secondary development of the built-in H–B module using the FISH language. Triaxial compression tests were conducted on bedded marble and sandstone specimens with different bedding dip angles under uniaxial compression and confining pressures of 40, 80, and 100 MPa to examine their stress–strain responses and failure characteristics. Comparisons between experimental results and predictions from existing failure criteria show that the proposed criterion provides improved prediction accuracy and effectively captures the variation in strength with bedding dip angle and confining pressure. Numerical triaxial tests were further performed on Martinsburg Slate specimens with bedding dip angles of 0°, 45°, and 90° under confining pressures of 50, 100, and 200 MPa. The results indicate a clear transition from elastoplastic softening to ductile deformation with increasing confining pressure. The compressive resistance follows the order α = 0° > α = 45° > α = 90°, highlighting the role of bedding-induced strength asymmetry in the brittle–ductile transition of bedded rocks.