A Three-Dimensional Nonlinear Strength Criterion for Rocks Considering Both Brittle and Ductile Domains

A three-dimensional nonlinear strength criterion for rocks considering both brittle and ductile domains is proposed through the combination of the segmented meridian function and a generalized deviatoric function with one parameter. The segmented meridian function is composed of the Hoek–Brown criterion, the smoothing transition surface, and the modified Drucker–Prager cap model. Besides, two deviatoric functions characterizing the smoothness and convexity based on the Matsuoka–Nakai criterion are suggested to describe the initial yield stage (brittle domain) and compaction yield cap stage (ductile domain). To verify the accuracy of the proposed strength criterion, six representative sets of true triaxial experimental data were selected from the existing literature, including two types of rocks, namely Dunham dolomite, KTB amphibolite, Mizuho trachyte, and Westerly granite that are independent of hydrostatic pressure in the brittle domain, and Bentheim sandstone and Castlegate sandstone which are dependent on hydrostatic pressure in the brittle–ductile domain. The results show that the experimental data are evenly distributed on the surface of the failure envelope in the three-dimensional principal stress space, demonstrating that the proposed strength criterion can accurately describe and predict the strength change of rocks in both brittle and ductile domains.