Criteria for Residual Strength and Brittle-Ductile Transition of Brittle Rock

The quantitative links between macroscopic criteria and microscopic mechanisms remain limited for understanding the difference in failure characteristics of rock. This study develops a mathematical framework to evaluate both the peak and residual strength of rock based on elastic fracture mechanics. A new indicator, σ∗1−σ∗3, is introduced to characterize the brittle-to-ductile transition (BDT). The model incorporates microcrack friction and intergranular sliding to predict the transition point. Validation against experimental data confirms that the model describes the relationship between critical stress and confining pressure. The experimental result indicates that microcrack friction and macro sliding show opposite effect on the BDT stress. The proposed framework not only elucidates the BDT mechanisms but also offers practical guidance for laboratory testing, analytical modeling, and numerical simulation.