Rock Brittle–Ductile Transition Under Coupled Confining Pressure and Strain Rate Effects: A Model Based on Peak and Residual Strengths

Mechanical response and failure mechanisms of sandstone under water–rock interaction: a multi-scale study and constitutive modeling

Analytical Model of Seepage Pressure Effect on Dynamic Compressive Fractures Caused by Microcrack Growth in Brittle Rocks

The dynamic compression fracture of brittle rock under seepage pressure is a critical issue for deep underground engineering. It directly influences the stability and safety of the surrounding rock during blasting or seismic loading. However, research on the mechanisms of microcrack evolution under these coupled conditions is still lacking. The relationship between microcrack evolution and macroscopic mechanical properties also remains poorly understood. This study develops a micro–macrofracture model grounded in the wing microcrack propagation framework, integrating both mechanical and chemical interactions between free water and rock. Mechanically, it incorporates seepage pressure, dynamic Stefan force, and dynamic fracture toughness. Chemically, it accounts for the effects of saturated water on rock mechanical parameters. This model characterizes the total stress–strain constitutive behavior of brittle rock under varying seepage pressures during dynamic compression failure, encompassing both strain-hardening and strain-softening phases. This result is validated against experimental data. It accounts for the influence of seepage pressure on both the initial crack and the newly formed wing crack. The seepage pressure weakens the wedging force F W on the initial crack while enhancing the seepage tensile force F P on the wing crack, which constitutes the seepage pressure-driven crack growth mechanism. Furthermore, under the combined effects of dynamic loading and free water, the dynamic Stefan force F S and the dynamic fracture toughness K ICD serve as the mechanism for inhibiting crack growth. The combined influences of seepage pressure, confining pressure and initial crack characteristics on the dynamic mechanical behavior of brittle rock under seepage pressure are discussed.

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.

Dynamic Progressive Failure and Energy-Driven Damage Evolution of Coal–Sandstone Composite Specimens Under Impact Loading: Coupling Effects of Component Ratio

Overburden rotation and mining disturbance promote deep coal fracture and spalling, potentially inducing dynamic hazards, while the coal–rock thickness ratio largely governs the composite’s dynamic response and failure severity. Based on the geological conditions of a typical deep coal mine, SHPB tests were performed on coal–sandstone composite specimens with four systematically varied coal-to-rock ratios (C:R = 1:0, 2:1, 1:1, and 1:2). High-speed photography and the digital speckle correlation method (DIC) were integrated to capture displacement, strain, energy, and fragmentation fields throughout progressive dynamic compression. Experimental data revealed four findings: (1) Crack development follows a sequential evolution process of initiation, propagation, and failure. Higher impact air pressure accelerates crack development and coalescence, resulting in a higher degree of specimen fragmentation and fewer large blocks. Within the tested range of coal–rock ratios, an increase in the rock proportion accelerates coal fracture, which is attributed to the significantly higher density and hardness of rock compared to coal. (2) Energy evolution consistently follows three stages: absorption, accumulation, and dissipation. Under identical impact pressure, a higher rock ratio elevates equivalent stiffness and wave impedance, leading to monotonic increases in peak stress, peak strain, absorbed energy, and dissipated energy. (3) The fragmentation degree exhibits a pronounced dependence on impact pressure. Specifically, for the pure coal specimen (C:R = 1:0), when the impact pressure increases from 0.3 MPa to 0.7 MPa, the mass percentage of coarse debris (>30 mm) drops from 73.37% to 18.57%, whereas that of fine particles (<4 mm) rises from 15.69% to 35.24%. (4) Under identical impact conditions, a higher rock proportion leads to increasing trends in all measured indicators, including peak stress, strain, and energy accumulation and dissipation, which are consistent with the superior mechanical properties of the rock. Based on these observations, it can be inferred that the wave impedance mismatch and stiffness ratio at the coal–rock interface play a key role in controlling stress wave transmission/reflection and strain incompatibility; however, the individual contribution of each factor warrants further dedicated investigation.

Entry-scale investigation on shale roof model calibration considering anisotropic brittle failure in U.S. coal seams

In U.S. underground coal mines, immediate/main roofs are usually composed of laminated shale, which exhibits strong anisotropic brittle failure behavior due to the presence of bedding planes. Existing numerical models often fail to accurately capture this behavior, as they neglect the dependence of strength and elastic properties on the orientation of bedding planes and lack comprehensive calibration against underground measurements. To address these limitations, this study investigates five key U.S. coal seams—Lower Kittanning, Pittsburgh, Pocahontas No. 3, Blue Creek, and Sunnyside—by developing and applying an anisotropic brittle failure criterion within a FLAC3D entry-scale model. The model explicitly accounts for strength and Young’s modulus anisotropy, cohesion-weakening friction-strengthening (CWFS) behavior, and dilatational response based on plastic shear strain. A systematic calibration procedure is proposed to ensure realistic representation of field conditions: (1) Calibration of vertical and horizontal stresses; (2) Roof sag and cable loads calibration; and (3) Verification of anisotropic brittle failure characteristics. The model simulates vertical stresses from 5 MPa to 48 MPa and horizontal stresses from 6 MPa to 42 MPa, covering a broad range of geological conditions across U.S. coal seams. The calibrated model provides a more accurate representation of stress distribution, roof sag, cable loads, and failure characteristics in shale roofs compared to conventional approaches. Furthermore, the simulation results presented anisotropic brittle failure characteristics under four types of mining geological conditions: (1) Highly laminated shale roofs. (2) High horizontal stress conditions. (3) Deep mines with a three-pillar system. (4) Deep mines with a one-pillar system. This research enhances the understanding of anisotropic brittle failure characteristics in laminated shale roofs at an entry-scale. An entry-scale FLAC3D model incorporating strength and Young’s modulus anisotropy, CWFS behavior, and dilatational response is developed and calibrated across five U.S. coal seams. The model simulates vertical stresses from 5 MPa to 48 MPa and horizontal stresses from 6 MPa to 42 MPa, covering a broad range of geological conditions. Anisotropic brittle failure characteristics are analyzed across four types of mining geological conditions: laminated shale roofs, high horizontal stress, deep mines with three-pillar, and one-pillar systems. An entry-scale FLAC3D model incorporating strength and Young’s modulus anisotropy, CWFS behavior, and dilatational response is developed and calibrated across five U.S. coal seams. The model simulates vertical stresses from 5 MPa to 48 MPa and horizontal stresses from 6 MPa to 42 MPa, covering a broad range of geological conditions. Anisotropic brittle failure characteristics are analyzed across four types of mining geological conditions: laminated shale roofs, high horizontal stress, deep mines with three-pillar, and one-pillar systems.

Research on the Stability of Arc-Fractured Rock–Concrete Composites: Mechanical Response and Energy Evolution

To mitigate the violent movement of overlying strata in goaf areas, rock–concrete composite support systems are widely utilized. However, the mechanical behavior of such systems under the influence of complex pre-existing defects, such as arc-shaped fractures, remains insufficiently understood. This study aims to clarify the failure mechanisms and the evolution of stability in these composites by evaluating the influence of fracture inclination angles. A synergistic methodology was adopted, combining laboratory uniaxial compression tests with discrete-element method simulations. Based on energy dissipation theory and the strain equivalence hypothesis, a statistical damage constitutive model was established to bridge the gap between microscopic damage and macroscopic mechanical response. The results demonstrate that fracture inclination significantly dictates the energy partitioning and crack propagation patterns within the composite. The established constitutive model, validated by numerical results ( R 2 > 0.999), effectively quantifies how increasing inclination angles enhance energy absorption efficiency and retard structural damage progression. Due to the high toughness of the concrete component, the composite maintains substantial residual bearing capacity, preventing instantaneous failure. These findings provide a robust theoretical framework and practical guidance for optimizing support designs in deep underground excavations with intricate geological defects.