Numerical Investigation of Rock–Backfill Composite Fracture Evolution Laws Under Deep Mining and Filling Stress Paths

Numerical modeling of excavation-induced fracturing in rock foundations: a case study from the tectonically active Zagros Region

Influence of random hole ratio on dynamic mechanical behavior and crack evolution of sandstone

Fracture Process Zone Evolution in Tight Sandstone Under Crack-Parallel Stress: A DIC Study

Crack-parallel stress modifies the near-tip stress state and may influence the development of the fracture process zone (FPZ) in rock. However, the spatial and temporal evolution of the FPZ during hydraulic fracturing cannot be reconstructed from the final fracture morphology alone. In this study, visual hydraulic-fracturing experiments were conducted on seven tight-sandstone specimens, with crack-parallel stress varied from 0 to 10 MPa while the other experimental conditions were kept consistent. Time-resolved full-field digital image correlation (DIC), combined with displacement–strain cross-calibration, was used to continuously track the initiation, expansion, localization, and coalescence of the FPZ, as well as the evolution of the traction-free crack tip and crack opening displacement (COD) on the specimen surface. The observations showed that the macroscopic traction-free crack did not form instantaneously but developed through progressive localization and coalescence of distributed damage within the FPZ. At the specimen level, the tests under nonzero crack-parallel stress exhibited shorter maximum FPZ lengths (14.7–30.6 mm) and lower critical COD values (10.5–27.5 μm) than the single 0 MPa reference specimen (80.9 mm and 38.2 μm, respectively). Given the limited replication, these differences are treated as descriptive specimen-level observations. The critical COD also varied non-monotonically across the tested stress levels. Three specimen-level FPZ–crack initiation patterns were identified: localized, matrix-nucleation, and diffuse-to-localized patterns. Their occurrence indicates that crack-parallel stress modifies near-tip confinement and crack-opening conditions, while specimen-scale heterogeneity and local defect distribution influence damage localization and the crack initiation site. These time-resolved observations reveal the spatiotemporal transition from distributed FPZ damage to traction-free crack formation, providing process-level information that cannot be obtained from the final fracture state alone.

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.

Mechanical and Permeability Properties of Cemented Tailings Backfill Under Seepage-Stress Coupling

This study addresses stability degradation of cemented unclassified tailings backfill (CTB) under seepage-stress coupling in deep water-rich metal mines. CTB specimens with diverse mix proportions were prepared to explore their mechanical and permeability responses under varying seepage water pressures, and a response surface regression model was built to quantify multi-factor interactive effects on permeability. Results reveal that increased seepage pressure degrades CTB mechanical performance, while the degradation rate gradually declines. Higher cement-tailings ratios amplify the weakening effect of seepage pressure on elastic modulus. The permeability-strain evolution curve of CTB resembles its σ-ε, and the strain at peak permeability kmax always exceeds peak stress strain. The interaction between cement-tailings ratio and seepage water pressure dominates the variation in kmax and kmin. This work deepens the understanding of CTB seepage-mechanical behaviors and offers experimental references for proportion design and stability assessment of CTB in water-rich underground mines.

Numerical Simulation of Crack Propagation in Concrete with Prefabricated Array Fractures Based on the Discrete Element Method

Concrete readily develops cracks under service loads, which poses severe risks to the overall safety of engineering structures. In this work, the discrete element method (DEM) integrated with PFC2D 5.0 numerical software is adopted to construct a mesoscale concrete numerical model containing pre-existing internal fractures, and uniaxial compressive loading simulations are subsequently carried out. Unlike previous studies that predominantly examined isolated fracture parameters, this work systematically investigates the coupled effects of fracture inclination angle, length, and quantity on crack propagation mechanisms at the mesoscale, and for the first time establishes a quantitative relationship between microcrack spatial distribution patterns and macroscopic mechanical degradation. Parametric analyses are performed to quantify the influences of fracture geometric characteristics, including fracture inclination angle (30°, 45°, 60°), fracture length (short, long and extra-long), fracture quantity (4, 8 and 16), as well as the comparison between intact and fractured concrete specimens. The fracture quantities of 4, 8, and 16 are selected to represent low, medium, and high levels of initial defect density within the concrete matrix, corresponding to approximately 1%, 2%, and 4% of the total specimen area, respectively, thereby enabling a systematic investigation into the progressive deterioration of mechanical performance with increasing internal damage severity. The whole evolution process of crack initiation, crack propagation and ultimate failure patterns of concrete is systematically explored. Numerical results reveal that specimens with larger fracture angles exhibit higher compressive strength yet generate abundant newly formed microcracks, whereas low-angle prefabricated fractures are prone to triggering abrupt brittle failure. Specimens embedded with shorter fractures achieve superior mechanical strength and develop denser, more intensive microcrack distributions; in contrast, long pre-existing fractures drastically degrade compressive strength while limiting the generation of secondary cracks. Reducing the number of internal defects simultaneously improves compressive strength and expands the coverage range of the induced fracture network. Specimens with 16 prefabricated fractures deliver the weakest mechanical performance, owing to the excessively high initial defect density inside the matrix. In comparison with fractured samples, intact concrete without pre-set fractures achieves better comprehensive performance in terms of compressive strength, deformation compatibility and uniform microcrack development. A core conclusion drawn from this study is that the total quantity of microcracks cannot serve as a direct indicator to evaluate the damage degradation degree of concrete; instead, the spatial distribution pattern of microcracks dominates the deterioration level. Evenly scattered microcrack populations maintain relatively high residual strength, whereas the concentrated coalescence of microcracks into continuous penetrating macrocracks leads to an abrupt decline in structural load-carrying capacity. The findings of this research can provide theoretical references for stability evaluation and safety diagnosis of defective concrete structures in practical engineering.