Fractal Characterization of Mining-Induced Crack Evolution and Energy Release in Ultra-Thick Hard Strata

Quantifying crack evolution in ultra-thick hard strata is important for understanding mining-induced failure and energy release. Taking the 6306 working face at the Dongtan Coal Mine as a case study, physical similarity experiments and UDEC-Trigon simulations were combined with box-counting analysis to investigate crack fractal evolution and the influence of rock compressive strength. The numerical results were used to examine the correspondence between crack fractal dimensions and model released energy. The results show that localized cracks progressively propagate upward and laterally and coalesce into an extensive network, forming a failure region narrower at the top and wider at the base. The physical-model crack fractal dimension increases from 1.2386 to a maximum of 1.3910 and subsequently fluctuates slightly, reaching 1.3798. Tensile crack fractal dimensions increase progressively before exhibiting small fluctuations, whereas shear crack fractal dimensions follow a sequence of slow growth, rapid increase, pronounced decrease, and renewed increase. During the principal period of crack development, the maximum increases in tensile and shear crack fractal dimensions relative to the beginning of this period are 0.1861 and 0.1637, respectively. The corresponding increase in calculated released energy is 1.7126 × 1010 J, accounting for 60.32% of its total recorded net increase. Higher calibrated compressive strength suppresses early crack formation and restricts spatial propagation and coalescence, resulting in lower fractal dimensions. As failure progresses, tensile crack fractal dimensions under different strength conditions gradually converge, whereas shear crack fractal dimensions retain a greater dependence on strength. These findings characterize the distinct evolution of tensile and shear crack networks and their observed association with model energy release.