Fractal Gradation Effects on Dynamic Response and Failure of Cemented Coal Gangue Backfill Composites

This study investigates the effect of coal gangue aggregate fractal gradation on the dynamic mechanical behavior and impact failure mechanism of cemented coal gangue backfill composites. Four aggregate gradations with different mass fractal dimensions were designed, and static compression and split Hopkinson pressure bar (SHPB) dynamic compression tests were conducted. The effects of fractal dimension and strain rate on stress-strain response, dynamic peak strength, dynamic increase factor (DIF), deformation modulus, energy dissipation, and failure morphology were analyzed. The results show that the composites exhibit a clear strain-rate strengthening effect, with dynamic strength, DIF, and deformation modulus increasing as strain rate increases. Aggregate fractal dimension has a nonlinear regulatory effect on mechanical performance. Among the four tested gradations, the specimen with D_f = 2.41 exhibits the best overall static and dynamic bearing performance, which is attributed to a more continuous coarse-particle skeleton and improved fine-particle filling. When the fractal dimension is too low, insufficient fine-particle filling leads to discontinuous contacts and larger pores; when it is too high, excessive fine particles weaken coarse-particle interlocking and promote matrix-dominated deformation. Energy analysis and failure observations further indicate that an intermediate fractal gradation improves energy absorption and delays unstable crack propagation. These findings provide a reference for gradation optimization and dynamic stability evaluation of coal gangue-based cemented backfill materials.