Evaluation of the Energy Consumption and Fractal Characteristics of Different Length-Diameter Ratios of Coal under Dynamic Impact

Coal samples having the same diameter (50 mm) and different length-diameter ratios (l/d), i.e., 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0 were tested under dynamic uniaxial impact compression using the Split Hopkinson Pressure Bar (SHPB) experimental system. This study evaluates: (a) The effects of l/d on the energy consumption law and fractal characteristics of coal crushing; (b) The effects of l/d and stress balance on energy dissipation; (c) The effects of l/d and energy consumption density on the fractal characteristics of coal crushing. The findings under different l/d are as follows: (1) The coal samples show similar stress-strain curve shapes in stages including elastic, plastic, and failure stage, which is an "open" shape, the proportion of plastic stage increases, and strain-softening occurs; (2) The dynamic compression dissipation energy and energy consumption ratio of coal shows the same trend, showing two stages with the increase of length-diameter ratio, which increases linearly in the first stage and overall decreases step-by-step; (3) The average particle size increases while fractal dimension of fragmentation decreases linearly, which endorses the decreasing trend of fragmentation degree; (4) It is determined that there is a power relationship between fractal dimension and energy dissipation density; (5) A new index Crushing Density Energy Efficiency (CDEE) is proposed, which can be used to characterize the rock-breaking efficiency of crushing energy consumption under different conditions. This index is inversely proportional to l/d. The research results can provide a basis for the design of top coal caving mining, and the determination of blasting parameters.