Powder Mass of Coal After Impact Crushing: A New Fractal-Theory-Based Index to Evaluate Rock Firmness

Firmness is one of the most important physical properties of rock, and indicates the rock’s ability to resist damage. It has considerable relevance to mining, blasting, tunneling, construction, and other engineering fields. In this study, the fractal particle-size-distribution theory was used to calculate the surface areas of coal particles after impact crushing. Combining the surface area with the energy input, a new index, fs, that can characterize the surface energy consumption was established. A total of 84 groups of impact crushing experiments were conducted on six samples from different coal mines, and their fs values were obtained. The effects of different initial particle sizes and impact numbers on fs were discussed. To verify the rationality of the fs approach, the tensile strengths of 900 particles were tested via single-particle uniaxial compression, and the strength distribution law was determined. The results show that there are significant linear positive correlations between both the tensile strength and modified Protodyakonov coefficient of coal and fs, indicating that fs can be used to evaluate rock firmness. This new index is of considerable significance to risk assessment of coal and gas outbursts, and is expected to be widely applied for firmness measurement of drilling cuttings and soft rocks.