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, f s , 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 f s values were obtained. The effects of different initial particle sizes and impact numbers on f s were discussed. To verify the rationality of the f s 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 f s , indicating that f s 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.

中文翻译：

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冲击破碎后煤粉质量：一种新的基于分形理论的岩石硬度评估指标

硬度是岩石最重要的物理性质之一，表示岩石抵抗破坏的能力。它与采矿、爆破、隧道、建筑和其他工程领域具有相当大的相关性。在这项研究中，分形粒度分布理论被用来计算冲击破碎后煤颗粒的表面积。将表面积与能量输入相结合，建立了一个可以表征表面能量消耗的新指数 fs 。对来自不同煤矿的 6 个样品进行了 84 组冲击破碎实验，得到了它们的 fs 值。讨论了不同初始粒径和冲击数对 fs 的影响。为了验证 fs 方法的合理性，通过单颗粒单轴压缩测试了900个颗粒的抗拉强度，确定了强度分布规律。结果表明，煤的抗拉强度和修正Protodyakonov系数与fs均呈显着的线性正相关，表明fs可用于评价岩石的硬度。这一新指标对煤与瓦斯突出的风险评估具有重要意义，有望广泛应用于钻屑和软岩的硬度测量。