Calculating changes in fractal dimension of surface cracks to quantify how the dynamic loading rate affects rock failure in deep mining

The split-Hopkinson pressure bar (SHPB) and digital image correlation (DIC) techniques are combined to analyze the dynamic compressive failure process of coal samples, and the box fractal dimension is used to quantitatively analyze the dynamic changes in the coal sample cracks under impact load conditions with different loading rates. The experimental results show that the fractal dimension can quantitatively describe the evolution process of coal fractures under dynamic load. During the dynamic compression process, the evolution of the coal sample cracks presents distinct stages. In the crack propagation stage, the fractal dimension increases rapidly with the progress of loading, and in the crack widening stage, the fractal dimension increases slowly with the progress of loading. The initiation of the crack propagation phase of the coal samples gradually occurs more quickly with increasing loading rate; the initial cracks appear earlier. At the same loading time point, when the loading rate is greater, the fractal dimension of the cracks observed in the coal sample is greater.