Theoretical analysis and experimental research on the energy dissipation of rock crushing based on fractal theory

• The energy consumption model of rock crushing is developed based on fractal and fracture mechanics theory.
• A quantitative relationship between the energy consumption and average size of rock fragments are obtained.
• A calculation method for determining the rock fracture surface energy is introduced according to the SHPB tests.
• The theoretical model is suitable for predicting energy required for rock dynamic crushing with reasonable accuracy.

The relationship between energy consumption and the rock fragment size distribution is a basic question in rock fragmentation. Based on fractal rock mechanics and fracture mechanics theory, a new model of energy consumption during rock fragmentation is proposed. Moreover, dynamic uniaxial compressive tests on granite and sandstone under five different impact velocities are conducted with the split Hopkinson pressure bar (SHPB) device, the fragment size distribution of broken rock is obtained by sieving and the energy dissipation in the process is analyzed. The results from the tests show that fragments resulting from rock breakage under impact loading exhibit fractal features; the larger the fractal dimension, the higher the degree of rock fragmentation. Notably, the energy consumption density is inversely correlated with the average size of the rock fragments: with an increasing energy consumption density, the average size decreases significantly and the fracture surface area increases accordingly. Additionally, the SHPB tests enable determination of the fracture surface energy of granite and sandstone, and the energy consumption density is calculated based on the theoretical model and found to be in good agreement with the experimental results.