Constitutive relation of energy dissipation damage of heterogeneous coal samples under different loading rates

In order to explore the influence of loading rate on the mechanical response of heterogeneous coal samples，the uniaxial compression tests of heterogeneous coal samples under different loading rates were carried out based on SAM⁃2000 rock mechanics test system. The results show that with the increase of loading rate，the larger the size of the coal dust splashes，the farther the splashes distance，the worse the integrity and the more violent the energy release degree of the coal sample，which belongs to the split⁃shear composite failure mode. The peak strength and elas⁃ tic modulus both increase approximately vertically and then increase steadily with the increase of the loading rate，and satisfy the Rational5 relation of the rational function. The peak strain first decreased rapidly and then gradually became stable，satisfying the attenuation exponential function. With the increase of the loading rate，the total energy at the peak point firstly increase approximately vertically and then decreases steadily，and the elastic energy firstly increase approximately vertically and then increases steadily，both of which meet the rational function Rational5 relation.With the in⁃ crease of loading rate，the dissipation energy produces two inflection points. It drops to the first inflection point approx⁃ imately vertically and then rises to the second inflection point approximately vertically and then decreases rapidly.With the increase of loading rate，the specific energy absorption first increases vertically to the inflection point，then decreases rapidly，and then gently decreases. The proportion of elastic energy at peak is higher than that at failure，and the difference between the two is at least 40.12%. At the peak，the total energy is dominated by elastic en⁃ ergy，supplemented by dissipative energy，and vice versa at failure;Constitutive relations of energy dissipation damage of coal samples under different loading rates are derived with high fitting degree.