Dynamic mechanical properties and damage constitutive model of coal in Brazilian splitting under impact load

In the process of deep coal seam mining, the dynamic damage and failure of coal under impact load disturbance are key factors triggering major dynamic disasters. To explore the dynamic tensile properties of coal samples under impact loads, the Split Hopkinson Pressure Bar (SHPB) test system was adopted to perform dynamic splitting tensile tests on coal samples under varying impact velocities, while a high-speed camera was utilized to record the crack initiation and propagation processes of the samples. The dynamic tensile mechanical properties of coal samples under varying impact velocities were systematically investigated, and the failure processes and modes of coal samples in the dynamic Brazilian splitting tests were analyzed in detail. Based on the combined element model theory and statistical damage theory, a dynamic damage constitutive model for coal was established, and its rationality was verified by means of experimental data. The test results indicated that the peak tensile strength of coal samples exhibited a positive proportional relationship with impact velocity, whereas the peak strain showed an inverse proportional relationship with impact velocity. This phenomenon implied that as the impact velocity increases, the deformation response time of coal samples is significantly shortened, and macroscopic fracture occurs with only minimal deformation. In the dynamic splitting tests, a central main crack initiated in the central region of coal samples, followed by the continuous propagation, coalescence, and eventual penetration of microcracks, ultimately resulting in the complete fracture of the samples. Notably, stress concentration occurred near the pressure bar end faces, accompanied by the formation of crushing zones. As impact velocity rose, the energy absorbed by coal samples similarly increased, and incident, reflected, transmitted, and dissipated energies all exhibited an upward trend. Among these, incident energy showed the steepest growth slope; transmitted energy had the smallest variation range and the gentlest growth slope; and the growth slopes of dissipated and reflected energies of coal samples were approximately equal. The energy dissipation density of coal samples increased linearly with increasing impact velocity. This demonstrates that as impact velocity increases, high energy input induces rapid energy transfer and accumulation in the coal matrix, with local regions sustaining higher energy densities, thereby enhancing the fracture degree of coal samples. Based on the Zhu-Wang-Tang model and statistical damage theory, damage characteristics of specific elastic components were incorporated into plastic elements. The Zhu-Wang-Tang constitutive model was then modified, and accordingly, a viscoelastic-elastoplastic dynamic damage constitutive model was established for coal subjected to Brazilian splitting under impact loads. This model effectively characterized the elastic and plastic stages of coal under impact loads and accurately reflected the dynamic stress-strain relationships of coal under different impact velocities, thus verifying the reliability of the constitutive model.