Dynamic constitutive model and damage characteristics of coal-rock combined body under three-dimensional static and cyclic impact loading

To investigate the mechanical behavior and damage characteristics of coal-rock combined body under three-dimensional static and cyclic impact loading,this study employs an improved Split Hopkinson Pressure Bar (SHPB) testing system to conduct experiments on rock-coal-rock structured specimens. The stress-strain curves and failure modes of the specimens were analyzed under varying strain rates and confining pressures. A dynamic constitutive model was established to reflect the strain rate,stress characteristics of coal-rock,and confining pressure effects. The influence of impact incident energy and confining pressure on damage evolution was systematically examined. Results demonstrated that the dynamic stress-strain curves exhibited nonlinear characteristics,with failure primarily occurring in the coal interlayer through shear-tensile composite failure modes. Specimen fragmentation severity displayed pronounced strain rate dependence. The proposed constitutive model achieved high consistency with experimental data. Damage evolution progressed through three distinct phases:an elastic phase with a low damage growth rate,a stable crack propagation phase characterized by gradual damage accumulation,and a post-peak phase featuring abrupt damage escalation. Under constant confining pressure,cumulative damage increased monotonically with an increase in either the number of impacts or the incident energy. For a fixed incident energy level,cumulative damage decreased with increasing confining pressure. The inverse logistic function effectively quantified damage evolution patterns. These findings provide critical theoretical insights for controlling dynamic disasters in deep coal-rock engineering.