Energy evolution and fatigue damage of cemented coal gangue materials under triaxial stepwise cyclic loading

Revealing the energy evolution and fatigue damage mechanisms of cemented coal gangue under cyclic loading conditions is of great engineering significance for improving the accuracy of long-term stability evaluation and design reliability of underground engineering filling and reinforcement structures. In this study, stepwise cyclic loading tests were performed on coal gangue under varying confining pressures and particle gradations. An energy-based fatigue damage variable was constructed from dissipated energy, and a low-cycle fatigue damage evolution model was established to quantitatively characterize damage accumulation under cyclic loading. The results reveal stage-dependent evolution of stress-strain behavior, elastic energy, and dissipated energy, with pronounced hysteresis and accelerated energy dissipation preceding failure. A non-monotonic trend characterized by an initial increase followed by a subsequent decrease is exhibited by elastic energy, dissipated energy, and cumulative dissipated energy with increasing confining pressure. A reasonable gradation is conducive to forming a stable skeleton structure and delaying fatigue failure. The fatigue damage variable constructed on the basis of dissipated energy exhibits a characteristic reverse S-shaped evolution with the normalized number of loading cycles. The low-cycle fatigue damage model is demonstrated to effectively capture the fatigue evolution of cemented coal gangue under varying stress levels and material conditions. These findings provide a robust theoretical basis for the evaluation of mechanical behavior and the engineering application of cemented coal gangue under cyclic loading.