Damage evolution and failure behavior of coal-rock combination subjected to different cyclic loading paths and loading rates: Insights from energy-driven effects

• Loading rate significantly governs energy-driven behavior, mechanical properties, and macro-micro degradation of coal-rock composites under cyclic loading. • Increasing loading rates from 0.05 to 0.15 mm/min reduces loading time by 32.39% (path I) and 48.60% (path II), while increasing crack counts by 1.66-fold and 1.41-fold, respectively. • Higher loading rates expand energy storage limits and promote transmatrix and shear crack formation, with cracks preferentially propagating along primary weak surfaces. • These findings provide a theoretical basis for predicting and mitigating damage and failure in coal-rock structures subjected to cyclic mining disturbances.