Mechanical Damage and Energy Evolution of Grout–Sandstone Composites with Different Height Ratios Under Graded Cyclic Loading

To investigate the load-bearing behavior and damage evolution characteristics of the grout–sandstone composite structure formed by the consolidated grout and overlying key stratum after bed-separation grouting under mining-induced stress disturbances, uniaxial compression and multilevel cyclic loading–unloading tests were conducted on grout–sandstone composites with different height ratios. The failure modes, mechanical responses, acoustic emission (AE) characteristics, energy evolution, and cumulative damage behavior were comprehensively analyzed. The results show that the grout–sandstone composites exhibit a significant height-ratio effect, with the peak strength of the G40-S60 specimen being 51.06% higher than that of the pure grout specimen. Under multilevel cyclic loading–unloading, the peak strengths of the specimens decrease by 1.73%~24.52% compared with those under conventional uniaxial loading. The high-strain zones progressively expand with increasing stress levels, while cyclic disturbance promotes local irreversible deformation and damage accumulation, causing the composites to evolve from localized instability under monotonic loading to progressive deterioration. The energy evolution exhibits a clear loading path dependence, and significant differences are observed in the partitioning of elastic strain energy and dissipated energy among specimens with different height ratios. The damage variable established based on cumulative dissipated energy exhibits distinct stress-level-triggered and stepwise increasing characteristics. These findings provide a theoretical basis for evaluating the stability of the grout–key-stratum composite supporting structure after bed-separation grouting and for assessing the effectiveness of grouting reinforcement.