Stability and grouting treatment of collapse goaf in shallow coal seams

Based on the key stratum theory, a “short masonry beam” mechanical model was established to analyze the surface subsidence mechanism above the studied coal-mine goaf in a selected mining area of Ningxia, China. Rather than treating the short masonry beam model as a new standalone theory, this study combines roof-block instability analysis with grouting-induced fracture propagation simulation to clarify the relationship between structural instability and grouting reinforcement in shallow-buried collapse goaf. The model examines roof rock instability through two modes: rotational deformation and sliding failure, revealing the process from overburden failure to surface subsidence. A discrete element numerical model for fracturing grouting in layered rock was also developed to study the effects of bedding dip angle, spacing, and lateral pressure coefficient on fracture propagation. Under the adopted site-specific parameters, rotational instability may occur when the calculated effective load-layer thickness exceeds 286.9 m; this value refers to the load-bearing overburden thickness involved in roof-block instability rather than the mining depth itself. The sliding instability risk increases when the blockiness index exceeds 0.9. During grouting, fractures primarily propagate along bedding planes near the injection hole, aligning with the dip angle. Fracture growth is rapid initially, then stabilizes. Smaller bedding spacing promotes longer and more micro-fractures along bedding, with faster propagation within bedding than in the rock matrix. Bedding dip and maximum principal stress direction jointly control fracture extension and displacement distribution. This study provides a theoretical and engineering reference for managing shallow goafs and ensuring surface construction safety.