Objective In abandoned mines, the storage zones of free gas are closely associated with overburden fractures in goaves. To accurately estimate free gas resources in abandoned mines, it is necessary to thoroughly investigate the rupture mechanisms of blocks in main roofs in goaves, as well as the overburden fractures and rupture trace morphologies in goaves.

Methods Based on the masonry beam theory, this study established a mechanical model for the primary cantilever beam of a main roof. The analytical solutions of the stress components in the primary cantilever beam were analyzed using the stress inverse method, and the mathematical expression of periodic rupture traces was derived based on the Mohr-Coulomb failure criterion. Using the general rock mechanical parameters of the main roofs of goaves of various coal seams in the Panyi Mine in the Huainan mining area, Anhui Province, this study analyzed the stresses and strains of the primary cantilever beam, along with the strain energy density of the beam under different elastic moduli and Poisson's ratios. The rupture traces were calculated and plotted using the Maple software, and the influences of the internal friction angle and cohesive force on the rupture traces were analyzed. By constructing the experimental platform for physical simulation of mining face 1252-1 in the Panyi Mine using similar materials, this study analyzed the fracture network in the overburden in the goaf using the ImageJ software.

Results and Conclusions  The results indicate that the rupture of the primary cantilever beam of a main roof was primarily affected by horizontal and shear stresses, with tensile-shear failure predominating. The primary cantilever beam fracturing occurred initially in the compressed zone on its upper surface and then propagated toward the compressed zone on its lower surface. Substituting the overburden parameters of goaves in the Panyi Mine into the rupture trace expression yielded two parallel L-shaped rupture traces (i.e., rupture traces I and II). The rupture traces extended vertically from the top of the simulated block downward until inflection points and then propagated back downward to the bottom of the block. With an increase in the cohesive force, the number of rupture traces increased from two to three. Fracture traces I and II exhibited an L-shaped pattern, extending to the right side, whereas rupture trace III gradually extended vertically to the bottom of the block. The scanning results of overburden fractures in the goaf obtained using ImageJ software revealed that zones I-1 and I-2 were median-elevation gas enrichment areas, while zones II-1 and II-2 were high-elevation gas enrichment areas. The results of this study provide a scientific basis for designing the locations of gas drainage boreholes in an abandoned mine while also offering a reference for similar mines.