Deformation Characteristics and Breakage Mechanism of Thick-Hard Roof Based on a Medium-Thick Plate Mechanical Model

To solve the whole cutting-off and large-area weighting of thick-hard roof led by the high-intensity mining in working face, the mechanical mechanism of the impact pressure of thick-hard top working face in the Shendong mining area is studied. The thick-hard roof in the Shendong mining area is characterized by large thickness, high strength, and difficulty in caving, which frequently triggers strong mine pressure, coal wall spalling, rock bursts, and mining-induced seismicity. Traditional thin-plate theory ignores transverse shear deformation and cannot satisfy the calculation accuracy requirements of thick-hard strata with a large thickness–width ratio, so it is necessary to establish a more accurate medium-thick plate mechanical model. By analyzing the boundary conditions of the thick-hard-roof working face in the Shendong mining area, the mechanical model of the medium-thick plate under four typical boundary conditions is established. Then, the finite integration method is used to solve the deflection, bending moment, and shear force of the thick-hard roof under the four boundary conditions. Through the programming operation, the influence laws of the deflection, bending moment, and shear force of the thick-hard roof are analyzed. The results show that under tensile failure, the cracks expand along the long side. Then, the cracks occur on the short side of the thick roof. Along the short side, the cracks occur in the middle and expand on the short side of the two sides with the increase in plate thickness, and the bending moment and shear values gradually decrease. For the medium plate of the same thickness, as the width-to-length ratio increases, the deflection value gradually increases, and the bending moment and shear value gradually decrease. The research results reveal the deformation and breaking rules of thick-hard roofs based on the mechanical model of thick plates, which lays a theoretical foundation for the study of the coal-wall plate impact-pressure mechanism induced by the instability of thick-hard roofs.