Deep beam theory-based mechanical analysis of water-resisting key strata of coal seam floors in a deep mining environment

Objective An increase in the mining depth of mines poses a more serious threat from highly confined karst water, resulting in water hazards like water inrushes and collapse on the mining faces of coal seams. The key technique used to address this issue is to determine the water pressure resistance of the water-resisting key stratum of the coal seam floor in a deep mining environment. Methods This study simplified a water-resisting key stratum into a rock beam model and then dealt with this model using the deep beam theory in the prediction of water inrushes in deep mining. Specifically, by combining theoretical analysis with numerical simulation, this study sliced the deep beam into shallow beams based on the bending mechanical characteristics of the deep beam and previous research results. Then, according to the elastic force distribution of various shallow beams, it was assumed that the interlayer compressive stress σ_y was a cubic function and presented a slicing technique to determine the bending stress of the deep beam. Finally, the calculated results were compared with the elastic mechanic solutions and the FLAC^3D simulation results. Results and Conclusions The results indicate that the stress and displacement obtained through the slicing of the deep beam were closer to the numerical simulation results, yielding more accurate calculation results with errors less than 10%. As the number of shallow beams increased, more accurate calculation results were obtained. However, the increased amplitude of the accuracy gradually decreased, necessitating appropriate slicing of the deep rock beam model in engineering applications. Furthermore, errors increased with the height/span length (h/l) ratio. Therefore, appropriate slicing widths are required, otherwise errors will increase. An example of a water-resisting key stratum of a coal seam floor demonstrates that a h/l ratio exceeding 0.2 suggests a typical deep beam. In this case, the maximum tensile stress calculated using conventional elastic mechanics exhibited an error reaching up to 40.6%, exerting a negative impact on properly determining the risks of water inrushes in the water-resisting key stratum. In contrast, the deep-beam slicing method manifested higher accuracy in solving stress, thus serving as a significant guide for the prediction of water inrushes from deep coal seam floors.