随着矿井开采深度增加，来自高承压岩溶水威胁增大，导致煤层工作面出现涌水、突水等水害现象，分析深部开采环境下煤层底板隔水关键层抵抗水压力强度是解决这一现象的重要内容之一。

为解决此问题，将隔水底板简化为岩梁模型，并运用深梁理论解决深部开采突水预测中的岩梁模型问题，采用理论分析和数值模拟相结合的方法，根据深梁弯曲力学特点，结合前人研究成果，将深梁条分成浅梁，通过弹性力学单根浅梁受力分布形式假定层间挤压应力σ_y为三次函数，给出深梁弯曲应力求解的条分技术，并将计算结果与弹性力学解、FLAC^3D模拟结果进行对比。

结果表明，深梁条分解得到的应力及位移与数值解结果趋势更为接近，计算结果更为精确，相对误差均在10%以内，同时，随着条分层数增加，精度也增加，但提高幅度逐渐降低，因此，工程应用中针对深部岩梁模型条分到一定程度即可；随着高跨比不断增加，精度误差也在增加，说明条分层宽度不宜过大，否则造成误差增加；底板隔水关键层实例表明，当隔水关键层高跨比大于0.2时，为典型的深梁问题，常规弹性力学的最大拉应力求解结果误差较大，相对误差达到40.6%，给正确判定关键层突水危险性带来不利影响，此时采用深梁条分法求解应力精度较高，可为深部煤层底板突水预测研究起到重要的指导作用。

An increase in the mining depth of mines poses a more serious threat from highly confined karst water, resulting in water hazards like water inflow and inrushes on the mining faces of coal seams. The key content used to address this issue is to analyze the water pressure resistance of the water-resisting key stratum of the coal seam floor in a deep mining environment.

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.

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 relative error 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 relative 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.