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将煤层、直接顶处理为弹性地基,考虑开挖扰动产生的支承压力影响,建立采场顶板的力学分析模型,采用分段函数描述工作面前方顶板所受的支承压力,结合连续条件和自然边界条件求解模型并获得了岩梁的弯矩、剪力和挠度的解析表达式;采用matlab软件得到坚硬顶板的变形与内力曲线。通过分析可知:1)在支承压力最大值处,岩梁的变形、最大正(负)弯矩都近似与应力集中程度成正比关系,同时也是岩梁可能发生断裂的关键位置;2)在开挖影响范围内,随着Winkler地基系数k的增大岩梁变形减小;3)随着开采宽度的增大,原点距应力集中区域较远,所以变形较小,但是最大变形处至煤壁距离不变。
The coal seam is directly treated as an elastic foundation. Considering the effect of supporting pressure caused by excavation disturbance, a mechanics analysis model of stope roof is established. Using the piecewise function, the supporting pressure on the roof in front of the working face is described. Combining the continuous conditions and the natural boundary Conditional solution model and get the analytical expression of bending moment, shear force and deflection of rock beam; using matlab software to get the deformation and internal force curve of hard roof. The analysis shows that: 1) At the maximum support pressure, the deformation and the maximum positive (negative) moment of rock beam are approximately proportional to the degree of stress concentration and are also the key positions where the rock beam may break; 2) With the increase of the Winkler foundation coefficient k, the deformation of the rock beam decreases; 3) As the mining width increases, the origin is far away from the stress concentration area, so the deformation is small, but the distance from the maximum deformation to the coal wall constant.