基于弹性地基梁采场坚硬顶板变形与内力的解析计算

Analytical solution for deformation and internal force of hard roof in stope based on elastic foundation beam

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。

Processing coal seams and immediate roof as elastic foundation, with the effect of abutment pressure produced by excavation disturbance in consideration, the mechanical analysis model of stope roof was established; the abutment pressure on the rock beam in front of working face was expressed through the piecewise function; the analytical expressions of bending moment, shear force and deforma- tion were obtained through the combination of continuous conditions and natural boundary conditions; the curve on the deformation and internal force of hard roof was obtained through the software of Mat- lab. The analysis has shown that 1） The deformation of beam, the maximum positive （negative） bending moment is approximately proportional to the stress concentration coeffxeient in the position of the maximum abutment pressure, the key section where fracture may occur in the rock beam; 2） The defor- mation of rock beam decreases with the Winkler ground coefficient k in the excavation influence range; 3） The distance between the origin and the stress concentration zone increases with the roadway width, so the deformation at x=0 reduced gradually; however, the distance from the position of the maximum deformation to lateral wall remains unchanged.