中文摘要：

坚硬项板断裂的理论解是矿山岩体力学中未获得较好解决的课题。为研究裂纹发生对坚硬项板内力、挠度和应变能的影响，沿采场中轴线取单位宽度的岩层结构，将煤壁前方煤层和直接顶视为弹性地基，假定在裂纹萌生初始阶段顶板上方荷载不变，以最大拉应变强度条件为裂纹发生条件，对周期来压模型裂纹萌生初始阶段的坚硬顶板进行分析，得到满足裂纹面边界条件、自然边界条件和连续条件的裂纹萌生初始阶段弯矩、剪力和挠度表达式。根据表达式，采用Matlab软件的数值计算、绘图和放大功能给出算例。算例表明：（1）裂纹萌生截面在煤壁前方，其位置在见报道的顶板超前断裂位置范围内。裂纹截面后方及采空区的顶板下沉量随裂纹生长而明显地增大。在裂纹截面前方顶板挠度则发生“反弹”，与现场检测到的顶板“反弹”特性一致；（2）煤壁后方顶板弯矩、剪力不变。煤壁前方因裂纹萌生顶板的弯矩、应变能全面减小。在裂纹前方剪力全面减小，在裂纹面附近剪力发生波动；（3）煤壁到前方15m是裂纹发生坚硬顶板应变能释放的集中区。煤壁前方坚硬顶板内力和弹性应变能减小，使岩层系统往安全方向发展。所得研究结果对于采场顶板状况判断有一定的指导作用和参考价值。

英文摘要：

Theoretical solution of fracturing of hard roof has not been well solved in rock mechanics. A strata of unit width along middle axis of stope was considered to study the influence of cracks on the internal forces, deflections and strain energy of hard roof. The coal seam and the immediate roof in front of coal wall were considered to be elastic. The load above roof was assumed to be invariable during the initial stage of cracking. The maximum strain was used as a criterion of crack occurrence. Expressions for bending moment, shear force and deflection of hard roof at its initial stage of cracking due to periodic pressure were derived satisfying the conditions of continuity, natural boundaries and boundaries of crack surfaces. Numerical examples computed with Matlab were presented. Section of crack initiation was in front of coal wall. The settlements of the roof behind the cracked surface and gob were increased remarkably with the development of cracks. The deflection of the roof in front of the cracked surface rebounded, which agreed with the characteristics of the monitored field results. The values of bending moments and shear forces behind coal wall were invariant. While, the bending moment and strain energy in front of coal wall decreased because of crack initiation. The shear forces in front of the crack surface decreased, and fluctuated near the crack surface. The position 15 m ahead of coal wall is an area of concentrated strain energy released from the hard roof and crack occurring. The internal force and strain energy in front of coal wall decreased which was beneficial safety-wise.