裂纹发生初始阶段的坚硬顶板内力变化和“反弹”特性分析
Variation of internal force and rebound property of hard roof at initial stage of cracking
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摘要: 为研究超前裂纹对坚硬顶板内力变化的影响和顶板“反弹”、“压缩”特性,将煤壁前方煤层和直接顶视为弹性地基,假定在裂纹发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,对初次来压前的坚硬顶板进行分析,求得满足裂纹面边界条件、自然边界条件和连续条件的裂纹发生初始阶段顶板内力和挠度形式解中全部系数。据所得表达式,采用Matlab软件给出算例。算例表明:①裂纹面在煤壁前方,其位置在见报导的顶板超前断裂位置范围内。采空区的顶板下沉量随超前裂纹生长而明显地增大。在裂纹面附近区域顶板挠度发生反弹, 在反弹区前方存在压缩区,与现场监测到的顶板“反弹”、“压缩”特性一致。②末排支护为顶板弯矩反弯点,随超前裂纹生长,末排支护前方顶板上侧受拉弯矩全面减小,而其后方顶板下侧受拉弯矩全面增大。煤壁前方顶板剪力随裂纹生长逐渐减小,煤壁后方顶板剪力不变。所得结果对于采场顶板状况的判断有一定的参考价值。Abstract: To study the influence of advanced cracking on internal force of hard roof and rebound and compression properties of the roof, the coal seam and the immediate roof in front of coal wall are considered as elastic foundation, and the load above the roof is assumed to be invariable during the initial stage of cracking. The maximum strain is used as the criterion for crack occurrence. All coefficients for the internal force and deflection of hard roof at its initial stage of cracking due to the first weighting are derived to satisfy the boundaries of crack surfaces, natural boundaries and conditions of continuity. Numerical examples computed with MATLAB are presented. The results show: (1) Section of crack initiation is in front of coal wall, which can be seen from the reported scope of the advanced cracking location of the roof. The settlements of the gob roof increase remarkably with the development of cracks. The deflection of the roof in front of the cracked surface rebounds and also a compression region exists ahead of the rebound region, which agrees with the characteristics of the monitored field results. (2) The place of the end row supports is an unbending point. The values of the bending moments of the roof in front of the end row supports decrease entirely because of crack initiation, while those behind the end row supports increase. The shear forces in front of coal wall decrease because of crack initiation, while those behind coal wall are invariant. It has some reference value for the evaluation of stope roof condition.