Variation of internal force and rebound property of hard roof at initial stage of cracking

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.