标题：Analysis of bending moment, shear force, deflection and strain energy of hard roof at initial stage of cracking during periodic pressures
作者：Pan, Yue ;Gu, Shitan
作者机构：[Pan, Yue ] School of Civil Engineering, Qingdao Technological University, Qingdao, Shandong 266520, China;[Gu, Shitan ] College of Resources and Envi 更多
来源：Yanshilixue Yu Gongcheng Xuebao/Chinese Journal of Rock Mechanics and Engineering
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 stop 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.