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Abstract 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.
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Received: 25 September 2013
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2014, Vol. 33 
