An elastoplastic problem is formulated in which the boundary part of the seam in front of the face, as well as the part of the collapsed rock layer behind the face, are in the limit stress state. In a rock massif along the coal seam at its full capacity, the face of a rectangular section moves to the right. The rocks in the vicinity of the working are under the conditions of plane deformation. The characteristics of the of the coal seam strength are significantly inferior to the characteristics of the strength of the rocks of the enclosing massif but exceed the characteristics at the contact of the seam with the rest of the massif. The edge part of the coal seam in front of the working is in the limit stress state. Behind the working, a layer of a massif of rock that collapsed from above is formed after the coal extraction. The collapse of rocks starts from the roof of the working and extends into the depth of the massif at some angle to the horizon. Depending on the mining and geological conditions, this angle varies between 40–50°. The maximum thickness of the collapsed rock layer is determined by the conditions of cleavage, at which the upper layers rely on the collapsed rocks, preventing their further significant displacement.
The elastic-plastic problem of the stress state of the boundary part of the seam mined by the working is reduced to the second boundary problem of the elasticity theory, which is solved by the method of boundary integral equations. The parameters of the bearing pressure in the boundary part of the seam (in front of the face) slightly vary with the growth of the face span. The parameters of the limit stress zone in the collapsed layer behind the mine working in the entire range of variation of its span are an order of magnitude larger than the dimensions of the bearing pressure zone in the boundary part of the mined seam in front of the face. The maximum stresses in the collapsed rock layer are on average 1.5 times less than the maximum stresses in the boundary part of the mined seam.
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