The problem of stress distribution in a rock mass in the vicinity of in-seam working is solved by the fundamental methods of deformable solid mechanics in two stages. At the first stage, the problem of the limit stressed state of the coal seam marginal zones is solved using the methods of flowing medium mechanics. The criterion for the onset of the limit state is the simultaneous observance of the Coulon — Mohr condition on the seam and the Mohr — Kuznetsov condition on its contact with the lateral rocks. At the second stage, by replacing the limit stress zone of the seam with stresses acting on the contact of the seam with the massif allows to reduce elastic-plastic problem to the boundary integral equation of the marginal task of the elasticity theory. The problem is solved by the method of successive approximations at each step of the iterative process: the size of limit stress zone is set, and then this equation is solved by the method of mechanical square, and then the stresses along the contact of the seam with massif are calculated. The calculations will be finished if the static boundary conditions are met at the boundary of the elastic and limit stress zone.

The plot of the reference pressure along the contact of the seam with the surrounding massif with small characteristics of the seam strength at its contact is a combination of alternating sections with constant and variable stresses. If these strength characteristics are close to the strength characteristics of the seam itself, the number of sections with constant stresses is reduced, and if they are equal, only one horizontal section remains.

Dependences are established related to the parameters of the seam limit stress zone on the strength characteristics at its contact with the massif. The graphs of changes in the width of the limit stress zone of the seam have the view of decreasing functions over the entire interval of changes in the internal friction angle at this contact. The graphs of the distribution of the stress concentration coefficient for small values of the internal friction angle at the seam contact

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