Based on the fundamental methods of solid mechanics, the model is built related to the geomechanical state of the rock mass containing the coal bed and two workings passed through it. The model takes into account that the strength characteristics of the layer is inferior to the strength characteristics of the solid mass, but higher than the strength characteristics on the contact of the layer with the solid mass.
The problem of the layer state in the extremely stressed zone is reduced to the nonlinear differential equation of hyperbolic type. This equation is solved by the method of characteristics based on resolving a number of boundary value problems of the layer limit state. Strength calculation of the coal pillar is made by calculating its safety factor.
Breaking load on the coal pillar is determined by the integration of the expression of vertical normal stresses in its roof. Actual load on the coal pillar is determined in two ways. The first method is the integration of the expression of the vertical component of normal stresses along the roof of the pillar obtained from the solution of the elastoplastic problem. At the second method the actual load is calculated as the weight of the rock mass located between axes of the workings.
The values of the actual load on the coal pillar, as well as the safety factors obtained by each of two above methods, differ by less than 10%.
The graph of decreasing in the safety margin of the pillar with an increase in the span of the first working with a fixed value of the span of the second working and the constant width of the pillar is characterized by slightly decreasing curve. Widening of the coal pillar significantly increases its safety factor. For example, the increase in its width of the coal pillar by 2 m at the fixed safety factor allows to lengthen the span of one working several times.