Framing the solution to the problem of coal seam state by the methods of the mechanics of granular materials
Introduction. It is essential to reliably estimate the geomechanical state of marginal zones at a mineable coal seam in order to ensure mining balance and safety. Research aim is to build the model of the state of a coal seam in its marginal zone based on the fundamental methods of the mechanics of granular materials, make calculations within the framework of the model, analyze the results and compare them with the results obtained by the well-known methods. Methodology. The problem of the stressed state of coal seam marginal zones is implemented by means of numerical solution of three boundary value problems of limit equilibrium theory for a range of typical areas situated in these zones. The criterion of limit state beginning is concurrent compliance with Coulomb-Mohr stratum condition and Mohr-Kuznetsov condition along the contact with rock wall. Results. It has been shown that the components of stress field change non-monotonically along the seam roof. Sections with constant stresses are changed by sections with stresses nonlinear increase. With distance from the marginal part into the depth of the massif, the size of sections with constant stresses decreases. The obtained stress results have been compared with the results obtained with the use of voltage change exponential formula. The dimensions of seam marginal zone have been determined with rather close results of two approaches. Summary. Polynomial approximation of the obtained graphs allows accurately replace the results of numerical solution to the limit state problem by analytical functions and simplify the solution to the problem of the enclosing rock stressed state.