Analysis on Limit Equilibrium Zone of Coal Pillar in Mining Roadway Based on Mechanical Model of Elastic Foundation Beam

To reasonably determine the limit equilibrium zone width, a coal pillar was simplified as a half-infinite load-bearing beam while its weak floor rock mass was assumed to be a continuous elastic foundation according to the mechanical characteristics of the coal pillar. This paper develops the Winkler elastic foundation beam model of a coal pillar under high bearing pressure using the elastic foundation beam analytic method. Furthermore, the deflection, diversion, bending moment, and shear force at any interface of the coal pillar are studied based on a mechanical model of the coal pillar under different bearing pressures. A theoretical calculation formula for the width of the limit equilibrium zone of the coal pillar is put forward under conditions where a shear slip appears on the elastic–plastic interface of the coal pillar. The results show that the limit equilibrium zone width of the coal pillar is closely related to the buried depth of the roadway, volumetric weight of the overburden, the stress concentration factor, the width of the elastic zone, the elastic characteristic value of the floor, the lateral pressure coefficient, the cohesive force, and the internal friction angle on the elastic-plastic interface of the coal pillar. Taking an 850–875 m section of the transport gateway of the 13503 face in a Wangcun coal mine as an example, the theoretical limit equilibrium zone width of the coal pillar is calculated after the other parameters were determined. On this basis, the deformation and failure of the coal pillar in a range of 6 m is tested using a borehole scope. The theoretical width of the limit equilibrium zone of the coal pillar is almost consistent with the results of the field test.