This paper identifies the stress redistribution of protected seams under the influence of coal pillars and a divisional management strategy for methane control. A coal pillar that is reserved in the protective seam greatly affects the abutment stress, the O-shaped circle’s evolution and the stress distribution. The strain-soften model was conducted using FLAC3D numerical analysis software to investigate the stress redistribution in the protected seam mining process. The results show that the abutment stress reaches a maximum value of 1.25 times the original stress when a protected seam coal face lies in the center of the coal pillar’s affected zone. The O-shaped circle is divided into two parts by the coal pillar, and its developmental width is closely associated with the protected seam mining stage and the developmental height of the “three zones”, especially the fractured zone. The stress redistribution of protected seam is rarely affected by the coal pillar when the distance is greater than 26 m. Both the total increased stress belt of the coal pillar affected zone and the total decreased stress belt of the other zones along the vertical direction significantly influence the methane migration. We propose a divisional management strategy that supplies a theoretical basis and technical guidance for methane control.
The aim of this work is to study oscillation properties for a scalar linear difference equation of mixed type ∆x(n) + ∑ q k=−p ak(n)x(n + k) = 0, n > n0, where ∆x(n) = x(n + 1) − x(n) is the difference operator and {ak(n)} are sequences of real numbers for k = −p, . . . , q, and p > 0, q > 0. We obtain sufficient conditions for the existence of oscillatory and nonoscillatory solutions. Some asymptotic properties are introduced.