Development an instability model for bord-and-pillar goaf using elastic foundation plate theory

Bord-and-pillar mining has been widely used in northwestern China, and lots of remains of coal resources such as coal pillars, roof coal, bound coal and so on, is a significant waste. Furthermore, the accidents caused by the instability of bord-and-pillar goaf are commonly faced problems. These accidents may have detrimental effects on mining areas residents in the form of injury, disability or fatality as well as mining company due to downtimes, interruptions in the mining operations, destruction of land resources, environmental pollution and so on. Therefore, studying on instability mechanism of bord-and-pillar goaf for the assessment and management of ground collapse accidents and pillars recovery is essential. In this paper, the instability mechanism of bord-and-pillar goaf was analyzed based on mining geological and mechanical conditions. Aiming at hard roof goaf, a detailed analysis was developed, in which the pillars were equivalent to continuous elastic Foundation, the roof was equivalent to the elastic foundation plate, a mechanical model of foundation plate on elastic foundation is established, the synergetic instability process of coal pillar-and-roof system was studied, in addition, the mechanical conditions and math criterion of roof failure and the overall instability of coal pillar-and-roof system was given. The results show that bord-and-pillar goaf failure is a pillar-and-roof synergetic instability process, whit pillars' effective area reducing, the roof will fail gradually, this will strengthen the pressure on pillars and accelerate pillars yield, if the effective area lower than its critical value, the goaf will collapse suddenly.