Controlled Roof Collapse during Secondary Mining in Coal Mines

The problem considered is an investigation of the possible collapse of the roof between the pillar next to be mined in secondary coal mining and the first line of pillar remnants called snooks. The roof rock between the pillar, which is the working face, and the snook is modelled as an Euler-Bernoulli beam acted on at each end by a horizontal force and by its weight per unit length. The beam is clamped at the pillar and simply supported (hinged) at the snook. The dimensionless differential equation for the beam and the boundary conditions depend on one dimensionless number . We consider the range of values of before the displacement and curvature first become singular at . The model predicts that for all practical purposes, the beam will break at the clamped end at the pillar. The failure of the beam for values of greater than is investigated computationally. 1. Introduction We consider the challenge posed by coal mine pillar extraction [1, 2]. Secondary mining involves revisiting a mine and extracting coal from the pillars. The mining of these pillars commences from the area furthest away from the point of entry of the mine. This exercise involves cutting the existing pillars into smaller pillars called snooks. As each section is mined, the roof must collapse in a controlled manner in order to pose no safety risk to those miners operating underground. We analyse the behaviour of the roof of the mine between the pillar next to be mined and the first line of snooks. This is the work area and must be safe for the miners. 2. Model In Figure 1, a mining panel in shown prior to pillar extraction. The tunnels are excavated in coal which are approximately 5？m to 7？m wide. They are excavated in a fixed pattern crossing at right angles creating a checker board layout. The coal between the tunnels forms the pillars which support the overburden rock. The width of the pillars is approximately 10？m to 20？m wide and is a function of the depth of the mine. The height of the tunnels ranges from 3？m to 4？m. Secondary mining is carried out in two stages. In the initial stage, approximately 5 to 10 pillars are removed and the roof is left to collapse. This stage is modelled in [2]. Following this, adjacent pillars are mined and smaller sections are left to collapse. The purpose of this paper is to model the second stage in the extraction process. Figure 2 shows the snooks after pillar extraction. The pillars are cut to leave four snooks, approximately 2？m, one at each corner. The snooks have to be small enough to fail when the miners are a safe distance (about the width