An analytical approach to the design of coal pillars

"A computer program is described which will analyze the stability of coal pillars. The extent of the peripheral failed zone and the central elastic core of the pillar, the stress distribution across the pillar and its strength can be determined by a ""sliceby- slice"" analysis technique. The program incorporates a brittle/pseudo-ductile transition point so that a pillar may fail by brittle fracture or pseudo-ductile yield. It is shown that:(i) There is a minimum pillar stress below which fracture cannot initiate; hence there is a minimum pillar strength. (ii) In specific circumstances (narrow pillars) , once fracture initiates at the pillar edge it must propagate immediately to the pillar centre. This unstable situation is called ""catastrophic"" failure and might be regarded as a model of a pillar ""burst "". (iii) For wider pillars, the failed zone ex tends gradually into the pillar as the loading increases until it reaches the pillar centre when the pillar is deemed to have f ailed. This is called the point of ""ultimate"" failure.The critical pillar widths to avoid catastrophic and ultimate failure can be calculated.A hypothetical analysis of five rib pillars is given to illustrate the application and the results obtained from the model. The model is then used to analyze three case histories taken from the literature. The first demonstrates the applicability of the brittle/pseudo-ductile failure criteria for Pittsburgh coal. The second compares the pillar strength formulae derived here with those of Salamon and Munro(13) and Bieniawskiou . The final case history compares the model analysis with field stress measurements in a yielding pillar. In all cases the model results are compatible with the case histories."