Coal pillar load calculation by pressure arch theory and near field extraction ratio

A method for calculating the load acting on a pillar of coal in a bord-and-pillar mine is described for the purpose of back analysing pillar failure or assessing the stability of a panel of pillars. The method is applicable to pillars of arbitrary plan shape and accounts for the spatial position of the pillar with respect to the other pillars, un-mined coal, and the network of roadways. Calculation of the extraction ratio within the pillar’s zone of influence defined by the depth dependent load transfer distance accounts for the pillar’s spatial position in the mine layout. An advantage of this approach is its suitability for computer programming for the automated analysis of hundreds of pillars. In this paper, pillars are analysed by the new method, and by tributary area theory, with the results from the new method comparing favourably to elastic three dimensional numerical analysis. Finally, an example of coal mine pillar failure from the literature that neither could be satisfactorily back-analysed by the traditional factor of safety approach nor by two-dimensional numerical modelling is considered. With the proposed, approach 42 of the 54 pillars in the observed failed pillar region are predicted to have a safety factor below the recommended value for long term stability and of these, three pillars are predicted to have an FoS of 1.18. With tributary area theory every pillar, including all those outside the failed pillar region, is predicted to have an FoS less than 1.2.