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## Journal of the Southern African Institute of Mining and Metallurgy

*On-line version* ISSN 2411-9717

*Print version* ISSN 2225-6253

#### Abstract

VAN DER MERWE, J.N. and MATHEY, M.. **Probability of failure of South African coal pillars**.* J. S. Afr. Inst. Min. Metall.* [online]. 2013, vol.113, n.11, pp.849-857.
ISSN 2411-9717.

Following the Coalbrook disaster in 1960, research into coal pillar strength resulted in the adoption of the concept of a safety factor in the design of stable pillars in South African coal mining. The safety factor on its own can be regarded as only a relative measure of stability. It stands to reason that a pillar with a higher safety factor will be 'more stable' than a pillar with lower safety factor, but how much more stable cannot be quantified. Links between the safety factor and the probability of failure (PoF) were established for two new coal pillar strength formulae. The method behind the determination of the probability of failure was a comparison of the observed number of failures to a predicted number of stable cases for each safety factor in the entire population of pillars in South Africa. The prediction of the latter was made by fitting characteristic distribution curves *(lognormal, Weibull,* and *gamma* density distributions) to the samples of stable cases in the database and extrapolating the responding frequency distributions by a constant factor. The resulting PoF per safety factor is significantly less than previously assumed. A more accurate approach to the solution for the link between safety factor and the probability of failure would be to determine regional or seam-specific probabilities of failure. However, this would require more statistical evidence for the separate regions or seams to improve the meaningfulness and reliability of the predictions. The amount of data available at present is not considered sufficient for this purpose. It is shown that the pillar strength formula derived by means of the maximum likelihood function results in larger pillars than with the formula derived by means of the overlap reduction technique for the same safety factor, but that the PoF of the larger pillars is less than that for the smaller pillars obtained with the alternative formula. Compared on the basis of the same pillar sizes, the PoF derived for the two different formulae are in close agreement. This conclusion confirms that basing design on PoF as opposed to a safety factor is much more satisfactory, and it also removes the ambiguity arising out of using different strength formulae. It is concluded that a PoF of 1% for general bord and pillar workings could be obtained with a safety factor of 1.3 by using the maximum likelihood formula, and 1.4 by using the minimum overlap formula. Significant benefits in extraction can be expected from the use of either of the new formulae, basing the design on a PoF of 1% for general underground workings.

**Keywords
:
**coal pillar failure; probability of failure of coal pillars; probability of failure.