Probability of failure of South African coal pillars
JN van der Merwe, M Mathey
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.