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首页> 外文期刊>Journal Of The South African Institute Of Mining & Metallurgy >Probability of failure of South African coal pillars
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Probability of failure of South African coal pillars

机译：南非煤炭支柱倒闭的可能性

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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, Weibutt, 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 meani ngfulness 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.
机译：在1960年的柯布鲁克（Coalbrook）灾难之后，对煤柱强度的研究导致在南非煤矿开采的稳定柱设计中采用了安全系数的概念。本身的安全系数只能视为相对稳定性的度量。有理由认为，安全系数较高的支柱将比安全系数较低的支柱``更稳定''，但无法量化多少稳定性。安全系数与失败概率（PoF）之间建立了联系用于两个新的煤柱强度公式。确定失败概率的方法是，将南非全部支柱人群中每个安全系数的观察到的失败次数与预计的稳定案例数进行比较。后者的预测是通过将特征分布曲线（对数正态分布，Weibutt和gamma密度分布）拟合到数据库中稳定案例的样本并以恒定因子外推响应频率分布来进行的。每个安全系数得出的PoF明显小于先前的假设。解决安全系数和故障概率之间联系的一种更准确的方法是确定区域或特定于接缝的故障概率。但是，这将需要更多的统计证据来说明单独的区域或接缝，以提高预测的意义和可靠性。目前认为可用的数据量不足以实现此目的。表明，通过最大似然函数得出的支柱强度公式比通过重叠减少技术得出的支柱强度公式得出的支柱强度更大。安全系数，但较大支柱的PoF小于使用替代公式获得的较小支柱的PoF。在相同的支柱大小的基础上进行比较，两个不同公式得出的PoF紧密一致。该结论证实，基于PoF而不是安全系数的设计更加令人满意，并且消除了因使用不同强度公式而引起的歧义。结论是，对于一般的波峰和支柱工作，PoF可以为1％使用最大似然公式得出的安全系数为1.3，使用最小重叠公式得出的安全系数为1.4。可以使用两种新配方中的任意一种，在一般地下作业的PoF为1％的基础上设计，都有望在萃取中带来显着的收益。

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