The pioneers in the field of coal pillar strength in South Africa were M.D.G. Salamon and A.H. Munro, who preferred to use statistical hack-analysis of failed and intact pillars to determine the pillar strength, and Z.T. Bieniawski, whose attempt was based on the direct strength determination of coal pillars using specimens of various sizes. At the time when the original statistical analysis was performed, 27 cases of failed pillar workings were considered suitable for inclusion in the database of failed pillars. The databases of failed and stable pillar cases have recently been updated to include cases of pillar failure that occurred in the past few years (Van der Merwe and Mathey, 2013a). The work described in this paper relates to a review of pillar strength formulae using the latest available data and using two different approaches to the analysis.A dear distinction was found between pillar failure in the so-called ?weak coal' areas, comprising the Klip River, Vaal Basin, and Free State coalfields, and the rest of the areas in South Africa. It was not possible to derive satisfactory strength formulae for the "weak coal' areas using either the maximum likelihood or the overlap reduction technique of analysis. The pillars in these areas tended to fail at much higher safety factors, calculated by using the strength formulae developed for the 'normal coal' areas. It is postulated that the mode of failure may be different in these areas.This distinction reinforces the notion that coals in different areas have different characteristics and that there is scope to develop site-specific strength formulae. However, the scarcity of data for the different areas prohibits the development of reliable formulae at this stage, and therefore the broad distinction of 'weak' and 'normal' coals has to suffice for the present.The updated databases resulted in only slightly different strength formulae for the different approaches to the analysis than were obtained previously. Both the maximum likelihood and the overlap reduction technique resulted in usable formulae.The maximum likelihood technique resulted in a closer grouping around the average safety factor of unity for the failed cases, while the overlap reduction technique resulted in better distinction between cases of failed and stable pillars.For the same pillar geometries, the overlap reduction formula predicted lower strength than the maximum likelihood formula for pillars with width-to-height ratios less than 1.88, and higher strength for pillars with higher width-to-height ratios.Further work is required to review the squat pillar formula in the light of these new formulae, as the transition between the formulae presented here and the squat pillar formula is no longer continuous.In similar vein, the previous work to predict the stable life-span of coal pillars should also be reviewed using the latest available data.
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机译：南非煤炭支柱实力领域的先驱是M.D.G. Salamon和A.H. Munro，他们更倾向于使用统计分析分析失败和完好无损的支柱来确定支柱强度，以及Z.T. Bieniawski的尝试是基于使用各种尺寸的标本直接确定煤柱的强度。在进行原始统计分析时，有27例发生故障的支柱工作被认为适合列入失败的支柱数据库。失败和稳定的支柱案例数据库最近进行了更新，以包括过去几年发生的支柱失败案例（Van der Merwe和Mathey，2013a）。本文描述的工作涉及使用最新的可用数据并使用两种不同的分析方法来审查支柱强度公式。在所谓的``弱煤''区域（包括Klip）中，支柱破坏之间存在着明显的区别河流，瓦尔盆地和自由邦煤田，以及南非的其他地区。使用最大似然分析或重叠减少分析技术无法得出“弱煤”地区令人满意的强度公式。使用开发的强度公式计算，这些区域的支柱在较高的安全系数下往往会失效。对于“普通煤”地区，假定这些地区的破坏模式可能有所不同。这种区别进一步强化了这样的观念，即不同地区的煤具有不同的特征，并且存在制定特定地点强度公式的范围。由于不同地区的数据稀缺，因此无法在此阶段开发可靠的公式，因此，目前``弱''和``普通''煤的广泛区别就足够了。更新的数据库仅得出了略有不同的强度公式与以前获得的分析方法不同，最大似然和重叠减少技术最大似然法可以将失败案例的平均安全系数统一为一个更紧密的分组，而重叠减少技术则可以更好地区分失败和稳定的支柱案例。重叠减少公式预测的宽高比小于1.88的柱子的强度低于最大似然公式，而宽高比高的柱子的强度更高。鉴于这些新公式，由于此处介绍的公式与下蹲式公式之间的转换不再是连续的，同样，应该使用最新的可用数据来回顾先前的预测煤柱稳定寿命的工作。
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