Probability and reliability analysis of pillar stability in South Africa

A deterministic approach is frequently used in engineering design. In this quantitative design methodology, a safety factor, which is typically a strength-to-stress ratio, is derived as an index for the stability assessment of the engineering design. In underground coal mining applications such as pillar design, however, the inputs of pillar design are variables. This is widely overlooked in the deterministic approach. A probabilistic approach assessing the probability of failure or reliability of a system might be an alternative to the conventional quantitative methodology. This approach can incorporate the degree of uncertainty and deviations of variables and provide more versatile and reliable results. In this research, the reliability of case histories from stable and failed pillars of South Africa presented by Merwe and Mathey is examed. The updated Salamon and Munro strength formula (S-M formula) and Merwe and Mathey strength formula (M-M formula) are evaluated through a probabilistic approach. It is concluded that stable pillar cases have a reliability value greater than 0.83 while the reliability value of failed pillar cases are slightly larger than 0.50. There seems to be a positive relation between safety factor and reliability. The reliability of a pillar increases with pillar width but decreases with depth of cover, pillar height and entry width. The reliability analysis also confirms that M-M strength formula has a better distinction between the stable and failed pillar cases.