Probabilistic Approach to Coal Pillar Design

The classical approach to engineering design involves the purely deterministic calculation of the factor of safety, the ratio of strength to stress. The factor of safety is an easy calculation to perform in many circumstances, and it is very easy to interpret the results. The simplicity of the method is both a strength and a weakness. The results of the deterministic factor of safety calculation are simple to determine and interpret, but they have no ability to account for the uncertainty present in the inputs or outputs. Uncertainty is prevalent in geotechnical engineering applications. This uncertainty can stem from spatial variability, poor sampling, a dynamically changing environment, etc. Probability analyses allow input parameters to take the form of a distribution rather than a single value, making them uniquely equipped to handle the uncertainty inherent in geotechnical engineering design considerations. A stochastic approach also has the benefit of providing results as a probability of failure, which is more meaningful than a factor of safety. Though stochastic modeling is becoming more common in many geotechnical applications, it is still not widely used for coal pillar design. The objectives of this study are to justify the concept of using a stochastic approach to coal pillar design and to compare the results of a simple stochastic analysis to those of standard industry practice. A simple synthetic study was performed to compare the results of a probabilistic analysis of coal pillar design to the results obtained from running ARMPS, which is published by NIOSH. Normal distributions were assigned to each input parameter that is required to determine the factor of safety of a single coal pillar. The probability of failure resulting from the synthetic study was found to be more conservative than the ARMPS stability factor. A probabilistic approach to coal pillar design is discussed in comparison to the traditional deterministic approach. The greatest strengths of the probabilistic approach were determined to be the effective handling of uncertainty and the increased meaning of the inputs and outputs inherent to a probabilistic approach.