Probabilistic Analysis for Mine Design, Using Coal Pillar Design to Illustrate its Potential Usefulness

"Analytical engineering design is based upon a trial-and-error iterative and deterministic process. Within this process, the engineer obtains some estimated values, plugs them into de facto closed-form equations, and receives output, which is expected to be a single number that serves as the basis for the design. This number is typically a factor of safety, or some other equivalent strength-stress ratio. This provides the engineer with a quick and relatively quantitative design methodology. This can create problems however, because in mining applications, the actual in situ system is highly variable, complex and often chaotic, which can lead to potentially incorrect conclusions that result in unsafe designs. A more appropriate and reliable approach is a probabilistic analysis for engineering design. This process is used widely in civil and other engineering disciplines, but is often overlooked for applications in coal mine design. Additionally, it seems the amount of past studies using this approach, especially in coal mine design, are rather limited. Considering how the probabilistic approach can account for uncertainty in parametric values and how unpredictable a mining design can be, the authors believe that this approach has potential in mining. This paper will focus on a summary of past studies related to probabilistic analysis in coal mine pillar design and provide recommendations for future work that could improve design reliability. INTRODUCTIONFeasibility and fundamental design procedures for excavations often start with an assessment of mine openings, pillar design, and the surrounding structure by using a deterministic approach with closedform solutions (ex. Bienawski, Obert-Duvall). These are reliable methods, but designers know that the inputs in these closed-form solutions are estimates at best and do not incorporate any degree of uncertainty. This is therefore not an optimal design procedure.A more appropriate design should incorporate some uncertainty because of the chaotic and variable nature of geology and mining conditions in general. In an attempt to account for uncertainty, a probabilistic approach can be adopted, which accounts for deviations in variables and provides a more optimum design solution. By applying a probabilistic approach, a designer can look at multiple failure scenarios at the same time instead of using the same deterministic design over and over."