This paper is based on a Monte Carlo simulation of a problem where a coal mine is divided into two sections (East and West) by a dyke such that the East section experiences no pillar failures while the West does despite having the same safety factor. This may prompt one to mine the East section at a lower safety factor arguing that the East section must be logically stronger compared to the West section. Probabilistic evaluation using Monte Carlo simulation is useful in clearing such misconceptions. It brings more light to the extent of dismissing (step by step) an argument which would have seemed to be originally reasonable (like in this paper). The simulation undertaken utilizes observations of road width, mining height and mining depth for both sections. A sensitivity analysis was carried out in order to select the most appropriate formula for solving the problem between the power formula and the linear formula. The linear formula was considered to be the best as it gave the same stability as the power formula but enabling mining to smaller pillar size. This enables stable, safe and sustainable utilization of mineral resources. A detailed analysis of both sections using the linear formula showed that contrary to one’s argument, both sections are over designed with actually the West section, which is failure ridden, being more over designed than the East section. West section failure is attributed to more variability in observations compared to the East section.


Probability and Risk in Rock Engineering is one of the crucial pieces which make up the Rock Engineering Puzzle. The Probabilistic approach enables Engineers to evaluate risk and make decisions within reliable confidence limits. Probability and Risk utilizes statistical observations and powerful assessment tools such as Monte Carlo simulation (MC), First order second moment solutions and fault tree diagrams in coming up with a solution to an engineering problem. This approach leads to justifiable designs such as slope stability, rock mass characterization, layout of underground excavations and design of support systems among others.

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