Probabilistic key block analysis of a mine ventilation shaft stability – a case study

Abstract

In this study, the probabilistic key block analysis was applied to evaluate the stability of a mine ventilation shaft developed in a rock mass of granite. The key blocks were identified based on the block theory. The variations of discontinuity orientations were fitted with the Beta distribution and taken into consideration. The key block forming probabilities were analyzed. For simplification of calculations the first-order second-moment (FOSM) approximation was employed for probability estimation. With the considerations of the rock properties as random variables and applications of several statistical analysis tools, the key block failure probabilities, the probabilistic distribution of safety factors, and the probabilistic distribution of potential maximum key block volumes were analyzed. The analysis indicated that although the safety factor calculated based on the mean values of the variables was above 1.0 for the stability of the most critical key block, the block had a considerable probability of failure with a significant rock volume due to variations in discontinuity orientations and rock properties. Without promptly applying supports to the rock excavation, the shaft had a significant likelihood of failure.