Incorporating Parameter Variability in Rock Mechanics Analyses: Fuzzy Mathematics Applied to Underground Rock Spalling

Although fuzzy analysis has been widely developed, its use in rock mechanics and rock engineering is limited. Here, it has been used to evaluate the potential for underground rock spalling at the boundary of a circular excavation in terms of rock strength and in situ rock stress, given the uncertainty in both of these input parameters. Using standard techniques from fuzzy mathematics, we develop an expression for the fuzzy factor of safety, and extend this to form the crisp parameters Safety Certainty Value and its complement, the Failure Certainty Value. Plots of the Failure Certainty Value in terms of the in situ stress ratio and rock strength/stress ratio show the effect of uncertainty on the assessment of stability. From these plots, we illustrate how the relative importance of uncertainty in the input parameters can be assessed, with the associated ramifications for site investigation and subsequent engineering design.