In this paper we show how the appropriate uncertainty model to apply in an analysis depends on the nature of the available information. We explore this through the analysis of a rock slope using probabilistic models that incorporate alternative subjectively assigned probability distributions. These alternatives mimic the opinion of multiple experts. The results are shown to depend strongly on the shape of the input distributions, and hence the expert opinion utilised. We conclude by showing that an analysis using fuzzy mathematics is more appropriate than a probabilistic approach when objective data are limited or absent, and present a novel technique for decision making using the results of a fuzzy analysis.


In rock engineering, practitioners are often required to make critical decisions based on little or no objective data. This lack of information requires subjective estimation of parameters used in any analysis, and thus introduces uncertainty.

Some have suggested that even with little or no information, stochastic methods can be used to make pragmatic decisions by adopting a subjective view of probability (Aven 2010, Lindley 2000). This forms the basis of the Bayesian approach, which suggests that expert opinion can be applied to assign precise probability distributions (so-called ‘priors’) based solely on the knowledge or judgement of an expert. Within this framework, a probability distribution function (PDF) represents an expert's subjective degree of belief in a value's probability of occurrence. However, others argue that the subjective assignment of priors can lead to misinformed decisions and dissonance amongst experts (Ferson & Ginzburg 1996). In this paper, we investigate the latter argument via a case study on slope stability – that of the previously published Sau Mau Ping Road slope in Hong Kong (Hoek 2007).

In this paper we compare the results from Monte- Carlo simulation based on a subjectivist approach to probability and a non-probabilistic approach using fuzzy sets. We show the significant differences in design decisions that may result depending on the model adopted to characterise and propagate uncertainty.

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