Quasi-Stochastic Analysis of Uncertainty for Modelling Structurally Controlled Failures

In one approach to predicting the behaviour of rock masses, effort is being devoted to the use of probabilistic methods to model structures interior to a rock mass (sometimes referred to as ‘inferred’ or ‘stochastic’ structures). The physical properties of these structures (e.g. position, orientation, size) are modelled as random parameters, the statistical properties of which are derived from the measurements of a sample of the population (sometimes referred to as ‘deterministic’ structures). Relatively little attention has been devoted to the uncertainty associated with the deterministic structures. Typical geotechnical analyses rely on either an entirely stochastic analysis, or deterministic analyses representing the structures with a fixed shape (i.e. disc), position, size, and orientation. The simplifications assumed for this model introduce both epistemic and stochastic uncertainties. In this paper, it is shown that these uncertainties should be quantified and propagated to the predictions of behaviour derived from subsequent analyses. We demonstrate a methodology which we have termed quasi-stochastic analysis to perform this propagation. It is shown that relatively small levels of uncertainty can have large influence on the uncertainties associated with geotechnical analyses, such as predictions of block size and block stability, and therefore this methodology can provide the practitioner with a method for better interpretation of these results.