Reliability analysis of rock mass response by means of Random Set Theory

When the parameters required to model a rock mass are known, the successive step is the calculation of the rock mass response based on these values of the parameters. If the latter are not deterministic, their uncertainty must be extended to the predicted behavior of the rock mass. In this paper, Random Set Theory is used to address two basic questions: (a) is it possible to conduct a reliable reliability analysis of a complex system such as a rock mass when a complex numerical model must be used? (b) is it possible to conduct a reliable reliability analysis that takes into account the whole amount of uncertainty experienced in data collection (i.e. both randomness and imprecision)?

It is shown that, if data are only affected by randomness, the proposed procedures allow the results of a Monte Carlo simulation to be efficiently bracketed, drastically reducing the number of calculations required. This allows reliability analyses to be performed even when complex, non-linear numerical methods are adopted.

If not only randomness but also imprecision affects input data, upper and lower bounds on the probability of predicted rock mass response are calculated with ease. The importance of imprecision (usually disregarded) turns out to be decisive in the prediction of the behavior of the rock mass.

Applications are presented with reference to slope stability, the convergence-confinement method and the Distinct Element Method.