This report was presented orally at Workshop WI held as a part of EUROCK '93 on Monday, June 6 from 16:30 to 18:30. The purpose of this report, of the preceding introduction by the Workshop Chairman, Professor W. Wittke and the subsequent contributions by the four panel members, Dres. N. Grossmann, D. Fourmaintraux, U. Trunk and J. Muralha, was to trigger discussion of the topic, "uncertainty, reliability and risk". This happened and a lively discussion followed. A short summary of the most important results of the discussion will be given at the end of this report. In addressing the questions of "What can we do - what can we not do in uncertainty, reliability and risk applied to Rock Engineering?", four issues representing the usual decision making sequence in geotechnical engineering are discussed in this report, and they were also the topics of the panel member contributions.

A good way to consider these four steps in the decision making sequence and to judge how well the uncertainty related problems are solved is through examples. Each of the following four sections will deal with an example, namely, the persistence problem, the joint aperture problem, tunnel cost and time estimates and exploration strategy. I will try, after a brief introduction of each case, to show how the four decision making steps are applied, and draw conclusions on our capabilities to work with uncertainty.


Joints (fractures) in rock masses are usually not persistent which has significant effects on most rock engineering problems, most notably on problems involving flow and stability (Fig. 1). Traditionally, for instance in slope stability problems, persistence was considered using Jenning's relations (Fig. 2). However, one does not really know the rock bridge lengths b, and, given the much higher resistance of intact rock compared to joints, this lack of geometric knowledge translates into substantial uncertainty regarding rock mass resistance. Stochastic joint modelling (e.g. Dershowitz, et al., 1988) produced a real breakthrough in that it allows one, at least in principle, to sample data on joint geometry and to formulate geologic models (Fig. 3). It is then possible to incorporate the geologic models in reliability models to predict rock slope performance as also illustrated in Fig. 3 and explained in more detail, e.g. in Einstein et al. (1983, 1992). Similar reliability modelling is possible for flow problems (Dershowitz et aI., 1985, Long et aI., 1985) and deformation problems (Dershowitz, 1993) involving joints. Decisions can then be made e.g. using risk analysis, as also indicated in Fig. 3. While, on this basis, the persistence problem appears to have been solved, reality shows that we have quite a way to go. In Fig. 4 some of the unresolved problems are listed. The unresolved problems are in getting the data (information collection) and structuring it in representative models (inference procedures). I he inadequacy of the performance models is mainly related to lacking knowledge on the mechanical effect of rock bridges and their deformation and fracture modes.

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