ABSTRACT:

One of the major problems in rock mechanics and rock engineering is uncertainty. Typical problems in geomechanics are highly complex and their parameters are only known to a limited extent. Different techniques are available to cope with this situation. This paper analyses the uncertainty of numerical parameters and its representation and consequences. The approaches to the representation of uncertain parameters range from the use of a global factor of safety, through interval analysis and fuzzy mathematics to probabilistic analysis. These approaches represent the uncertain parameter on different levels of information and knowledge. The approaches will be presented with examples from a rock mechanics context and discussed with respect to their assumptions, capabilities and limitations. Criteria for the selection of the appropriate approach are discussed based on the concept of level-of-information. The approaches and criteria presented will enable engineers to represent uncertainty of different levels in their analyses. The method to deal with uncertainty can be changed within the life of a project as uncertainty decreases and information increases.

RESUME:

Un des problèmes les plus importants dans Ie domaine de la mecanique des roches et de son application est I'incertitude. Les taches habituelles sont hautement complexes et les paramètres ne sont qu'en partie connus. Cet article traite de l'incertitude des paramètres numeriques et des differentes approches permettant de les prendre en consideration. Les approches dependent du type d'informations contenues dans Ie paramètre et vont de I'utilisation d'un facteur global de certitude, de l'analyse d'intervalles, de la technique d'ensembles flous (fuzzy sets) jusqu'au calcul de probabilites. Ces approches seront expliquees et commentees à laide d'exemples du domaine de la mecanique des roches et les critères dutilisation seront discutes.

ZUSAMMENFASSUNG:

Unsicherheit ist ein besonderes Problem irn Felsbau und der Felsmechanik: Typische Aufgaben sind hoch komplex und die Parameter nur teilweise bekannt. Der vorliegende Aufsatz behandelt die Unsicherheit numerischer Parameter und die unterschiedlichen Ansatze fur ihre Beruecksichtigung. Die Ansatze unterscheiden sich durch den jeweils charakteristischen Informationsgehalt der Parameter und reichen vom Gebrauch eines globalen Sicherheitsfaktors uebel'die Interval-Analyse und die Reprasentierung durch unscharfe Mengen (fuzzy sets) bis zu probabilistischen Verfahren. Die Verfahren werden an Beispielen aus der Felsmechanik erlautert und diskutiert sowie ihre Anwendungskriterien erörtert.

1.INTRODUCTION

One of the major problems is geomechanics is uncertainty. STARFIELD & CUNDALL [11] describe the typical problem in geomechanics as data limited and highly complex, and so the inputs to the models of such systems can only be determined to a limited amount by experiments, or have their origin in expert opinion. Furthermore, the model system itself is only a model of the reality and does not cover all the phenomena of the real world. These are examples of uncertainty. Ignoring uncertainty can lead to results with which we have unknown confidence, and uneconomic and/or unsafe results or designs may be the consequence. Working with uncertainty is universal in rock mechanics, but many of the techniques are unknown to most of the rock mechanics community. For example, what can we use fuzzy sets for, and when should which technique be applied? This paper gives an overview of the different methods to deal with uncertainty, together with recommendations for their use and limitations in rock engineering practice. The scope of the paper is limited to numerical methods, although all the methods which have been proposed for dealing with uncertainly fall into two classes: non numerical and various numerical methods.

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