For the probabilistic stability analysis of rock wedges formed by two discontinuities the First and Second Order Reliability method is used. This asymptotic method needs a continous formulation of the limit state. In the stochastic model the orientations, trace lengths and shear parameters are defined as basic random parameters. The importance measures of the variables are determined. The possibility to use of partial safety factors for the wedge analysis is discussed. The influence of water pressure on safety level is examined in an example.


L' analyse probabiliste de la stabilite de roches tetraedriques formees par deux discontinuites est effectuee à I' aide des methodes du premier et du second ordre de la theorie de la fiabilite. Ces methodes asymptotiques necessitent une fonction d'etat limite continue. L' orientation des plans de glissements, les longueurs d' affleurement et les coefficients de cisaillement sont modelises par des variables aleatoires, Les importances relatives de ces variables sur les resultats des calculs fiabilistes sont precisees. La possible utilisation de coefficients de securite pour s 'assurer de la stabilite de roches tetraedriques est consideree. Enfin, l' influence de la pression de l 'eau sur le niveau fiabilite est etudiee dans un example.


Die Zuverlassigkeitstheorie erster und zweiter Ordnung wird fuer die probabilistische Standsicherheitsanalyse tetraedrischer Felskeile verwendet. Fuer die Anwendung dieses asymptotischen Verfahrens ist eine stetige Formulierung der Grenzzustands erforderlich. Die Trennflachenrichtungen, die Ausbiβlangen und die Scherparameter werden im stochastischen Modell als Zufallsvariable definiert. Die Gewichte und Sensitivitaten der Basisvariablen werden bestimmt. Es wird untersucht, ob die Verwendung von Partialsicherheitsfaktoren fuer die Standsicherheitsanalyse von Felskeilen möglich ist. Der Einfluβ von Wasserdruck auf das Sicherheitsniveau wird an einem Beispiel untersucht.


The stability of rock wedges is influenced by random rock parameters. In deterministic stability analysis, the dispertion of parameters is taken into consideration by using reduced or modified mean values and calculating the safety factor for different combinations of parameters. However it is not possible to calculate the probability of failure or the reliability in this way. With probabilistic methods, it is possible to evaluate the reliability of systems depending on random and fixed parameters and quantify the influence of deterministic and random parameters on the reliability. Design rules are often based on limit state definitions, e.g. failure of slopes or foundations. Therefore it is necessary to find a mechanical model representing the real problem. Sliding of tetrahedral rock wedges is such a model often used for the design of rock slopes and walls of underground openings (JOHN, 1970; HOEK and BRAY, 1974 and 1981; WITTKE, 1965). As a rigid block method, this gives only information about the ultimate limit state and not about the serviceability limit state. It is necessary to keep in mind that the limitations and necessary simplifications of the model influence the results for the deterministic safety factor as well as for the reliability or probability of failure. A more detailed discussion of the theoretical background is given in MURALHA and TRUNK (1993) and TRUNK (1993).


To evaluate the influence of random rock parameters, the model of the tetrahedral rock wedge is chosen. In the first step, only failure by sliding is calculated. The failure by rotation and toppling of wedges is not considered. The use of a simple and established mechanical model makes an interpretation of the probabilistic results easier. The model determines the parameters that must be described in the stochastic model by means of distribution functions and their parameters like mean value and standard deviation.

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