ABSTRACT:

A joint set is characterized by several geometrical parameters - attitude, intensity, area, and aperture -, which have to be determined from measurements performed on natural or man-made observation surfaces of the rock mass. However, many engineering problems can not be adequately solved if only the most probable values of the involved parameters are known, as the search for safe solutions asks for the analysis of all unfavorable, but still possible scenarios. The knowledge of the confidence limits of the estimates of the different joint set parameters allows the engineer to determine which unfavorable combinations of those parameters have still a reasonable probability of occurrence, and, thus, must be taken into consideration in the design of the work. The paper gives information about the confidence limits for some estimates of the different joint set parameters.

RÉSUMÉ:

Une famille de diaclases est caracterisee par plusieurs paramètres geometriques - attitude, intensite, aire et ouverture -, qui doivent être determines à partir de mesures realisees sur des surfaces d' observation du massif rocheux naturelles ou faites par I'homme. Cependant, beaucoup de problèmes d'ingenierie ne peuvent pas être adequatement resolus si rien que les valeurs plus probables des paramètres en cause sont connues, puisque la recherche de solutions sûres requiert l'anaIyse de tous les scenarios defavorables, mais encore possibles. La connaissance des limites de confiance des estimateurs des differents paramètres des familIes de diaclases permet à l'Ingenieur de determiner quelles combinaisons defavorables de ces paramètres ont encore une probabilite d'occurrence raisonnable, et doivent, done, être prises en consideration dans Ie projet de l'œuvre, La communication donne des informations sur les limites de confiance pour quelques estimateurs des differents paramètres des familles de diaclases.

ZUSAMMENFASSUNG:

Eine Kluftschar wird durch mehrere geometrische Parameter - Stellung, Starke (Klueftigkeit), Flache, und Öffnung _ gekennzeichnet, die anhand von Messungen bestimmt werden muessen, die an natuerlichen oder durch Menschen hergestellten Beobachtungsflachen des Gebirges ausgefuehrt werden. Viele Probleme der Ingenieurkunst können jedoch nicht zweckmaßig gelöst werden, wenn nur die wahrscheinlichsten Werte der betreffenden Parameter bekannt sind, da die Suche nach sicheren Lösungen die Analyse aller unguenstigen, doch noch möglichen Szenarien erfordert. Die Kenntnis der Vertrauensgrenzen der Schatzwerte der verschiedenen Kluftscharparameter gestattet dem Ingenieur zu bestimmen, welche unguenstigen Kombinationen jener Parameter noch eine vernuenftige Geschehenswahrscheinlichkeit haben, und, folghch, beim Entwurf der Arbeiten in Betracht gezogen werden muessen. Die Mitteilung gibt Auskunft ueber die Vertrauensgrenzen fuer einige Schatzwerte der verschiedenen Kluftscharparameter.

1
INTRODUCTION:

The joint system of a rock mass is usually formed by several joint sets and a certain number (less than 20 % of the occurring joints) of randomly oriented joints, although, for engineering purposes, in most cases, only the major joint sets are considered. A joint set, i.e., a group of joints which are approximately parallel to each other, is characterized by several geometric parameters - attitude, intensity, area, and aperture -, which have to be determined from measurements performed on the natural or man- -made observation surfaces of the rock mass. These measurements correspond to a, usually, biased sample of the geometric joint characteristics, which allows, after the due correction of any existing sampling bias, and, generally, by using the maximum likelihood principle, to estimate the different most probable joint set parameters. However, many engineering problems cannot be adequately solved if only the most probable values of the involved parameters are known as the search for safe solutions asks for the analysis of all unfavourable, but still possible scenarios. The knowledge of the confidence limits of the estimates of the different joint set parameters allows the engineer to determine which unfavourable combinations of those parameters have still a reasonable probability of occurrence, and, thus, must be taken into consideration in the design of the work.

2
ATTITUDE:
2.1
Definition

The attitude of a joint describes its orientation in the space, independently from its location, and assuming that it is plane. The attitude of a joint is, in general, quantified through the 2 parameters, strike and dip.

2.2
Statistical distribution

The distribution of the attitudes of the joints of a joint set is modelled by a bivariate normal distribution on the tangent plane at the mean attitude (Grossmann 1985).

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