This paper proposes a methodology allowing the use of the convergence-confinement method to design concrete tunnel linings even when the far field stress state is anisotropic. Closed-form models are used to predict both the ground reaction and the lining reaction curves. It is shown that two interaction diagrams are required to define the non-uniform ground-lining contact pressure used to calculate the lining thickness. The way the two diagrams are obtained and the manner the results they yield are combined are described. The methodology is illustrated with practical cases. A comparison with finite element analysis results for two cases is made.


La presente communication propose une approche qui permet d'utiliser la methode convergence-confinement pour concevoir des revêtements de tunnellorsque I'etat de contraintes prealable est anisotrope. Les courbes de reaction du massif ainsi que les courbes de reaction du revêtement sont calculees à l'aide de modèles mathematiques analytiques. П est montre que deux diagrammes d'interaction sont necessaires pour definir la fonction de la pression de contact massif-revêtement requise pour calculer l'epaisseur du revêtement. La façon d'obtenir ces deux diagrammes et la manière de combiner les resultats qu'ils donnent sont decrites, La methodologie est illustree à l'aide de cas pratiques. Une comparaison est faite avec les resultats obtenus pour deux cas en utilisant des analyses par elements finis.


Diese Veröffentlichung beschreibt eine Methodologie die mit der Hilfe des Gebirgskennlinienverfahrens die Bemessung von Betontunnelauskleidungen, eben in einem anisotropen Primarspannungsfeld,ermöglicht. Die Gebirgskonvergenzkurven und die Ausbaureaktionskurven werden durch mathematische Modelle analytisch berechnet. Es wird gezeigt dass zur Verkleidungsbemessungzwei Zusammenwirkungsdiagramme nötig sind. Die Methode wie man dieses zwei Diagramme bekommt und zusammensetzt um zur Verkleidungsbemessung notwendigen ungleichformigen Gebirgsdruck zu bestimmen, wird dann beschrieben. Die neue Methodologie wird mit einigen praktischen Beispiele illustriert und ihre Gueltigkeit durch ein Vergleich mit den Resultaten der Methode der Finiten Elemente ueberprueft.


Great progress has been made in the field of rock support in mining and underground construction over the last decade. Nevertheless, the convergence-confinement ground support design method (also known as the characteristic line method) is still receiving considerable attention as it is currently used and discussed by numerous authors. The popularity of this method is mainly due to its clarity and versatility. Used primarily for the design of artificial ground support, the technique has been applied also to the design of mine pillars (e.g., Sarkka, 1984; Gill et al., 1994). Thirty to forty years ago, pioneering work of a number of authors (e.g., Lauffer and Seeber, 1961; Pacher, 1964; Lombardi, 1970) has allowed the design of artificial tunnel support through the convergence-confinement method when it is installed close to the tunnel advancing face. With this approach, the instantaneous convergence of the rock mass around the tunnel is partly counteracted by the support, leading to its loading. One of the first attempts to introduce the long-term strength concept in the determination of ground pressure on artificial support by the convergence-confinement method was made by Ladanyi (1974). With this approach, two limiting ground reaction curves were considered. One for the short-term response (t=0+) and another for the long-term response (t= (0). For intermediate times, it was assumed that the surrounding rock mass, undergoes a continuous deterioration. This deterioration involves a decrease in the modulus of deformation of the rock mass as well as a gradual loss of strength. With Ladanyi's concept, it can be assumed that the tunnel support is installed close to the advancing face and both instantaneous and time-dependent convergence restrictions contribute to the loading of the former.

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