Convergence Confinement method is a plane strain approximation of supported tunnel annalysis which is currently used in practice. However, efficiency of this method suffers from undetermination of the instant of support activation. A new approach including three dimensional tunnel problems, is proposed to remove such drawback in a self governing way. The methodology has been set up from analyses on direct calculations on a simplified reference three dimensional tunnel problem.


La methode de convergence Confinement est une methode courante d'analyse de tunnels, qui est une approximation en deformation plane. Toutefois, cette methode souffre de l'indetermination sur Ie moment d'activation du soutènement. On propose une nouvelle approche etendue au cas tridimensionnel, qui lève une telle indetermination de manière autonome. La procedure a ete elaboree à partir d'une analyse direct d'un problème simplifie type de tunnel.


Die Kennlinienmethode wird haufig bei der Auslegung von Tunnels angewandt. Hierbei wird naherungsweise ebene Deformation angenommen. Der Zeitpunkt zu dem sich der Tunnel verformt ist mit dieser Methode nicht bestimmbar. Wir schlagen ein neues dreidimensionales Model vor, anhand des sen bisher mit der erwahnten Methode nicht berechenbare Aufgaben lösbar sind. Dieses Verfahren wurde ausgehend von einem vereinfachten Rechenbeispiel entwickelt.


In deep tunnels, support of the walls are fundamental elements which contribute to the stability of rockmass. This action, of three dimensional nature, involves an intricate interplay between the construction phases, rock mass and support behavior. In spite of constant progress achieved in three dimensional numerical analyses, approximate plane strain analyses of tunnel sections are very useful for engineers and currently used in practice. In order to reproduce the effects of tunnel face excavation and progress, these methods use either varying softening of elements inside tunnel section, or a variable fictitious stress state at the tunnel wall, as in convergence confinement method. However, efficiency of these approaches are impeded by a serious drawback which is concerned with the undetermination of the instant for support activation. This factor appears as a very important interaction parameter between support and rock mass. In this paper, a method is proposed to eliminate satisfactorily such indetermination, without modifying much the nature of calculations. This results in a new approach of the Convergence Confinement Method, which appears as self governing, independent of the particular behaviour of the rockmass and the support system.


In order to learn out general rules for deriving systematically the instant for support activation, we analyse a typical reference tunnelling problem (Figure 1) containing the main elements of actual deep tunnelling problem: - constant advance rate (steady state hypothesis), which is implicitely supposed in CY-CF Method - full face excavation. - rotationnal symmetry of tunnel geometry. - three-dimensional effets on support produced by tunnel face proximity (distance Do to the leading edge of the tunnel), and anisotropic initial stress state defined by principal stresses h vertical, and h, z, horizontal, with the latter parallel to tunnel axis. The methodology is based on comparing direct calculations performed on that reference problem, to those of the approximate plane strain analysis. For direct calculations (excavation, support placement), a specific numerical tool has been built up, taking advantage of the peculiar hypotheses of the problem. There results in a very interesting and versatile Finite Element program, based on the steady state algorithm (Nguyen Q.S & al. 1981, Maitournam 1989), which allows to treat the sequential problem on a fixed geometry; and a Fourier's development of solutions in the angular direction (Zienkiewick 1977, Winnicki & Zienkiewick 1979, Hanafy & Emery 1980), which replaces the three dimensional problem by a succession of two dimensional problems.

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