We present two new simplified plane strain approaches, according to the framework of Convergence-Confinement Method, for analysis of deep axisymmetric tunnels driven in elastoplastic media. These approaches take into account correctly the face-support interaction and are in good agreement with direct axisymmetric calculations.


On presente deux nouvelles approches simplifiees en deformation plane, suivant le principe de la methode de Convergence- Confinement, pour Ie calcul des tunnels profonds en milieu elastoplastique. Ces approches prennent en compte correctement I'interaction entre Ie front de taille et Ie soutenement, et donnent un bon accord avec les calculs directs en axisymetrie.


Wir stellen zwei neue vereinfachte Modelle ebener Deformation vor, nach der "Convergence-Confinement" Methode, fuer die Berechnung tiefer tunnel in elastoplastischer Umgebung. Diese Modelle beruecksichtigen die Wechselwirkung zwischen Oberflache und Untergrund und Iiefern eine sehr gute Übereinstimmung mit der direkten axisymmetrischen Berechnung.


It is well understood that a supported tunnel behaves as a three dimensional structure for which the strain and the stress fields are strongly influenced by details of the technology of excavation and the construction sequence, which sometimes can hardly be introduced in numerical models, even when adopting complex 3D FEM. Nevertheless for predimensioning purpose it is interesting to use simplified methods for tunnel analysis. In this paper we present two new simplified methods of tunnel dimensioning as improvements of the well known convergence confinement method (AFTES.1983), which transforms the 3D problem into a 1D plane strain one. The lining is a ring of constant thickness e, made of an homogeneous and isotropic material and it is set at a distance do from the tunnel face. The face is plane and vertical. According to all these hypothesis, the tunnel problem becomes an axisymmetrical problem. Moreover, if the tunnel face is far from the studied section (x) the displacement field is radial (plane strain condition). In this case the problem can be studied in the plane and the interaction between the two previously described structures is now defined by one single scalar parameter: the confinement Pi (radial action of the rockmass on the lining). The associated parameter is the closure of the tunnel wall Ui· In the convergence-confinement method(CV-CF), it is assumed that an equivalent closure Ui of the tunnel can be achieved through a plane strain analysis of a given section submitted to uniform fictitious pressure Pi which decreases from P to zero as the face of the unlined tunnel advances. If a lining is placed, Pi is the confining action. Figure 2 shows the convergence curve CV and the confinement curve CF in the diagram Pi - Ui, that can be considered as a summary of what information we have about both structures. The equilibrium of the tunnel is given by the intersection of the two curves at point E(PE, UE): PE is the pressure exerted by the rockmass on the lining at the end of the construction process (i.e.x) and UE is the final closure of the wall. Indeed the parameter Uo is fundamentaly of three dimensional nature and should be studied through 3D (or axisymmetrical) numerical analyses. The solutions proposed in AFTES (1983) show that uncertainty on determination of that parameter remained one main drawback of the CV-CF method, mainly in case of non elastic behavior.


A renewed effort since years 1989, testified by some "state of the art" works (Corbetta, 1990; Bernaud, 1991; Panet, 1993; Nguyen-Minh, 1994), has allowed to achieved the final forms presented herein.

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