The wall displacements and the loading of tunnel supports increase with lapse in time. This report deals with the different models which were used for the analysis of practical cases. The increase of displacements and pressures with time are brought about: - on one hand, by the progress of the tunnel face, - on the other hand, by the time-dependent mechanical properties of the rock masses. The models take into account both, or separately these two factors. The rheological behaviours of rock are viscoelastic, viscoplastic or include the swelling characteristics for some type of rocks. This report points out the main limitations of the models.


La convergence et les sollicitations des soutènements croissent generalement dans le temps. Ce rapport traite des differents modèles qui ont ete effectivement utilises dans l'analyse de cas concrets. L'accroissement des deformations et des sollicitations en fonction du temps est dû; - d'une part à la progression des travaux de creusement, - d'autre part au comportement rheologique des massifs rocheux. Les modèles utilises prennent en compte ces facteurs separement ou simultanement. Les comportements rheologiques sont viscoelastiques, viscoplastiques ou font intervenir le gonflement de certaines roches. Le rapport soul igne les principales limites des modèles utilises.


Die Deformationen entlang des Hohlraums und der auf die Tunnelauskleidung wirkende Drucknehmen im allgemeinen mit der Zeit zu. In diesem Bericht werden die fuer die tatsachliche Untersuchung praktischer Falle eingesetzten verschiedenen Modelle dargestellt. Die Gruende fuer den Zuwachs an zeitabhangigen Verformungen und Druck sind folgende: - Einerseits die Weiterentwicklung der Tunnelausbohrung, - Andrerseits die zeitabhangigen mechanischen Eigenschaften der Felsmassen. Die eingesetzten Modelle beruecksichtigen entweder nur einen der o.g. Faktoren, oder beide zusammen. Das rheologische Verhalten ist viskoelastisch oder viskoplastisch; er kann auch die Quellung gewisser Felsarten einbeziehen. Im βericht werden die Hauptgrenzen fuer den Einsatz der Modelle hervorgehoben.

The rational design of underground works support must be based on the analysis of the ground support interaction. The ultimate loading of the support is related to the deformations which occur after their placement. They depend upon many factors: the initial state of equilibrium - the ground behaviour - the stiffness characteristics of the support system - the excavation and support timings and procedures. In some cases, the final equilibrium is reached almost immediately after the excavation; on the contrary, in other cases, it is clear that increases of deformations and loadings go on over a long period of time after excavation. These facts have been well established for instance, by the measurements carried out on old tunnels in France. The Mont-Cenis railway tunnel, the first alpine underground route between France and Italy, is such an example. The most part of this tunnel has been driven in calcareous schists with an overburden somewhere over 1500 m. About one century after construction, stresses in the masonry lining measured by the flat jack technique, are of the order of some Mega Pascals; theses values are meaningful and, without any doubt, much larger than those existing at the end of the construction; the masonry lining was built far behind the excavation section and a long time after; the space between the ground and the lining was poorly blocked by unbounded rock pieces. The deformations which bring about an increase of the loads acting on the support are due to: - the processes of excavation - the rock mass rheological behaviour. The models which have been developped recently for tunnel support analysis have promoted a more complete understanding and a better assessment of these phenomena. For the sake of clarity, frequent reference will be made to the simple case of a circular tunnel driven in an homogeneous and isotropic medium; to satisfy axisymmetry, isotropic initial stresses will also be assumed.


During excavation, deformations have a purely static cause. As the face is advanced, the conditions of equilibrium change, and convergence, rock displacements of the tunnel walls, occurs behind the face. The analysis of the convergence on a certain length behind the face is a three-dimensional problem which has been analysed by numerical models. It has been shown that it is possible to consider with a sufficient approximation, considering other uncertainties, that this problem is equivalent to a plane strain problem (Fig. 1). In the plane strain problem, it is considered that a radial stress σ r is applied on the wall of the tunnel, and is decreased gradually from its initial value σ° to zero for an unsupported tunnel; in this model, the face effect is replaced by a fictitious supporting pressure equal to (1 - λ) σ° in such a way to get the same value of convergence. The face advance is simulated by the increment of the coefficient λ.

This content is only available via PDF.
You can access this article if you purchase or spend a download.