In this paper is presented a study on the inelastic behaviour of underground galleries in the presence of temperature fields, using analytical models. After the presentation of an elastoplastic model, capable of analysing irreversible behaviour, this model is then extended to the case of viscoplastic behaviour, in order to take into account creep effects as well. The very simple analytical solutions provide a powerful means to put into evidence the principal phenomena involved, and to derive useful conclusions for the dimensioning of underground galleries subjected to thermal loading. A few applications are given as illustrative examples.
Dans cet article, on presente une etude sur Ie comportement anelastique des galeries souterraines sous I'effet de temperature, en s'appuyant sur les modèles analytiques. Après la presentation des principaux resultats du modèle elastoplastique, celui-ci est ensuite etendu au comportement elasto-viscoplastique pour prendre en compte, en plus de l'irreversibilite, les effets differes. Les solutions explicites permettent de mettre en evidence d'une manière pertinente les principaux phenomènes mis en jeux, et de degagerdes conclusions utiles pour Ie dimensionnement des galeries souterraines soumises à un chargement thermique. Quelques applications sont donnees en gui se d'illustration.
Eine Studie ueber das nicht-elastische Verhalten von Tunneln in der Gegenwart von Temperaturfeldern unter Benutzung von analytischen Modellen wird vorgestellt. Nach der Prasentation eines elasto-plastischen Modells das die Analyse von irreversiblem Verhalten erlaubt, wird das Modell auf den Fall eines visco-plastischen Verhaltens ausgedehnt um KriechefIekte zu beruecksichtigen. Die sehr einfachen analytischen Lösungen erlauben die Darstellung der Hauptphanomene und die Ziehung von Schlussfolgerungen bezueglich der Dimensionierung von Tunneln under höheren Temperaturen. Einige Anwendungsbeispiele werden vorgestellt.
The mechanical behaviour of a tunnel under isothermal conditions is now well known for a large class of material behaviours, particularly thanks to the development of the convergence-confinement method and the pioneering work of Egger (1973), Panet and Guellec (1974), Panet (1976), and Berest and Minh (1983), and the recent contribution of Bernaud and Rousset (1988). On the other hand, new problems arise for which temperature plays an important role, such as the underground coal gasification, extraction of geothermal energy, deep petroleum borings, and the underground repositories of nuclear wastes. However, contrary to the isothermal case, simple mechanical models useful for the analysis of such problems are much less abondant. Among the few existing analytical solutions, we can mention those of Bland (1956) and Mendelsen (1968) on an elastoplastic tube subject to a stationary temperature field and a variable internal pressure. But the stationarity of the temperature and the assumption of face flow (the stress parallel to the tunnel axis remains the intermediate stress) restrain the domain of application of such models. It should be emphasized that the co-existence of face flow and corner flow in the case of axisymmetry complicates substantially the problem. The absence of such phenomenon under spherical symmetry simplifies significantly the resolution process, and analytical solutions are more accessible. Special mentions should be given to the model of Berest (1986) on the thermoplastic behaviour of an infinite solid, later generalised to viscoplastic behaviour by Berest and Rousset (1986), which appear to be theoretically well demonstrated. Other more complicated models (Minh and Schmitt (1986, 1987), Ishikawa and Hata (198)), take into account more general material behaviours, but need more elaborated numerical computations, and cease to be really analytical. In this paper, two analytical solutions are presented: the first on elastoplastic, and the second on elasto-viscoplastic behaviour of a tunnel subject to internal heating. Some illustrative examples will be given, following the theoretical developpements.
