The optimization of the shape of large rectangular-like caverns with rounded corners is studied, for various far field stresses, and internal pressures. It is shown where around the cavern the rock becomes dilatant, where compressible, where instantaneous failure or creep failure is to be expected. Also it is shown where around the cavern a fast creep convergence of the walls will take place.
On etudie la forme optimal d'une caverne rectangulaire avec coins arrondis. Plusiers possibles contraintes à l'infinite ont ete considerees et plusieurs pressions internes. On montre où autour de la caverne la roche devienne dilatante, où compressible, où une rupture instantanee ou un endommagement par fluage est possible, On montre aussi où autour de la caverne la convergence rapide des parois par fluage est envisagee.
Fuer die Optimirung der Form grosser Kavernen mit rechteckigem Querschnitt und unter-schiedlich gerundeten Ecken wir der Einfluss verschiedener "far field"-Spannungen und verschiedener innerer Druecke untersucht. Es wird berechnet, wo das Falsgestein in der Umgebung der Kaverne dilatant und wo es kompressibel reagiert, und wo instantaner Bruch oder Kriechbruch zu erwarten ist. Ferner wird ermittelt, wo in der Kaverne besonders schnelle Konvergenz auftritt.
Underground excavations of some other shape than circular are quite often used either in mining engineering, or in petroleum engineering (caverns used for storage of petroleum products), or in civil engineering (underground deposits, garages, railway stations, etc.). Quite often these caverns are either square-like or rectangular-like in shape (Dawson and Munson 1983, Borns and Stormont 1989, Munson and Devries 1991, Frayne et al.1993, Mraz et al.1991), i.e. their cross sections are either squares or rectangles, with more or less rounded corners, the third dimension being much larger than the dimensions of the cross section. This allows us to consider the problem to be a plane strain problem. The design of such kind of caverns is done usually by numerical methods, in most cases either FEM or BEM (Cravero et al.1993, Del Greco et al.1993, Kikuchi et al.1993, Saari 1987, Honecker and Wulf 1988). What concerns the model used for the rock involved, one has used in most cases Hooke's law, though occasionally some rheological models were used as well (Cravero et al.1993, Del Greco et al.1993, Honecker and Wulf 1988, Kikuchi et al.1993, Lux and Schmidt 1993, Nguyen-Minh and Pouya 1992, Saari 1987, Stormont et al.1992, Vouille et al.1993). In conjunction with the above problem, we have put ourselves four main questions. First, is it possible to find an exact elastic solution describing the state of stress, strain and displacement around a rectangular-like cavern? Secondly, if the first answer is positive, is it possible to determine where around the cavern a failure is to be expected, and can we determine the amount of rock involved in failure? Thirdly, having in mind that very many such kinds of caverns are excavated in order to build repositories for radioactive wastes, or for other hazardous wastes, while in some other cases such caverns are used as deposits for gases or liquids under pressure, an important question is to see if we can ensure that by the excavation procedure itself we are not producing significant damage by microcracking to the rock surrounding the cavern. This would seriously jeopardyse the effectiveness of the cavern. Finally, we would like to know where around the cavern a significant closure by creep is to be expected soon after excavation, how can we influence it by the design of the cavern shape, where would it be more efficient to install some support, etc.
