A finite element program is developed for the analysis of underground openings excavated at considerable depth or in weak rocks. A rock mass response model based on the Hoek-Brown failure criterion dependent on rock type and rock mass quality is incorporated into the program. Any desired post-failure stress-deformation behaviour, including strain softening, can be considered. The practical implications of this research are demonstrated by analysing the northern section of the St. Gotthard highway tunnel and its safety gallery.
Un programme d' elements finis est developpe pour l'analyse des ouvrages souterrains excaves a' grande prnfondeur ou dans des roches fragiles. Un modèle de comportement pour le massif rocheux qui est bas sur le critère de rupture de Hoek et Brown et qui depend du type de roche et de la qualite'du massif rocreux est incorpore' au programme. Tous les types de comportement contrainte-deformation peuvent être pris en compte; y compris Le radoucissement. Les implications pratiques de cette recherche sont de'montrees par une analyse de la section nord du tunnel rootier du St. Gotthard et de sa galerie de se'curite'.
Ein "finite Element" Programm wird, fuer die Analyse von unterirdischen Ausgrabungen die sehr tief oder in schwachen Felsgesteinen ausgebohrt werden, entwickelt. Ein Felsmassemuster, basierend auf das Hoek-Brown Kriterium, abhangig von der Felskategorie und von der qualitat der Felsmasse, ist in dem Programm einbegriffen. Alle gewuenschten"post-failure" Druckdeformationen können beruecksichtigt werden, einschliesslich des Festigkeitsabfall. Die praktischen anwendungen dieser Forschungwerden durch die Analyse des nördlichen Teiles des St. Gotthard Tunnels und seines Sicherheitstollens dar gestellt.
In -analyses involving the stability, safety and economy any of underground excavations, it is essential to account for the probable response of the surrounding rock mass as realistically as possible. In this research, attention is given to the case of openings excavated at considerable depth or in weak rocks, in which the induced stresses reach the available strength in some part of the rock mass surrounding the excavation. Failures controlled by the geological structure of the rock mass are not considered. The finite element method is suited to the treatment of such problems, because any shape and sequence of excavation, initial stress field and rock mass behaviour, as well as the interactive nature of the load-deformation characteristics of both rock mass and support system can be considered. The post-failure behaviour of rock masses accounted for in previous finite element analyses is generally oversimplified and unrealistic. With the improved knowledge of mechanical behaviour of rock masses, it is now evident that a realistic rock mass behaviour model should be based on a yield criterion dependent on rock type and rock mass quality, such as the Hoek-Brown criterion (Hoek and Brown,1980), am also be able to account for any experimentally determined post-failure stress-strain relationship including strain softening. Thus the principal aim of this research is to develop a finite element Program incorporating such a rock mass behaviour model for more realistic and economiic design of underground excavations. In order to model correctly most excavation sequences it would be necessary to carry out a three-dimensional analysis, but since this would be very expensive it is supposed here that the rock mass is in a state of plane strain. The techniques discussed here can in principle be applied to the three-dimensional case.
For the complete description of the elasto-plastic behaviour of rocks, a yield criterion, post-failure strength-strain relationship and treatment of plastic volumetric strains must be specified: i) Yield criterion: The failure criterion proposed by Hoek and Brown (1980) is adopted. It is assumed that the rock mass is reasonably continuous, isotropic and homogeneous with either very widely or closely spaced joints. ii) post-failure behaviour: The progressive failure of rock masses is modeled by linear variation of the empirical parameters mp and s with maximum principal plastic strain, ε p/1-a convenient scalar measure of plastic straining and an index of the amount structural change (Figure 1). In particular the reduction of s has strong physical significance, because it call simulate the transition of intact rocks (s = 1.0) to completely broken rock masses (s = 0.0), i.e. the complete stress-strain history. In order to provide every possible type of post-failure behaviour one may obtain from experimental results, the model is designed to account for strain hardening, perfectly plastic and strain softening rock behaviours. The associated flow role (APR) is assumed for strain hardening and perfectly plastic behaviours as shown in Figure 1 (ε p/1 < ε p/1 p). This assumption is generally supported by experimental data. However, the normality condition seems to disappear when the rock is fractured or poorly interlocked (Brown et al., 1982, 1983). This implies that using the associated flow role in the strain softening and residual strength regions may give unrealistically large displacement predictions.
