This paper deals with comparative computations for a shotcrete lined railway tunnel with 30 m of overburden. In the computations the jointed rock is simulated either by a discrete or by a homogeneous model. In addition to the joint spacing, the orientation and the persistence of the discontinuities were varied.


Cet article presente les resultats d'un etude numerique pour un tunnel de chemin de fer avec une couvenure de 30 m, qui est stabilise par un coque en beton projete. Dans les conduites du calcul la roche fracturee est simulee par un modele discrete ainsi qu'un modele homogene. Les parametres changes sont l'espacemern, l'orientation et Ie degre de seperation des discontinuites


In diesem Beitrag wird ueber vergleichende Berechnungen fuer einen mit Spritzbeton gesicherten Eisenbahntunnel mit 30 m Überdeckung berichtet. Dabei wird zum einen ein diskretes und zum anderen ein homogenes (verschmiertes) Modell fuer den klueftigen Fels untersucht. Neben dem Trennflachenabstand werden die Raumstellung und der Durchtrennungsgrad der Trennflachen variiert.

1 lntroduction

In order to calculate the loading and deformation of the lining of tunnels, mainly two numerical methods are used, namely the Finite Element Method (FEM) and the Distinct Element Method (DEM). Within the FEM the rock is treated as a continuum, which is subdivided into finite elements. The elements are connected to each other by a finite number of nodal points. With this procedure a set of equations can be established to determine the displacements of the nodal points. From these displacements the stress strain- state of each element can be derived. Within the DEM the rock is treated as a composition of single blocks, which can move individually and even separate from each other and develop new contacts according to the individual loading. One way to compute the movements of the blocks as well as their internal deformation is to use a timestepping algorithm (HART 1991). The numerical methods mentioned above are associated with the two main methods of developing a model of jointed rock, i.e. the discrete model and the homogeneous model (Fig. I) By means of a discrete model, it is possible to deal with the discontinuities and the rock separately, according to their characteristic deformability and strength. The stress-strain behavior of the substitute material is usually anisotropic, because it takes into account the deformability and strength of both the discontinuities and the intact rock. Despite the fact that the FEM is mostly used for homogeneous models it is also possible to simulate discontinuities in a discrete fashion.

2 Examples for systems of discontinuities

In Germany, most types of rock found just below the surface are of sedimentary or metamorphic origin. In Figs. 2–7 several examples of these types of rock can be seen Fig. 2 first shows a Devonian clay slate (WITTKE 1990). Its schistosity can be assigned either to the joint fabric or to the grain fabric. Fig. 3 depicts a bedded sandstone with a low content of mudstone, taken from the "Mittlerer Buntsandstein" formation (FEISER 1988). Here the spacing of the gently dipping bedding parallel discontinuities is about 0.2 m, whereas the spacing of the non-persistent vertical joints is about two or three times this distance.

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