C. Kropik, H.A. Mang:
"Computational Mechanics of the Excavation of Tunnels";
Engineering Computations, 13 (1996), 7; S. 49 - 69.
Currently, the great majority of structural analyses of tunnels is performed by means of 2D finite element (FE) models. In general, the Drucker-Prager or the Mohr-Coloumb failure criterion is employed. In order to match the analysis results to the results from measurements on site, a number of parameters are introduced on the basis of practical experience. These parameters are aimed at compensating the neglect of the third dimension of the problem. This procedure is frequently admissible. It fails, however, for non-standard situations, such as cross-drifts, where three-dimensional effects are significant. For such situations an adequate 3D analysis tool is needed. It must be able to reflect the material properties correctly. However, it must be numerically efficient and robust.
Relatively little work concerning large-scale 3D analyses of the excavation of tunnels has been published in the open literature. Previous wotk was done, e.g. by Gebhard . He investigated the driving of a circular tunnel considering an elastoplatic material model. Eberhardsteiner et al [2,3] performed simulations of the driving of a tunnel junction, using a hybrid BE-FE technique and a Drucker-Prager material model.
In the presented paper an elasto-viscoplstic cap model is used for the modelling of soil. A multisurface rotating crack model, accounting for ageing effects is employed for the young shotcrete of the tunnel lining. Numerical effectiveness is achieved through formulation of both models in the framework of the return mapping algorithm and derivation of algorithmic tangent moduli.
In the following section, basic formulae for the cap model, the return mapping algorithm for updates of stresses and history variables and the linearization in the context of determination of the algorithmic elastoplastic tangent moduli will be described briefly. Moreover, the extension of the algorithm to elasto-viscoplastic will be discussed. The usefulness of the cap model will be demonstrated by means of tests on remoulded, saturated clay . Finally, an assessment of the material parameters for the cap model for the clayey slits of Vienna will be made.
The next section deals with the shotcrete model developed by Meschke . It is based on the plasticity theory for ageing materials. This theory is characterized by the development of inealstic strains solely because of the time-dependence of the modulus of elasticity which is increasub during the hydration process of the shotcrete. Thereafter, the fundamentals of the New Austrian Tunnelling Method (NATM) will be briefly discussed.
In the last section details of the analysis of an underground railway tunnel will be presented. The analysis results will be compared with results from field measurements.
 Gebhard, P.O.K., "Nichtlineares Materialverhalten bei der räumlichen Berechnung eines Tunnelvortriebs im Lockergestein", in Wunderlich et al., Berichte aus dem konstruktiven Ingenieurbau, Vol.2, Technische Universität München, Munich, 1991.
 Eberhardsteiner, J., Hofstetter, G., Kropik, C. and Mang, H.A., "Elasto-viscoplastic three-dimensional hybrid BE-FE stress analysis of the excavation of tunnels", in Manolis, G. and Davies, T. (Eds.), Boundary Element Techniques in Geomechanics, Computational Mechanics Publications, 1993, p.327-58.
 Eberhardsteiner, J., Kropik, C., Mang, H.A. and Meschke, M., "Material modelling and elasto-viscoplastic stress analysis of a tunnel junction", in Siriwardane, H.J. (Ed.), Computer Methods and Advances in Geomaterials (IACMAG), A.A. Balkema, Rotterdam, 1994.
 Topolnicky, M., "Observed stress-strain behaviour of remoulded saturated clay and examination of two constitutive models", Veröffentlichungen des Institutes für Bodenmechanik und Felsmechanik der Universität Fridericiana, Vol.107, 1987.
 Meschke, G., " A multisurface visco-plastic model for shotcrete. Algorithmic aspects and finite element analyses of tunnel linings." in Mang, H., Bicanic, N. and de Borst, R. (Eds.) Proceedings of the International Conference on Computational Modelling of Concrete Structures, Pineridge Press, Swansea, 1994, pp. 935-50.