The paper is concerned with the numerical simulation of tunnel advance using the Finite Element and Boundary Element methods. On practical examples the advantages and disadvantages of each method and their applicability to certain classes of tunnelling problems will be shown.
Le rapport contend la simulation numerique du progression du tunnel a I'aide de la methode des elements finis et de la methode des elements limites. Au moyen des examples pratiques on mont les avantages ales desavantages chacune methode aussie bien que I'utilite pratique en fonctions differents. ZUSAMMENFASSUNG: Der Bericht befasst sich mit der numerischen Simulation des Tunnelvortriebs mit Hilfe der Methode der Finiten Elemente und der Methode der Randelemente. An Hand von praktischen Beispielen werden die Vor- und Nachteile jeder Methode sowie die Anwendbarkeit auf unterschiedliche Aufgabenstellungen im Tunnelbau gezeigt.
Despite significant advances made in numerical simulation methods the accuracy of the results, as far as deformations and stresses are concerned, is not comparable to that achieved for example, in structural engineering. This is mainly due to the fact that the material the tunnel is built in, namely rock or soil, is extremely heterogeneous and has a large variation in its mechanical properties. Futhermore the rock mass is transected by Joints and faults and, in some cases, discontinuous behaviour may play an important role. In contrast to problems in structural engineering where loadings are specified, in tunnelling we usually have very little knowledge of the stress field in the rock/soil prior to excavation. Last but not least, tunnelling involves a complex sequence of excavation and construction with new materials (shotcrete, rock bolts) being introduced at various stages. For these reasons numerical simulation plays a different role in tunnelling and, in many cases, we do not require specific values of stresses or displacements but may be interested instead if zones in the rock mass are potentially unstable, or in major trends (i.e. areas of high stress vs. low stress) rather than in exact numerical values. Furthermore, because of the difficulty in determining virgin stresses and geological features ahead of the tunnel face numerical simulation methods themselves, in conjunction with field measurements, may be used to obtain the information, as will be shown. In the following we will briefly review the state of practical applications of numerical simulation in tunnelling. Next we will examine the use of two of the main methods of simulation, namely, the Finite Element Method (F.E.M.) and the Boundary Element Method (B.E.M.).
Most numerical simulations carried out to date have been 2-D analysis using the F.E.M. At present, 3-D models cannot be considered as a standard tool for practical tunnel design because of the expenditure with respect to manpower and computer resources involved. To a large extent their practical application is restricted to investigate specific details, as for example, stresses in the shotcrete lining of tunnel intersections. However tunnelling is definitely a 3-D problem and restricting oneself to two dimensions may lead to significant deviations when compared to actual field behaviour. Plane strain models, for example, are only able to predict displacements and stresses some distance from the tunnel face and cannot account for stress redistribution and displacement ahead and in the vicinity of the face. This, however is very important for tunnels constructed with the New Austrian Tunnelling Method (NATM) which uses complex excavation sequences and support measures like shotcrete and rock bolts. Furthermore, if major inhomogeneities and faults are present then simplified 2-D analyses may lead to results which are in significant error.