Analyses of Natm-Tunnels with 2-D And 3-D Finite Element Method
To model the NATM shotcrete method of tunnelling we apply both 2D and 3D discretisations. The more or less traditional 2D approach is computationally simple, but it requires certain assumptions about the so-called beta-factor to be made. Therefore we also
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C. Vogt Stuttgart University, Stuttgart, Germany P. Bonnier Plaxis BV, Rhoon, The Netherlands P .A. Vermeer Stuttgart University, Stuttgart, Germany
ABSTRACT: To model the NATM shotcrete method of tunnelling we apply both 2D and 3D discretisations. The more or less traditional 2D approach is computationally simple, but it requires certain assumptions about the so-called beta-factor to be made. Therefore we also perform 3D FEM analysis for comparison. Attention is focused on a tunnel in sedimentary clay rock. This rock is heavily overconsolidated and as a consequence it involves high horizontal stresses. The impact of high !{.,values on tunnel contraction and surface displacements is shown to be significant.
1. INTRODUCTION
In tunnel design the FEM is gaining in importance due to its ability to take into account the interactions between the tunnel lining and the surrounding subsoil. P~cularly for the analysis of shallow tunnels the FEM is becoming increasingly important as it also provides predictions of surface settlements. The stress and strain conditions arround an NATM-tunnel (New Austrian Tunnel Method) are influenced by the parameters of the subsoil and the method of excavation. When a tunnel is excavated in several sections (transverse and longitudinal) there are a large number of different states to be analysed. Every excavation state implies a change to the stresses and strains. The unsupported tunnel stretch causes the ground to arch over the excavated section supported by the lining behind it and by the surrounding ground (Fig. 1).
A. Cividini (ed.), Application of Numerical Methods to Geotechnical Problems © Springer-Verlag Wien 1998
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C. Vogt, P. Bonnier and P.A. Vermeer
Fig. 1: Stress distribution around face of the heading, Schikora (1988)
2. FEM CALCULATIONS AND B-METHOD The stresses and strains due to the excavation of a tunnel can only be modelled realistically by means of 3-dimensional calculations. However, for reasons of time and costs 2-dimensional analyses are usually conducted. All deformations which take place before the lining is introduced are taken into account either through a numerical method of stiffness reduction or a method of load reduction. The magnitude of this reduction must be estimated on the basis of experience or in situ measurements. An example using the B-method, i. e. a stress reduction method, is given below. The B-method consists of unloading by reducing the loads at the nodes along the edge of the tunnel. This means that in the analyses the soil inside the tunnel is first of all replaced by single node loads corresponding to the initial stresses. Then these tunnel support loads are gradually decreased down to a prescribed percentage (B) of the initial ones. In a second stage the tunnel lining is introduced and the remaining loads are taken by the lining. The stages involved in a multi-staged excavation are shown in Fig. 2. The value of the B-factor depends principally on the length of the unsupported section, the time schedule of excavation as well as on the
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