Tunnel Analysis for the North Downs Channel Tunnel Rail Link

Abstract

The Channel Tunnel Rail Link (CTRL) is the most significant railway infrastructure project to be constructed in the United Kingdom since the construction of the Channel Tunnel over a decade ago. The CTRL has been constructed using the New Austrian Tunelling Method (NATM). The NATM has been successfully used in Metro tunnel construction for over 30 years. This article summarises the application of DIANA’s phased analysis capabilities to model the staged nature of the NATM excavation process. Thus the removal and addition of elements and the variation of their material properties during the analysis have been considered.

Figure 1: Location of the North Downs Tunnel

Introduction

A cross section of the tunnel configuration is shown in Figure 2. The method of tunnel construction uses the principles of the NATM, which is known to be effective for tunnelling in rock mass. In this type of construction, initial support to the tunnel is provided by a conventional shotcrete primary lining that is locally reinforced by a combination of mesh and lattice arch girders and rock bolts.

Figure 2: Tunnel Cross Section

The excavation is performed in three stages: starting with the top crown heading followed by the bench and then the invert as illustrated in Figure 3.

Figure 3: Typical construction sequence

Geology

The geology along the tunnel is shown in Figure 4. The tunnel will encounter the Lewes (750m), New Pit (1400m) and Holywell Chalks (1043m). In total, ten representative cross-sections along the length of the tunnel have been analysed using DIANA.

Figure 4: Geology along the tunnel alignment

The constitutive behaviour of the ground has been modelled using the modified Mohr-Coulomb model. The coefficient of horizontal earth pressure K0 has been based on the results of pressuremeter testing and the back analysis of case history data from other tunnels in chalk. A parametric study of K0 between 0.5 and 1.0 has been undertaken which led to a value of 0.8 being considered in the final analyses. This coefficient influences overall behaviour and is only used in the first (stress initialisation) phase. In general, the degree of arching effect is proportional to the magnitude of K0.

Stress Relief

In this analysis, a 2-dimensional plane strain model has been used to describe what is essentially a 3-dimensional problem. The 3-dimensional aspect concerns the approaching tunnel, which has a tendency to cause the ground in front of it to soften. This has the beneficial effect of reducing the loads generated in the lining since the tunnel front, although softened, can still offer some supporting capacity and this can therefore remove some undue conservatism in the lining design. The key to 2-dimensional analysis of tunnel excavation is to apply the correct amount of stress relief so that the stresses around the excavation accurately capture these 3-dimensional effects.

One method of simulating stress relief is by reducing the equilibrating load on the free surface. In DIANA this is achieved by executing START steps. If the load increments total 1.0 then 100% of the equilibrating load on the free surface will be removed. If the load increments total 0.4 then 40% of the equilibrating load will be removed and the free surface will be supported by 60% of the equilibrating load. This method has been described in the article for the Korean subway analysis (DIANA World 1995, Issue No. 2). Miller Civil Engineering have adopted an alternative approach in that 100% removal of the equilibrating load is undertaken and the supporting capacity offered by the softened tunnel front is represented by new tunnel elements which have been given a reduced stiffness (Swoboda, 1979). The stress redistribution that occurs in and around these reduced stiffness elements during the START steps simulates the 3-dimensional stress relieving effects of the approaching tunnel front.

Figure 5: Contours of resultant total displacement after stress relief

Tunnel Lining

In this analysis, the objective was to determine the required thickness of primary lining to ensure stability of the tunnel. In the NATM, concrete is sprayed onto the free surface to form the concrete lining. During its ageing and hydration, the material properties of the concrete change. The real behaviour of sprayed concrete lining is complex and much research has been undertaken in recent years into the question of appropriate material models to apply. From this research it has been widely accepted that young concrete is capable of tolerating higher levels of deformation than those which a fully mature lining could sustain. Accordingly, the concept of a reduced theoretical modulus for young concrete has been developed (Zachow, Alkhiami). This route has been followed for this analysis in which both young and mature concrete properties have been specified.

A linear-elastic-perfectly-plastic von-Mises model with the properties as summarised in Table 1 have been used and the transition from young to mature concrete properties has been modelled in a static manner by way of a phased analysis. This method has proved sufficient for the purposes of this investigation but an alternative albeit a more complex method is also available in DIANA. This would involve the simulation of the ageing process of the young concrete by using creep models that are made a function of ambient influences such as maturity, temperature and concentration.

Table 1: Concrete stiffness and strength properties

Concrete cracking has also been modelled using a multi-directional fixed crack model with a constant no-tension cut-off, brittle cracking and full shear retention.

Modelling

The finite element mesh has been created in FEMGEN and is two-dimensional and symmetric about the left-hand boundary as shown in Figure 6. To minimise edge effects the mesh has been sufficiently extended in the horizontal and vertical directions. The model has been restrained against horizontal movement along the left and right boundaries and the base has been fully restrained.

Figure 6: Mesh used for CTRL tunnel analysis

The mesh consists of quadratic plane strain elements and quadrilateral rather than triangular elements have primarily been used. A higher mesh density has been specified in the region of the tunnel to minimise the discretisation error in this area. In certain phases of the analysis (Table 2) the stiffness of the crown and bench has been reduced to model stress relief. For this purpose, duplicate elements have been defined in FEMGEN and assigned a separate group name so that these elements may be called up at the relevant phases with ease. The tunnel lining has been discretised by quadratic beam elements so that the curvature of the lining could be captured so as to improve the accuracy of the computed axial forces and bending moments generated in the lining. Sufficiently stiff beams have been incorporated at the base of the crown and bench lining to spread the load into the soil and to circumvent numerical problems associated with point load contact. After creation of all elements, the model has been fully merged to ensure that continuity is satisfied between all mesh components.

Table 2: Description of the phases considered for the tunnel analysis

Assessment of Results

The design of the primary lining has been based on BS8110, Part 1. Capacity charts for the concrete sections have been developed by assuming that the tunnel linings act as an unreinforced short column subjected to bending and direct forces. A typical capacity chart for a concrete lining is shown in Figure 7.

Figure 7. Typical capacity chart

The concrete lining as modelled in the finite element analysis is deemed acceptable if the bending moments and corresponding axial forces generated in the lining are found to be situated within the envelope of Figure 6.

Figures 8 and 9 show the deformed shape of the tunnel at the end of the analysis and the corresponding regions of plasticity developed in the ground around the tunnel.

Figure 8: Final deformed shape of tunnel (magnification factor 100)

Figure 9: Plastic region around the tunnel

Literature

• R. Zachow: “Dimensionierung zweischaliger Tunnel im Fels auf der Grundlage von in-situ-Messungen”, Forschungsergebnisse aus dem Tunnel-und Kavernenbau Universität Hannover, Ed. Prof. R.B.Rokahr.
• Hassan Alkhiami: “Ein Näherungsverfahren zur Abschätzung der Belastung einer Spritzbetonkalotte auf der Grundlage von in-situ-Messunge”, Forschungsergebnisse aus dem Tunnel-und Kavernenbau Universität Hannover, Ed. Prof. R.B.Rokahr.
• Swoboda, G. (1979). Finite element analysis of the New Austrian Tunneling Method (NATM). Proc. 3rd Int. Conf. on Num. Methods in Geomechanics, Aachen, vol 2, pp 581-586.

January 2000