Displacement control in tunnels excavated by the NATM: 3-D numerical simulations

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Abstract

The high cost of urban space has significantly increased the demand for tunnels in big urban centres. In such areas, settlements induced by the tunnel excavation may cause serious damage to nearby structures. Therefore, it is necessary to investigate effective means of controlling tunnel-induced settlements. In many countries, tunnels in soils and rocks are constructed using the New Austrian Tunnelling Method (NATM). This is mainly due to its flexibility to adapted to different ground conditions and use of simple equipments. Tunnel designs by NATM are generally based on empirical methods taking into account local experiences. The method is said to be observational and the construction process may be changed according to the observed response of the earth mass, acquired by means of proper instrumentation. Induced displacements are empirically controlled by adjusting the speed of excavation, distance between tunnel face and support, partial-face excavation and closure of invert. The relative importance of these techniques in the final displacements is analysed in this paper using 3-D numerical analyses with the Finite Element Method.

Introduction

The high cost of urban space has significantly increased the demand for tunnels in big urban centres. The stress disturbance caused by tunnel excavations induces movements in the earth mass and ultimately at the surface. Excavation-induced settlements may cause serious damages to nearby structures (Sozio, 1998; Mair, 1998). The need to control settlements is widely recognized and new construction methods are constantly developed.

The introduction of equipments using “shields” was very effective for settlement control. The shield provides temporary support for the area under excavation, thus reducing stress disturbance and settlements. Highly mechanized shields and “tunnel boring machines” (TBMs) have been devised and used with success in several parts of the world (Milligan, 1998; Kurihara, 1998; Herrenknecht, 1998; Kuwahara, 1999). Many of these machines try to balance the earth pressure in the excavation face, providing extra safety against face instabilization and also reducing settlements. Some machines, like “earth pressure balance” (EPB) shields, apply this pressure mechanically; others, such as “slurry shield machines”, apply face pressure hydraulically. Shields and TBMs, however, are generally purpose-made machines and only justify economically for relatively long tunnels. Some machines show low flexibility as to geometry shape and curvatures in the tunnel line. Although these problems can be solved with high technology and proper design (Ueda et al., 1998), these are not always available or are not affordable in many situations.

In many countries, tunnels in soils and rocks are constructed using the New Austrian Tunnelling Method (NATM). Despite some recent criticism (Kovari, 1994), this method presents a series of advantages and it is likely to continue being used for a long time in the future. NATM preference is credit mainly to its flexibility to adapt to different soil conditions and to the simplicity of equipments used for tunnelling.

NATM is not a rigid method, but rather a design philosophy based on three main principles. The first principle is that the soil or rock mass must be considered as an active part of the tunnel structure, capable of sustaining part of the load due to the excavation. Soil conditions may be improved by grouting, anchors and other techniques if necessary. Tunnel shape should be optimized in order to reduce stress concentration. Generally the excavation may be executed with partial-face, according to local experience in order to reduce the deformation level. The second NATM principle is related to the tunnel lining. It should be installed in an optimized way, such as to complement the mass support capacity and to control excessive deformation. Tunnel lining should work as a thin wall cylinder and present sufficient flexibility to allow a desirable degree of soil mass deformation and yet be strong enough to absorb shear stresses and moments. Shotcrete lining is very common for fitting well into these requirements (Palermo and Helene, 1998). It should also be emphasized that tunnel lining is only fully activated when the arc is closed. The third NATM principle is related to instrumentation. The basic design is based on local experiences, but the excavation method may be changed during construction, according to measurement data. The method is said to be observational.

Therefore, the main artifices for controlling settlements in NATM are: to improve soil conditions; to adopt partial-face excavation; to control the length of the unsupported longitudinal span and closure of the lining invert. Application of these techniques is based on empirical knowledge and local experience and may be adjusted according to observation. The use of numerical analyses with techniques such as the finite element method (FEM), could be of great value for this type of design. Numerical analyses work as a kind of model test in which many relevant design variables can be investigated in parametric studies. In this way it is possible to quantify the relative importance of each possible intervention in order to choose the most effective from the economic and safety point of view.

The use of numerical analyses to help tunnel design has already broken academic frontiers and is becoming more popular among practicing engineers. The constant evolution of processing capabilities of personal computers and the development of user friendly computer programs will surely made this an irreversible trend. Negro and Queiroz (2000) presented an interesting compilation of more than 65 papers they found in recent literature. They showed that by far the FEM is the most popular method, accounting for 96% of the published cases, and the remaining cases used the finite differences method (FDM) or others. Also they noted that 92% of the published analyses were still performed in two dimensions, under the hypothesis of plane strain conditions. Another relevant fact was that most analyses still used simple models, mostly elastic-perfectly plastic.

The fact that so many of the numerical analyses are still performed under 2-D plane strain approach is somewhat worrying. It is widely recognized that the tunnel excavation process induces a typically 3-D stress and strain field. A significant amount of disturbance is induced ahead of the excavation front. That produces pre-convergence and surface displacements before the passage of the excavation front. Panet and Guenot (1982) reported pre-convergence values of about 27% of the final displacement, using a 3-D simulation and an elastic model. Higher values, up to 50%, have been observed in field measurements and computational analyses in soft ground tunnelling (e.g., Moraes, 1999). Some tentative methods try to incorporate part of this 3-D effect into 2-D analyses (Panet and Guenot, 1982; Rowe and Lee, 1992; Parreira and Azevedo, 1994). A systematic comparison between 2-D and 3-D models, using FDM with programs Flac2D and Flac3D, was published by Oreste et al. (1999). It is shown that for correct evaluation of displacements and stresses around low overburden tunnels, it is necessary to use 3-D numerical models. This is even more important in cases where ground reinforcement techniques are used.

Three-dimensional finite element simulations, however, still represent a heavy computational effort for most available personal computers. Most of the computing time is demanded by the solver routines in FEM programs. Many programs that are well established for 2-D analyses use direct methods, such as Gauss elimination possibly with some type of profile storage like skyline. Solution time increases exponentially with the number of unknowns and a highly discretized non-linear simulation may demand time counted in days with presented personal computers. Therefore, it is important that developers concentrate more programming time in efficient iterative solvers, which become more effective than direct schemes for large systems (Mroueh and Shahrour, 1999). Besides, 3-D analyses demand proper pre and post-processing facilities, which are not available in most commercial codes.

Nevertheless the number of 3-D analyses published in literature is rapidly increasing. On the proceedings of the same conference where Negro and Queiroz (2000) presented their compilation on numerical analyses, one can find 13 papers about different aspects of 3-D simulations. This trend should rapidly increase as new and more efficient 3-D codes become available. Swannell and Hencher (1999) investigated some available software for 2-D and 3-D cavern design. The authors recognize the benefits of such tools, but advert to the danger of unskilful users without a proper understanding of the underlying principles of tunnel design.

A major project has been established in Austria with the objective of developing a framework for the application of computer based numerical simulation tools. The project integrates the main aspects of tunnel design, including data acquisition, material modelling, 3-D numerical modelling and visualization (Beer and Plank, 1999). Different 3-D numerical modelling techniques are being investigated, such as finite element (FEM), finite difference (FDM), boundary element (BEM) and distinct element (DEM) methods. Encouraging results were reported using coupled FEM/BEM technique.

Numerical simulation of tunnels excavated with shields and TBMs is somewhat easier to perform than NATM excavated tunnels. In the first case, known displacements are generally imposed to the excavation boundaries; whereas NATM requires the release of forces computed from ground stresses. Force application requires more robust implementation for non-linear problems. A few 3-D simulations of shield and TBM tunnels have been reported in recent literature (Akagi and Komiya, 1996; de Borst et al., 1996; Swoboda and Mansour, 1996; Swoboda and Abu-Krisha, 1999; Dias et al., 2000). Many relevant aspects of NATM tunnelling using 3-D numerical simulations have also been reported in recent papers.

Isolated aspects of 3-D numerical simulation of tunnels have been reported by many authors. The influence of the coefficient of earth pressure at rest (K0) in settlements induced by NATM and shield tunnelling was studied by Guedes de Melo and Santos Pereira (2000), using 2-D and 3-D FEM analyses with program ABAQUS. The effects of NATM excavation sequence on the settlement pattern of shallow tunnels have been studied in laboratory models and appropriately simulated with 3-D-FEM analyses using sophisticated constitutive models by Nakai et al. (1997) and Nakai et al. (2000).

Several ground treatment techniques to improve stability and/or reduce settlements of bored tunnels are described in literature. These include compensation grouting, jet grouting, permeation grouting, ground freezing, pre-lining and bolting (Shirlaw, 1996). The use of compensation grouting is rapidly increasing. It involves the injection of grouts, which, due to their nature, do not permeate the ground. The grout under pressure forms fractures (fracture grouting) or bulbs (compaction grouting), which induce displacement of the ground. By measuring ground movements and adjust the grouting, it is possible to greatly reduce the effects on adjacent structures and facilities. The efficiency of compensation grouting in settlement control was simulated numerically by Soga et al. (2000), using FLAC3D finite difference code.

Many authors have studied the influence of bolts and anchors on mass movements, as well as the influence of lining stiffness (e.g., Lauro and Assis, 1998). These models do not account for the construction stage of the lining and also disregard axial forces in the longitudinal direction. The 3-D effect on lining segments of TBM excavated tunnels is reported by van der Horst et al. (1999) using ANSYS program. Bakker et al. (2000) also show the evaluation of stresses in segment lining of the second Heinenoord tunnel in Holland using the same 3-D FEM package. Dasari et al. (1996) discussed the influence of shotcrete stiffness in the settlements induced by NATM excavations simulated with 3-D FEM using the program CRISP.

A tunnelling technique that is becoming popular in many countries is the so-called “Umbrella Method”. Long steel pipes are drilled around the tunnel periphery ahead of the tunnel face prior to the excavation. Grouting is applied through these tubes to improve the surround ground. The umbrella-shaped shell formed by this process not only stabilizes the tunnel crown and cutting face, but also reduces ground settlements. Shirakawa et al. (1999) describe a successful project in Japan using this method, which was simulated with 3-D FEM analyses. Yoo and Shin (2000) present parametric analyses of the influence of sub-horizontal pipes on the deformation behaviour of tunnel face using 3-D FEM simulations.

Numerical analyses with the finite element method are used in this paper to simulate the full 3-D stages that characterize an NATM tunnel excavation. Some relevant techniques for settlement control are investigated and their relative importance is state based on the numerical results. These include partial-face excavation, free span distance and support activation.

Section snippets

Numerical approximations

A series of 3-D simulations using the finite element method were performed in order to investigate the influence of the following aspects: (a) unsupported distance between the excavation face and the installation of support lining; (b) partial-face excavation; (c) closure of invert arc and full activation of support.

The finite element code used in these analyses is called ALLFINE, developed by Farias (1993). Several new aspects were introduced in the program to facilitate 3-D analyses of tunnel

Preliminary analyses

A given cross-section may be divided into smaller regions as in Fig. 2(a). The support lining is divided into lining heading or roof (CR), lining sides (CS) and lining invert (CI). The soil zone is divided in heading (SR), bench (SB), sides (SS) and invert (SI). The tunnel will be divided along the longitudinal direction in smaller segments (not in the sense of lining segment in shield tunnelling). In order to illustrate the 3-D excavation, all regions of a cross-section are schematically

Some possible NATM advance sequences

In this section a few analyses are performed to investigate the influence of how one advances the tunnelling process. Eight different excavation sequences were investigated with different sequences for support installation, face partition and invert closure. The cases are illustrated in Table 1.

Fig. 12 shows the maximum displacement evolution against face distance for the eight cases analysed in this section. As pointed out earlier, support installation and partial-face excavation affect the

Conclusions

A series of 3-D numerical analyses were performed using the finite element with a simple linear elastic model to simulate tunnel excavations using NATM. The following conclusions may be drawn.

A significant percentage of the final stabilized settlement is induced before face passage. This can only be adequately reproduced in 3-D analyses. Important aspects such as load transfer in the longitudinal direction due to soil arching cannot be represented in 2-D analyses. However, for a proper

Acknowledgements

The authors acknowledge the financial support of the Brazilian National Research Council (CNPq).

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