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Enhancing Numerically-Predicted ground movements patterns due to shield tunnelling in clays

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Abstract A numerical technique capable of adequately representing the states of stress release associated with shield tunnelling in clay is presented. Tunnel excavation is simulated using a deconfinement method characterised by differential unloading scheme in terms of tangential and radial components. The former is intended to simulate the effect of the machine driving through clays, whereas the later is intended to simulate the gap closure behind the shield tail. A test problem previously solved by Burghignoli et al. [1] is resolved here. The results obtained from the proposed procedure using the finite-element method were found in very good agreement with their measured counterparts, and superior to those obtained previously for the subsurface movements. Keywords: shield tunnelling , deconfinement method, tunnel excavation, gap closure, ground movement, finite-element analysis. 1 Problem Statement Predictions from the conventional numerical techniques for simulating shallow-tunnel excavation are normally found in poor agreement with the measured ground response . These techniques (e.g., the deconfinement method) usually predict ground settlement troughs that are relatively wider and flatter than those of the normal Gaussian distribution, proved to be in good agreement with the observed response. In the commonly-used deconfinement method (e.g., Panet and Guenot [2]; Bernat and Cambou [3]; Bernat et al. [4]; Abdel-Fattah [5]), the initial geostatic loads acting on the tunnel perimeter prior to excavation are progressively reduced till a predefined ground loss (a predefined settlement trough volume) takes place.

Paper 276 Enhancing Numerically-Predicted Ground Movement Patterns due to Shield Tunnelling in Clays T.T. Abdel-Fattah, A.Y. Akl, H.A. Hodhod and A.M. Abdel-Rahman Department of Soil Mechanics and Foundation Engineering Housing and Building Research Centre, Giza, Egypt Department of Civil Engineering Faculty of Engineering, Cairo University, Giza, Egypt

Civil-Comp Press, 2005. Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing, B.H.V. Topping (Editor), Civil-Comp Press, Stirling, Scotland.

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2 Numerical simulation of the excavation process

Simulation of the excavation process using the finite-element method may be carried out through removal of the soil elements that represent the soil mass excavated during a certain excavation stage. The equivalent nodal forces caused by the removal of these elements may be expressed as:

{ } [ ] [ ] [ ] { } [ ] { } [ ] { } { }Ewv

Tw

v

T

v

T

v

T fdvNdvPBdvNdvBf ++= (1) where { }f = equivalent nodal forces vector, [ ]B = strain-displacement transformation matrix, [ ] = effective stress matrix before excavation, { } = vector of effective body forces, { }wP = vector of pore pressure before excavation, { }w = vector of fluid weight forces, and { }Ef = vector of nodal forces equivalent to external loading (e.g., pressure).

The third and fourth terms in Equation (1) account for the effect of the presence of a ground water table during excavation. For excavation through water-bearing layers, the effect of the hydrostatic water pressure has to be incorporated in the calculations of the loads acting on the excavation perimeter. This is true regardless of the type of analysis (i.e., effective stress or total stress) performed. In some earlier research works (e.g., Esmail [6]; Mansur [7]; Bernt and Cambou [3]), the effect of the water pressure was neglected simply because the excavation loads were calculated from an effective stress analysis.

In the general-purpose finite-element codes with techniques for performing phased analyses (e.g., DIANA[8]), the excavation process can directly be simulated by specifying the elements that are active at the beginning of each analysis phase, and adopting a deconfinement ratio equivalent to the volume loss desired. But, the use of this procedure does not usually result in predictions for the ground movements that agree well with the field observations. Better predictions for the ground movements can be obtained if the excavation equivalent nodal forces are known in terms of either vertical and horizontal components, or radial and tangential ones. This allows for applying these force components with their desired ratios either simultaneously or independently on the excavation perimeter or even part of it. These force components have to be calculated using a special-purpose F.E. code since this is not featured in most general-purpose F.E. codes such as DIANA which

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is used here to conduct the F.E. analyses. Accordingly, a self-developed F.E. code namely DIATUN is used here as will be presented in the following section. It is proposed to incorporate the effect of excavation in the F.E. analysis using the radial and tangential components of the excavation equivalent nodal forces since this is more representative to the construction stages.

3 Proposed excavation technique (DIATUN)

In order to determine the equivalent nodal forces that develop around the excavation boundary due to a specific deconfinement scheme, a F.E. code namely, DIATUN [5] has been developed. This code is used concurrently with the programme DIANA as follows. First, the nodal numbering, joint coordinates and element topologies are inputted into DIATUN, such that the nodal connectivity and Gauss point numbering in both DIATUN and DIANA are consistent. Second, the DIANA outputs for the gauss point stresses, and pore pressures calculated during the phase that precedes the excavation one, are inputted into DIATUN. Integration of Equation (1) is performed using the Gauss-Legendre numerical integration scheme. Two sets of the equivalent nodal force components are then outputted by DIATUN. The first is due to effective stresses, whereas the second is due to pore water pressures. In this way, different deconfinement percentages can be assigned to these two sets if desired by the user. The outputs can optionally be obtained due to either the global coordinate system or the tunnel local cylindrical coordinate system. The use of the later coordinate system allows for applying different deconfinement percentages for both the radial and tangential directions, if required. The equivalent nodal forces determined by DIATUN are then inputted into the subsequent DIANA's excavation phase.

4 Available techniques for enhancing numerically-predicted settlement trough shape

A number of simplified procedures were introduced to obtain better numerical predictions for the ground response. Burghignoli et al. [1] suggested the use of two different reduction factors for both the vertical and horizontal components of the initial geostatic loads acting on the tunnel perimeter prior to excavation. Further, two sets of factors may independently be applied to both lower and upper tunnel halves. The results obtained using the finite-difference method using this procedure were found in very good agreement with their measured counterparts.

Bloodworth [9] proposed the introduction of an additional external restraint to the tunnel lining at either the spring line or invert, (Figure 1). This procedure, that involves volume loss modelling via shrinkage of the tunnel lining, aimed at improving the agreement between the finite-element results and the centrifuge observations, since the former predicted yielding and large displacements of a significant region of the soil beneath the tunnel. The results obtained from the F.E. analyses showed that both options of fixity may result in better estimations for the

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settlement trough. Yet, the trough resulting from imposing fixity at the invert was found to be a better approximation to the Gaussian model.

Brinkgreve and Broere [10] argued that the flatter settlement troughs obtained from the F.E. analyses are due to the underestimation of the soil stiffness in the small-strain region (region away from the tunnel). To validate this statement, the results obtained from a F.E. analysis were reproduced using soil stiffness five times higher than the original stiffness. This resulted in development of plasticity in a zone around the tunnel, and consequently reduced soil stiffness in that zone. In other words, the soil stiffness is lower around the tunnel and higher away from it. The results obtained using this procedure showed somewhat improved shape of the settlement trough.

Figure1: Options for external restraint to tunnel lining to improve settlement trough width predictions (Bloodworth [9])

5 Proposed Technique for enhancing numerically-predicted settlement trough shape

In most cases, the ground settlement trough obtained from a numerical analysis does not satisfactorily agree with the measured ground response. This is likely due to the use of techniques for simulating excavation that are not capable of sufficiently describing the unloading pattern associated with the excavation process. It is, therefore, attempted here to introduce a technique in which the unloading pattern adopted is adequately representative to the states of stress release caused by excavation, and this may result in better estimations for the ground response from F.E. analyses. Due to its relevance to the technique proposed here, the ground behaviour due to tangential unloading is briefly described below.

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5.1 Patterns of ground movements due to tangential unloading Bernat et al. [4] presented the results of pure shear unloading as part of the 2-D numerical analyses carried out for Lyons metro tunnel in France. They mentioned that th