Keywords: excavation, finite element method, convergence measurements, convergence confinement method, tunnel, stochastic analysis.

This paper presents a modification to the conventional finite element method in plane strain conditions to address the problem of successive excavation of linear parts of tunnels. Although the successive excavation is a three-dimensional mechanical problem, the designers often prefer two-dimensional analysis owing to the considerably simple and transparent geometric model and fast computations as compared to the three-dimensional solution.

Currently, the convergence confinement method [1] is a common approach allowing us to take into account the longitudinal effects of a two-dimensional finite element scheme. Although this method describes a series of phenomena associated with a progressive excavation, its accuracy fundamentally depends on the value of the parameter lambda typically chosen by the user on the basis of empirical formulas and personal experience.

It is therefore of considerable interest to objectify the two-dimensional approximation whilst keeping its simplicity. Such a goal can be successfully achieved by combining the numerical analysis with in-situ measurements [2]. Particularly, by taking advantage of the convergence curves in the longitudinal direction obtained during excavation, both in front of and behind the tunnel heading, it is possible to extend the general formulation into three dimensions whilst maintaining the two dimensional format of the finite element mesh [3].

The main idea behind the suggested method is to express the influence of excavation of a single segment of soil not only in the particular cross-section but in the entire soil body in front of and behind the profile examined. This is achieved by introducing special finite elements which have a common triangular section but are of infinite length in the longitudinal direction. The longitudinal approximations of the displacement field adopt the evolution of the convergence measurements, while standard linear shape functions are kept in the element triangular cross section.

A profile corresponding to the city road tunnel Blanka in Prague and the corresponding convergence measurement was examined to verify the method. The results show that the method provides reasonably accurate results when compared to convergence confinement method without the need to subjectively determine the lambda parameter. It also significantly reduces the computational time of more accurate but complex three-dimensional analysis thus allowing for the use in stochastic analysis [4].

1

M. Panet, A. Guenot, "Analysis of convergence behind the face of a tunnel", Proc. Tunnelling, 82, London, 197-204, 1982. doi:10.1016/0148-9062(83)91744-8

2

J. Barták, J. Machácek and J. Pacovský, "Observation measuring of the earth covered traffic tunnel structure in the quarry Hvízdalka", Tunel, 1, 6-9, 1998.

3

T. Janda, J. Šejnoha, M. Šejnoha, "Improved modeling of tunel excavation with two-dimensional finite elements", Proc. Recent Developments in Structural Engineering, Mechanics and Computations, Millpress, Rotterdam, 2007.

4

J. Šejnoha, E. Novotná, O. Špacková, D. Jarušková, "Pragmatic probabilistic models for quantification of tunnel excavation risk", submitted to Acta Geodyn. Geomater, 2011.

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