Keywords: fibre reinforced concrete, tunnel linings, high temperature, fire defence, numerical analysis, coupled problem.

This work is focused on the influence of extremely elevated temperatures on tunnel linings created from fibre reinforced concrete with selected fibres. In order to do this, extensive experiments have been carried out in the Czech Republic and in Austria at TU Innsbruck. Chemo mechanical results are obtained from Raman spectroscopy (in cooperation with VŠCHT at Prague).

The results from experiments delivered conclusions, which seem to be obvious from the qualitative point of view. Such experiments are found in published papers, but quantification of the results is mostly concentrated on partial problems and is very general. In our case an attempt for complex results was made and fully mirrored in the numerical analysis.

Before the numerical studies were performed, a formulation of the problem of combustion in tunnels and surrounding rock was proposed. As an extremely high temperature is contemplated, formulas for this sort of problem had to be prepared very attentively. A general continuous formulation is put forward and a weak formulation is suggested following the continuous formulation. A finite element model is prepared for numerical applications, where certain simplifications are introduced.

Selected results and comments are listed below:

• In most cases the influence of fire, in our case of the geometry of the lining, is restricted to the concrete.

• The deterioration of the face of the lining is very rapid, while inside the domain of the lining the loss of local bearing capacity is dependent on the quality of fibres: both steel and glass fibres support the stiffness, but due to the high temperature and the water (vapour) and air expansion, change of their density and other phenomena extreme stresses are attained, which cannot be sustained by the material; better material behaviour appears when using natural fibres, or basalt fibres, which are annealed and the space remaining around them is then filled by the vapour and the air. Immediately after applying the high temperature at the face of concrete specimens, extravasations of condensed water were observed.

• The numerical model proved to be very capable of describing the successive or sudden change of temperature. Uniquely, the larger extent of experiments must precede the numeric computation although very many parameters can be obtained from public sources, such as from the internet. This is the case of the dependence of water and air pressure on temperature, for example. Others, such as changes in material properties such as plastic behaviour, creep, and the like, have to be verified by experiments. In our study, changes in the material stiffness tensor are taken into account.

• The values of elastic modulus published in most literature approaches zero after much lower temperature than 12000°C (required by the standards). The experiments carried out on specimens from fibre reinforced concretes show much higher temperature resistance and more general formulas have been employed in the numerical analysis. Poisson's ratio is attaining its limiting value (here considered as 0.45) beyond 2000°C, approximately.

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