Keywords: three-dimensional smoothed particle hydrodynamics, high temperature, mechanical properties.

A mechanical property of material combining both concrete and reinforcing fibers is a very important problem for engineers, particularly if a loading due to extreme temperature is applied to tunnel linings from fiber reinforced concrete (FRC) [1]. It is now commonly recognized that the actual behavior of concrete subjected to high temperature is a result of many factors, including both environmental factors and constituent materials. Among the mechanical factors, the heating rate and the peak temperature are the two main factors which have a significant influence on FRC. For given fibers (Dramix and straight steel fibers, and polypropylene), the mechanical properties are imported from experiments. As the mechanical and physical properties change nonlinearly, besides a set of experiments in furnaces also additional laboratory tests have been conducted to improve the characteristics of the material of tunnel lining and rock to improve the formulations and to prepare more accurate input data for programming codes. The above mentioned impacts of the change of temperature are investigated using a very powerful numerical tool, smooth particle hydrodynamics (SPH) [2]. This method belongs to a typical meshless method, which is well adjusted to extreme and sudden increase of loading (in our case it is a sudden change of temperature). After reformulating the problem into a form obeying boundary conditions being suitable for application of the SPH method, the three-dimensional problem can be solved. The restriction to two dimensions, having been solved before in a couple of papers by the authors, [3], for instance, is now removed and local peaks of temperature can be described in a much more accurate and realistic way. The fire is triggered in the upper quarter of the tunnel lining. The relaxation of tractions along the interface between the tunnel lining and the surrounding rock is accomplished (the tractions are equal to zero) as the load due to the fire is assumed to occur a long time after the completion of construction of the tunnel. The most extreme temperature of 600°C was considered as the experiments showed a failure of the FRC material exceeding the mentioned temperature. Simultaneous nonlinear equations are first briefly formulated, involving stress analysis, influence of pore pressure, change of temperature, moisture, and degree of saturation. Nonlinear mechanical properties are involved in the change of intrinsic parameters according to the results from experimental studies.

1

S. Peskova, P. Prochazka, "Impact of high temperature against structures of tunnel linings", CTU Reports, 12(1), 150, 2008.

2

R.A. Gingold, J.J. Monoghan, "Smoothed particle hydrodynamics theory and application to non-spherical stars", Monthly Notices of Royal Astronomical Society, 180, 375-389, 1977.

3

P.P. Prochazka, S. Peskova, "Application of Smooth Particle Hydrodynamics to solving Problems with Exacting Conditions", in B.H.V. Topping, L.F. Costa Neves, R.C. Barros, (Editors), "Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 96, 2009. doi:10.4203/ccp.91.96

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