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Computational Science, Engineering & Technology Series
ISSN 1759-3158
Edited by: B.H.V. Topping, Z. Bittnar
Chapter 3

Concrete Structures Subject to High Temperature

C.E. Majorana+, D. Gawin*, F. Pesavento+ and B.A. Schrefler+

+Department of Structural and Transportation Engineering, University of Padova, Italy
*Department of Building Physics and Building Materials, Technical University of Lodz, Poland

Full Bibliographic Reference for this chapter
C.E. Majorana, D. Gawin, F. Pesavento, B.A. Schrefler, "Concrete Structures Subject to High Temperature", in B.H.V. Topping, Z. Bittnar, (Editors), "Computational Structures Technology", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 3, pp 63-91, 2002. doi:10.4203/csets.7.3
Keywords: concrete, heat, mass, thermo-chemical damage, mechanical damage.

To analyse hygro-thermal and mechanical phenomena in porous media two different approaches are used: phenomenological and mechanistic ones. In phenomenological approach moisture and heat transport are described by diffusive type differential equations with temperature- and moisture content- dependent coefficients. Models of such a kind usually give very accurate predictions when applied to phenomena similar to those used to adjust model parameters and often very inaccurate for different situations. In other words, they are very accurate for interpolation and rather poor for extrapolation of the known experimental results. Another shortcoming of this approach is the very non-linear character of equation coefficients, which requires performing of numerous and time consuming experimental tests. Moreover, various physical phenomena are lumped together and model parameters often have not clear physical interpretation. In this approach there is not any distinction between different phases of water which are generally treated as a moisture, hence phase changes cannot be taken into account.

In mechanistic models, governing equations are usually more complicated formally, but their coefficients have clear physical meaning and often are related to classical material parameters. When some relations between structure parameters and transport properties are found, usually they are valid for a class of similar materials, e.g. cellular concrete, ceramic materials, etc. Often models of this group are obtained from microscopic balance equations written for particular constituents of the medium, which are then averaged in space, e.g. by means of Volume Averaging Technique, mixture theory or homogenisation theory. Mass and energy fluxes are usually expressed by means of gradients of thermodynamic potentials causing them, e.g. temperature, capillary pressure, water vapour concentration etc. Phase changes and related to them mass- and energy sources (sinks) are usually taken into account. Moreover, some additional couplings, e.g. effect of material damaging on intrinsic permeability or capillary and vapour pressures (moisture content) on skeleton stresses, can be considered.

Nowadays, most models of hygro-thermal phenomena in concrete at high temperature are based on a phenomenological approach [1,2]. In the framework of the Brite Euram III BRPR-CT95-0065 "HITECO" project, entitled "Understanding and industrial application of High Performance Concretes in High Temperature Environment" a new, mechanistic model of mass and energy transport in deforming concrete at high temperature has been developed.

Concrete is treated as a multiphase system with the voids of the skeleton filled partly with the liquid water (in three forms: capillary, physically adsorbed and chemically bound water) and partly with the gas phase (considered as an ideal gas).

Different physical mechanisms governing the liquid and gas transport in the pores of partially saturated concrete are clearly distinguished, i.e. capillary water and gas flows driven by their pressure gradients, adsorbed water surface diffusion caused by saturation gradients, as well as air and vapour diffusion driven by vapour density gradients [3].

Thermally induced deterioration due to strains at material meso-scale and due to concrete dehydration, called thermo-chemical damage (and a modification of stress- strain curve) is here introduced in a framework of the isotropic non-local damage theory.

Recently, the application range of the model has been extended to temperatures above the critical point of water for evaluating the behaviour of concrete structures subjected to very elevated temperatures, in the interval 400$ ^o$C-1200$ ^o$C, [4]. These values can be reached during fire in tunnels with catastrophic consequences in terms of human begins and economical costs. An example concerning a C60 column subjected to ISO-Fire standard conditions is shown.

Z.P. Bazant, W. Thonguthai, "Pore pressure and drying of concrete at high temperature", J. Engng. Mech. Div. ASCE, 104, 1059-1079, 1978.
Z.P. Bazant, W. Thonguthai, "Pore pressure in heated concrete walls: theoretical prediction", Mag. Concr. Res., 31(107), 67-76, 1979.
D. Gawin, C.E. Majorana, B.A. Schrefler, "Numerical analysis of hygro-thermal behaviour and damage of concrete at high temperature", Mech. Cohes.-Frict. Mater., 4, 37-74, 1999. doi:10.1002/(SICI)1099-1484(199901)4:1<37::AID-CFM58>3.0.CO;2-S
D. Gawin, F. Pesavento, B.A. Schrefler, "Modelling of Hygro-Thermal Behaviour And Damage of Concrete at Temperature Above the Critical Point of Water", Int. J. Numer. Anal. Meth. Geomech. 26, 537-562, 2002. doi:10.1002/nag.211.abs

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