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Computational Science, Engineering & Technology Series
ISSN 1759-3158
Edited by: B.H.V. Topping
Chapter 14

Stress-Strain Experimental Based Modelling of Concrete under High Temperature Conditions

V.A. Salomoni1, C.E. Majorana1 and G.A. Khoury2

1Department of Construction and Transportation Engineering, Faculty of Engineering, University of Padua, Italy
2Department of Civil and Environmental Engineering, Imperial College, London, United Kingdom

Full Bibliographic Reference for this chapter
V.A. Salomoni, C.E. Majorana, G.A. Khoury, "Stress-Strain Experimental Based Modelling of Concrete under High Temperature Conditions", in B.H.V. Topping, (Editor), "Civil Engineering Computations: Tools and Techniques", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 14, pp 319-345, 2007. doi:10.4203/csets.16.14
Keywords: concrete, high temperature, LITS, coupling, chemo-thermo-hydro-mechanical modelling.

This paper takes the experimental strain behaviour of three nuclear reactor type plain concretes exposed under load (0 and 20%) in the unsealed condition to a 14-day two-thermal cycle test to a temperature ranging from 110 to 600o [1] as the basis for the fully coupled 3D finite element NEWCON code [2, 3].

The works [1-3] highlighted the nature of strain behaviour during virgin heating, which was fundamentally different from that during the subsequent three thermal cycles owing to the development of the load induced thermal strain (LITS) in concrete heated under load. Shrinkage arising from moisture loss or chemical dissociations was another strain that was more predominant during first heating. Significant "delayed" LITS and shrinkage strain components were evident during the early few hours at constant temperature following the first thermal transient, which then slowly dissipated during the few days period at constant temperature. The last three thermal transients were characterised by the absence of LITS and by the development of expansive crack-inducing and chemical rehydration forces. These were more evident in concretes tested without load. It is from these results that the concept of "concrete specific critical temperature" emerged. Up to a critical temperature, a second thermal cycle would not cause significant additional damage. At higher temperatures, the effect of thermal cycling, particularly for unloaded concrete, would be to cause marked progressive cracking.

Hence, the above data and information are employed in a predictive finite element structural modelling for both nuclear reactor and fire applications, making use of the NEWCON code, representing an updated version of DAMVIS, VISCO and DAMAGE codes [2, 4].

Concrete is treated as a multiphase system where the voids of the skeleton are partly filled with liquid and partly with a gas phase [5]. The liquid phase consists of bound water (or adsorbed water), which is present in the whole range of water contents of the medium, and capillary water (or free water), which appears when water content exceeds so-called solid saturation point Sssp [6], i.e. the upper limit of the hygroscopic region of moisture content. The gas phase, i.e. moist air, is a mixture of dry air (non-condensable constituent) and water vapor (condensable gas), and is assumed to behave as an ideal gas.

The approach here is to start from a phenomenological model [2, 4, 7, 8], originally developed by Bazant et al. [9-11], in which mass diffusion and heat convection-conduction equations are written in terms of relative humidity, to an upgraded version in which its non-linear diffusive nature is maintained as well as the substitution of the linear momentum balance equations of the fluids with a constitutive equation for fluxes, but new calculations of thermodynamic properties for humid gases are implemented too, to take into account different phases as well as high ranges of both pressure and temperature; to enhance the model's predictive capabilities, a predictor-corrector procedure is supplemented to check the exactness of the solution.

As regards the mechanical field, NEWCON couples shrinkage, creep, chemo-thermo-mechanical damage and plasticity effects under medium and high temperature levels.

G.A. Khoury, "Strain of heated concrete during two thermal cycles. Part 3: isolation of strain components and strain model development", Mag.Concrete Res., 58(7), 421-435, 2006. doi:10.1680/macr.2006.58.7.421
C.E. Majorana, V. Salomoni, B.A. Schrefler, "Hygrothermal and mechanical model of concrete at high temperature", Mat. Struct., 31(210), 378-386, 1998. doi:10.1007/BF02480710
G.A. Khoury, C.E. Majorana, F. Pesavento, B.A. Schrefler, "Modeling of heated concrete", Mag. Concrete Res., 54(2), 77-101, 2002. doi:10.1680/macr.
C.E. Majorana, V.A. Salomoni, "Parametric analyses of diffusion of activated sources in disposal forms", J. Haz. Materials, A113, 45-56, 2004. doi:10.1016/j.jhazmat.2004.06.008
P. Baggio, C.E. Majorana, B.A. Schrefler, "Thermo-hygro-mechanical analysis of concrete", Int. J. Num. Methods in Fluids, 20, 573-595, 1995. doi:10.1002/fld.1650200611
F. Couture, W. Jomaa, J.R. Ruiggali, "Relative permeability relations: a key factor for a drying model", Transp. Por. Media, 23, 303-335, 1996. doi:10.1007/BF00167101
B.A. Schrefler, L. Simoni, C.E. Majorana, "A general model for the mechanics of saturated-unsaturated porous materials", Mat. Struct., 22, 323-334, 1989. doi:10.1007/BF02472501
C.E. Majorana, V. Salomoni, S. Secchi, "Effects of mass growing on mechanical and hygrothermic response of three-dimensional bodies", J. Mat. Proc. Tech., PROO64/1-3, 277-286, 1997. doi:10.1016/S0924-0136(96)02577-0
Z.P. Bazant, "Pore pressure, uplift, and failure analysis of concrete dams", Int. Commission on Large Dams, Swansea, UK, 1975.
Z.P. Bazant, W. Thonguthai, "Pore pressure and drying of concrete at high temperature", J. Eng. Mat. Div., ASME, 104, 1058-1080, 1978.
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