Abstract
A constitutive model for the analysis of deformations of concrete subject to transient temperature and pressures is proposed. In these severe conditions concrete structures experience spalling phenomenon, which is the violent or non-violent breaking off of layers or pieces of concrete from the surface of a structural element when it is exposed to high and rapidly rising temperatures. This process can lead to a loss of load-bearing capacity, trough a loss of section and a loss of protection to steel reinforcement. Many different form of spalling exist, but probably the most dangerous is explosive spalling, because it is sudden and capable to result in a general collapse of the structure.
The constitutive model includes thermo-chemical and mechanical damage for taking into account the deterioration of the material due to mechanical loads, high temperatures and chemical changes and it is introduced into a general coupled mathematical model of hygro-thermo-chemomechanical behaviour of concrete structures.
In this constitutive model the so called free thermal strains, which are the concrete strains during first heating, are decomposed in three main contributions: thermal dilatation strains (treated in a manner usual in thermomechanics), shrinkage strains (modelled by means of the effective stress principle) and thermo-chemical strains (which take into account for the thermo-chemical decomposition of the concrete and which are related to thermo-chemical damage). Thermo-mechanical strains occurring during first heating of concrete under load, known as LITS (Load Induced Thermal Strains), are also included in the framework of thermodynamics of porous media. The proposed model is applied to an illustrative example that demonstrates its capabilities.
Résumé
Nous proposons un modèle pour l'étude des déformations du béton sous variations de température et pression. Dans ces conditions extrêmes, le béton subit l'écaillage qui est une rupture violente ou non de couches ou pièces de béton sur la surface d'éléments structurels soumis à haute température ou température augmentant rapidement. Ce fait peut produire une diminution de la capacité portante à travers une diminution de la section ou la perte de protection du maillage. Il y a différentes formes d'écaillage mais le plus dangereux est probablement l'écaillage explosif car il est sans préavis et entraîne l'écroulement de la structure.
Le modèle constitutif inclut l'endommagement thermochimique et mécanique pour prendre en compte la détérioration du matériau due aux charges mécaniques, aux hautes températures et aux chargements chimiques.
Tout ceci est introduit dans un modèle mathématique couplé pour la description du comportement hygrothermochimique et mécanique des structures en béton. Dans ce modèle constitutif, les déformations thermiques libres, c'est à dire les déformations dans le béton pendant le premier échauffement sont décomposés en trois parties: déformations dues à la dilatation thermique (traitées selon la manière habituelle de la thermomécanique), déformations dues au séchage (modèles à l'aide des contraintes effectives) et déformations thermochimiques (qui prennent en compte la décomposition thermochimique du béton et qui sont liées à l'endommagement thermochimique). Les déformations thermomécaniques qui ont lieu pendant le premier échauffement du béton sous charge, généralement connues sous le nom de LITS (Load Induced Thermal Strain) sont aussi inclues dans le cadre de la thermodynamique des milieux poreux. Le modèle proposé est appliqué à un exemple pour démontrer ses capacités.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bažant, Z.P. and Thonguthain, W., ‘Pore pressure and drying of concrete at high temperature’,J. Engng. Mech. ASCE 104 (1978) 1059–1079.
England, G.L. and Khoylou, N., ‘Moisture flow in concrete under steady state non-uniform temperature states: experimental observations and theoretical modelling’,Nucl. Eng. Des. 156 (1995) 83–107.
Bažant, Z.P. and Kaplan, M.F., ‘Concrete at High Temperatures: Material Properties and Mathematical Models’, (Longman, Harlow, 1996).
Phan, L.T., ‘Fire performance of high-strength concrete: a report of the state-of-the-art’, Res. Report NISTIR 5934, pp. 105. National Institute of Standards and Technology, Gaithersburg, 1996.
Phan, L.T., Carino, N.J., Duthinh, D. and Garboczi, E. (eds.), Proc. Int. Workshop on Fire Performance of High-Strength Concrete, Gaithersburg (MD), USA, February 13–14, 1997. NIST Special Publication 919, NIST, 1997.
Brite Euram III BRPR-CT95-0065 HITECO, Understanding and industrial application of High Performance Concrete in High Temperature Environment—Final Report, 1999.
Ulm, F.-J., Acker, P. and Levy, M., ‘The “Chunnel” fire. II. Analysis of concrete damage’,J. Eng. Mech. ASCE 125(3) (1999) 283–289.
Ulm, F.-J., Coussy, O. and Bažant, Z., ‘The “Chunnel” fire. I. Chemoplastic softening in rapidly heated concrete’,J. Eng. Mech., ASCE 125(3) (1999) 272–282.
Gawin, D., Majorana, C.E. and Schrefler, B.A., ‘Numerical analysis of hygro-thermic behaviour and damage of concrete at high temperature’,Mech. Cohes.-Frict. Mater. 4 (1999) 37–74.
Bentz, D.P., ‘Fibers, percolation, and spalling of highperformance concrete’,ACI Materials Journal 97(3) (2000) 351–359.
Nechnech, W., Reynouard, J.M. and Meftah, F., ‘On modelling of thermo-mechanical concrete for the finite element analysis of structures submitted to elevated temperatures’, in: Proc. Facture Mechanics of Concrete Structures, R. de Borst, J. Mazars, G. Pijaudier-Cabot, J.G.W. van Miers, Eds Swets & Zeiltinger, Lisse 2001) 271–278.
Phan, L.T., Lawson, J.R. and Davis, F.L., ‘Effects of elevated temperature exposure on heating characteristics, spalling, and residual properties of high performance concrete’,Mater. Struct. 34 (March 2001) 83–91.
Sullivan, P.J.E., ‘Deterioration and spalling of high strength concrete under fire’, Offshore Technology eport 2001/074, HSE Books, Sudbury, 2001, pp. 77.
Gawin, D., Pesavento, F. and Schrefler, B.A., ‘Simulation of damage—Permeability coupling in hygro-thermo-mechanical analysis of concrete at high temperature’,Commun. Mumer. Meth. Engrg. 18 (2002) 113–119.
Gawin, D., Pesavento, F. and Schrefler, B.A., ‘Modelling of hygro-thermal behaviour and damage of concrete at temperature above the critical point of water’,Int. J. Numer. anal. Meth. Geomech. 26 (2002) 537–562.
Phan, L.T. and Carino, N.J., ‘Eflects of test conditions and mixture proportions on behavior of high-stength concrete exposed to high temoperature’,ACI Materials Journal 99(1) (2002) 54–66.
Gawin, D., Pesavento, F. and Schrefler, B.A., ‘Modelling of hygro-thermal behaviour of concrete at high temperature with thermo-chemical and mechanical material degradation’,Comput Methods Appl. Mech. Engrg. 192 (2003) 1731–1771.
Khoury, G.A., ‘Strain components of nuclear-reactor-type concretes during first heating cycle’,Nuclear Engineering and Design 156 (1995) 313–321.
Baroghel-Bouny, V., Mainguy, M., Lassabatère, T. and Coussy O., ‘Characterization and identification of equilibrium and transfer moisture properties for ordinary and highperformance cementitious materials’,Cem. Concr. Res. 29 (1999) 1225–1238.
Schrefler, B.A. and Gawin, D., ‘The effective stress principle: incremental of finite form’?,Int J. Numer. Anal. Meth. Geomech. 20 (1996) 785–815.
Gray, W.G. and Schrefler, B.A., ‘Thermodynamic approach to effective stress in partially saturated porous media.”Eur. J. Mech. A/Solids 20 (2001) 521–538.
Mazars, J., ‘Application de la mécanique de l'endommagement au comportement non linéire et la rupture du béton de structure’, Thèse de Doctorat d'État, L.M.T., Universit'e de Paris, Fance, 1984.
Mazars, J., ‘Description of the behaviour of composite concretes under complex loadings through continuum damage mechanics’, Proc. Tenth U.S. National Congress of Applied Mechanics, J.P. Lamb (ed.), ASME, 1989.
Pijaudier-Cabot, G., ‘Non local damage’, in H.B. Mühaus (ed.), ‘Continuum Models for Materials with Microstructure’, chapter 2 (Wiley & Sons, Chichester, 1995) 105–143.
Kachanov, M.D., ‘Time of rupture process under creep conditions”,Izvestia akademii nauk 8 (1958) 26–31 (in Russian).
Hssanizadeh, S.M. and Gray, W.G., ’General conservation equations for multi-phase systems: 1. Averaging procedure’,Adv. Water Resources 2 (1979) 131–144.
Hassanizadeh, S.M. and Gray, W.G., ‘General conservation equations for multi-phase systems: 2. Mass, Momenta, energy and entropy equations’,Adv. Water Resources 2 (1979) 191–203.
Hassnizaded, S.M. and Gray, W.G., ‘General conservation equations for multi-phase systems: 3. Constitutive theory for porous media flow’,Adv. Water Resources 3 (1980) 25–40.
Lewis, R.W. and Schrefler, B.A., ‘The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media’ (Wiley & Sons, Chichester, 1998).
Schrefler, B.A., ‘Mechanics and thermodynamics of saturated-unsaturated porous materials and quantitative solutions’,Applied Mechanics Review 55(4) (2002) 351–388.
Gawin, D., ‘Modelling of Coupled Hygro-Thermal Phenomena in Buidling Materials and Building Components’, Pub. of Ŀódź Technical University No. 853, Editions of Ŀódź Technical University, Ŀódź, 2000Polish).
Pesavento, F., Non-linear modelling of concrete as multiphase porous material in high temperature conditions, Ph.D. thesis, University of Padova, Padova, 2000.
Zienkiewicz, O.C. and Taylor R.L., ‘The Finite element Method, vol. 1: The Basis’ (Butterworth-Heinemann, Oxford, 2000).
Koury, G.A., Grainger, B.N. and Sullivan, P.J.E., ‘Transient thermal strain of concete: literature review, conditions within specimens and behaviour of individual consituents’,Mag. concrete Research 37 (132) (1985) 131–144.
Thelandersson, S., ‘Modeling of combined thermal and mechanical action on concrete’,J. Engng Mech. ASCE 113(6) (1987) 893–906.
Pearce, C.J., Davie, C.T., Nielsen, C.V. and Bićanić, N., ‘A transient creep model for the hygral-thermal-mechanical analysis of concrete’, Onate E. & Owen D.R.J. (eds) Proc. Int. Conf. on Computational Plasticity COMPLAS VII (on CD), 1–19, CIMNE, Barcelona, 2003.
Consolazio G.R., Mc Vay M.C. and Rish. J.W., ‘Measurement and prediction of pore pressure in cement mortar subjected to elevated temperature’, NIST SP 919, Proc. Int. Workshop on Fire Performance of High Strength Concrete, Phan L.T., Carino N.L., Duthin D. and Garboczi E. (eds), NIST, Gaithersburg, MD, February 13–14, 1997, 125–148.
Chaboche, J.L., ‘Continuum damage mechanics: Part I—General concepts’,J. Applied Mech,55 (1988) 59–64.
Bourgeois, F., Furlion, N. and Shao, J.F., ‘Modelling of elstoplastic damage due to desiccation shirinkage’,Int. J. Numer. Anal. Meth. Geomech. 26 (2002) 759–774
Coussy, O., ‘Mechanics of Porous Continua’ (Wiley, Chichester, 1995)
Author information
Authors and Affiliations
Additional information
Editorial Note Prof. Bernhard SCHREFLER is a RILEM Senior Member.
Rights and permissions
About this article
Cite this article
Gawin, D., Pesavento, F. & Schrefler, B.A. Modelling of deformations of high strength concrete at elevated temperatures. Mat. Struct. 37, 218–236 (2004). https://doi.org/10.1007/BF02480631
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02480631