Abstract
Based on the theory of mixtures, a coupled thermo-hygro-mechanical (THM) damage model for concrete subjected to high temperatures is presented in this paper. Concrete is considered as a mixture composed of solid skeletons, liquid water, water vapor, dry air, and dissolved air. The macroscopic balance equations of the model consist of the mass conservation equations of each component and the momentum and energy conservation equations of the whole medium mixture. The state equations and the constitutive model used in the model are given. Four final governing equations are given in terms of four primary variables, i.e., the displacement components of soil skeletons, the gas pressure, the capillary pressure, and the temperature. The processes involved in the coupled model include evaporation, dehydration, heat and mass transfer, etc. Through the process of deformation failure and the energy properties, the mechanics damage evolution equations are established based on the principle of conversation of energy and the Lemaitre equivalent strain assumption. Then, the influence of thermal damage on the mechanical property is considered.
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Schrefler, B. A., Brunello, P., Gawin, D., Majorana, C. E., and Pesavento, F. Concrete at high temperature with application to tunnel fire. Computational Mechanics, 29(1), 43–51 (2002)
Guian, S. K. Fire and life safety provisions for a long vehicular tunnel. Tunnelling and Underground Space Technology, 19(4–5), 316 (2004)
Feist, C., Aschaber, M., and Hofstetter, G. Numerical simulation of the load-carrying behavior of RC tunnel structures exposed to fire. Finite Elements in Analysis and Design, 45, 958–965 (2009)
Bazant, Z. P. and Kaplan, M. F. Concrete at High Temperatures: Material Properties and Mathematical Models, Longman, Harlow (1996)
Gawin, D., Pesavento, F., and Schrefler, B. A. Towards prediction of the thermal spalling risk through a multi-phase porous media model of concrete. Comput. Methods Appl. Mech. Engrg., 195, 5707–5729 (2006)
Ulm, F. J., Coussy, O., and Bazant, Z. P. The “chunnel” fire, I: chemoplastic softening in rapidly heated concrete. J. Eng. Mech. ASCE, 125(3), 272–282 (1999)
Kalifa, P., Menneteau, F. D., and Quenard, D. Spalling and pore pressure in HPC at high temperatures. Cement and Concrete Research, 30(12), 1915–1927 (2000)
Kodur, V. K. R. and Phan, L. Critical factors governing the fire performance of high strength concrete systems. Fire Safety Journal, 42, 482–488 (2007)
Baggio, P., Majorana, C. E., and Schrefler, B. A. Thermo-hygro-mechanical analysis of concrete. Int. J. Num. Meth. Fluids, 20, 573–595 (1995)
Gawin, D., Majorana, C. E., and Schrefler, B. A. Numerical analysis of hygro-thermal behaviour and damage of concrete at high temperature. Mech. Cohes.-Frict. Mater., 4, 37–74 (1999)
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, 1731–1771 (2003)
Tenchev, R. and Purnell, P. An application of a damage constitutive model to concrete at high temperature and prediction of spalling. International Journal of Solids and Structures, 42, 6550–6565 (2005)
Li, X. K., Li, R. T., and Schrefler, B. A. A coupled chemo-thermo-hygro-mechanical model of concrete at high temperature and failure analysis. Int. J. Numer. Anal. Meth. Geomech., 30, 635–681 (2006)
Bary, B., Ranc, G., Durand, S., and Carpentier, O. A coupled thermo-hydro-mechanical-damage model for concrete subjected to moderate temperatures. International Journal of Heat and Mass Transfer, 51, 2847–2862 (2008)
Luzio, G. D. and Cusatis, G. Hygro-thermo-chemical modeling of high performance concrete, I: theory. Cement and Concrete Composites, 31, 301–308 (2009)
Ponta, S. D., Meftahb, F., and Schrefler, B. A. Modeling concrete under severe conditions as a multiphase material. Nucl. Eng. Des., 24(3), 562–572 (2011)
Harmathy, T. Z. Effect of Moisture on the Fire Endurance of Building Materials, No. 385, ASTM, Philadelphia, 74–95 (1965)
Anderberg, Y. Cracking phenomena of HPC and OC. International Workshop on Fire Performance of High-Strength-Concrete, NIST (eds. ai]Phan, L. T., Carino, N. J., Duthinh, D., and Garboczi, E.), National Institute of Standards and Technology, Gaithersburg, MD, 69–73 (1997)
Schrefler, B. A., Khoury, G. A., Gawin, D., and Majorana, C. E. Thermo-hydro-mechanical modelling of high performance concrete at high temperatures. Engineering Computations, 19(7), 787–819 (2002)
Thomas, H. R. and Sansom, M. R. Fully coupled analysis of heat, moisture and air transfer in unsaturated soil. ASCE J. Eng. Mech., 121(3), 392–405 (1995)
Nechnech, W., Meftah, F., and Reynouard, J. M. An elasto-plastic damage model for plain concrete subjected to high temperature. Eng. Struct., 24, 597–611 (2002)
Bowen, R. M. Theory of Mixtures, Academic Press, New York (1976)
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)
Gawin, D. and Schrefler, B. A. Thermo-hydro-mechanical analysis of partially saturated porous materials. Engrg. Comput., 13, 113–143 (1996)
Gregg, S. J. and Sing, K. S. W. Adsorption, Surface Area and Porosity, Academic Press, London (1982)
ASHRAE Handbook. Fundamentals, ASHRAE, Atlanta (1993)
Gray, W. G. and Schrefler, B. A. Thermodynamic approach to effective stress in partially saturated porous media. Eur. J. Mech. A/Solids, 20, 521–538 (2001)
Harmathy, T. Z. and Allen, W. L. Thermal properties of selected masonry unit concretes. ACI Journal, 70, 132–142 (1973)
Schneider, U. and Herbst, H. J. Permeabilitaet und porositaet von Beton bei hohen temperaturen (in German). Deutscher Ausschuss Stahlbeton, 403, 23–52 (1989)
Furbish, D. J. Fluid Physics in Geology: An Introduction to Fluid Motions on Earth’s Surface and Within Its Crust, Oxford University Press, Oxford (1997)
Qin, B., Chen, Z. H., Fang, Z. D., Sun, S. G., Fang, X. W., and Wang, J. Analysis of coupled thermo-hydro-mechanical behavior of unsaturated soils based on theory of mixtures I. Appl. Math. Mech. -Engl. Ed., 31(12), 1561–1576 (2010) DOI: 10.1007/s10483-010-1384-6
Chen, Y. F., Zhou, C. B., and Jing, L. R. Modeling coupled THM processes of geological porous media with multiphase flow: theory and validation against laboratory and field scale experiments. Comput. Geotech., 36(8), 1308–1329 (2009)
Bear, J. Dynamics of Fluids in Porous Media, Dover, New York (1988)
Mikhalyuk, A. V. and Zakharov, V. V. Dissipation of dynamic-loading energy in quasi-elastic deformation processes in rocks. Journal of Applied Mechanics and Technical Physics, 8(2), 312–318 (1996)
Stefeler, E. D., Epstein, J. S., and Conley, E. G. Energy partitioning for a crack under remote shear and compression. International Journal of Fracture, 120(4), 563–580 (2003)
Xie, H. P., Ju, Y., and Li, L. Y. Criteria for strength and structural failure of rocks based on energy dissipation and energy release principles. Chinese Journal of Rock Mechanics and Engineering, 24(17), 3003–3010 (2005)
Lemaitre, J. How to use damage mechanics. Nuclear Engineering and Design, 80(3), 233–245 (1984)
Yang, S. Q., Xu, W. Y., and Su, C. D. Study on the deformation failure and energy properties of marble specimen under triaxial compression. Engineering Mechanics, 24(1), 136–142 (2007)
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Project supported by the National Natural Science Foundation of China (No. 50979112)
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Li, Zy., Liu, Yx. Coupled thermo-hygro-mechanical damage model for concrete subjected to high temperatures. Appl. Math. Mech.-Engl. Ed. 33, 465–482 (2012). https://doi.org/10.1007/s10483-012-1564-x
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DOI: https://doi.org/10.1007/s10483-012-1564-x