Nonlinear Constitutive Model for Concretes at Early Ages Considering the Hydration Reaction
Publication: Journal of Engineering Mechanics
Volume 149, Issue 2
Abstract
Hygro-thermal and hydration behaviors exist in concretes at early ages, which inevitably affect their mechanical properties. Accompanying water consumption in the concrete, there are several irreversible thermodynamic processes, including hydration heat production and strength growth. By considering coupled deformation, heat conduction, and a hydration reaction, a thermodynamically consistent continuum theory is developed for concrete at early age. At first, to satisfy the dissipation inequality, the energy dissipation caused by these irreversible processes can be tentatively described by introducing a hydration extent , so that a hydration kinetic equation considering the temperature and stress effects is established by linking the reaction rate with the concentrations of reactants. Compared to the Arrhenius linear relation between the reaction rate and chemical affinity, this nonlinear hydration kinetic equation is applicable to complex hydration reactions. Then, a fully coupled nonlinear constitutive model is constructed to interpret the thermo-chemical-mechanical interactions, whose numerical implementation is generated in commercial software ABAQUS using UEL (user-defined element) subroutines. Particularly, the model is used to predict the evolution of elastic modulus and temperature of two kinds of concretes under adiabatic testing: ordinary concrete (OC) and high performance concrete (HPC), which shows good agreement with experimental results. Furthermore, some examples are numerically studied to illustrate the interactions among mechanical deformation, hydration reaction, and heat conduction in concrete at early ages.
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Data Availability Statement
All models and computer codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant No. 11932005).
References
Banthia, N., and R. Gupta. 2006. “Influence of polypropylene fiber geometry on plastic shrinkage cracking in concrete.” Cem. Concr. Res. 67 (3): 299–331. https://doi.org/10.1016/j.cemconres.2006.01.010.
Behnke, R., H. Dal, and M. Kaliske. 2011. “An extended tube model for thermo-viscoelasticity of rubberlike materials: Parameter identification and examples.” Proc. Appl. Math. Mech. 11 (1): 353–354. https://doi.org/10.1002/pamm.201110168.
Bentz, D. P., and O. M. Jensen. 2004. “Mitigation strategies for autogenous shrinkage cracking.” Cem. Concr. Compos. 26 (6): 677–685. https://doi.org/10.1016/S0958-9465(03)00045-3.
Cervera, M., J. Oliver, and T. Prato. 1999. “Thermo-chemo-mechanical model for concrete. I: Hydration and aging.” J. Eng. Mech. 125 (9): 1018–1027. https://doi.org/10.1061/(asce)0733-9399(1999)125:9(1018.
Chanvillard, G., and L. D’Aloia. 1997. “Concrete strength estimation at early age: Modification of the method of equivalent age.” ACI Mater. J. 94 (6): 520–530. https://doi.org/10.1097/MAJ.0b013e3180959e4e.
Chen, J., H. Wang, K. M. Liew, and S. Shen. 2019. “A fully coupled chemomechanical formulation with chemical reaction implemented by finite element method.” J. Appl. Mech. 86 (4): 041006. https://doi.org/10.1115/1.4042431.
De Schutter, G., and L. Taerwe. 1996. “Degree of hydration-based description of mechanical properties of early age concrete.” Mater. Struct. 29 (6): 335–344. https://doi.org/10.1007/BF02486341.
Drozdov, A. D. 2014. “Self-oscillations of hydrogels driven by chemical reactions.” Int. J. Appl. Math. 6 (3): 1450023. https://doi.org/10.1142/s1758825114500239.
Gao, X., H. Ba, and J. Qi. 2004. “Study on relationship between water-cement mass ratio and early age shrinkage of concrete.” J. Tongji Univ. 32 (1): 67–71. https://doi.org/10.1007/BF02911033.
Gawin, D., F. Pesavento, and B. A. Schrefler. 2006a. “Hygro-thermo-chemo-mechanical modelling of concrete at early ages and beyond. Part I: Hydration and hygro-thermal phenomena.” Int. J. Numer. Methods Eng. 67 (3): 299–331. https://doi.org/10.1002/nme.1615.
Gawin, D., F. Pesavento, and B. A. Schrefler. 2006b. “Hygro-thermo-chemo-mechanical modelling of concrete at early ages and beyond. Part II: Shrinkage and creep of concrete.” Int. J. Numer. Methods Eng. 67 (3): 332–363. https://doi.org/10.1002/nme.1636.
Hattel, J. H., and J. Thorborg. 2003. “A numerical model for predicting the thermomechanical conditions during hydration of early-age concrete.” Appl. Math. Modell. 27 (1): 1–26. https://doi.org/10.1016/S0307-904X(02)00082-3.
Henkensiefken, R., D. Bentz, T. Nantung, and J. Weiss. 2009. “Volume change and cracking in internally cured mixtures made with saturated lightweight aggregate under sealed and unsealed conditions.” Cem. Concr. Compos. 31 (7): 427–437. https://doi.org/10.1016/j.cemconcomp.2009.04.003.
Kim, J. H., R. P. Ferron, and S. P. Shah. 2012. “Fresh concrete and its significance for sustainability.” J. Sustainable Cem.-Based Mater. 1 (1–2): 16–23. https://doi.org/10.1080/21650373.2012.726821.
Kovler, K., and N. Roussel. 2011. “Properties of fresh and hardened concrete.” Cem. Concr. Res. 41 (7): 775–792. https://doi.org/10.1016/j.cemconres.2011.03.009.
Li, W. G., Z. Y. Huang, G. Q. Hu, W. H. Duan, and S. P. Shah. 2017. “Early-age shrinkage development of ultra-high-performance concrete under heat curing treatment.” Constr. Build. Mater. 131 (Jan): 767–774. https://doi.org/10.1016/j.conbuildmat.2016.11.024.
Li, X., and D. Wuyang. 2012. “Research on method of separating autogenous shrinkage from thermal deformation of concrete at early ages.” Appl. Mech. Mater. 193–194 (Aug): 486–490. https://doi.org/10.4028/www.scientific.net/AMM.182-183.486.
Lura, P., O. M. Jensen, and K. van Breugel. 2003. “Autogenous shrinkage in high-performance cement paste: An evaluation of basic mechanisms.” Cem. Concr. Res. 33 (2): 223–232. https://doi.org/10.1016/S0008-8846(02)00890-6.
Maciulaitis, R., M. Vaiciene, and R. Zurauskiene. 2009. “The effect of concrete composition and aggregates properties on performance of concrete.” J. Civ. Eng. Manage. 15 (3): 317–324. https://doi.org/10.3846/1392-3730.2009.15.317-324.
Nishiyama, M., H. Higuchi, and T. Yanagida. 2002. “Chemomechanical coupling of the forward and backward steps of single kinesin molecules.” Nat. Cell Biol. 4 (10): 790–797. https://doi.org/10.1038/ncb857.
Poluektov, M., A. B. Freidin, and L. Figiel. 2018. “Modelling stress-aected chemical reactions in non-linear viscoelastic solids with application to lithiation reaction in spherical si particles.” Int. J. Eng. Sci. 128 (Jul): 44–62. https://doi.org/10.1016/j.ijengsci.2018.03.007.
Qin, B., and Z. Zhong. 2021. “A theoretical model for thermo-chemo-mechanically coupled problems considering plastic flow at large deformation and its application to metal oxidation.” Int. J. Solids Struct. 212 (Mar): 107–123. https://doi.org/10.1016/j.ijsolstr.2020.12.006.
Reese, S., and S. Govindjee. 1997. “Theoretical and numerical aspects in the thermo-viscoelastic material behaviour of rubber-like polymers.” Mech. Time-Depend. Mater. 1 (4): 357–396. https://doi.org/10.1023/A:1009795431265.
Tomlinson, D., F. Moradi, H. Hajiloo, P. Ghods, A. Alizadeh, and M. Green. 2017. “Early age electrical resistivity behaviour of various concrete mixtures subject to low temperature cycling.” Cem. Concr. Compos. 83 (Oct): 323–334. https://doi.org/10.1016/j.cemconcomp.2017.07.028.
Ulm, F. J., and O. Coussy. 1996. “Strength growth as chemo-plastic hardening in early age concrete.” J. Eng. Mech. 122 (12): 1123–1132. https://doi.org/10.1061/(asce)0733-9399(1996)122:12(1123.
Ulm, F. J., and O. Coussy. 1998. “Couplings in early-age concrete: From material modeling to structural design.” Int. J. Solids Struct. 35 (31–32): 4295–4311. https://doi.org/10.1016/S0020-7683(97)00317-X.
Wei, Y., S. M. Liang, W. Q. Guo, and W. Hansen. 2017. “Stress prediction in very early-age concrete subject to restraint under varying temperature histories.” Cem. Concr. Compos. 83 (Oct): 45–56. https://doi.org/10.1016/j.cemconcomp.2017.07.006.
Yang, G., Y. K. Wu, H. Li, N. X. Gao, M. Jin, Z. L. Hu, and J. P. Liu. 2021. “Effect of shrinkage-reducing polycarboxylate admixture on cracking behavior of ultra-high strength mortar.” Cem. Concr. Compos. 122 (Sep): 104117. https://doi.org/10.1016/j.cemconcomp.2021.104117.
Zhang, X. L., and Z. Zhong. 2017. “A coupled theory for chemically active and deformable solids with mass diffusion and heat conduction.” J. Mech. Phys. Solids 107 (Oct): 49–75. https://doi.org/10.1016/j.jmps.2017.06.013.
Zhong, Z., B. Qin, and J. Chen. 2021. “A coupled theory for soft materials at finite strain with heat conduction, diffusion and chemical reactions.” Comput. Mater. Sci. 188 (Feb): 110189. https://doi.org/10.1016/j.commatsci.2020.110189.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 149 • Issue 2 • February 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jun 15, 2022
Accepted: Sep 29, 2022
Published online: Nov 28, 2022
Published in print: Feb 1, 2023
Discussion open until: Apr 28, 2023
ASCE Technical Topics:
- Aging (material)
- Concrete
- Constitutive relations
- Continuum mechanics
- Coupling
- Deterioration
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering materials (by type)
- Engineering mechanics
- High-performance concrete
- Hydration
- Kinetics
- Laminating
- Materials characterization
- Materials engineering
- Materials processing
- Mathematics
- Solid mechanics
- Structural engineering
- Structural members
- Structural systems
- Thermodynamics
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