DOI QR코드

DOI QR Code

The origins and evolution of cement hydration models

  • Xie, Tiantian (Tennessee Technological University Cookeville) ;
  • Biernacki, Joseph J. (Tennessee Technological University Cookeville)
  • Received : 2010.05.26
  • Accepted : 2010.12.23
  • Published : 2011.12.25

Abstract

Our ability to predict hydration behavior is becoming increasingly relevant to the concrete community as modelers begin to link material performance to the dynamics of material properties and chemistry. At early ages, the properties of concrete are changing rapidly due to chemical transformations that affect mechanical, thermal and transport responses of the composite. At later ages, the resulting, nano-, micro-, meso- and macroscopic structure generated by hydration will control the life-cycle performance of the material in the field. Ultimately, creep, shrinkage, chemical and physical durability, and all manner of mechanical response are linked to hydration. As a way to enable the modeling community to better understand hydration, a review of hydration models is presented offering insights into their mathematical origins and relationships one-to-the-other. The quest for a universal model begins in the 1920's and continues to the present, and is marked by a number of critical milestones. Unfortunately, the origins and physical interpretation of many of the most commonly used models have been lost in their overuse and the trail of citations that vaguely lead to the original manuscripts. To help restore some organization, models were sorted into four categories based primarily on their mathematical and theoretical basis: (1) mass continuity-based, (2) nucleation-based, (3) particle ensembles, and (4) complex multi-physical and simulation environments. This review provides a concise catalogue of models and in most cases enough detail to derive their mathematical form. Furthermore, classes of models are unified by linking them to their theoretical origins, thereby making their derivations and physical interpretations more transparent. Models are also used to fit experimental data so that their characteristics and ability to predict hydration calorimetry curves can be compared. A sort of evolutionary tree showing the progression of models is given along with some insights into the nature of future work yet needed to develop the next generation of cement hydration models.

Keywords

Acknowledgement

Supported by : National Science Foundation (NSF)

References

  1. Avrami, M. (1939), "Kinetics of phase change I", J. Chem. Phys., 7, 1103-1112. https://doi.org/10.1063/1.1750380
  2. Avrami, M. (1940), "Kinetics of phase change II", J. Chem. Phys., 8, 212-224. https://doi.org/10.1063/1.1750631
  3. Bentz, D. (1997), "Three dimensional computer simulation of portland cement hydration and microstructure development", J. Am. Ceram. Soc., 80, 3-21. https://doi.org/10.1111/j.1151-2916.1997.tb02785.x
  4. Bentz, D. (2006), "Influence of water-to-cement ratio on hydration kinetics: simple models based on spatial considerations", Cement Concrete Res., 36(2), 238-244. https://doi.org/10.1016/j.cemconres.2005.04.014
  5. Bezjak, A. (1980), "On the determination of rate constants for hydration processes in cement pastes", Cement Concrete Res., 10, 553-563. https://doi.org/10.1016/0008-8846(80)90099-X
  6. Bezjak, A. (1983), "Kinetics analysis of cement hydration including various mechanistic concepts. I Theoretical development", Cement Concrete Res., 13, 305-318. https://doi.org/10.1016/0008-8846(83)90029-7
  7. Biernacki, J. and Xie, T. (2011), "An advanced single particle model for C3S and alite hydration", J. Am. Ceram. Soc., 94(7), 2037-2047. https://doi.org/10.1111/j.1551-2916.2010.04352.x
  8. Bishnoi, S. and Scrivener, K. (2009a), "Studying nucleation and growth kinetics of alite hydration using ${\mu}ic$", Cement Concrete Res., 39, 849-860. https://doi.org/10.1016/j.cemconres.2009.07.004
  9. Bishnoi, S. and Scrivener, K. (2009b), ${\mu}ic$: A new platform for modeling the hydration of cements", Cement Concrete Res., 39, 266-274. https://doi.org/10.1016/j.cemconres.2008.12.002
  10. Brown, P.W., Franz, E., Frohnsdorff, G. and Taylor, H.F.W. (1984), "Analyses of the aqueous phase during early $C_3S$ hydration", Cement Concrete Res., 14, 257-262. https://doi.org/10.1016/0008-8846(84)90112-1
  11. Brown, P.W. (1985), "A kinetic model for the hydration of tricalcium silicate", Cement Concrete Res., 15, 35-41. https://doi.org/10.1016/0008-8846(85)90006-7
  12. Brown, P. (1989), "Effect of particle size distribution on the kinetics of hydration of tricalcium silicate", J. Am. Ceram. Soc., 72(10), 1829-1832. https://doi.org/10.1111/j.1151-2916.1989.tb05986.x
  13. Brouwers, H.J.H. (2004), "The work of powers and brownyard revisited - Part 1", Cement Concrete Res., 34(9), 1697-1716. https://doi.org/10.1016/j.cemconres.2004.05.031
  14. Bullard, J. (2007), "Approximate rate constants for non-ideal diffusion and their application in a stochastic model", J. Phys. Chem., 111, 2084-2092. https://doi.org/10.1021/jp0658391
  15. Bullard, J. (2008), "A determination of hydration mechanisms for tricalcium silicate using a kinetic cellular automaton model", J. Am. Ceram. Soc., 91(7), 2088-2097. https://doi.org/10.1111/j.1551-2916.2008.02419.x
  16. Bullard, J.W., Jennings, H.M., Livingston, R.A., Nonat, A., Scherer, G.W., Schweitzer, J.S. and Scrivener, K.L. (2011), "Mechanisms of cement hydration at early ages", Cement Concrete Res., 41(12), 1208-1223. https://doi.org/10.1016/j.cemconres.2010.09.011
  17. Cahn, J. (1956), "The kinetics of grain boundary nucleated reaction", Acta Metall., 4, 449-459. https://doi.org/10.1016/0001-6160(56)90041-4
  18. Evans, J.W. and De Jonghe, L.C. (1991), The production of inorganic materials, Macmillan Publishing Co., New York, 541.
  19. Garboczi, E.J. and Bentz, D.P. (1991), Fundamental computer simulation models for cement-based materials, J. Skalny, S. Mindess (Eds.), Materials Science of Concrete II, American Ceramic Society, Westerville, OH, 249-273.
  20. Garrault, S. and Nonat, A. (2001), "Hydration layer formation on tricalcium and dicalcium silicate sufaces: experimental study and numerical simulation", Langmuir, 17, 8131-8138. https://doi.org/10.1021/la011201z
  21. Gartner, E.M. (1997), "A proposed mechanism for the growth of C-S-H during the hydration of tricalcium silicate", Cement Concrete Res., 27(5), 665-672. https://doi.org/10.1016/S0008-8846(97)00049-5
  22. Ginstling, A. and Brounshtein, B. (1950), "Concerning the diffusion kinetics of reactions in spherical particles", J. Appl. Chem., USSR, 23, 1327-1338.
  23. Jander, V. (1927), "Reaktionen im festen zustande bei hoheren temperaturen", Z. Anorg. Allg. Chem., 163, 1-30. https://doi.org/10.1002/zaac.19271630102
  24. Jennings, H.M. and Johnson, S.K. (1986), "Simulation of microstructure development during the hydration of a cement compound", J. Am. Ceram. Soc., 69(11), 790-795. https://doi.org/10.1111/j.1151-2916.1986.tb07361.x
  25. Johnson, W.A. and Mehl, R.F. (1939), "Reaction kinetics in processes of nucleation and growth", Trans. AIME 135, 416-441.
  26. Kolmogorov, A.N. (1937), "k, Statisticheskoi teori kristallizatsii metallov", Izv. Akad. Nayuk CCCR, 2, 355-359.
  27. Kondo, R. and Kodama, M. (1967), "On the hydration kinetics of cement", Semento Gijutsu Nenpo, 21, 77-82.
  28. Knudsen, T. (1984), "The dispersion model for hydration of Portland cement I general concepts", Cement Concrete Res., 14, 622-630. https://doi.org/10.1016/0008-8846(84)90024-3
  29. Livingston, R.A. (2000), "Fractal nucleation and growth model for the hydration of tricalcium silicate", Cement Concrete Res., 39, 1853-1860.
  30. Navi, P. (1999), "Effects of cement size distribution on capillary pore structure of the simulated cement paste", Comput. Mater. Sci., 16, 285-293. https://doi.org/10.1016/S0927-0256(99)00071-3
  31. Nonat, A. (2005), "Modeling hydration and setting of cement", Ceramics, 92, 247-257.
  32. Pignat, C. (2005), "Simulation of cement paste microstructure hydration, pore space characterization and permeability determination", Mater. Struct., 38, 459-466. https://doi.org/10.1007/BF02482142
  33. Pommersheim, J.M., Clifton, J.R. and Frohnsdorff, G.J. (1982), "Mathematical modeling of tricalcium silicate hydration", Cement Concrete Res., 12, 765-772. https://doi.org/10.1016/0008-8846(82)90040-0
  34. Pommersheim, J.M. (1985), "A kinetic model for the hydration of tricalcium silicate", Cement Concrete Res., 15, 35-41. https://doi.org/10.1016/0008-8846(85)90006-7
  35. Pommersheim, J.M. (1987), "Effect of particle size distribution on hydration kinetics", Mater. Res. Soc. Symp. Proc., 85, 301-306.
  36. Taplin, J. (1968), "On the hydration kinetics of hydraulic cements", Proc. Fifth. Intern. Symp. Chem. Cem, Tokyo, 337-348.
  37. Taplin, J. (1972), "Steady-state kinetic model for solid-fluid reactions", J. Chem. Phys., 59, 194-199.
  38. Thomas, J.J. (2007), "A new approach to modeling the nucleation and growth kinetics of tricalcium silicate hydration", J. Am. Ceram. Soc., 90(10), 3282-3288. https://doi.org/10.1111/j.1551-2916.2007.01858.x
  39. Thomas, J. (2009), "Hydration kinetics and microstructure development of normal and $CaCl_2$-accelerated tricalcium silicate pastes", J. Phys. Chem., 113(46), 19836-1984.
  40. Thomas, J.J., Bierancki, J.J., Bullard, J.W., Bishnoi, S., Dolado, J.S., Scherer, G.W. and Luttge, A. (2010), "Modeling and simulation of cement hydration kinetics and microstructure development", Cement Concrete Res., 41(12), 1257-1278.
  41. van Breugel, K. (1995), "Numerical simulation of hydration and microstructural development in hardening cement-based materials (1) theory", Cement Concrete Res., 25(2), 319-331. https://doi.org/10.1016/0008-8846(95)00017-8
  42. van Breugel, K. (1995), "Numerical simulation of hydration and microstructural development in hardening cement-based materials (2) applications", Cement Concrete Res., 25(3), 522-530. https://doi.org/10.1016/0008-8846(95)00041-A

Cited by

  1. The effect of water-to-cement ratio on the hydration kinetics of tricalcium silicate cements: Testing the two-step hydration hypothesis vol.42, pp.8, 2012, https://doi.org/10.1016/j.cemconres.2012.05.009
  2. Development of Carbon Nanotube Modified Cement Paste with Microencapsulated Phase-Change Material for Structural–Functional Integrated Application vol.16, pp.12, 2015, https://doi.org/10.3390/ijms16048027
  3. Study on functional and mechanical properties of cement mortar with graphite-modified microencapsulated phase-change materials vol.105, 2015, https://doi.org/10.1016/j.enbuild.2015.07.043
  4. Creep and shrinkage effects in service stresses of concrete cable-stayed bridges vol.13, pp.4, 2014, https://doi.org/10.12989/cac.2014.13.4.483
  5. An advanced single-particle model for C3S hydration - validating the statistical independence of model parameters vol.15, pp.6, 2015, https://doi.org/10.12989/cac.2015.15.6.989
  6. Growth of Calcium Hydroxide Islands in Tricalcium Silicate-Based Cements at Early Age vol.95, pp.9, 2012, https://doi.org/10.1111/j.1551-2916.2012.05259.x
  7. A Multi-Ionic Continuum-Based Model for C3S Hydration vol.98, pp.10, 2015, https://doi.org/10.1111/jace.13703
  8. Modeling cement hydration by connecting a nucleation and growth mechanism with a diffusion mechanism. Part II: Portland cement paste hydration vol.23, pp.6, 2016, https://doi.org/10.1515/secm-2013-0259
  9. Modeling cement hydration by connecting a nucleation and growth mechanism with a diffusion mechanism. Part II: Portland cement paste hydration vol.23, pp.6, 2016, https://doi.org/10.1515/secm-2013-0259
  10. A new hydration kinetics model of composite cementitious materials, part 1: Hydration kinetic model of Portland cement vol.103, pp.3, 2011, https://doi.org/10.1111/jace.16845