Analytical Method for Evaluating Calcium Diffusion Coefficient of Partially Leached Cement Paste
Publication: Journal of Materials in Civil Engineering
Volume 33, Issue 8
Abstract
This paper aims at presenting an analytical method for evaluating the calcium diffusion coefficient of partially leached cement paste. The analytical method is developed based on a two-scale model of partially leached cement paste. On the first scale, the solid phase in partially leached cement paste is modeled as a two-phase composite material, composed of a matrix of calcium silicate hydrate () gel and inclusions of unhydrated cement and undissolved calcium hydroxide (CH) crystal. The relative calcium diffusion coefficient is derived analytically by the differential effective medium scheme. On the second scale, partially leached cement paste is treated as a system consisting of the solid phase and spheroidal capillary pores; the percolation behavior of capillary pores near the critical volume fraction is considered. In combination with percolation theory, the effective medium approach is modified to evaluate the calcium diffusion coefficient of partially leached cement paste. The depolarization factor is expressed in terms of the critical volume fraction of capillary pores, and the percolation exponents are calibrated from computer simulation data. Finally, the validity of the analytical method is verified with computer simulation data and experimental results collected from the literature. It is concluded that the proposed analytical method can predict the calcium diffusion coefficient of partially leached cement paste with reasonable accuracy.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The financial support of the National Natural Science Foundation of the People’s Republic of China (Grant Nos. 51779227, 51878615, and 51978619) is gratefully acknowledged.
References
Adenot, F., and M. Buil. 1992. “Modelling of the corrosion of the cement paste by deionized water.” Cem. Concr. Res. 22 (2–3): 489–496. https://doi.org/10.1016/0008-8846(92)90092-A.
Alonso, C., M. Castellote, and C. Andrade. 2006. “Ground water leaching resistance of high and ultra high performance concretes in relation to the testing convention regime.” Cem. Concr. Res. 36 (9): 1583–1594. https://doi.org/10.1016/j.cemconres.2006.04.004.
Babaahmadi, A., and L. P. Tang. 2016. “Development of an electro-chemical accelerated aging method for leaching of calcium from cementitious materials.” Mater. Struct. 49 (1–2): 705–718. https://doi.org/10.1617/s11527-015-0531-8.
Bejaoui, S., and B. Bary. 2007. “Modeling of the link between microstructure and effective diffusivity of cement pastes using a simplified composite model.” Cem. Concr. Res. 37 (3): 469–480. https://doi.org/10.1016/j.cemconres.2006.06.004.
Bentz, D. P., and E. J. Garboczi. 1991. “Percolation of phases in a three-dimensional cement paste microstructural model.” Cem. Concr. Res. 21 (2–3): 325–344. https://doi.org/10.1016/0008-8846(91)90014-9.
Bentz, D. P., and E. J. Garboczi. 1992. “Modeling the leaching of calcium hydroxide from cement paste—Effects on pore-space percolation and diffusivity.” Mater. Struct. 25 (9): 523–533. https://doi.org/10.1007/BF02472448.
Cai, W. Z., S. T. Tu, and J. M. Gong. 2006. “A physically based percolation model of the effective electrical conductivity of particle filled composites.” J. Compos. Mater. 40 (23): 2131–2142. https://doi.org/10.1177/0021998306062312.
Carde, C., G. Escadeillas, and A. H. François. 1997. “Use of ammonium nitrate solution to simulate and accelerate the leaching of cement pastes due to de-ionized water.” Mag. Concr. Res. 49 (181): 295–301. https://doi.org/10.1680/macr.1997.49.181.295.
Carde, C., and R. François. 1997. “Effect of the leaching of calcium hydroxide from cement paste on mechanical and physical properties.” Cem. Concr. Res. 27 (4): 539–550. https://doi.org/10.1016/S0008-8846(97)00042-2.
Constantinides, G., and F. J. Ulm. 2004. “The effect of two types of C-S-H on the elasticity of cement-based materials: Results from nanoindentation and micromechanical modelling.” Cem. Concr. Res. 34 (1): 67–80. https://doi.org/10.1016/S0008-8846(03)00230-8.
Feng, P., C. W. Miao, and J. W. Bullard. 2014. “A model of phase stability, microstructure and properties during leaching of portland cement binders.” Cem. Concr. Compos. 49 (May): 9–19. https://doi.org/10.1016/j.cemconcomp.2014.01.006.
Garboczi, E. J., and D. P. Bentz. 1992. “Computer simulation of the diffusivity of cement-based materials.” J. Mater. Sci. 27 (8): 2083–2092. https://doi.org/10.1007/BF01117921.
Gérard, B., C. Le Bellego, and O. Bernard. 2002. “Simplified modelling of calcium leaching of concrete in various environments.” Mater. Struct. 35 (254): 632–640.
Haga, K., S. Sutou, M. Hironage, S. Tanaka, and S. Nagasaki. 2005. “Effects of porosity on leaching of Ca from hardened ordinary portland cement paste.” Cem. Concr. Res. 35 (9): 1764–1775. https://doi.org/10.1016/j.cemconres.2004.06.034.
Hansen, T. C. 1986. “Physical structure of hardened cement paste: A classical approach.” Mater. Struct. 19 (6): 423–436. https://doi.org/10.1007/BF02472146.
Le Bellégo, C., B. Gerard, and G. Pijaudier-Cabot. 2000. “Chemo-mechanical effects in mortar beams subjected to water hydrolysis.” J. Eng. Mech. 126 (3): 266–272.
Mainguy, M., C. Tognazzi, J. M. Torrenti, and F. Adenot. 2000. “Modelling of leaching in pure paste and mortar.” Cem. Concr. Res. 30 (1): 83–90. https://doi.org/10.1016/S0008-8846(99)00208-2.
Ottavi, H., J. P. Clerc, G. Giraud, J. Roussenq, E. Guyon, and C. D. Mitescu. 1978. “Electrical conductivity of a mixture of conducting and insulating spheres: An application of some percolation concepts.” J. Phys. C: Solid State Phys. 11 (7): 1311–1328. https://doi.org/10.1088/0022-3719/11/7/021.
Patel, R. A., J. Perko, D. Jacques, G. De Schutter, G. Ye, and K. Van Breugel. 2018. “A three-dimensional lattice Boltzmann method based reactive transport model to simulate changes in cement paste microstructure due to calcium leaching.” Constr. Build. Mater. 166 (Mar): 158–170. https://doi.org/10.1016/j.conbuildmat.2018.01.114.
Phung, Q. T., N. Maes, D. Jacques, G. De Schutter, and G. Ye. 2016a. “Investigation of the changes in microstructure and transport properties of leached cement pastes accounting for mix composition.” Cem. Concr. Res. 79 (Jan): 217–234. https://doi.org/10.1016/j.cemconres.2015.09.017.
Phung, Q. T., N. Maes, D. Jacques, J. Perko, G. De Schutter, and G. Ye. 2016b. “Modelling the evolution of microstructure and transport properties of cement pastes under conditions of accelerated leaching.” Constr. Build. Mater. 115 (Jul): 179–192. https://doi.org/10.1016/j.conbuildmat.2016.04.049.
Pichler, C., A. Saxer, and R. Lackner. 2012. “Differential-scheme based dissolution/diffusion model for calcium leaching in cement-based materials accounting for mix design and binder composition.” Cem. Concr. Res. 42 (5): 686–699. https://doi.org/10.1016/j.cemconres.2012.02.007.
Sahimi, M. 1994. Applications of percolation theory. London: Taylor & Francis.
Saito, H., and S. Nakane. 1999. “Comparison between diffusion test and electromechanical acceleration test for leaching degradation of cement hydration products.” ACI Mater. J. 96 (2): 208–212.
Snyder, K. A., and J. R. Clinfton. 1995. 4SIGHT manual: A computer program for modelling degradation of underground low level water concrete vaults. Washington, DC: US Dept. of Commerce.
Sugiyama, T., W. Ritthichauy, and Y. Tsuji. 2003. “Simultaneous transport of chloride and calcium ions in hydrated cement systems.” J. Adv. Concr. Technol. 1 (2): 127–138. https://doi.org/10.3151/jact.1.127.
Torquato, S. 2002. Random heterogeneous materials: Microstructure and macroscopic properties. New York: Springer.
Wan, K. S., Y. Li, and W. Sun. 2013. “Experimental and modelling research of the accelerated calcium leaching of cement paste in ammonium nitrate solution.” Constr. Build. Mater. 40 (Mar): 832–846. https://doi.org/10.1016/j.conbuildmat.2012.11.066.
Wong, P. Z., J. Koplik, and J. P. Tomanic. 1984. “Conductivity and permeability of rocks.” Phys. Rev. B 30 (11): 6606–6614. https://doi.org/10.1103/PhysRevB.30.6606.
Yang, H., L. H. Jiang, Y. Zhang, Q. Pu, and Y. Xu. 2012. “Predicting the calcium leaching behaviour of cement pastes in aggressive environments.” Constr. Build. Mater. 29 (Apr): 88–96. https://doi.org/10.1016/j.conbuildmat.2011.10.031.
Zheng, J. J., X. Z. Zhou, and Z. M. Wu. 2010. “A simple method for predicting the chloride diffusivity of cement paste.” Mater. Struct. 43 (1–2): 99–106. https://doi.org/10.1617/s11527-009-9473-3.
Zheng, J. J., X. Z. Zhou, H. Y. Xing, and X. Y. Jin. 2015. “Differential effective medium theory for chloride diffusivity of concrete.” ACI Mater. J. 112 (1): 3–10.
Information & Authors
Information
Published In
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Aug 7, 2020
Accepted: Jan 4, 2021
Published online: May 24, 2021
Published in print: Aug 1, 2021
Discussion open until: Oct 24, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Jiajie Li, Zhenghong Tian, Xiao Sun, Yuanshan Ma, Hengrui Liu, Working state determination for concrete internal vibrator using genetic simulated annealing clustering method, Case Studies in Construction Materials, 10.1016/j.cscm.2022.e01163, 17, (e01163), (2022).