Abstract
A nonlinear diffusion model for the drying of concrete, previously developed at Northwestern University and embedded in some design codes, was improved and calibrated on the basis of recent more extensive experimental data from the literature as well as theoretical considerations. The improvements include a new equation for the dependence of the self-desiccation rate on pore humidity and hydration degree; an updated equation for the decrease of moisture permeability at decreasing pore humidity; new equations to predict the permeability and diffusivity parameters from the and ratios, hydration degree, the type of concrete; and new equations to capture the nonlinearity of the sorption isotherm as a function of pore humidity and water-cement ratio. Furthermore, the recent idea that the pore humidity drop is the driving force, rather than a side effect, of the autogenous shrinkage is verified.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Partial financial support from the US Department of Transportation, provided through Grant No. 20778 from the Infrastructure Technology Institute of Northwestern University, and from the NSF under Grant No. CMMI-1129449, are gratefully appreciated.
References
Abrams, M., and D. Orals. 1965. “Concrete drying methods and their effect on fire resistance.” In Moisture in materials in relation to fire tests. Reston, VA: ASTM.
Abrams, M. S., and G. Monfore. 1965. Application of a small probe-type relative humidity gage to research on fire resistance of concrete. Skokie, IL: Portland Cement Association.
Ali, W., and G. Urgessa. 2014. “Computational model for internal relative humidity distributions in concrete.” J. Comput. Eng. 2014: 1–7. https://doi.org/10.1155/2014/539850.
Baroghel-Bouny, V., P. Mounanga, A. Khelidj, A. Loukili, and N. Rafa. 2006. “Autogenous deformations of cement pastes. Part II: W/C effects, micro–macro correlations, and threshold values.” Cem. Concr. Res. 36 (1): 123–136. https://doi.org/10.1016/j.cemconres.2004.10.020.
Bažant, Z., A. Donmez, E. Masoero, and S. R. Aghdam. 2015. “Interaction of concrete creep, shrinkage and swelling with water, hydration, and damage: Nano-macro-chemo.” In Proc., CONCREEP 10, 1–12. Reston, VA: ASCE.
Bažant, Z. P., and A. Donmez. 2016. “Extrapolation of short-time drying shrinkage tests based on measured diffusion size effect: Concept and reality.” Mater. Struct. 49 (1): 411–420. https://doi.org/10.1617/s11527-014-0507-0.
Bažant, Z. P., and M. Jirásek, 2017. Creep and hygrothermal effects in concrete structures. Dordrecht, Netherlands: Springer.
Bažant, Z. P., and G.-H. Li. 2008. “Comprehensive database on concrete creep and shrinkage.” ACI Mater. J. 105 (6): 635–637.
Bažant, Z. P., and L. J. Najjar. 1971. “Drying of concrete as a nonlinear diffusion problem.” Cem. Concr. Res. 1 (5): 461–473. https://doi.org/10.1016/0008-8846(71)90054-8.
Bažant, Z. P., and L. J. Najjar. 1972. “Nonlinear water diffusion in nonsaturated concrete.” Mater. Struct. 5 (1): 3–20. https://doi.org/10.1007/BF02479073.
Bažant, Z. P., and S. Rahimi-Aghdam. 2016. “Diffusion-controlled and creep-mitigated ASR damage via microplane model. I: Mass concrete.” J. Eng. Mech. 143 (2): 04016108. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001186.
Bažant, Z. P., and S. Rahimi-Aghdam. 2018. “Century-long durability of concrete structures: Expansiveness of hydration and chemo-mechanics of autogenous shrinkage and swelling.” In Computational Modelling of Concrete Structures: Proc., Conf. on Computational Modelling of Concrete and Concrete Structures (EURO-C 2018), 15. London: CRC Press.
Bentz, D. P. 1997. “Three-dimensional computer simulation of portland cement hydration and microstructure development.” J. Am. Ceram. Soc. 80 (1): 3–21. https://doi.org/10.1111/j.1151-2916.1997.tb02785.x.
Bentz, D. P. 2006. “Influence of water-to-cement ratio on hydration kinetics: Simple models based on spatial considerations.” Cem. Concr. Res. 36 (2): 238–244. https://doi.org/10.1016/j.cemconres.2005.04.014.
Bentz, D. P., O. M. Jensen, A. Coats, and F. P. Glasser. 2000. “Influence of silica fume on diffusivity in cement-based materials. I: Experimental and computer modeling studies on cement pastes.” Cem. Concr. Res. 30 (6): 953–962. https://doi.org/10.1016/S0008-8846(00)00264-7.
Constantinides, G., F.-J. Ulm, and K. Van Vliet. 2003. “On the use of nanoindentation for cementitious materials.” Mater. Struct. 36 (3): 191–196. https://doi.org/10.1007/BF02479557.
Daian, J.-F. 1988. “Condensation and isothermal water transfer in cement mortar Part I—Pore size distribution, equilibrium water condensation and imbibition.” Transp. Porous Media 3 (6): 563–589. https://doi.org/10.1007/BF00959103.
Danielson, U. 1962. “Heat of hydration of cement as affected by water-cement ratio.” In Proc., 4th Int. Symp. on the chemistry of cement, Paper IV-S7, 519–26. Washington, DC: US Dept. of Commerce.
Dönmez, A., and Z. P. Bažant. 2016. “Shape factors for concrete shrinkage and drying creep in model B4 refined by nonlinear diffusion analysis.” Mater. Struct. 49 (11): 4779–4784. https://doi.org/10.1617/s11527-016-0824-6.
fib (International Federation for Structural Concrete). 2012. Model code 2010: Final draft. Lausanne, Switzerland: fib.
Gawin, D., F. Pesavento, and B. A. Schrefler. 2006. “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.
Grasley, Z. C., and D. A. Lange. 2004. “Modeling drying shrinkage stress gradients in concrete.” Cem. Concr. Aggregates 26 (2): 1–8. https://doi.org/10.1520/CCA12302.
Grasley, Z. C., and C. K. Leung. 2011. “Desiccation shrinkage of cementitious materials as an aging, poroviscoelastic response.” Cem. Concr. Res. 41 (1): 77–89. https://doi.org/10.1016/j.cemconres.2010.09.008.
Halamičková, P., R. J. Detwiler, D. P. Bentz, and E. J. Garboczi. 1995. “Water permeability and chloride ion diffusion in portland cement mortars: Relationship to sand content and critical pore diameter.” Cem. Concr. Res. 25 (4): 790–802. https://doi.org/10.1016/0008-8846(95)00069-O.
Hanson, J. 1968. “Effects of curing and drying environments on splitting tensile strength of concrete.” J. Proc. 65 (7): 535–543. https://doi.org/10.14359/7495.
Hua, C., P. Acker, and A. Ehrlacher. 1995. “Analyses and models of the autogenous shrinkage of hardening cement paste: I. Modelling at macroscopic scale.” Cem. Concr. Res. 25 (7): 1457–1468. https://doi.org/10.1016/0008-8846(95)00140-8.
Hubler, M. H., R. Wendner, and Z. P. Bažant. 2015a. “Comprehensive database for concrete creep and shrinkage: Analysis and recommendations for testing and recording.” ACI Mater. J. 112 (4): 547–558. https://doi.org/10.14359/51687453.
Hubler, M. H., R. Wendner, and Z. P. Bažant. 2015b. “Statistical justification of Model B4 for drying and autogenous shrinkage of concrete and comparisons to other models.” Mater. Struct. 48 (4): 797–814. https://doi.org/10.1617/s11527-014-0516-z.
Jennings, H. M. 2000. “A model for the microstructure of calcium silicate hydrate in cement paste.” Cem. Concr. Res. 30 (1): 101–116. https://doi.org/10.1016/S0008-8846(99)00209-4.
Jennings, H. M., and S. K. Johnson. 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.
Jensen, O. M. 2007. Internal curing of concrete-state-of-the-art report of RILEM Technical Committee 196-ICC. Bagneux, France: RILEM Publications.
Ji, T. 2005. “Preliminary study on the water permeability and microstructure of concrete incorporating nano-.” Cem. Concr. Res. 35 (10): 1943–1947. https://doi.org/10.1016/j.cemconres.2005.07.004.
Jiang, Z., Z. Sun, and P. Wang. 2006. “Internal relative humidity distribution in high-performance cement paste due to moisture diffusion and self-desiccation.” Cem. Concr. Res. 36 (2): 320–325. https://doi.org/10.1016/j.cemconres.2005.07.006.
Kim, J.-K., and C.-S. Lee. 1999. “Moisture diffusion of concrete considering self-desiccation at early ages.” Cem. Concr. Res. 29 (12): 1921–1927. https://doi.org/10.1016/S0008-8846(99)00192-1.
Laurens, S., J.-P. Balayssac, J. Rhazi, and G. Arliguie. 2002. “Influence of concrete relative humidity on the amplitude of ground-penetrating radar (GPR) signal.” Mater. Struct. 35 (4): 198–203. https://doi.org/10.1007/BF02533080.
Lin, F., and C. Meyer. 2009. “Hydration kinetics modeling of portland cement considering the effects of curing temperature and applied pressure.” Cem. Concr. Res. 39 (4): 255–265. https://doi.org/10.1016/j.cemconres.2009.01.014.
Luan, Y., and T. Ishida. 2013. “Enhanced shrinkage model based on early age hydration and moisture status in pore structure.” J. Adv. Concr. Technol. 11 (12): 360–373. https://doi.org/10.3151/jact.11.360.
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.
McLaughlin, C., and T. Magee. 1998. “The determination of sorption isotherm and the isosteric heats of sorption for potatoes.” J. Food Eng. 35 (3): 267–280. https://doi.org/10.1016/S0260-8774(98)00025-9.
Nguyen, H., S. Rahimi-Aghdam, and Z. P. Bažant. 2018. “Time lag in measuring pore humidity in concrete by a gage in finite cavity.” Mater. Struct. 51 (1): 18. https://doi.org/10.1617/s11527-018-1143-x.
Nielsen, L. F. 1991. A research note on sorption, pore size distribution, and shrinkage of porous materials. Lyngby, Denmark: Laboratoriet for Bygningsmaterialer.
Nilsson, L.-O. 1980. Hygroscopic moisture in concrete-drying, measurements & related material properties. Lund, Sweden: Division of Building Materials, Lund Institute of Technology.
Nilsson, L.-O. 2002. “Long-term moisture transport in high performance concrete.” Mater. Struct. 35 (10): 641–649. https://doi.org/10.1007/BF02480357.
Poyet, S. 2009. “Experimental investigation of the effect of temperature on the first desorption isotherm of concrete.” Cem. Concr. Res. 39 (11): 1052–1059. https://doi.org/10.1016/j.cemconres.2009.06.019.
Qomi, M. A., et al. 2014. “Combinatorial molecular optimization of cement hydrates.” Nat. Commun. 5 (1): 4960. https://doi.org/10.1038/ncomms5960.
Rahimi-Aghdam, S., Z. P. Bažant, and F. C. Caner. 2017a. “Diffusion-controlled and creep-mitigated ASR damage via microplane model. II: Material degradation, drying, and verification.” J. Eng. Mech. 143 (2): 04016109. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001185.
Rahimi-Aghdam, S., Z. P. Bažant, and G. Cusatis. 2019. “Extended microprestress-solidification theory for long-term creep with diffusion size effect in concrete at variable environment.” J. Eng. Mech. 145 (2): 04018131. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001559.
Rahimi-Aghdam, S., Z. P. Bažant, and M. A. Qomi. 2017b. “Cement hydration from hours to centuries controlled by diffusion through barrier shells of CSH.” J. Mech. Phys. Solids 99: 211–224. https://doi.org/10.1016/j.jmps.2016.10.010.
Rasoolinejad, M., S. Rahimi-Aghdam, and Z. P. Bažant. 2018. “Statistical filtering of useful concrete creep data from imperfect laboratory tests.” Mater. Struct. 51 (6): 153. https://doi.org/10.1617/s11527-018-1278-9.
Sørensen, E. V., F. Radjy, and E. Sellevold. 1979. “Water vapor permeability of hardened cement paste.” Ph.D. thesis, Dept. of Civil Engineering, Technical Univ. of Denmark.
Taylor, H. F. 1997. Cement chemistry. London: Thomas Telford.
Tennis, P. D., and H. M. Jennings. 2000. “A model for two types of calcium silicate hydrate in the microstructure of portland cement pastes.” Cem. Concr. Res. 30 (6): 855–863. https://doi.org/10.1016/S0008-8846(00)00257-X.
van Breugel, K. 1997. “Simulation of hydration and formation of structure in hardening cement-based materials.” Ph.D. thesis, Dept. of Civil Engineering, TU Delft.
West, R. P., and N. Holmes. 2005. “Predicting moisture movement during the drying of concrete floors using finite elements.” Constr. Build. Mater. 19 (9): 674–681. https://doi.org/10.1016/j.conbuildmat.2005.02.014.
Xi, Y., Z. P. Bažant, and H. M. Jennings. 1994. “Moisture diffusion in cementitious materials adsorption isotherms.” Adv. Cem. Based Mater. 1 (6): 248–257. https://doi.org/10.1016/1065-7355(94)90033-7.
Information & Authors
Information
Published In
Copyright
©2019 American Society of Civil Engineers.
History
Received: Mar 11, 2018
Accepted: Oct 3, 2018
Published online: Mar 6, 2019
Published in print: May 1, 2019
Discussion open until: Aug 6, 2019
ASCE Technical Topics:
- Chemical processes
- Chemistry
- Climates
- Concrete
- Diffusion
- Diffusion (porous media)
- Engineering materials (by type)
- Engineering mechanics
- Environmental engineering
- Humidity
- Hydration
- Hydrologic engineering
- Hydrology
- Laminating
- Materials characterization
- Materials engineering
- Materials processing
- Meteorology
- Moisture
- Nonlinear analysis
- Permeability (material)
- Sorption
- Structural analysis
- Structural engineering
- Thermodynamics
- Transport phenomena
- Water and water resources
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.