Calculation of Shrinkage Stress in Early-Age Concrete Pavements. I: Calculation of Shrinkage Strain
Publication: Journal of Transportation Engineering
Volume 139, Issue 10
Abstract
This paper focuses on modeling of the distribution of shrinkage strain in early-age concrete pavements. In the modeling, an integrative model for autogenous and drying shrinkage predictions of concrete at an early age is introduced first. Second, a model taking both cement hydration and moisture diffusion into account synchronously is used to calculate the distribution of the interior humidity in concrete. The previous two models are experimentally verified independently by a series of shrinkage and interior humidity tests on three types of concretes with different compressive strengths. Using the models, the distribution of shrinkage strain in early-age concrete pavement (with respect to drying of the pavement surface) is calculated. The model results show the development of interior humidity inside of the pavement because the concrete cast obeys a two-stage mode, i.e., a vapor-saturated stage with 100% relative humidity (Stage 1) and a stage with the relative humidity gradually decreasing (Stage 2). The duration of Stage 1 increases with respect to the location, i.e., from the slab top to bottom. Within Stage 1, a uniform shrinkage strain is expected throughout the slab. By contrast, the shrinkage gradient along the slab depth is obvious in Stage 2. The maximum and minimum shrinkages occur at the slab top and bottom, respectively. The distribution of the shrinkage strain along the pavement depth is nonlinear and the nonlinearity is strong where it is close to the drying face. Concrete strength can significantly influence the magnitude of the shrinkage strain within the slab. For a given age and location, an increased concrete strength corresponds with an increased shrinkage strain and shrinkage gradient.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This paper has been supported by a grant from the National Science Foundation of China (No. 50978143) and a grant from National Basic Research Program of China (No. 2009CB623200) to Tsinghua University.
References
Akita, H., Fujiwara, T., and Ozaka, Y. (1997). “A practical procedure for the analysis of moisture transfer within concrete due to drying.” Mag. Concrete Res., 49(179), 129–137.
Ayano, T., and Wittmann, F. H. (2002). “Drying, moisture distribution, and shrinkage of cement-based materials.” Mater. Struct., 35(3), 134–140.
Baroghel-Bouny, V., Mainguy, M., Lassabatere, T., and Coussy, O. (1999). “Characterization and identification of equilibrium and transfer moisture properties for ordinary and high-performance cementitious materials.” Cement Concrete Res., 29(8), 1225–1238.
Bazant, Z. P., and Najjar, L. J. (1972). “Nonlinear water diffusion in nonsaturated concrete.” Mater. Struct., 5(25), 3–20.
Bissonnette, B., Pierre, P., and Pigeon, M. (1999). “Influence of key parameters on drying shrinkage of cementitious materials.” Cement Concrete Res., 29(10), 1655–1662.
Chanvillard, G., and Daloia, L. (1997). “Concrete strength estimation at early age: Modification of the method of equivalent age.” ACI Mater. J., 94(6), 220–227.
Gutsch, A. W. (1998). “Properties of fresh concrete, experiments and modeling.” Ph.D. thesis, Braunschweig Univ. of Technology, Brunswick, Germany.
Hou, D., Zhang, J., and Gao, Y. (2012). “Simulation of temperature field of concrete pavement at early age.” Eng. Mech., 29(6), 151–159 (in Chinese).
Jensen, O. M., and Hansen, P. F. (2001). “Water-entrained cement-based materials: I. Principles and theoretical background.” Cement Concrete Res., 31(5) 647–654.
Kim, J. K. (2001). “Estimation of compressive strength by a new apparent activation energy function.” Cement Concrete Res., 31(2), 217–225.
Kjellsen, K., and Detwiler, R. J. (1993). “Later-age strength prediction by a modified maturity model.” ACI Mater. J., 90(3), 220–227.
Nilsson, L. O. (2002). “Long-term moisture transport in high performance concrete.” Mater. Struct., 35(10), 641–649.
Pane, I., and Hansen, W. (2002). “Concrete hydration and mechanical properties under nonisothermal conditions.” ACI Mater. J., 99(6), 534–542.
Parrott, L. J. (1995). “Influence of cement type and curing on the drying and air permeability of cover concrete.” Mag. Concrete Res., 47(171), 103–111.
Powers, T. C., and Brownyard, T. L. (1948). Studies of the physical properties of hardened Portland cement paste (nine parts), Journal of the American Concrete Institute, Vol. 43 (Bulletin 22), Research Laboratories of the Portland Cement Association, Chicago.
Rastrup, E. (1954). “Heat of hydration.” Mag. Concrete Res., 6(17), 127–140.
Zhang, J., Hou, D., and Chen, H. (2011a). “Experimental and theoretical studies on shrinkage of concrete at early-ages.” J. Mater. Civ. Eng., 23(3), 312–320.
Zhang, J., Hou, D., Gao, Y., and Sun, W. (2011b). “Determination of moisture diffusion coefficient of concrete at early-age from interior humidity measurements.” Dry. Technol., 29(6), 689–696.
Zhang, J., Hou, D., and Han, Y. (2012). “Micromechanical model of autogenous and drying shrinkages of concrete.” Constr. Build. Mater., 29(3), 230–240.
Zhang, J., Hou, D. W., and Sun, W. (2010). “Experimental study on the relationship between shrinkage and interior humidity of concrete at early age.” Mag. Concrete Res., 62(3), 191–199.
Zhang, J., Qi, K., and Huang, Y. (2009). “Calculation of moisture distribution in early-age concrete.” J. Eng. Mech., 135(8), 871–880.
Zhang, Z. B., and Zhang, J. (2006). “Experimental study on the relationship between shrinkage strain and environmental humidity of concrete.” J. Build. Mater., 6(6), 720–723 (in Chinese).
Information & Authors
Information
Published In
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Mar 17, 2011
Accepted: Oct 10, 2012
Published online: Oct 12, 2012
Discussion open until: Mar 12, 2013
Published in print: Oct 1, 2013
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.