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A Stochastic Multi-scale Model for Predicting the Thermal Expansion Coefficient of Early-age Concrete

S. Liu1, X. Liu2, X. F. Guan3, P.F. He1, Y. Yuan2

Institute of Applied Mechanics, Tongji University, Shanghai , China.
Department of geotechnical engineering, Tongji University, Shanghai, China.
Department of Mathematics, Tongji University, Shanghai 200092, China.
Corresponding author. Email:

Computer Modeling in Engineering & Sciences 2013, 92(2), 173-191.


Early performance of mass concrete structures is very sensitive to the thermal expansion characteristics of concrete. As a kind of multi-phase composite, concrete has different material composition and microscopic configuration in different scales. Its thermal expansion coefficient (CTE) depends not only on the physical and mechanical properties of the constituents, but also on their distribution. What’s more, CTE is also time-dependent with the procedure of hydration. This research proposes a stochastic multi-scale model for analyzing CTE of concrete. In the developed model, concrete macro-scale is divided into three different levels: cement paste scale, mortar scale and concrete meso-scale; a specific representative element volume (REV) is described by introducing stochastic parameters; and the asymptotic expansion theory is employed to realize the connection between different scales. Then, by a comparison study with experimental results and Rosen- Hashin bounds at mortar scale, the effectiveness of this model has been validated. And, the influence of aggregate’s type and volume fraction on CTE of concrete is further investigated. The analysis results show that the proposed model can effectively estimate the CTE of concrete at early-age through taking the influence of material composition and configuration into consideration.


Cite This Article

Liu, S., Liu, X., Guan, X. F., He, P., Yuan, Y. (2013). A Stochastic Multi-scale Model for Predicting the Thermal Expansion Coefficient of Early-age Concrete. CMES-Computer Modeling in Engineering & Sciences, 92(2), 173–191.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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