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Constitutive Modeling of Early-Age Concrete by a Stochastic Multi-scale Method

S. Liu1, X. Liu2,3, Y. Yuan2, H. A. Mang4
Department of Civil Engineering, Tongji University, Shanghai, China.
State Key Laboratory for Hazard Reduction in Civil Engineering, Tongji University, Shanghai, China.
Corresponding author. Email: (X. Liu)
Institute of Mechanics of Materials and Structures, Vienna University of Technology, Vienna, Austria.

Computer Modeling in Engineering & Sciences 2014, 100(3), 157-200.


A nonlinear viscoelastic constitutive model for early age concrete is presented in this paper. In this model, time-dependent properties, such as the elastic modulus, and thermal and autogenous shrinkage deformations, are computed by a stochastic multi-scale method, in which three different scales are specified according to the requirement of separation of scales, and different scales are linked by means of the asymptotic expansion theory with the help of specific representative volume elements (RVE). Thus, a cross-scale research from the cement paste to the macro structure of concrete is realized, and performance-based optimization of cement-based materials becomes possible. The developed constitutive model is implemented in commercial finite element software. Then, by means of a comparative study involving a numerical simulation and a full-scale experiment of a segment of the Hong Kong-Zhuhai-Macao immersed tunnel to obtain the temperature field and the strain field, the proposed constitutive model is validated. Thus a completely cross-scale constitutive model from the cement paste to the macro structure of concrete is realized, avoiding a variety of non-standardized and highly specialized test methods for concrete. After that, the stress field of the structure is analyzed. It is a prerequisite for structural analysis aimed at the investigation of cracking. Finally, taking different kinds of cement and aggregate as example, combinatorial optimization of material is conducted. And it is concluded that the type of cement and aggregate has an important influence on the early-age performance of investigated immersed tunnel. P.O.42.5 cement and limestone appears to be a good choice for control of cracking in engineering practice.


Constitutive modeling, Early-age concrete, Stochastic multi-scale method, Thermal deformations, Autogenous shrinkage.

Cite This Article

Liu, S., Liu, X., Yuan, Y., Mang, H. A. (2014). Constitutive Modeling of Early-Age Concrete by a Stochastic Multi-scale Method. CMES-Computer Modeling in Engineering & Sciences, 100(3), 157–200.

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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