Keywords: plasticity, concrete, modelling, hardening, solidification, hydration, degree of hydration, Chen plasticity model.

This paper describes an extension of Chen plasticity model [1] for use with concrete in the very early ages. Since the Chen plasticity model is very suitable for modelling of hardened concrete due to the different strengths considered in compression and tension, it was sought to make use of this model also for the description of mechanical behaviour of hardening concrete. The material parameters considered in the modelling have to be dependent on the progressing hydration. The hydration is quantified with help of the degree of hydration.

The Chen plasticity model is a three-parameter model for concrete displaying isotropic hardening [1]. This model expresses the elastoplastic behaviour of concrete. The typical behaviour of concrete is varying stress-strain characteristic under tension and compression. Two different, but similar, functions were proposed for each of the loading surfaces, in the compression-compression region, , and in the tension-tension or tension-compression regions, .

All material parameters using in the Chen plasticity model are functions of the evolutionary function. The evolutionary function, as its name implies, is introduced in order to describe the evolutionary changes in the microstructure of solidifying and hardening concrete and therefore to control the mechanical behaviour of concrete in the modelling, as shown in the paper [2]. Therefore it is obvious that the loading surfaces are changing with increasing time.

To illustrate the applicability of the presented approach, a real structure was considered. The Border bridge is a part of the newly constructed D8 highway connecting Prague and Dresden. This composite bridge is approximately 500 metres long and overpasses a deep valley. The intermediate columns are approximately 50 metres tall, which prohibits pumping concrete directly from the bottom of the valley to the bridge deck, which is designed as a reinforced concrete slab. Therefore, the concrete needs to be transported to the location of placement across the already finished reinforced concrete deck. The main objective was to describe the behaviour of the concrete deck under compressive load corresponding to the truck carrying fresh concrete. Therefore, the deformation of the prematurely loaded concrete deck by truck tires was investigated.

However, the human factor, variation of properties of the single constituents, weather conditions, all those factors influence the ultimate performance of the concrete structure, and not all factors can be described by a standard probabilistic parametric distribution. The work presented in references [3] and [4] proposes a method for assessment of the ultimate performance of concrete structures using the concept of the fuzzy set theory. An approach to fuzzification of the Chen plasticity model described above was presented in reference [3]. A similar fuzzification procedure was presented in reference [4], where the varying settlement of a tall reinforced concrete wall during construction was quantified with respect to the uncertainties contained in the material description.

This paper describes combination of the Chen plasticity model and the function of evolution of microstructure. Due to this modification of the Chen plasticity model it is possible to use the model for solidifying and hardening concrete. Therefore, all material parameters of the Chen plasticity model are defined with the evolutionary function of the microstructure of the concrete. The input data can be obtained experimentally with simple standard testing methods. This model shows the possibility of using the Chen plasticity model not only for hardened concrete but also for hardening concrete with a yet evolving microstructure. The presented model was applicated on a real structure. With the help of this model the deformations of hardening concrete slab in various ages were analysed, especially the vertical displacements under loading representing the truck tyre. The extension of the modified model for treating uncertainty is also possible. In this paper a procedure of how to extend the proposed model is shown so that the effect of uncertainty of the material description can be quantified.

1

W.F. Chen, "Plasticity in reinforced concrete", Osborne-McGraw-Hill, New York, 1982.

2

P. Štemberk and T. Tsubaki, "Modeling of Solidifying Concrete under One-Dimensional Loading", Proc. of JCI, Vol.25, No.1, 587-592, 2003.

3

J. Kruis, P. Štemberk , "Material Model of Hardening Concrete with Uncertainties", Proc. of the Seventh International Conference on Computational Structures Technology, Lisbon, pp.1-10, 2004. doi:10.4203/ccp.79.207

4

J. Kruis, P. Štemberk , "Fuzzification of Chen plasticity model of Concrete", Computational Plasticity VIII - Fundamentals and Applications. Barcelona, pp. 747-750, 2005.

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