Keywords: creep, hardening concrete, experiment, fuzzy, sets, model, Poisson's ratio.

Besides the technologies aimed at delivering required quality either at lower cost or earlier, the new trends in the building industry, dictated by investors, also concentrate in expediting construction processes. In concrete structures, the very limiting factor is the characteristic feature of concrete, the hydration. The common practice in erecting concrete structures is to interrupt the construction after placement and treatment of concrete in a formwork in order to allow concrete to reach a necessary degree of hydration, so that the construction may continue. Targeting this issue, another inherent feature of hardening concrete surfaces, the lack of a sufficient experiment-supported knowledge base. The experimental data on fresh concrete is rather extensive, which is mainly due to investigations into workability of fresh concrete. Also, the volume of experimental data on the already hardened concrete, which is being gathered ever since concrete was pronounced a building material, is huge. On the other hand, the experimental data on solidifying and hardening concrete is quite scarce, among the few [1,2,3,4], which is the consequence of difficulties in experimental work related to the transition of concrete from a liquid into a solid accompanied by the rapid hydration. From the above, it was concluded that a simple material model with a small number of identifiable parameters is suitable for hardening concrete. And, the uncertainty included in the input parameters, stemming from the scarcity of experimental data, should be also considered.

The objective of this study is the definition of a material model for hardening concrete which can describe the behaviour of hardening concrete subjected to short- time and sustained loading. The model is based on the solidification theory proposed by Bazant [5], which helps to avoid unnecessary difficulties related to dealing with a binomial integral. This means that the effect of aging is expressed separately by a function describing the evolution of hydration, while the remaining parameters of the model are considered to be non-aging. The reason for such a definition is the fact that, generally, all parameters are a function of hydration, which also facilitates the identification of material parameters from experimental data. The linear, or nonlinear, dependence of a material parameter on the function of hydration is considered. The effects of loading speed and load level, which are primarily important in respective analyses of hardening concrete under short-time and sustained loading, are also included in the model. The model is defined in a general three-dimensional form, since hardening concrete is usually subject to constraining effects, e.g. by formwork, where a multi-dimensional analysis is desirable. A numerical example is added to show the applicability of the proposed model in simulations of hardening concrete which is loaded at extremely early ages.

Based on the nature of available experimental data on hardening concrete, a modification of the proposed model is done with respect to the uncertainty of input material parameters in terms of the theory of fuzzy sets, as was also done in [6].

The theory of fuzzy sets was developed to deal with information whose character is vague, imprecise of uncertain, rather than random. The theory of fuzzy sets is tightly related to the theory of possibility and thus it can be used to constrain the possible distribution of results by clearly stating the asymptotic values acquired by a material model. In such modelling, the material parameters are expressed by fuzzy numbers whose membership function defines the degree of confidence. The membership function ranges from 0, the extreme values, to 1, the most common value. The fuzzy numbers can be decomposed to the so-called ?-cuts, which are intervals of confidence associated to a degree of confidence. Then the problem expressed by fuzzy numbers can by solved with help of interval arithmetics, which is a well-established discipline.

It is believed that this approach to dealing with uncertainty of input data, which does not possess a clear statistical description, can represent an alternative in assessment of behaviour of concrete structures. The fuzzy analysis is shown in an illustrative example.

1

Okamoto, H., "A Study on Creep Properties of Concrete at Very Early Age", in "The 30th Japan Congress on Materials Research", 171-174, 1987.

2

Bergström, S.G., Byfors, J., "Properties of Concrete at Early Ages", 32nd Meeting of RILEM Permanent Committee, Rio de Janeiro, 265-274, 1979.

3

Štemberk, P., Tsubaki, T., "Lateral Deformation of Solidifying Concrete under Uniaxial Loading", in "Proceedings of JSCE annual conference", Tokushima, JSCE, CD-ROM, 2003.

4

Štemberk, P., Tsubaki, T., "Response of Solidifying Concrete in Penetration and Pullout Tests", in "Proceedings of the 4th International Summer Symposium", JSCE, Kyoto, 2002.

5

Bazant, Z.P., Prasannan, S., "Solidification Theory for Concrete Creep", Journal of Engineering Mechanics, ASCE, 115(8), 1691-1725, 1989. doi:10.1061/(ASCE)0733-9399(1989)115:8(1691)

6

Valliapan, S., Pham, T.D., "Fuzzy Logic Applied to Numerical Modelling of Engineering Problems", Computational Mechanics Advances, 2, 1995.

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