Keywords: micromechanical analysis, hydration model, heat of hydration, elastic properties, cellular automata, multi-objective optimization, curve fitting, regression, parameters estimation, evolutionary algorithms, optimization.

Modelling of hydrating concrete represents a challenging task especially due to the multiscale nature and missing mathematical formulation of several underlying phenomena. Soft computing techniques, namely the cellular automata-based hydration model, genetic algorithms and Kriging approximations, bring another alternative to tackle a~description of complex systems such as hardening concrete. Missing physical and mathematical description is replaced by cellular automata providing a robust framework. Here, the automata will describe ongoing chemical reaction during concrete hydration and the formation of cement microstructure.

The objectives of the next part include stochastic sensitivity analysis between input parameters of cement paste and its response in terms of hydration heat and Young's modulus. Such an approach is hardly to be achieved experimentally due to the hundreds of evaluations which are time-consuming, or exhibit the statistical nature of cement paste and testing device. The reproducibility in virtual tests is guaranteed although the link microstructure-property does not have to exist or even can be wrong. Therefore virtual modelling is exploited particularly for well established and validated simulations, i.e. for the heat evolution and Young's modulus of cement paste.

Next, the hydration model is presented in a multiscale task demonstrating an optimization of cooling pipes in a massive concrete member. The objective is aimed at quantifying maximum concrete temperatures with variable parameters. Coupling between microscale and structural scale is used from [1].

The question arises whether results from the virtual model can be trusted. Our proposed solution is based on a so-called robust optimization. Here, Kriging metamodel is applied at prediction of hydration heat solely from experimental datasets. The method gives good prediction when monotonicity evolution of hydration heat is assumed. Then, the multiobjective optimization is carried out, optimizing maximal Young's modulus and minimizing hydration heat. Moreover, the previously mentioned Kriging approximation is used as an estimation of accuracy of the cellular automata prediction. We are supported by two proxies - the value of a mean square error of the approximation tells us how far we are from the nearest experimental data point whereas the difference between the Kriging and cellular automata expresses either lack of fit or inability of a model to properly describe experimental results. The final comparison with the hydration model shows long-term underestimation with regards to experiments.

[1]

V. Smilauer, T. Krejcí, "Multiscale Model for Temperature Distribution in Hydrating Concrete", International Journal for Multiscale Computational Engineering, 7(2), 2009. doi:10.1615/IntJMultCompEng.v7.i2.50

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