Keywords: cement paste, hydration model, elasticity, numerical homogenization, hydration heat, optimisation.

The hardening mixture of cement and water, termed cement paste, plays an important role in structural concrete. Fine and coarse aggregates, typically present from 60% to 80% of the concrete volume, act as an elastic restraint on the cement paste system and remain rather intact by the cement hydration process. The focus is at the level of cement paste in terms of modelling and optimisation in order to design tailored material and an optimum casting process.

The objectives of this contribution is to shed light on the role and sensitivity of input parameters to hydration heat and elastic properties. The adopted methodology includes the formulation of the problem, generating the sets of input data, calculating the response, and performing statistical sensitivity analysis with optimisation. Evolution of elastic properties and hydration heat in Portland cements are understood in a sophisticated way and can be simulated realistically during virtual testing.

The digital microstructural model CEMHYD3D is used for the simulation of cement paste hydration [1]. The following effects were considered: cement fineness, cement chemical composition, distribution of clinker minerals in cement grains, gypsum content, water-to-cement ratio, and saturated/sealed curing conditions.

Negligible effects were found on released heat for variations of the amount of gypsum, type of autocorrelation file, C₄AF content, and saturated/sealed curing conditions. The C₃A content has a significant effect when the released heat is quantified for variations in the degree of hydration (DoH) of 0.3 or 0.5.

Determination of the Young's modulus is based on a linear elastic homogenization [2]. Results show that the water-to-cement ratio is the input parameter with the greatest influence on the Young's modulus.

The multi-objective optimisation problem was formulated, with the goal of finding such a set of input parameters which maximizes the Young's modulus while minimizing hydration heat at the time of 28 days of hydration. An applied multi-objective optimisation algorithm is based on an evolutionary algorithm called Pareto archived evolution strategy (PAES) [3]. The Pareto front after 500 iterations of PAES algorithm found the hydration heat in the range 168 - 247 J/(g of cement) with Young's moduli between 32.16 and 39.01 GPa.

1

D.P. Bentz, "CEMHYD3D: A Three-Dimensional Cement Hydration and Microstructure Development Modeling Package. Version 3.0.", Tech. Rep., NIST Building and Fire Research Laboratory, Gaithersburg, Maryland, 2005.

2

V. Šmilauer, Z. Bittnar, "Modelling of Microstructural Evolution of Concrete under Work Conditions and in Hardening Process", in Civil Engineering Computations: Tools and Techniques, B.H.V. Topping, (Editor), Saxe-Coburg Publications, UK, 347-367, 2007. doi:10.4203/csets.16.15

3

J.D. Knowles, D.W. Corne, "Approximating the nondominated front using the Pareto Archived Evolution Strategy", Evolutionary Computation, 8(2), 149-172, 2000. doi:10.1162/106365600568167

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