Conference, Proceedings

Thermomechanical modelling of maturing concrete mixture
Stanislav Šťastník, Jiří Vala, Jaroslav Nováček
Faculty of Civil Engineering, Brno University of Technology,
Veveří 95, CZ ‐ 602 00 Brno, Czech Republic,
email: stastnik.s@fce.vutbr.cz, vala.j@fce.vutbr.cz, novacek.j@fce.vutbr.cz
Abstract: Concrete is a natural composite whose properties are determined by hygro‐thermo‐chemo‐
mechanical processes at early age of its existence. Namely in the case of massive structures such processes
should be controlled carefully to guarantee the optimal behaviour of a structure according to its proposed
use. The complete mathematical model of heated concrete, treated as a multi‐phase porous material,
consists i) of 20 balance equations, coming from the mass, momentum and energy balance laws for
continua with microstructure, corresponding to solid concrete, liquid mixture, water vapour and dry air,
coming from the mass, momentum and energy balance laws for continua with microstructure and ii) of a
set of constitutive relationships, identified by laboratory experiments. Some preliminary simulation
results are available.
Keywords: Material properties of early‐age concrete, thermodynamic principles, hygro‐thermo‐chemo‐
mechanical modelling, partial differential equations of evolution.
Introduction
Quantitative analysis of early‐age behaviour of concrete is a rather complicated multi‐physical
problem. Every reliable thermomechanical model of maturing concrete mixture should include
at least a) reversible elastic deformation, b) viscous creep of material and c) volume changes,
unlike a) and b) independent of external loads, namely c1) autogenous volume changes, driven
by chemical shrinkage of cement particles, c2) subsequent thermal expansion, c3) drying caused
by water loss into environment and c4) later carbonation. Three principal internal and external
influences are 1) internal hydration heat, generated by the hydration hydraulic processes, 2)
ambient temperature variation, connected with ambient humidity variation (natural or artificial
ones), 3) external mechanical loads; thus evidently hygro‐thermo‐chemo‐mechanical modelling
and simulation is needed.
Moreover, the proper quantitative study such physical and chemical processes should be
supported by the multi‐scale analysis: especially [4] for samples prepared as mixtures of
cement, water and air distinguishes anhydrous‐cement scale (from 10 ‐8 to 10 ‐6 m), cement‐paste
scale (from 10 ‐6 to 10 ‐4 m) with growing crystals and capillary phenomena, mortar scale (about
10 ‐2 m) with particles included in a seemingly homogenous matrix and macroscale (about 10 ‐1 m)
for a natural composite. The physical formulations come i) in [1] from common
phenomenological relations with a large number of model parameters, ii) in [7] from
phenomenological coefficients in Onsager reciprocity relations and Gibbs‐Duhem conditions,
iii) in [2] and [4] from mechanistic calculations at representative volume elements for
multiple scales and, alternatively, iv) in [3] and [5] from thermodynamic conservation
principles applied to hybrid mixture theory.
The mathematical and computational homogenization techniques cannot be assigned to i), ii),
iii), iv) exactly; their applicability is also limited by reasonable quantitative data from laboratory
measurements (at all considered scales) and corresponding observations in situ. In the rough
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