Moisture transport in cementitious materials. Periodic homogenization and numerical analysis

Abstract

This article presents a new approach based on periodic homogenisation for the computation of moisture diffusion coefficients in porous media. Experimental data allow fixing the parameters in the homogenised model. A series of parametric simulations are performed in order to compute the homogenised moisture diffusion coefficient through a gradual complexity of elementary cells approaching the microstructure of the cementitious materials tested.

Cet article présente une nouvelle approche, basée sur l’homogénéisation périodique, pour le calcul des coefficients de diffusion de l’humidité dans les milieux poreux. Les données expérimentales permettent la fixation des paramètres du modèle homogénéisé. Une série de simulations paramétriques sont effectuées afin de calculer le coefficient de diffusion de l’humidité homogénéisé à travers une complexité progressive de cellules élémentaires approchant la microstrucutre des matériaux cimentaires testés.

Keywords:

• moisture transport
• periodic homogenisation
• unsaturated flow
• Richards equation
• numerical modelling

Mots-Clés:

• Transport d’humidité
• Homogénéisation périodique
• Ecoulement partiellement saturé
• Equation de Richards
• Modélisation numérique

Notes

1. Where the governing continuity equations associated with boundary.

2. To ensure the unicity of the solution of problem (9).

3. The mixtures were manufactured by VINCI Construction.

4. Under isothermal condition, we have and . For the concretes and , we have .

5. Analytical solution only exist in very simple geometries of microstructure (see for example Mchirgui et al., 2013; Quintard, 1993).

6. Let us note that concretes have very low porosities (between 12 and 15%), so that a simple elementary cell composed only of a circular inclusion does not enable to reach these low porosities. However, the square inclusion (considered in the next section) can reach lowest ones.

7. We recall that the liquid phase is assumed to be a thin film deposed on the solid phase .

8. This assumption is justified for the hygroscopic regime studied, given the low water contents considered.

9. In this model, the moisture diffusion coefficient is assumed to be piecewise constant with respect to the relative humidity.