Determination of the macroscopic chloride diffusivity in cementitious by porous materials coupling periodic homogenization of Nernst-Planck equation with experimental protocol

Olivier Millet, Abdelkarim Ait-Mokhtar, Ouali Amiri

Abstract


In this paper, we propose a macroscopic migration model for cementitious porous media obtained from periodic homogenization technique. The dimensional analysis of Nernst-Planck equation leads to dimensionless numbers characterizing the problem. According to the order of magnitude of the dimensionless numbers, the homogenization of Nernst-Planck equation leads at the leading order to a macroscopic model where several rates can be coupled or not. For a large applied electrical field accelerating the transfer of ionic species, we obtain a macroscopic model only involving migration. A simple experimental procedure of measurement of the homogenized chlorides diffusivity is then proposed for cement-based materials. 


Full Text:

PDF

References


A.A.S.H.T.O., Sampling and testing for total chloride ion in concrete and concrete raw materials, AASHTO standard, Washington, 1982, 260–282.

Amiri O., Aït–Mokhtar A., Dumargue P., Optimisation de l’exploitation de l’essai d’électrodiffusion d’ions chlorures dans le béton, Revue Française de Génie Civil, 2000, 4(2–3), 161–173.

Amiri O., Aït–Mokhtar A., Dumargue P, Touchard G., Electrochemical modeling of chloride migration in cement based materials. Part I: Theoretical basis at microscopic scale, Electrochimica Acta, 2001 (46), 1267–1275.

Amiri O., Aït–Mokhtar A., Dumargue P., Touchard G., Electrochemical modeling of chloride migration in cement based materials. Part II: Experimental study, calculation of chlorides flux, Electrochimica Acta, 2001, 46, 3589–3597.

Andrade C., Calculation of chlorides diffusion in concrete from migration measurements, Cement and Concrete Research, vol. 1993, 23, 724–742.

Auriault J. L., Strzelecki T., On the electro-osmotic flow in a saturated porous medium, International Journal of Engineering Science, 1981, 19(7), 915–928.

Auriault J. L., Lewandowska J., Diffusion/adsorption/advection macrotransport in soils, Eur. J. Mech. A/Solids, 1996, 15(4), 681–704.

Bensoussan A., Lions J. L., Papanicolaou G., Asymptotic analysis for periodic structures, Studies in Mathematics and its applications, J. L. Lions, G. Papanicolaou and R. T. Rockafellar Editors, 1978.

Friedmann H., Amiri O., Aït-Mokhtar A., Dumargue P., A direct method for determining chloride diffusion coeffcient by using migration test, Cement and Concrete Research, 2004 (34), 1967–1973.

Hamdouni A., Millet O., Classification of thin shell models deduced from the nonlinear three-dimensional elasticity. Part I: the shallow shells and Part II: the strongly bent shells, Arch. Mech., 2003, 55(2), 135–175 and 177–219.

MilletO.,HamdouniA.,Cimeti`ereA.,Aclassificationofthinplatemodelsbyasymptoticexpansionof nonlinear three-dimensional equilibrium equations, Int. J. of Non-Linear Mechanics, 2001, vol. 36, 165–186.

Moyne C., Murad M., Macroscopic Behavior of Swelling Porous Media Derived from Micromechanical Analysis, Transport in Porous Media, 2003, 50, 127–151.

Moyne C., Murad M., A Two-Scale Model for Coupled Electro-Chemo-Mechanical Phenomena and Onsager’ Reciprocity Relations in Expansive Clays: I Homogenization Analysis, Transport in Porous Media, 2006, 62, 333–380.

Offner F. F., Nernst-Planck-Poisson Diffusion Equation: Numerical Solution of the Boundary Value Problem, J. theor. Biol., 1971, 31, 215–227.

Ollivier J. P., Marchand J., Nilsson L. O., Méthodologie de prévision de la pénétration des ions chlorures par

diffusion dans le béton, Proceedings of the international RILEM workshop, Arles, France, 1996, 166–195.

Samson E., Marchand J., Beaudoin J. J., Describing ion diffusion mechanisms in cement-based materials

using the homogenization technique, Cement and Concrete Research, 1999, 29, 1341–1345.

Sanchez Palencia E., Non-homogeneous media and vibration theory, Lecture notes in Physics, Springer-

Verlag, 1980.

Schmidt F., Rostasy F. S., A method of the calculation of the chemical composition of the concrete pore

solution, Cement and Concrete Research, 1993, 23, 1159–1168.

Tang L., Nilsson L. O., Rapid determination of chloride diffusivity of concrete by applying an electrical field,

ACI Materials Journal, 1992, 89, 49–53.

Truc O., Ollivier J. P., Nilsson L. O., Numerical simulation of multi-species transport through saturated concrete during a migration test - MsDiff code, Cement and Concrete Research, 2000, 30, 1581–1592.




DOI: http://dx.doi.org/10.1260/175095408784300234

Copyright (c) 2016 The International Journal of Multiphysics