M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 1972.

A. Phil, Thermodynamics and Statistical Mechanics : Equilibrium by Entropy Maximisation, 2002.

J. Auriault, Heterogeneous Media : is an Equivalent Homogeneous Description Always Possible ?, Int. J. Engrg Sci, vol.29, pp.785-795, 1991.

J. Auriault and E. Sanchez-palencia, Etude du Comportement Macroscopique d'un Milieu Poreux Saturé Déformable, J. Mécanique, vol.16, issue.4, pp.575-603, 1977.

H. Callen, Thermodynamics and an Introduction to Thermostatics, 1985.

S. Carnie and Y. C. Chan, The Statistical Mechanics of the Electrical Double Layer : Stress Tensor and Contact Conditions, J. Chem. Phys, vol.74, issue.2, pp.1293-1297, 1981.

X. Chen and M. A. Hicks, Influence of Water Chemical Potential on the Swelling of Water Sensitive Materials, Computers and Structures, vol.88, pp.1498-1505, 2010.

B. V. Derjaguin, N. Churaev, V. Muller, and . Surface-forces, , 1987.

A. Dominijanni and M. Manassero, Modelling the Swelling and Osmotic Properties of Clay Soils. Part II : The Physical Approach, International Journal of Engineering Science, vol.51, pp.51-73, 2012.

F. G. Donnan, The Theory of Membrane Equilibria, Chem. Rev, vol.1, pp.73-90, 1924.

L. Dormieux, P. Barboux, O. Coussy, and P. Dangla, A macroscopic model of the swelling phenomenon of a saturated clay, Eur. J. Mech. A Solids, vol.16, pp.981-1004, 1995.
URL : https://hal.archives-ouvertes.fr/hal-00586537

L. Dormieux, E. Lemarchand, and O. Coussy, Macroscopic and Micromechanical Approaches to the Modelling of the Osmotic Swelling in Clays, Transport in Porous Media, vol.50, pp.75-91, 2003.
URL : https://hal.archives-ouvertes.fr/hal-02538015

W. Ehlers, A. Acartürk, and N. Karajan, Advances in Modelling Saturated Soft Biological Tissues and Chemically Active Gels, Archive of Applied Mechanics, vol.80, issue.5, pp.467-478, 2010.

R. Evans, The Nature of the Liquid-Vapour Interface and Other Topics in the Statistical Mechanics of Non-Uniform, Classical Fluids, Advances in Physics, vol.28, issue.2, pp.143-200, 1979.

A. Gajo and B. Loret, The Mechanics of Active Clays Circulated by Salts, Acids and Bases, Journal of the Mechanics and Physics of Solids, vol.55, pp.1762-1801, 2007.

J. Hansen and I. R. Mcdonald, Theory of Simple Liquids. Third Edition, 2006.

J. P. Hansen, G. M. Torrie, and P. Vieillefosse, Statistical Mechanics of Dense Ionized Matter. VII. Equation of State and Phase Separation of Ionic Mixtures in a Uniform Background, Physical Review A, vol.16, issue.5, pp.2153-2168, 1977.

D. Henderson, L. Blum, and J. L. Lebowitz, An Exact Formula for the Contact Value of the Density Profile of a System of Charged Hard Spheres near a Charged Wall, J. Electroanal. Chem, vol.102, pp.315-319, 1979.

T. L. Hill, Statistical Mechanics : Principles and Selected Applications, 1956.

R. J. Hunter, Zeta Potential in Colloid Science : Principles and Applications, 1981.

R. J. Hunter, Introduction to Modern Colloid Science, 1994.

J. H. Irving and J. G. Kirkwood, The Statistical Mechanical Theory of Transport Processes. IV. The Equation of Hydrodynamics, J. Chem. Phys, vol.18, issue.6, pp.817-829, 1950.

J. Israelachvili, Intermolecular and Surface Forces, 1992.

J. D. Jackson and . Electrodynamics, , 1962.

R. Kjellander and S. Mar?elja, Correlation and image charge effects in electric double layers, Chemical Physics Letters, vol.112, issue.1, pp.49-53, 1984.

R. Kjellander and S. Mar?elja, Inhomogeneous Coulomb Fluids with Image Interactions Between Planar Surfaces. I, J. Chem. Phys, vol.82, issue.4, pp.2122-2135, 1985.

R. Kjellander and S. Et-mar?elja, Interaction of Charged Surfaces in Electrolyte Solutions, Chemical Physics Letters, vol.127, issue.4, pp.402-407, 1986.

R. Kjellander and S. Mar?elja, Inhomogeneous Coulomb fluids with image interactions between planar surfaces. III. Distribution functions, J. Chem. Phys, vol.88, issue.11, pp.7138-7146, 1988.

R. Kjellander, Inhomogeneous Coulomb fluids with image interactions between planar surfaces. II. On the anisotropic hypernetted chain approximation, J. Chem. Phys, vol.88, issue.11, pp.7129-7137, 1988.

F. Lado, Hypernetted-Chain Solutions for the Two-Dimensional Classic Electron Gas, Physical Review B, vol.17, issue.7, pp.2827-2832, 1978.

F. Lado, Numerical Fourier Transform in One, Two, three Dimensions for Liquid State Calculations, Journal of Computational Physics, vol.8, pp.417-433, 1971.

L. D. Landau and E. M. Lifchitz, Electrodynamics of Continuous Media, 1960.

S. A. Lima, M. A. Murad, C. Moyne, and D. Stemmelen, A Three-Scale Model of pH-Dependent Flows and Ion Transport with Equilibrium Adsorption in Kaolinite Clays : I. Homogenization Analysis, Transport in Porous Media, vol.85, pp.23-44, 2010.

M. Lozada-cassou, The Force Between Two Planar Electrical Double Layers, J. Chem. Phys, vol.80, issue.7, pp.3344-3349, 1984.

M. Lozada-cassou and E. Díaz-herrera, Three Point Extension for the Hypernetted Chain and Other Integral Equation Theories, J. Chem. Phys, vol.92, issue.2, pp.1194-1210, 1990.

J. Mainka, M. A. Murad, C. Moyne, and S. A. Lima, A New Modified Effective Stress Principle for Unsaturated Swelling Clays Rigorously Derived from Microstructure, 2013.

V. Marry, J. F. Dufreche, M. Jardat, G. Meriguet, P. Turp et al., Dynamics and Transport in Charged Porous Media, Coll. and Surf. A, vol.222, pp.147-153, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00173458

D. A. Mcquarrie, Statistical Mechanics. University Science Books, 2000.

L. Mier-y-teran, S. H. Suh, S. White, and H. T. Davis, A Non-Local Free-Energy Density-Functional Approximation For the Electrical Double Layer, J. Chem. Phys, vol.92, issue.8, pp.5087-5098, 1990.

J. K. Mitchell, Fundamentals of Soil Behavior, 1993.

C. Moyne and M. A. Murad, Electro-Chemo-Mechanical Couplings in Swelling Clays Derived from Micro/Macro Homogenization Procedure, International Journal of Solids and Structures, vol.39, pp.6159-6190, 2002.

C. Moyne and M. A. Murad, Macroscopic Behaviour of Swelling Porous Media Derived from Micromechanical Analysis, Transport in Porous Media, vol.50, pp.127-151, 2003.

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

C. Moyne and M. A. Murad, A Two-Scale Model for Coupled Electro-Chemo-Mechanical Phenomena and Onsager's Reciprocity Relations in Expansive Clays : II Computational Validation, Transport in Porous Media, vol.63, pp.13-56, 2006.

M. A. Murad and C. Moyne, Micromechanical Computational Modeling of Expansive Porous Media, C. R. Mecanique, vol.330, pp.865-870, 2002.

M. A. Murad and C. Moyne, A Dual-Porosity Model for Ionic Solute Transport in Expansive Clays, Computational Geosciences, vol.12, pp.47-82, 2008.

W. Olivares and D. A. Mcquarrie, Interaction Between Electrical Double Layers, J. Phys. Chem, vol.84, pp.863-867, 1980.

A. C. Rocha, Modelos Computacionais Multiescala de Meios Porosos Expansivos Derivados a Partir da Mecânica Estatística, Dissertação de Mestrado. LNCC, 2013.

E. Sanchez-palencia, Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics, 1980.

J. F. Springer, M. A. Pokrant, F. A. Stevens, and . Jr, Integral Equation Solutions for the Classical Electron Gas, J. Chem. Phys, vol.88, issue.11, pp.7129-7137, 1973.

T. Zixiang, L. Mier-y-teran, H. T. Davis, L. E. Scriven, and H. S. White, Non-Local Free-Energy Density-Functional Theory Applied to the Electrical Double Layer. Part I : Symmetrical Electrolytes, Molecular Physics, vol.71, issue.2, pp.369-392, 1990.

T. Zixiang, L. E. Scriven, and H. T. Davis, Interactions between Primitive Electrical Double Layers, J. Chem. Phys, vol.97, issue.12, pp.9258-9266, 1992.

E. Thiele, Equation of State of Hard Spheres, J. Chem. Phys, vol.39, 1963.

S. Torquato, Random Heterogeneous Materials : Microstructure and Macroscopic Properties, 2002.

J. P. Valleau, R. Ivkov, and G. M. Torrie, Colloid stability : The Forces between the Charged Surfaces in an Electrolyte, J. Chem. Phys, vol.95, issue.1, pp.520-533, 1991.

. Van-olphen, An Introduction to Clay Colloid Chemistry : for Clay Technologists, Geologists, and Soil Scientists, 1977.

E. Waisman and J. L. Lebowitz, Mean Spherical Model Integral Equation for Charged Hard Spheres. I. Method of solution, J. Chem. Phys, vol.56, issue.6, pp.3086-3093, 1972.

E. Waisman and J. L. Lebowitz, Mean Spherical Model Integral Equation for Charged Hard Spheres. II. Results, J. Chem. Phys, vol.56, issue.6, pp.3093-3099, 1972.

M. S. Wertheim, Exact Solution of the Percus-Yevick Equation for Hard Spheres, Phys. Rev. Lett, vol.10, 1963.

E. Wernersson and R. Kjellander, On the Effect of Image Charges and Ion-Wall Dispersion Forces on Electric Double Layer Interactions, J. Chem. Phys, vol.125, 2006.

, Pour comprendre la situation à la nanoéchelle et prendre en compte les corrélations entre les ions de taille finie, des modèles plus élaborés que l'équation de Poisson-Boltzmann sont construits. Le premier combine la théorie de la fonctionnelle de densité (DFT) et l'approximation de la moyenne sphérique (MSA) pour décrire les corrélations ioniques ; le second résout l'équation de Ornstein-Zernike dans le cadre de l'approximation Hyper Netted Chain (HNC). La mécanique du système à la nanoéchelle est ensuite analysée soigneusement à partir du tenseur intermoléculaire de Irving-Kirkwood et la vérification de l'équilibre mécanique fournit un test de la qualité des modèles étudiés, Ce travail est consacré à l'étude des effets électro-chimio-mécaniques pour des argiles (smectites) saturées par un électrolyte aqueux en utilisant les outils de la mécanique statistique

, Une méthode d'homogénéisation périodique est utilisée pour effectuer un double changement d'échelle (nano, micro, macro) et obtenir les lois constitutives macroscopiques : définition de la pression de gonflement et propriétes de transport dans une approche à double porosité. Enfin, le modèle de trois échelles est appliqué à la simulation d

, Mots-clés : mécanique statistique, argile gonflante, homogénéisation, milieu poreux, pression de disjonction