.. Celluleséquivalentescelluleséquivalentes-cylindriques-de-section-elliptique, 57 3.3.1 Description géométrique de la cellulé equivalente, p.58

.. Estimations-basées-sur-l-'´-ecoulement-de-poiseuille, 78 3.5.1 Ecoulement de Poiseuille avec glissement aux parois, p.79

D. Matériaux, 90 4.1.1 Origines, aspect et préparation des matériaux, p.93

R. Et-relative-au-gaz and .. , 103 4.3.1 Caractérisation du réseau poreux, p.112

J. Atkinson, The Mechanics of Soils and Foundations, 1993.

J. L. Auriault and E. Sanchez-palencia, Etude du comportement macroscopique d'un milieu poreux saturé déformable, Journal de Mécanique, vol.16, pp.575-603, 1977.

J. Barthélémy, Approche micromécanique de la rupture et de la fissuration dans les géomatériaux, Thèse de doctorat, Ecole Nationale des Ponts et Chaussées, 2005.

J. Barthélémy, Dormieux : A micromechanical approach to the strength criterion of drucker-prager materials reinforced by rigid inclusions, International Journal for Numerical and Analytical Methods in Geomechanics, vol.28, pp.7-8565, 2004.

J. Barthélémy, Effective Permeability of Media with a Dense Network of Long and Micro Fractures, Transport in Porous Media, vol.452, issue.1950, pp.153-178, 2009.
DOI : 10.1007/s11242-008-9241-9

J. Barthélémy and L. Dormieux, Micromechanical approach to the modelling of compaction at large strains, Computers and Geotechnics, vol.30, issue.4, pp.321-338, 2003.
DOI : 10.1016/S0266-352X(03)00006-5

J. G. Berryman, Computing variational bounds for flow through random aggregates of spheres, Journal of Computational Physics, vol.52, issue.1, pp.142-162, 1983.
DOI : 10.1016/0021-9991(83)90021-9

J. G. Berryman, Measurement of spatial correlation functions using image processing techniques, Journal of Applied Physics, vol.57, issue.7, pp.2374-2384, 1985.
DOI : 10.1063/1.334346

J. G. Berryman and G. W. Milton, Normalization constraint for variational bounds on fluid permeability, The Journal of Chemical Physics, vol.83, issue.2, pp.754-760, 1985.
DOI : 10.1063/1.449489

F. Bignonnet, Dormieux : FFT-based homogenization of permeability using a hashin-shtrikman type variational framework, Poromechanics V, pp.1245-1254, 2013.

F. Bignonnet and L. , FFT-based bounds on the permeability of complex microstructures, International Journal for Numerical and Analytical Methods in Geomechanics, vol.33, issue.20-22, pp.1707-1723, 2014.
DOI : 10.1002/nag.2278
URL : https://hal.archives-ouvertes.fr/hal-01084229

F. Bignonnet, L. Dormieux, and E. Lemarchand, Strength of a matrix with elliptic criterion reinforced by rigid inclusions with imperfect interfaces, European Journal of Mechanics - A/Solids, vol.52, 2014.
DOI : 10.1016/j.euromechsol.2015.02.003
URL : https://hal.archives-ouvertes.fr/hal-01160108

F. Bignonnet, K. Sab, L. Dormieux, S. Brisard, and A. Bisson, Macroscopically consistent non-local modeling of heterogeneous media, Computer Methods in Applied Mechanics and Engineering, vol.278, pp.218-238, 2014.
DOI : 10.1016/j.cma.2014.05.014

J. Bleyer and P. De-buhan, Yield surface approximation for lower and upper bound yield design of 3D composite frame structures, Computers & Structures, vol.129, pp.86-98, 2013.
DOI : 10.1016/j.compstruc.2013.08.011
URL : https://hal.archives-ouvertes.fr/hal-00870789

M. J. Blunt, M. D. Jackson, M. Piri, and P. H. , Valvatne : Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multi-phase flow, Advances in Water Ressources, pp.1069-1089, 2002.

C. Boutin, Study of permeability by periodic and self-consistent homogenisation, European Journal of Mechanics - A/Solids, vol.19, issue.4, pp.603-632, 2000.
DOI : 10.1016/S0997-7538(00)00174-1
URL : https://hal.archives-ouvertes.fr/hal-00943756

S. Brisard, Analyse morphologique et homogénéisation numérique -applicationàapplication`applicationà la pâte de ciment, Thèse de doctorat, 2011.

S. Brisard, FFT-based methods for the mechanics of composites: A general variational framework, Computational Materials Science, vol.49, issue.3, pp.663-671, 2010.
DOI : 10.1016/j.commatsci.2010.06.009
URL : https://hal.archives-ouvertes.fr/hal-00722339

S. Brisard and L. Dormieux, Combining galerkin approximation techniques and the principle of hashin and shtrikman to improve two fft-based numerical methods for the homogenization of composites, Computer Methods in Applied Mechanics and Engineering, pp.217-220197, 2012.

S. Cariou, Couplage hydro-mécanique et transfert dans l'argilite de Meuse/Haute- Marne : approches expérimentale et multi-´ echelle, Thèse de doctorat, ´ Ecole Nationale des Ponts et Chaussées, 2010.

W. Chen, J. Liu, F. Brue, F. Skoczylas, C. Davy et al., Water retention and gas relative permeability of two industrial concretes, Cement and Concrete Research, vol.42, issue.7, pp.1001-1013, 2012.
DOI : 10.1016/j.cemconres.2012.04.003
URL : https://hal.archives-ouvertes.fr/hal-00702563

A. T. Chwang and T. Y. Wu, Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows, Journal of Fluid Mechanics, vol.76, issue.04, pp.787-815, 1975.
DOI : 10.1063/1.1730995

G. Dassios, The fundamental solutions for irrotational and rotational Stokes flow in spheroidal geometry, Math. Proc. Camb, 2007.
DOI : 10.1016/S0020-7225(02)00004-6

G. Dassios, M. Hadjinicolaou, and F. , Coutelieris et A. Payatakes : Stokes flow in spheroidal particle-in-cell models with happel and kuwabara boundary conditions, Int. J

G. Dassios, Vafeas : On the spheroidal semiseparation for stokes flow, Research Letters in Physics, 2008.

P. De-buhan, Approche fondamentale du Calcuì a la Rupture des ouvrages en sols

P. De-buhan and L. Dormieux, On the validity of the effective stress concept for assessing the strength of saturated porous materials: A homogenization approach, Journal of the Mechanics and Physics of Solids, vol.44, issue.10, pp.441649-1667, 1996.
DOI : 10.1016/0022-5096(96)00046-4
URL : https://hal.archives-ouvertes.fr/hal-00111515

D. N. Dewhurst, R. M. Jones, and M. D. Raven, Microstructural and petrophysical characterization of Muderong Shale: application to top seal risking, Petroleum Geoscience, vol.8, issue.4, pp.371-383, 2002.
DOI : 10.1144/petgeo.8.4.371

M. Doi, A New Variational Approach to the Diffusion and the Flow Problem in Porous Media, Journal of the Physical Society of Japan, vol.40, issue.2, pp.567-572, 1976.
DOI : 10.1143/JPSJ.40.567

L. Dormieux, L. Jeannin, E. Bemer, T. H. Le, and J. Sanahuja, Micromechanical models of the strength of a sandstone, International Journal for Numerical and Analytical Methods in Geomechanics, vol.330, issue.4, pp.249-271, 2010.
DOI : 10.1002/nag.804

L. Dormieux, L. Jeannin, and N. Gland, Homogenized models of stress-sensitive reservoir rocks, International Journal of Engineering Science, vol.49, issue.5, pp.386-396, 2011.
DOI : 10.1016/j.ijengsci.2010.12.010

L. Dormieux, A. Molinari, and D. Kondo, Micromechanical approach to the behavior of poroelastic materials, Journal of the Mechanics and Physics of Solids, vol.50, issue.10, pp.2203-2231, 2002.
DOI : 10.1016/S0022-5096(02)00008-X
URL : https://hal.archives-ouvertes.fr/hal-00140491

L. Dormieux and D. Kondo, Approche microm??canique du couplage perm??abilit?????endommagement, Comptes Rendus M??canique, vol.332, issue.2, pp.135-140, 2004.
DOI : 10.1016/j.crme.2003.11.003

H. Ene and E. Sanchez-palencia, Equations et phénomènes de surface pour l'´ ecoulement dans un modèle de milieu poreux, Journal de Mécanique, pp.73-108, 1975.

E. Fathi, A. Tinni, and I. Y. , Correction to Klinkenberg slip theory for gas flow in nano-capillaries, International Journal of Coal Geology, vol.103, pp.51-59, 2012.
DOI : 10.1016/j.coal.2012.06.008

M. Frémond, Frià a : Analyse limite. comparaison des méthodes statique et cinématique, C.R. Acad. Sci. Paris, vol.286, pp.107-110, 1978.

M. Frigo and S. G. Johnson, The Design and Implementation of FFTW3, Proceedings of the IEEE, vol.93, issue.2, pp.216-231, 2005.
DOI : 10.1109/JPROC.2004.840301

Y. C. Fung and P. Tong, Classical and computational solid mechanics, 2001.

J. A. Given, Stell : Improved permeability bounds for highly polydisperse materials. Physics of Fluids A : Fluid Dynamics, pp.1929-1936, 1990.

S. Gounand, Introduction la méthode desélémentsdeséléments finis en mécanique des fluides incompressibles . CommissariatàCommissariatà l' ´ Energie Atomique et auxÉnergiesaux´auxÉnergies Alternatives, 2012.

M. Gueguin, G. Hassen, J. Bleyer, and P. De-buhan, An optimization method for approximating the macroscopic strength criterion of stone column reinforced soils, Proceedings of the 3rd International Symposium on Computational Geomechanics, pp.484-494, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00860900

A. Gurson, Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I???Yield Criteria and Flow Rules for Porous Ductile Media, Journal of Engineering Materials and Technology, vol.99, issue.1, pp.2-15, 1977.
DOI : 10.1115/1.3443401

Z. Hashin, The Spherical Inclusion With Imperfect Interface, Journal of Applied Mechanics, vol.58, issue.2, pp.444-449, 1991.
DOI : 10.1115/1.2897205

Z. Hashin and S. Shtrikman, On some variational principles in anisotropic and nonhomogeneous elasticity, Journal of the Mechanics and Physics of Solids, vol.10, issue.4, pp.335-342, 1962.
DOI : 10.1016/0022-5096(62)90004-2

Z. He, L. Dormieux, and D. Kondo, Strength properties of a Drucker???Prager porous medium reinforced by rigid particles, International Journal of Plasticity, vol.51, pp.218-240, 2013.
DOI : 10.1016/j.ijplas.2013.05.003
URL : https://hal.archives-ouvertes.fr/hal-00871515

Z. He, L. Dormieux, E. Lemarchand, and D. Kondo, Cohesive Mohr???Coulomb interface effects on the strength criterion of materials with granular-based microstructure, European Journal of Mechanics - A/Solids, vol.42, pp.430-440, 2013.
DOI : 10.1016/j.euromechsol.2013.06.009
URL : https://hal.archives-ouvertes.fr/hal-00946078

Y. Jung and S. Torquato, Fluid permeabilities of triply periodic minimal surfaces, Physical Review E, vol.72, issue.5, 2005.
DOI : 10.1103/PhysRevE.72.056319

E. H. Kennard, Kinetic theory of gases, 1938.

L. J. Klinkenberg, The permeability of porous media to liquid and gases API 11th mid-year meeting, API Drilling and Production Practices, pp.200-213, 1941.

D. Kong, Z. Cui, Y. Pan, and K. Zhang, On the papkovich-neuber formulation for stokes flows driven by a translating/rotating prolate spheroid at arbitrary angles, Int. J. Pure App. Math, vol.75, pp.455-483, 2012.

K. Krabbenhoft, A. Lyamin, and S. Sloan, Formulation and solution of some plasticity problems as conic programs, International Journal of Solids and Structures, vol.44, issue.5, pp.1533-1549, 2007.
DOI : 10.1016/j.ijsolstr.2006.06.036

W. Kreher, Residual stresses and stored elastic energy of composites and polycrystals, Journal of the Mechanics and Physics of Solids, vol.38, issue.1, pp.115-128, 1990.
DOI : 10.1016/0022-5096(90)90023-W

S. Kuwabara, The Forces experienced by Randomly Distributed Parallel Circular Cylinders or Spheres in a Viscous Flow at Small Reynolds Numbers, Journal of the Physical Society of Japan, vol.14, issue.4, pp.527-532, 1959.
DOI : 10.1143/JPSJ.14.527

J. Leblond, G. Perrin, and P. Suquet, Exact results and approximate models for porous viscoplastic solids, International Journal of Plasticity, vol.10, issue.3, pp.213-235, 1994.
DOI : 10.1016/0749-6419(94)90001-9

Y. Maalej, L. Dormieux, and J. Sanahuja, Elastic nonlinear behaviour of a granular medium : micromechanical approach, Comptes Rendus Mécanique, vol.8, pp.461-466, 2007.

Y. Maalej, L. Dormieux, and J. Sanahuja, Micromechanical approach to the failure criterion of granular media, European Journal of Mechanics - A/Solids, vol.28, issue.3, pp.647-653, 2009.
DOI : 10.1016/j.euromechsol.2008.10.010

S. Maghous, L. Dormieux, and J. Barthélémy, Micromechanical approach to the strength properties of frictional geomaterials, European Journal of Mechanics - A/Solids, vol.28, issue.1, pp.179-188, 2009.
DOI : 10.1016/j.euromechsol.2008.03.002

S. Maghous, Détermination du critère de résistance macroscopique d'un matériau hétérogènè a structure périodique, Thèse de doctorat, ´ Ecole Nationale des Ponts et Chaussées, 1991.

J. C. Michel and H. Moulinec, A computational scheme for linear and non???linear composites with arbitrary phase contrast, International Journal for Numerical Methods in Engineering, vol.58, issue.12, pp.139-160, 2001.
DOI : 10.1002/nme.275

C. A. Miller and S. Torquato, Diffusion-controlled reactions among spherical traps: Effect of polydispersity in trap size, Physical Review B, vol.40, issue.10, pp.7101-7108, 1989.
DOI : 10.1103/PhysRevB.40.7101

C. J. Modica and S. G. Lapierre, Estimation of kerogen porosity in source rocks as a function of thermal transformation: Example from the Mowry Shale in the Powder River Basin of Wyoming, AAPG Bulletin, vol.96, issue.1, pp.87-108, 2012.
DOI : 10.1306/04111110201

A. Moghadam and R. Chalaturnyk, Expansion of the Klinkenberg's slippage equation to low permeability porous media, International Journal of Coal Geology, vol.123, pp.2-9, 2013.
DOI : 10.1016/j.coal.2013.10.008

V. Monchiet, A polarization-based FFT iterative scheme for computing the effective properties of elastic composites with arbitrary contrast, International Journal for Numerical Methods in Engineering, vol.21, issue.3, pp.1419-1436, 2012.
DOI : 10.1002/nme.3295
URL : https://hal.archives-ouvertes.fr/hal-00687816

H. Moulinec and P. Suquet, A fast numerical method for computing the linear and non linear properties of composites, Comptes Rendus de l'Académie des Sciences, pp.1417-1423, 1994.

H. Moulinec, A numerical method for computing the overall response of nonlinear composites with complex microstructure, Computer Methods in Applied Mechanics and Engineering, vol.157, issue.1-2, pp.69-94, 1998.
DOI : 10.1016/S0045-7825(97)00218-1
URL : https://hal.archives-ouvertes.fr/hal-01282728

N. I. Muskhelishvili, Some basic problems of the mathematical theory of elasticity, 1954.
DOI : 10.1007/978-94-017-3034-1

J. Nadah, F. Bignonnet, C. A. Davy, F. Skoczylas, D. Troadec et al., Microstructure and poro-mechanical performance of Haubourdin chalk, International Journal of Rock Mechanics and Mining Sciences, vol.58, pp.149-165, 2013.
DOI : 10.1016/j.ijrmms.2012.11.001

T. Nguyen and V. Monchiet, Bonnet : A fourier based numerical method for computing the dynamic permeability of periodic porous media, European Journal of Mechanics B/Fluids, vol.37, 2013.

F. Pastor, D. Kondo, and J. Pastor, 3D-FEM formulations of limit analysis methods for porous pressure-sensitive materials, International Journal for Numerical Methods in Engineering, vol.39, issue.212, pp.847-870, 2013.
DOI : 10.1002/nme.4527

B. T. Porodnov, P. E. Suetin, S. F. Borisov, and V. D. , Experimental investigation of rarefied gas flow in different channels, Journal of Fluid Mechanics, vol.42, issue.03, pp.417-438, 1974.
DOI : 10.1063/1.1693786

S. Prager, Viscous Flow through Porous Media, Physics of Fluids, vol.4, issue.12, pp.1477-1482, 1961.
DOI : 10.1063/1.1706246

B. Revil-baudard and O. , New three-dimensional strain-rate potentials for isotropic porous metals: Role of the plastic flow of the matrix, International Journal of Plasticity, vol.60, pp.101-117, 2014.
DOI : 10.1016/j.ijplas.2014.04.003

A. Richelsen and V. Tvergaard, Dilatant plasticity or upper bound estimates for porous ductile solids, Acta Metallurgica et Materialia, vol.42, issue.8, pp.2561-2577, 1994.
DOI : 10.1016/0956-7151(94)90198-8

J. Robinet, P. Sardini, D. Coelho, D. Jean-claude-parneix, S. Pret et al., Effects of mineral distribution at mesoscopic scale on solute diffusion in a clay-rich rock: Example of the Callovo-Oxfordian mudstone (Bure, France), Water Resources Research, vol.42, issue.4, 2012.
DOI : 10.1029/2011WR011352
URL : https://hal.archives-ouvertes.fr/hal-00827642

J. Rubinstein and S. Torquato, Flow in random porous media: mathematical formulation, variational principles, and rigorous bounds, Journal of Fluid Mechanics, vol.1, issue.-1, pp.25-46, 1989.
DOI : 10.1016/0301-9322(82)90047-7

J. Salencon, An introduction to the yield design theory and its applications to soil mechanics, European Journal of Mechanics, vol.9, pp.477-500, 1990.

J. Salençon, Calcuì a la rupture et analyse limite, 1983.

J. Sanahuja, Impact de la morphologie structurale sur les performances mécaniques des matériaux de construction : application au plâtre etàet`età la pâte de ciment, Thèse de doctorat, ´ Ecole Nationale des Ponts et Chaussées, 2008.

J. Sanahuja and L. Dormieux, R??sistance d'un milieu poreux ?? phase solide h??t??rog??ne, Comptes Rendus M??canique, vol.333, issue.11, pp.818-823, 2005.
DOI : 10.1016/j.crme.2005.09.008

A. Sangani, Slow flow through a periodic array of spheres, International Journal of Multiphase Flow, vol.8, issue.4, pp.343-360, 1982.
DOI : 10.1016/0301-9322(82)90047-7

A. Schofield and P. , Wroth : Critical State Soil Mechanics, 1968.

F. Sharipov, Data on the velocity slip and temperature jump coefficients In Thermal and Mechanical Simulation and Experiments in Micro-Electronics and Micro-Systems, Proc. 5th Int.Conf. EuroSimE (Belgium), pp.243-249, 2004.

W. Shen, L. Dormieux, D. Kondo, and J. Shao, A closed-form three scale model for ductile rocks with a plastically compressible porous matrix, Mechanics of Materials, vol.59, pp.73-86, 2012.
DOI : 10.1016/j.mechmat.2012.12.008
URL : https://hal.archives-ouvertes.fr/hal-00946070

F. Skoczylas and E. Dana, Gas relative permeability and pore structure of sandstones, International Journal of Rock Mechanics and Mining Sciences, 1999.

Y. Song, Rétention d'eau et microstructure fine de l'argilite de Bure, Thèse de doctorat, 2014.

P. Suquet, Analyse limite et homogénéisation, CRAS, vol.296, pp.1355-1358, 1983.

P. Suquet, Effective behavior of nonlinear composites, Continuum Micromechanics, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00214215

P. Tardif, Hamonville : Modélisation et simulation du transport advectif et diffusif en milieu poreux monophasique et diphasique, Thèse de doctorat, ´ Ecole Nationale des Ponts et Chaussées, 2006.

V. Tarnow, Airflow resistivity of models of fibrous acoustic materials, The Journal of the Acoustical Society of America, vol.100, issue.6, pp.3706-3713, 1996.
DOI : 10.1121/1.417233

S. Timoshenko and J. N. Goodier, Theory of elasticity, 1951.

J. Tölke, C. Baldwin, Y. Mu, N. D. Fang, A. Grader et al., Computer simulations of fluid flow in sediment : from images to permeability. The Leading Edge, pp.68-74, 2010.

S. Torquato, Microstructure characterization and bulk properties of disordered two-phase media, Journal of Statistical Physics, vol.33, issue.5-6, pp.843-873, 1986.
DOI : 10.1007/BF01020577

S. Torquato, Effective stiffness tensor of composite media???I. Exact series expansions, Journal of the Mechanics and Physics of Solids, vol.45, issue.9, pp.1421-1448, 1997.
DOI : 10.1016/S0022-5096(97)00019-7

S. Torquato and B. Lu, Rigorous bounds on the fluid permeability : Effect of polydispersivity in grain size. Physics of Fluids A : Fluid Dynamics, pp.487-490, 1990.

P. Vafeas, Dassios : Stokes flows in ellipsoidal geometry, J. Math. Physics, p.47, 2006.

P. Vincent, P. Suquet, Y. Monerie, and H. Moulinec, Effective flow surface of porous materials with two populations of voids under internal pressure: II. Full-field simulations, International Journal of Plasticity, vol.56, pp.74-98, 2014.
DOI : 10.1016/j.ijplas.2013.11.012
URL : https://hal.archives-ouvertes.fr/hal-00912637

H. L. Weissberg and S. Prager, Viscous Flow through Porous Media. III. Upper Bounds on the Permeability for a Simple Random Geometry, Physics of Fluids, vol.13, issue.12, pp.2958-2965, 1970.
DOI : 10.1063/1.1692887

A. Wiegmann, Computation of the permeability of porous materials from their microstructure by fff-stokes, Berichte des Fraunhofer ITWM, vol.129, 2007.

J. Willis, Bounds and self-consistent estimates for the overall properties of anisotropic composites, Journal of the Mechanics and Physics of Solids, vol.25, issue.3, pp.185-202, 1977.
DOI : 10.1016/0022-5096(77)90022-9