N. Alcantar, J. Israelachvili, and J. Boles, Forces and ionic transport between mica surfaces: implications for pressure solution, Geochimica et Cosmochimica Acta, vol.67, issue.7, pp.1289-1304, 2003.
DOI : 10.1016/S0016-7037(02)01270-X

R. Aris, Vectors, Tensors, and the basic Equations of Fluid Mechanics, 1989.

J. Barlow, Optimal stress locations in finite element models, International Journal for Numerical Methods in Engineering, vol.2, issue.2, pp.243-251, 1976.
DOI : 10.1002/nme.1620100202

R. C. Bathrust, Diagenetic fabrics in some British Dinantian limestones, Geological Journal, vol.104, issue.1, pp.11-36, 1958.
DOI : 10.1002/gj.3350020103

R. M. Bowen and J. C. Wiese, Diffusion in mixtures of elastic materials, International Journal of Engineering Science, vol.7, issue.7, pp.689-722, 1969.
DOI : 10.1016/0020-7225(69)90048-2

J. S. Chester, S. C. Lenz, F. M. Chester, and R. A. Lang, Mechanisms of compaction of quartz sand at diagenetic conditions, Earth and Planetary Science Letters, vol.220, issue.3-4, pp.435-451, 2004.
DOI : 10.1016/S0012-821X(04)00054-8

C. Chiu and H. Gao, Stress singularities along a cycloid rough surface, International Journal of Solids and Structures, vol.30, issue.21, pp.2983-3012, 1993.

R. L. Coble, A Model for Boundary Diffusion Controlled Creep in Polycrystalline Materials, Journal of Applied Physics, vol.34, issue.6, pp.1679-1682, 1963.
DOI : 10.1063/1.1702656

S. W. Den-brok and J. Morel, The effect of elastic strain on the microstructure of free surfaces of stressed minerals in contact with an aqueous solution, Geophysical Research Letters, vol.42, issue.8, pp.603-606, 2001.
DOI : 10.1029/2000GL011461

G. Dhatt and G. Touzot, Une présentation de la méthode des éléments finis, 2ème édition, Éditions Maloine, 1984.

E. Gundersen, F. Renard, D. K. Dysthe, K. Bjorlykke, and B. Jamtveit, Coupling between pressure solution creep and diffusive mass transport in porous rocks, Journal of Geophysical Research: Solid Earth, vol.69, issue.B11, pp.1-19, 2002.
DOI : 10.1029/2001JB000287

Y. C. Fung, Foundations of solid mechanics New Jersey, 1965. [13] H. Gao. A boundary perturbation analysis for elastic inclusions and interfaces, International Journal of Solids and Structures, vol.28, issue.6, pp.703-725, 1991.

H. Gao, STRESS ANALYSIS OF HOLES IN ANISOTROPIC ELASTIC SOLIDS: CONFORMAL MAPPING AND BOUNDARY PERTURBATION, The Quarterly Journal of Mechanics and Applied Mathematics, vol.45, issue.2, pp.149-168, 1992.
DOI : 10.1093/qjmam/45.2.149

J. Ghoussoub, Modélisation du mécanisme de déformation, transfert en solution, à l'échelle du joint de grain, 2000.

J. Ghoussoub and Y. M. Leroy, Solid???fluid phase transformation within grain boundaries during compaction by pressure solution, Journal of the Mechanics and Physics of Solids, vol.49, issue.10, pp.2385-2430, 2001.
DOI : 10.1016/S0022-5096(01)00012-6

URL : https://hal.archives-ouvertes.fr/hal-00111330

J. W. Gibbs, On the equilibrium of heterogeneous substances, The scientific Papers of J. Willard Gibbs, 1961.
DOI : 10.2475/ajs.s3-16.96.441

J. Gratier, Experimental pressure solution of Halite by an indenter technique, Geophysical Research Letters, vol.324, issue.15, pp.1647-1650, 1993.
DOI : 10.1029/93GL01398

J. Gratier, Le fluage des roches par dissolution-cristallisation sous contrainte dans la croûte supérieure, pp.267-287, 1993.

J. Gratier, F. Renard, and P. Labaume, How pressure solution creep and fracturing processes interact in the upper crust to make it behave in both a brittle and viscous manner, Journal of Structural Geology, vol.21, issue.8-9, pp.1189-1197, 1991.
DOI : 10.1016/S0191-8141(99)00035-8

J. P. Gratier and R. Guiguet, Experimental pressure solution-deposition on quartz grains: the crucial effect of the nature of the fluid, Journal of Structural Geology, vol.8, issue.8, pp.189-200, 1986.
DOI : 10.1016/0191-8141(86)90030-1

J. P. Gratier, L. Jenatton, D. Tisserand, and R. Guiguet, Indenter studies of the swelling, creep and pressure solution of Bure argillite, Applied Clay Science, vol.26, issue.1-4, pp.459-472, 2004.
DOI : 10.1016/j.clay.2003.12.035

A. J. Gratz, Solution-transfer compaction of quartzites: Progress toward a rate law, Geology, vol.19, issue.9, pp.901-904, 1991.
DOI : 10.1130/0091-7613(1991)019<0901:STCOQP>2.3.CO;2

S. R. De-groot and P. Mazur, Non-equilibrium Themodynamics, 1984.

J. Guarrigues, La méthode des éléments finis, 2002.

W. He, A. Hajash, and D. Sparks, Creep compaction of quartz aggregates: Effects of pore-fluid flow--A combined experimental and theoretical study, American Journal of Science, vol.303, issue.2, pp.73-93, 2003.
DOI : 10.2475/ajs.303.2.73

W. K. Heidug and Y. M. Leroy, Geometrical evolution of stressed and curved solid-fluid phase boundaries: 1. Transformation kinetics, Journal of Geophysical Research: Solid Earth, vol.95, issue.B1, pp.505-515, 1994.
DOI : 10.1029/93JB02573

R. Hellmann, P. J. Renders, J. Gratier, and R. Guiguet, Experimental pressure solution compaction of chalk in aqueous solutions. Part 1. Deformation behavior and chemistry, Walter-Rock Interactions, Ore deposits, and Environnmental Geochemistry : A tribute to David A. Crerar, pp.129-152, 2002.

E. Hinton and J. S. Campbell, Local and global smoothing of discontinuous finite element functions using a least squares method, International Journal for Numerical Methods in Engineering, vol.98, issue.3, pp.461-480, 1974.
DOI : 10.1002/nme.1620080303

D. W. Houseknecht, Influence of Grain Size and Temperature on Intergranular Pressure Solution, Quartz Cementation, and Porosity in a Quartzose Sandstone, SEPM Journal of Sedimentary Research, vol.54, issue.2, pp.348-0361, 1984.
DOI : 10.1306/212F8418-2B24-11D7-8648000102C1865D

D. W. Houseknecht, Assessing the relative importance of compaction processes and cementation to reduction of porosity in sandstones, The American Association of Petroleum Geologists Bulletin, vol.71, pp.633-642, 1987.

D. W. Houseknecht, Intergranular pressure solution in four quartzose sandtsones, Journal of Sedimentary Petrology, vol.58, issue.2, pp.228-246, 1988.

T. J. Hugues, The finite element method -Linear Static and Dynamic Finite Element Analysis, 1987.

D. Koehn, J. Arnold, B. Jamtveit, and A. Malthe-sorenssen, Free surface dissolution of stresses solids, Journal of the Virtual Explorer, vol.14, 2003.

P. Labaume and I. Moretti, Diagenesis-dependence of cataclastic thrust fault zone sealing in sandstones. Example from the Bolivian Sub-Andean Zone, Journal of Structural Geology, vol.23, issue.11, pp.1659-1675, 2001.
DOI : 10.1016/S0191-8141(01)00024-4

P. Labaume, S. Sheppard, and I. Moretti, Structure and hydraulic behaviour of cataclastic thrust fault zones in sandstones, Sub-Andean Zone, Bolivia, Journal of Geochemical Exploration, vol.69, issue.70, pp.69-70487, 2000.
DOI : 10.1016/S0375-6742(00)00097-2

P. Labaume, S. Sheppard, and I. Moretti, Fluid flow in cataclastic thrust fault zones in sandstones, Sub-Andean Zone, southern Bolivia, Tectonophysics, vol.340, issue.3-4, pp.141-172, 2001.
DOI : 10.1016/S0040-1951(01)00144-5

F. K. Lehner, Thermodynamics of rock deformation by pressure solution, Deformation Processes in Minerals, Ceramics and Rocks, pp.296-333, 1990.
DOI : 10.1007/978-94-011-6827-4_12

F. K. Lehner, A model for intergranular pressure solution in open systems, Tectonophysics, vol.245, issue.3-4, pp.153-170, 1995.
DOI : 10.1016/0040-1951(94)00232-X

F. K. Lehner and J. Bataille, Nonequilibrium thermodynamics of pressure solution, Pure and Applied Geophysics PAGEOPH, vol.78, issue.No. 4, pp.53-8585, 1984.
DOI : 10.1007/BF00879649

F. K. Lehner and Y. M. Leroy, Sandstone Compaction by Intergranular Pressure Solution, Mechanics of Fluid-Saturated Rocks, pp.115-168
DOI : 10.1016/S0074-6142(03)80019-0

URL : https://hal.archives-ouvertes.fr/hal-00112505

Y. M. Leroy and W. K. Heidug, Geometrical evolution of stressed and curved solid-fluid phase boundaries: 2. Stability of cylindrical pores, Journal of Geophysical Research: Solid Earth, vol.95, issue.B1, pp.517-530, 1994.
DOI : 10.1029/93JB02572

D. Leythaeuser, O. Borromeo, F. Mosca, R. Di-primio, M. Radke et al., Pressure solution in carbonate source rocks and its control on petroleum generation and migration. Marine and Petroleum Geology, pp.1-717, 1995.

K. W. Liu, Deep-burial diagenesis of the siliciclastic Ordovician Natal Group, South Africa, Sedimentary Geology, vol.154, issue.3-4, pp.177-189, 2003.
DOI : 10.1016/S0037-0738(02)00161-6

R. Marfil, M. Scherer, and M. J. Turrero, Diagenetic processes influencing porosity in sandstones from the Triassic Buntsandstein of the Iberian Range, Spain, Sedimentary Geology, vol.105, issue.3-4, pp.203-219, 1996.
DOI : 10.1016/0037-0738(95)00138-7

. Ph, P. Mestat, and . Humbert, Référentiel de tests pour la vérification de la programmation des lois de comportement dans les logiciel d'éléments finis, Bulletin des Laboratoires des Ponts et Chaussées, vol.230, pp.23-38, 2001.

C. Misbah, F. Renard, J. P. Gratier, and K. Kassner, Dynamics of a dissolution front for solids under stress, Geophysical Research Letters, vol.71, issue.6, p.31, 2004.
DOI : 10.1029/2003GL019136

URL : https://hal.archives-ouvertes.fr/hal-00105688

J. Morel and S. W. Brok, Increase in dissolution rate of sodium chlorate induced by elastic strain, Journal of Crystal Growth, vol.222, issue.3, pp.637-644, 2001.
DOI : 10.1016/S0022-0248(00)00931-3

N. I. Muskhelichvili, Some basic problems of the mathematical theory of elasticity : fundamental equations plane theory of elasticity, torsion and bending, 1953.
DOI : 10.1007/978-94-017-3034-1

A. R. Niemeijer, C. J. Spiers, and B. Bos, Compaction creep of quartz sand at 400???600??C: experimental evidence for dissolution-controlled pressure solution, Earth and Planetary Science Letters, vol.195, issue.3-4, pp.261-275, 2002.
DOI : 10.1016/S0012-821X(01)00593-3

R. Raj, Creep in polycrystalline aggregates by matter transport through a liquid phase, Journal of Geophysical Research: Solid Earth, vol.5, issue.B6, pp.4731-4739, 1982.
DOI : 10.1029/JB087iB06p04731

F. Renard, D. K. Dysthe, J. Feder, B. Bjørlykke, and B. Jamtveit, Enhanced pressure solution creep rates induced by clay particles: Experimental evidence in salt aggregates, Geophysical Research Letters, vol.51, issue.7, pp.1295-1298, 2001.
DOI : 10.1029/2000GL012394

F. Renard, J. P. Gratier, and B. Jamtveit, Kinetics of crack-sealing, intergranular pressure solution, and compaction around active faults, Journal of Structural Geology, vol.22, issue.10, pp.1395-1407, 2000.
DOI : 10.1016/S0191-8141(00)00064-X

F. Renard, A. Park, P. Ortoleva, and J. Gratier, An integrated model for transitional pressure solution in sandstones, Tectonophysics, vol.312, issue.2-4, pp.97-115, 1999.
DOI : 10.1016/S0040-1951(99)00202-4

J. D. Rimstidt and H. L. Barnes, The kinetics of silica-water reactions, Geochimica et Cosmochimica Acta, vol.44, issue.11, pp.1683-1699, 1980.
DOI : 10.1016/0016-7037(80)90220-3

P. F. Robin, Pressure solution at grain-to-grain contacts, Geochimica et Cosmochimica Acta, vol.42, issue.9, pp.1383-1389, 1978.
DOI : 10.1016/0016-7037(78)90043-1

E. H. Rutter, The Kinetics of Rock Deformation by Pressure Solution [and Discussion], Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.283, issue.1312, pp.203-219, 1976.
DOI : 10.1098/rsta.1976.0079

J. Salençon, Mécanique des milieux continus (Tomes I, II et III) Éditions de l'École Polytechnique, 2000.

P. M. Schutjens, Intergranular pressure solution in halite aggregates and quartz sands : an experimental investigation, 1991.

P. M. Schutjens and C. J. Spiers, Intergranular pressure solution in NaCl : Grainto-grain contact experiments under the optical microscope. Oil and Gas Science and Technology -Rev, IFP, vol.54, issue.6, pp.729-750, 1999.

H. A. Sheldon, J. W. Wheeler, R. H. Worden, and M. J. Cheadle, An Analysis of the Roles of Stress, Temperature, and pH in Chemical Compaction of Sandstones, Journal of Sedimentary Research, vol.73, issue.1, pp.64-71, 2003.
DOI : 10.1306/070802730064

I. Shimizu, Kinetics of pressure solution creep in quartz: theoretical considerations, Tectonophysics, vol.245, issue.3-4, pp.121-134, 1995.
DOI : 10.1016/0040-1951(94)00230-7

C. J. Spiers and P. M. Schutjens, Densification of crystalline aggregates by fluid-phase diffusional creep, Deformation Processes in Minerals, Ceramics and Rocks, pp.296-333, 1990.
DOI : 10.1007/978-94-011-6827-4_13

C. J. Spiers, P. M. Schutjens, R. Brzesowsky, and C. Peach, Experimental determination of constitutive parameters governing creep of rocksalt by pressure solution, Deformation Mechanisms, Rheology and Tectonics, pp.215-227, 1990.
DOI : 10.1144/GSL.SP.1990.054.01.21

D. J. Srolovitz, On the stability of surfaces of stresses solids, Acta Metallica, vol.32, issue.2, pp.621-625, 1989.

R. Tada, R. Maliva, and R. Siever, A new mechanism for pressure solution in porous quartzose sandstone, Geochimica et Cosmochimica Acta, vol.51, issue.9, pp.2295-2301, 1987.
DOI : 10.1016/0016-7037(87)90282-1

R. Tada and R. Siever, Experimental knife-edge pressure solution of halite, Geochimica et Cosmochimica Acta, vol.50, issue.1, pp.29-36, 1986.
DOI : 10.1016/0016-7037(86)90045-1

N. Takeno, T. Ishido, and J. W. Pritchett, Alteration zonation of silica minerals in geothermal system ? A numerical simulation based on reaction-transport model, Proceedings 20th New Zealand Geothermal Workshop, pp.259-264, 1998.

C. Wang, Applied elasticity, 1953.

R. P. Wintsch and K. Yi, Dissolution and replacement creep: a significant deformation mechanism in mid-crustal rocks, Journal of Structural Geology, vol.24, issue.6-7, pp.1179-1193, 2002.
DOI : 10.1016/S0191-8141(01)00100-6

P. Wriggers, Computational contact mechanics, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00466790

X. Yang, Pressure solution in sedimentary basins: effect of temperature gradient, Earth and Planetary Science Letters, vol.176, issue.2, pp.233-243, 2000.
DOI : 10.1016/S0012-821X(99)00321-0

O. C. Zienkiewicz, R. L. Taylor, and J. M. Too, Reduced integration technique in general analysis of plates and shells, International Journal for Numerical Methods in Engineering, vol.4, issue.2, pp.275-290, 1971.
DOI : 10.1002/nme.1620030211

O. C. Zienkiewicz and J. Z. Zhu, The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique, International Journal for Numerical Methods in Engineering, vol.31, issue.7, pp.1331-1364, 1992.
DOI : 10.1002/nme.1620330702

. Zlamal, Superconvergence and Reduced Integration in the Finite Element Method, Mathematics of Computation, vol.32, issue.143, pp.663-685, 1978.
DOI : 10.2307/2006479