A. and N. En, Eurocode 2 ? Calcul des structures en béton ? partie 2: ponts en béton-Calcul et dispositifs constructives ? Annexe nationale à la NF EN, 1992.

A. and N. En, Applications ferroviaires -Voie -Traverses et supports en béton, pp.13-230, 1999.

N. Baghdadi, F. Toutlemonde, and J. Seignol, Modélisation de l'effet des contraintes sur l'anisotropie de l'expansion dans les bétons atteints de réactions de gonflement interne, Conférence AUGC

N. Baghdadi, J. Seignol, and F. Toutlemonde, 2007-b) Modélisation du couplage chimico mécanique pour calculer une structure en béton atteinte de réaction sulfatique interne, 18ème Congrès Français de Mécanique, p.295, 2007.

N. Baghdadi, J. F. Seignol, R. Martin, J. Renaud, and F. Toutlemonde, 2008-a) Effect of early age heat-treatment on the expansion due to delayed ettringite formation: experimental study and model Calibration, 2nd Euro-Mediterranean Symposium on Advances in Geomaterial and structures AGS2008, pp.661-666, 2008.

N. Baghdadi, F. Toutlemonde, and J. F. Seignol, Chemo-mechanical model describing the expansion due to internal sulfate attack : numerical simulation, Concrete Modelling CONMOD'08, pp.58291-298, 2008.

R. Barbarulo, Comportement des Matériaux Cimentaires : actions des sulfates et de la température, Thèse de doctorat, 2002.

R. Barbarulo, H. Peycelon, S. Prené, and J. Marchand, Delayed ettringite formation symptoms on mortars induced by high temperature due to cement heat of hydration or late thermal cycle, Cement and Concrete Research, vol.35, issue.1, pp.125-131, 2005.
DOI : 10.1016/j.cemconres.2004.05.041

V. Baroghel-bouny, Caractérisation des pâtes de ciment et des bétons ? Méthodes, annalyses, interprétations, 1994.

V. Baroghel-bouny, M. Mainguy, T. Lassabatere, and O. Coussy, Characterization and identification of equilibrium and transfer moisture properties for ordinary and high-performance cementitious materials, Cement and Concrete Research, vol.29, issue.8, pp.1225-1238, 1999.
DOI : 10.1016/S0008-8846(99)00102-7

URL : https://hal.archives-ouvertes.fr/hal-00586623

L. Berntsson and S. Chandra, Deterioration of concrete in swimming pools in the south of Sweden, ACI Materials Journal, vol.85, issue.6, pp.489-494, 1988.

X. Brunetaud, Etude de l'influence des paramètres sur la cinétique et l'intensité de la réaction sulfatique interne au béton, 2005.

B. Capra and J. P. Bournazel, « Modelling of alkali aggregate reaction induced mechanical effects in concrete, Proceedings of the International Conference on Concrete : from material to structure, pp.260-267, 1996.

B. Capra and A. Sellier, Modelling of alkali-aggregate reaction: orthotropic behaviour and numerical simulations , Concrete science and engineering, pp.56-70, 2002.

R. W. Carlson, Drying shrinkage of large concrete members, Journal of American Concrete Institute, vol.33, pp.327-336, 1937.

P. Ciarlet, introduction à l'analyse numérique matricielle et à l'optimisation, 2006.

J. Clément, Recalage des températures du béton de la semelle de la pile P1. Rapport d'activité n°34208699 -Verrieres -A.I.O.A, p.1, 2001.

M. Collepardi, Damage by delayed ettringite formation, concrete international, pp.69-74, 1999.

M. Collepardi and J. Olagot, The influence of microcracking and high sulfate clinker cements on expansion following cures at 20 and 90°C. Internal Sulfate Attack and Delayed Ettringite Formation, Proceedings of the International RILEM TC 186-ISA Workshop. PRO 35, 2004.

C. W. Correns, Growth and dissolution of crystals under linear pressure, Disc, pp.267-271, 1949.

O. Coussy and F. J. Ulm, Creep and plasticity due to chemo-mechanical couplings, Archive of Applied Mechanics 66, pp.523-535, 1996.

S. Diamond, Delayed ettringite formation ??? Processes and problems, Cement and Concrete Composites, vol.18, issue.3, pp.205-215, 1996.
DOI : 10.1016/0958-9465(96)00017-0

R. L. Day, The Effect of Secondary Ettringite Formation on the Durability of Concrete : A literature Analysis. Research and Development Bulletin RD108T, Portland Cement Association, 1992.

L. Divet, Les réactions sulfatiques internes au béton: contribution à l'étude des mécanismes de la formation différée de l'ettringite, Thèse de doctorat, Conservatoire National des Arts et Métiers, 2001.

L. Divet, F. Guerrier, L. Mestre, and G. , Existe-t-il un risque d'attaque sulfatique endogène dans les pièces en béton de grande masse ?, Bulletin des Laboratoires des Ponts et Chaussées, vol.213, pp.59-72, 1998.

S. Duszak and W. Et-kurdowski, Effects of Cement Parameters on Expansion Associated with DEF, Proceedings of the International RILEM TC 186-ISA Workshop on Internal Sulfate Attack and Delayed Ettringite Formation, pp.229-234, 2002.

M. R. Fairbairn, Smeared cracking FEM simulation of Alkali-silica expansion using a new macroscopic coupled model, Proceeding of the 12th International conference on Alkaliaggregate reaction in concrete ICAAR2004, pp.104-114, 2004.

C. Famy, Expansion of heat-cured mortars, Thèse de doctorat, 1999.

C. Famy, K. Scrivener, A. Atkinson, and A. Brough, Influence of the storage conditions on the dimensional changes of heat-cured mortars, Cement and Concrete Research, vol.31, issue.5, pp.795-803, 2001.
DOI : 10.1016/S0008-8846(01)00480-X

C. Famy, K. L. Scrivener, and A. R. Brough, Role of Microstructural Characterization in Understanding the Mechanism of Expansion Due to Delayed Ettringite Formation, proceedings of the International RILEM TC 186-ISA Workshop on Internal Sulfate Attack and Delayed Ettringite Formation, pp.167-172, 2002.

J. R. Flatt and G. W. Scherer, Thermodynamics of crystallization stresses in DEF, Cement and Concrete Research, vol.38, issue.3, pp.1729-1736, 2002.
DOI : 10.1016/j.cemconres.2007.10.002

Y. Fu and J. J. Beaudoin, Mechanisms of Delayed Ettringite Formation in Portland Cement Systems ACI, Materials Journal, vol.93, issue.4, 1996.

Y. Fu, J. Ding, and J. J. Et-beaudoin, Expansion of portland cement mortar due to internal sulfate attack, Cement and Concrete Research, vol.27, issue.9, pp.1299-1306, 1997.
DOI : 10.1016/S0008-8846(97)00133-6

Y. Fu, Delayed Ettringite Formation in Portland Cement Products, Thèse de doctorat, 1996.

E. J. Garboczi, Stress, displacement, and expansive cracking around a single spherical aggregate under different expansive conditions, Cement and Concrete Research, vol.27, issue.4, pp.495-500, 1997.
DOI : 10.1016/S0008-8846(97)00029-X

B. Godart, G. Kittel, and P. Fasseu, Manuel d'identification des réactions de degradation interne du béton dans les ouvrages d'art, 1999.

J. P. Gomes, Analysis of concrete dams under swelling processes , proceedings of the 12th international conference on alkali-aggregate reaction in concrete, pp.1148-1157, 2004.

L. A. Graf-noriega, Effect of Relative Humidity on Expansion and Microstructure of Heat cured Mortars, 2007.

L. Granger, Comportement différé du béton dans les enceintes de centrales nucléaires : analyse et modélisation, Thèse de Doctorat, Ecole Nationale des Ponts et Chaussées, 1995.

P. E. Grattan-bellew and J. Beaudoin, Effect of aggregate particle size and composition on expansion of mortar bars due to delayed ettringite formation, Cement and Concrete Research, vol.28, issue.8, pp.1147-1156, 1998.
DOI : 10.1016/S0008-8846(98)00084-2

E. Grimal, Caractérisation des effets du gonflement provoqué par la réaction alcali-silice sur le comportement mécanique d'une structure en béton thèse de doctorat, 2007.

. Grimal, Drying shrinkage mechanisms in Portland cement pastes, Journal of the American Ceramic Society, vol.70, pp.5-323, 1987.

D. Heinz, Deleterious Formation of Ettringite-like Phases in Heat-treated Mortars and Concretes, Thesis (Doctor of Engineering), 1986.

D. Heinz and U. Ludwig, Mechanism of secondary ettringite formation in mortars and concretes subjected to heat treatment, Concrete durability, American Concrete Institute, pp.2059-2071, 1987.

D. Heinz, U. Ludwig, and I. Rüdiger, Delayed ettringite formation in heat treated mortars and concretes, Concrete Precasting Plant and Technology, vol.11, pp.56-61, 1989.

D. Heinz, M. Kalde, U. Ludwig, and I. Ruediger, Present State of Investigation on Damaging Late Ettringite Formation (DLEF) in Mortars and Concretes Ettringite ? The Sometimes Host of Destruction, pp.177-178, 1999.

W. Hime, Delayed Ettringite Formation A Concern for Precast Concrete?, PCI Journal, vol.41, issue.4, pp.26-30, 1996.
DOI : 10.15554/pcij.07011996.26.30

W. G. Hime, S. Et, and . Marusin, Delayed Ettringite Formation : Many Questions and Some Answers In : Ettringite The sometimes host of destruction, pp.199-206, 1999.

D. Hobbs, Cracking of concrete attributed to delayed ettringite formation, Proceeding of the eleventh annual BCA/concrete society conference on hier education and the concrete industry, pp.51-60, 2001.

P. Humbert, A. Dubouchet, G. Fezans, and D. Remaud, CESAR-LCPC, un progiciel de calcul dédié au génie civil, pp.7-37, 2005.

A. F. Inderwick, Leistungsfaehigkeit einiger Betonschwellen in Nordamerika Performance of some concrete railway cross ties in North America, Betonwerk und Fertigteil- Technik/Concrete Precasting Plant and Technology, pp.118-122, 1972.

V. Johansen, N. Thaulow, and J. Skalny, Simultaneous presence of alkali ??? silica gel and ettringite in concrete, Advances in Cement Research, vol.5, issue.17, pp.23-29, 1993.
DOI : 10.1680/adcr.1993.5.17.23

S. Kelham, The influence of cement composition on the volume stability of mortars, volume SP 177,chapter Ettringite ? The sometimes host of destruction, pp.27-45, 1999.

S. Kelham, The effect of cement composition and fineness on expansion associated with delayed ettringite formation, Cement and Concrete Composites, vol.18, issue.3, pp.171-177, 1996.
DOI : 10.1016/0958-9465(95)00013-5

C. Larive, Apports combinés de l'expérimentation et la modélisation à la compréhension de l'alcali-réaction et de ses effets mécaniques, 1998.

C. D. Lawrence, Laboratory studies of concrete expansion arising from delayed ettringite formation, 1993.

C. D. Lawrence, Delayed Ettringinte Formation: An issue?, Materials Science of Concrete IV J. Skalny & S. Mindess, pp.113-154, 1995.

C. D. Lawrence, Mortar expansions due to delayed ettringite formation. Effects of curing period and temperature, Cement and Concrete Research, vol.25, issue.4, pp.903-914
DOI : 10.1016/0008-8846(95)00081-M

C. D. Lawrence, Long-term expansion of mortars and concretes, volume SP 177, chapter Ettringite ? Thesometimes host of destruction, pp.105-123, 1999.

M. Lewis, Heat curing and delayed ettringite formation in concretes, Thèse de doctorat, 1996.

M. C. Lewis, K. L. Scrivener, and S. Kelham, Heat Curing and Delayed Ettringite Formation, MRS Proceedings, vol.60, pp.67-76, 1995.
DOI : 10.1557/PROC-370-67

K. Li, O. Coussy, and C. Larive, Modélisation chimico-mécanique du comportement des bétons affectés par la réaction d'alcali-silice, p.43, 2004.

N. Louarn and C. Larive, Alcali-réaction et réaction sulfatique: synthèse des études microscopiques d'expertises de ponts dégradés, Bulletin de Liaison des Laboratoires des Ponts et Chaussées, vol.184, pp.57-69, 1993.

A. Pavoine and L. Divet, Réactivité d'une formule de béton vis-à-vis d'une réaction sulfatique interne, Technique et méthodes LPC Pavoine A. et Divet L. Essai d'expansion résiduelle sur carotte de béton extraite de l'ouvrage, LPC, vol.59, 2003.

. Lrpc-d-'aix-en-provence, Inspection détaillée de l'ouvrage, Nom de l'ouvrage: Viaduc de Fozieres, Direction Departementale de l'equipement des l'Herault, 1997.

R. Martin, D. Seigert, and F. Toutlemonde, Etude expérimentale des effets mécaniques de la réaction sulfatique interne ? Rapport d'avancement phase 1, 2006.

R. P. Martin, D. Seigert, and F. Toutlemonde, Experimental Analysis of Concrete Structures Affected by DEF, pp.333-340, 2008.
DOI : 10.1002/9781118623565.ch61

URL : https://hal.archives-ouvertes.fr/hal-00586928

R. P. Martin, Analyse sur structures modèles des effets mécaniques de la réaction sulfatique interne, Ecole Nationale des Ponts et Chausses, 2009.

S. L. Marusin, SEM Studies of Concrete Failures Caused by Delayed Ettringite Formation, Proceedings of the 4th Euroseminar on Microscopy Applied to Building Materials, p.15, 1993.

S. L. Marusin, 1993-b) SEM Studies of DEF in Hardened Concrete, Proceedings of the 15th International Conference in Cement Microscopy, pp.289-299, 1993.

S. L. Marusin, A Simple Treatment to Distinguish Alkali -Silica Gel From Delayed Ettringite Formations in Concrete, Magazine of Concrete Research, pp.163-166, 1994.

S. L. Marusin, Concrete Failure Caused by Delayed Ettringite Formation, Case Study, 3rd CANMET/ACI International Conference on Durability of Concrete, pp.79-94, 1994.

V. Michaud and R. Suderman, Solubility of Sulfates in High SO3 Clinkers, Ettringite: the Sometimes Host of Destruction, ACI International, pp.177-179, 1999.

P. K. Metha, Mechanism of Expansion Associated with Ettringite Formation, Cement and Concrete Research, vol.3, pp.1-6, 1973.

H. G. Midgeley and K. Pettifer, The micro structure of hydrated super sulphated cement, Cement and Concrete Research, vol.1, issue.1, pp.101-104, 1971.
DOI : 10.1016/0008-8846(71)90086-X

R. Mielenz, «Investigation of prestressed concrete railway tie distress» Concrete International, pp.62-68, 1995.

S. Multon, Evaluation expérimentale et théorique des effets mécaniques de l'alcaliréaction sur des structures modèles, 2004.

S. Multon and F. Toutlemonde, Effect of applied stresses on alkali???silica reaction-induced expansions, Cement and Concrete Research, vol.36, issue.5, pp.912-920, 2006.
DOI : 10.1016/j.cemconres.2005.11.012

S. Multon, F. X. Barin, B. Godart, and F. Toutlemonde, Estimation of the Residual Expansion of Concrete Affected by Alkali Silica Reaction, Journal of Materials in Civil Engineering, vol.20, issue.1, pp.154-62, 2008.
DOI : 10.1061/(ASCE)0899-1561(2008)20:1(54)

I. Odler, Hydratation, Setting, and Hardening of Portland Cement, in Lea's Chemistry of Cement and Concrete, pp.288-289, 1998.

I. Odler and Y. Chen, Effect of cement composition on the expansion of heat-cured cement pastes, Cement and Concrete Research, vol.25, issue.4, pp.853-862, 1995.
DOI : 10.1016/0008-8846(95)00076-O

I. Odler and . Y. Chen, On the delayed expansion of heat cured Portland cement pastes and concretes, Cement and Concrete Composites, vol.18, issue.3, pp.181-185, 1996.
DOI : 10.1016/0958-9465(95)00014-3

C. Ouyang, A. Nanni, and W. Chang, Internal and external sources of sulfate ions in portland cement mortar: two types of chemical attack, Cement and Concrete Research, vol.18, issue.5, pp.699-709, 1988.
DOI : 10.1016/0008-8846(88)90092-0

A. Pavoine, Evaluation du potentiel de réactivité des bétons vis-à-vis de la formation différée de l'ettringite, Thèse de doctorat, 2003.

N. Petrov and A. Tagnit-hamou, Is microcracking really a precursor to delayed ettringite formation and consequent expansion?, ACI Materials Journal, vol.101, issue.6, pp.442-447, 2004.

N. Petrov, Combined Effect of Different Factors on Concrete Expansion due to DEF, Thèse de doctorat, 2003.

J. Piau, N. Dtnl, and . Texo, CESAR-LCPC version Standard ? Manuel théorique : Les modules de diffusion non linéaire, p.5, 1991.

A. B. Poole, Introduction to alkali-aggregate reaction in concrete, in « The alkali-silica reaction in Concrete, 1992.

J. Pourchez, F. Valdivieso, P. Grosseau, R. Guyonnet, and B. Guilhot, Kinetic modelling of the thermal decomposition of ettringite into metaettringite. Cement and Concrete Research, pp.2054-2060, 2006.
URL : https://hal.archives-ouvertes.fr/emse-00449727

S. Poyet, Etude de la dégradation des ouvrages en béton atteints par la réaction alcali silice : Approche expérimentale et modélisation numérique multi-échelles des dégradations dans un environnement hydro-chemo-mécanique variable, 2003.

V. Saouma and L. Perotti, Constitutive Model for Alkali Aggregate Reactions, American Concrete Institute, Materials Journal, vol.103, issue.3, pp.194-202, 2006.

F. W. Scott, Ettringite: Cancer of Concrete, p.72, 1997.

K. Scrivener, D. Damidot, and C. Famy, Possible mechanisms of expansion of concrete exposed to elevated temperatures during curing (Also known as DEF) and implications for avoidance of field problems, Cem. Concr. Aggr, CCAGDP, vol.21, issue.1, pp.93-101, 1999.

K. L. Scrivener, A. Guidoum, and V. Mathier, Role of cracks in delayed ettringite formation. Workshop on Internal Sulfate Attack and Delayed Ettringite Formation, RILEM proceedings PRO 35 p, pp.259-262, 2004.

G. W. Scherer, Stress from crystallization of salt, Cement and Concrete Research, vol.34, issue.9, pp.1613-1624, 2004.
DOI : 10.1016/j.cemconres.2003.12.034

J. F. Seignol, T. T. Ngo, and F. Toutlemonde, Modeling of the coupling between moisture and alkali-silica reaction in concrete, in computational modelling of concrete structure, proceeding of EURO-C, pp.27-30639, 2006.

A. Sellier, Modélisations probabilistes du comportement de matériaux et de structures en génie civil, Thèse de doctorat de l'Ecole Normale Supérieure de Cachan, 2006.

A. Sellier and B. Capra, Modélisation physico-chimique de la réaction alcali-granulats, pp.445-481, 1997.

A. Sellier, B. Capra, C. Tognazzi, and S. Poyet, Couplage dégradation?diffusion, chapitre 8 de la communication : La dégradation des bétons?couplage fissuration?dégradation chimique, sous la direction de, Plas dans la série : communications en mécanique, éditions Hermès, 1999.

A. Shayan and G. W. Quick, Relative importance of deleterious reactions in concrete: formation of AAR products and secondary ettringi te, Advances in Cement Research, vol.4, issue.16, pp.149-157, 1991.
DOI : 10.1680/adcr.1992.4.16.149

A. Shayan and G. W. Quick, 1992-a) Microscopic Features of Cracked and Uncracked Concrete Railway Sleepers, ACI Materials Journal, vol.89, issue.4, pp.348-361

A. Shayan and G. W. Quick, 1992-b) Sequence of Formation of Deleterious Alkali-Aggregate Reactivity Products and Secondary Ettringite in the Same Mortar and Concrete Specimens, Proceedings of the 14th International Conference on Cement Microscopy, pp.11-21

A. Shayan and G. W. Quick, Alkali-Aggregate Reaction in Concrete Railway Sleepers From Finland, Proceedings of the 16th International Conference on Cement Microscopy, pp.69-79, 1994.

Y. Shimada, V. C. Johansen, F. M. Miller, and T. O. Mason, Chemical Path of Ettringite Formation in Heat-cured Mortar and Its Relationship to Expansion: A Literature Review, p.46, 2005.

P. Soroushian and M. Elzafraney, Damage effects on concrete performance and microstructure, Cement and Concrete Composites, vol.26, issue.7, pp.853-859, 2004.
DOI : 10.1016/j.cemconcomp.2003.05.001

J. Stark, K. Bollmann, and J. Seyfarth, Investigation into delayed ettringite formation in concrete, Proceedings of the 9th International Congress on the Chemistry of Cement, pp.348-354, 1992.

M. Steiger, Crystal growth in porous materials???II: Influence of crystal size on the crystallization pressure, Journal of Crystal Growth, vol.282, issue.3-4, pp.455-469, 2005.
DOI : 10.1016/j.jcrysgro.2005.05.008

J. P. Skalny and N. Thaulow, Sulfate attack in North America, Proceedings of the 1st international conference on thaumasite in cementitious materials, pp.63-70, 2002.

H. F. Taylor, Delayed ettringite formation, Advances in Cement and Concrete, pp.122-131, 1994.
DOI : 10.1016/S0008-8846(01)00466-5

H. Taylor, C. Famy, and K. Scrivener, Delayed ettringite formation, Cement and Concrete Research, vol.31, issue.5, pp.683-693, 2001.
DOI : 10.1016/S0008-8846(01)00466-5

. Tepponen, Damages in concrete railway sleepers in Finland, pp.199-209, 1987.

J. M. Torrenti, L. Granger, M. Diruy, and P. Genin, Modélisation du retrait du béton en ambiance variable , Revue Française de Génie Civil, pp.4-687, 1997.

F. J. Ulm, Couplages thermocémomécaniques dans les béton, Laboratoire centrale des ponts et chaussées O, p.31, 1999.

G. J. Verbeck and R. A. Helmuth, « Structures and physical properties of cement paste, 5th International Symposium on Chemistry of Cement, pp.1-36, 1968.

. Viaduc-de-foziere, NC202c Descente de Charge, A75 section Pegairolles -Lodeve Nord, Réparation du viaduc de Foziere, 2006.

K. Willam and E. P. Warnke, Constitutive Models for the Triaxial Behaviour of Concrete, Proc., Int. Assoc. Bridge Struct. Eng, vol.19, pp.1-30, 1975.

R. Yang, C. Lawrence, C. Lynsale, and J. Sharp, Delayed ettringite formation in heat-cured Portland cement mortars, Cement and Concrete Research, vol.29, issue.1, pp.17-25, 1999.
DOI : 10.1016/S0008-8846(98)00168-9

Z. Zhang, J. Olek, and S. Diamond, Studies on delayed ettringite formation in early-age, heat-cured mortars, Cement and Concrete Research, vol.32, issue.11, pp.1729-1736, 2002.
DOI : 10.1016/S0008-8846(02)00862-1

D. Annexes and . Texo, Série de cas tests servant à modéliser la RSI : Tube épais

. Objectif-du-test, Enchaînement de calculs pour modéliser la réaction sulfatique interne : 1 : tubpl_hum : calcul du champ de teneur en eau, 2 : tubpl_ther : calcul du champ de température, 3 : tubpl_texo : calcul de l'évolution de la température au jeune âge, p.Bidimensionnel

. Nb, noeuds : 28 Nb. éléments : 5 Nb, p.1

. Nb, noeuds : 28 Nb. éléments : 6 Nb

. Nb, noeuds : 28 Nb. éléments : 6 Nb

A. Figure, Evolution du champ de l'humidité dans les trois cas de figures (tube épais) à T f, Calcul THERMIQUE AU JEUNE ÂGE A -Axisymétrique (2D) B -Plane (2D)

A. Figure, Evolution du champ de la température au jeune âge dans les trois cas de figures (tube épais) à T f

. Conditions-aux-limites, Les conditions aux limites sont de types déplacements, afin d'empêcher tout mouvement de corps rigide Aucune force (volumique ou surfacique) n'est appliquée au tube

A. Figure, 12 Conditions limites appliquées au tube RHO = 0 ; YOUNG = 35000

. Conditions-aux-limites, Les conditions aux limites sont de types déplacements, afin d'empêcher tout mouvement de corps rigide Aucune force (volumique ou surfacique) n'est appliquée au tube

. Conditions-aux-limites, Les conditions aux limites sont de types déplacements, afin d'empêcher tout mouvement de corps rigide Aucune force (volumique ou surfacique) n'est appliquée au tube