A. Abbas, Ecoulement gazeux dans les bétons partiellement saturés : application á la mesure de perméabilité, 1998.

A. Abbas, M. Carcasses, and O. , Gas permeability of concrete in relation to its degree of saturation, Materials and Structures, vol.32, p.38, 1999.

P. Acker, Comportement mécanique du béton : apport de l'apporche physicochimique, Retraits et ssurations du béton : Causes, mécanismes, modèles, 1988.

P. Acker, M. Mamillan, and B. Miao, Drying and shrinkage of concrete: the case of massive parts, Serviceability and Durability of Construction Materials, 1990.

V. Baroghel-bouny, Caractérisation des pâtes de ciment et des bétons, 1994.

. Méthodes,

J. Baron, Le béton hydraulique : connaissance et pratique. .Les retraits de la pâte de ciment, 1982.

H. F. El-baroudy, The strength, shrinkage, and creep of concrete as aecting the design of re-inforced concrete structures containing liquids, 1940.

F. M. Bartlett and . Macgregor,

J. G. , Eect of moisture condition on concrete core strengths, In: Materials Journal, vol.91, issue.3, p.227236, 1994.

Z. P. Baºant, A. B. Hauggaaed, S. Baweja, and F. , , 1997.

, Microprestress-solidication theory for concrete creep. I: Aging and drying eects

, Journal of Engineering Mechanics, vol.123, issue.11, p.11881194

Z. P. Baºant and J. Chern, Concrete creep at variable humidity : constitutive law and mechanism, Material and Structures, vol.18, issue.1, p.120, 1985.

Z. P. Baºant and F. H. Wittmann, Creep and Shrinkage in Concrete Structures, 1982.

Z. P. Baºant and Y. Xi, Drying creep of concrete : constitutive model and new experiments separating its mechanisms, Materials and Structures, vol.27, p.314, 1994.

F. Beltzung and F. H. Wittmann, Role of disjoining pressure in cement based materials, Rencontres AUGCIBPSA, vol.35, p.23642370, 2005.

F. Benboudjema, Modélisation des déformations diérées du béton sous sollicitations biaxiales. Application aux enceintes de connemant de bâtiments réacteurs des centrales nucléaires, 2002.

J. Bisschop, L. Pel, and J. G. Van-mier, Eect of aggregate size and paste volume on drying shrinkage microcracking in cement-based composites, Creep, Shrinkage and Durability Mechanics of Concrete and other Quasi-Brittle Materials, Proc. of CONCREEP-6 at MIT, p.81, 2001.

, Bibliography/References

A. Shamaa and M. , Etude sur le risque de développement d'une réaction sulfatique interne et de ses conséquences dans les bétons de structure des ouvrages nucléaires, 2012.

X. Brunetaud, Étude de l'influence de différents paramètres et de leurs interactions sur la cinétique et l'amplitude de la réaction sulfatique interne au béton, Thesis, École Centrale des Arts et Manufactures « École Centrale, 2005.

P. Grattan-bellew, J. Beaudoin, and V. Vallee, Effect of aggregate particle size and composition on expansion of mortar bars due to delayed ettringite formation, Cement and Concrete Research, vol.28, pp.1147-1156, 1998.

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.

B. Kchakech, Etude de l'influence de l'échauffement subi par un béton sur le risque d'expansions associées à la Réaction Sulfatique Interne, 2015.

, Réactivité d'un béton vis-à-vis d'une réaction sulfatique interne. Essai de performance, techniques et méthodes des laboratoires des ponts et chaussées, 2007.

P. J. Monteiro and P. K. Mehta, The transition zone between aggregate and type K expansive cement, Cement and Concrete Research, vol.16, pp.111-114, 1986.

N. F. En, Essai pour béton durci -résistance à la compression des éprouvettes, pp.12390-12393, 2003.

A. E. Moore and H. F. Taylor, Acta Crystallographica, vol.26, issue.4, pp.386-393, 1970.

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.

A. Pavoine, X. Brunetaud, and L. Divet, The impact of ciment parameters on Delayed Ettringite Formation, vol.34, pp.521-528, 2012.

, Determination of the fracture energy of mortar and concrete by means of threepoint bend tests on notched beams" References, RILEM 95

H. F. Taylor, C. Famy, and K. L. Scrivener, Delayed ettringite formation, Cem. Concr. Res, vol.31, pp.683-693, 2001.

M. Shamaa, S. Lavaud, L. Divet, G. Nahas, and J. Torrenti, Coupling between mechanical and transfer properties and expansion due to DEF in a concrete of a nuclear power plant, Nucl. Eng. Des, vol.266, pp.70-77, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01727440

, Impact of drying cycles on the swelling of concrete samples with calcareous aggregates. Experimental data and numerical simulation

M. Malbois, / Construction and Building Materials, vol.207, pp.396-402, 2019.

M. M. Karthik, J. B. Mander, and S. Hurlebaus, Experimental behavior of large reinforced concrete specimen with ASR and DEF deterioration, J. Struct. Eng, vol.144, issue.8, p.4018110, 2018.

A. Pavoine, X. Brunetaud, and L. Divet, The impact of cement parameters on delayed ettringite formation, Cem. Concr. Compos, vol.34, pp.521-528, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00853358

I. Odler and Y. Chen, Effect of cement composition on the expansion of heat-cured cement pastes, Cem. Concr. Res, vol.25, pp.853-862, 1995.

S. Kelham, The effect of cement composition and fineness on expansion associated with delayed ettringite formation, Cem. Concr. Compos, vol.18, pp.171-179, 1996.

X. Brunetaud, R. Linder, D. Duragrin, and D. Damidot, Effect of curing conditions and concrete mix design on the expansion generated by delayed ettringite formation, Mater. Struct, vol.40, pp.567-578, 2007.

P. J. Monteiro and P. K. Mehta, The tranzition zone between aggregate and type k expansive cement, Cem. Concr. Res, vol.16, pp.111-114, 1986.

P. E. Grattan-bellew, J. J. Beaudoin, and V. G. Vallee, Effect of aggregate particle size and composition on expansion of mortars bars due to delayed ettringite formation, Cem. Concr. Res, vol.28, issue.8, pp.1147-1156, 1998.

X. Brunetaud, Etude de l'influence de différents paramètres et de leurs intéractions sur la cinétique et l'amplitude de la réaction sulfatique interne, 2005.

M. Shamaa, S. Lavaud, L. Divet, J. B. Colliat, G. Nahas et al., Influence of limestone filler and of the size of the aggregates on def, Cem. Concr. Compos, vol.71, pp.175-180, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01726822

C. D. Lawrence, Mortar expansions due to delayed ettringite formation. Effect of curing period and temperature, Cem. Concr. Res, vol.25, pp.903-914, 1995.

B. Kchakech, Etude de l'influence de l'échauffement subi par un béton sur le risque d'expansions associées à la réaction sulfatique interne, 2015.

A. E. Moore and H. F. Taylor, Crystal structure of ettringite, Acta Crystallogr. A, vol.26, issue.4, pp.386-393, 1970.

C. Famy, K. L. Scrivener, A. Atkinson, and A. R. Brough, Influence of the storage conditions on the dimensional changes of heat-cured mortars, Cem. Concr. Res, vol.31, pp.795-803, 2001.

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

L. Graf, Effect of relative humidity on expansion and microstructure of heatcured mortars, Portland Cem. Assoc, p.50, 2007.

R. Martin, Experimental analysis of the mechanical effects of delayed ettringite formation on concrete structures, 2010.

M. Shamaa, S. Lavaud, L. Divet, G. Nahas, and J. Torrenti, Influence of relative humidity on delayed ettringite formation, Cem. Concr. Compos, vol.58, pp.14-22, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01214456

M. M. Karthik, J. B. Mander, and S. Hurlebaus, ASR/DEF related expansion in structural concrete: model developments and validation, Constr. Build. Mater, vol.128, pp.238-247, 2016.

A. Sellier and S. Multon, Chemical modelling of delayed ettringite formation for assessment of affected concrete structures, Cem. Concr. Res, vol.108, pp.72-86, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02045241

M. M. Karthik, J. B. Mander, and S. Hurlebaus, Modeling ASR/DEF expansion strains in large reinforced concrete specimens, J. Struct. Eng, vol.144, issue.7, p.4018085, 2018.

B. Nedjar, A time dependent model for unidirectional fibre-reinforced composites with viscoelastic matrices, Int. J. Solids Struct, vol.48, pp.2333-2339, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00668049

B. Nedjar and R. L. Roy, An approach to the modeling of viscoelastic damage. Application to the long-term creep of gypsum rock materials, Int. J. Numer. Anal. Methods Geomech, vol.37, pp.1066-1078, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00668051

N. Baghdadi, Modélisation du couplage chimico-mécanique d'un béton atteint d'une réaction sulfatique interne, 2008.

C. Larive, Apports combinés de l'expérimentation et de la modélisation à la compréhension de l'alcali-réaction et de ses effets mécaniques, Laboratoire Central des Ponts et Chaussées, OA, vol.28, 1998.

J. Seignol, N. Baghdadi, and F. Toutlemonde, A macroscopic chemo-mechanical model aimed at re-asseeement of def-affected concrete structures, International Conference on Computational Technologies in Concrete Structures, CTCS'09, pp.422-440, 2009.

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

B. Nedjar, On a concept of directional damage gradient in transversely isotropic materials, Int. J. Solids Struct, pp.56-67, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01320776

A. Shamaa, M. , S. Lavaud, L. Divet, and J. B. Colliat, Inuence of limestone ller and of the size of the aggregates on DEF, Cement and Concrete Composites, vol.71, p.175180, 2016.

A. Shamaa, M. , S. Lavaud, L. Divet, and G. Nahas, Coupling between mechanical and transfer properties and expansion due to DEF in a concrete of a nuclear power plant, Inuence of relative humidity on delayed ettringite formation, vol.266, p.1422, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01727440

A. Shamaa and M. , Etude du risque de développement d'une réaction sulfatique interne et de ses conséquences dans les bétons de structure des ouvrages nucléaires, 2012.

N. Bagdadi, Modélisation du couplage chimico-mécanique d'un béton atteint d'une réaction sulfatique interne, 2008.

R. Barbarulo, 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, p.125131, 2005.

R. Barbarulo, Comportement des matériaux cimentaires : actions des sulfates et de la température, 2002.

Z. Bazant, Nonlinear water diusion in nonsaturated concrete, Matériaux et constructions 5(25), p.320, 1972.

H. Bouzabata, Swellings due to alkali-silica reaction and delayed ettringite formation: Characterisation of expansion isotropy and eect of moisture conditions, In: Cement and Concrete Composites, vol.34, issue.3, p.349356, 2012.

X. Brunetaud, Eect of curing conditions and concrete mix design on the expansion generated by delayed ettringite formation, Materials and Structures, vol.40, p.567578, 2007.

X. Brunetaud, Etude de l'inuence de diérents paramètres et de leurs interactions sur la cinétique et l'amplitude de la réaction sulfatique interne au béton, 2005.

D. Damidot and F. P. Glasser, Thermodynamic investigation of the CaO-Al2O3-CaSO4-H2O system at 25°C and the inuence of Na2O, Cement and Concrete Research, vol.23, issue.1, p.221238, 1993.

R. L. Day, The Eect of Secondary Ettringite Formation on the Durability of Concrete: A Literature Analysis, Tech. rept. Portland Cement Association, 1992.

S. Diamond, Delayed ettringite formation : A current assessment, Internal Sulfate Attack and Delayed Ettringite Formation, Proceedings of the International RILEM TC 186-ISA Workshop, 2004.

L. Divet and R. Randriambololona, Delayed Ettringite Formation: The Eect of Temperature and Basicity on the Interaction of Sulphate and C-S-H Phase, Cement and Concrete Research, vol.28, issue.3, p.357363, 1998.

L. Divet, Les réactions sulfatiques internes au béton : contribution à contribution à l'étude des mécanismes de la formation diérée de l'ettringite, 2001.

, Conservatoire National des Arts et Métiers

G. Escadeillas, Some factors aecting delayed ettringite formation in heatcured mortars, Cement and Concrete Research, vol.37, issue.10, p.14451452, 2007.

C. Famy, Expansion of heat-cured mortars, 1999.

C. Famy, Inuence of the storage conditions on the dimensional changes of heat-cured mortars, Cement and Concrete Research, vol.31, p.795803, 2001.

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

. Cnrc and C. Ottawa,

Y. Fu, J. Ding, and J. J. Beaudoin, Expansion of portland cement mortar due to internal sulfate attack, Cement and Concrete Research, vol.27, issue.9, p.12991306, 1997.

B. Godart and L. Divet, Lessons learned from structures damaged by delayed ettringite formation and the French prevention strategy, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00945667

L. Graf, Eect of relative humidity on expansion and microstructure of heat-cured mortars, Portland Cement Association, p.50, 2007.

P. E. Grattan-bellew, J. J. Beaudoin, and V. G. Vallee, EFfect of aggregate particle size and composition on expansion of mortars bars due to delayed ettringite formation, Cement and Concrete Research, vol.28, issue.8, p.11471156, 1998.

D. Heinz and M. Kalde, Present State of Investigation on Damaging Late Ettringite Formation (DLEF) in Mortars and Concretes in Ettringite the Sometimes Host of Destruction, ACI International SP 177-1, p.114, 1999.

D. Heinz and U. Ludwig, Mechanism of Secondary Ettringite Formation in Mortars and Concretes Subjected to Heat Treatment, ACI 100, p.20592072, 1987.

D. Heinz, U. Ludwig, and I. Rudiger, Delayed ettringite formation in heat treated mortars and concretes, Concrete Precasting Plants and Technology, vol.11, p.5661, 1989.

W. G. Hime and S. L. Marusin, Delayed ettringite formation: many questions and some answers -Ettringite, the sometimes host of destruction, ACI International SP-177, p.199206, 1999.

M. M. Karthik, J. B. Mander, and S. Hurlebaus, ASR/DEF related expansion in structural concrete: model developments and validation, Construction and Building Materials, vol.128, p.238247, 2016.

S. Kelham, The eect of cement composition and neness on expansion associated with delayed ettringite formation, Cement and Concrete Composites, vol.18, pp.171-179, 1996.

C. Larive, Apports combinés de l'expérimentation et de la modélisation à la compréhension de l'alcali-réaction et de ses eets mécaniques, Laboratoire Central des Ponts et Chaussées, OA 28, 1998.

C. D. Lawrence, Mortar expansions due to delayed ettringite formation. Eect of curing period and temperature, Cement and Concrete Research, vol.25, p.903914, 1995.

C. D. Lawrence, Long-term expansion of mortars and concretes, volume SP 177, chapter Ettringite the sometimes host of destruction. American Concrete Institute International, 1999.

N. Leklou, Contribution à la connaissance de la réaction sulfatique interne, 2008.

G. Li, P. L. Bescop, and M. Moranville, Expansion Mechanism Associated with the Secondary Formation of the U Phase in Cement-Based Systems Containing High Amounts of Na2SO4, Cement and Concrete Research, vol.26, p.195201, 1996.

M. C. Lewis, K. L. Scrivener, and K. S. , Heat Curing and Delayed Ettringite Formation, Materials Research Society Symposium Proceedings, Boston, Massachusetts, p.6776, 1995.

A. Magnus, N. Lars-olof, and M. Ben-haha, A method to determine the critical moisture level for unsaturated transport of ions, Materials and Structures (RILEM), p.5365, 2015.

R. Martin, Experimental analysis of the mechanical eects of Delayed Ettringite Formation on concrete structures, 2010.

R. Martin, O. O. Metalssi, and F. Toutlemonde, Importance of considering the coupling between transfer properties, alkali leaching and expansion in the modelling of concrete beams aected by internal swelling reactions, Construction and Building Materials, vol.49, p.2330, 2013.

R. P. Martin, Experimental evidence for understanding DEF sensitivity to early-age thermal history, RILEM PRO-85, vol.3, p.4554, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00851462

P. K. Mehta, Mechanism of Expansion Associated with Ettringite Formation, Cement and Concrete Research, vol.3, p.16, 1973.

R. Mensi, P. Acker, and A. Attolou, Séchage du béton: analyse et modélisation, Materials and Structures, vol.21, p.310, 1988.

P. J. Monteiro and P. K. Mehta, The tranzition zone between aggregate and type K expansive cement, Cement and Concrete Research, vol.16, p.111114, 1986.

A. E. Moore and H. F. Taylor, Crystal Structure of Ettringite, Acta Crystallographica, vol.26, issue.4, p.386393, 1970.

S. Multon, Evaluation expérimentale et théorique des eets mécaniques de l'Alcali-Réaction sur des structures modèles, 2003.

B. Nedjar, On a concept of directional damage gradient in transversely isotropic materials, International Journal of Solids and Structures, p.5667, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01320776

B. Nedjar and R. Roy, An approach to the modeling of viscoelastic damage. Application to the long-term creep of gypsum rock materials, International Journal for Numerical and Analytical Methods in Geomechanics, vol.37, p.10661078, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00668051

I. Odler and Y. Chen, Eect of cement composition on the expansion of heat-cured cement pastes, Cement and Concrete Research, vol.25, issue.4, p.853862, 1995.

A. Pavoine, X. Brunetaud, and L. Divet, The impact of cement parameters on Delayed Ettringite Formation, Cement and Concrete Composites, vol.34, p.521528, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00853358

A. Pavoine, Évaluation du potentiel de réactivité des bétons vis-à-vis de la formation diérée de l'ettringite, 2003.

N. Petrov, Eets combinés de diérents facteurs sur l'expansion des bétons causée par la formation diérée de l'ettringite, 2003.

T. Ramlochan, The eect of pozzolans and slag on the expansion of mortars cured at elevated temperature: Part I: Expansive behaviour, Cement and Concrete Research, vol.33, issue.6, p.807814, 2003.

S. Sahu and N. Thaulow, Delayed ettringite formation in Swedish concrete railroad ties, Cement and Concrete Research, vol.34, issue.9, p.16751681, 2004.

S. Silva and A. , The use of y ash and metakaolin for the prevention of alkali-silica reaction and delayed ettringite formation in concrete, Performance based evaluation and indicators for concrete durability: proceedings of the International Rilem Workshop, 2006.

K. L. Scivner and H. F. Taylor, Delayed ettringite formation: a microstructural and microanalytical study, Advances in Cement Research, vol.20, p.139146, 1993.

J. Seignol, N. Baghdadi, and F. Toutlemonde, A macroscopic chemo-mechanical model aimed at re-asseeement of DEF-aected concrete structures, International Conference on Computational Technologies in Concrete Structures, CTCS'09. Korea, p.422440, 2009.

A. Sellier and S. Multon, Chemical modelling of Delayed Ettringite Formation for assessment of aected concrete structures, Cement and Concrete Research, vol.108, p.7286, 2018.

H. F. Taylor, C. Famy, and K. L. Scrivener, Delayed ettringite formation, Cement and Concrete Research, vol.31, p.683693, 2001.

M. Thomas, Diagnosing delayed ettringite formation in concrete structures, Cement and Concrete Research, vol.38, issue.6, p.841847, 2008.

J. Torrenti, Modeling Concrete Shrinkage under Variable Ambient Conditions, ACI Materials Journal, vol.96, p.3539, 1999.

K. Tosun, Eect of SO3 content and neness on the rate of delayed ettringite formation in heat cured Portland cement mortars, Cement and Concrete Composites, vol.28, p.761772, 2006.

R. Yang, Delayed ettringite formation in heat-cured Portland cement mortars, Cement and Concrete Research, vol.29, issue.1, p.1725, 1999.

Z. Zhang, J. Olek, and S. Diamond, Studies on delayed ettringite formation in heat-cured mortars: II -Characteristics of cement that may be susceptible to DEF, Cement and Concrete Research, vol.32, issue.11, p.17371742, 2002.