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CONCRACK 3 – RILEM-JCI International Workshop on Crack Control of Mass Concrete and Related Issues Concerning Early-Age of Concrete Structures, 15-16 March 2012, Paris, France

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EARLY AGE BEHAVIOR OF MASSIVE CONCRETE STRUCTURES: FROM EXPERIMENTS TO NUMERICAL SIMULATIONS

Farid Benboudjema (1), Matthieu Briffaut (2), Adrien Hilaire (1), Jean-Michel Torrenti (3) and Georges Nahas (1,4)

(1) LMT/ENS Cachan/CNRS UMR8535/UPMC/PRES UniverSud Paris, Cachan, France

(2) Laboratoire Sols Solides Structures et Risques (3S-R), Université Joseph Fourier, Grenoble, France

(3) Université Paris Est, IFSTTAR, Materials Department, Paris, France

(4) Institut de radioprotection et de sûreté nucléaire, Fontenay-aux-Roses, France

Abstract

Cracking at early-age is an important problem in massive concrete structures. Indeed, autogenous and thermal shrinkage may be (partially) restrained by previous lift, due to temperature gradient ... This cracking depends highly on the concrete mix (impacting shrinkages, Young’s modulus, creep ...), the (mechanical, thermal, wind ...) boundary conditions ... It is difficult to study it with an experimental device in laboratory conditions, due to the needed massive character of the concrete structures which is needed in order to be representative. Therefore, an original device has been developed consisting of heating a brass ring, with concrete cast around. The results are then used to validate the adopted model. Creep in compression and tension, including the effect of temperature has been investigated. Some numerical simulations are performed in order to highlight the influence of creep, its interaction with cracking and boundary conditions. Finally, the model is applied to the CEOS test. Résumé

La fissuration au jeune âge dans les structures massives en béton est un enjeu majeur. En effet, le retrait endogène et thermique peut être (partiellement) empêché par les levées précédentes, du fait des gradients thermiques ... Cette fissuration dépend fortement de la composition du béton (impactant les retraits, le module de Young, le fluage...) les conditions aux limites (mécaniques, thermique, vent...)... Il est très difficile de l'évaluer en conditions de laboratoire, du fait du caractère massif nécessaire pour être représentatif. Par conséquent, un dispositif original a été développé consistant à chauffer un anneau en laiton, autour duquel un anneau en béton est coulé. Les résultats obtenus permettent de valider le modèle développé. Une étude du fluage en compression et en traction, incluant l'effet de la température a été menée. Des simulations numériques sont effectuées afin de mettre en évidence l'influence du fluage, son interaction avec la fissuration et des conditions aux limites. Finalement, le modèle est utilisé pour simuler les essais réalisés dans le projet CEOS.


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1. INTRODUCTION At early age in massive concrete structures, cracking may occur during hardening. Indeed,

hydration is an exothermic chemical reaction (temperature in concrete may overcome 60°C [1-3]). Therefore, if autogenous and thermal strains are restrained (self restraint, construction joints), compressive stresses and then tensile stresses rise, which may reach the concrete strength and induce cracking in a real structure. For instance, Ithurralde [3] observed several crossing cracks (opening up to 0.5 mm) in a 1.2 m width concrete wall (representative of French nuclear power plant containment), cast on a concrete slab. For structures like tanks or nuclear containment vessels, this cracking may significantly increase concrete permeability and reduce tightness. For other massive structures (bridges, tunnels…) serviceability may be reduced due to the penetration of aggressive species (such as carbon dioxide, sulfate and chloride ions).

Cracking highly depends on creep (essentially basic creep in massive structures). However, the question whether creep strains are the same in compression (such tests are “classical”) and in tension (difficult to perform) is not fully resolved. This literature review highlights the fact that there is no consensus in scientific community regarding basic creep in tension. Moreover, at early age, concrete structures can reach 60°C and thus, an important effect of this temperature evolution is expected on the concrete behaviour and especially on the basic creep strains rate. Therefore, both compressive and tensile creep test have been performed and the effect of temperature have been studied on compressive test. The obtained results will be presented in the first part of this paper. Next, a new configuration of restrained shrinkage ring test is presented. Indeed, thermal shrinkage does not occur in such device, whereas in massive structures thermal strains restraint (due to internal restraint, i.e. temperature gradients or due to construction joints) is the main phenomena involved in cracking [2, 4]. Therefore, a device, which is an evolution of the classical restrained shrinkage ring test, has been developed to study the cracking due to restrained thermal shrinkage in laboratory conditions [17] (in order to be representative of a massive structure). The second part is devoted to modelling of early age behaviour: influence of boundary conditions and basic creep strains at early age (age effect and temperature effect), including coupling between cracking and creep, and dissymmetric effect in compression/tension. This study is based on the RG8 experiment (CEOS national project, [5]) and on a concrete mix which is representative of a nuclear power plant which are used for numerical simulations.

2. EXPERIMENTAL RESULTS

2.1 Creep experiment Compressive and tensile creep tests have been performed in which the loading level is

equal to 30 % of the compressive/tensile strength at the loading age (calculated from compressive/tensile (splitting) test on 11x22 cm cylindrical specimen) to stay in primary creep domain and avoid non linearity of creep stains with regards to the load rate and/or failure due to tertiary creep. The specimens (7x7x28 cm in compression, 30x11cm cylindrical specimen in tension) are placed in a controlled room at 20°C and protected from drying with a double aluminium adhesive layer. For these tests, hydraulic loading frames (calibrated with a load cell) are used in compression, whereas pneumatic loading frame (alimented by a


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pneumatic compressor) is used in tension. The strains measurements are performed on 2 or 3 measurement lines, and for each loading age, at least 3 specimens are tested.

Compressive and tensile creep stains are displayed in Figure 1. These results suggest that for the studied concrete, at early age, compressive and tensile creep strains are almost similar (the maximum difference is 20 %). As previously aforementioned in the introduction, there is still no consensus on this subject.

Figure 1: Specific basic creep strain in compression and tension at early-age.

In massive structures, the concrete temperature can overcome 60°C. Thus, an important effect of this temperature evolution is expected on the concrete behaviour and especially on the basic creep strains rate. Compressive basic creep test are performed in a temperature controlled room with the same device presented previously. Basic creep strains of 8 specimens (submitted to three temperature histories) are compared in Figure 2:

• a constant temperature of 20°C during cure and 20°C during the test (20 - 20 - 20°C) • a constant temperature of 20°C during cure and 60°C during the test (20 - 60 - 60°C) • a constant temperature of 20°C during cure and a temperature decrease from 60°C to

20°C during the test (20 - 60 - 20°C)

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-20

-10

00 1 2 3 4 5

Basi

c cr

eep

stra

ins

(µm

/m/M

Pa)

Temps (jours)

Compressive test (CT =20°C ; TT = 60°C

Compressive test (CT=20°C ; TT = 20°C)

Compressive test (CT=20°C; TT = 60-20°C)

Time (days)

Compressive test: 20 – 20 – 20°CCompressive test: 20 – 60 – 60°C

Compressive test: 20 – 60 – 20°C

Figure 2: Evolution of specific creep strain for 3 different temperature histories.


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Figure 2 shows that the temperature effect on basic creep strains in compression is important because strains measurements obtained at 60°C are close to twice of the one measured at 20°C. For the test with a temperature decrease (rate of 0.6°C/h), the basic creep strains are more important than for a stable temperature of 60°C. This could be explained by thermal transient creep [6]. However, Bazant et al. [7] and Sabeur and Meftah [8] suggest that these strains correspond respectively to drying creep (the specimens are here protected against moisture loss) or dehydration and only exist above 100°C. It needs still to be resolve, some (parasite) water loss may have occurred during our experiments.

2.2 Thermal ring test [17]

The ring test proposed in this study, aiming at predicting the behaviour and the cracking of concrete at early age of massive structures (like nuclear power plant containment) is a thermally controlled device. Its principle is to create the thermal strain effects by increasing the temperature of the brass ring in order to expand it and to reproduce a stress rate similar to the one of a real massive structure. In this case, the expansion of the ring is restrained by the external concrete layer (the thermal dilatation coefficient of the brass is about 3 times higher than the concrete one). This induces compressive stresses in the ring and therefore tensile stresses in concrete. The temperature evolution of the brass ring is punctually regulated by water circulation into the ring, created by a thermostatic bath (Figure 3). The brass ring strains are measured by 3 strains gages placed at 120° and two temperature probes are placed in an opposite way on a same diameter.

The specimen dimensions in the active ring test have been chosen to obtain a concrete ring section of 10cm x 10cm. Since drying is 103 to 106 times slower than heat transfer, and because the formwork is removed 15 days after casting (in nuclear power plants), massive structures at early-age are almost in endogenous conditions (except for the external concrete skin). Therefore, tests are performed with no hydrous exchange with the environment (the concrete ring is covered with an adhesive aluminum layer: the weight loss is less than 0.1 % after 7 days). It should be noticed that this device is well adapted to describe cracking during concrete lift, but cannot retrieve thermal stresses due to self restraint (temperature gradient inside the thickness). However, numerical simulations show that, for the studied concrete (and associated structure), thermal stresses due to self restraint do not lead to cracking [2].

Figure 3: Thermal active ring test


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Figure 4: Typical evolution of orthoradial strain in the brass (mean, maximal and minimal

values).

Figure 4 displays the evolution of internal (brass) orthoradial strain. At the beginning of the test (Phase I, up to 10 h), the temperature increase is due to the (exothermic) hydration reaction. It induces an increase of brass strain. Next, a decrease of temperature is observed (the heat losses are greater than the hydration heat release, phase II).An associated thermal shrinkage is observed. Then (after 24h, phase III), the temperature rise is imposed by the thermostatic bath with a rate of 0.35°C/h. An experimental crack, corresponding to a gap in the strain evolution, occurs for a brass ring temperature value of 51.5°C (experimental crack width was about 650 µm). Indeed, after cracking, stresses are relaxed by the debonding of the concrete ring from the brass ring. Besides, the crack crosses the entire concrete specimen section and furthermore, continues through the concrete aggregates.

3. MODEL FOR EARLY-AGE BEHAVIOR

The principal features of the numerical model are presented above.

3.1 Chemo-thermal model The prediction of early-age behavior required to know the evolution of the concrete hydration. This evolution can be achieved by the use of a chemical affinity [9] and considering that the reaction is thermo-activated following the Arrhenius law [10]:

( ) ⎟⎠⎞

⎜⎝⎛−=

RTEA aexp~ ξξ& (1)

where Ea is the activation energy [J.mol-1], R is the ideal gas constant 8.3145 [J.K-1mol-1], T is the temperature [K], ξ is the hydration degree and ( )ξA~ is the chemical affinity [s-1].

The energy balance equation, which includes the heat release due to hydration reaction, is solved to obtain the temperature evolution:


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( ) ξ&& LTkTC +∇∇= (2)

in which L is the latent hydration heat [J.m-3], k is the thermal conductivity [W.m-1.K-1] and C is the volumetric heat capacity [J.m-3.K-1], which are assumed to be constant. The boundary conditions are of convective type: the convective heat flux ϕ [W.m-2] reads:

( )nexts TTh −=ϕ (3)

where Ts is the temperature on the surface [K], Text is the ambient temperature [K] and h is the exchange coefficient including convection and radiation (after linearization) [11]:

For natural convection: 34,

3/1,13,0 moyT

GrclkGrclTg

h f σεαν

β+⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

×

×Δ××=

(2)

For forced convection: 34Re,

3/12/1Re,664,0 moyT

clkclV

h f σεαν

ν+

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛⎟⎠⎞

⎜⎝⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ ×=

(4)

3.2 Autogenous and thermal shrinkage Autogenous shrinkage auε and thermal strain thε can be modelled by the following equations:

1ε ξκ−=au and 1ε )( 0TTth −=α with +∞ −

−=

0

0

ξξξξξ (5)

where κ is a constant material parameter, 0ξ is the mechanical percolation threshold, ∞ξ is the final hydration degree and

+⋅ is the positive part operator.

3.3 Elastic and damage model

The mechanical behaviour of concrete is modelled by an elastic damage model coupled with creep. The Young modulus E and the tensile strength ft increase due to hydration as follows [12, 13]:

( ) EaEE ξξ ∞= and ( ) ftatt ff ξξ ∞= (6)

where ∞E and ∞tf are the final Young modulus and tensile strength, respectively (i.e. when

∞= ξξ ) [GPa], aE and aft are constant material parameters. The relationship between apparent stressesσ , effective stressesσ , damage D (adapted from [14]), elastic stiffness tensor E , elastic strains eε , basic creep strains bcε , total strains ε , and previously defined strains reads:

( ) ( ) ( ) ( ) ( )( )thaubce DDD εεεεEεEσσ &&&&& −−−−=−=−= ξξ 11~1 (7)


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High stress levels lead to non-linear creep strains (which may induce failure). Following Mazzotti and Savoia [15], a part (parameter β) of creep strains εbc (see next section) is included into the expression of the equivalent strain defined by Mazars [14,19]:

++++= bcebce εεεε ββε :ˆ (8)

3.4 Basic creep model The model takes into account directly effects of hydration. In order to reproduce the (partial) reversible part of basic creep, Kelvin-Voigt and dashpot chains are used. The strains can be obtained by solving the following differential equations [2]:

( )( ) ( )ξ

σεξξτετ i

bc

ibci

bc

ibci

bcibc

ibc kk

k &&

&&&

~1 =⎟⎟⎠

⎞⎜⎜⎝

⎛++ and ( ) j

bcibc εξησ &=~ (9)

where ibcτ is the characteristic time (constant), ( )ξi

bck and ( )ξη jbc are the spring stiffness and

viscosity, respectively (increasing with the hydration degree) and σ~ is the previously defined effective stress (equation 7). The stiffness parameter for each unit is calculated with the following equation [12]:

( ) ψξξ

ξ608.1081.2

473.0_ −

= ∞ibc

ibc kk and ( ) ψξ

ξηξη

608.1081.2473.0

_ −= ∞

jbc

jbc (10)

where ibck ∞_ and j

bc ∞_η are the final stiffness and viscosity, respectively. The characteristic time is assumed to be constant for the Kelvin-Voigt unit.

Figure 5: Basic compressive creep strains divided by tensile one from different authors: a

review of the literature.

Experimental results of the literature show that basic creep in compression and tension are somehow different in terms of amplitude and kinetic: some authors found greater creep in compression than in tension; others found an opposite results (see Figure 5, for a review). This may due to uncertainty (creep strains in tension are very low in term of amplitude), micro-cracking (due to strains incompatibility, gradient, localized defaults ...). In order to be


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able to predict macroscopically dissymmetric creep in tension/compression and so as to extend the model to multi-axial stress state, the previous equations are modified:

ibc

ibc ε→ε and ( ) ( )[ ]−−++ −++−+→ σσσσ ννγννσ 11 (11)

where ν is the creep Poisson ratio taken equal to the elastic one and γ is a material parameter, controlling the difference between creep in compression and tension. Therefore, only 4 parameters (for 1 Kelvin-Voigt unit and 1 dashpot unit) need to be identified to estimate creep strains in concrete, from early-age to long term, including the partial recovery and the asymmetric behaviour tension/compression.

4. NUMERICAL SIMULATIONS Using experimental results presented in § 2 (as well as other experimental data) and the

presented model, numerical simulations are performed using Cast3m finite element code [16]. The objectives are to highlight the influence creep (as well as interaction with cracking and creep dissymmetry) and thermal boundary conditions (which are not well known for outside structures).

4.1 Basic creep The comparison between experimental and predicted basic creep strains (using 3 Kelvin-

Voigt units) is displayed on the Figure 6. The parameters are identified simultaneously on all the tests (each loading age) by a least squares method. One can see that the model predicts correctly the effect of age and the strains evolution during the loading period and also after unloading. This type of model turns out to predict also correctly basic creep strains for different loading histories and effect of temperature on basic creep [17].

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00 2 4 6 8 10 12 14

Basi

c cr

eep

stra

ins(

µm/m

/MPa

) Time (days)

Tload = 24h

Tload = 32h

Tload = 64h

Tload = 120h

Model 3KV+AM

Figure 6: Compressive basic creep strains: Loading age effect (Tload = age at loading).

Comparison between experimental results and model prediction.

4.2 Influence of thermal boundary conditions Investigating the maximal temperature reached at early age can be a good way to study the

massive structure sensibility to cracking (due to restrained thermal and autogenous shrinkage)


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and delayed ettringite formation (DEF). Besides, the early age cracking can be a consequence of a high temperature gradient between the core and the surface of an element. Both effects have been studied for a massive wall (thickness: 1.2m; height: 2m; length: 20m, see Figure 7) and with the assumption that the wind direction is parallel to the wall.

wind0

10

20

30

40

35

40

45

50

55

60

05

1015

20

Wind velocity (Km/h)

Tmax (°C)

External temperature (°C)

60‐62

55‐60

50‐55

45‐50

40‐45

35‐40

Figure 7: Maximal temperature Tmax reached in a massive wall (thickness 1.2m) with respect

to wind velocity and external temperature

In this study, only the external conditions (wind velocity and external temperature) are sources of variability but for an application to a real case, materials properties variability must also be taken into account (total heat release, concrete thermal conductivity, etc. [18]). Besides, the initial concrete temperature has a significant effect on the maximal temperature but to avoid this third parameter, we used a relationship between the external temperature Text and the initial concrete one Tini, proposed by Torrenti and Buffo-Laccarrière [18].

010

20

30

40

21

22

23

24

25

26

27

28

29

0

10

20

Wind velocity (Km/h)

Tsurface ‐ Text(°C)

External temperature (°C)

28‐29

27‐28

26‐27

25‐26

24‐25

23‐24

22‐23

21‐22

Tcore –Tsurf (°C)

Figure 8: Temperature difference between the core and the surface in a massive wall (thickness 1.2 m) with respect to the wind velocity and of the external temperature

The results of this study are resumed on figure 7 and 8. One can see on the figure 7 a slight effect of wind velocity on maximal temperature. This can be explained by the fact that, as the thermal concrete conductivity is rather low, the thermal exchange conditions at the core are


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close to adiabatic ones. On the contrary, the evolution of the maximal temperature due to the external temperature is quasi-linear. This can be explained by the fact that the initial temperature is assumed to be a linear function of the external temperature. On contrary to the previous results, the wind velocity has a high effect on "temperature gradient" (Figure 8), whereas the external temperature has a slight one. This indicates that with regards to these two phenomena, there are no optimal casting conditions (it is recalled that autogenous and drying shrinkage are not considered).

4.3 Dissymmetry of creep: effect on stresses As mentioned previously, there is no consensus on the tensile creep of concrete at early-

age (see the comparison in Figure 5) and at long term. In most cases, only compressive creep tests are performed, since they are easier to perform. Besides, stresses (compression/tension) may change during service life of concrete structures.

Time after loading [days]

Specific creep [M

pa‐1]

Time [hours]

Stresses [P

a]Without creepWith creepWith dissymmetrical creep, γ = 2Temperature

Figure 9: Comparison between simulated (thick lines) and experimental evolutions of strains (left). Stress and temperature evolutions versus time in a 1.2 m thick massive wall [3] (right)

In order to show the impact of this dissymmetrical behavior, material parameters were identified on experimental results for creep of Briffaut et al. [17] (see the results in Figure 9 at left). Using a value of γ = 2.57 (see equation 11), numerical simulations were performed on a 1.2 m thick concrete structures [3]. The results shown in Figure 9 (right) highlight a difference which is greater than the difference between the results obtained with and without the taking into account or not of creep (after 10 days). However, the difference occurs only after 4 days.

4.4 Simulation of RG8 specimen: influence of creep and creep/cracking coupling Numerical simulations are performed on a large beam specimen realized for ConCrack

international Benchmark (for Control of Cracking in Reinforced Concrete Structures, [5]). After casting, the structure is thermally isolated and protected from drying during 48 hours. Then, the isolation and the formwork are removed and the structure is kept during two months outside. During the entire test, longitudinal strains of the structure are globally restrained by two metallic struts.

Numerical simulations on the active thermal ring test [17] and on RG8 beam show that the coupling between creep and cracking should be taken into account in order to retrieve


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experimental simulations (i.e. the occurrence of 1 crack at least). Indeed, as displayed in Figure 10 and Table 1, no cracking is predicted with an approach where creep is not coupled with damage (3 cracks appear during the experiment at different times). Taking into account creep reduces drastically the crack opening. However, it should be emphasized that only 2 (considering the symmetry) cracks occur, as 3 cracks (the first one in the center of the specimen) have been reporting during the experiments.

1

2 4

Damage01

Figure 10: Damage field on the RG8 beam for different creep approach: 1 = without creep, 2 = Creep without coupling with cracking, 3 & 4 = creep coupled with cracking for 2 different

meshes (3 is not displayed but it is very similar to 4)

Table 1: Predicted crack opening for different models

Model Without creep (1)

Creep without coupling with cracking (2)

Creep coupled with cracking,

mesh 1 (3)

Creep coupled with cracking,

mesh 2 (4) Crack opening [µm] 359 0 158 152

5. CONCLUSION An experimental campaign coupled with a numerical analysis has been presented. The

study of creep in compression and tension, with the effect of temperature on concrete representative of a French nuclear power plant confirms that temperature accelerates the creep rate and amplitude. In this study, few differences between compression and tension have been found. In the literature, the results are very controversial. A device devoted to the analysis of cracking in massive structures has been developed consisting of heating a brass ring around a concrete specimen. This device allows for studying coupling between creep and cracking in tension at early-age.

Numerical simulations were performed on massive concrete structures (RG8 beam and a massive wall) to analyze the effect of creep including the dissymmetry compression/tension and the coupling with cracking, and the effect of thermal boundary conditions including the effect of wind. They show that: • The coupling between creep and cracking partially allows for retrieving experimental

results on the ring test and the RG8 beam experiment; • At early-age, there is a sign change of stresses (compression followed by tension) in

restrained massive structures. Taking into account dissymmetrical creep in tension and


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compression leads to results which are noticeably different from results obtained with considering equal creep in tension and compression;

• Wind has a negligible effect on the maximal temperature reached, but a significant effect on temperature gradient.

REFERENCES

[1] Cook, W. D., Miao, B., Aïtcin, P. C. and Mitchell, D., ‘Thermal stresses in large high-strength concrete columns’, ACI materials journal 89 (1992) 61-68.

[2] Benboudjema, F. and Torrenti, J.-M., ‘Early-age behaviour of concrete nuclear containments’, Nuclear Engineering and Design 238 (2008) 2495-2506.

[3] Ithurralde, G., ‘The permeability observed by the prescriber’, in the ‘Colloque Béton à hautes performances’, Ecole Normale Supérieure, Cachan, 1989. (in French)

[4] Lykke, S., Skotting, E. and Kjaer, U., ‘Prediction and Control of Early-Age Cracking: Experiences from the Oresund Tunnel’, Concrete International 22 (2000) 61-65.

[5] ConCrack: International Benchmark for Control of Cracking in R.C. Structures, in 'www.concrack.org', 2011.

[6] Hauggaard, A. B., Damkilde, L. and Hansen, P. F., ‘Transitional thermal creep of early age concrete’, Journal of Engineering Mechanics 125(4) (1999) 468-465.

[7] Bažant, Z.P., Hauggaard, A.B., Baweja, S. and Ulm, F.J., ‘Microprestress-solidification theory for concrete creep. I: Aging and drying effects’, Journal of Engineering Mechanics 123(11) (1997) 1188-1194.

[8] Sabeur, H. and Meftah, F., ‘Dehydration creep of concrete at high temperature’, Materials and Structures 41(1) (2008) 17-30.

[9] Ulm, F.-J. and Coussy, O., ‘Couplings in early-age concrete: from material modelling to structural design’, International Journal of Solids and Structures 35(31-32) (1998) 4295-4311.

[10] Regourd, M. and Gauthier, E., ‘Behavior of cement submitted to accelerate hardening’, Annales de I’ITBTP 179 (1980) 65-96. (in French)

[11] Briffaut, M., Benboudjema, F., Torrenti, J.-M. and Nahas, G., ‘Early age behaviour of a massive concrete structure: Effects of thermal boundary conditions and thermal properties evolutions on temperature and stress fields’, publication accepted in EJECE, 2011.

[12] de Schutter, G., ‘Degree of hydration based Kelvin model for the basic creep of early age concrete’, Materials and Structures 32 (1999) 260-265.

[13] Stefan, L., Benboudjema, F., Torrenti, J.M. and Bissonnette, B., ‘Prediction of elastic properties of cement pastes at early ages’, Computational Materials Science, 47(3) (2010) 775-784.

[14] Mazars, J., 'A description of micro and macroscale damage of concrete structures', Engineering Fracture Mechanics' 25(5-6) (1986) 729-737.

[15] Mazzotti, C. and Savoia, M., ‘Nonlinear Creep Damage Model for Concrete under Uniaxial Compression’, Journal of Engineering Mechanics, 129(9) (2003) 1065-1075.

[16] Cast3m, Commissariat à l'Energie Atomique CEA - DEN/DM2S/SEMT, Cast3m finite element code, available at http://www-cast3m.cea.fr/

[17] Briffaut, M., Benboudjema, F., Torrenti, J.-M. and Nahas, G., ‘Numerical analysis of the thermal active restrained shrinkage ring test to study the early age behavior of massive concrete structures’, Engineering Structures, 33(4) (2011) 1390-1401.

[18] Torrenti, J.M. and Buffo-Lacarrière, L., ‘On the variability of temperature fields in massive concrete structures at early age’, in ‘2nd International Symposium on Service Life Design for Infrastructures’, Proceedings of an International Conference, Delft, 2010 893-900.

[19] Torrenti, J. M., Nguyen, V. H., Colina, H., Le Maou, F., Benboudjema, F. and Deleruyelle, F., ‘Coupling between leaching and creep of concrete’, Cement and Concrete Research 38(6), (2008) 816-821.