CESAR-LCPC: Concrete at early age
The hydration reaction of the cement is highly exothermal. The concrete hardens by exposure to rising temperature, which may reach as high as 50°C within solid structures. Cement hydration represents a thermo-activated reaction, which signifies that the speed of this chemical reaction increases with temperature .

Moreover, concrete is an aging material, i.e. its mechanical properties (modulus of elasticity, strength) evolve as a function of the level of progress in the cement hydration reaction. The consumption of water during the hydration reaction leads to chemical shrinkage coupled with capillary shrinkage. When prevented, these various shrinkages, along with the temperature gradients, induce stresses of such intensity that they may wind up exceeding the tensile stress of the material undergoing maturation and hence lead to cracking. This cracking, in turn, affects the durability of concrete structures .

The TEXO and MEXO modules have been developed to enable modeling these phenomena. TEXO serves to compute both the temperature and degree of hydration fields, used to express the material's state of hardening. These results are then input in the MEXO module in order to determine the displacement and stress fields, in the aim of predicting the risk of cracking at early age.
TEXO module
The TEXO module is primarily a computation module intended for the simultaneous resolution of the heat equation and the macroscopic kinetic law of hydration that specifies the evolution of degree of hydration :

where:
is the Arrhenius constant ;
and is the normalized affinity, which depends solely on the degree of hydration x and the composition of the concrete used. This function is determined in TEXO on the basis of a calorimetric test .

The TEXO module thus leads to determining both the temperature and degree of hydration fields; it allows incorporating the effects of heat treatment (e.g. stoving, the installation of insulating tarpaulin or heating resistors). Besides these various solutions intended to minimize gradients, this time-dependent module enables highlighting the influence of the date of formwork removal. Furthermore, it is also possible to simulate the subsequent concreting on an older concrete .

For further details, the user is referred to the work of Piau (Acker et al., 1992), Torrenti et al. (1992), and Ulm and Coussy (1995a, 1995b).

examples of temperature fieldexamples of temperature field
figure 1: examples of temperature field (Itech study on behalf of BEC-DRAGADOS-FCC)

MEXO module
The MEXO module has primarily been set up as an incremental elastic mechanical resolution module with displacement-based (and eventually loading-based) boundary conditions, in which both dilatation and heat shrinkage / chemical shrinkage are taken into account.

Subsequent to a computation using the TEXO module, it is possible with the help of MEXO:
  • to determine the mechanical effects (displacements, stresses) of the evolution in both temperature and degree of hydration in early-age concrete structures
  • to predict the risk of cracking.


Concrete hardening
Regarding the evolution of the modulus , Byfors' law has been adapted for MEXO and placed in the following form :


Application of Byfors' law results in reducing the data necessary for modeling concrete hardening to :
  • : Young's modulus of the hardened material ;
  • : Threshold of the hardened material (= degree of hydration at the time of setting).

Figure 2 shows the evolution in Young's modulus vs. degree of hydration for both an ordinary concrete (OC) and a high performance concrete (HPC), as determined with Byfors' law and then compared with the experimental values.

Figure 2: Evolution in Young's modulus during early age, according to Laplante's experimental values (1993)
and Byfors' law used in the MEXO module, for both an ordinary concrete (OC, W/C = 0.5) and a high performance concrete (HPC, W/C = 0.3; S/C = 0.1). 		Degree of hydratation

Coefficient of dilatation and chemical shrinkage
For early-age concrete, the coefficient of chemical dilatation, b , governs the incorporation of endogenous shrinkage in MEXO and ultimately proves to be non-constant, as conveyed in Figure 3, which shows the evolution in endogenous shrinkage vs. degree of hydration for both concretes presented in Figure 2. As part of an initial approach, this coefficient is assumed constant in MEXO, thus coinciding with the total endogenous shrinkage recorded for a concrete.

Evolution of endogenous shrinkage for both an ordinary concrete

Figure 3: Evolution of endogenous shrinkage for both an ordinary concrete (OC, W/C = 0.5)
and a high performance concrete (HPC, W/C = 0.3; S/C = 0.1)
[experimental values developed by Laplante (1993)]

Bibliographical references
Modelling Thermal and Hygrometric Effects in Concrete ACKER P., PIAU J.M., RADOUANT I. (1987)
Modelling Thermal and Hygrometric Effects in Concrete
IABSE Colloquium, Delft, pp. 285-292.

High performance concrete for a nuclear containment de LARRARD F., ITHURRALDE G., ACKER P., CHAUVEL D. (1990)
High performance concrete for a nuclear containment
2nd International Conference on Utilization of High Strength Concrete, Berkeley
ACI SP 121-28.

La simulation numérique des effets de l'hydratation du béton TORRENTI J.M., PATIES C., PIAU J.M., ACKER P., de LARRARD F. (1992)
La simulation numérique des effets de l'hydratation du béton
Colloque StruCoMe, Paris, 12 pages.

Modeling of thermochemomechanical couplings of concrete at early age ULM F.J., COUSSY O. (1995a)
Modeling of thermochemomechanical couplings of concrete at early age
Journal of Engineering Mechanics, ASCE, Vol. 121, N° 7, pp. 785-794.

Strength growth on chemo-plastic hardening in early age concrete ULM F.J., COUSSY O. (1995b)
Strength growth on chemo-plastic hardening in early age concrete
Journal of Engineering Mechanics, ASCE, vol. 122, n°12, Dec. 1996, pp. 1123-1131.

Modelling the early age behaviour of a low heat concrete bulkhead sealing an underground tunnel. Didry O., Gray M.N., Cournut A., and Graham J. (2000)
Modelling the early age behaviour of a low heat concrete bulkhead sealing an underground tunnel.
Can. J. Civ. Eng./Rev. Can. Génie Civ., Vol. 27(1), pp. 112-125 (2000)

géotechnique, tunnels, fondations, structures, cesar-lcpc un logiciel pour le genie civil