1. Introduction#

In the context of studies of the long-term behavior of concrete structures, a preponderant part of the deformations measured on structures concern the delayed deformations that appear in concrete during its life. We speak of « shrinkage » when the deformation is measured on a specimen not subjected to loading and of « creep » when the deformation takes place under loading. The exchanges of water between the test piece and the environment influence the final deformation considerably. This observation traditionally gives rise to subsequent distinctions on delayed deformations. A distinction is then classically made between withdrawals at a young age, desiccation withdrawal, clean creep and desiccation creep. We recall the delayed deformations of a concrete structure in order to locate the portion of the deformation calculated in this document:

  • at a young age without burden:

  1. endogenous withdrawal (1 day - 1 year)

    caused by a thermo-hydration reaction.

  1. thermal shrinkage (1 hour — 1 day)

  • in the medium term without load: the shrinkage of desiccation (a few months — a few years) depending on the dimensions of the structure caused by the drying which results in the evaporation of some of the water not used in the hydration process.

  • long-term under load:

  1. Clean creep, which is the portion of creep in concrete that would be observed during a test without exchanging water with the outside.

  2. Desiccation creep in addition to clean creep is the part of the total creep directly linked to the departure of water affecting the concrete which undergoes mechanical loading on the one hand and drying on the other hand.

The model presented here is dedicated to the modeling of delayed deformation associated with creep, clean and desiccation. In code_aster, the template is used under the name BETON_BURGER.

Clean creep. The first concrete creep model introduced in code_aster (see [R7.01.01] and [bib4]) was developed in order to predict longitudinal creep deformations under uniaxial stresses. The generalization of this model, in order to take into account a state of multiaxial stresses, is then carried out by means of an arbitrary Poisson’s ratio of creep, which is constant and equal to, or close to, the elastic Poisson’s ratio. However, the determination a posteriori of the effective creep Poisson’s ratio shows its dependence on the loading path. Moreover, the concrete of certain structures in Park EDF, such as nuclear reactor confinement enclosures, is subject to a state of biaxial stresses. This observation led to the development of the proper creep deformation law UMLV (University of Marne-la-Vallée, partner in the development of this model) for which the Poisson’s creep ratio is a direct consequence of the calculation of the main deformations.

For its part, model BETON_UMLV assumes constant long-term deformation rates, a rheology that seems unlikely in view of the experimental results from Brooks’s work [bib7]. By maintaining the structure of model BETON_UMLV, we add a non-linearity to the long-term deformation rates to correct this point, a methodology also used by Sellier et al. [bib6]. The new model developed is described as phenomenological.

The deformation of the creep itself is strongly affected by the humidity of the concrete. This dependency is taken into account by law BETON_BURGER (as was the case for BETON_UMLV). The effect of temperature in natural creep deformations is also taken into account in law BETON_BURGER via an Arrhenius law.

Experimentally, natural creep deformations also present aging behavior: the deformation after a time \(\Delta t\) depends on the age of the material at the time of loading. This aspect of concrete behavior is not taken into account in this model.

Desiccation creep. The model proposed here is that of Bazant [bib10]. It is a purely viscous law.