Formulaciones tridimensionales de la retracción y la fluencia del hormigón. Significado y errores de las extrapolaciones unidimensionales de la fluencia

3-Dimensional formulations of concrete shrinkage and creep. Meaning and errors of creep 1-dimensional extrapolations

Massive concrete structures suffer deformations along the time (in all directions) due to shrunkage and creep. These deformations produce different delayed effects and interact with thermal actions, such effects, in general not negligible, must be taken into account in the design and the construction of such structures; in particular for dams and other large concrete structures having an evolutive construction and considering that for them at first stages creep and shrinkage, as well as hardening heat, can be very important. In this work, a revision of creep formulations in three dimensions (3-D), based on two coefficients (which seems the correct one, in spite of the bibliography), has been developed. For this framework, it has been stablished the meaning of the simple approaches consisting of extrapolations of one dimensional creep behaviour to 3-D, both the one normally used at the time-dependent analysis of these strutures and another that has been proposed here. Besides, the errors of such aproaches have been studied and their causes: A) only one creep coefficient is taken into account, instead of two; B) the one-dimensional coefficient corresponds to uniaxial stress conditions, so making impossible to consider that creep coefficients depend on the multiaxial stress state. The option of applying the coefficient divided by modulus E to every stress for obtaining its corresponding delayed strain, without coupled terms, the one proposed here, has less errors in comparison with the option of applying it to every initial strain, in the same way. On the other hand, for each delayed deformation, the first one keeps the classic stress formulation of the creep general case.