Solidification Theory for Aging Effect on Stiffness and Basic Creep
The rate of concrete creep not only attenuates with the load duration but also decreases, at a decaying rate, with the age at loading. This phenomenon, called aging, complicates the mathematical modeling of creep. Since the phenomenological approach that deals with age-dependent material properties has no physical underpinning, we embark on a more physical approach, based on the analysis of solidification of cement, which is the physical cause of aging (aside from microprestress relaxation, discussed in the next chapter). We show that one can attribute the aging to the growth of volume fraction of a nonaging constituent of hydrating cement, approximately considered as the C-S-H. The fact that this constituent can be considered as nonaging brings about a considerable simplification of the material model. Then, we show how the concept of solidification requires the compliance curves for different ages at loading not to diverge with time from each other, which in turn rules out creep recovery curves with nonmonotonic decay. We also explain the problems with creep compliance models giving a relaxation curve that crosses to the opposite sign. We compare the behavior of a number of models from the literature and design codes, and we show that many of them lead to divergence of compliance curves or to relaxation crossing to the opposite sign, at least under certain specific conditions. We conclude by pointing out the thermodynamic restrictions on rheological Kelvin and Maxwell chains and their implications for the properties of compliance and relaxation functions.