Hygro-thermo-chemo-mechanical modelling of concrete at early ages and beyond. Part II: shrinkage and creep of concrete

In Part I of this paper (Int. J. Numer. Meth. Eng., in print) a mechanistic model of hygro-thermochemical performance of concrete at early ages has been introduced. Additionally, as compared to the existing models (e.g. J. Eng. Mech. (ASCE) 1995; 121(7):785–794; 1999; 125(9):1018–1027), an effect of relative humidity on cement hydration rate and associated hygro-thermal phenomena have been taken into account. Here we deal with mechanical performance of concrete at early ages and beyond, and in particular, evolution of its strength properties (aging) and deformations (shrinkage and creep strains), described by using the effective stress concept. This allow us for explanation and modelling of phenomena known from experiments, like drying creep (e.g. Mathematical Modeling of Creep and Shrinkage of Concrete. Wiley: Chichester, 1988), or some additional strains, as compared to pure shrinkage, which appear during autogenous deformations of a maturing, sealed concrete sample (e.g. Cement Concrete Res. 2003; 33:223–232). Creep is described by means of the modified microprestress-solidification theory by Bazant et al. (J. Eng. Mech. (ASCE) 1997; 123(11):1188–1194; 1195–1201), with some modifications to take into account the effects of temperature (Comput. Struct. 2002; 80:1511–1521) and relative humidity (Int. J. Numer. Meth. Eng., in print; Proceedings of the 5th World Congress for Computational Mechanics (WCCM), Vienna, Austria, 7–12 July 2002), on concrete aging. Shrinkage strains are modelled by using the effective stress principle in the form introduced by Gray and Schrefler (Eur. J. Mech. A/Solids 2001; 20:521–538; Appl. Mech. Rev. (ASME) 2002; 55(4):351–388), giving a good agreement with experimental data also for lower values of relative humidity. Two numerical examples showing comparison of the results obtained by means of our model with some published experimental data are presented. The third one, concerning 2D axial symmetric case,proves numerical robustness of the developed software. All these examples demonstrate the possibilities of the model to analyse both autogenous deformations in maturing concrete and creep phenomena, including drying creep, in concrete elements of different age, sealed or drying, exposed to external load or without any load