Hygro-thermo-chemo-mechanical modelling of concrete at early ages and beyond. Part I: Hydration and hygro-thermal phenomena

Part I of the paper presents a new numerical model of hygro-thermal and hydration phenomena in concrete at early ages and beyond. This is a solidification-type model where all changes of material properties are expressed as functions of hydration degree, and neither as maturity nor as equivalent hydration period as in maturity-type models. A mechanistic approach has been used to obtain the governing equations, by means of an averaging theory of Hassanizadeh and Gray, also called hybrid mixture theory. The developments start at the micro-scale and balance equations for phases and interfaces are introduced at this level and then averaged for obtaining macroscopic balance equations. Constitutive laws are directly introduced at macroscopic level. The final equations, mass (water species and dry air), energy and momentum balance equations, have been written in terms of the chosen primary variables: gas pressure, capillary pressure, temperature and displacements. An evolution equation for the internal variable, hydration degree, describes hydration rate as a function of chemical affinity, considering in addition to the existing models, an effect of the relative humidity on the process. The model takes into account full coupling between hygral, thermal and chemical phenomena, as well as changes of concrete properties caused by hydration process, i.e. porosity, density, permeability, and strength properties. Phase changes and chemical phenomena, as well as the related heat and mass sources are considered. Two examples showing possibilities of the model for analysis of autogenous self-heating and self-desiccation phenomena, as well as influence of the ambient relative humidity and the concrete element dimensions upon hygro-thermal performance and shrinkage of the elements, are presented and discussed.