Next: Incorporation of Mineral
The microstructural model is described in more detail elsewhere [3,4]. In the model, space is represented as a three-dimensional array of cubic volume elements, called pixels, arranged on a simple cubic lattice. For this study, the three-dimensional array is 100 pixels on a side, so that a total of one million pixels are present. Each pixel is assigned to be a single phase. For C3S hydration, the phases of interest are C3S, CH, C-S-H, and porosity, which is assumed to be water-filled. The usual cement chemistry notation is used, where C=CaO, S=SiO2, H=H2O, A=Al2 O3, and F=Fe2O3. Additionally, an element may be assigned to be an inert or pozzolanic mineral admixture particle. Initially, C3S particles, modelled as digitized spheres, are placed at random locations in the three-dimensional box to achieve a desired w/c ratio. The particles are not allowed to overlap and periodic boundaries are used to eliminate artificial edge effects.
Hydration is represented as a series of dissolution/ diffusion/ reaction steps. These steps are illustrated schematically in Fig. 1 for a two-dimensional microstructure. For each hydration cycle, C3S pixels in contact with pore water are eligible for random dissolution. Based on the number of pixels that dissolve, extra "diffusing" species (representative of a unit volume of dissolved reactant) are added to the available pore space to maintain the correct volume stoichiometry. If n pixels dissolve, producing n C-S-H diffusing o species, 0.7n extra C-S-H diffusing species and 0.61n CH diffusing species are added to the pore space. The factors 0.7 and 0.61 are taken from data on C3S hydration provided by Young and Hansen .
Figure 1: Diagram of steps in microstructure model
The diffusing species execute random walks within the pore space until they react to form solid hydration products. When diffusing C-S-H species encounter a C3S surface, or a solid C-S-H surface that was formed earlier during the hydration, they stick to it, forming more solid C-S-H. Thus, the mechanism for formation of C-S-H combines aspects of both the through solution (diffusion) and topochemical mechanisms for C-S-H formation outlined in the literature [3,7]. CH, conversely, forms by a nucleation and growth mechanism. That is, for each random step taken by a diffusing CH species, there is a probability that it will nucleate at its current location. This probability is exponentially proportional to the number of CH diffusing species remaining in the pore solution. Additionally, if a diffusing CH element encounters a solid CH surface, it sticks, resulting in growth of the CH crystal. When all diffusing species generated by a given dissolution have reacted, a new hydration cycle is begun by performing another dissolution step.
The w/c ratio and degree of hydration, , of the model cement are calculated as follows. If f is the initial volume fraction of cement, then
where it is assumed that the specific gravity of C3S or cement is 3.2 . After m cycles, degree of hydration is given by
where f(m) is the volume fraction of C3S in the cement after m cycles of the hydration.