As with any model, the results of the 3-D cement hydration model are dependent on the underlying assumptions that have been made in creating it. Because of the current state of knowledge of cementitious systems, numerous assumptions had to be incorporated into the current version of the model. While an effort has been made to include as many realistic features into the model as possible, only time will tell if the underlying assumptions are indeed reasonable. However, the usefulness of a model may be somewhat independent of the validity of the underlying assumptions. If a model, even one formulated on what are subsequently proven to be invalid or partially valid assumptions, leads to new fruitful avenues of research or provides accurate predictive capabilities, it has served a valuable purpose.
While not exhaustive, the following is an attempt to list the major assumptions underlying the current version of the NIST microstructure model. First, as mentioned previously, we are assuming digitized spherical shapes for all of the cement particles. While the particles in Figs. 2 and 3 definitely exhibit somewhat elongated shapes, spheres appear to be a reasonable simplification. From a computational standpoint, the generation of ellipsoidal shapes or even randomly oriented non-uniform particles would be straightforward. To do this, however, some measures of the three-dimensional nature of the cement particles would have to be derived from the two-dimensional images or perhaps directly assessed on three-dimensional x-ray microtomographic images [30]. A further assumption of the initial 3-D cement particle image generation is that the PSD for the gypsum is the same as that for the ground cement clinker. Here, if the PSD of the gypsum had been assessed separately in the case of added, as opposed to interground, gypsum, that information could be directly included in the 3-D generation algorithms.
Concerning the phases present in the cement clinker, currently, the sodium and potassium sulfate are not accounted for in the model. These alkali sulfates are known to effect the early reactivity of cements [8]. The imaging techniques described previously could be extended by acquiring x-ray images for Na and K. Then, it would be necessary to hypothesize the reactions in which the alkali ions (Na+ and K+) participate and the amount of substitution of these ions for Ca++, etc. in the already-considered hydration products. Due to these and other complications, the current version of the hydration model focuses on the post-induction period of the hydration of portland cement, as our major interest lies in the long term properties of cement-based materials.
Concerning the cement hydration model itself, all diffusing species "randomly diffuse" at the same rate in the available pore space. However, a higher mobility for calcium, aluminate, and sulfate ions is implied by the rule that, upon dissolution, diffusing C3A, diffusing CH, and diffusing gypsum are located at totally random locations in the available pore space. This results in a somewhat uniform distribution of these species in the pore space. Conversely, diffusing FH3, diffusing C-S-H, and diffusing ettringite are located at or near the dissolution source, implying a lower mobility for the iron and silicate ionic species and leading to localized concentration profiles. Additionally, no explicit relationships to ion concentrations and solubility products are considered during model execution. (It should be noted that recent efforts by other research groups have concentrated on developing reaction-diffusion models for cement hydration which explicitly account for solubility products and diffusion coefficients for the relevant species [31]). As mentioned previously, the dissolution probability of ettringite is biased to avoid a buildup of diffusing ettringite species in the pore space. Similarly, the dissolution probabilities of CH and C3AH6 are also adjusted based on the current "concentrations" of diffusing species. Further assumptions are the form of the equation for the nucleation probabilities provided in Equation 5 and the provision for C3AH6, ettringite, and monosulfoaluminate to co-exist. Although, in the latter case, the C3AH6 and ettringite should lead to the formation of more monosulfoaluminate, the kinetics of this reaction could be quite slow in a hydrated cement paste system, leading to local regions where one of the three phases is dominant, such that all three phases would be detected in a hydrated cement paste [8]. As further experimental and theoretical data becomes available, the model can be adapted to better represent the physical reality since the overall framework of a cellular-automata-based model is inherently flexible [23].