Figure 1: Limiting coarse and fine aggregate particle size distributions used in computer experiments.
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For modelling concrete, the computational volume, typically between 8 cm3 and 27 cm3, is filled with hard spheres, representing aggregates, each surrounded by a constant thickness soft shell, representing the interfacial transition zone [11]. Thus, we are assuming that the interfacial transition zone thickness is not a function of the aggregate size, but is rather controlled by the median size of the much smaller cement particles [12]. Once again, the aggregates are placed into the computational volume in order from largest to smallest in size and periodic boundaries are employed. While the hard core aggregates may not overlap one another, the soft shell interfacial transition zones are free to overlap one another and partially overlap another aggregate. For this study, limiting (i.e., extreme) PSDs for the coarse and fine aggregates were chosen based on the recommendations found in ASTM C33 [13]. Cumulative volume fraction curves for the limiting distributions are shown in Figure 1. For this study, the coarse aggregate was of nominal size 12.5 to 4.75 mm and the ratio of coarse to fine aggregate volume was fixed at 1.5:1. Basheer et al. [14] have observed only a minor influence of coarse to fine aggregate volume ratio, within the range of 2:1 to 1.43:1, on concrete permeation properties.
Figure 1: Limiting coarse and fine aggregate particle size distributions used in computer experiments.
In addition to executing simulations for systems containing only aggregates and cement paste, studies were also conducted in which air voids were introduced into the concrete. The air voids are considered equivalent to aggregate particles in terms of their effects on chloride ion diffusivity, i.e., they are assigned a relative diffusivity of 0 and lead to the formation of additional ITZ regions throughout the concrete [15]. For this study, a fixed air void size distribution was used for all of the simulations based on a logarithmic probability density function, g(x), given by [16]:
where do is the modal diameter and
is the standard deviation of
the logarithms, respectively. Here, this equation was utilized with a modal
diameter of 30 µm and a standard deviation
of 0.736 (giving a specific surface of 300 cm-1), as in Ref.
[16]. Air voids smaller than 100 µm
in diameter were not
included in the model, as they are similar in size to the cement particles.
Figure 2: Linkages between microstructure models for mortar and cement paste for predicting diffusivity of mortar or concrete. In the mortar model (left), inclusions are red, ITZ regions are yellow, and bulk paste is blue. In the cement paste images, cement particles are yellow, water-filled porosity is black, and the flat rectangular aggregate is red. In the hydrated image (upper right), calcium hydroxide is purple and calcium silicate hydrate gel is grey. The parameters and arrows (center) indicate the flow of information between the models.
