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For modelling concrete at the millimeter scale, the computational volume,
typically
8000-
27000 mm3, is filled with hard spheres, representing aggregates, each surrounded by a
constant thickness soft shell, representing the ITZ [9]. We assume that the ITZ
thickness is not a function of the aggregate size, but is rather controlled by the median size of the
much smaller cement particles [10]. A recent paper used quantitative measurements of
electrical conductivity to claim that the thickness of the ITZ becomes smaller for smaller
aggregate particles [11]. This claim is discussed in Appendix A, where it is shown that the
use of an approximate analytical equation for the concrete conductivity in Ref. [10] can
erroneously give this result.
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 ITZ's are free to overlap aggregates and each other in the placement process. A range of particle size distributions (PSD's) for the coarse and fine aggregates were chosen based on the recommendations found in ASTM C33 [12]. Sieve analyses of these four PSD's are shown in Table 1. The designations for the aggregate PSD's are cfcc, cffc, ffcc, and fffc. There are two (somewhat arbitrary) parts of the aggregate PSD, the fine particles and the coarse particles [12]. There are two limits of each PSD, a coarser one and a finer one, which results in four possible PSD's: cfcc=coarser fine particles, coarser coarse particles; cffc=coarser fine particles, finer coarse particles; ffcc=finer fine particles, coarser coarse particles; and fffc=finer fine particles, finer coarse particles. The seive analyses reflect these designations, which can be seen upon inspection of Table 1. 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.
| Sieve parameters | Fraction of aggregate volume contained in sieve | ||||
| DL (mm) | DH (mm) | cfcc | fffc | ffcc | cffc |
| 0.075 | 0.15 | 0 | 0.04 | 0.04 | 0 |
| 0.15 | 0.30 | 0.02 | 0.08 | 0.08 | 0.02 |
| 0.30 | 0.60 | 0.08 | 0.12 | 0.12 | 0.08 |
| 0.60 | 1.18 | 0.1 | 0.1 | 0.1 | 0.1 |
| 1.18 | 2.36 | 0.12 | 0.09 | 0.06 | 0.15 |
| 2.36 | 4.75 | 0.06 | 0.06 | 0 | 0.12 |
| 4.75 | 9.525 | 0.26 | 0.33 | 0.24 | 0.35 |
| 9.525 | 12.7 | 0.3 | 0.18 | 0.3 | 0.18 |
| 12.7 | 19.05 | 0.06 | 0 | 0.06 | 0 |
Table 1: Aggregate particle size distributions for various concretes. D stands for particle diameter.
Air voids were also introduced into some of the concretes. The air voids were considered to be equivalent to aggregate particles in terms of their effects on ionic diffusivity. They were assigned a diffusivity of 0 and an associated ITZ region like the aggregates [13]. We are assuming that the air voids were not filled with water. Concrete exposed to water for a long period of time may actually have the air voids filled with water. For this study, a fixed air void size distribution was used for all of the simulations based on a logarithmic probability density function [14]. Air voids smaller than 100 µm in diameter were not included in the model, as they are similar in size to the cement particles. Further details of the aggregate/air void systems used can be found in Ref. [8].