Changes have been made to the hydration model since the first percolation study was carried out . The changes involve continuous dissolution and reaction and cement chemistry. The original model dissolved some cement, diffused and reacted all dissolved cement, then dissolved some more, in a cyclic fashion. The current version of the hydration model operates in a more continuous dissolution/reaction mode, although still retaining the concept of cycles. By changes in cement chemistry is meant that now the model can handle full portland cement chemistry vs. only being able previously to handle pure C3S pastes. Because of these changes, it was important to go back and investigate the effect of particle size distribution, and re-check the effect of water:cement (w/c) ratio. The models considered in this section are all 1003 size models, with a resolution of 1 µm / pixel.
A realistic particle size distribution for the original cement particles was used, and the effect of w/c ratio and cement chemistry studied. The particle size distribution for the C3S models to be considered comes from the thesis of Boumiz , and the particle size distribution for the portland cement models comes from the CCRL 115 standard cement  (details of the cement are in Ref. ).
Figure 1 shows the "fraction connected" for the capillary pore space for the C3S model plotted vs. degree of hydration (top) and capillary porosity (bottom), for values of w/c ratio varying between 0.3 and 0.6. This version of the model includes continuous dissolution of particles. Notice, in the bottom graph of Fig. 1, how all the curves collapse to approximately a single curve, with a common percolation threshold of about 0.22. That means, for this range of w/c ratios, that the capillary pore space becomes topologically disconnected when its total volume fraction falls below 22 % of the total cement paste volume. This value, 22 %, is different than the number reported in the earlier work , of 18 %. We have done careful simulations to show that this difference is not due to any of the small changes in the model carried out since 1991, like continuous vs. cyclic dissolution, but rather due to differences in cement particle size distribution, as will be shown below.
Figure 1: Showing the fraction of the capillary pore space that is part of a connected pathway for various water:cement ratio C3S pastes as a function of (top) the degree of hydration, and (bottom) the capillary porosity, using the particle size distribution of Boumiz .
Figure 2 shows results for capillary porosity percolation for two different cement systems, at two different w/c ratios. In both cases, only four sizes of particles were used, with diameters of 3, 9, 13, and 19 pixels. In one case, equal numbers of each size particle were used, while in the other case, equal volumes of particles were used. The equal number case is almost identical to that used in the earlier work . In Fig. 2, we see pairs of results that look very similar, except that the percolation thresholds, as seen in the bottom parts of the figures, are significantly different between the two cases. The equal number case, which has an average particle diameter heavily weighted towards the larger particles, has a percolation threshold of about 16 %, close to that found in the earlier work. The equal volume case, which has a much broader distribution, has a percolation threshold of about 21 %, much closer to the results found in Fig. 1. Other work on portland cement particles has shown that for this resolution system, 1 µm per pixel, as long as the cement particle size distribution is reasonably broad, the capillary percolation threshold will be about 20 % to 22 % .
Figure 2: Showing the fraction of the capillary pore space that is part of a connected pathway for two water:cement ratio C3S cement pastes, as a function of (top) the degree of hydration, and (bottom) the capillary porosity. Two discrete four-size particle size distributions were used: one with equal numbers of particles in each class (no), and one with equal volumes of particles in each class (wt).
A question that has arisen in other work, and has now become important for the model work, is: how close are C3S results to results on portland cement? The model has incorporated full portland cement chemistry for some time now , and the percolation results should be compared to the C3S-only model. Figure 3 shows the same kind of results as was shown in Fig. 1, but for a portland cement, the NIST 115 standard cement. The resemblance to Fig. 1 is striking, with almost exactly the same percolation threshold, about 21 %. So we can safely say that there is no difference in the capillary pore space percolation characteristics between portland cement paste and C3S cement paste, as both models distribute hydration products both on the cement (C3S) particle surfaces and within the available pore space in a similar manner.
Figure 3: Showing the fraction of the capillary pore space that is part of a connected pathway for three water:cement ratio portland cement pastes as a function of (top) the degree of hydration, and (bottom) the capillary porosity, using the NIST 115 particle size distribution.
The percolation of other phases can also be considered, and comparisons made between C3S and portland cement pastes. Figure 4 shows the percolation data for the C-S-H phase for C3S pastes, and Fig. 5 shows the equivalent for a NIST 115 portland cement paste. The qualitative shape and behavior of the two systems are identical, with a percolation threshold for the C3S paste of about 0.225, while the portland cement paste had a percolation threshold of about 0.18. So in this case, there is a quantitative difference between the percolation aspects of the two systems. If we consider a C3S paste and a NIST 115 paste at the same water:cement ratio, and the same degree of hydration, we find that the ratio of C-S-H volume fractions between the two pastes is about the same as the ratio between the C-S-H percolation thresholds. Both pastes are producing about the same total volume of hydration products. In the NIST 115 case, there are other products that help to cover the surfaces of the cement particles, allowing the C-S-H produced to be more efficient at bridging between particles, thus allowing a lower volume fraction to still percolate.
Figure 4: Showing the fraction of the C-S-H phase that is part of a connected pathway for three water:cement ratio C3S cement pastes, as a function of (top) the degree of hydration, and (bottom) the volume fraction of the C-S-H phase, using the Boumiz particle size distribution .
Figure 5: Showing the fraction of the C-S-H phase that is part of a connected pathway for three water:cement ratio portland cement pastes, as a function of (top) the degree of hydration, and (bottom) the volume fraction of the C-S-H phase, using the NIST 115 particle size distribution.
Figures 6 and 7 show the CH percolation information for C3S and portland cement pastes, respectively. These two systems both have a CH percolation threshold of about 0.155. The noise seen in Fig. 7 is due to the fact that a mechanism for CH dissolution and recrystallization was allowed in the portland cement system. The noise was caused by dissolution and recrystallization of key small crystals, that did not change the volume fraction of CH very much, but changed the connectivity a lot. One might imagine small crystals that completed a key "bridge" that just connected two large masses of CH. If these small crystals should dissolve, a large amount of connectivity would be lost, but not a large amount of CH. The CH phase forms in the available pore space between cement particles, so its percolation threshold is less sensitive to cement chemistry.
|Figure 6: Showing the fraction of the CH phase that is part of a connected pathway for three water:cement ratio C3S cement pastes, as a function of (top) the degree of hydration, and (bottom) the volume fraction of the CH phase, using the Boumiz particle size distribution .|
Figure 7: Showing the fraction of the CH phase that is part of a connected pathway for three water:cement ratio portland cement pastes, as a function of (top) the degree of hydration, and (bottom) the volume fraction of the CH phase, using the NIST 115 particle size distribution.