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Since the microstructural model provides a complete spatial representation of all phases present during hydration of C3S, the percolation characteristics of the solid products, CH and C-S-H, can also be assessed. As described earlier, the CH forms by a random nucleation and growth process within the available pore space. Although generally seen as discontinuous in two dimensions, as the hydration proceeds, the CH product does become connected in three dimensions. This two-dimensional discontinuity is again in general agreement with Scher and Zallen's hypothesis [11], as the 0.45 phase fraction they predict is required for continuity in two dimensions is never achieved, since the maximum amount of CH produced during hydration is about 20% [25].
Figure 6a provides a plot of the fractional
connected CH as a function of degree
of hydration for C3S pastes of w/c ratios
of 0.45, 0.5, 0.6, and 0.7. It is relatively late in the
overall hydration process, 
> 0.5,
that enough CH is produced for the phase to become
connected in three dimensions. The higher the w/c ratio, the more hydration required for the CH
to become connected, as less total volume of CH is formed at a given degree of hydration. The
fractional connected CH levels off at a value of approximately 0.9, as opposed to 1.0, as there are
always discrete clusters of CH, surrounded by C-S-H and porosity, which are disconnected from
the rest of the CH.
The fractional connected CH is plotted against the total CH phase fraction in Fig. 6b. As was observed for porosity, representing the data in this manner results in a single curve, independent of w/c ratio, for the range of w/c ratios investigated in this study. Since the disappearance of pore space and the formation of CH are both basically random site processes, it is not so surprising that total phase fraction controls the percolation characteristics of each. From Fig. 6b, it can be observed that the CH phase starts to achieve continuity when 12-15% CH has been formed, in reasonable agreement with the 3-d "universal" value of 16% [11]. Interestingly, continuity of the CH within the capillary porosity is achieved at higher w/c ratios without causing discontinuity of the capillary porosity itself (see Fig. 2) for w/c = 0.6 and 0.7). This simultaneous continuity of multiple phases is only possible in (at least) three dimensions [9].
The observation that the CH ultimately becomes connected in three dimensions has major implications in terms of degradation processes for low w/c ratio cements containing greater than 15% CH. Any degradation process (acid attack, leaching, etc.) which destroys (i.e. dissolves) the CH phase will create a connected pore network within the sample. Since the CH phase is initially connected, the pore network left behind after its degradation must also be connected. Thus, at low w/c ratios, an initially discontinuous capillary pore structure may be converted to a highly connected one when degradation of the CH phase occurs. This would mean that, for example, the chloride diffusivity D, which had been previously controlled by the microporosity of the C-S-H gel, would now be again controlled by the capillary pore space, resulting in an increase in D which could be as much as ten or a hundred-fold or even more.
Because the total amount of C-S-H formed per dissolved unit volume of
C3S is large relative to the CH formed,
the C-S-H phase percolates much earlier in the hydration process. Fig.
7a shows a plot of the fractional connected C-S-H vs. degree of hydration for w/c ratios
of 0.45, 0.5, 0.6, and 0.7. The C-S-H phase is seen to percolate early in the
hydration process at
< 0.4. Unlike the CH phase which attained a maximum fractional connectivity of only
0.9, the C-S-H phase exhibits a maximum connected fraction of 1.0, as no
discrete clusters of C-S-H exist after 50% hydration. This difference in
maximum connectivity can largely be attributed
to the C-S-H being a surface product which forms only around
C3S particles and the CH
being a pore product which forms at random locations in the pore space.
The C-S-H percolation is unlike that of porosity or CH in that it is not strongly influenced by w/c ratio, as the curves for different w/c ratios in Fig. 7a nearly overlap. This is because between the w/c ratios of 0.45 and 0.7, there is only about a 15% change in initial porosity, and so only a correspondingly small change in inter-particle distances. To percolate, shells of C-S-H must connect across these distances, so if these distances do not change much, the degree of hydration needed to achieve percolation won't change much either. Comparing Figs. 2a and 7a, it can be observed that the C-S-H and capillary porosity are simultaneously connected for at least a portion of the hydration process. At lower w/c ratios, as the porosity becomes disconnected, the C-S-H phase becomes highly connected, so that the major pathways for diffusive transport will switch from the capillary pore network to the connected porous C-S-H network. At higher w/c ratios, even at complete hydration, the C-S-H, CH, and porosity are all partially continuous, so that the capillary porosity network will remain the largest contributor to diffusive transport.
In Fig. 7b, the fractional connected C-S-H is plotted against total C-S-H. As with the CH and porosity, plotting the data in this manner results in a single percolation curve. From the plot, 17-20% C-S-H is required to form a continuous pathway throughout the microstructure, in reasonable agreement with the hypothesis of Scher and Zallen [11].
