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Effect of w/c ratio

To study the effect of leaching on cement pastes with different w/c ratios, hydrated microstructures were created for neat cement pastes with w/c ratios ranging from 0.35 to 0.6. This range of values was selected, based on previous results [10], because the capillary pore space remains continuous at all degrees of hydration for a w/c of 0.6, but closes off at some critical degree of hydration, α_c, for w/c < 0.57. For example, α_c 0.76 for a w/c of 0.45. Two hundred cycles of hydration resulted in degrees of hydration of 0.80 to 0.91 for the range of w/c pastes studied (Table 1). The results from pastes with w/c of 0.45 and 0.60 will be discussed to provide a contrast between originally disconnected and connected capillary pore space systems.

The capillary pore space percolation results are shown in Figs. 4a and 4b for these two cement pastes. The abscissa in both plots is total capillary porosity φ, and the ordinate is the fraction of the capillary pore space that forms a connected cluster spanning the computational cell. Immediately after mixing, this fraction must start at 1, since the pore space is just the space around isolated cement particles, and so must be completely connected. As hydration proceeds, pockets of pores become isolated by the growth of reaction products, so the connected fraction slowly decreases from 1. This happens in both the 0.6 (Fig. 4a) and 0.45 (Fig. 4b) w/c ratio pastes. For the 0.45 w/c ratio paste, near the percolation threshold, φ_c 0.18 , small amounts of additional reaction products can close off large regions of pore space by filling-up the narrow critical "necks" that are keeping the pore space connected, so that the connected fraction decreases much more rapidly.

Figure 4a: Connected fraction of capillary pore space vs. capillary porosity for pastes with w/c = 0.60 during hydration and during subsequent leaching.

Figure 4b: Connected fraction of capillary pore space vs. capillary porosity for pastes with w/c = 0.45 during hydration and during subsequent leaching.

Figs. 4a and 4b shows these decreases in pore connectivity during hydration, followed by an increase in this value during the leaching process, much as would be expected. The hydration and leaching curves for the w/c = 0.6 paste, in Fig. 4a, nearly overlap, as the capillary pore space never becomes less than 70% connected, so that the leaching process is, to a good approximation, merely the reverse of hydration in terms of its effects on pore space connectivity. It should be noted, though, that the leaching curve would fail to achieve a connected pore fraction of 1, as even if all of the CH could be removed, some pore space regions would remain that were closed off by C-S-H (surface product) alone, and so could not be re-opened by the dissolution of CH.

At the lower w/c ratio of 0.45, however, the leaching and hydration curves do not overlap. In Fig. 4b, the capillary porosity φ for the "fully" hydrated system has become less than φ_c, so that the capillary pore space has become entirely closed off during hydration. As CH is dissolved away, the pore space then becomes re-connected (percolates) at a lower value of φ_c 0.16 . Two reasons for this behavior are proposed.

First, during hydration, both surface and pore products are forming to close off the capillary pore space. However, only the pore products are susceptible to leaching, so that the reconnection of the capillary pore space during leaching is not simply the reverse of its disconnection during hydration. It is assumed that the pore products are more important than the surface products in closing off the pore space, because they fill-in the gaps between surface product shells. Because of this, it might be expected that the capillary pore space would repercolate at a lower φ_c, since the pores that were filled with C-S-H after φ became less than φ_c would not necessarily need to be dissolved to reconnect the pore space. The same critical pathways that were closed when φ < φ_c would be opened up through CH dissolution but at a lower net φ, because of the added C-S-H, which is undisturbed by CH dissolution.

A second reason that the capillary pore space repercolates at a lower value of φ than the original φ_c is that any CH cluster closing off a critical capillary pore space "neck" is somewhat more likely to be dissolved, since it is in contact with pore space on at least two faces. Conversely, CH clusters that are surrounded by C-S-H have a lesser effect on pore space percolation and a smaller probability of dissolution, since they contact fewer pore pixels. Therefore, while the hydration process distributes CH with equal probability in all pore space regions, the leaching process has a greater effect upon the CH clusters that were most important in closing off the capillary pore space.

The 0.45 w/c ratio cement paste example illustrates one dramatic effect that leaching can have on cement paste: a material in which the capillary pore space was initially discontinuous may be transformed into a material with a continuous capillary pore structure. This latter system will be much more susceptible to degradation, as the transport of ions which was originally dominated by "slow" transport through the C-S-H gel phase will now be dominated by "fast" transport through the percolated capillary pore structure. This effect could be even more prominent in plain portland cement paste mortars and concrete. In these materials, the interfacial zones between aggregate and cement paste consist mainly of capillary pores and large CH crystals [8,14]. After dissolution of the CH, little if any solid material will remain in the interfacial zone regions, almost certainly resulting in large increases in diffusivity and permeability, especially if the interfacial zones themselves form a connected pathway for transport.

In Fig. 5, the relative diffusivities D/D_o for the 0.6 and 0.45 w/c cement pastes are plotted against φ. The solid curve is a percolation-theory-based fit to data simulated on model cement pastes with 0.4 < w/c < 0.6, at many different degrees of hydration, and is given by [6]

where H(φ − φ_c ) = 0 for φ < φ_c , H(φ − φ_c ) = 1 for φ > φ_c, and φ_c = 0.18. In Fig. 5, it is clear that leaching can result in increases of relative diffusivity by a factor of ten or more. The relative diffusivity values for the w/c = 0.6 paste eventually exceed the solid curve. This effect is due to the fact that when comparing leached and unleached samples that have the same value of φ, there is much more C-S-H (and less CH) in the leached sample, so that the leached material must have a slightly higher relative diffusivity as discussed further below.

Figure 5: Relative diffusivity D/D_o vs. capillary porosity for cement pastes with w/c = 0.45 and 0.60, subjected to leaching.

The relative diffusivity values for the 0.45 w/c ratio paste at low values of φ initially follow the solid curve, but soon significantly exceed this curve as leaching progresses. There are two reasons for this behavior. First, as was shown in Fig. 4b, at the same value of φ (when φ > 0.16), the fraction of the pore space in the leached 0.45 w/c ratio paste that is connected across the sample is greater than that in the unleached paste. Since it is the spanning part of the pore space that carries the majority of the flow, a larger fraction of the pore space being connected will result in higher diffusivity values [6].

A second, more minor, reason is that at a fixed φ, the solid phase of a leached paste will contain a higher fraction of C-S-H gel than an unleached paste. This difference in C-S-H content will be greater for the lower w/c ratio cement pastes as they contain more cement initially. Since the percolated C-S-H phase contributes to diffusive transport, a higher C-S-H content will result in slightly higher values for relative diffusivities as also observed in the 0.6 w/c paste.

In Fig. 5, the relative diffusivity for the leached 0.45 w/c ratio paste system exceeds that of the 0.60 w/c ratio paste, up to the highest porosities attainable (φ 32%) by the 0.45 w/c ratio paste. However, since the 0.6 w/c ratio paste can ultimately be leached to significantly higher porosities, its relative diffusivity eventually is the larger. This can be seen in Fig. 5 as the relative diffusivities ultimately obtainable for the 0.60 system (at φ 43%) exceed the maximum observed for the 0.45 system (at φ 32%) by a factor of two.

Leaching results for a range of w/c ratios, 0.35 to 0.60 in increments of 0.05, are provided in Table 1. The effects of leaching of fixed percentages of CH on the relative increase in diffusivity are given. For each w/c ratio, 200 cycles of hydration were performed, resulting in the degrees of hydration shown in the table. The column labelled "D/D_o (hyd)" is the value of the diffusivity after hydration was stopped but before leaching was begun. D/D_o (leached) is the value of the diffusivity after a given amount of leaching has taken place. As can be seen from these results, leaching of as little as 10% of the CH formed during hydration can increase diffusivity by up to a factor of two. Ultimately, if all of the CH is dissolved, increases in diffusivity by a factor of nearly 50 may be observed.

                D/D_o (leached) / D/D_o (hyd)
                                                                              % CH leached

The data in the column labelled "100%" shows that the ratio of the diffusivity after 100% leaching, to the diffusivity attained before leaching, decreases as the water:cement ratio increases. According to this measure, the lower w/c ratio pastes are actually more affected by leaching, as larger proportional changes in diffusivity occur during leaching. However, the final diffusivity attained after 100% leaching still monotonically decreases with w/c ratio. This diffusivity can be obtained from Table 1 by multiplying together the two columns labelled "D/D_o (hyd)" and "100%". According to this measure, which has more physical meaning and practical implications, the lower w/c ratio pastes are less affected by leaching, since the maximum attainable diffusivity after complete leaching of the CH decreases with w/c ratio.