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Figures 2 and 3 show cumulative intrusion curves for a series of six mortars of increasing sand content for cement paste without and with silica fume, respectively. Although samples were prepared with nine different aggregate contents, in the interests of clarity, only six aggregate contents are given for each case in Figs. 2 and 3. The remaining distributions fall between their appropriate neighbors in the plots. Each curve shown is the average of three or four separate tests. In both cases, the curves for the plain cement paste show a typical distribution with a sharp threshold diameter at about 0.1 micrometer for the sample without silica fume and 0.05 micrometers for the one containing 10% silica fume. Critical to this investigation, the intrusion curves for the mortars differ from the ones for the plain cement pastes, particularly at pore diameters larger than the paste threshold diameter. The addition of aggregate increases the pore volume detected at diameters larger than the paste samples' thresholds. Further, the threshold for the distributions becomes less distinct with increasing sand content, even for the mortars with only 15.7% sand.
Figure 2: Cumulative pore size distributions for mortars without silica fume, as measured by mercury intrusion porosimetry.
Figure 3: Cumulative pore size distributions for mortars with silica fume,
as measured by mercury intrusion porosimetry.
Figure 3: Cumulative pore size distributions for mortars with silica fume, as measured by mercury intrusion porosimetry.
Based on these threshold diameter values, the intrudable pore volume for the mortars can be divided into pro and post-threshold volumes representing the intrudable pores larger and smaller than the threshold diameter for the cement paste without sand, respectively. These results are given in Figs. 4 and 5 for the two sets of mortar specimens. Three of the nine data points in Figs. 4 and 5 correspond to the three curves not shown in Figs. 2 and 3. Although there is some scatter de in the data, trends are present. For the mortars without silica fume, there is a sudden increase in the pro-threshold volume as the sand content is increased from 44.8% to 48.6%, suggesting the occurrence of a critical or percolation phenomenon. For the mortars with silica fume, the effect is much more subtle with limited evidence for percolation occurring at about 40% aggregate volume fraction.
Figure 4: Pro and post-threshold pore volumes for varying sand contents for mortars without silica fume.
Figure 5: Pro and post-threshold pore volumes for varying sand contents for mortars with silica
Figure 5: Pro and post-threshold pore volumes for varying sand contents for mortars with silica fume.
Initially, as sand is added to the cement paste, interfacial zones are formed around each aggregate but remain relatively isolated due to the low sand content. For the mercury to reach these interfacial zones, it must first intrude through the denser bulk paste. Some increase in the intruded pro-threshold pore volume will be observed due to the few interfacial zones that overlap the edges of the specimen and isolated clusters of interior interfacial zones that connect these "edge" interfacial zones. Thus, the sharp threshold observed for the cement paste with no sand will be lost. However, as more and more sand is added, the isolated interfacial zone clusters become larger and begin to connect one to another to greatly increase the volume of interfacial zones that are directly accessible (i.e. not via the denser bulk paste) from the outside of the system. Eventually, when enough sand is present, nearly all interfacial zones will be interconnected and the interfacial zone system will nearly saturate the system. The mercury intrusion results suggest this percolation phenomena to occur at a sand volume fraction of 45- 49% for the mortars without the silica fume.
Interfacial zone percolation can be more generally examined using the hard core/soft shell computer model. To do this, the interfacial zone of soft shell thickness was varied between 10 and 40 micrometers (based on SEM evidence) and the fraction of the total interfacial zone volume that was part of a percolated pathway determined as a function of sand volume fraction. The results for this computer experiment are provided in Fig. 6. As expected, when the interfacial zone thickness decreases, a larger sand volume fraction is required to cause percolation of the interfacial zone porosity. This suggests that reducing the interfacial zone thickness is one method for decreasing the likelihood of interfacial zone percolation. Methods for decreasing interfacial zone thickness, including using a finer cement, mineral admixtures such as silica fume, or a lightweight absorptive or cement clinker aggregate have been investigated based on a computer model that simulates interfacial zone microstructural development at the micrometer level . Results suggested that these measures could indeed improve the density and homogeneity of the interfacial zone microstructure relative to the bulk paste. Experimental evidence for engineering interfacial zone microstructure by developing an ideal aggregate has been presented recently .
Figure 6: Computer model interfacial zone percolation results for varying sand volume fractions and interfacial zone thicknesses.
By comparing the results in Figs. 2 and 6, an interfacial zone thickness most consistent with the mercury intrusion results can be determined. In Fig. 6, the 10 micrometer curve can be eliminated on the basis that very little difference was observed in the experimental intrusion curves shown in Fig. 2 as the sand volume was increased from 48.6% to 55.4%, suggesting that both systems are nearly 100% percolated. Additionally, the large increase in intruded pro-threshold pore volume in Figs. 2 and 4 as the sand content is increased from 44.8% to 48.6% suggests that the 44.8% system is either unpercolated or much less percolated than the 48.6% sand system. This eliminates the 25, 30, and 40 micrometer curves from consideration since for these, a sand content of 44.8% would be greater than 95% percolated. Thus, the interfacial zone thickness most consistent with the mercury intrusion results is found to be 15-20 micrometers.
An interfacial zone thickness of 15-20 micrometers is somewhat less than the 40-50 micrometer value commonly measured using the SEM technique [3,4,5]. However, this higher value is generally based on the distance at which the porosity finally decreases to its bulk paste value. Since the largest interfacial zone pores are typically those observed closest to the aggregate surface, it is logical that the mercury intrusion technique would measure a somewhat smaller interfacial zone than the SEM technique. Recently, similar results for interfacial zone thickness have been based on a simple analysis of the mercury intrusion curves for plain paste and concrete and the surface area of the aggregate . The estimated interfacial zone thickness of 25-30 micrometers is in general agreement with our intrusion and model results.
The model can also be applied to interfacial zone percolation in concrete. For the concrete mixes presented by Winslow and Lui , the interfacial zones are found to be highly (> 75 %) interconnected for an interfacial zone thickness of 20 micrometers, in agreement with the large amount of pro-threshold (coarse) porosity observed during the actual mercury intrusion experiment . The hard core/soft shell computer model can also determine the fraction of cement paste within a given distance of an aggregate surface in a typical mortar or concrete. Using the aggregate size distributions provided in Table 1 and Ref. , results shown in Fig. 7 indicate that nearly all of the paste is within 100 micrometers of an aggregate, in general agreement with the SEM-based observations of Diamond et al. . Furthermore, 20-40% of the total cement paste is within 20-30 micrometers of an aggregate, which is the region typically classified as interfacial zone. This volume fraction of the total cement paste contained within interfacial zones is again in agreement with the recently presented results of Uchikawa et al. . As shown by the model, this amount of interfacial zone paste is more than sufficient to create a percolated pathway through a typical mortar or concrete specimen.
Figure 7: Fraction of total cement paste within a given distance of an aggregate surface.
The ultimate effect of percolated interfacial zones on mechanical and transport properties of concrete is somewhat uncertain. Certainly, the increases in compressive strength due to the incorporation of silica fume into concrete have been linked to an improved interfacial zone microstructure [20,21]. Effects of interfacial zone microstructure and connectivity on transport and durability properties have been studied much less. Ping et al.  have recently observed increases in electrical conductivity due to the presence of interfacial zones while Costa et al.  have noted similar effects on water permeability. The increase in transport may be subtle because in adding each aggregate to the concrete, we are replacing a somewhat porous cement paste volume with a non-porous aggregate surrounded by an even more porous interfacial zone. The fact that the permeability of concrete is generally one to two orders of magnitude higher than that of cement paste , however, would suggest that interfacial zone percolation may be detrimental in terms of the transport and long term durability of concrete.
Interestingly, the mercury intrusion results for mortars containing silica fume, in Fig. 3, are quite similar to those for mortars without silica fume. Feldman  has obtained similar intrusion curves for mortars with and without silica fume prepared at a water-to-solids (w/s) ratio of 0.6, while Delage and Aitcin  have observed the presence of these "macro-pores" in field concretes containing 15% silica fume at w/c ratios of 1.0, 0.67, and 0.56. It has been suggested that these larger pores are due to the dissolution of early age calcium hydroxide crystals as they react pozzolanically with the silica fume at 1 day and beyond. Conversely, Scrivener and Gartner  identified the large pores they observed in interfacial zones as isolated hollow hydration shells (Hadley grains) left behind when small cement particles dissolve and hydrate rapidly. In any case, for these pores to be detected in quantity by the mercury at low pressures, they must interconnect and form a percolated pathway throughout the microstructure (i.e. they cannot exist as isolated structures). This seems unlikely if the pores are all due to hollow hydration shells but could occur if some of the coarse porosity is due to dissolved calcium hydroxide. The calcium hydroxide phase can attain a volume fraction of 10-15% at 1 day in pastes containing silica fume before decaying due to the pozzolanic reaction . If the connected porosity is partially due to dissolving calcium hydroxide crystals, its effects might be reduced by using a lower w/c ratio or a higher concentration of silica fume. While these larger pores have been observed microscopically, more research is needed to determine the phase(s) from which they originate.