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Results and Discussion

The calculated chloride diffusion coefficients for the mixes are shown in Tables 1 and 2 for the 0.4 w/c and 0.5 w/c ratio mixes, respectively. The coefficient of variation, CV, is also presented. The permeability results are graphed in Figure 3, which plots permeability vs. degree of hydration for the two w/c ratios and the four sand contents. As would be expected, the diffusivities and permeabilities are higher for the 0.5 w/c ratio systems than for their 0.4 w/c counterparts, due to the higher initial capillary porosity in a 0.5 w/c system.

Sand volume (%) Degree of hydration* (%) tD (hours) D (m2/s x 10−11) Average D D (simulation) CV (%)
0 54−55 72.2, 69.0, 69.5 1.64, 1.72, 1.71 1.69 2.18 2.1
0 59−60 115.4, 109.1, 111.4 1.02, 1.09, 1.16 1.09 1.16 5.2
35 65−70 150.0, 156.1 0.76, 0.72 0.74   3.9
45 50-57 53.2, 51.0, 48.1 2.23, 2.31, 2.45 2.33   3.9
45 65-67 67.5, 69.2, 59.1 1.72, 1.52, 2.13** 1.62 (1.79**)   6.2 (15**)
55 55-61 20.9, 42.1 5.73**, 2.8 (4.27**) 2.8   (35**)
55 66-72 138.0, 130.0 0.78, 0.85 0.82   4.3

Table 1: Chloride Diffusion Coefficients for 0.4 w/c Ratio Mixes (*=degree of hydration at start and end of test, **=result excluded from average due to high variability)

Garboczi and Bentz [11] have utilized computer simulation to develop an equation for the diffusivity of cement paste as a function of capillary porosity. The values measured here experimentally for the paste specimens can be compared to the equation:

where D/Do is the relative diffusivity, φ is the capillary porosity fraction, and H is the Heaviside function (taking a value of 0 when (φ − 0.18) < 0 and a value of 1 otherwise). For Cl− ions, Do has a value of about 1.5 x 10−9 m2/s at room temperature [12]. For hardened cement paste, based on the analysis of Powers and Brownyard [13], as modified by Young and Hansen [14], the capillary porosity can be estimated as:

where α is the degree of hydration measured for the sample. For the w/c = 0.40 data presented in Table 1, the agreement with this equation is excellent, with an average variation of less than 10% between the simulation (column 6) and experimental (column 5) values.

Sand volume (%) Degree of hydration* (%) tD (hours) D (m2/s x 10−11) Average D D (simulation) CV (%)
0 46-48 15.8, 17.4 7.95, 7.12 7.54 12.88 5.5
0 55-56 40.0, 37.0, 36.0 2.78, 3.00, 3.11 2.96 8.12 4.6
35 70-73 125.0, 115.0 0.92, 0.99 0.96   3.7
45 53-55 22.2, 20.3, 19.6 5.16, 5.76, 6.07 5.66   6.7
45 70-72 63.3, 64.6, 66.1 1.8, 1.78, 1.8 1.79   0.5
55 55-57 22.6, 22.2 4.93, 5.66 5.3   6.9
55 70-73 125.0, 130.0 0.86, 0.82 0.84   2.4

Table 2: Chloride Diffusion Coefficients for 0.5 w/c Ratio Mixes

For the w/c = 0.50 data, the simulation values are on the average a factor of two times greater than the values measured experimentally, an acceptable agreement. The analysis presented here does not include the effects of binding of the chloride ions by reaction with or adsorption by the phases present in the cement paste. Computer simulation studies have shown that the binding capacity of a paste can be important in slowing down the ingress of chloride ions into a cement paste specimen [15]. Although binding cannot be ignored, it should not be a factor in comparing pastes to mortar specimens at a constant w/c ratio as the binding per unit volume paste should be constant.

Introducing inert sand particles into the cement paste resulted in higher diffusivities and permeabilities even though the sand particles are relatively impenetrable compared with cement paste. This is in agreement with the general observation that the permeability of concrete is one to two orders of magnitude higher than that of neat cement paste [16]. The difference seems to be more pronounced as hydration proceeds. This suggests that the differences between the transport coefficients of the paste and mortar are due to the different pore structure developed in the presence of sand particles. The coefficient of variation of the calculated diffusion coefficients was less than 10%. Only two samples yield significantly different results, which could be caused by such defects as a large air bubble inside the sample. These two samples were excluded from the final analysis.

The permeability results provide some indication that interfacial zone percolation is occurring between 35 and 45% sand for the 0.4 w/c ratio systems. For these systems, statistical

Figure 3: Permeability vs. degree of hydration for 0.4 and 0.5 w/c ratio mixes.

analysis indicates that at the 95% confidence level, the differences between the 0% sand and all other sand contents are significant, differences between the 35% sand and the 45- 55% sand contents are generally significant, and differences between the 45 and 55% sand contents are never significant. The results for the 0.5 w/c systems are less clear with the 35 and 55% sand contents having nearly the same permeabilities and the 45% sand system a significantly lower permeability. Part of the difficulty in comparing results at different sand contents is the variable porosity (air contents) of the various mortars and pastes.

The critical pore radius (or maximum continuous pore radius) showed that the largest fraction of interconnected pores in mortars have greater radii than in the paste. This difference between paste and mortars was much less pronounced at 0.5 w/c ratio. However, there was a great difference between the range of the critical pore radius with continuing hydration. When hydration of the samples increased from 50% to 73%, the critical radius decreased from 65 nm to 17 nm for the 0.4 w/c ratio mortars, while for the 0.5 w/c ratio mortars this decrease was from 140 nm to 20 nm.

It might be expected that there are relationships between the two transport rates measured in this study and the pore structure characteristics. Roy and Li [17] investigated the relationship between the rapid chloride permeability (total charge passed in six hours) and mean pore radius for ordinary portland cement pastes as well as for cements containing supplementary cementing materials. They observed that the chloride transport rate increased linearly with mean pore radius, which was defined as the pore radius at which 50% of the pore volume was intruded in the pore size range considered. Roy [18] pointed out that the mean pore radius and the critical pore radius had similar values in most cementitious materials. Since the critical radius represents the grouping of the largest fraction of interconnected pores influencing the transport properties, the relationship between the critical pore radius and the chloride diffusion was examined in the present work. The diffusion coefficient, determined from the accelerated concentration cell test described above, was plotted against the critical pore radius of the corresponding mix for the two w/c ratios [Fig. 4]. A well correlated linear relationship between chloride diffusion and critical pore radius was observed, especially for the 0.5 w/c ratio mixes (r2 for 0.5 w/c ratio was 0.972 and r2 for both w/c ratios was 0.931).

For cement pastes with w/c between 0.23 and 1.0, Nyame and Illston [19] have previously shown that permeability can be represented by a power-law function of critical pore radius with a best-fit exponent of 3.28. Figure 5 shows a log-log plot of the results obtained in this study. Here, the best-fit line has a slope of 3.35, in excellent agreement with the results given in [19], while exhibiting a comparable amount of scatter. Usually, permeability is related to a characteristic length scale raised to the power of two [20]. However, in these same equations, a term usually appears to account for the tortuosity of the porous media, which also appears in equations for diffusivity. Because the diffusivity itself has been shown to be a linear function of critical radius, one might expect that permeability would be a function of critical radius to the (2+1=3) third power, not that different from the calculated values of about 3.3. This hypothesis can be tested more rigorously by the application of the theory of Katz and Thompson to the data set obtained in this study.

Figure 4: Chloride diffusion coefficient vs. critical pore radius (Cr) for portland cement pastes and mortars.

The basic Katz-Thompson relationship (6) states that

where dc is the critical pore diameter, F is the formation factor (equivalent to Do/D [11]), and c is a constant, taken to be 226 in the original work of Katz and Thompson [6], but which can assume other values depending on the assumptions that are made concerning pore geometry. This relationship has been applied quite successfully to predicting the permeabilities of sedimentary rocks [6]. The current study is unique in that it is the first known study where formation factor, permeability, and critical pore diameter were determined for a common set of samples of cement-based materials. Recently [21,22], two attempts have been made to evaluate this relationship for cement-based materials. The first used data sets which lacked information on formation factor, and so estimated F from available MIP curves [21]. The second used values of F (or Do/D) measured experimentally [22], using impedance spectroscopy techniques on a series of specimens similar to those used by Nyame and Illston [19]. The results of El-Dieb and Hooton in [21] indicated that the Katz-Thompson relationship was generally not valid for cement-based materials. However, the results of Christensen et al. in [22] found the permeabilities determined using the Katz-Thompson

Figure 5: Permeability vs. critical pore radius (Cr) for portland cement pastes and mortars.

relationship to be within an order of magnitude of those observed experimentally, with larger deviations at the later hydration times. This agreement could be somewhat further improved by using a constant other than the value of 226 originally suggested by Katz and Thompson. Also, it is crucial to note that while conductivities, diffusivities, and water permeabilities are measured on never-dried samples, the critical pore diameter, dc, is typically measured by MIP on dried samples. When dc is of a magnitude associated with capillary pores, implying that the capillary pores are still percolated, the effect of drying on the relevant pore structure should be negligible. However, when dc is of C-S-H gel pore size (< 40 nm), then the effect of drying could become more important. If the measured values of dc do not reflect the true pore structure due to drying artifacts and cracking then, obviously, the Katz-Thompson relation is less likely to be accurate. One alternative to using MIP would be to utilize desorption isotherms to estimate the critical pore diameter [23]. Figure 6 shows a plot of the permeability predicted by the Katz-Thompson relationship against that measured experimentally for the two w/c ratios examined in this study. Here, a constant of 180 was selected to provide the best fit to the experimental data. Figure 6 shows that the Katz- Thompson relationship predicts the experimental permeabilities for the 0.5 w/c ratio systems within a factor of five but consistently overestimates the permeabilities for the 0.4 w/c ratios, particularly at the later stages of hydration. These results are in general agreement with those presented in [21], which, using a value for c of 226 and estimating F, found that the Katz- Thompson relationship overestimated permeabilities for w/c ratios of 0.25 and 0.36 and also those given in [22], which showed this relationship to be adequate for systems with w/c between 0.47 and 1.0. Thus, it would seem that Equation 5 can perhaps be used for systems with relatively high w/c ratio systems but not for lower w/c ratios. This could be an effect of the capillary porosity percolation [24] and the changing pore structure of cement-based materials as a function of w/c and hydration as was discussed above, and the effect of drying on measurements of dc when dc is clearly of gel pore magnitude, as is the case for the latest hydration stages of the 0.4 w/c ratio systems. The results of [24] imply that the critical degree of hydration at which the capillary pores become disconnected is 0.66 for 0.4 w/c, and 0.86 for 0.5 w/c. So for α αc, one would predict that the paste transport is dominated by capillary pores, and for α > αc, by C-S-H gel pores. Looking at Figure 1, it is clear that for many of the later hydration points studied, the 0.4 w/c transport will be dominated by gel pores, since α > αc. This is reflected in the small changes in dc with hydration, especially for the 0% sand data, as the gel pore sizes do not change with hydration but are determined by C-S-H morphology [23]. The contribution of interfacial zone pores for the mortars changes this picture somewhat. In Figure 2, however, all of the 0.5 w/c data studied is in the α  αc regime, and one sees very large changes in dc with hydration, even for the 0% sand specimens. The value of dc is clearly picking up the progressive reduction of the diameter of the still- percolated capillary pores, which are dominating transport. Because the measurement of these capillary pore diameters is less affected by drying, one might then expect that the Katz-Thompson relation would work better for the 0.5 w/c systems than for the 0.4 w/c systems.

Figure 6: Predicted (Katz-Thompson) permeability vs. measured permeability for Portland cement pastes and mortars.

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