3. Results and Discussion

Silica fume influences the microstructural development of hydrating cement paste in concrete through at least three mechanisms. First, because of its small particle size, silica fume packs more efficiently in the ITZ region than the larger cement particles do. This is illustrated in Fig. 1, which plots the variation in volume fraction of cement and silica fume (for a unit cement paste basis) with distance from the single aggregate surface for an initial microstructure, for a concrete with w/c=0.4 and a 10 % silica fume addition on a mass basis. When viewing Fig. 1, it should be kept in mind that the results shown are for packing digitized "spherical" particles, and that in continuum space, even the volume fraction of the much smaller silica fume would decrease within 1 µm or so of the aggregate surface (due to inefficient packing of spheres against a "flat" wall).

Due to these packing limitations, the cement volume fraction is seen to decrease significantly as the aggregate surface is approached, so that the water volume fraction naturally increases. The very fine silica fume particles are more or less evenly distributed within this water phase and therefore actually exhibit an increase in volume fraction in the ITZ relative to the bulk paste. Thus, the ratio of silica fume to cement is much higher in the ITZ region than it is in the bulk paste. This "extra" silica fume in the ITZ region will participate in pozzolanic reactions, resulting in a denser, more homogeneous ITZ microstructure [22].

Figure 1: Model results for initial cement and silica fume volume fractions vs. distance from center of aggregate surface for a w/c=0.4 concrete with 10 % silica fume addition on a mass basis. Note that the ITZ is seen to extend approximately 15 µm into the cement paste, corresponding to the "median" cement particle diameter.

Second, silica fume reduces the overall porosity in a concrete. These first two effects of silica fume can be seen clearly in Fig. 2, which contrasts the variation in capillary porosity in the cement paste with distance from the surface of an aggregate particle for w/c=0.4 systems with silica fume additions of 0 % and 10 %. Because we are considering a silica fume addition, the initial overall porosity is slightly reduced due to the additional volume occupied by the silica fume. Still, after hydration, the overall porosity is further reduced, due to the pozzolanic reaction. Furthermore, the porosity gradient in the ITZ region is also significantly reduced. This improvement in microstructure is achieved despite the fact that after 2000 cycles of hydration, the degree of hydration of the cement in the 0 % silica fume system is 0.843, while that in the one with 10 % silica fume is only 0.775 (due to water availability/space limitations).

Figure 2: Model results for capillary porosity fraction (in the cement paste) vs. distance from center of aggregate surface for w/c=0.4 concretes hydrated for 2000 cycles using the NIST model. Top two lines indicate initial capillary porosities and lower two correspond to capillary porosities after hydration.

Silica fume has a third extremely significant effect on the microstructure of hydrating cement paste. The pozzolanic C-S-H gel produced from silica fume appears to have an inherent chloride ion diffusivity that is approximately 25 times less than that of C-S-H gel formed from conventional cement hydration [11]. In part I of this paper [11], the following equation was developed for estimating the relative diffusivity of a cement paste with silica fume as a function of capillary porosity, $\phi$, and silica fume content, CSF:

$$\frac{D}{D_0}(\phi,CSF)= \frac{0.0004}{\beta(CSF)} + \frac{0.... ...(CSF)} \cdot \phi^2 + 1.7 \cdot (\phi-\phi_c)^2 H(\phi-\phi_c)$$ (2)

where D is the diffusivity of chloride ions in the cement paste, D₀ is their corresponding diffusivity in bulk water, $\phi_c$_c is the capillary porosity at which the capillary pore space depercolates (0.17), H is the Heaviside function (H(x)= 1 when x> 0 and 0 otherwise), and $\beta(CSF)$ (CSF) is a function of the silica fume addition that can be approximated by:

$\beta(CSF)~=~1.0~~~~~~~~~~~~~~~~~~~~CSF <= 0.025$

$$\beta(CSF)~=~1.0~-~48.6 \cdot CSF~+~2330. \cdot (CSF)^2~-~11400. \cdot (CSF)^3~~~~~0.025 < CSF <= 0.12\\$$ (3)

$\beta(CSF)~=~9.0~~~~~~~~~~~~~~~~~~~~~~~~~~CSF > 0.12$

The upper bound value of 9.0 for silica fume additions greater than 12 % is a conservative estimate, as the experimental data of Jensen [17] indicates further significant improvements in performance for silica fume additions up to 20 % (which are not explained by the current versions of the microstructural models [11]). This is not an issue for the 5 % silica fume additions where the local silica fume content rarely exceeds 10 %, but is an issue for the overall silica fume additions of 10 %, where the average silica fume content in the ITZ regions may slightly exceed 16 %. Because we have taken a conservative approach, our predictions of the improvements due to silica fume will be lower bounds on what may actually be experienced in practice.

At the concrete level, it is necessary to determine the influence of the increased ITZ diffusivity on the overall diffusivity of the concrete composite. Rather than executing the concrete level HCSS model for each of the 36 computer experiment runs, the ratio of D_ITZ/D_bulk was varied systematically for both of the aggregate volume fractions being considered in this study. Because of the densifying nature of silica fume on ITZ microstructure, it was necessary to execute the HCSS model for cases both where the ITZ region had an enhanced diffusivity relative to that of the bulk cement paste ( D_ITZ/D_bulk  > 1) and vice versa ( D_ITZ /D_bulk < 1). Figure 3 shows the values obtained for the ratio of D_eff to D _bulk for the various values of D_ITZ /D_bulk. Previously, Garboczi et al. [16] have shown that such data can be described by a relationship of the form:

$$\frac{D_{eff}}{D_{bulk}}= \frac{a~+~b X~+~c X^2}{1~+~d X}$$ (4)

where X is the ratio D_ITZ/D _bulk. This equation was fitted to the two data sets shown in Fig. 3; the resulting coefficients are provided in Table 1. It is clear from the coefficients in Table 1 and the data in Fig. 3 that, all other things being equal, an increase in aggregate volume fraction will result in a decrease in concrete diffusivity for the aggregate gradation and ITZ thickness examined in this study, in agreement with the experimental results of Buenfeld and Okundi for a limited set of concretes [23]. Of course, this computer study neglects the effects of segregation, bleeding, and improper consolidation, all of which could lead to increased diffusivities as the volume fraction of aggregates is increased in "real-world" concretes.

Figure 3: Ratio of D_eff/D_bulk vs. D_ITZ/D _bulk for aggregate volume fractions of 0.62 and 0.70. Solid and dashed lines are fits of equation 4 to the simulation data points.

Table 1: Coefficients from fitting equation 4 to simulation data

Vagg	a	b	c	d
0.62	0.2195	0.09296	0.00317	0.1709
0.70	0.1483	0.07806	0.00353	0.1686

Table 2: Diffusion coefficients for the 36 concrete mixtures (t _ITZ=15 µm)

w/c	CSF(%)	$\alpha$	Vagg(%)	Dbulk/D0	DITZ/Dbulk	Dconc x 10-12m2/s
0.3	0	0.686	70	0.000641	1.29	0.243
0.3	0	0.746	70	0.000491	1.15	0.181
0.4	0	0.757	70	0.001580	6.81	1.123
0.4	0	0.843	70	0.000959	4.03	0.537
0.5	0	0.799	70	0.016700	3.02	8.334
0.5	0	0.876	70	0.008230	4.45	4.813
0.3	5	0.644	70	0.000199	0.69	0.066
0.3	5	0.688	70	0.000168	0.65	0.055
0.4	5	0.726	70	0.000387	3.64	0.208
0.4	5	0.799	70	0.000273	1.08	0.099
0.5	5	0.773	70	0.005500	3.49	2.906
0.5	5	0.857	70	0.000971	8.90	0.789
0.3	10	0.615	70	0.000063	0.97	0.022
0.3	10	0.655	70	0.000055	0.86	0.019
0.4	10	0.714	70	0.000112	4.43	0.065
0.4	10	0.775	70	0.000081	1.19	0.030
0.5	10	0.768	70	0.001640	6.79	1.164
0.5	10	0.845	70	0.000145	17.45	0.172
0.3	0	0.686	62	0.000662	1.26	0.337
0.3	0	0.755	62	0.000491	1.16	0.246
0.4	0	0.758	62	0.001850	5.07	1.386
0.4	0	0.844	62	0.001030	3.20	0.662
0.5	0	0.794	62	0.019300	2.23	11.190
0.5	0	0.877	62	0.009620	2.98	6.053
0.3	5	0.647	62	0.000193	0.68	0.089
0.3	5	0.690	62	0.000162	0.63	0.074
0.4	5	0.732	62	0.000378	4.87	0.279
0.4	5	0.809	62	0.000258	0.98	0.126
0.5	5	0.772	62	0.006850	3.13	4.374
0.5	5	0.853	62	0.001250	7.95	1.112
0.3	10	0.632	62	0.000061	0.98	0.030
0.3	10	0.669	62	0.000055	0.89	0.026
0.4	10	0.721	62	0.000114	2.90	0.071
0.4	10	0.785	62	0.000081	1.11	0.040
0.5	10	0.765	62	0.002380	4.90	1.761
0.5	10	0.842	62	0.000153	20.90	0.215

The diffusivity results obtained for the 36 different concrete mixtures are summarized in Table 2. The final values for D _conc are seen to span nearly three orders of magnitude. When examining the variation of the ratio D_ITZ /D_bulk with respect to the independent variables, interestingly, for lower w/c ratios, this ratio generally decreases with increasing hydration, while for w/c=0.5, the converse is true. This is due to the specific nature of the relationship between capillary porosity and diffusivity (eqn. 2). For a given cement paste system, the ratio of D_ITZ /D_bulk will rise to a maximum with increasing hydration (as the bulk capillary porosity depercolates before that contained in the ITZ regions), and then fall as both the ITZ and bulk paste capillary porosities become depercolated [10,24].

The values of D_conc given in Table 2 were fitted to the functional form provided in eqn. 1, resulting in the following predictive equation for concrete diffusivity as a function of mixture proportions and expected degree of hydration:

$$log_{10} (D_{conc})= -13.75~-~0.82 (\frac{w}{c})~+~32.55 {(\frac{w}{c})}^2~+~8.374 CSF~+~15.36 (CSF)^2~$$ (5)

$~~~~+23.15 (\frac{w}{c})CSF~+~5.79 \alpha ~-~21.10 (\frac{w}{c}) \alpha ~-~43.15 (CSF) \alpha ~-~1.705 V_{agg}$

where D is in units of m²/s. As shown in Fig. 4, which plots the predicted values vs. those obtained from the computer experiment, eqn. 5 generally predicts the simulated results within 25 % of the actual value. This is considered to be a reasonable prediction considering that, as mentioned earlier, the simulated values span nearly three orders of magnitude.

Figure 4: Predicted vs. computed diffusion coefficients for the concretes examined in this computer experiment. Solid line indicates a one to one relation between predicted and calculated values. Dotted lines indicate a factor of 1.25 (25 %) above and below the calculated values.

Equation 5 can also be used to predict the relative improvement in diffusion resistance offered by various addition levels of silica fume. This is most easily formulated as the multiplicative increase in diffusion resistance for a given silica fume addition (due to the logarithm form of eqn. 5) and specific values of w/c ratio and degree of hydration. In this case, the multiplicative increase is given by:

$$\frac{D_{conc}(CSF=0)}{D_{conc}(CSF)}~=~10^{- [(8.374-43.15 \alpha + 23.15 (\frac{w}{c})) \cdot CSF +15.36 (CSF)^2]}.$$ (6)

Since both w/c and $\alpha$ are variables in eqn. 6, we will fix $\alpha$ and plot the variation in the dependent variable with w/c ratio for four different silica fume additions (2.5 %, 5 %, 7.5 %, and 10 %). Figures 5 and 6 provide examples of the results for $\alpha =0.6$ = 0.6 and $\alpha =0.675$ = 0.675, respectively. In both of these figures, it is clear that silica fume is more effective in reducing diffusivity in lower w/c ratio concretes. This is in agreement with the rapid chloride permeability measurements of Berke and Roberts [5]. For the lower w/c ratios (e.g., 0.3), the addition of 10 % silica fume may decrease the chloride ion diffusivity by a factor of 15 or more.

A more quantitative evaluation against experimental data can be made using the data sets of Hooton et al. [6] and of Alexander and Magee [25]. Hooton et al. measured concrete diffusivity by a number of methods for three different water to cementitious materials (w/b) ratios and three different silica fume replacement levels. For comparison purposes, we shall consider their diffusion results generated in the long term, from a modified chloride ponding test [6]. It is worth noting, however, that the relative improvement provided by the silica fume is nearly constant for all of the different "diffusion" coefficients measured in [6]. This, in spite of the fact, that for a given concrete, the different tests may produce results that vary by up to a factor of three [6]. Because in the current computer experiment, the w/c ratio is maintained constant and silica fume additions are considered, the experimental data reported in [6] must first be transformed to the same parameter space. Thus, the w/b=0.35 mixture with a 12 % silica fume replacement corresponds very closely

Figure 5: Computed multiplicative increase in diffusion resistance due to silica fume addition vs. w/c ratio for an assumed degree of hydration of 0.6. Filled data points indicate the experimental data of Alexander and Magee [25].

Figure 6: Computed multiplicative increase in diffusion resistance due to silica fume addition vs. w/c ratio for an assumed degree of hydration of 0.675. Filled data points indicate the experimental data of Hooton et al. [6] (7.7 % and 13.8 %) and of Alexander and Magee [25] (10 %).

to a w/c=0.4 mixture with a 13.8 % silica fume addition. Similarly, the w/b=0.4 mixture with a 7 % silica fume replacement corresponds to approximately a w/c=0.44 mixture with a 7.7 % silica fume addition. Alexander and Magee measured the chloride conductivity of 28 day-old concretes with and without 10 % silica fume additions, using a conductivity cell of their own design [25].

Of course, an estimate of the degree of hydration of the actual concretes evaluated is required; this will surely vary with w/c ratio and silica fume addition. For this comparison, the simplifying assumption was made that the degree of hydration of all of the concretes of Hooton et al. [6] is 0.675. For the 28 day-old specimens of Alexander and Magee [25], the experimental results are plotted on both figures as the degree of hydration should be somewhere between the values of 0.6 and 0.675. The experimental results were then plotted along with the simulation data in Figs. 5 and 6. The agreement between experimental data and simulation results is quite reasonable for these two limited sets of data. For the experimental systems of Alexander and Magee, it would be expected that the w/c=0.49 specimens would have hydrated to a slightly lesser degree than the w/c=0.56 specimens, hence the observed agreement between the w/c=0.49, $\alpha$=0.6 results and also between the w/c=0.56, $\alpha$=0.675 results.

Several limitations must be kept in mind when considering the developed equation for predicting diffusivity. First, it assumes that the concrete is saturated and free from defects (such as cracking or other local inhomogeneities). Second, it also assumes that chloride ion transport is the only phenomenon occuring within the microstructure. The experimental results of Jensen [17] have indicated that when leaching (of calcium hydroxide and other components from the cement paste) and diffusion of chloride ions occur simultaneously, the measured diffusion coefficients are approximately a factor of 2.5 greater than those obtained under non-leaching conditions. Thus, the exact experimental conditions used for evaluating a concrete diffusivity have a major influence on the measured coefficients. If leaching conditions will be present in the actual concrete exposure, the coefficients predicted by eqn. 5 may need to be increased by up to a factor of 2.5, to provide a conservative estimate of field performance. Given the highly variable field exposure conditions, etc., it may be better to use the developed equation in a relative sense to predict the expected relative improvement in performance (service life) by the addition of silica fume to a base concrete mixture. And, of course, eqn. 5 has been developed for w/c ratios between 0.3 and 0.5, silica fume additions between 0 % and 10 %, aggregate volume fractions between 0.62 and 0.70, and degrees of hydration between about 0.6 and 0.9. Extrapolation beyond this range of parameters using the developed equation may yield predictions of limited validity and should be performed only with extreme caution.