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The above analysis points out the need for measuring the degree of hydration of concrete samples to enable an accurate prediction of concrete diffusivity. Unfortunately, there is currently no standard method for performing this assessment. While this property may be assessed indirectly based on continuous heat release measurements , the most typical method is the measurement of non-evaporable water content, which can be used on aged specimens without a continuous monitoring of the progress of hydration, as long as carbonation is not an issue. Here, the degree of hydration is estimated based on the weight loss of a sample when heated from about 105ºC to around 1000ºC. While straightforward experimentally, one issue to be considered is the size of the sample necessary to obtain a representative volume of the concrete. For cement pastes, very small samples, less than one gram, are quite representative, but for concrete, samples this small could result in sampling a volume entirely composed of aggregate or entirely composed of the matrix cement paste. Another question to consider would be: for a fixed sampling volume, what shape should the sample be? To explore these issues, the microstructure model for concrete used in this study has been extended.
Basically, for a fixed size distribution and volume fraction of aggregate, the resultant 3-D (27 cm3) volume of concrete has been subdivided using different basic shapes: cubes (a x a x a), plates (a x a x b, a > b, a=3), and prisms (a x a x b, a < b, b=3). The volume is then exhaustively sampled using these shapes and the standard deviation in the resultant estimates of volume fraction of aggregates determined. The lower this standard deviation, the more likely that a specific chosen volume based on this shape will be representative of the concrete as a whole. Using the coarsest distributions in Figure 1 for both the coarse and fine aggregates, results of this analysis are shown in Figures 7 and 8 for aggregate volume fractions of 60 and 75%, respectively. In both graphs, it is quite clear that the use of plates for the sampling element is superior to either prisms or cubes. Thus, grinding away a finite thickness layer of a concrete cylinder to obtain a representative sample should yield the most accurate estimate of degree of hydration. Perhaps this result is not surprising, since planar samples are commonly used for the determination of air void content in concrete via ASTM C457  and Hooton et al. are typically using 1-mm thick grindings to obtain representative chloride distributions of mortars and concretes [2,31].
Figure 7: Standard deviation in estimated volume fraction of aggregate vs. sample volume for three different sampling element shapes with an aggregate volume fraction of 60%.
Figure 8: Standard deviation in estimated volume fraction of aggregate vs. sample volume for three different sampling element shapes with an aggregate volume fraction of 75.7%.
For the aggregate volume fraction of 75%, ten simulations using the plate sampling were conducted and pooled to determine an estimate of the standard deviation in aggregate volume fraction. Using these estimates and a t-value of 2.0 (for a large sample at the 95% confidence level) , Table 3 summarizes the expected uncertainty at the 95% confidence level in the average aggregate volume fraction for selecting n slices of a fixed thickness. As the allowable sample volume (thickness) becomes larger, the number of samples required to be within a fixed value, say 0.02, of the actual volume fraction decreases. For example, for the size distribution considered in this study, this accuracy level can be achieved by taking two samples that are 3 x 3 x 0.75 cm3, whereas ten samples that are 3 x 3 x 0.10 cm3 would be required. It is then straightforward to calculate how this deviation might affect the accuracy of the measured degree of hydration. For example, consider a w/c ratio of 0.4 cement paste at a degree of hydration of 0.75. For an aggregate volume fraction of 75%, there will be 5.66 grams of aggregate per gram cement (assuming specific gravities of 3.2 and 2.65 for the cement and aggregates, respectively). If the aggregate contents in the samples selected for analysis are actually 73% or 77%, assuming that a constant volume sample is used, the degree of hydration will be calculated as 0.81 and 0.69, respectively. Substituting these values into Eqn. 4 results in diffusivities ranging between 0.77 x 10-12 and 1.8 x 10-12 m2/s, a factor of over two in variation, highlighting the importance of obtaining an accurate estimate of the degree of hydration for quantitative studies.
|Table 4: Expected Uncertainty in Aggregate Volume Fraction Estimate|