# Water Demand (or Specific Surface) of Aggregate as a Dominating Factor for SCC Composition Design
## 5 Discussion  
Figures 10 and 11 present the results of the analyses of models (15)-(18). To make the comparison between models easier, the calculations were made assuming the constants \(\chi_{i}=1\). The model based on the Bolomey formula is presented in a separate figure due to the different magnitude of the obtained values. Figure 10: The correlation between \(\mathrm{V_{p}}\) and \(\mathrm{t_{rel}}\) for ONT (15), Stern (17) and RSS (18) models, assuming \(\chi_{i}=1\). Figure 9: V-funnel test results (\(t_{V}\)). A very high level of fit was achieved in all cases (R\({}^{2}\) between 0.95 and 0.985). This means that all four presented models are verified positively and that there is no need to work on the new model. It also means that the water demand/specific surface area of the aggregate can certainly be treated as the dominant parameter that determines the cement paste content necessary to achieve self-compactibility limit of SCC. That is why this line may be called the \"minimum paste demand line\". Additionally, there is a clear indication that non-linear models (i.e., by [PERSON] and [PERSON]) are more precise (98% of good fit vs. 95.2% for the linear ones). Next, the constants of all models were calibrated so as to obtain the same \(t_{rel}\) at the point of the average value of \(V_{p}=350.5\) dm\({}^{3}\)/m\({}^{3}\). \(\chi_{O}=1.55\) was assumed as a reference point. The results of this calibration are shown in Figure 12. Noteworthy here is a slightly different angle of inclination of the line obtained for the ONT model. The special feature of this model is the use of volume units to determine \(\sum_{i}\). It can be hypothesized that this is related to the lack of the factor \(\varphi_{a}\) in the denominator of the expression in the \(t_{relO}\) model (15), but confirming this hypothesis would require the use of additional models using volume units. Table 3 lists the \(\chi_{i}\) parameter values depending on the adopted reference value \(\chi_{O}\). The match between the \(\chi_{i}\) values and the type of aggregate used should be treated as a rough indication, as even small changes in \(V_{p}\) alter the obtained \(\chi_{i}\) values significantly. Additionally, the table shows the difference in \(t_{rel}\) value in these cases. The difference between the cases of ideal spheres and crushed aggregate is 24.4%, so it is a very important one. The replacement of rounded river origin coarse aggregate by the crushed one is smaller, but still significant (8.5%). Only the difference between rounded coarse aggregate and a grit is acceptable (ca. 3.5%). This means that the comparability of the \(t_{rel}\) determination results between different sets of aggregates of the same type should be considered limited but not excluded, contrary to comparison between different types of aggregate, which is highly questionable. Figure 11: The correlation between V\({}_{\rm{ZP}}\) and t\({}_{\rm{rel}}\) for the Bolomey (16) model, assuming \(\chi_{\rm{i}}=1\). Theoretically, it is possible to determine the value of \(\chi_{O}\) using Equation (11) directly, i.e., putting the real values of \(V_{exc}\) calculated by definition as a difference between \(V_{p}\) and a loose packing density of aggregate. Unfortunately, this method is highly questionable, as it has a very high risk of obtaining a very large dispersion of results. Each change--even a very small one in the paste content (\(V_{p}\)), which does not affect the measured consistency (e.g., 3 dm\({}^{3}\)/m\({}^{3}\))--significantly shifts the paste demand line along both axes. The coefficient \(\chi_{i}\), on the contrary, influences the \(t_{rel}\) axis only. This is demonstrated in Figure 13 by the \"one composition\" line; a change in \(D_{0}\) by 5 cm was achieved at \(\Delta V_{p}\) from the range of around 15-20 dm\({}^{3}\). Figures 13-15 present the three basic SCC consistency measures influence on the \(t_{rel}\) values, using the example of ONT model (15), assuming \(\chi_{O}=1\). The correlation is always linear, and the lines are more or less parallel.