# Water Demand (or Specific Surface) of Aggregate as a Dominating Factor for SCC Composition Design
## 2 Methods
### Models of Water Demand/Specific Surface Area Based on Aggregate Grading Curve  
The specific surface area of the aggregate depends on many parameters: texture, roughness, shape factor, sphericity coefficient, etc. (see for instance Refs. [29; 30; 31; 32; 33; 34]). Unfortunately, these parameters are very difficult to assess directly. That is why it was decided to use the simplest solution relating water demand to the single parameter: grain size distribution of the rounded aggregate. Many models of this type were created at the beginning of the development of concrete technology. For example, the monograph [12] describes seven of them by [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON]. According to this source, all these models can be divided into two groups: those similar to the [PERSON] model [36] and those similar to the [PERSON] one [37]. Therefore, only these two models are presented in detail below. [PERSON] [36] presented the following formula for the water demand of the \(j\) fraction  
\[w_{aBj}=k\frac{1}{\sqrt[3]{d_{j-1}d_{j}}} \tag{2}\]  
where:  
\(k\)--consistency coefficient of the concrete mix (proportional to the thickness of the water film on the aggregate grains; value constant for all fractions in consideration);  
\(d_{j}\)--maximum grain size contained in a given aggregate fraction (mm);  
\(d_{j-1}\)--minimum size of grain contained in a given aggregate fraction (mm). As in the European standard set of sieves (i.e., acc. to EN-933-1 [38]) \(d_{j}=2\ d_{j-1}\):  
\[w_{aBj}=k\ \frac{1}{\sqrt[3]{\frac{1}{2}d_{j}^{2}}}=\ k^{\prime}\ d_{j}^{-2/3} \tag{3}\]  
[PERSON] [37] provided the formula for the water demand of the fraction \(j\):  
\[w_{aSj}=k\left[\frac{1}{0.5\left(\log\ d_{j-1}+\log\ d_{j}\right)}\right]^{3} \tag{4}\]  
\(d\) values are to be put here in \(\mu\)m.  
Again, assuming the European set of sieves, one can write that  
\[w_{aSj}=k\left[0.5\left(\log\frac{d_{j}}{2}+\log\ d_{j}\right)\ \right]^{-3} \tag{5}\]  
The water demand of the entire aggregate is obtained in both cases from the weighted average of the mass share of fraction \(j\) (\(y_{j}\)) in the grain size distribution (i.e., it is assumed that \(\sum_{j=1}^{n}y_{j}=100\%\)). \[w_{a}=k\frac{\sum_{j=1}^{n}y_{j}w_{aj}}{\sum_{j=1}^{n}y_{j}}=k^{\prime}\sum_{ j=1}^{n}y_{j}w_{aj} \tag{6}\]  
The third model taken for comparison is the above-announced method for calculating the specific surface area presented by [PERSON], [PERSON], and [PERSON] (partly following the so-called [PERSON]'s approach) [15], hereinafter referred to as the ONT model. The author used this solution in an extension of the method [3], detailed in Ref. [15]. The formula for the specific surface area \(\mathrm{S_{SO}}\) according to these authors is as follows:  
\[S_{\mathrm{SO}}=\frac{1}{\phi_{a}}\sum_{i=1}^{n}\frac{f_{i}}{k_{i}}\frac{\phi_ {at}}{d_{mi}} \tag{7}\]  
where:  
\(\phi_{a}\)--volume concentration (absolute volume) of aggregate in the total volume of concrete mix (typically in \(\mathrm{dm}^{3}/\mathrm{m}^{3}\));  
\(\phi_{a\ i}\)--volume concentration of aggregate grains of fraction \(i\);  
\(d_{mi}\) --average diameter of grains of fraction \(i\);  
\(k_{i}\)--volumetric shape factor for fraction \(i\) (for a sphere \(k=\pi/6\));  
\(f_{i}\)--surface shape factor for fraction \(i\) (for a sphere \(f=\pi\)). Below, for simplicity, it is assumed that for a given aggregate both \(f_{i}\) and \(k_{i}\) are constant. It is a reasonable assumption for rounded aggregate, but it may not work in the case of the crushed one, see e.g., [39; 40]. Then, it can be written that  
\[S_{\mathrm{SO}}=\frac{1}{\phi_{a}}\frac{f}{k}\sum_{i=1}^{n}\cdot\frac{\phi_{ ai}}{d_{mi}} \tag{8}\]  
A similar formula, but in mass units, is also given in Ref.