# Water Impermeability of Self-Compacting Fly-Ash-Containing Concrete
## 3 Results and Discussion  
To perform the experiments, a three-level five-factor plan Ha\({}_{5}\)[23] was used, which provides for the possibility of obtaining quadratic polynomial models. Conditions for planning experiments are given in Table 2. The experimental planning matrix and compositions of concrete mixtures are given in Table 3, and the results of experimental data are in Table 4. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Factors**} & \multicolumn{5}{c}{**Levels of Variation**} & \multirow{2}{*}{**Interval**} \\ \hline
**Natural** & **Coded** & \(-\)**1** & **0** & **+1** & \\ \hline Water–cement ratio, W/C & \(X_{1}\) & 0.3 & 0.4 & 0.5 & 0.1 \\ \hline Water consumption, kg/m\({}^{3}\) & \(X_{2}\) & 170 & 180 & 190 & 10 \\ \hline Sand content in the volume of sand and aggregate (r) & \(X_{3}\) & 0.34 & 0.41 & 0.48 & 0.07 \\ \hline Fly ash consumption (D), kg/m\({}^{3}\) & \(X_{4}\) & 50 & 150 & 250 & 100 \\ \hline Specific surface area of ash (S), m\({}^{2}\)/kg & \(X_{5}\) & 290 & 390 & 490 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Conditions for planning experiments. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**No. **} & \multicolumn{5}{c}{**Planning Matrix**} & \multicolumn{5}{c}{**Concrete Compositions**} \\ \cline{3-10}  & & & & & **Water Consumption,** & **Cement Consumption,** & **kg/m\({}^{3}\)** & **r** & **D, kg/m\({}^{3}\)** & **S, m\({}^{2}\)/kg** \\ \cline{2-10}  & \(X_{1}\) & \(X_{2}\) & \(X_{3}\) & \(X_{4}\) & \(X_{5}\)** & **[**]** &  
The composition of concrete at each point of the matrix was calculated using the method described in [24]. As a result of the statistical processing of the experimental data, polynomial models were obtained, which are shown in Table 5.  
The analysis of the models shows that the water-cement ratio has a decisive influence on water impermeability and strength. It is also the main factor determining water separation (Figure 1). Thus, at an ash consumption of 90 kg and W/C = 0.3, the water separation value is 0.25 g/L, and with an increase in W/C to 0.5, the water separation increases to 1.45 g/L (Figure 1). A significant increase in the water resistance of self-compacting fly-ash-containing concrete at a W/C of less than 0.4-0.5 (Figure 2) can be explained by a decrease in internal water separation of concrete mixtures. The increase in the water impermeability of self-compacting concrete is also associated with its strength (Figure 3) and optimal ash consumption (Figures 2 and 4). Figure 1: Water separation isolines (g/L) of self-compacting fly-ash-containing concrete mixtures: (**a**) water consumption is 180 kg/m\({}^{3}\); r = 0.41; S = 490 m\({}^{2}\)/kg. (**b**) W/C = 0.4; water consumption is 180 kg/m\({}^{3}\); r = 0.41. \begin{table}
\begin{tabular}{c c} \hline
**Properties** & **Mathematical (Polynomial) Models** \\ \hline \multirow{4}{*}{Water impermeability (\(W\), MPa)} & \(W=1.04-0.16X_{1}-0.09X_{3}+0.09X_{4}-\) \\  & \(-0.08X_{5}+0.06X_{1}^{2}+0.13X_{2}^{2}+\) \\  & \(+0.09X_{3}^{2}-0.22X_{4}^{2}-0.17X_{5}^{2}-\) \\  & \(-0.06X_{1}X_{3}-0.07X_{1}X_{4}+\) \\  & \(+0.05X_{2}X_{5}-0.02X_{3}X_{5}\) \\ \hline \multirow{2}{*}{Compressive strength, (\(\oint_{c}\), MPa)} & \(f_{c}=59.7-10.47x_{1}-5.69x_{3}+5.77x_{4}-4.97x5+4.08x_{1}^{2}+8.43x_{2}^{2}+\) \\  & \(+5.56x_{3}^{2}-14.22x_{4}^{2}-10.79x_{5}^{2}-3.98x_{1}x_{3}+2.93x_{2}x_{5}-1.44 x_{3}x_{5}\) \\ \hline \multirow{4}{*}{Water separation (\(WS\), g/L)} & WS = 0.37 - 0.35X_{1}+0.51X_{2}+0.75X_{3}-0.56X_{4}-0.45X_{5}-\) \\  & \(-0.15X_{2}^{2}+0.57X_{3}^{2}-0.15X_{4}^{2}+0.23X_{5}^{2}-0.09X_{1}X_{2}-\) \\  & \(-0.09X_{1}X_{3}-0.22X_{1}X_{5}+0.41X_{2}X_{3}-0.33X_{2}X_{4}-\) \\  & \(-0.28X_{2}X_{5}-0.32X_{3}X_{4}-0.32X_{3}X_{5}+0.2X_{4}X_{5}\) \\ \hline \end{tabular} (8)  
\end{table} 
Table 5: The resulting polynomial models. Figure 4: Diagram of water impermeability of self-compacting fly ash concrete at water consumption is 180 kg/m\({}^{3}\); r = 0.41; S = 390 m\({}^{2}\)/kg.