# Model-Based Methods to Produce Greener Metakaolin Composite Concrete
## 2 The Strength Evaluation Model
### Verification of the Strength Evaluation Model
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \begin{tabular}{c} **Water/** \\ **Binder** \\ **(kg/m3)** \\ \end{tabular} & \begin{tabular}{c} **Binder** \\ **Percentage** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Metakaolin** \\ **Superplasticizer** \\ **(\% of Binder)** \\ \end{tabular} & \begin{tabular}{c} **Sand** \\ **(kg/m3)** \\ \end{tabular} & \begin{tabular}{c} **5 to10 mm** \\ **Coarse** \\ **Aggregate** \\ **(kg/m3)** \\ \end{tabular} & \
\begin{tabular}{c} **10 to 20 mm Coarse** \\ **Aggregate** \\ **(kg/m3)** \\ \end{tabular} &
\begin{tabular}{c} **Water** \\ **(kg/m3)** \\ \end{tabular} \\ \hline \multirow{4}{*}{0.65} & \multirow{4}{*}{285} & – & 0.24 & \multirow{4}{*}{730} & \multirow{4}{*}{400} & \multirow{4}{*}{800} & \multirow{4}{*}{185} \\  & & 5 & 0.38 & & & & \\  & & 10 & 0.58 & & & & \\  & & 15 & 0.77 & & & & \\  & & 20 & 1.15 & & & & \\  & & 25 & 1.54 & & & & \\ \hline \multirow{4}{*}{0.60} & \multirow{4}{*}{310} & – & 0.13 & \multirow{4}{*}{710} & \multirow{4}{*}{400} & \multirow{4}{*}{800} & \multirow{4}{*}{185} \\  & & 5 & 0.26 & & & & \\ \cline{1-1}  & & 10 & 0.43 & & & & \\ \cline{1-1}  & & 15 & 0.69 & & & & \\ \cline{1-1}  & & 20 & 1.04 & & & & \\ \cline{1-1}  & & 25 & 1.30 & & & & \\ \hline \multirow{4}{*}{0.52} & \multirow{4}{*}{355} & – & 0.11 & \multirow{4}{*}{670} & \multirow{4}{*}{400} & \multirow{4}{*}{800} & \multirow{4}{*}{185} \\  & & 5 & 0.39 & & & & \\ \cline{1-1}  & & 10 & 0.50 & & & & \\ \cline{1-1}  & & 15 & 0.80 & & & & \\ \cline{1-1}  & & 20 & 1.15 & & & & \\ \cline{1-1}  & & 25 & 1.45 & & & & \\ \hline \multirow{4}{*}{0.45} & \multirow{4}{*}{410} & – & 0.21 & \multirow{4}{*}{625} & \multirow{4}{*}{400} & \multirow{4}{*}{800} & \multirow{4}{*}{185} \\  & & 5 & 0.42 & & & & \\ \cline{1-1}  & & 10 & 0.67 & & & & \\ \cline{1-1}  & & 15 & 0.84 & & & & \\ \cline{1-1}  & & 20 & 1.18 & & & & \\ \cline{1-1}  & & 25 & 1.55 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mixtures of specimens. Adapted with permission from ref. [26]. Copyright 2018 Elsevier. Based on the results of concrete strength at various ages [26], the strength coefficients \(A_{1}\), \(A_{2}\), and \(A_{3}\) of Equation (1) were calculated as 37.91, 116.71, and 6.48 MPa, respectively. These strength coefficients do not vary for different mixtures and ages. The strength coefficient of metakaolin \(A_{2}\) is much higher than that of cement \(A_{1}\). This may be because metakaolin has higher SiO\({}_{2}\) content than cement. Higher SiO\({}_{2}\) content is helpful for the formation of secondary calcium silicate hydrate, which is the essential hydration product for concrete strength [28; 29]. Figure 4a-d shows that at early ages, metakaolin composite concrete has less strength than plain concrete. At early ages, more metakaolin means lower concrete strength. When older, metakaolin composite concrete has greater strength than plain concrete because of the pozzolanic reaction of metakaolin. In other words, the proposed strength development model can reflect the crossover phenomenon of the strength between plain concrete and metakaolin composite concrete [30]. Moreover, the strength development model also found the strength development of concrete does not start immediately, but starts at a threshold age. Before this threshold age, the strength is zero, and after this threshold age, the strength is higher than zero. The threshold age is like final setting age. In concrete terminology, final setting is the starting time for hardening. In addition, the strength development model shows that as the water/binder ratio reduces, the strength of the concrete increases. Given a certain water content, larger quantities of binder have two effects. One is increasing the available binder for hydration, and the other is decreasing the  
Figure 3: Degrees of reaction of metakaolin in cement–metakaolin blends. (**a**) reaction extent of metakaolin: water/binder ratio 0.65. (**b**) reaction extent of metakaolin: water/binder ratio 0.45.