## 2 Reverification of the Multicomponent Hydration Model
### Investigation of Hydration Degrees Based on the Original Model  
The validity of the original multicomponent hydration model was investigated in comparison with the hydration degrees of the portland cement clinkers presented in the past studies [17; 18; 19; 20]. The experimental conditions are summarized in Table 1. Each sample is made of paste, and the compositions necessary for the analysis are described in the references. The hydration degree of each clinker \(i\) in the analysis is defined by the ratio of the accumulated heat (\(\overline{Q}_{i}\)) to the terminal one (\(\overline{Q}_{i,\infty}\)).  
In this paper, only a few parts of all the comparisons are presented in Figures 6 and 7 as representatives due to limited space In Figure 6 based on Reference [18], the numerical C\({}_{2}\)S was greatly overestimated but C\({}_{3}\)S was slightly underestimated. Focusing on C\({}_{2}\)S in particular, although the experimental results present a strong dependency on temperature such that hydration progresses more significantly at higher temperatures, the analysis could not trace the tendency, resulting in the small differences regardless of the curing temperatures. This might suggest the possibility that the setting of the thermal activity of C\({}_{2}\)S in the original model was lower than expected. A similar possibility was confirmed also in comparison with References [17; 19] although it is not presented in this paper. In Figure 7 based on Reference [20], the numerical value of C\({}_{2}\)S by the analysis was overestimated regardless of the cement type. More precisely, the degree of the overestimation appeared more significantly in the case of the higher ratio of C\({}_{3}\)S to C\({}_{2}\)S cement. It was supposed that this discrepancy was influenced by the modification factors of the heat generation rates of C\({}_{3}\)S and C\({}_{2}\)S, namely the coefficient \(r_{i}\).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Curing Condition** & **Type of Cement** & **Blane Value** & **Measurement of** & **Evaluation** & **Reference** \\  & **(W/C)** & **[cm\({}^{2}\)/g]** & **Hydration Degree** & **Method** & **Reference** \\ \hline \multirow{4}{*}{Sailing at 10, 20, 30 \({}^{\circ}\)C} & HPC [1] & 5123 & C\({}_{3}\)S & \multirow{4}{*}{X-ray diffraction (XRD)/internal standard method} & \multirow{4}{*}{Hyeon [17]} \\  & OPC [2] & 4227 & C\({}_{2}\)S & X-ray diffraction (XRD)/internal standard method & \\ \cline{1-1}  & MPC [3] & 4346 & C\({}_{3}\)A & (XRD)/internal standard method & \\ \cline{1-1}  & High Belite (50\%) & 4530 & C\({}_{4}\)AF & & \\ \hline \multirow{4}{*}{Water curing at 3, 20, 35, 50 \({}^{\circ}\)C after sealing for 2 days at 20 \({}^{\circ}\)C} & OPC [2] & \multirow{4}{*}{3190} & C\({}_{3}\)S (50\%, 40\%, 30\%) & \multirow{4}{*}{3190} & C\({}_{3}\)S (50\%, 40\%, 30\%) & \\ \cline{1-1}  & OPC [2] & 4227 & C\({}_{2}\)S & X-ray diffraction (XRD)/internal standard method & \\ \cline{1-1}  & MPC [17] & 4346 & C\({}_{3}\)A & (XRD)/internal standard method & \\ \cline{1-1}  & High Belite (50\%) & 4530 & C\({}_{4}\)AF & & \\ \hline \multirow{4}{*}{Water curing at 3, 20, 35, 50 \({}^{\circ}\)C after sealing for 2 days at 20 \({}^{\circ}\)C} & OPC [2] & 3160 & C\({}_{3}\)S (50\%, 40\%, 30\%) & \\ \cline{1-1}  & MPC [3] & 3210 & C\({}_{2}\)S & XRD/Rietveld (50\%, 40\%) & \\ \cline{1-1}  & LPC [4] & 4300 & & \\ \hline \multicolumn{6}{c}{* Measured only in the case of W/C = 50\%. 1) High early strength Portland Cement; 2) Ordinary Portland Cement; 3) Moderate heat Portland Cement; 4) Low heat Portland Cement.} \\ \end{tabular}
\end{table}
Table 1: Experimental conditions in the past studies using various types of portland cement.