## 2 Reverification of the Multicomponent Hydration Model  
### Overview of the Original Multicomponent Hydration Model  
In the original model [2; 10; 11], hydration and heat generation components in cement including clinkers such as C\({}_{3}\)S, C\({}_{2}\)S, C\({}_{3}\)A, C\({}_{4}\)AF and supplementary cementitious materials (SCMs) such as blast furnace slag (SG) and fly ash (FA) are treated independently, with the respective reference heat rate being accumulated according to their configuration ratios. The total reference heat rate of blended cement is formulated in Equation (1).  
\[\begin{split}\overline{H}=\sum p_{i}\overline{H_{i}}=p_{\text{C3A }}\Big{(}&\overline{H}_{\text{C3A}ET}+\overline{H}_{\text{C3A}} \Big{)}+p_{\text{C4A}}\Big{(}\overline{H}_{\text{C4A}FET}+\overline{H}_{\text{ C4A}F}\Big{)}+p_{\text{C3S}}\overline{H}_{\text{C3S}}\\ &+p_{\text{C2S}}\overline{H}_{\text{C2S}}+p_{\text{SC}} \overline{H}_{\text{SG}}+p_{FA}\overline{H}_{FA}\end{split} \tag{1}\]  
where \(i\) is clinker mineral or SCM, \(\overline{H}\) is the sum of the heat rates for all reactions, \(\overline{H}_{i}\) is the heat generation rate of mineral \(i\) per unit weight, \(p_{i}\) is the weight composition, and \(\overline{H}_{\text{C3A}ET}\) and \(\overline{H}_{\text{C4A}FET}\) are both heat generation rates during the formation of ettrinigite.  
Further, \(\overline{H}_{i}\) is formulated under an isothermal condition based on Arrhenius' law in Equation (2).  
\[\overline{H}_{i}=\gamma_{i}\cdot\beta_{i}\cdot\lambda_{i}\cdot r_{i}\cdot \overline{H}_{i\cdot T_{0}}(Q_{i})exp\left\{-\frac{E_{i}}{R}\bigg{(}\frac{1}{T }-\frac{1}{T_{0}}\bigg{)}\right\} \tag{2}\]  
where \(E_{i}\) is the activation energy of component \(i\), \(R\) is the gas constant, \(\overline{H}_{i\cdot T_{0}}\) is the reference heat generation rate of component \(i\) at reference temperature \(T_{0}\) (= 293 K) and is also a function of the accumulated heat rate \(Q_{i}\), which is corrected according to the ratio of the specific surface area to the standard one, \(T\) is the real temperature, \(\gamma_{i}\) is a coefficient expressing the delaying effect of the chemical admixture and FA in the initial exothermic hydration process, \(\beta_{i}\) is a coefficient expressing the reduction in the heat generation rate due to the reduced availability of free water (precipitation space), \(\lambda_{i}\) is a coefficient expressing the change in the heat generation rate of the powder admixtures, such as SG and FA, due to a lack of calcium hydroxide in the liquid phase, and \(r_{i}\) is a coefficient expressing changes in the heat generation rate in terms of the interactions between C\({}_{3}\)S and C\({}_{2}\)S in portland cement. Overall, the minimum coefficient is used as a reducing ratio when the value of several coefficients is less than unity. Then, \((-E_{i}/R)\) is defined as thermal activity.  
Here, the coefficient \(r_{i}\), which is related to clinker configuration, is further explained. The reactivity of calcium silicates, such as C\({}_{3}\)S and C\({}_{2}\)S, is dependent on the concentration of calcium ions in solution, and generally C\({}_{2}\)S is more sensitive than C\({}_{3}\)S [15; 16]. In this aspect, the heat generation rates of C\({}_{3}\)S and C\({}_{2}\)S are improved from the standard settings by the respective modification factors according to  
Figure 5: Configuration of this study.  
the mineral composition of portland cement. The modification impact is regarded as greater on C\({}_{2}\)S than C\({}_{3}\)S in terms of the sensitivity to the calcium ion concentration.