## 2 Reverification of the Multicomponent Hydration Model
### Overview of the Original Model Related to Micro-Pore Structures and Moisture Equilibrium/Transports  
The law of mass conservation governing the moisture balance in a system is expressed by Equation (3) [1; 24]. \[\frac{\partial\theta_{w}}{\partial t}+div(J(\theta_{w},T,\
abla\theta_{w}, \
abla T))+Q=0 \tag{3}\]  
where \(\theta_{w}\) is the mass moisture in a unit volume of concrete, \(J\) is moisture flux, \(T\) is temperature and \(Q\) is a sink term. The first term corresponds to the potential term for the moisture in a porous material, which is expressed by Equation (4) [1; 24]. \[\frac{\partial\theta_{w}}{\partial t}=\frac{\partial(\rho_{l}\partial S)}{ \partial t} \tag{4}\]  
where \(\rho_{l}\) is the density of liquid water, \(\varphi\) is porosity and \(S\) is degree of saturation of porosity. In this way, the potential term is closely related to transition of both micro-pore structures and degree of saturation. The second term of Equation (3) is a moisture flux term, which is expressed by the formulation driven by pore pressure, vapor pressure and temperature gradients [1; 24]. Then, the sink term can be obtained directly from the multicomponent hydration model. The amount of free water available for hydration in the sink term, \(w_{free}\), is defined in Equation (5) [1; 2]. \[w_{free}=\frac{w_{total}-\sum w_{i}}{C} \tag{5}\]  
where \(w_{total}\) is the unit water content, \(w_{i}\) is the water consumed and fixed by the reaction of constituents and \(C\) is the unit cement content. \(w_{total}\) and \(C\) depend on a given mixture. The amount of water bound by each reaction can be determined by multiplying the bound water ratio obtained from the reaction equation of each mineral by the degree of hydration calculated by the multicomponent hydration model. The amount of free water can be used perfectly for hydration, wherever it is, in the original model [1; 24]. In the modeling of micro-pore structures in DuCOM, pores in cement paste are classified into interlayer, gel and capillary pores, according to sizes, formation process and whether or not the pore space is available for precipitating cement hydrates. Capillary pores are located outside cement \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Type of** & **Density** & **Blane Value** & \multicolumn{4}{c}{**Mineral Composition [\%]**} \\
**Cement** & **[g/cm\({}^{3}\)]** & **[cm\({}^{2}\)/g]** & **C\({}_{3}\)S** & **C\({}_{2}\)S** & **C\({}_{3}\)A** & **C\({}_{4}\)AF** \\ \hline OPC (N) & 3.15 & 3260 & 59.4 & 13.9 & 9.6 & 9.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mineral composition and physical property of the cement used in the adiabatic mass temperature rise tests [23]. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Type of** & **Casting** & \multirow{2}{*}{**W/C [\%]**} & \multicolumn{4}{c}{**Unit Weight (kg/m\({}^{3}\))**} & \multicolumn{2}{c}{**Chemical**} & \multicolumn{1}{c}{**Air**} \\
**Cement** & **Tem.** [°C]** & & **Water** & **Cement** & **Sand** & **Aggregate** & **Admixture [C\%]** & **Content[\%]** \\ \hline \multirow{5}{*}{
\begin{tabular}{c} OPC \\ (N) \\ \end{tabular} } & 20 & 57.1 & 160 & 280 & 870 & 1005 & 0.25 & 5.3 \\ \cline{2-9}  & 10 & & & & & & 4.0 \\ \cline{1-1} \cline{2-9}  & 20 & 47.1 & 160 & 340 & 847 & 978 & 0.25 & 5.5 \\ \cline{1-1} \cline{2-9}  & 30 & & & & & & & 6.0 \\ \cline{1-1} \cline{2-9}  & 20 & 40.0 & 160 & 400 & 823 & 951 & 0.25 & 5.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Details of the mixtures and the experimental conditions in the adiabatic mass temperature rise tests [23]. particles and they correspond to spaces which are not yet filled with cement hydrates. Interlayer and gel pores are formed with hydration products during the hydration process. In the model, gel pores are defined as the summation of pores contained in hydrates and tiny spaces surrounded by adjacent hydrates. Gel pores are the spaces which are unavailable for precipitation of hydration products at ordinary temperature.