## Appendix A Model Description  
### Phase-Equilibrium Model  
This model was used to define the amount of cement hydrate phases that can react reversibly with an aqueous solution to achieve equilibrium. PHREEQC was employed to carry out thermodynamic equilibrium calculations [23]. When a pure phase is no longer in equilibrium with a solution, it will dissolve or precipitate. The equilibrium reactions are expressed by the mass-action equations as  
\[K_{p}=\prod_{i}(\gamma_{i}c_{i})^{n_{i,p}} \tag{1}\]  
where \(K_{p}\) is the thermodynamic equilibrium constant for phase \(p\), \(\gamma_{i}\) is the activity coefficient of ion \(i\) (\(-\)), \(c_{i}\) is the concentration of ion \(i\) (mol/L), and \(n_{i,p}\) is the stoichiometric coefficient of ion \(i\) in phase \(p\) (\(-\)). The activity coefficients were calculated based on the Pitzer model, and the activity coefficients of the cations, \(\gamma_{M}\), and anions, \(\gamma_{X}\), were given by Reference [38]. \[ \begin{array}{c}\ln\gamma_{M}=z_{M}^{2}F+\sum\limits_{a}m_{a}(2B_{Ma}+ZC_{Ma})+ \sum\limits_{c}m_{c}\left(2\phi_{MC}+\sum\limits_{a}m_{a}\psi_{Mca}\right)\\ \hskip 14.226378 pt+\sum\limits_{a<a^{\prime}}\sum\limits_{a}m_{a}m_{a^{\prime} }\psi_{aa^{\prime}M}+|Z_{M}|\sum\limits_{c}\sum\limits_{a}m_{c}m_{a}C_{ca} \end{array}  \tag{2}\]  
\[ \begin{array}{c}\ln\gamma_{X}=z_{X}^{2}F+\sum\limits_{c}m_{c}(2B_{cX}+ZC_{CX} )+\sum\limits_{a}m_{a}\left(2\phi_{Xa}+\sum\limits_{c}m_{c}\psi_{Xac}\right)\\ \hskip 14.226378 pt+\sum\limits_{c<c^{\prime}}\sum\limits_{a}m_{c}m_{c^{\prime} }\psi_{cc^{\prime}X}+|Z_{X}|\sum\limits_{c}m_{c}m_{a}C_{ca}\end{array}  \tag{3}\]  
where \(m_{i}\) is the molarity of \(i\); subscript \(M\), \(c\), and \(c^{\prime}\) denote cations; and \(X\), \(a\), and \(a^{\prime}\) denote anions. The double summations \(c<c^{\prime}\) and \(a<a^{\prime}\) denote all pairs of dissimilar cations and anions respectively. \(B\) is the function of experimentally measuring parameters \(\beta^{0}\), \(\beta^{1}\), and \(\beta^{2}\), \(C\), \(\varphi\), and \(\psi\). The term \(F\) is defined by  
\[F=-A^{\phi}\left[\frac{\sqrt{I}}{1+b\sqrt{I}}+\frac{2}{b}\ln\left(1+b\sqrt{I} \right)\right]+\sum\limits_{c}\sum\limits_{a}m_{c}m_{a}B^{\prime}_{ca}+\sum \limits_{c<c^{\prime}}m_{c}m_{c^{\prime}}\phi^{\prime}_{cc^{\prime}}+\sum \limits_{a<a^{\prime}}m_{a}m_{a^{\prime}}\phi^{\prime}_{aa^{\prime}} \tag{4}\]  
where \(b\) equal to 1.2 and \(I\) is ionic strength. The Debye-Huckel osmotic parameter \(A^{\phi}\) is given by  
\[A^{\phi}=\frac{1}{3}(2\pi N_{0}\rho_{w}/1000)^{1/2}(e^{2}/D_{X}T) \tag{5}\]  
where \(\rho_{w}\) is the density of water, \(N_{0}\) is the Avogadro constant, \(e\) is the charge of electron, \(D\) is the dielectric constant, and \(\kappa\) is the Boltzmann constant. Pitzer interaction parameters used in the calculations were collected from various references [30; 31; 32]. Cement hydrate phases are defined by chemical reaction, an equilibrium constant, and enthalpy. The thermodynamic equilibrium constant, \(K_{p}\), at a given temperature \(T\) (K) can be expressed as  
\[K_{p}=\exp\left(-\frac{\Delta_{r}G_{T}^{0}}{RT}\right) \tag{6}\]  
where \(\Delta_{r}G_{T}^{0}\) is the standard Gibbs energy of reaction at temperature \(T\) and \(R\) is the universal gas constant (8.31451 J/(mol K)). The standard Gibbs energy of reaction is expressed as  
\[\Delta_{r}G_{T}^{0}=\sum\Delta_{f}G_{T,products}^{0}-\sum\Delta_{f}G_{T, reactants}^{0} \tag{7}\]  
where \(\Delta_{f}G_{T}^{0}\) is the Gibbs free energy of formation for a species at a given temperature \(T\).