## Appendix A Model Description
### Cement Hydration Model  
The cement hydration model proposed by [PERSON] and [PERSON] (1984) was used to estimate the hydration degree of each cement clinker mineral as a function of time [39]. The model is described in detail elsewhere [21,27,40]. [PERSON] and [PERSON] [39] derived a set of empirical equations to describe the hydration rate, \(R_{t}{}^{m}\), of an individual clinker mineral \(m\) at time \(t\) (\(m=C_{3}S\), \(C_{2}S\), \(C_{3}A\), \(C_{4}AF\)):  
Nucleation and growth  
\[R_{t,1}^{m}=\frac{K_{1}}{N_{1}}[1-\alpha_{t}^{m}]\left\{-\ln(1-\alpha_{t}^{m}) \right\}^{(1-N_{1})} \tag{10}\]  
Diffusion  
\[R_{t,2}^{m}=\frac{K_{2}(1-\alpha_{t}^{m})^{2/3}}{1-(1-\alpha_{t}^{m})^{1/3}} \tag{11}\]  
Hydration shell formation  
\[R_{t,3}^{m}=K_{3}(1-\alpha_{t}^{m})^{N_{3}} \tag{12}\]  
The associated empirical parameters in the equations are tabulated in Table 1, as reported by [27,40]. The minimum among above the rates (\(R_{t,1}^{m}\), \(R_{t,2}^{m}\), \(R_{t,3}^{m}\)) is considered to be the controlling rate. The hydration degree of clinker mineral \(m\) at the time \(t\), \(\alpha_{t}^{m}\), is calculated from the hydration degree of the mineral at the previous time step (\(\alpha_{t-1}{}^{m}\)), the time interval (\(\Delta t\)), and hydration rate of the clinker mineral at the previous time step (\(R_{t-1}{}^{m}\)) as  
\[\alpha_{t}^{m}=\alpha_{t-1}^{m}+\Delta t\cdot\min\bigl{(}R_{t-1,1}^{m},R_{t-1,2 }^{m},R_{t-1,3}^{m}\bigr{)}\cdot\beta_{w/c}\cdot\lambda_{RH}\cdot\frac{A}{A_{0 }}\cdot\exp\left[\frac{E_{a}^{m}}{R}\left(\frac{1}{T_{0}}-\frac{1}{T}\right)\right] \tag{13}\]  
where,  
\[\begin{array}{l}\beta_{w/c}=\left[1+3.333\times\left(H^{m}\times w/c-\alpha_{ t-1}\right)\right]^{4}\hskip 42.679134 pt\text{if }\alpha_{t}\ >\ H^{m}\ \times\ w/c\\ \beta_{w/c}=1\hskip 28.452756 pt\text{if }\alpha_{t}\ \leq\ H^{m}\ \times\ w/c\end{array} \tag{14}\]\[\lambda_{RH}=\left(\frac{RH-0.55}{0.45}\right)^{4} \tag{11}\]  
where \(H^{m}\) is the critical degree of the clinker mineral \(m\), \(w\)/\(c\) is the water to cement ratio, \(\alpha_{t-1}\) is the total hydration degree of cement at the previous time step, \(A\) is the Blaine surface area of cement (m\({}^{2}\)/kg), \(A^{0}\) is the reference surface area of cement (385 m\({}^{2}\)/kg), \(E_{a}{}^{m}\) is the apparent activation energy of clinker mineral \(m\) (J/mol), \(T_{0}\) is the reference temperature (293.15 K), and \(RH\) is the relative humidity. The adapted values for \(H^{m}\) and \(E_{a}{}^{m}\) are based on the work by [PERSON] et al. (2008a; 2008b), and are given in Table 10.  
The total hydration degree of cement, \(\alpha_{t}\), relative to the total clinker content at time \(t\) is expressed by  
\[\alpha_{t}=\frac{f^{\mathrm{C_{3}}S}\alpha_{t}^{\mathrm{C_{3}}S}+f^{\mathrm{C _{2}}S}\alpha_{t}^{\mathrm{C_{2}}S}+f^{\mathrm{C_{3}}A}\alpha_{t}^{\mathrm{C _{3}}A}+f^{\mathrm{C_{4}}AF}\alpha_{t}^{\mathrm{C_{4}}AF}}{f^{\mathrm{C_{3}}S }+f^{\mathrm{C_{2}}S}+f^{\mathrm{C_{3}}A}+f^{\mathrm{C_{4}}AF}} \tag{12}\]  
where \(f^{m}\) is the relative mass fraction of the cement clinker mineral \(m\).  
PHREEQC was coupled with Excel(r) to carry out thermodynamic calculations at each time step. PHREEQC performed speciation and batch-reaction calculations to calculate the solution composition and the kind and amounts of precipitated phases, based on a thermodynamic dataset and input parameters. The calculations on the dissolution rate of clinker minerals were carried out in Excel(r), and the necessary data were transferred to PHREEQC as input parameters. The coupled model is described in a previous work [21], and used in here to simulate hydration reaction of cement in sodium sulphate environment.