## 3 Simulation Results and Discussions
### Hydration of Portland Cement with Sodium Sulphate  
It has been reported that the U-phase could be formed in the hydration of PC with a high amount of Na\({}_{2}\)SO\({}_{4}\)[33; 34], and the thermodynamic equilibrium constant for the phase was reported in Reference [35]. Studies on the U-phase are very limited, and only a very few studies have reported on the U-phase in cementitious materials [33; 34; 35]. Further, the reported thermodynamic data are questionable, because the U-phase can easily be formed for the reported equilibrium constant in hydrating PC in the absence of Na\({}_{2}\)SO\({}_{4}\) from the hydration model (Appendix A.2). However, the formation of U-phase has not been reported in the hydration of PC without Na\({}_{2}\)SO\({}_{4}\). The authors' recent experimental study showed that the U-phase was formed early in hydration of PC and slag-blended cementitious materials, and the phase was changed to ettrinigite with hydration time [36]. Furthermore, the temperature significantly influenced the formation of U-phase. More detailed experimental work and thermodynamic modelling is necessary to understand the conditions in which the U-phase forms, and its thermodynamic properties. Therefore, the U-phase is not considered in this study, and its formation and thermodynamic properties will be described in future work.  
In order to simulate the core of the waste drum that contains the mixture of Na\({}_{2}\)SO\({}_{4}\) and cementitious materials, the temperature profiles shown in Figure 4 were adopted as the curing temperature [8], which was needed to increase the solubility of Na\({}_{2}\)SO\({}_{4}\) as well. Phase assemblage and pore solution profiles of PC hydration with 25% of Na\({}_{2}\)SO\({}_{4}\) by weight for the dramatic change of temperature (Figure 4) are shown in Figure 5, along with the phase assemblage for PC without Na\({}_{2}\)SO\({}_{4}\). In comparison to Figure 3, the temperature increase accelerated the hydration of clinker minerals and destabilised the ettrinigite, leading to more monosulfoaluminate formation (Figure 5A). The addition of sodium sulphate modified the mineralogy of hydrated cement (Figure 5B). The formation of mirabilite and ettrinigite at room temperature, in addition to other hydrates, filled the available pore space, but a very small or negligible amount of thenarlite was observed at high temperature in the presence of Na\({}_{2}\)SO\({}_{4}\). Further, the formed mirabilite and ettrinigite were destabilised at high temperature, giving large amounts of pore space. However, mirabilite was formed again once the system cooled down to room temperature, as was ettrinigite, which was produced as the dissolution of monosulfoaluminate and hemicraboaluminate. Mirabilite and ettrinigite were the main sulphate-bearing phases as PC hydrated with Na\({}_{2}\)SO\({}_{4}\) and they filled the pore significantly and may  
Figure 3: Activity coefficient equation on Portland cement hydration: (**A**) hydrate assemblage and (**B**) pore solution changes from PHREEQC.dat + extended Debye-Huckel equation; (**C**) hydrate assemblage and (**D**) pore solution changes from Pitzer.dat + Pitzer equation for activity coefficient.  
induce cracking in the system, which supports the experimental data [34; 37]. The ionic concentration in the pore solution showed a high concentration of Na\({}^{+}\) and SO\({}_{4}\)\({}^{2-}\) later in the process, which was in equilibrium with Na\({}_{2}\)SO\({}_{4}\) crystals and cement hydrates (Figure 5C). Further, high silicate concentration in the pore solution was obtained for the PC hydrates with Na\({}_{2}\)SO\({}_{4}\). This was due to differences in the composition of CASH solid solution (Figure 6). The addition of Na\({}_{2}\)SO\({}_{4}\) decreased the fraction of CASH\({}_{5}\)CA and increased that of CSH Jen, which released high concentrations of silica into the pore solution to form a low Ca/Si ratio of CASH.  
Figure 4: The temperature variation in the hydration calculations.  
Figure 5: \(Cont.\)