## 3 Simulation Results and Discussions
### Subplate Ingress into Hydrated Portland Cement  
One-dimensional reactive transport calculations with multispecies effect were performed to assess the performance of hydrated PC (described in Section 3.2) exposed to sodium sulphate solution. The PC was hydrated with 25% of sodium sulphate at varying temperatures (Figure 4) before it was exposed to external solution. Pore solution concentration, phase assemblage, and porosity from the hydration model at 28 days of hydration, as given in Figure 5B,C, were used as initial input values for the reactive transport model. The multispecies diffusion was performed by solving Equation (A16), considering main species such as Na\({}^{+}\), SO\({}_{4}^{2-}\), K\({}^{+}\), Ca\({}^{2+}\), Al\({}^{3+}\), H\({}_{4}\)SiO\({}_{4}\), and OH\({}^{-}\). Self-diffusion coefficients of ions in free water for a specified temperature were used as diffusion coefficients and tortuosity value was equal to 1. The concentration of ionic species at the exposure surface (\(x=0\)) was set to 10% of Na\({}_{2}\)SO\({}_{4}\) (1564.5 mmol/L and 782.25 mmol/L for Na\({}^{+}\) and SO\({}_{4}^{2-}\) respectively), while other ions were set to zero and the final boundary condition was set to zero flux. It should be noted that the concentration of Na\({}^{+}\) and SO\({}_{4}^{2-}\) were higher in pore solution (Figure 5C) than that in exposure solution. Figure 9 shows mineralogical distribution resulting from chemical reaction of PC hydration products with ingress of sulphate ions for 1000 years, together with changes of hydration products at 100 mm from the exposure surface as a function of hydration time. The dissolution of mirabilite, portlandite, and monocarboulimate, due to high concentration of sulphate ions in the pore solution, caused the formation of secondary ettrinigite and thaumasite as the chemical reaction of hydration products with sodium sulphate ingress. In the conventional sulphate attack in cementitious materials, the ingress of sulphate ions, the concentration of which is almost negligible in the pore solution of cementitious materials, reacts with dissolved portlandite to form gypsum and then ettrinigite, due to  
Figure 8: Influence of Na\({}_{2}\)SO\({}_{4}\) concentration on hydrated PC, at (**A**) 25 \({}^{\circ}\)C and (**B**) 80 \({}^{\circ}\)C.  
reaction with monosulfoaluminate [11]. However, in this study, sulphate ions were diffused from pore solution to external solution, because PC was hydrated with 25% of sodium sulphate before exposure. Therefore, the dissolution of hydrates, which were in equilibrium with high concentration of sulphate ions in the pore solution (Figure 5C) before the exposure, was the main mechanism. The precipitation of secondary products and dissolution of hydrates changed the porosity of the matrix, and the porosity was fed back to change the diffusion coefficients of ions (Equation (A16)). The dissolution increased the porosity of the matrix; this, in turn, enhanced further leaching of ions. Although the simulation results are not verified with experimental data in this study, they are consistent with published modelling results and experimental data [11; 20; 37]. As shown in Figure 9B, a significant alteration was observed close to the exposure surface at the beginning, which increased the porosity for around 10 years of exposure, but CASH was stable throughout the exposure period. The modelling approach and simulation results presented in this paper provide a promising method to evaluate the durability performance of encapsulated low-or intermediate level waste in cementitious materials on very long time scales. The solid solution, thermodynamic equilibrium, reaction kinetics, and reactive transport processes have been considered to understand the chemical mechanisms involved during solidification, and the solidified materials exposed to external sulphate attack. Therefore, the proposed approach can be used not only for assessing the durability of materials, but also for materials design for sodium sulphate containing nuclear waste.