## 4 Results
### Numerical Prediction with Hygro-Chemo-Thermo Transport Model
To evaluate the scalability of the parallel algorithm, meshes with 3000, 6000, 12,000, and 24,000 nodes were used, while increasing the number of processors up to 32. As shown in Figure 6, when the number of processors increased, the problem size assigned to each processor decreased, and the speed-up gradually improved. For instance, in the case of 24,000 nodes, the speed-up achieved with eight processors approached the ideal conditions, and the efficiency was nearly one, as illustrated in Figure 7. In contrast, for the 3000-node \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Species** & **Unit** & **K\({}^{+}\)** & **Na\({}^{+}\)** & **Cl\({}^{-}\)** & **OH\({}^{-}\)** & **Ca\({}^{2+}\)** \\ \hline Charge number & & +1 & +1 & \(-1\) & \(-1\) & +2 \\ \hline Diffusion coefficient & m\({}^{2}\)/s & 4.0 \(\times\) 10\({}^{-11}\) & 2.8 \(\times\) 10\({}^{-11}\) & \
\begin{tabular}{c} Refer to \\ Equation (15) \\ \end{tabular} & 5.3 \(\times\) 10\({}^{-10}\) & 1.6 \(\times\) 10\({}^{-11}\) \\ \hline Initial condition & at top surface & mol/L & 0 & 0.513 & 1.053 & 0 & 0.27 \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Cement type \\ Water-cement ratio \\ \end{tabular} } & mol/L & 0.0995 & 0.0389 & 0 & 0.1384 & 0 \\ \hline \multicolumn{2}{c}{Cement type} & & & I/II & \\ \hline \multicolumn{2}{c}{Water-cement ratio} & & & 0.55 & \\ \hline Volume fraction of aggregate & & & 0.65 & \\ \hline Outside RH/Temperature & \%/\({}^{\circ}\)C & & 100/20 \({}^{\circ}\)C, 35 \({}^{\circ}\)C, 50 \({}^{\circ}\)C & \\ \hline Inside RH/Temperature & \%/\({}^{\circ}\)C & & 60/20 \({}^{\circ}\)C & \\ \hline Total analysis duration & day & & 400 & \\ \hline Time step & day & & 0.5 & \\ \hline Relative tolerance (Rtol) & & & 10\({}^{-4}\) & \\ \hline Absolute tolerance (Atol) & & & 10\({}^{-10}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material parameters and input data for numerical analysis. case, the speed-up increased more slowly when more than two processors were used, due to the cost of communication between processors. In unsaturated concrete, the relative humidity (RH) significantly influences the diffusion of ionic species [5]. As shown in Figure 5, to observe the ingress of various ions from the top surface of the concrete, a boundary condition consisting of a mixture of sodium chloride (NaCl) and calcium chloride (CaCl\({}_{2}\)) was applied. Specifically, the top surface of the concrete specimen was exposed to 3% NaCl and 3% CaCl\({}_{2}\) solutions. Additionally, the initial conditions included the presence of K\({}^{+}\), Na\({}^{+}\), and OH\({}^{-}\) ions in the concrete's pore solution. Figure 8 presents the simulation results of the relative humidity profile over depth under unsaturated conditions for the different durations (20, 50, 100, 200, and 400 days) of numerical analysis. A moisture gradient was established from the external RH of 100% toward the internal RH of 60%, indicating that a gradient was formed from the exposed surface toward the interior of the concrete. The results demonstrate that the moisture front migrated inward over time and eventually converged to 100% RH, reaching a steady-state condition. In practice, this moisture gradient enhanced the transport of chloride, sodium, and calcium ions, thereby accelerating their penetration rates. Figure 6: Speed-up according to the number of nodes and processors. Figure 7: Efficiency according to the number of nodes and processors. Figure 9 shows the total chloride concentration profiles with respect to depth. Figure 9a illustrates the effect of the water-cement (W/C) ratio, while Figure 9b demonstrates the effect of temperature on chloride ion ingress. The results indicate that although the W/C ratio influenced the rate of ion transport, temperature played a more dominant role in accelerating the diffusion rate under the same W/C ratio. Figure 10 presents the ion concentration profiles of Na\({}^{+}\), Ca\({}^{2+}\), K\({}^{+}\), and OH\({}^{-}\) after 400 days.