## 4 Results
### Numerical Prediction with Hygro-Chemo-Thermo Transport Model  
In the previous section, a Parallel Finite Element (FE) program was developed using the Hygro-Chemo-Thermo transport model and validated through comparison with experimental studies. In this section, the developed transport model was used to examine the effects of temperature and relative humidity (RH) on the diffusion of various ions. The geometry of the concrete specimen used for numerical analysis is shown in Figure 5a, with dimensions of 15 cm in height and 30 cm in width. The boundary conditions were set to reflect real environmental conditions, where various types of deicing salts are commonly used. Accordingly, the specimen was assumed to be exposed to a 3% NaCl and 3% CaCl\({}_{2}\) solution. The external temperature conditions were set at 20 \({}^{\circ}\)C, 35 \({}^{\circ}\)C, and 50 \({}^{\circ}\)C, while the internal concrete temperature was maintained at 20 \({}^{\circ}\)C. Additionally, the initial concentrations of Na\({}^{+}\) and K\({}^{+}\) ions in the pore solution were determined based on the chemical composition of cement provided by the manufacturer [48]. All surfaces except the top were assumed to be silicone-coated to prevent moisture exchange, and the internal relative humidity (RH) was set at 60%. The numerical model assumed a long-term ponding condition, where chloride and moisture diffusion occurred in the same direction. The total analysis duration was 400 days, with a time step of 0.5 days. To ensure numerical accuracy, two convergence tolerance conditions were applied: a relative tolerance (Rtol) of \(10^{-4}\) and an absolute tolerance (Atol) of \(10^{-10}\). To solve the large sparse matrix, the Krylov Subspace Method (KSP) GMRES solver with an additive Schwarz preconditioner was employed, as detailed in Figure 1 of the previous section. The mesh structure used for numerical analysis is shown in Figure 5b. It consisted of approximately 3000 nodes and 6000 triangular elements. The entire mesh was divided into eight sub-meshes, each containing an approximately equal number of elements. Additionally, the number of nodes at the subdomain boundaries was minimized to enhance the computational efficiency during parallel processing. A parallel finite element method was  
Figure 5: Information of the numerical analysis. (**a**) Geometry information, (**b**) mesh generation with subdomain. employed to solve the coupled moisture, temperature, and multi-ion diffusion problem. In this analysis, relative humidity (H\({}_{\text{m}}\)) and five ionic species (Cl\({}^{-}\), Na\({}^{+}\), Ca\({}^{2+}\), K\({}^{+}\), OH \({}^{-}\)), defined by the Nernst-Planck equation, were spatially discretized. For time integration, the semi-implicit Crank-Nicholson method was applied. The key material parameters and input data used in the analysis are summarized in Table 3. These include the diffusion coefficients, initial concentrations at the top surface and in the pore solution, the water-to-cement ratio (W/C ratio), the volume fraction of aggregates, relative humidity, and temperature. The numerical simulations were conducted under unsaturated conditions, where the relative humidity inside and outside the concrete differed. All ion concentrations were expressed in mol/L as input parameters, whereas the total ionic concentration was expressed as the percentage of ion mass per unit mass of the solution (%). To evaluate the performance of the parallel FE algorithm, it is necessary to consider the concepts of speed-up and efficiency. The definitions of speed-up, \(S_{P}(n)\), and efficiency, \(E_{P}(n)\), are shown in Equations (39) and (40). \[S_{P}(n)=\frac{T_{s}(n)}{T_{p}(n)} \tag{39}\]  
\[E_{p}(n)=\frac{S_{P}(n)}{p} \tag{40}\]  
where \(T_{s}(n)\) is the time taken by the code to execute on a single processor, \(T_{p}(n)\) is the time taken for the same code to execute on p processors, and \(P\) is the number of processors.