## 4 Results of FEA  
### Beam Controlled by Flexure  
Figure 13 shows the comparison between test (FB-C0: comparison specimen without corrosion) and analysis (Case-1: uncorroded flexural beam specimen). Table 3 outlines the results of FEA with 12 variables (\(\beta=1\) down to \(\beta=0.4\)). The ultimate load of the comparison specimen is 87.3 kN (Table 2) as the analysis result, approximately 107% the experimental value, 81.6 kN (Table 2). The deflection at the ultimate load in analysis vs. test was 115.9 vs. 116.7 mm, respectively, i.e., 99%, demonstrating that the analysis result using VecTor2 shows a very similar behavior to the test result. These results indicate that the applied FEA model effectively simulates the control specimen, and that the structural performance reduction of flexural beams caused by rebar corrosion can be defined as the relationship between the reduction in bonding factor (\(\beta\)) and the performance degradation factor (\(\phi\)) caused by corrosion.  
Figure 13: Comparison between test and analysis results of flexural beam specimen.  
On a related note, Figure 14 shows the correlation between \(\beta\) and \(\phi\) of each FEA case presented in Table 3, and Figure 15 shows that between average potential difference in voltage (mV) and performance degradation factor (\(\phi\)) of each flexural specimen tested in our prior research [1]. The FEA-derived bonding factor (\(\beta\)) and performance degradation factor (\(\phi\)) can be approximated by Equation (10) using regression analysis, and its R\({}^{2}\) = 0.94, which indicates a very high correlation. The mV and \(\phi\) of each specimen tested in the aforementioned prior research can be approximated by Equation (11).  
\[\phi=(0.36-\beta)^{-1}+101\,\left(Analysis\,:\,\text{R}^{2}=0.94\right) \tag{10}\]  
\[\phi=0.05(\text{mV})+100\,\left(Test\,:\,\text{R}^{2}=0.78\right) \tag{11}\]  
\(\phi\) expressed by Equations (10) and (11) is a coefficient representing the reduction in structural performance induced by rebar corrosion (experiment) and bonding performance (analysis) of flexural beams, which represent the same physical value from the engineering aspect. Therefore, using Equations (10) and (11), the relationship between the bonding factor (\(\beta\)) and the average potential difference in voltage (mV) can be defined by Equation (12). Figure 16 is a schematic representation of the \(\beta\)-mV correlation.  
\[\text{mV}=\frac{1.36-\beta}{0.018-0.05\beta} \tag{12}\]  
\begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Cases**} & \multirow{2}{*}{**Bonding Factor (\(\beta\))**} & \multicolumn{2}{c}{**Ultimate**} & \multirow{2}{*}{**Dissipation Energy**} & \multirow{2}{*}{**Performance Degradation**} \\ \cline{3-3} \cline{5-6}  & & **Load** & **Deflection** & & **(kN-mm)** & **Factor \(\phi\) (\%)** \\ \hline Case-1 & 1.00 & 87.3 & 115.9 & 8840.26 & 100.0 \\ \hline Case-2 & 0.90 & 84.7 & 114.9 & 8756.35 & 99.05 \\ \hline Case-3 & 0.80 & 84.3 & 112.57 & 8553.4 & 96.76 \\ \hline Case-4 & 0.70 & 82.7 & 111.37 & 8305.69 & 95.  
Figure 14: Relationship between bonding factor (\(\beta\)) and performance reduction factor (\(\phi\)) of flexural beam specimens (FEM analysis).  
Figure 15: Relationship between average potential difference in terms of voltage (mV) and performance reduction factor (\(\phi\)) of flexural beam specimens (Test).  
By interrelating the correlation between \(\beta\) and \(\phi\) derived from FEA as expressed by Equation (10) and that between average potential difference in voltage (mV) and performance degradation factor (\(\phi\)) as expressed by Equation (11), a \(\phi\)-\(\beta\)-mV correlation curve of the flexural beam can be proposed by integrating the \(\beta\)-mV correlation, as expressed by Equation (12) with respect to \(\phi\).