# Curable Area Substantiation of Self-Healing in Concrete Using Neutral Axis
## 4 Results and Discussion
### Self-Healing Assessment Based on the Flexural Strength  
The maximum load in case of the 3 rd loading and the load at the unloading point of the same specimen were compared. Figure 9 shows the average ratios of cases for different healing periods: the blue square box denotes the results of the specimens cured in water, and the red triangle denotes the results of the specimens cured in air. As the figure indicates, all ratios are more than 1.0, which means the maximum load in case of the 3 rd loading was higher than the load at the unloading point. This phenomenon in which the peak load of the 3 rd loading after the healing process is higher than the previous peak load has been reported in previous studies [23; 36]. The average ratio appears to increase as the age increases, but it does not increase considerably. The loads of the 3 rd loading and the 2 nd loading at CMOD = 0.05 mm of the same specimen were compared. The maximum load of the 3 rd loading must be accompanied by the age effect because it involves the uncracked part as well. To exclude the age effect to the extent as much as possible, the loads under the same damage conditions must be compared. Figure 10 shows the average ratios of the 2 nd loading and the 3 rd loading, and these load values were obtained when CMOD was 0.05 mm. In this comparison, the increasing trend was more evident when the aging period was longer, especially in the case of a specimen cured in air. However, the ratios of the cases 7-28-A and 2-49-A show values than lower 1.0; the maximum load after healing in air was lower than the load at the unloading point. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Case** & \multicolumn{2}{c}{**7-28**} & \multicolumn{2}{c}{**7-49**} & \multicolumn{2}{c}{**7-70**} & \multicolumn{2}{c}{**28-49**} & \multicolumn{2}{c}{**49-70**} \\ \hline Healing condition & Water & Air & Water & Air & Water & Air & Water & Air & Water & Air \\ \hline \hline \multicolumn{1}{c}{\textbackslash{}} & Peak load of 1 st loading & 4.48 & 4.43 & 4.61 & 4.46 & 4.85 & 4.26 & 4.88 & 4.92 & 5.83 & 5.63 \\ \hline \multicolumn{1}{c}{\textbackslash{}} & Unloading point & 3.83 & 3.70 & 4.19 & 3.72 & 4.36 & 3.63 & 4.25 & 4.38 & 5.21 & 4.91 \\ \hline \multicolumn{1}{c}{\textbackslash{}} & Maximum load of 3 rd loading & 4.46 & 3.88 & 5.01 & 3.88 & 5.08 & 4.20 & 4.32 & 4.26 & 4.83 & 4.53 \\ \hline \multicolumn{1}{c}{\textbackslash{}} & 0.85 & 0.83 & 0.91 & 0.84 & 0.90 & 0.85 & 0.87 & 0.89 & 0.89 & 0.87 \\ \hline \multicolumn{1}{c}{\textbackslash{}} & 1.16 & 1.04 & 1.19 & 1.04 & 1.16 & 1.17 & 1.03 & 0.98 & 0.93 & 0.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average load and ratio. Figure 9: Ratios between the maximum load in the case of 3 rd loading and unloading load in case of 1 st loading (different healing periods). Figure 11 shows the average ratios of the maximum load of the 3 rd loading and the load at the unloading point with different crack inducement times. As can be seen, the ratios decrease as the crack inducement time increases, regardless of the curing condition. However, the average ratios of the 3 rd loading and the 2 nd loading at CMOD = 0.05 mm do not show any significant decrease trend, as in Figure 12.  
Compared to the results in Figures 9 and 11, the results in Figures 10 and 12 show more clearly the changes in the healing conditions and periods. A clearer difference is thought to be due to comparing flexural strength under certain conditions as the same CMOD, which is different from similar previous studies [23; 36]. Three-point bending test with a notch is considered to be more advantageous in controlling comparative conditions than experiments of other criteria such as permeability or chloride transport [32; 41; 42; 43]. Figure 11: Ratios between the maximum load of the 3 rd loading and the unloading load of the 1 st loading (different crack inducement times). Figure 12: Ratios between load of 3 rd loading and load of 2 nd loading with CMOD = 0.05 mm (different crack inducement time).