# Curable Area Substantiation of Self-Healing in Concrete Using Neutral Axis
## 4 Results and Discussion
### Self-Hailing Assessment Based on Initial Flexural Stiffness  
A comparison of the initial flexural stiffness between the 2 nd loading and the 3 rd loading directly and quantitatively showed the changes before and after healing. The reloading after the crack inducement process degraded the performance of the specimen, even if the crack did not propagate further, because the microcracking zone accumulated damage and gradually turned into a bridging zone. Both the maximum strength and the initial flexural stiffness in case of the 2 nd loading decreased slightly as a result of this damage accumulation. These two parameters varied depending on the healing period and the crack inducement time, and the self-healing assessment was quantified by comparing the degree of variation. As described above, the maximum strength clearly reflects not only the healing effect but also the age effect, so only the initial flexural stiffness was compared. The ratio of the slope of the 3 rd loading to the slope of the 2 nd loading could be expected to be greater than 1.0 if there was a positive effect during the healing period. A value less than or equal to 1.0 means that there was no positive effect, not even the age effect. This value was considered to represent the healing effect in this study and used as a quantitative marker in self-healing assessments. The initial flexural stiffness in case of the 3 rd loading increased as the length of the healing period increased. For curing in freshwater, in Cases 7-28-W, 7-49-W, and 7-70-W, it can be seen that all the initial flexural stiffness values in case of the 3 rd loading are steeper than those in case of the 2 nd loading, as shown in Figure 7a-c; these results represent a positive effect. However, in Cases 7-28-A and 7-49-A, with healing in air, the slope in case of the 3 rd loading decreases. Only in Case 7-70-A, in which the specimen was healed for 63 days, a positive effect was observed. This finding is similar to the results of [PERSON] et al. [36], but a direct comparison of the same specimen before and after the healing makes our results more concrete. This is evident from the quantitative comparison of the slopes, as shown in Figure 13. Although there are deviations, the average healing effect increased with increasing healing time, especially the healing effect was greater than 1.0 in the cases of all specimens cured in water. The healing effect in case of the specimens cured in air was lower than 1.0 for 21 days of healing period (7-28), but it increased remarkably and reached a level similar to that of the specimens cured in water for 63 days (7-70). These results indicate that the healing effect depends on the healing period, regardless of the healing circumstance. The initial flexural stiffness in case of the 3 rd loading decreased with delayed crack inducement time. The curve of Case 7-28-W shows a positive effect, but the curves of Cases 28-49-W and 49-70-W are below the 2 nd loading curve despite the fact that the specimens were cured in water. Furthermore, all specimens cured in air showed no positive effect, i.e., the 3 rd loading curves are below the 2 nd loading curves. Figure 14 shows the quantitative changes according to the crack inducement time. Despite curing in water, the healing effect decreased significantly as the crack inducement time was delayed. A more unexpected phenomenon can be seen in the results of specimens cured in air; all average healing effects with different crack inducement times were almost the same and less than 1.0. Figure 13: Ratios between flexural stiffness of 3 rd loading and that of 2 nd loading (different healing periods). These results indicate that the healing effect is strongly influenced by the crack inducement time and the curing circumstance if the healing period is constant. The results of the flexural strength comparison and the initial flexural stiffness comparison are similar if we look at the results themselves.