# Curable Area Substantiation of Self-Healing in Concrete Using Neutral Axis
## 4 Results and Discussion
### Crack Depths and Neutral Axises  
The real crack depth with CMOD = 0.05 mm was observed to be about 20 mm. It was observed by means of an ink injection after the crack inducement, and several surplus specimens of seven days of age were used for this purpose because the largest number of specimens was prepared for the seven cases. A cellophane adhesive tape was attached to both sides of the specimens to prevent ink leakage, and red ink was injected from the notch. Next, after sufficient time provision for ink injection and drying (24 h), reloading was applied to split the specimens. Figure 15 shows the cracked area stained by red ink injection. The crack depth was calculated by dividing the area stained with red ink by the specimen width, and the average crack depth of the specimens of seven days of age was about 20 mm. Five additional specimens of 28 days of age showed a crack depth of about 20 mm as well, although the deviation in their crack depths was larger than that in case of the seven-day-old specimens. Figure 14: Ratios between flexural stiffness of 3 rd loading and that of 2 nd loading (different crack inducement times). Meanwhile, the neutral axis ascended to about 44 mm. Figure 16 shows the change in the position of the neutral axis with changes in the CMOD. The neutral axis was estimated from seven strains measured by successive strain gauges, so slight scattering can be seen at the beginning of load introduction. Initially, the neutral axis was located at about 33 mm from the notch tip, which corresponds to the center of the un-notched section. It moved upward gradually with increasing CMOD and was located at 40-50 mm at CMOD = 0.05 mm. It changed insignificantly during the unloading process, but in the case of a few specimens, the neutral axis moved slightly upward. There was a minor difference among each of the specimens, and the differences in the position of the neutral axis when fully unloaded averaged 44 mm. The movement of the neutral axis in the 2 nd loading almost followed the trail of the unloading, and it could not be distinguished. This result confirms that the 2 nd loading did not induce additional crack propagation. Accordingly, there was a difference of about 24 mm between the neutral axis and the actual crack depth when CMOD = 0.05 mm. [PERSON] and [PERSON] mentioned that the fracture process zone of concrete comprises the microcracking zone and the bridging zone [44]. In the microcracking zone,  
Figure 16: The behavior of the neutral axis with CMOD. Figure 15: Investigation of crack depth by ink injection. (**a**) Stained crack part; (**b**) measured crack depth. the concentrated stress near the crack tip causes the existing defects and pores to expand. Moreover, the interface between aggregates and the cement matrix is weakened, and the two components began to separate. These deteriorations develop into the bridging zone, and the stress in this area starts to dissipate. This stress dissipation in the bridging zone is expressed as the tension-softening relationship of concrete. A fully separated section is considered a stress-free crack. The stress-free crack area was obviously stained with the injected red ink, and a portion of the bridging zone was also likely stained. Consequently, it can be expected that the microcracking zone and the bridging zone are located at about 24 mm between the neutral axis and the actual crack depth, as shown in Figure 17.  
The neutral axis of the 3 rd loading followed the neutral axis trace of the 2 nd loading almost equally, regardless of the case. Figure 18 shows the typical stress-neutral axis curves of the specimens with different healing periods, and Figure 19 shows the typical stress-neutral axis curves of the specimens with different crack inducement times. Compare to Case 7-70-W (Figure 18c) and Case 49-70-A (Figure 19f), which are the strongest and the weakest healing effects in terms of the flexural strength and the initial flexural stiffness.