# Curable Area Substantiation of Self-Healing in Concrete Using Neutral Axis
## 3 Self-Healing Assessment
### Neutral Axis Estimation  
The strain distribution of the area in which crack propagation was expected to occur was investigated by the attached successive strain gauges. In the preliminary experiment, seven strain gauges were attached at intervals of 10 mm from 5 mm above the notch end, as shown in Figure 4, and the vertical strain distribution in the lower part of the load point was obtained, as shown in Figure 5. The crack induced at the end of the notch can obviously be expected to advance past this part in the three-point bending test with a notch. The strain showed a relatively linear distribution under the initial low load but it gradually changed to a nonlinear distribution with increasing load. The nonlinearity of the strain distribution may be ascribed to stress concentration due to the notch  
Figure 3: Initial flexural stiffness of the 2 nd and 3 rd loading.  
Figure 2: Typical Load-CMOD (crack mouth opening displacement) curves (Case: 7-28-A).  
and tensile softening of the tensile part. The exact stress distribution could not be estimated directly from this strain distribution, even if the elastic modulus were to be known, because the stress-strain relationship of the tensile failure part remains unknown. However, it is known that in parts wherein the strain is zero, the stress is zero as well. In other words, the position of the neutral axis can be estimated.  
The neutral axis clarifies the quantification of the healing effect. The neutral axis is probably located at the center of the cross-section at the beginning of the loading. It moves along with the crack's propagation. In the bending test, the crack propagation is limited to the tensile side below the neutral axis. This indicates that the neutral axis explicitly indicates the area wherein self-healing is possible. Meanwhile, the neutral axis does not move without further crack propagation, so it is expected to not move in the 2 nd loading conducted just after the crack inducement (1 st loading). Thereafter, if this stress neutral axis changes after the healing period, such change can be ascribed to the self-healing effect as a physical recovery. The movement of the neutral axis depends on the physical recovery, and it is relatively unaffected by changes in material properties owing to the age effect.  
The position of the neutral axis was estimated by seven successive strains gauges installed at intervals of 10 mm on the specimen in this study. Physical measurements at intervals less than 10 mm were not possible, and the interval selected herein seemed to be sufficient to reflect any changes in strain in the entire area. A few scattered data of the strain gauge attached underneath the loading point were detected, but the neutral area showed continuous data. The neutral axes were estimated by quadratic polynomial regression of the strain results obtained from the seven strain gauges at each point in time, as shown in Figure 6 and Table 3. As can be seen, the neutral axis moves upward the cross-section as the load increases and the crack propagates.  
Figure 4: Seven strain gauges for investigation of the vertical strain distribution.  
Figure 5: Strain distribution with different loads.