# Evaluation of Unfilled Sheath in Concrete Structures Using Response Waveform in Time Domain
## 5 Conclusions  
This study, in order to overcome the difficulty of conventional internal defect evaluation, proposed a new evaluation method called DVA that uses Difference value as the evaluation index. The proposed method is validated experimentally by performing the model tests. The demonstrated results show that DVA detects the sheath as well as the conventional evaluation methods, and further, it suggests that DVA detects the relatively small defect that is not detected by the conventional method. The findings and conclusions of the research are summarized as follows:  
* It is confirmed that the magnitude and distribution of Difference value depend on the number of data \(N\). This arises from the influence of the input decays in the later part of the time history, and Difference value decreases if \(N\) is large because the influence of the input is averaged. Conversely, the Difference value is larger if the \(N\) is adequately small since the influence of the input is emphasized. On the other hand, if the number of data does not satisfy the contact time of the steel ball, the Difference value decreases because the reflected wave has no interference with the time history and the input  
Figure 23: Contours of the evaluation results for Case_3: (**a**) DVA; (**b**) Dominant frequency.  
Figure 22: Contours of the evaluation results for Case_2: (**a**) DVA; (**b**) Dominant frequency.  
condition and surface do not change. Further, if the number of data is not sufficient to cover the target thickness, of the defects depth and contact time, it is difficult to properly evaluate the internal defect. In addition, even if the thickness condition is complied with, the evaluation of internal defects becomes difficult because the difference value of the defects area is not characteristically increased with a small number of data. In contrast, as the number of data increases, the change of Difference value at the location of the defect is emphasized by the change of the reflected wave between the measurement surface and the defect and the change in the propagation path. From these results, it is revealed that DVA evaluates the position of the sheath correctly by choosing the appropriate \(N\).
* The depth of the internal defect has the small influence for the magnitude of the difference value, and it is difficult to evaluate the depth of the defect of the same size from the magnitude of the difference value. However, it is confirmed that the difference value increases area if the defect is deep. This result suggests that the depth of the defect is possibly evaluated from the distribution of the difference values.
* It is confirmed that the size of the defect has a great influence of the difference value, and it is suggested that the size of the internal defect can be evaluated by difference values.
* Finally, comparing the evaluation results of the conventional method and DVA, it is found that DVA has the equivalent capability, and furthermore, it has the potential to evaluate relatively small defects that are not detected by the conventional method  
Conceptualization, K.I. and Y.K.; Methodology, K.I.; Validation, K.I., Y.K., K.O. and K.N.; Formal analysis, K.I.; Data curation, K.I.; Writing--original draft preparation, K.I.; Writing--review and editing, Y.K., K.O. and K.N.; Visualization, K.I.; Supervision, Y.K., K.O. and K.N. All authors have read and agreed to the published version of the manuscript. This research received no external funding. The contours of this study (Figures 21-23) were drawn using \"RINEARN Graph 3D\". This software is completely free of charge, and we would like to express our gratitude to it for giving us a good output for this study. The authors declare no conflict of interest.