# Evaluation of Unfilled Sheath in Concrete Structures Using Response Waveform in Time Domain
## 3 Experiment Conditions  
In this study, model tests are performed for the validation of DVA with four concrete specimens in which an unfilled sheath is embedded. The specimen is made of concrete with the same mixing conditions using portland cement, and each specimen has the same configuration as illustrated in Figure 9a,b. A spiral sheath of 1300 mm in length is buried at 600 mm in the Y coordinate system and 50 mm in the Z coordinate system in the specimens, as shown in Figure 9. Figure 10a,b show a photograph of the specimen_1. In this experiment, four specimens are prepared with two grout filling patterns of 100% and 0% for each sheath diameter. The sheaths adopted are 63 mm and 33 mm in diameter. Table 2 shows the conditions of the sheaths. It is assuming that grout with 100% filling ratio simulates sound condition and the grout with 0% filling ratio simulates unsound condition. Difference value is calculated by using the response waveforms of the same sheath with different filling ratio and evaluate the unfilled sheath from the distribution of the calculated difference value. In addition, the influence of sheaths of different diameters is examined by comparing the difference values that are calculated by using the response waveforms of the different sheath and filling ratio. \begin{table}
\begin{tabular}{c c c}
**Specimen\_No.** & **Sheath Size: \(\varphi_{S}\)** & **Filling Ratio** \\ Specim\_1 & & 100\% \\ Specim\_2 & 63 mm & 0\% \\ Specim\_3 & & 100\% \\ Specim\_4 & 33 mm & 0\% \\ \end{tabular}
\end{table} 
Table 2: Sheath conditions. Figure 8: Example of waveform normalization: (**a**) Before normalization; (**b**) After normalization. Figure 11 show the schematic diagram of the structure and sweep direction of the input and measurement points. As shown in Figure 11, the distance between the input point and the measurement point is fixed at 50 mm, and the measurement is performed for each measurement point. Moreover, this measuring unit advances in the X-axis direction at a 100 mm interval and if the measurement is completed on the line, it is moved in the Y-axis direction at 50 mm intervals for further measurement to be performed. Thus, measurement and movement are repeated, and the measurement is performed at the condition of the coordinate positions of the input points in Table 3. The total number of measurement points is 45. Figure 10: Photograph of the concrete specimen_1: (**a**) Front side of specimen; (**b**) Cross-section of specimen. Figure 9: Schematic diagram of the specimen_1 and specimen_2: (**a**) Front side of specimen; (**b**) Cross-section view of configuration and the sheath. The receiving sensor is a high sensitivity acceleration sensor, and accelerometers are installed in the Z-axis direction to the X-Y plane, and impacts are made in the Z-axis direction. In this experiment, 5 measurement waveforms are recorded at the same measurement point, and the average waveform of the normalized waveforms is created, and the Difference value is calculated by using the averaged waveform. A comparative example of the waveform after all of the processing is shown in Figure 12.  
Figure 11: Schematic diagram of the structure and sweep direction of the input and measurement points.