# Influence of Soil Parameters on Detecting Voids behind a Tunnel Lining Using an Impact Echo Method
## 3 Experimental Study
### Water Content Alteration
#### 3.2.2 Vibration Responses Affected by Existence of Void  
Figure 13 illustrates the typical time histories of three test case groups for different water contents, with and without voids behind the concrete plate. Obvious differences were observed due to the existence of voids. Under the same water content conditions, the voids induced larger vibration amplitudes and longer attenuation durations. Table 4 lists the average threshold numbers for 10%, 1% and 0.1% of the peak value under different test cases. For different water content cases, the number of threshold peaks for the void conditions was obviously larger than those for non-void conditions. That is, the existence of a void behind the concrete plate induced slower vibration attenuation. With increasing water content, the number of threshold peaks decreased for all cases, and the vibration attenuation became faster. According to Equation (1), fractal analysis can also be applied to the waveforms in Figure 13. Figure 14 shows the box-counting dimensions for different water content cases. Each value was averaged using 10 useful data points. For both the void and non-void conditions, with increasing water content, the counting dimension value decreased. Nevertheless, compared to the non-void conditions, the dimension alteration was not obvious. Furthermore, for each water content case, the existence of the void induced a sharp increase in the dimensions. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Water** \\ **Content** \\ \end{tabular} } & \multicolumn{2}{c}{**Threshold of 10\% of Peak**} & \multicolumn{2}{c}{**Threshold of 1\% of Peak**} & \multicolumn{2}{c}{**Threshold of 0.1\% of Peak**} \\  & \multicolumn{2}{c}{**Value**} & \multicolumn{2}{c}{**Value**} & \multicolumn{2}{c}{**Value**} \\ \cline{2-7}  & **Without Void** & **With Void** & **Without Void** & **With Void** & **Without Void** & **With Void** \\ \hline \(\omega_{1}=0.3\%\) & 5.3 & 8.5 & 9.0 & 13.3 & 23.3 & 33.0 \\ \hline \(\omega_{1}=8.2\%\) & 3.8 & 8.3 & 7.5 & 13.0 & 20.8 & 32.0 \\ \hline \(\omega_{1}=15.3\%\) & 3.5 & 8.3 & 7.3 & 12.5 & 19.5 & 30.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Number of threshold peaks under different test cases. Figure 12: Acceleration frequency spectra for different water content cases. In summary, the box-counting dimension could effectively evaluate the void quantitatively, and alteration of the water content had little influence on the void inspection result. Figure 14: Fractal box-counting dimensions for different water content cases. Figure 13: Typical acceleration waveforms for void and non-void conditions for different water content cases: (**a**) cases W1 and W1v, (**b**) cases W2 and W2v and (**c**) cases W3 and W3v. Figure 15 illustrates the typical Fourier spectra of three test case groups for different water contents, with and without voids behind the concrete plate. Under different water content conditions, the void always induced a dominant frequency at between 1640 and 1690 Hz. That is, the void could cause wave reflection and energy concentration in the frequency domain. Moreover, alteration of the water content had little effect on void detection. Figure 16 illustrates the time-frequency spectra for three water content cases with and without voids by using wavelet transforms. The energy distribution of the acceleration responses were clearly observed. Figure 16a,c,e demonstrate that with increasing water content, the energy attenuation duration became shorter, the frequency distribution became wider and the amplitude became smaller. Similar to the Fourier spectrum, peak values around 800 to 1100 Hz were observed more clearly for cases W2 and W3 than for case W1. Furthermore, the energy around 800 and 1100 Hz has a longer duration. Comparing (a), (c) and (e) with (b), (d) and (f) of Figure 16, it can clearly be observed that the existence of voids induced a greater vibration energy concentration and a longer attenuation time.