# Influence of Soil Parameters on Detecting Voids behind a Tunnel Lining Using an Impact Echo Method
## 3 Experimental Study  
### Soil Density Alteration  
Soils with three mass densities were tested, namely cases D1, D2 and D3, as listed in Table 1. When changing the density, the sand box was divided into nine parts from top to bottom and marked with a 10 cm height for each. For case D1, the soils were loaded nine times and each part of the soil was weighted. As the box volume was known, it was easy to calculate the bulk density, \(\rho_{1}=1578\) kg/m\({}^{3}\), and the densities \(\rho_{2}\) and \(\rho_{3}\) could be obtained by ramming. Figure 4 illustrates the typical time histories of the three test cases with three different densities. It can clearly be seen that with an increase in density, the peak amplitude value decreased; furthermore, a smaller soil density induced faster attenuation. In order to quantify the attenuation trend, the number of threshold crossings, or simply \"counts\" in acoustic emission terminology, was examined [14; 26]. The threshold of the waveform peak value was defined as 10%, 1% and 0.1% of the first peak value of the waveforms. The total number of threshold crossings can reflect the attenuation speed. If the threshold was set to be large, for example, 10%, only larger oscillations were counted. For each case, the tests  
Figure 3: Impact location and layout of measuring points. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Equipment** & **Picture** & **Manufacturer** & **Model** & **Main Parameters** \\ \hline \hline \multirow{6}{*}{Dynamic hand hammer} & \multirow{6}{*}{\begin{tabular}{c} Dytran Instruments, Inc., \\ Chatsworth, CA, \\ USA \\ \end{tabular} } & \multirow{6}{*}{\begin{tabular}{c} Dytranpulse\({}^{\text{m}}\) \\ 5800B4T \\ \end{tabular} } & \multirow{6}{*}{\begin{tabular}{c} Hammer head weight: \\ 100 g \\ Sensitivity: 10 mV/lbf \\ Measurement range: \\ 500 lbf \\ Maximum impact load: \\ 1000 lbf \\ \end{tabular}} \\ \hline \multirow{6}{*}{Accelerometer} & \multirow{6}{*}{\begin{tabular}{c} Lance Technologies \\ Inc., Copley, OH, \\ USA \\ \end{tabular} } & \multirow{6}{*}{\begin{tabular}{c} Lance LC0156A \\ Lance LC0156A \\ Lance LC0156A \\ Lance LC0156A \\ Resolution: 0.02 mg \\ \end{tabular} } \\ \hline \multirow{6}{*}{Data acquisition} & \multirow{6}{*}{\begin{tabular}{c} China Orient \\ Institute of Noise \& \\ Vibration, Beijing, \\ China \\ \end{tabular} } & \multirow{6}{*}{\begin{tabular}{c} INV3062T \\ \end{tabular} } & \multirow{6}{*}{\begin{tabular}{c} Maximum sampling \\ frequency: 51.2 kHz \\ \end{tabular} } \\ \hline \multirow{2}{*}{Laptop} & \multirow{2}{*}{\
\begin{tabular}{c} Lenovo, Beijing, \\ China \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} Thinkpad \\ \end{tabular} } \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Main equipment for dynamic non-destructive testing (NDT). were repeated four times, and the results are shown in Figure 5. For larger densities, the number of threshold counts was smaller, i.e., the vibration attenuated faster. It can be concluded that if the density was large, the impedance difference between the soil and concrete was small, and accordingly, the reflection energy was weak. In the following analysis, fractal theory was employed to calculate the box-counting dimensions of different vibration signals in the time domain. Fractal theory, proposed by [PERSON] (1967), is used to describe complex shapes, such as coastlines and rivers that cannot be described using Euclidean geometry. However, these complex systems should have the characteristic of self-similarity, such that the internal rules of them can be expressed using fractal theory. The vibration responses are random fractal signals fulfilling the criterion of statistical self-similarity [PERSON] (1967). Figure 4: Acceleration waveforms for different density cases. Figure 5: Number of counts for thresholds of **(a)** 10%, **(b)** 1% and **(c)** 0.1% of the peak value. The counting dimension is an important index of fractal theory used to describe the internal rules of complex shapes.