# Influence of Soil Parameters on Detecting Voids behind a Tunnel Lining Using an Impact Echo Method
## 2 Experimental Outline
### Setup and Sensor Location  
The dimensions of the sand box were 0.6 m \(\times\) 0.6 m \(\times\) 0.9 m. Four steel plates were connected with bolts on the bottom, back, left and right sides. A concrete plate with dimensions of 0.58 m \(\times\) 0.8 m \(\times\) 0.05 m was installed on the front side. The concrete plate surface required sanding to ensure a tight contact between the plate and the sensor base. Polystyrene foam pads were installed between the soil and steel plates to reduce the wave reflection from the steel boundaries. The research demonstrated that the boundary effect was the lowest when the thickness and width ratio of the elastic pads was between 2% and 4% [24]. Accordingly, the thickness of the pads was selected to be 0.02 m. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Case** \\ **Description** \\ \end{tabular} } & \multicolumn{2}{c}{**Case Number**} & \multirow{2}{*}{\begin{tabular}{c} **Mass Density** \\ **(kg/m\({}^{3}\))** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Water Content** \\ **(\%)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Void Dimension** \\ **(mm \(\times\)mm \(\times\)mm \(\times\)mm)** \\ \end{tabular} } \\ \cline{2-6}  & D1 & - & \(\rho_{1}=1578\) & & - \\ \cline{2-6}  & D2 & - & \(\rho_{2}=1629\) & \(\omega_{1}\) & - \\ \cline{2-6}  & D3 & D3v & \(\rho_{3}=1656\) & & \(V_{1}\) \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} Water content \\ alteration \\ \end{tabular} } & W1 & W1v & \multirow{2}{*}{\(\rho_{3}\)} & \(\omega_{1}\) = 0.3 & \(V_{1}\) \\ \cline{2-6}  & W2 & W2v & \(\omega_{2}\) = 8.2 & \(V_{1}\) \\ \cline{2-6}  & W3 & W3v & \(\omega_{3}\) = 15.3 & \(V_{1}\) \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Void dimension \\ alteration \\ \end{tabular} } & - & V1 & \multirow{2}{*}{\(\rho_{3}\)} & \multirow{2}{*}{\(\omega_{1}\)} & \(V_{1}\) = 150 \(\times\) 150 \(\times\) 100 \\ \cline{2-6}  & - & V2 & & \(V_{2}\) = 100 \(\times\) 100 \(\times\) 100 \\ \cline{2-6}  & - & V3 & & \(V_{3}\) = 50 \(\times\) 50 \(\times\) 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test cases. Table 2 lists the main tools or instruments used for soil sample preparation. In order to obtain uniform soil particles, according to the _Standard for engineering classification of soil_ (GB/T 50145-2007) [25], the pore sizes of the test sieves were determined to be 0.5, 0.25 and 0.075 mm, and finally, soils with sizes between 0.25 and 0.5 mm were used for the test. In order to change the soil density, a ramming hammer was used to ram the soil layer by layer, where the hammer mass was 6.5 kg. Each drop height was maintained at 30 cm. Furthermore, an electronic platform scale (manufactured by Huaying weighing instrument Co., Ltd, Yongkang, Zhejiang, China), tarpaulin, constant temperature oven (manufactured by Shuli Instrument Co., Ltd, Shanghai, China), weighting box and electronic balance (manufactured by Shenzhen Meifu Electronic Co., Ltd, Shenzhen, Guangdong, China) were employed during the soil sample preparation. Table 3 lists the main equipment used for the dynamic NDT, including a dynamic hand hammer, accelerometer and an INV3062T high-precision portable data acquisition system. The data acquisition hardware was connected to a PC via a USB interface. All these instruments were calibrated prior to the test. The accelerometer was bonded to the concrete plate surface. The impact location was 2 cm from the sensor. For the cases with a changing density and water content, the accelerometer was fixed at the centre of the concrete plate (Figure 3). By using the IE method, responses at the concrete plate centre were obtained. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Tool/ Instrument** & **Picture** & **Description** & **Tool/ Instrument** & **Picture** & **Description** \\ \hline \hline \multirow{4}{*}{Test sieves} & \multirow{4}{*}{ \begin{tabular}{c} **Sieve soil with** \\ pore sizes of 0.5, 0.25 and 0.075 mm \\ \end{tabular}  } & \multirow{4}{*}{\