# Influence of Soil Parameters on Detecting Voids behind a Tunnel Lining Using an Impact Echo Method
## 3 Experimental Study
### Void Size Alteration  
The void size is another important factor that affects NDT results. During NDT in practice, the void location is unknown; thus, the influence of the distance between the impact and detection points should also be taken into account. Accordingly, for the changing void size cases, the impact and sensor locations were moved along numbered measuring points (Figure 17) to aid in analysing the void size influence and its impact areas. In Figure 17, the distance between neighbouring points is 2.5 cm. In order to describe the void size influence quantitatively, only the box-counting dimension analysis is presented in this sub-section.  
Figure 16: Energy time-frequency distribution diagram for different water content cases.  
As indicated in Table 1, the soil density was maintained at \(\rho_{3}=1656\) kg/m\({}^{3}\) and the water content was \(\omega_{1}=0.3\%\), and three different void sizes were designed: \(V_{1}=150\times 150\times 100\) mm\({}^{3}\) (case V1), \(V_{2}=100\times 100\times 100\) mm\({}^{3}\) (case V2) and \(V_{3}=50\times 50\times 100\) mm\({}^{3}\) (case V3). Empty boxes of three different sizes were pre-embedded behind the plate, where the areas were marked with different colours (Figure 17).  
For case V1, the box-counting dimension values along the vertical and horizontal measurement lines are plotted in Figure 18. It can be seen that within the plate area behind where the void is located, the dimension value remained stable; however, at the void area edge (points 4 and 10), the dimension values decreased sharply. Moreover, the values continued to decrease along the measurement lines. The values at points 7 and 13 were already similar to those of the non-void condition (case D3, see Figure 7).  
For cases V2 and V3, the values of the box-counting dimensions along two orthogonal directions are plotted in Figures 19 and 20, respectively, where similar results can be observed. At the void area edge (points 3 and 9 for case V2; points 2 and 8 for case 3), the dimension values decreased sharply. Moreover, the values continued to decrease along the measurement lines. The values at points 6 and 12 (for case V2) or points 5 and 11 (for case V3) remained stable and were already similar to those of the non-void condition (case D3, see Figure 7).  
Figure 21 illustrates that the box-counting dimension varied with the void size for different measuring points. Generally, the dimension values decreased with the void size, but it was not obvious when the measuring point was far away from the void centre.  
Figure 17: Numbering of measuring points.  
Figure 18: Box-counting dimensions for case V1: (**a**) along the vertical measurement line and (**b**) along the horizontal measurement line.  
Accordingly, it is suggested that the orthogonal measurement lines should be plotted during the practice test. The impact and measurement points should be moved and the box-counting dimensions should be calculated for the vibration signals. If the dimension value is obviously enlarged, a potential void may exist behind the concrete structure.  
Figure 19: Box-counting dimensions for case V2: (**a**) along the vertical measurement line and (**b**) along the horizontal measurement line.  
Figure 20: Box-counting dimensions for case V3: (**a**) along the vertical measurement line and (**b**) along the horizontal measurement line.