## 2 Experimental Study  
### Experimental Outline  
Impact echo method is based on the stress wave that is excited by an impact force. During the impact echo test, an impact force is applied on the surface of the structure by a hammer. The generated stress waves which include the body waves (P wave and S wave) and the surface wave (Rayleigh wave) propagate in the structure. Reflections and refractions happen at the interface of two media with different wave impedance. The reflectional signals are then collected by the sensor adjacent to the impact point. The P wave propagates faster than other types of waves, and if the transducer is placed close to the impact point, the response is dominated by P-wave echoes ([PERSON] et al., 2012). The signals are recorded and restored by the data acquisition instrument and are analysed in the computer. The response signals are analysed in the time domain, the frequency domain and the time-frequency domain. Finally, the property of the structure, such as the location of void and the thickness of the structure ([PERSON] et al., 2013), can be detected from the patterns of waveform versus time and spectra versus frequency. The test flew is shown in Figure 1.  
When the IE method is used to detect the thickness of a slab structure, the excited P wave reflects in the slab structure repetitively, which forms a periodic modal related to the thickness of the slab. In turn, the resonance frequency corresponding to the thickness occurs. Therefore, the thickness of a slab structure can be detected by the thickness frequency according to the IE method. When there is a void in the slab, the excited frequency needs to be higher than the thickness frequency. For example, if the velocity of the P wave is 4000 m/s and the depth of the void is 0.2 m, the resonance frequency is calculated as about 10 kHz, which should be contained in the excited frequency range. Therefore, when a void is inside the slab structure, another resonance frequency corresponding to the void can be seen except for the resonance frequency related to the thickness. Then the void can be detected by the IE method by observing the resonance frequencies. In the situation of detecting voids behind the tunnel lining, the resonance frequencies of the conditions with and without void will be the same, which are both related to the thickness of the tunnel lining. Thus, the void cannot be detected by the difference in the resonance frequency. However, a void can be recognised by IE method due to different responses caused by different reflective ratios. The reflective ratios are caused by the distinct difference in the wave impedance among tunnel lining, soil and air. The wave impedance \(Z\) is expressed as:  
\[Z=\rho V_{\text{P}}, \tag{1}\]  
where \(\rho\) is density and \(V_{\text{P}}\) is P wave velocity. For the P waves propagate from structure A to structure B, the reflective ratio is expressed as:  
\[R=\frac{A_{\text{r}}}{A_{\text{i}}}=\frac{Z_{\text{B}}-Z_{\text{A}}}{Z_{\text {B}}+Z_{\text{A}}}, \tag{2}\]  
where \(A_{\text{r}}\) is the reflected amplitude and \(A_{\text{i}}\) is the incident amplitude. When \(Z_{\text{A}}\) is much larger than \(Z_{\text{B}}\), the reflected ratio \(R\) is closed to \(-1\), which means the amplitude of the reflected wave remains the same, while the phase of the reflected changes. This situation happens at the interface of tunnel lining and air, where almost all of the energy is reflected. When \(Z_{\text{A}}\) is approximately equal to \(Z_{\text{B}}\), the reflected ratio \(R\) is closed to 0, which means most of the energy propagates through the interface. This situation is similar to the condition that the tunnel lining is tightly surrounded by the soil. This section presents the design of a laboratory principle experiment (Figure 2), whereby different signal analysis approaches were then employed to compare the vibration responses for the conditions A and B.  
Figure 1: Test flow chart.