## 2 Experimental Study
### Experimental Outline
The experiment was carried out in a brick box of size \(3.6\times 0.94\times 1.44\) m\({}^{3}\) (Figure 2(a)). A rockwood material with a thickness of 0.1 m was placed inside the bunker to weaken the wave reflection at the boundaries. The soil was filled into the bunker. The horseshoe tunnel models were buried in the soil. The cross-sectional size of the tunnel model was 1:16 of a real railway tunnel and the thickness of the tunnel model was 0.025 m (Figure 2(b)). The tunnel models were made of polyvinyl chloride (PVC) material instead of the concrete. The material coefficients of the soil, the concrete, the PVC, and the air are shown in Table 1. The wave impedance of the PVC and the concrete is within one order of magnitude, which is much larger than the wave impedance of the air. This illustrates that the concrete tunnel can be instead by the PVC, a cheaper material, in this principle experiment. Two different conditions (A and B) were designed. Condition A referred to a tight contact between the tunnel lining and the surrounding soils. The reflected ratio \(R_{\text{A}}\) at the interface is \(-0.31\). For Condition B, a void behind the tunnel wall was modelled using a pre-embedded empty box of \(285\times 145\times 155\) mm\({}^{3}\) placed between the lining and the soil. The reflected ratio \(R_{\text{B}}\) at the interface is \(-1\). Figure 3: The test system. Figure 2: The basic principle of detecting the void behind tunnel lining by impact-echo (IE) method. The test system consisted of a hand hammer, two unidirectional accelerometers, a data acquisition instrument with 16 channels, and a computer. The hand hammer, consisted of a hammer head, a force sensor and a hammer body, was used to apply an impact force on the tunnel model. The type of the hammer is Dytran Dytranpulse(tm)5800B4T, developed by the Dytran Instruments company in California, USA. The head of the hammer is made by aluminium with the weight of 100 g and Young's modulus of 70 GPa. There is a special acceleration compensated piezoelectric force sensor in the hammer head at the striking face, ensuring a smooth frequency spectrum, which is used to measure the value of the impact force. The hammer has a sensitivity of 10 mV/lbf and a maximum force of 1000 lbf. The upper limit of the frequency range is 75 kHz. The type of unidirectional accelerometers is LC0104, developed by LANCE in Ohio, USA. They are used to collect the accelerations perpendicular to the tunnel lining, which has a sample frequency range of 0.5 Hz-9000 Hz, a sensitivity of 100 mV/g, a resolution of 0.0002 g, and an acceleration range of 50g. The type of data acquisition instrument is INV3018C, developed by the China Orient Institute of Noise & Vibration (COINV). The testing point B was arranged at the tunnel lining behind the empty box on the right tunnel model, while testing point A was arranged at the same location on the left tunnel model, as shown in Figure 3a. According to the thickness and the P wave velocity of the tunnel lining in the test, the thickness resonance frequency is obtained approximately at 28,800 Hz. Since the thickness frequency of the two conditions is the same, this experiment of detecting the void behind tunnel lining does not intend to focus on the amplitude of resonance frequency, but to analyse the dynamic responses of these two conditions in a lower frequency range. The sampling frequency of the accelerometers is set at 2560 Hz. The impact points are 2 cm nearer to the testing points. For each condition, the impact was repeated 10 times. For each time, the peak of impact force is controlled to be close to 400 N, and the sampling frequency is 2560 Hz, as shown in Figure 4. It should be noted that the hammer should be controlled to be perpendicular to the surface of the tested object. To obtain this goal, the coherence function of the response and the force was calculated in each test. If the coherence function was close to 1, the impulse force would be qualified. Otherwise, the data would be removed.