# Numerical Study of Pressure Attenuation Effect on Tunnel Structures Subjected to Blast Loads
## 4 Results  
### Pressure Reduction Module Effect Analysis  
#### 4.1.1 Linear Tunnel with Expansion Chamber Explosion  
The variation of blast attenuation inside the tunnel of this experiment is shown in Figure 5. Due to the nature of explosion characteristics, the pressure decayed extremely  
Figure 4: Schematic diagram of numerical models of pressure reduction modules. rapidly with time and space. As a result, for different charge weights, a larger scattering of the pressures could be found at the measurement point P1 compared to P4. According to the experimental results, the transfer of the blast inside the tunnel decreased as the distance increased. In order to know the blast attenuation characteristic of the expansion chamber, as designed by enlarging the section, we analyzed and discussed the blast transfer rate and variation rate of the expansion chamber. In terms of the blast transfer rate, the linear tunnel with expansion chamber was tested, and when the blast was transferred from the smaller tunnel section (pressure transducer P3 position) to the expansion chamber with a larger section (pressure transducer P4 position), the blast transfer attenuation in P3 and P4 was analyzed. In terms of pressure attenuation rate, the linear tunnel with expansion chamber and the pure linear tunnel was tested, and the pressure attenuation in the P4 position was analyzed and discussed. The effect of the expansion chamber on the pressure transfer rate was described using the pressure transducers in positions P3 and P4. When the quantity of C-4 explosive was 100 g, and the blast had not been transferred to the expansion chamber, the measured blast value (P3) was 282.81 kPa. When the blast was transferred to the expansion chamber (P4), the measured blast value was 189.52 kPa. Therefore, the blast transfer rate in pressure transducer position P4 was 0.67; in other words, when the blast was transferred from position P3 with the smaller tunnel section (side length 30 cm) to position P4 with the larger tunnel section (side length 60 cm), the blast was diffusively attenuated by enlarging the section, and the blast attenuation amplitude was 33%. The blast transfer rate (\(R_{transfer}\)) was expressed as follows:  
\[R_{transfer\_expansion}=\frac{P4_{expansion}}{P3_{expansion}} \tag{3}\]  
where \(P3_{expansion}\) and \(P4_{expansion}\) are the measured blast at the pressure transducer positions, \(P3\) and \(P4\), respectively. When the quantity was changed (150-350 g), the blast was transferred from the smaller tunnel section (position P3) to the expansion chamber (position P4), and the range of blast transfer rate was 0.57 to 0.82. When the quantity of the explosive was \(\leq\)350 g, the expansion chamber design mode could reduce the blast transfer rate to 0.7, meaning the blast was transferred from P3 to P4, and the blast could be attenuated by 30% by enlarging the tunnel section. The effect of the expansion chamber on the pressure attenuation rate was tested using a pure linear tunnel and the linear tunnel with an expansion chamber. The pressure attenuation in position P4 was analyzed and discussed. When the quantity of C-4 explosive  
Figure 5: Comparison diagram of explosion experiment results of linear tunnel with expansion chamber. was 100 kg, the measured blast value of the expansion chamber (P4) was 189.52 kPa, and the measured blast value of the pure linear tunnel (P4) was 271.77 kPa. Therefore, in pressure transducer position P4, the pressure attenuation rate of the expansion chamber was 0.70, as compared with the pure linear tunnel. The blast attenuation rate (\(R_{attenuate}\)) is expressed as follows:  
\[R_{attenuate\_expansion}=\frac{P4_{expansion}}{P4_{linear}} \tag{4}\]  
where \(P4_{linear}\) is the measured blast at the pressure transducer position, \(P4\), in the linear tunnel.