# Numerical Study of Pressure Attenuation Effect on Tunnel Structures Subjected to Blast Loads
## 4 Results
### Pressure Reduction Module Effect Analysis
#### 4.1.3 Linear Tunnel with Double-Pressure Relief Orifice Plate Explosion
When the quantity was changed (150-350 g), the blast was transferred from the larger tunnel section (P3) and through the double-pressure relief orifice plate (P4); thus, the range of the blast transfer rate of the double-pressure relief orifice plate was 0.16 to 0.24. According to this study, when the quantity of explosive was \(\leq\)350 g, the double-pressure relief orifice plate design mode could reduce the blast transfer rate to 0.18, meaning the blast was transferred from P3 to P4, and the blast could be attenuated by 82% by reducing the tunnel section and changing the path. The effect of the double-pressure relief orifice plate on the pressure attenuation rate was tested by using the pure linear tunnel and the linear tunnel with a double-pressure relief orifice plate. The pressure attenuation in position P4 was analyzed and discussed. When the quantity of C-4 explosive was 100 g, the measured blast value of the double-pressure relief orifice plate (P4) was 38.18 kPa, and the measured blast value of the pure linear tunnel was 271.77 kPa. Therefore, in pressure transducer position P4, the pressure attenuation rate of the double-pressure relief orifice plate was 0.14, as compared with the pure linear tunnel. The blast attenuation rate (\(R_{attenuate}\)) is expressed as follows:  
\[R_{attenuate\_double\_orifice}=\frac{P4_{double\_orifice}}{P4_{linear}} \tag{8}\]  
According to Table 3, when the quantity of explosive was \(\leq\)350 g, the pressure attenuation rate in P4 was 0.20; in other words, when the pure linear tunnel was equipped with the double-pressure relief orifice plate, the blast in P4 was attenuated by 80%, as compared with the pure linear tunnel (without the pressure relief orifice plate). In addition, according to a comprehensive comparison of pressure transducer positions P1 to P3, before the blast was transferred to the double-pressure relief orifice plate, as the tunnel specimen model was consistent, the blast transfer of the pure linear tunnel was approximate to that of the linear tunnel with double-pressure relief orifice plate (pressure attenuation rate was 0.86 to 0.94), which matched the estimated result. In terms of numerical simulation, the numerical simulation result of the linear tunnel with a double-pressure relief orifice plate and the experimental blast are compared in Table 3. According to this numerical simulation, when the quantity of explosive was \(\leq\)350 g, the blast was transferred from position P3 to position P4, and the blast transfer rate of the double-pressure relief orifice plate was 0.15. Therefore, the blast attenuation amplitude, as predicted by numerical simulation using tunnel section reduction and blast transfer path detour, could be 85%. In terms of the blast transfer rates of the experiment  
Figure 9: Comparison diagram of double-pressure relief orifice plate explosion experiment results. and numerical simulation, the blast transfer rate of the double-pressure relief orifice plate obtained by experimental analysis was 0.18 (blast was attenuated by 82%), and the blast transfer rate predicted by numerical simulation was 0.15 (blast is attenuated by 85%); thus, the blast predicted by numerical simulation was approximate to the experimental result. The transfer of the blast inside the tunnel is shown in Figure 10.  
Table 4 shows the percentage error between the experimental and numerical results of the three models. Although significant difference was observed in some cases, especially the double-orifice plate at P3, most cases agreed with the test results. It is worth noting that it is challenging to simulate a perfect match with the field test, especially in an explosion test, where highly nonlinear dynamic loading exists. The quality and density variation of explosive charge could also cause inconsistency. In addition, the inherent limitation of the continuum FE model may also cause variation. The results might be improved by upgrading the data acquisition system or further investigating the material parameters used in the model.