# 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
When the quantity of the explosive was \(\leq\)350 g, the pressure attenuation rate in P4 was 0.77, meaning with the expansion chamber, the blast in P4 was attenuated by 23%, as compared with the pure linear tunnel (without an expansion chamber). In addition, according to the comprehensive comparison of pressure transducer positions P1 to P3, before the blast was transferred to the expansion chamber, as the tunnel specimen model was consistent, the blast transfer of the pure linear tunnel was approximate to that of the linear tunnel with an expansion chamber (pressure attenuation rate was 0.95 to 1.06), which matched the estimated result. Generally speaking, the expansion chamber designed by enlarging the section was very effective on blast attenuation. In terms of the blast transfer rate, the blast was transferred from the smaller section (P3) to the expansion chamber with a larger section (P4), and the transfer rate was 0.70; thus, the blast can be attenuated by 30% by enlarging the section. In terms of the pressure attenuation rate, the pressure attenuation in P4 was discussed according to the experiments on the pure linear tunnel and the linear tunnel with expansion chamber. The findings show that the pressure attenuation rate was 0.77, meaning with the expansion chamber, the blast in P4 could be attenuated by 23%, as compared with the pure linear tunnel (without an expansion chamber). In terms of numerical simulation, the numerical simulation result of the linear tunnel with expansion chamber and the experimental blast are compared in Table 1. The simulation result shows that the blast inside the tunnel attenuated as the transfer distance increased, and the blast attenuation trend of numerical simulation was similar to that of the experiment; however, the experimental result was a little lower than the numerical simulation. The transfer of the blast inside the tunnel is shown in Figure 6. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{1}{c}{**Weight of C-4 (g)**} & \multicolumn{1}{c}{**100**} & **150** & **200** & **250** & **350** \\ \hline \multirow{4}{*}{Position} & P1 & Experiment & & 999.27 & 1276.14 & 1327.74 & 1834.18 & 2873.28 \\ \cline{2-7}  & Simulation & Explosion pressure (kPa) & 889.32 & 1207.76 & 1553.81 & 1725.41 & 2281.28 \\ \cline{2-7}  & Experiment & & 492.06 & 600.50 & 593.31 & 766.60 & 1158.69 \\ \cline{2-7}  & Simulation & Explosion pressure (kPa) & 591.04 & 747.45 & 872.07 & 967.59 & 1133.06 \\ \cline{2-7}  & P3 & Experiment & & 282.81 & 417.29 & 427.71 & 468.46 & 664.85 \\ \cline{2-7}  & Simulation & Explosion pressure (kPa) & 449.52 & 554.88 & 639.48 & 700.86 & 816.89 \\ \cline{2-7}  & Experiment & Explosion pressure (kPa) & 189.52 & 237.99 & 332.31 & 384.24 & 443.45 \\ \cline{2-7}  & Experiment & & 0.67 & 0.57 & 0.78 & 0.82 & 0.67 \\ \cline{2-7}  & P4 & & \multicolumn{4}{c}{Average: 0.7} \\ \cline{2-7}  & (L/D = 5.67) & & Explosion pressure (kPa) & 244.00 & 304.74 & 354.77 & 391.55 & 462.05 \\ \cline{2-7}  & Simulation & & 0.54 & 0.55 & 0.55 & 0.56 & 0.57 \\ \cline{2-7}  & & & \multicolumn{4}{c}{Average: 0.55} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of experiment and numerical results of linear tunnel with expansion chamber. of the pressure attenuation rate, the linear tunnel with a single-pressure relief orifice plate and the pure linear tunnel were tested, and the pressure attenuation in position P4 was analyzed and discussed. The blast transfer rate (\(R_{transfer}\)) is expressed as follows:  
\[R_{transfer\_single\_arifice}=\frac{P4_{sigle\_orifice}}{P3_{sigle\_orifice}} \tag{5}\]  
where \(P3_{sigle\_orifice}\) and \(P4_{sigle\_orifice}\) are the measured blast at the pressure transducer positon, \(P3\) and \(P4\), in the linear tunnel with single orifice plate attenuator, respectively.