## 4 Results and Discussion
### Effect of Ambient Temperature  
The variation characteristics of compression wave propagation in tunnels are influenced by ambient temperature. Analyzing the patterns of change in compression wave propagation under different ambient temperatures is crucial. Figure 21 depicts the influence of the ambient temperature on the steepening rate and attenuation ratio during compression wave propagation. The ambient temperatures are 323 K, 293 K, 273 K, and 253 K, respectively. As the ambient temperature decreases, both the steepening rate and attenuation ratio show an increasing trend. When air propagates at higher ambient temperatures, its speed increases, which affects the waveform changes of the compression waves during propagation. At lower temperatures, the nonlinear effects of compression waves are relatively larger. The increase in temperature enhances the frictional effects during the propagation of compression waves, suppressing their nonlinear effects and resulting in a decrease in the steepening rate. Mitigation Characteristics of Compression Waves Pressure Gradient in Different Tunnel Entrance Hoods  
The research results mentioned above indicate that the waveform significantly influences the propagation and evolution process of compression waves in very long tunnels. As the propagation distance increases, the mitigation performance of the tunnel entrance  
Figure 21: Effect of temperature on the steepening rate and attenuation ratio: (**a**) steepening rate; (**b**) attenuation ratio. hoods decreases. When compression waves propagate in very long tunnels, a thorough evaluation of the mitigation performance of the tunnel entrance hood is necessary to ensure its effectiveness. Figure 22 presents the relative increase in the maximum pressure gradient of the initial compression waves propagating in the tunnel over a 500 m length segment. The horizontal axis represents the pressure gradient at any propagation length (\(x\)), while the vertical axis represents the pressure gradient after propagating 500 m (\(x+500\)). When compression waves with different waveforms but identical pressure gradients propagate a distance of 500 m, their pressure gradients remain the same. This demonstrates that the steepening extent of the compression waves is closely correlated with the maximum pressure gradient of the compression waves. Therefore, reducing the maximum pressure gradient of the initial compression waves is highly effective in mitigating micro-pressure waves. Figure 23 illustrates the variation in the reduction rate of the maximum pressure gradient with the tunnel length when tunnel entrance hoods are installed. The mitigating effect of type A tunnel entrance hoods on compression waves is primarily concentrated within the first 4 km ahead of the tunnel, with an optimal reduction rate of 63%, observed at the 3 km mark; when greater than 4 km, the reduction rate drops to less than 15%. For a tunnel length of 9 km, the pressure gradient reduction rate is \(-2\%\), indicating that by the time the compression waves propagate to 9 km, the type A tunnel entrance hoods do not mitigate the compression waves but instead amplify their pressure gradient. The mitigating effect of type B tunnel entrance hoods on compression waves is primarily concentrated within the first 12 km ahead of the tunnel, reaching an optimal reduction rate of 95% at the 4 km mark. Greater than 14 km, the reduction rate drops to less than 40%. As the propagation distance of the compression waves increases, the mitigation performance of the tunnel entrance hoods for the pressure gradient shows a trend of initially increasing and then decreasing. This indicates that tunnel entrance hoods have a certain range of effectiveness in reducing the pressure gradient of compression waves. Therefore, in engineering design, appropriate tunnel entrance hoods should be selected based on the consideration of tunnel length to find the most reasonable matching relationship.