# Granular Flow Impact on Shed Tunnels and the Buffering Effect of Cushion Layers
## 3 Results
### Influence of Slope Angle
#### 3.1.2 Impact Force  
Figure 6 shows a comparison between the model test and numerical simulation results of the granular flow impacting a shed tunnel at a 45\({}^{\circ}\) angle. The high level of agreement throughout the entire process indicates that the parameters are reasonable and can accurately reflect the real sliding behavior of the granular materials. The entire impact process can be divided into the following stages: pre-impact; granular flow impacts the shed; a dead zone forms; continued rearward impact; the dead zone reaches the shed tunnel top; particle overflow; and deceleration and cessation. In the early stage of granular flow impacting the shed tunnel, the primary source of frontal normal impact force is the direct collision of particles. However, once a larger dead zone is formed, the frontal normal impact force is mainly generated by the rear portion of the granular flow impacting the dead zone and then indirectly transmitted to the tunnel.  
Figure 5: Velocity time history of the granular flow at different slope angles.  
Figure 6: _Cont_.  
According to the velocity analysis and the relationship between velocity and impact force, it is evident that the impact force of the granular flow varies with different slope angles. Figure 7a shows the time history curves of the frontal normal impact force for each angle. It is apparent that both the peak impact force and residual force increase with the angle. For instance, at a slope angle of 60\({}^{\circ}\), the peak impact force and residual force are approximately 565 N and 324 N, respectively, which are 3.3 times and 2.1 times higher than those at 40\({}^{\circ}\). At smaller angles, the time history curves of the impact force do not exhibit distinct peaks. However, as the slope angle increases to 50\({}^{\circ}\), a peak appears, and the higher the slope angle, the more pronounced the peak becomes. This is because at larger slope angles, the granular flow attains higher peak velocity and greater kinetic energy, resulting in more intense impacts on the shed tunnel.  
The time history curve of the normal impact force on the top surface of the shed tunnel is shown in Figure 7b. The peak impact force increases with an increase in the slope angle, but the amplitude is not as significant as that of the frontal normal impact force. For example, at a slope angle of 60\({}^{\circ}\), the peak impact force is around 225 N, which is 2.2 times higher than that at 40\({}^{\circ}\). Furthermore, the time at which the impact force reaches its peak  
Figure 6: Snapshots of the granular flow in the experimental test and numerical simulation. (**a**) \(t=0.7\) s; (**b**) \(t=1.0\) s; (**c**) \(t=1.3\) s; (**d**) \(t=1.6\) s; (**e**) \(t=2.5\) s.  
varies significantly with different slope angles. As the slope angle increases, the moment of impact on the top surface of the shed tunnel occurs earlier, and the advance is slightly greater than that of the frontal normal impact. After 2.0 s, the impact force gradually stabilizes, and the differences in impact force among the five angles are not significant, with all values being around 100 N. This is because after the granular flow comes to a rest, the residual force of the normal impact force on the top surface mainly comes from the self-weight of the particles accumulated on the top surface, and the volume of granular flow particles deposited on the top surface does not differ significantly among the five cases.