## 4 Validation and Analysis of Results
### Model Validation and Sand Barrier Principle Analysis
This is due to the height of the embankment altering the distribution characteristics of the flow field, leading to the formation of a wind speed reduction zone in front of the windward slope, which decreases the kinetic energy of the sand particles and effectively obstructs their movement. However, due to the limitations imposed by the embankment's height, some sand particles still possess sufficient kinetic energy to land on its surface. We can find that increasing the embankment height can effectively prevent sand particles from falling on the embankment surface, so windbreaks can be installed to prevent particles of sand from falling on the embankment surface. Figure 3: Leapfrog trajectories of sand particles with different grain sizes. Figure 4: Comparison of sand concentration for different types of mixed grain. Figure 7 shows the source analysis of sand-buried particles at different time steps. In this study, a sand-buried particle backtracking algorithm was written to capture sand-buried particles at three different time steps by utilizing the SPH method to observe the entire motion process of the particles. At 15,000 steps, most of the sand particles have begun to move; at 25,000 steps, the sand flow has already started to enter the stabilization phase; and at 35,000 steps, the sand flow has been in the stabilization phase for a certain period. Capturing the sand-buried particles at three different time-steps, it can be roughly found that the sand-buried particles are concentrated in the range of 0.005 m-0.009 m, and the approximate location of the peak of the sand-buried particles source at 0.008 m to set up a windbreak, as shown in Figure 8.  
Figure 5: Mixed grain size sand transport rate distribution along height. Figure 6: Concentration distribution of single grain size sand particles. As shown in Figures 9-11, demonstrating the concentration of sand particles after the installation of the windbreak shows that there are almost no sand particles on the roadway embankment surface and the two embankment surfaces with the foot of the slopes at both locations. As shown in Figure 11, the overall decrease in particle concentration with a windbreak is 97%, with a 96% decrease on the windward slope and a 98% decrease on the leeward slope. Figure 8: Particle model of windbreak embankment. Figure 7: Distribution of initial positions of sand buried particles. Figure 9: Distribution of windbreak embankment particle concentration. As shown in Figure 12, comparing the above two pictures, it can be found that the vortex location of the flow field appears near the windbreak after setting up the windbreak. This indicates that the velocity decay region of the flow field is shifted forward, and the sand particles are blocked by the windbreak wall in advance so that the sand particles do not have enough kinetic energy to run onto the embankment, thus effectively solving the sand burial problem of the embankment. This also demonstrates the validity of analyzing the initial positions of buried particles through a particle backtracking algorithm, thereby informing the implementation of effective sand control measures. As shown in Figure 13, the sand velocity distribution is compared between the two working conditions. In the embankment wind-sand flow field, the airflow field near the embankment is disturbed due to the disturbance of the embankment. Wind speeds decrease dramatically at the foot of windward slopes, creating a wind speed attenuation zone that significantly prevents the transport of sand particles. However, some sand particles still cross the embankment, and at the leeward slope, the velocity decreases abruptly due to a sudden change in velocity in the turbulent airflow field. After setting up the windbreak, the flow field around the windbreak is disturbed, and the particle velocity changes abruptly, forming a wind speed attenuation zone, which prevents the transport of sand particles. Figure 6.0 Distribution of particle concentration under different working conditions.