## 4 Validation and Analysis of Results  
### Model Validation and Sand Barrier Principle Analysis  
The jump trajectories of sand particles with different grain sizes are shown in Figure 3. When the wind-sand flow reaches the stabilization stage, the trajectories of the leapfrog motion of the five grain sizes of sand particles show typical characteristics. These trajectories show that the sand particles rise more slowly and fall more rapidly, showing an asymmetric parabolic shape. These observations are highly consistent with the sand grain leapfrog motion recorded by [PERSON] et al. [21] through wind tunnel experiments and high-speed photography. In addition, the jump height gradually decreases as the radius of the sand grains increases. This phenomenon can be attributed to the increase in particle mass due to the increase in particle size of the sand particles, which decreases the sand particles' jump height under the same airflow conditions. \begin{table}
\begin{tabular}{c c c} \hline
**Gas-Phase Particles** & **Sand Particles** & **Calculation Parameters** \\ \hline Diameter of gas particle & Diameter of sand particle & Karman constant \\ ds = 0.1 mm & ds = 0.1 mm & K = 0.4 \\ \hline Density of gas particle & Density of sand particle & Friction wind velocity \\ \(\rho_{\text{S}}=1.293\) kg\(\cdot\)m\({}^{-3}\) & pg = 2650 kg\(\cdot\)m\({}^{-3}\) & \(\mu^{*}\) = 0.13 m\(\cdot\)s\({}^{-1}\) \\ \hline Dynamic viscosity & Coefficient of friction & Time step \\ V = 1.8 \(\times\) 10\({}^{-5}\) & \(\mu\) = 0.4 & \(\Delta\)t = 1.0 \(\times\) 10\({}^{-5}\) s \\ \hline Mass of gas particle & Coefficient of restitution & Total time step \\ m = 0.523 kg & e = 0.85 & N = 50,000 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameter setting. As shown in Figure 4, the concentration of sand particles of different types of mixed grain sizes was compared. The concentration of sand particles of different grain sizes in all three pictures showed an exponential decay trend along the height variation, which is consistent with the experimental results of [PERSON] et al. (2018). In addition, it can be observed from Figure 4a,b that the larger the diameter of the sand grains, the slower the rate of concentration decay. This is due to the fact that larger-sized sand particles acquire more kinetic energy upon collision, causing their concentration to decay more slowly along the altitude. As shown in Figure 5, the mixed grain size sand transport rate varies along the height. The mixed grain size sand particles have a grain size of 0.05 mm, 0.10 mm, 0.15 mm, 0.20 mm, 0.25 mm, and the proportion of each is 45%, 25%, 15%, 10%, 5%. The figure reveals that both the mixture of particle sizes and the sediment transport rate for each particle size exhibit a trend of initially increasing and then decreasing. This pattern aligns with the \"overshoot\" phenomenon observed in the experiments by [PERSON] and [PERSON] (2018), where the distribution of sediment transport rate along the flow path exhibits characteristics of \"increase-saturation-decline-stabilization\". The figure also indicates that the sediment transport rate of sand particles decreases with increasing particle size. This is primarily due to smaller particles being more easily mobilized under wind forces, requiring less energy to reach greater heights and achieve higher velocities, in contrast to larger particles, which exhibit the opposite behavior. Figures 3-5 verify the correctness of the numerical simulation calculation method of wind-sand two-phase flow based on particle modeling of the SPH method. The concentration distribution of single-grain size sand particles is shown in Figure 6. At Step = 100, the sand is in the just-started phase, and the sand concentration hardly changes. At Step = 25,000, the wind-sand flow reaches a stabilization stage where the peak of sand concentration is concentrated before the windward slope of the embankment, but some sand particles still fall on the embankment surface.