# Similarity Model Test on Rainfall Scouring Mechanism of High-Speed Railway Subgrade Slope
## 3 Test Results and Discussions
### Equation Verification and Analysis of Incipient Flow Velocity  
For the initiation of slope erosion under various working conditions, the physical parameters of each group of slopes in the theoretical formula of incipient flow velocity, Equation (1) [29], include dry weight \(\gamma_{s}\), water weight \(\gamma_{w}\), slope gradient \(\theta\), hydraulic radius \(R\), cohesion \(C\), internal friction angle \(\varphi\), the frictional flow velocity \(f\) (\(U_{R}\cdot D/v\)), hydraulic slope \(J_{s}\), correction value \(\chi\), and roughness size \(k_{s}\), as shown in Table 8.  
\[U=5.75\sqrt{\frac{\left[(\gamma_{s}-\gamma_{w}+\gamma_{w}J_{s})(\tan\varphi \cos\theta-\sin\theta)+\frac{6C}{\pi D^{3}}\right]f(\frac{U_{R}D}{D})gD}{\gamma _{w}}}\log\left(12.27\frac{\chi R}{k_{s}}\right)} \tag{1}\]  
\begin{table}
\begin{tabular}{c c c} \hline
**Particle Size (mm)** & **Incipient Flow Velocity (cm/s)** & **Erosion Quantity (g)** \\ \hline
0.075–1 (R1) & 6.75 & 11.1 \\
1–2.5 (R2) & 10.59 & 3.8 \\
2.5–5 (R3) & 15.6 & 2.1 \\ \hline \end{tabular}
\end{table}
Table 7: Erosion and collecting condition of G5.  
Figure 15: Soil particle starting time and distribution of ponding depth.  
Substituting the data from Table 8 into theoretical Equation (1). Compared with the equation result (ER) and the model test result (TR), as shown in Figure 16, for particles with the same particle size, the increase in rainfall intensity, and the increase in slope gradient or decrease in soil cohesion could reduce the incipient flow velocity. Due to the contingency of the test results, the error was inevitable. Most of the TR is larger than the ER, that is, Equation (1) can play an early warning role in slope anti-scouring stability with safety. The single-factor analysis is discussed as follows:  
(1) Rainfall intensity impact on the incipient flow velocity  
The corresponding rainfall intensities of G1, G2 and G3 were 0.5 mm/min, 1.0 mm/min and 1.5 mm/min, respectively, with a scouring time for 40 min on the slope of 1:1.5. The incipient flow velocities of the three groups within the same particle size range were relatively close. Nevertheless, when the rainfall intensity increased, the slope surface saturated faster, resulting in a decrease in maintaining ponding depth. The reduction in ponding depth decreased the hydraulic radius, which reduced the incipient flow velocity of the same particle size.  
(2) Slope gradient impact on the incipient flow velocity  
The slope gradients of G2 and G5 were 1:0.5 and 1:1.25, with a scouring time of 40 min under a rainfall intensity of 1.0 mm/min. Comparing the ER of G2 and G5 with the TR, in G5, the larger the slope gradient was, the larger the maximum allowable incipient particle size, and the smaller the incipient flow velocity, that is, the easier the scouring erosion on the slope occurred.  
(3) Grading curve impact on the incipient flow velocity  
The grading curves of G2 and G4 were S1 and S2, as shown in Figure 2, with a scouring time of 40 min under a rainfall intensity of 1.0 mm/min on the slope of 1:1.5. The internal friction angles of G4 and G2 are the same, but the cohesion decreases by 32.1%. The decrease in shear strength made the water flow scour and transport R4 on the G4 slope with greater ease. Therefore, the exit of R1 improved the anti-scour ability of the coarse-grained soil slope.  
Figure 16: Comparison for the incipient flow velocity between theoretical formula and test results.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Groups**} & \(\gamma_{s}\) & \(\gamma_{tw}\) & \(\theta\) & \(R\) & \(C\) & \(\varphi\) & \(f(U_{s}D/v)\) & \(J_{s