## 3 Validation of the Coupling Model
### Calculation Results and Analysis  
#### 4.4.1 The Variation of the Volume Fractions of Fine Particles  
Figure 10 shows the evolution curves of the volume fractions of fine particles in saturated zone of railway subgrade. We can see from Figure 10 that:  
1. With the increase of time, the volume fractions of fine particles at the observation points 1 to 3 first increased and then decreased: at initial moment, the volume fraction of fine particles was 0.01; when time is between 1100 min and 1400 min, the volume fraction of fine particles at different observation points in the subgrade reaches the maximum. Subsequently, the volume fractions of fine particles decreases gradually to about 0.01. This indicates that the fine particles are eroded by the fluid and migrated with the fluid, which leads to the increase of the volume fractions of fine particles in the subgrade. As time goes by, fine particles are continuously eroded and flow out, leaving skeleton particles and larger particles in the subgrade which are difficult to migrate. Therefore, the volume fractions of fine particles decrease gradually.
2. For observation points 1 to 3, the volume fraction of fine particles at observation point 3 first reaches the maximum value, and then the volume fraction of fine particles at observation point 2 and 1 successively reaches the maximum value. The maximum volume fraction of the fine particles observed at point 1 is greater than that observed at point 2, the maximum volume fraction of the fine particles observed at point 2 is greater than that observed at point 3. The reasons are as follows: the seepage path of the fluid in the subgrade is from bottom to top, and the fluid erodes  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Initial porosity \(\phi_{0}\) & 0.33 \\ Maximum porosity \(\phi_{\text{max}}\) & 0.50 \\ Initial volume fraction of fine particles \(C_{0}\) & 0.01/0.03/0.07 \\ Critical volume fraction of fine particles \(C_{\sigma}\) & 0.30 \\ Initial permeability \(k_{0}\)/(m\({}^{2}\)) & \(7.80\times 10^{-12}\) \\ The dynamic viscosity coefficient of the fluid \(\mu_{l}\)/(Pa-s) & \(1.0\times 10^{-3}\) \\ The density of fluid \(\rho_{l}\)/(kg/m\({}^{3}\)) & 1000 \\ The density of fine particles \(\rho_{l}\)/(kg/m\({}^{3}\)) & 2380 \\ The erosion coefficient of fine particles \(\zeta\)/(m\({}^{-1}\)) & 1.0 \\ Fluid pressure \(p_{l\_{-inf}}\)/(kPa) & 40.0 \\ Elastic model \(E\)/(MPa) & 120 \\ Poisson’s ratio \(\
u\) & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Physical parameters for numerical calculation of subgrade model.  
fine particles, then carries fine particles from the lower part of the subgrade to the upper part of the subgrade. Therefore, the volume fraction of fine particles at the observation point 3 first reaches its maximum value. However, the fluid continuously erodes fine particles and the eroded fine particles migrate to the upper part of the subgrade and flow out of the subgrade from the upper boundary. Therefore, the maximum volume fraction of fine particles at observation point 1 is larger than that at other observation points.
3. As the observation point 4 is located at the lower boundary, it is the inflow boundary of fine particles, so the volume fraction of fine particles at the observation point 4 does not change.