## 3 Result Analysis and Verification
### Comparison under the Hypothesis of Non-Uniform Moisture Content  
In the previous section, we discussed the problem of unsaturated infiltration under uniform moisture content, while in actual engineering, the initial moisture content in soil is not uniformly distributed, but changes with depth. Therefore, the column model in Section 3.1 was used to obtain a moisture content distribution law that is close to the actual situation, where the initial saturation was set as 1, and the bottom (CD) was set as the drainage boundary, allowing it to drain freely for a sufficient time. After stabilizing, the results of the moisture content in the monitored section were extracted and substituted into Equation (12) for nonlinear fitting, as shown in Figure 9, and the fitting effect obtained is good. By inputting the results into the proposed model, the variation trend of the soil surface moisture content with time under different rainfall intensities can be obtained, as shown in Figure 10. Since the initial moisture content of shallow soil changes only slightly with  
Figure 8: Variation of wetting front depth with time. Figure 9: Variation trend of volume moisture content with depth. depth, the calculated variation trend of surface moisture content is similar to the hypothesis of the uniform moisture content. At the same time, it can be seen that the model proposed in this paper is in good agreement with the simulation results, and the maximum error is no more than 5%, as shown in Table 4.  
Figure 11a shows the variation trend of the surface moisture content with time under different hypotheses. It can be seen that the variation trend under two hypotheses is basically the same, and both increase nonlinearly with time. However, the calculated value under the non-uniform initial moisture content is larger than that under the uniform hypotheses, and the specific difference is shown in Figure 11b. Figure 11b shows the relationship between the surface moisture content and time differences under two hypotheses. It can be seen that when the rainfall intensity is small, the time difference increases more obviously, and it decreases accordingly with the increase in rainfall intensity. That is, before the critical moisture content is reached, to achieve the same surface moisture content, when the rainfall intensity is smaller, a longer amount of time is required under the uniform moisture content hypothesis compared to that under the non-uniform condition. When the rainfall intensity increases to a certain extent, the change in time difference is not obvious. The reason is that when the initial moisture content of shallow soil only slightly changes with depth, the rainfall intensity is greater, the surface moisture content increases faster, and most of the rainwater is used for the increase in the surface moisture content, which has little impact on the bottom. The variation law of the wetting front depth is shown in Figure 12 under different rainfall intensities. Figure 12a presents the results between the improved model (under uniform and non-uniform moisture content hypotheses) and the traditional model, whereas Figure 12b shows the FLAC simulation results. The analysis results between theoretical model and numerical simulation are shown in Table 5, where it can be seen that the \begin{table}
\begin{tabular}{c c} \hline \hline
**Rainfall Intensity (m/s)** & **Maximum Error (\%)** \\ \hline \(1\times 10^{-7}\) & 2.08 \\ \(5\times 10^{-7}\) & 3.84 \\ \(1\times 10^{-6}\) & 4.21 \\ \(2\times 10^{-6}\) & 3.89 \\ \(4\times 10^{-6}\) & 3.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Analysis of results for the non-uniform moisture content model. Figure 10: Variation trend of soil surface moisture content with time under the hypothesis of non-uniform moisture content. simulation is in good agreement with the improved model, but not with the traditional model, indicating the accuracy of the improved model.