## 3 Results and Discussion
### Infiltration and Infiltration Rate  
Previously, [PERSON] and [PERSON] made the following assumptions: the suction hydraulic head where wetting front has not reached is a constant, and the moisture content and permeability of the part where the wetting front has passed also remains unchanged [38]. Then, the total infiltration displacement per unit cross-sectional area \(q\) at a certain time can be calculated as follows:  
\[q=(\theta_{i}-\theta_{0})z \tag{1}\]  
where \(\theta_{i}\) is the moisture content of the part where the wetting front has passed; \(\theta_{0}\) is the moisture content of the part where the wetting front has not reached; and \(z\) is the length of the wetting front. Cumulative infiltration is the total amount of rainfall infiltrating into the ground:  
\[Q=A(\theta_{i}-\theta_{0})z \tag{2}\]  
If the soil moisture content behind the wetting front is not constant but varies continuously with increasing depth, then the increase in moisture content needs to be integrated along depth. The instantaneous infiltration rate is equal to the infiltration rate at the water boundary, which can be expressed by [PERSON]'s law as:  
\[i=\frac{1}{A}\frac{dQ}{dt}=(\theta_{i}-\theta_{0})\frac{dz}{dt} \tag{3}\]  
In Equation (3), \(i\) is the infiltration rate, cm/s; \(\theta_{i}-\theta_{0}\) is the difference in the moisture content between hydraulic heads 0 and \(i\); \(z\) is the length of the wetting front; and \(A\) is the cross-sectional area of the soil sample, where \(A=176.7146\) cm\({}^{2}\). Previously, various infiltration models have been established; the most typical ones are the [PERSON] model, the [PERSON] model and the Philip model [39; 40; 41], whose formulas are as follows:  
\[I(t)=at^{-n} \tag{4}\]  
where \(I(t)\) is the infiltration rate, mm/min; \(t\) is the infiltration time, min; and \(a\) and \(n\) are model parameters. [PERSON] model:  
\[I(t)=I_{f}+\Big{(}I_{i}-I_{f}\Big{)}e^{-ct} \tag{5}\]  
where \(I(t)\) is the infiltration rate, \(t\) is the infiltration time, \(I_{i}\) is the initial infiltration rate, \(I_{f}\) is the stable infiltration rate, and \(c\) is the model parameter. [PERSON] model:  
\[I(t)=I_{f}+\mathrm{b}t^{-0.5} \tag{6}\]  
where \(I(t)\) is the infiltration rate, \(t\) is the infiltration time, \(I_{f}\) is the stable infiltration rate, and \(b\) is the model parameter. In this section, the above models were used to fit the measured infiltration data to describe the soil column infiltration curve. Figure 8 shows the variation curves of moisture content versus time for the C1 soil column, C2 soil column and C3 soil column, and the cumulative infiltration of the soil column can be obtained by integrating over the vertical cross-section (Figure 9). The variation curve of the soil moisture content increment was divided into several straight line segments, and the curve integral was converted to calculate the area of geometric shapes to obtain the cumulative infiltration in each time period. The cumulative infiltration-time curve of the soil column obeyed a power function, which was similar to the displacement pattern of the wetting front. Figure 10 shows the instantaneous infiltration rate of the soil column, and the fitting parameters are listed in Table 5. The infiltration rate decreases sharply during the infiltration process and then is gradually stabilized, which is consistent with traditional infiltration theory. Due to differences in the initial structure or pore structure, the infiltration and infiltration rate of the C1 soil column are always greater than those of the C2 soil column. The C2 soil column and the C3 soil column have basically the same infiltration rate and infiltration at the initial stage, and both are influenced by rainfall intensity. As the rainfall infiltration progresses and ponding water appears on the soil column, the difference between the two gradually became evident, and both enter the pressure infiltration stage. Figure 8: Moisture content increment in the soil column section. Figure 9: Cumulative infiltration of the soil column.