## 2 Materials and Methods  
### Basic Material Properties  
Silica sands S1 and S7 were chosen for the physical model experiments as the fine material and coarse material, respectively, by the difference of D\({}_{50}\) and size distribution. Figure 2 shows the size distribution of S1 (fine material) and S7(coarse material) used in model experiment. Table 1 summarizes the specific properties of S1 and S7 used in the model experiments. The sieve tests were conducted using the JGS Geotechnical Society standard test methods (JGS0131-2009). \begin{table}
\begin{tabular}{c c c} \hline
**Description** & **Silica No 7** & **Silica No 1** \\ \hline Specific gravity Gs & 2.63 & 2.62 \\ Gravel content (\(>\)4.75 mm; \%) & 0 & 97.13 \\ Sand content (\%) & 87.31 & 2.86 \\ Fines content (\(<\)0.075 mm; \%) & 11.64 & 0 \\ D\({}_{10}\) (mm) & 0.043 & 2.26 \\ D\({}_{50}\) (mm) & 0.152 & 3.52 \\ D\({}_{60}\) (mm) & 0.165 & 4.21 \\ Maximum dry density (g/cm\({}^{3}\)) & 1.556 & 1.52 \\ Minimum dry density (g/cm\({}^{3}\)) & 1.271 & 1.3 \\ \hline \end{tabular}
\end{table} 
Table 1: Basic properties of sand materials. Figure 2: Grain size distribution of S1 and S7 in physical model experiments. The unsaturated hydraulic properties were measured by the variable head method (ASTM 2006) D2434-68. Table 2 and Figure 3a show the fitting parameters of the VG (van Genuchten-Mualem) model [21] and soil-water characteristic curves of silica No 1 and 7 in both the drying process and wetting process. The unsaturated hydraulic conductivities of sands were obtained by a pressure plate apparatus in the lab. As shown in Figure 3a, the drying (desorption) process and the wetting (absorption) process of the SWCCs of sand cause hysteretic behavior [15] for the same suction value, and the sand can retain more water in the drying process than in the wetting process. In the wetting process, the air entry value (AEV) of the fine layer (silica No 7) is about 1.5 kPa. The AEV of sand and gravel is about 0.45 kPa, being lower than the AEV of the fine layer. The capillary barrier effect occurs at the fine-coarse sand interface during rainfall infiltration. In Figure 3b, the unsaturated hydraulic conductivities of two types of sand are reported. The obtained values range between \(10^{-2}\) and \(10^{-7}\) cm/s under different suction conditions. The results show that the hydraulic conductivity of the coarse sand is higher than that of the fine sand at almost saturation, while it is significantly lower when the soil is unsaturated. The soil-water characteristic curves of the soil were modeled with the van Genuchten-Mualem model [5], as follows:  
\[S_{e}=[1+(-\alpha h)^{n}]^{-m}S_{e}\ =\ \frac{\theta-\theta_{r}}{\theta_{s}- \theta_{r}}m=1-\frac{1}{n}. \tag{1}\]  
In the above equation, the water retention curve is expressed in terms of the effective degree of saturation. \(\theta\) is the volumetric water content; \(\theta_{r}\) and \(\theta_{s}\) indicate the residual and saturated values of the water content, respectively; \(a\), \(m\), and \(n\) are the fitting parameters; \(h\) is the matric suction; \(a\) is a scaling parameter (units of m\({}^{-1}\)); and the exponents n and m are parameters that determine the shape of the retention curve. The hydraulic parameters are given in Table 2.