## 4 Laboratory SSCB Model Test under the Lateral No-Flow Condition
### Infiltration Behavior in the SSCB Model Test
#### 4.4.4 Measurement Results of the Diversion Lengths in the SSCB Model Test  
Figure 8a shows a sample situation in which a breakthrough occurred under the lateral no-flow condition. Here, the area comprised between A and B corresponds to the size of the model used for the laboratory model test. The breakthrough point was not easy to identify, because water infiltration from the interface between the sand and the gravel layers did not occur regularly over time. In addition, to determine the pattern of rainfall infiltration according to the sensor responses, we defined two types of diversion lengths in the SSCB model test (Figure 8a). One of them is the distance, LUDI (i.e., the untrained diversion length), which was measured at the position of breakthrough occurrence from base-line 2 (at the interface between the sand and gravel layers). After the completion of the model test (at \(t\) = 360 min) (Figure 7e), the LUDI values for each case were determined based on the infiltration of water from the front and back sides of the model under steady conditions. The LUDI for Case 1, Case 2, and Case 3 were 13.5 cm, 11.7 cm, and 0 cm, respectively. Notably, the horizontal length of LUDI was calculated by considering the 10\({}^{\circ}\) slope angle. The other type of diversion length considered here was the distance from baseline 2 to the occurrence point of the finger flow (LUDI) at the height of the soil moisture sensors (No. 3 and No. 4) installed in the gravel layer. After the completion of the model test, the sand and gravel layers were carefully dismantled up to the location of sensors installed in the gravel layer; then, the lengths of D1 and D2 were measured as shown in Figure 8b. Here, the lengths of D1 and D2 correspond to the dry and wet areas, respectively. The D1 values obtained for Case 1, Case 2, and Case 3 were 25.2 cm, 11.3 cm, and 0 cm, respectively (Figure 9). Notably, although some dry areas were detected at 7.8 cm in Case 3 (Figure 9c), the correspondent D1 value was determined as 0, since the left side of the soil tank was partially wet. The LUD2 values were calculated using the following formula: \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**I (mm/h)**} & **Time to Reach the Saturation** & **Time of Breakthrough** \\  & & **State of the Sand Layer** & **Occurrence** \\ \hline Case 1 & 20 & 180 min & 210 min \\ Case 2 & 50 & 85 min & 85 min \\ Case 3 & 100 & 45 min & 45 min \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Measurement results for each case. \(\text{L}_{\text{UD2}}=\text{D}_{1}\cdot\text{cos}\Phi\), where \(\Phi\) is the slope angle and those for Case 1, Case 2, and Case 3 were 24.8 cm, 11.2 cm, and 0 cm, respectively. The \(\text{L}_{\text{UD1}}\) and \(\text{L}_{\text{UD2}}\) values are all shown in Table 5.  
By comparing these results, we found that the larger the rainfall intensity, the larger the diversion length values were under the lateral no-flow condition. Notably, the highest diversion length values were found for Case 1, under I = 20 mm/h. In Case 2, under I = 50 mm/h, the \(\text{L}_{\text{UD1}}\) and \(\text{L}_{\text{UD2}}\) values were 13.3% and 54.8% lower than in Case 1. In Case 3, under extremely high rainfall intensity (I = 100 mm/h), our CB system collapsed. Since rainfall intensity has the greatest influence on the diversion lengths of the CB system,  
Figure 8: Definition of each length in the SSCB model test under the lateral no-flow condition: (a) definition of the diversion lengths (\(\text{L}_{\text{D}}\), and \(\text{L}_{\text{ED1}}\) and \(\text{L}_{\text{ED2}}\)); (b) definition of \(\text{D}_{1}\) and \(\text{D}_{2}\). Figure 9: Measurement results of D1 for each case: (a) Case 1; (b) Case 2; (c) Case 3.