## 4 Results and Discussion
### Numerical Study on the Performance of Three-Layer Covers with Capillary Barrier
#### 4.4.2 Comparison of the Diversion Length, Lateral Drainage, and Percolation of the Covers  
This section focuses on the diversion length, lateral drainage, and percolation within the three-layer cover with a capillary barrier. A model, 15 m in length, was employed to observe its lateral diversion capabilities. Layer thicknesses remained consistent in the experimental setup. The model's total height is 70 cm along the long edge and 30 cm along the short edge, introducing a 3% slope to the capillary barrier. This slope adjustment allows for natural gravitational water movement. The analyses utilized previously validated relationships. The lateral diversion length was computed using [PERSON] et al. 's [51] proposed method. Breakthrough points, identified where pore pressure dropped below the  
Figure 12: Volumetric water content variation with depth and time obtained from back analysis, (**a**) fine sand, (**b**) medium sand, (**c**) coarse sand, and (**d**) fine gravel. water entry value of the coarser layer at each time interval, determined the lateral diversion length in the model (see Figure 13). The model's boundary conditions closely resemble those used in the 1D experiments, with one notable difference: a review boundary condition was applied to the granular layer at the bottom edge. This condition aligns with the approach outlined in [PERSON] et al. 's study [33] (Figure 13). In the 1D tests, most rainfall primarily resulted in surface runoff. The numerical calculations adopted relatively low infiltration rates of 1 mm/day, 3.5 mm/day, and 8.6 mm/day. The numerical models account for changes in diversion length over time, alterations in the lateral flow of drained water within the granular layer over time, and the progression of percolation. A notable distinction emerged in the analysis of four sections under varying rainfall conditions (Figure 12). Unlike the one-dimensional experiments, numerical analyses revealed that fine gravel, coarse sand, and medium sand showed remarkably similar behavior over time. In one-dimensional scenarios, water retention at the interface without horizontal drainage eventually led to barrier failure. However, water mobility along the interface prolonged the barrier effect in two-dimensional configurations and inclined barriers. Lateral diversion predominantly occurs at the fine/coarse interface, where hydraulic conductivity tends to be highest [10]. The numerical analysis results concerning lateral diversion are attributed to the high permeability of the gravel material and coarse sand, which facilitates faster water movement at the interface and increases the barrier effect. Conversely, fine sand has a reduced performance due to its high water entry value and low permeability. Moreover, increased rainfall reduced diversion lengths in each section, as noted by [51], subsequently minimizing discrepancies between the sections. During the 8.6 mm/day infiltration, the increased infiltration rate may exceed the lateral drainage capacity. At this point, the impact of the hydraulic conductivity of the middle layer on the diversion becomes less apparent (Figure 14). Figure 13: Schematic view of the [PERSON] method (2009) [51]. The influence of the middle layer on lateral drainage was investigated during a relatively high rainfall event with an intensity of 8.6 mm/day (Figure 15). As expected, fine gravel showed the most effective lateral drainage performance, resulting in the highest lateral flow. Conversely, fine sand showed the poorest performance, with minimal lateral drainage due to its low permeability. For all soil types, lateral drainage started almost immediately after the capillary barrier effect completely disappeared, reached a maximum value, and remained stable. Comparisons of percolation in multi-layer covers at an infiltration rate of 3.5 mm/day were conducted to evaluate the influence of the middle layer (Figure 16). Additionally, numerical analysis assessed percolation within the clayey sand section (without any granular layer).