## 4 Discussion
### D Flow and Multi-Layer Slope Stability  
As is shown in Figure 17a, the blue color was used to stain the surface of the slope and to show the movement of rainfall water, and it was applied under the coarse layer to check that the capillary barrier still worked. At the beginning of case III, the water flow showed a vertical movement, mainly controlled by gravity, before the wetting front arrived at the interface. Secondly, the water flow could not go across the interface directly upward of the slope and showed a significant velocity component parallel to the inclined interface after the wetting front arrived [28]. Lateral diversion is essentially gravity-driven unsaturated drainage within the finer layer of a sloped capillary barrier [29; 30]. The unsaturated hydraulic conductivity is the maximum as the VWC of the upper finer soil increases with depth, where lateral diversion is concentrated at the fine-coarse interface. Besides, the diverting water will increase the water content in the downslope direction with the influence of the inclined angle, which may result in failure of the barrier and then infiltrate into the next layer. Figure 16: (**a**) Capillary barrier at the interface between different layers with different conductivities. (**b**) The relationship between the hydraulic conductivity and suction of silica No 1 and No 7. Figure 17: (**a**) Side view of the diversion length and breakthrough area of the capillary barrier (the movement and the breakthrough zone are shown by the blue dye traces); (**b**) calculation of the capillary diversion length \(L\). In Figure 17b, the maximum length of the capillary diversion can be calculated by [31]:  
\[K(\psi)=\frac{\left[1-(\alpha\psi)^{\text{mm}}\left[1+(\alpha\psi)^{\text{n}} \right]^{-\text{m}}\right]^{2}}{\left[1+(\alpha\psi)^{\text{m}}\right]^{\text{ m/2}}}*K_{s}\enspace, \tag{2}\]  
\[L\leq\tan(\beta)\frac{K(\psi)}{q}\left[\frac{1}{\alpha}+\left(\left|\psi_{a} \right|-\left|\psi_{w}^{*}\right|\right)\right] \tag{3}\]  
where, \(\psi\) is the matric suction in the soil; \(\psi_{w}^{*}\) is the water entry value of the coarse layer; \(\psi_{a}\) is the air entry value of the fine layer; \(\beta\) is the tilt angle of the slope (\({}^{\circ}\)); \(r\) is the infiltration rate (mm/h); \(K(\psi)\) is the hydraulic conductivity of the fine layer; and \(a\), \(m\), and \(n\) are the fitting parameters. Physical model experiments with a tilt angle \(\alpha=0^{\circ},7^{\circ},15^{\circ},\) and \(21^{\circ}\) were performed three times in order to ensure the repeatability of the results. An important point to be noted is that every physical model was assumed to be identical, but there were slight differences in the model construction and preparation process, which could have resulted in some dissimilarity between experiments. Taking this fact into account, the result of the capillary diversion length at different tilt angles (Figure 18a), which produced similar results, demonstrated the repeatability of the experiment. The pictures of failure situations in case III (tilt angle \(\alpha=7^{\circ}\)) are described in detail in Figure 18b. Although the details of soil piping of each experiment were unique, the results of different experiments were consistent. The capillary barrier effects caused by the inter-mediate coarser layer initially confines the rainwater infiltration in the uppermost soil. Depending on the characteristics of rainfall and the inclined angle condition, top finer soils are almost permanently unsaturated [32]. In some slope steeper than \(40^{\circ}\) at higher elevations, this may lead to instability of the top fine soil before capillary barrier breakthrough, when the coarse layer and bottom layer are still far from the point of saturation [33]. Depending on the slope angle and shear strength of soil, failure can occur at the bottom before complete saturation, while the pore water pressure is still negative. These phenomenon in natural slope seem to disprove the possibility of failure mechanism due to piping in this study.