# Stability Improvement Method for Embankment Dam with Respect to Conduit Cracks
## 3 Results and Discussion
### Seepage Line and Hydraulic Gradient: Numerical Analysis
#### 3.3.2 Change in Seepage Line  
The seepage line was examined based on the conditions of fluctuations in the water level after 2, 3, 10, and 24 h to provide additional evidence for the experimental results of conduit cracking.  
In Case 1--Crack (Figure 8a), the seepage line had a concave shape and was concentrated in the crack area of the conduit. This concave shape of the seepage line means that the leakage occurred in the conduit crack area and is considered a condition in which internal erosion can easily occur. Case 1--Reinforcement (Figure 8b) is a condition in which the crack area of the conduit is reinforced by the geomembrane, and the seepage line indicates a stable state, with the embankment functioning normally.  
Figure 8c,d show the improvement model, in which the sand layer and geotextile were applied to minimize internal erosion in this study. The seepage line of Case 2--Crack  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sample** & \(\mathbf{\theta_{s}}\) & \(\mathbf{\theta_{r}}\) & \(\mathbf{\alpha}\) & \(\mathbf{n}\) & \(\mathbf{m}\)(1\(-\)1/\(\mathbf{n}\)) \\ \hline Clay layer & 0.38 & 0.007 & 0.8 & 1.09 & 0.083 \\ Embankment & 0.46 & 0.034 & 1.6 & 1.37 & 0.270 \\ Sand layer & 0.43 & 0.045 & 14.5 & 2.68 & 0.627 \\ \hline \hline \end{tabular} \(\widehat{\theta_{r}}\) = residual water content, \(\theta_{s}\) = saturated water content, \(\alpha,\ n,\ m\) = curve fitting parameters.  
\end{table}
Table 4: Parameters of the soil–water characteristic curve used in the analysis.  
Figure 8: Changes in seepage line in current and improvement models: (**a**) Case 1—Crack, (**b**) Case 1—Reinforcement, (**c**) Case 2—Crack, (**d**) Case 2—Reinforcement.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sample** & \(\mathbf{\
u}\) & \(\mathbf{e_{0}}\) & \(\mathbf{c}\) & \(\mathcal{O}^{\circ}\) & \(\mathbf{k_{x}}\) \\  & & & **(kPa)** & & **(m/s)** \\ \hline Clay layer & 0.40 & 0.98 & 29.43 & 0 & \(3.70\times 10^{-9}\) \\ Embankment & 0.35 & 0.48 & 16.70 & 24 & \(2.37\times 10^{-7}\) \\ Sand layer & 0.33 & 0.50 & 0 & 33 & \(7.82\times 10^{-4}\) \\ Geotextile & 0.30 & - & - & - & \(1.00\times 10^{-3}\) \\ \hline \hline \end{tabular} \(\widehat{\
u}\) = Poisson’s rate, \(e_{0}\) = initial void ratio, \(c\) = cohesion, \(\mathcal{O}^{\circ}\) = internal friction angle, \(k_{x}\) = horizontal coefficient of permeability.  
\end{table}
Table 3: Parameters used in analysis.  
(Figure 8c) was formed at the crack site of the conduit for the initial 3 h, but the seepage line dropped to the end of the downstream slope under the water level condition at 24 h. These results show that the model not only reduces erosion due to the promotion of drainage in the sand layer above the clay layer but also provides a useful function to stably drain the seepage water inside the embankment. Case 2--Reinforcement (Figure 8d) is the condition in which the crack area of the conduit was reinforced by the geomembrane in the improvement model. Unlike Case 1--Reinforcement, the seepage line of Case 2--Reinforcement appeared to gather at the end of the downstream slope under all of the time conditions (0-24 h), which was interpreted as the condition in which the embankment is in its most stable state. The seepage lines analyzed in this study are considered to be valid data that can support the reliability of the internal erosion results in the model experiments.