# Failure Behavior Attributed to Internal Erosion Caused by Conduit Cracks in Homogeneous Embarment
## 3 Results and Discussion
### Finite Element Analysis
#### 3.3.1 PWP via Finite Element Analysis  
The analysis results provide useful information in that it is possible to properly identify the PWP variations due to the presence of conduit cracks inside the embankment. Figure 7 shows a two-dimensional cross-section obtained by extracting the point where the conduit was located (63 cm from the \(y\)-axis) in the three-dimensional cross-section. The evaluation location of the PWP was the fill zone (red circle: dashed line) below and above the conduit on the downstream slope side.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & \(\mathbf{\theta_{s}}\) & \(\mathbf{\theta_{r}}\) & \(\mathbf{\alpha}\) & \(\mathbf{n}\) & \(\mathbf{m(1-1/n)}\) \\ \hline Embankment & 0.46 & 0.034 & 1.6 & 1.37 & 0.270 \\ \hline \(\theta_{r}\) = Residual water content; \(\theta_{s}\) = saturated water content; \(\mathbf{\alpha}\), \(\mathbf{n}\), and \(\mathbf{m}\) = curve fitting parameters. & & & \\ \end{tabular}
\end{table}
Table 4: Parameters of the soil–water characteristic curve used in the analysis.  
Figure 6: Variations in pore-water pressure: (**a**) below the conduit (P1, P3, and P5) and (**b**) above the conduit (P2, P4, and P6).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & \(\mathbf{\
u}\) & \(\mathbf{e_{0}}\) & \(\mathbf{c}\) (\(\mathbf{k}\)Pa) & \(\mathbf{\emptyset}\) & \(\mathbf{k}\) (\(\mathbf{m/s}\)) \\ \hline Embankment & 0.35 & 0.48 & 16.7 & 24 & 2.32 \(\times\) 10\({}^{-6}\) \\ \hline \(v\) = Poisson’s ratio; \(\epsilon\) = initial void ratio; \(\epsilon\) = cohesion; \(\mathbf{\omega}\) = internal friction angle; \(k\) = coefficient of permeability. & & \\ \end{tabular}
\end{table}
Table 3: Parameters used in the analysis.  
Figure 8 shows the PWP distributions for variations in the PWP at (a) t = 30, (b) 120, (c) 155, and (d) 180 min. While the water level increased (\(t\) = 30 min), the PWP increased only slightly at the crack surface at the bottom of the conduit. The PWP above the conduit did not show any change and, thus, was considered an early stage of infiltration.  
While an HWL was maintained (\(t\) = 120 min), an increase in PWP was observed above the conduit through the crack hole; thus, it is considered that the seepage water had sufficiently reached the upper part of the conduit. The PWP distributions at 155 and 180 min were almost similar. The PWP above the conduit expanded along the conduit boundary, while the PWP at the downstream slope also increased.  
Figure 9 shows the PWP change calculated from the analysis. Above and below the conduit, the PWP change was more simplified than the experimental results. These results depend on whether they reflect the continuity of soil erosion and loss in the experiments  
Figure 8: Variations in the PWP at (**a**) \(t\) = 30; (**b**) 120; (**c**) 155; (**d**) 180 min (unit: kPa).  
Figure 7: Evaluation location of the PWP.  
and analysis. In the experiment, soil erosion or loss occurred on the crack surface of the conduit, gradually expanding to the weak spot. In contrast, the analysis represented only the movement and increase in hydraulic pressure at the crack surface of the conduit. Here, the soil parameters were the same regardless of the location of the analysis section; thus, PWP change was considered more stable than the experiment.  
The main difference between the experiment and analysis was the PWP variations of P3 and P4 measured at the center of the embankment. In the experiment, P3 and P4 showed PWP changes close to P1 and P2, which were installed on the upstream side, indicating that erosion occurred at the center of the embankment. In the analysis, there was ambiguity in the judgment of erosion. Therefore, the experimental results were empirical, and it may be appropriate to use the analysis results as basic data for experiments to estimate various phenomena caused by conduit cracks.