# Stability Improvement Method for Embankment Dam with Respect to Conduit Cracks
## 3 Results and Discussion
### Seepage Line and Hydraulic Gradient: Numerical Analysis
#### 3.3.3 Change in Hydraulic Gradient  
The initial stage of internal erosion depends on the relationship between the critical hydraulic gradient and the permeability coefficient of the soil [22,23], and it is known that the risk of piping increases under conditions in which internal erosion continues [24]. The hydraulic gradient for internal erosion is approximately one-fifth to one-third of the critical hydraulic gradient for soil stability, and a change in strength occurs at a hydraulic gradient of 0.5 or higher [25]. A stability evaluation to evaluate for the risk of internal erosion, as described above, has an important meaning, and the safety factor (Fs) calculated by the ratio of the critical hydraulic gradient and the exit hydraulic gradient is mainly used [26].  
In this study, the critical hydraulic gradient (I\({}_{\text{cr}}\)) of the model embankment was 0.99. The relationship between the critical hydraulic gradient and a standard safety factor (Fs) value of 2.0 can ensure safety only when the calculated exit hydraulic gradient (I\({}_{\text{exit}}\)) is less than approximately 0.5. In this study, based on the current model and the improvement model, the tendency of the hydraulic gradient was evaluated, and the hydraulic gradient for the reduction in internal erosion was analyzed numerically. Figure 9 shows the evaluation position of the exit hydraulic gradient at the boundary between the clay layer and the embankment layer on the downstream slope. Figure 10a,b show the comparison results of the hydraulic gradient over a period of time in the current model and the improvement model.  
As shown in Figure 10a, Case 1--Crack (current model) had a hydraulic gradient in the range of 3.6-4.0 between the clay layer and the embankment zone and exceeded the safety conditions for the internal erosion suggested in this study. In the current model, if a crack occurs in a conduit, erosion may be inevitable regardless of fluctuations in the water level, and it was determined that the possibility of it developing into a piping phenomenon is high. Case 2--Crack (improvement model) had a hydraulic gradient of 0.42-0.44 and satisfied the safety conditions for internal erosion. Despite the small scale of the cross-section of the drainage layer in Case 2--Crack, the hydraulic gradient was  
Figure 9: Location of hydraulic-gradient evaluation.  
reduced compared to Case 1--Crack; thus, the improvement model was confirmed to be effective for increasing the resistance to internal erosion.  
In Figure 10b, Case 1--Reinforcement (the current model) was a condition in which the embankment zone and conduit functioned normally without structural faults; thus, the hydraulic gradient was small. The hydraulic gradient showed a tendency to increase gradually but satisfied the safety condition for internal erosion. In Case 2--Reinforcement (improvement model), the hydraulic gradient tended to be partially irregular, but there was no increase. These results are considered to indicate stability against internal erosion.  
The hydraulic gradient results presented in this study are summarized as follows. As the hydraulic gradient calculated in the analysis has a wide range depending on the soil-water characteristics, physical properties of soil, and shape of the structure, the occurrence of piping cannot be guaranteed, even if the hydraulic gradient increases. However, because it can be an important indicator of anomalies that may cause the embankment to be unstable, the analytical approach has some rationality. In the improvement model, the sand layer suppresses the hydraulic gradient concentrated in the conduit crack area. Therefore, if the width and height of the sand layer are appropriately considered in the crack area of the conduit, internal erosion can be delayed. In addition, in terms of disaster reduction, it is expected that the risk of embankment failure due to piping can be reduced.