# Analysis of Failure Mode of Reinforced Embarments Overlying Voids Based on Discrete Method
## 3 Results
### Analysis of Displacement Field  
In order to analyze the effect of H/B on embankment soil displacement, three representative regions, 1, 2 and 3, were intercepted in the embankment. Region 1 and 3 are at the lower soil of the reinforced body, region 3 is further away from the loading plate compared to region 1, and region 2 is at the upper part of the reinforced body further away from the loading plate. Figure 8 shows a diagram of the relative positions of the regions (the solid red line represents the reinforced body).  
Figure 9 shows the displacement vector diagram of the soil inside each region of the embankment at different H/B. From the diagram, it can be obtained that when H = B (Figure 9a), the soil displacements in regions 1 and 3 are generally in a downward direction. The left part of region 2 is in a disorderly state, and other parts of region 2 is moving downward as a whole because of gravity. When H = 2B (Figure 9b), soil displacements are generally to the right in region 1 and generally downward in region 3. When H = 3B (Figure 9c), soil displacements are generally to the right in regions 1 and 3. As H/B increases, the soil in regions 1 and 3 is transformed from an overall downward vertical displacement to a horizontal displacement to the right. This is because  
Figure 8: Schematic diagram of the relative positions of the regions.  
Figure 7: Load–settlement curves for different void locations: (**a**) at different H/B; (**b**) at different L/B.  
the soils in regions 1 and 3 are subjected to more loads transferred from the embankment surface. The transferred loads cause a tendency for the displacements to move horizontally to the right. Comparing the soil displacement of region 2 at different H/B, it can be found that when H/B is transformed from 1 to 2, there is a significant increase in the width of the local slip surface in the upper part of the reinforced body, and when H/B is transformed from 2 to 3, the increase in the width of the slip surface is not significant at this time.  
In order to analyze the effect of L/B on embankment soil displacement, the four regions, 5, 6, 7 and 8, were intercepted in the embankment. The depth of the four regions was the same, and the top of the region was equal to the road base surface. The distance between the center of each region and the center of the loading plate was B, 2B, 3B and 4B, respectively. Figure 10 shows a schematic diagram of the relative positions of the regions (the solid red line represents the reinforced body).  
Figure 11 shows the soil displacement vectors in each region of the embankment at different L/B. When L/B is 1, 2, 3 and 4, respectively, the void is located directly below regions 5, 6, 7 and 8. When comparing the different L/B conditions, it can be found that the width of the soil region dominated by horizontal displacements in the upper part of the void gradually increases as L increases. When L/B < 4, the soil on the upper left side of the void is displaced horizontally to the right, while the soil on the upper part of the void and  
Figure 10: Schematic diagram of the relative positions of the regions.  
Figure 9: Soil displacement vector diagram of embankment at different H/B: (**a**) H = B, L = 0; (**b**) H = 2B, L = 0; (**c**) H = 3B, L = 0.  
the upper right side of the void is moved downward. This is due to the fact that the load transmitted from the embankment surface acts on the upper left area of the void, which is much greater than the self-weight of the soil, which causes the soil to have a tendency to move horizontally to the right. When L changes, the soil displacement in region 8 is always predominantly downward, which indicates that the change in L has less of an impact on the soil in region 8.