# Analysis of Load Transfer and the Law of Deformation within a Pile-Supported Reinforced Embankment
## 4 FEM Numerical Analysis
### Deformation Behavior  
The internal displacement and stress distribution of embankment obtained from each test have a similar law. The M3 test is used as an example in the next section to examine the embankment's deformation patterns. Figure 13 reveals the distribution of vertical displacement at various filling heights. The embankment is divided into different areas according to the distribution of vertical displacement, as shown in Figure 13. From Figure 13, it is clear that the embankment's internal displacement exhibits the traits listed below:  
1. When the embankment's height is relatively low, sliding surfaces penetrate the entire embankment, causing localized differential settlement at the embankment surface, which is a significant undesirable settlement for the building of roads and railroads. The area with a substantial settlement inside the embankment is outlined by a triangle, and the areas surrounding the triangle are two non-overlapping inverted triangles.
2. Two inverted triangular areas begin to overlap with the increase of embankment-filling height. The different settlement on the embankment surface is lessened when the soil-arching effect develops gradually.
3. With the increase in filling height, planes with the same settlement appear in the embankment. The embankment height is now adequate for the development of the whole soil arching. It also demonstrates that the soil-arching effect can inhibit the uneven settlement of the embankment surface.  
The embankment is divided into three zones, which respectively represent the central sliding zone (\(a_{1}\)), secondary sliding zone (\(a_{2}\)), and stable zone (\(a_{3}\)) under the condition of small \(h\), as shown in Figure 14a. Relatively large vertical displacements occur in the zone of \(a_{1}\) and \(a_{2}\), and the soil in the \(a_{1}\) starts to slide earlier than that in the \(a_{2}\). The lateral constraint of the secondary sliding area is weakened due to the movement of the particles in the \(a_{1}\). And the sliding friction at the contact surfaces between \(a_{1}\) and \(a_{2}\) is overcome by the particles in \(a_{2}\). Then the particles begin to move. Due to the occlusion and embedding action between particles, the differential settlement in the embankment gradually weakens when filling height is increased.  
Figure 13: Vertical displacement distribution inside of embankment, (**a**) h = 50 mm; (**b**) h = 150 mm; (**c**) h = 250 mm.  
The soil arching has fully formed when the embankment height is significant, as seen in Figure 14b. The embankment is separated into five zones based on vertical settlement: the sliding zone (\(b_{1}\)), compaction zone (\(b_{2}\)), stable zone (\(b_{3}\)), transition zone (\(b_{4}\)), and equal settlement zone (\(b_{5}\)). The downward sliding tendency occurs in the zone of \(b_{1}\) and \(b_{2}\) due to the overlying load. Meanwhile, the differential settlement in embankments is caused, which decreases with the increase of the distance from the embankment bottom, by the vertical constraint of the pile caps on the embankment. Comparing Figure 14a,b, It is evident that when the embankment height is low, the soil-arching efficiency cannot be thoroughly aroused and the differential settlement diffuses to the surface of the embankment. However, when the filling height reaches a particular level, the entire soil arching will occur in the embankment. There is a non-different settlement on the surface of the embankment due to the effective displacement control controllability of the soil arching. This further demonstrates that the soil-arching effect is crucial in regulating the uneven settlement of embankments.