## 3 Results and Discussion
### Effects of Gravel and Solidified Soil Embankment Materials  
Figure 4 shows significant differences in the total settlements between gravel embankments and solidified soil embankments. Case A and Case B represented gravel embankments under static and dynamic traffic loads, respectively; and Case C and Case D represented solidified soil embankments under static and dynamic loads, respectively. The total settlements curves of Case A and B exhibited inverted '\(\gamma\)' shape, whereas the total settlement curves of Case C and D exhibited oblique inverted '\(\gamma\)' shape. The red dotted lines represented the equal settlement planes of embankments. In comparison to gravel embankments, the total settlements of solidified soil embankments decreased obviously, the differential settlements between the top of pile (point A in Figure 1) and subsoil (point C in Figure 1) reduced as well. For instance, at point C in Case A, the total settlement reached 139.0 mm, whereas in Case C, it diminished to mere 6.7 mm. This finding indicates that solidified soil could effectively reduce the total settlements of embankments over the pile and soft soil. Figure 5 shows the distribution of the vertical stresses, along with the height of embankment. The vertical stress distribution exhibited a \"Z\" shape in the gravel embankment, aligning with the theoretical findings of [PERSON] and [PERSON] [38]. Specifically, as a result of the gravitational forces exerted by the fill materials, the vertical stress initially increased until reaching its maximum value at the outer soil arch surface. Subsequently, the stress decreased to a minimum value due to the soil arching effect occurring at the inner soil  
Figure 4: The settlements along the height of embankment for different filling materials. Figure 3: 3D unit cell models validation results along with the height of embankment: (**a**) total settlements [29], (**b**) vertical stress [29]. arch surface. Finally, the stress rose again under the influence of gravity acting on the fill materials. In contrast, the solidified soil embankment displayed only an outer soil arch surface. This implies that, compared with the gravel embankment, there was a larger soil arch area in solidified soil embankments. Notably, the substantial vertical stresses were observed in the upper portion of solidified soil embankment. Subsequently, the vertical stresses decreased as the distance from the bottom of the embankment decreased under dynamic loads (Case D). The vertical stress in the upper embankments can be attributed to the additional stress transferred from the dynamic loads. Furthermore, the vertical stresses at the top of subsoil (point C) in solidified soil embankment were around 2-3 kPa, merely one-seventh of the corresponding stress observed in the gravel embankment. The soil arch heights (\(h_{\text{sa}}\)) in gravel and solidified soil embankments are equal to the height of equal settlement, and are shown in Table 5. As can be clearly seen, dynamic load resulted in a slight increase in soil arching height in gravel embankments, which was consistent with the results proposed by [PERSON] and [PERSON] [29]. Similarly, the variation in the soil arch height in the solidified soil embankments followed a similar pattern. Compared with gravel embankments, the soil arch height in solidified soil embankments was significantly reduced, regardless of whether the load was static or dynamic. Figure 6 shows the variation in the axial force along the pile depth in gravel and solidified soil embankments. Within the height range of the pile cap, due to a sudden decrease in the cross-sectional area of the pile, the axial force increased. It is worth noting that the axial force exhibited a significant increase under dynamic load, particularly in the solidified soil embankment. This observation suggests that the piles bore the majority of the overlying load in the solidified soil embankments. The distribution patterns of axial force along the pile bodies varied depending on the embankment materials.