## 2 Model Experiments
### Results and Discussion
#### 2.5.1 Soil Deformations  
As shown in Figure 3a, there is no significant difference in surface settlement under all conditions, but deep settlement shows obvious differences. Large constrained displacement (definition: vertical displacement under unreinforced condition subtract vertical displacement under reinforced condition) is disadvantageous to compaction. For example, the constrained displacement at a depth of 150 cm is 6.07 cm, while it is 3.64 cm at ground surface. The maximum constrained displacement on conditions of A\({}_{1}\), A\({}_{2}\), A\({}_{3}\), and A\({}_{4}\) is 17.49 cm, 7.48 cm, 4.14 cm, and 2.42 cm, respectively. The constraining effect on settlement decreases gradually with the increase of embedding depth. Figure 3b shows the  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Level**} & \multicolumn{2}{c}{**Embedded Ratio**} & \multicolumn{2}{c}{**Number of Reinforced Layers**} & \multicolumn{2}{c}{**Interval of Reinforced Layers (cm)**} \\ \cline{2-6}  & **Value** & **Code** & **Value** & **Code** & **Value** & **Code** \\ \hline
1 & 2 & A\({}_{1}\) & 2 & B\({}_{1}\) & 2 & C\({}_{1}\) \\
2 & 3 & A\({}_{2}\) & 3 & B\({}_{2}\) & 4 & C\({}_{2}\) \\
3 & 4 & A\({}_{3}\) & 4 & B\({}_{3}\) & 6 & C\({}_{3}\) \\
4 & 5 & A\({}_{4}\) & 5 & B\({}_{4}\) &vertical displacement will be substantially reduced after reinforcement. The maximum constrained displacement at depths of 0 cm, 50 cm, 100 cm, and 150 cm is 6.32 cm, 18.99 cm, 11.06 cm, and 6.42 cm, respectively. B has a significant constraining effect on vertical displacement. For instance, compared with vertical displacement in unreinforced conditions, the surface constrained displacement below tapping point is 3.64 cm, 5 cm, 5.74 cm, and 6.32 cm in the conditions of B1, B2, B3, and B4, respectively. Figure 3c shows the increasing C has a negative effect on the constraining effect. Take the vertical settlement under the tamping central point as an example: in the conditions of C1, C2, C3, and C4, the constrained displacement of the surface is 3.64 cm, 3.48 cm, 2.65 cm, and 1.83 cm, respectively. However, the vertical displacement under the dynamic compaction is reduced significantly by geogrid reinforcement. The maximum constrained displacement provided by reinforced geogrid at depth of 0 cm, 50 cm, 100 cm, and 150 cm is 3.64 cm, 17.49 cm, 10.98 cm, and 6.08 cm, respectively. Overall, the reason for small surface constrained displacement is that the reinforced geogrid is relatively shallow and the surface vertical displacement is constrained by the first reinforced layer. As shown in Figure 4a, in the A1 condition, the reinforced geogrid is located at a depth of 80 cm and the lateral displacement below the geogrid is reduced substantially, the maximum displacement is close to the depth of 25 cm. In the A2 condition, the lateral displacement below the geogrid is reduced substantially and is smaller than in the A1 condition. With increased embedded depth, the reinforced geogrid has a small constraining effect on lateral displacement; thus, A3 and A4 show the same trend with that of unreinforced condition. As shown in Figure 4b,c, B and C have constraining effects on the lateral displacement of soil. Between the surface ground and the depth of 60 cm (where  
Figure 3: The vertical displacement under three factors: (**a**) embedded ratio; (**b**) number of reinforced layers; (**c**) interval of reinforced layers. constrained displacement reaches the minimum), the constrained displacement increased with depth of soil. The farther from the tamping point, the smaller the lateral displacement. The lateral displacement of soil under the geogrid is larger than the unreinforced displacement. It decreases with the increase of reinforced depth. The reason is that in reinforced conditions, the settlement of the soil above the geogrid is restricted by the geogrid and expanded laterally under instantaneous vertical compaction. Therefore, lateral displacement of the counterpart on unreinforced condition is smaller.