## 3 Analysis of Horizontal Bearing Characteristics
### Soil Pressure Distribution Laws  
Figures 5-7 illustrate the variations in soil pressure increments at different depths when the composite foundation with a pile-bucket diameter ratio of d/D = 0.5 reaches its ultimate load under diverse relative density conditions. In instances where the soil pressure increment at a measurement point registers as negative, it indicates that the foundation is subject to active soil pressure; conversely, a positive soil pressure increment indicates passive soil pressure exerted on the foundation. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Pile-Bucket Composite Foundation** & **Relative Density** &
\begin{tabular}{c} **Horizontal Ultimate** \\ **Bearing Capacity/N** \\ \end{tabular} & **Growth Ratio/\%** \\ \hline \multirow{2}{*}{Pile-bucket diameter ratio d/D = 0.5} & loose sand & 2.41 & \(-\)51.51 \\  & medium dense sand & 4.96 & 0.00 \\  & dense sand & 6.31 & 27.22 \\ \hline \multirow{2}{*}{Pile-bucket diameter ratio d/D = 0.417} & loose sand & 3.01 & \(-\)50.41 \\  & medium dense sand & 6.07 & 0.00 \\  & dense sand & 6.82 & 12.36 \\ \hline \multirow{2}{*}{Pile-bucket diameter ratio d/D = 0.357} & loose sand & 3.60 & \(-\)41.46 \\  & medium dense sand & 6.15 & 0.00 \\  & dense sand & 7.17 & 16.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Horizontal ultimate bearing capacity. Figure 4: Load-rotation relationship curves under different compactness. (**a**) Pile-bucket diameter ratio d/D = 0.5; (**b**) Pile-bucket diameter ratio d/D = 0.417; (**c**) Pile-bucket diameter ratio d/D = 0.357. As shown in Figure 5a, the soil pressure increment at the front of the upper bucket foundation consistently maintains a positive value, indicating that this measurement point consistently resides in the passive soil pressure zone. With an incremental load, the soil pressure increment at a depth of 0 mm decreases gradually, while the soil pressure increment at a depth of 0 mm decreases gradually, while the soil pressure increment at a depth of 0 mm decreases gradually. Figure 5: Soil pressure increment distribution of loose sand pile-bucket diameter ratio of 0.5. (**a**) Front side of the foundation; (**b**) Back side of the foundation. Figure 6: Soil pressure increment distribution of a medium dense sand pile-bucket diameter ratio of 0.5. (**a**) Front side of the foundation; (**b**) Back side of the foundation. Figure 7: Soil pressure increment distribution of a dense sand pile-bucket diameter ratio of 0.5. (**a**) Front side of the foundation; (**b**) Back side of the foundation. increment at a depth of 30 mm increases. Similar trends are observed at depths of 30 mm and 115 mm for the lower pile foundation. At a depth of 200 mm, the soil pressure increment initially decreases with the applied load, subsequently exhibiting an increased trend. The behavior could be attributed to the surface sand of the composite foundation being loose in the loose sand condition, limiting its capacity to offer substantial resistance as the load intensifies. In contrast, the lower soil body, compacted by the foundation, results in a denser arrangement of soil particles, affording greater soil resistance. Notably, the soil pressure increment at a depth of 30 mm for the upper bucket foundation significantly surpasses that at the pile foundation, indicating superior resistance of the bucket foundation to horizontal loads and a greater share of the horizontal load-bearing capacity in the composite foundation. In Figure 5b, the soil pressure increments at the back of the foundation at depths of 0 mm, 30 mm, and 115 mm all exhibit negative values, indicating that these measurement points consistently fall within the active soil pressure zone. Meanwhile, the soil pressure increment at a depth of 200 mm is positive and gradually increases with increasing load. Figures 6 and 7 correspond to the states of a medium dense sand state and dense sand state, respectively, showing the variations in soil pressure increments at various measurement points.