## 5 Analysis of Deformation Characteristics of Soil around the Foundation  
Analysis of the Deformation Mechanism of Soil around Pile-Bucket Composite Foundation under Different Compactness  
To understand the deformation mechanism of the surrounding soil under different relative density levels, the displacement field of the composite foundation under horizontal monotonic loading was analyzed using the PIV (particle image velocimetry) technique. Figure 14 shows the displacement vector map corresponding to the pile-bucket composite foundation with a pile-bucket diameter ratio of 0.5 under ultimate load conditions in loose sand and dense sand states. Figure 13: The relationship of ultimate bearing capacity with the pile-bucket diameter ratio. By comparing the displacement fields under the two relative density states, it is evident that the influence depth of the surrounding soil is approximately 0.5 times the burial depth in both relative density states. Additionally, the range of influence of the surrounding soil around the composite foundation presents a triangular distribution. As the displacement gradually increases, the composite foundation detaches from the rear soil, forming a settlement zone, while the front soil of the composite foundation forms a bulging zone. The comparative analysis in Figure 15 reveals that under loose sand conditions, the range of influence on the surface of the front sand of the foundation is approximately the bucket diameter under horizontal loading. Under dense sand conditions, the range of influence on the surface of the front sand is approximately 0.9 times the bucket diameter. A comparison of the displacement fields of the sand surface under the two relative density states indicates that in the dense sand state, owing to the high relative density of the sand, the front sand of the foundation primarily displaces along the loading direction. In the loose sand state, the relative density of the front sand is lower, leading to sand separating and compacting towards both sides. Analysis of the Soil Deformation Mechanism around a Pile-Bucket Composite Foundation under Different Pile-Bucket Diameter Ratios  
To understand the deformation mechanism of the surrounding soil under the action of different pile-bucket diameter ratios, the displacement fields of the surrounding soil for the composite foundation under loose sand conditions with pile-bucket diameter ratios of d/D = 0.5, 0.417, and 0.357 were analyzed. Figure 14: Displacement vector field under different compactness. (**a**) Loose sand; (**b**) Dense sand. Figure 15: The displacement vector field of soil surface under different compactness. (**a**) Loose sand; (**b**) Dense sand. Figure 16 illustrates the displacement vector maps corresponding to the ultimate load under loose sand conditions for pile-bucket diameter ratios of 0.417 and 0.357. In conjunction with the analysis in Figure 14a, it becomes apparent that as the pile-bucket diameter ratio decreases, the influence depth of the surrounding soil around the foundation significantly decreases and the impact of the pile foundation top on the soil in the composite foundation also decreases. This indicates that as the pile-to-bucket diameter ratio decreases, the composite foundation primarily resists horizontal displacement through the bucket foundation. Figure 17 presents the surface displacement vector maps of the soil under loose sand conditions for pile-bucket diameter ratios of 0.417 and 0.357. In tandem with the analysis in Figure 15a, it is evident that as the pile-bucket diameter ratio decreases, the contact area between the composite foundation and the front soil expands, thereby amplifying the horizontal bearing capacity of the composite foundation. This also validates the distribution law of incremental earth pressure in Section 3.2. As the pile-bucket diameter ratio decreases, the bucket foundation shoulders more load. This aligns with the research results obtained by [PERSON] et al.