# Spatial Deformation Calculation and Parameter Analysis of Pile-Anchor Retaining Structure
## 4 Engineering Background and Numerical Simulation Model
### Comparative Analysis of Results
#### 4.3.2 Comparison of Pile Deformation  
Figure 10 shows that the distribution of horizontal deformation of a single pile is small at the top and bottom, but large in the middle region, consistent with the assumed pile deformation curve in Figure 3. The top area of the pile undergoes less soil pressure behind the pile, resulting in relatively small deformation at the top of the pile. At the bottom of the pile, the pile mainly experiences passive soil pressure, leading to limited deformation. Due to the high active soil pressure in the middle of the pile and the limited deformation on both sides of the pile, the maximum deformation ultimately occurs in the middle of the pile. Furthermore, it can be inferred that the maximum horizontal deformation of piles increases for piles closer to the center of the foundation pit. This observation aligns with the assumption made in the theoretical calculation. Moreover, the maximum horizontal deformation of the pile is directly related to the maximum horizontal deformation of the crown beam. The point of maximum horizontal deformation for the crown beam corresponds to the centerline of the foundation pit, where the horizontal deformation of the pile also reaches its maximum value. This correlation further supports the relationship between the deformations of the pile and the crown beam in the context of the foundation pit. Figure 11 illustrates the horizontal deformation curve of piles at \(x=0\) m, \(x=35\) m, and \(x=70\) m Several observations can be made from the figure:  
(1) The horizontal deformation curve of the pile exhibits a distinctive 'V'-shaped distribution, but the position of the maximum deformation differs between the numerical simulation, theoretical calculation, and on-site monitoring data. Specifically, the numerical simulation indicates that the maximum deformation occurs at \(z=-20\) m, whereas the  
Figure 10: Cloud chart of pile horizontal deformation. Figure 9: Horizontal deformation curve of crown beam. on-site monitoring data show the maximum deformation at \(z=-26\) m. In contrast, the theoretical calculation predicts the maximum horizontal deformation of the pile to occur at \(z=-33\) m. This discrepancy in the results can be attributed to the simplifications made in the model assumptions and the limitations of the calculation method. It is clear that further research is necessary to enhance the accuracy and reliability of the results. (2) The horizontal deformation curve of a pile positioned at \(x=70\) m exhibits slight variations compared to a pile situated at \(x=35\) m. This phenomenon is further analyzed in Section 4.3.1. However, both the theoretical calculation and on-site monitoring data demonstrate that the deformation of a pile at \(x=70\) m is considerably larger than that of a pile at \(x=35\) m. In other words, for piles closer to the center line of the foundation pit, the horizontal deformation increases significantly. This observation confirms the trend that the horizontal deformation of the pile becomes more pronounced as it approaches the center of the foundation pit. (3) The maximum horizontal deformation values for the pile at \(x=0\) m are 8.5 mm (theoretical calculation), 10.3 mm (numerical simulation), and 7.8 mm (on-site monitoring). For the pile at \(x=35\) m, the maximum horizontal deformation values are 16.2 mm (theoretical calculation), 38.6 mm (numerical simulation), and 20.1 mm (on-site monitoring). Finally, for the pile at \(x=70\) m, the maximum horizontal deformation values are 36.5 mm (theoretical calculation), 40.3 mm (numerical simulation), and 33.2 mm (on-site monitoring). The close agreement between the theoretical calculation, numerical simulation, and on-site monitoring data demonstrates the practicality of the proposed models. However, it should be noted that the current calculation method has limitations. Simplifications have been made in the analysis process, such as neglecting the influence of pit existence, precipitation, stratification of the foundation soil, and nonlinear effects of the pit and soil.