# Spatial Deformation Calculation and Parameter Analysis of Pile-Anchor Retaining Structure
## 6 Conclusions  
This study focuses on the analysis of pile-anchorretaining structures in foundation pit engineering. A simplified spatial deformation model of the retaining structure is used, along with the principle of minimum potential energy, to derive a theoretical prediction formula for deformation. The formula is validated through comparisons with on-site monitoring data and numerical simulation results. The study also investigates the influence of various parameters on the deformation of the retaining structure. The key findings are as follows:  
1. The theoretical prediction formula and numerical simulation model demonstrate practical applicability, with small errors observed when compared to on-site monitoring results.  
Figure 14: Crown beam size and material strength.  
Figure 13: Pile size and material strength.  
2. The crown beam exhibits a 'V'-shaped horizontal deformation curve, and the proximity to the center line of the foundation pit correlates with greater horizontal deformation. The maximum horizontal deformation of the crown beam is measured at 13.23 mm (theoretical), 12.44 mm (numerical simulation), and 12.60 mm (on-site monitoring). The differences in the horizontal distribution arise due to the treatment of the crown beam and pile as a whole in the numerical simulation model.
3. The horizontal deformation curve of the pile also exhibits a 'V'-shaped distribution. The maximum horizontal deformation of the pile is observed at different depths (\(z\) = 33 m, \(z\) = 20 m, and \(z\) = 26 m) in the theoretical calculation, numerical simulation, and on-site monitoring, respectively. This discrepancy is attributed to the simplifications made in the theoretical calculation and numerical simulation, which do not account for the actual excavation steps. Future research can focus on modifying the spatial deformation curve of the retaining structure based on these findings.
4. The size and material strength of the waist beam and crown beam have negligible influence on the horizontal deformation of the pile. However, increasing the size and material strength of the pile significantly enhances the overall stiffness of the retaining structure, thereby reducing the horizontal deformation of the pile. Therefore, improving the size and material strength of the pile is crucial in minimizing the deformation of the retaining structure.  
Overall, this study provides valuable insights into the prediction and control of deformation in pile-anchorretaining structures, offering guidance for parameter design and material selection in similar engineering projects.  
Q.Y.: conceptualization, methodology, supervision, project administration. H.F.: methodology, software, data processing, writing--original draft. Y.Z.: validation, formal analysis, writing--review and editing. All authors have read and agreed to the published version of the manuscript.  
This work was supported by Hunan Provincial Education Department Foundation under grant no. 21C0681, and Natural Science Foundation of Hunan province under grant no. 2022 JJ50281.  
Not Applicable.  
The authors thank the Advanced Research Center, Central South University, for providing the experiment conditions. The authors also express special thanks to the editors and anonymous reviewers for their constructive comments.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.