## 5 Conclusions  
In this article, according to the engineering prototype, a model was designed based on similarity theory, and the retaining structure was innovatively manufactured by 3D printing technology. Two groups of indoor model excavation tests of the strutted retaining structures were carried out in sandy soil. The deformation characteristics and laws of the U-shape sheet pile strutted flexible retaining structures were compared and analyzed, and the following conclusions could be drawn:  
1. The finite integral method could effectively analyze strain data to obtain the lateral displacement distribution, with an average relative error of 1.76%, providing an effective method for calculating the lateral displacement of retaining structures.
2. With the increase in excavation depth, the displacement mode of the U-shape sheet pile strutted flexible retaining structure changed from the \"cantilever\" type to the \"bulge\" type and finally evolved into a complex displacement mode of the \"recurve bow\" type with both sides recurving and the middle protruding. The retaining structure's maximum lateral displacement spanned from 0.3% Z to 3.5% Z, with an average value of 0.756% Z, which was within the deformation range of a typical flexible retaining structure. This showed that the strut could successfully confine the wall's lateral displacement and achieve deformation control.
3. The distribution of the ground surface settlement of sand behind the wall increased with the excavation depth, from an \"exponential\" to a \"triangular\" mode, and ultimately evolved into a \"trough\" or \"trapezoid\" distribution mode. The maximum settlement at each excavation depth ranged from 0.1% Z to 1% Z, with an average value of 0.375% Z, indicating that the strutted retaining structure could effectively control the sandy filling. The nondimensionalized surface settlement points of the two groups of tests were scattered in zone I, which conformed to the settled law of sandy soil.
4. The normalized deformation relationship curve of the excavation reflected that the maximum lateral displacement and the maximum ground surface settlement increased with the increase in the excavation depth, and the ratio of maximum settlement to maximum lateral displacement (\(s_{max}/\delta_{max}\)) was between 0.5 and 1, with an average value of 0.54. This indicated that the maximum settlement behind the wall was about half of the maximum lateral displacement of the retaining structure, and the settlement deformation rate was always lower than the lateral displacement deformation rate.
5. The distribution of the bending moment varied with the excavation depth. As the excavation depth increased, the maximum bending moment increased, and the zero point of the reverse bending moved downward, presenting a multi-segment bending curve distribution.  
Conceptualization, J.H. and Z.Y.; methodology, J.H.; software, J.H.; validation, J.H. and Z.Y.; formal analysis, Z.Y.; investigation, J.H.; resources, Z.Y.; data curation, J.H.; writing--original draft preparation, J.H.; writing--review and editing, Z.Y.; supervision, Z.Y.; project administration, Z.Y.; funding acquisition, Q.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by East China University of Technology Graduate Innovation Fund, grant number YC2022-8612.  
Not applicable.  
The data are contained within the article.  
The authors wish to express sincere gratitude to the anonymous reviewers whose valuable opinions have made significant contributions to improving the overall quality of this article.  
The authors declare no conflict of interest.