## 3 Results
### Lateral Displacement Distribution and Analysis of the Retaining Structure  
Figure 14 shows the lateral displacement distribution curves of the single-layer and double-layer strutted retaining structures at various stages of the excavation. As shown in the figure, during the excavation of the first layer (\(Z=0.37\) m), there was significant lateral displacement in the middle and upper parts of the wall due to sand unloading in front of the retaining structure and displacement towards the excavation side under soil pressure behind the wall. The maximum displacement was at the top of the pile, with single-layer supports and double-layer struts measuring \(-4.64\) mm and \(-4.99\) mm, respectively. The lateral displacement of the retaining structure began to significantly decrease below the excavation surface, and the closer it was to the pile bottom, the closer it approached zero. The curve shape shows that the retaining structure's lateral displacement  
resembled the deformation characteristics of a cantilever beam under uniformly distributed loads, presenting a \"cantilever\" type displacement mode. When excavating the second layer (\(Z\) = 0.74 m), compared to excavating the first layer, the lateral displacement of the pile top was significantly reduced, but the maximum lateral displacement of the retaining structure remained at the top, at \(-\)4.02 mm. Due to sand lateral unloading, the middle of the retaining structure protruded towards the excavation side, indicating a preliminary trend of a \"bulge\"-type displacement mode. The above phenomenon suggested that the strut played a role, with just 0.017 mm of shrinkage at the strut. At this point, the strut axial forces in the two test groups were \(-\)0.63 kN and \(-\)0.64 kN, respectively. It was noticed that the displacement of the local area near the retaining structure's strut did not alter considerably. The retaining structure exhibited the typical recurve deformation of a flexible retaining structure at the strut and a certain point below the excavation bottom surface. During the excavation of the third layer (\(Z\) = 1.11 m), the lateral displacement of the retaining structure altered significantly, with notable variances between the two groups of tests. Firstly, the lateral displacement of the pile top of the single-layer strutted retaining structure was no longer the maximum, at \(-\)3.57 mm. The middle part of the retaining structure completely protruded towards the excavation side, showing a \"bulge-style\" displacement mode, with the maximum lateral displacement of \(-\)5.24 mm occurring at a sheet pile depth of 0.7 m. Secondly, the maximum lateral displacement of the double-layer  
Figure 14: Lateral displacement of the retaining structure. (**a**) The single-layer strut group; (**b**) the double-layer strut group. Figure 13: Comparison of test results for simply supported beams. strutted retaining structure remained at the top, at \(-4.24\) mm. The lateral displacement of the sheet pile's middle part protruded at the corresponding excavation site. Additionally, the strut contributed further, with an axial force of \(-1.39\) kN for a single-layer strut, which was roughly \(2.2\) times that of the excavation of the second layer. The first strut of the double-layer strut group had an axial force of \(-0.52\) kN, which was \(18.60\%\) less than the excavation of the second layer, and the second strut had an axial force of \(-1.565\) kN, which was roughly three times that of the first strut. This showed that the second strut had a significant impact. The significant recurve deformation at the retaining structure's strut suggested that the strut had a powerful limiting influence on the retaining structure's lateral displacement. It was also a characteristic of flexible retaining structure deformation, manifesting as the strut pushing the wall back, greatly limiting the lateral displacement in the middle part of the wall. Similarly, the retaining structure below the excavation bottom-surface sand had obvious recurve deformation.