## 5 Results and Discussion
### Change Rule of Horizontal Displacement of Sheet Pile  
Figure 15 presents the comparison between the implemented values of horizontal displacement at the top of the sheet pile in each group of model tests and the numerical simulation. The test outcomes reveal a gradual increase in horizontal displacement of the top of the sheet pile with the deepening of excavation. In Group A (single pipe pile),  
Figure 14: Numerical simulation results of overall horizontal displacement of pipe pile.  
the displacement values are distributed approximately symmetrically in the horizontal direction, with the centerline of the tie rod serving as the axis of symmetry. Furthermore, displacement magnitudes increase further away from the tie rod, forming a \"V\" distribution pattern that becomes more pronounced with increasing excavation depth. On the other hand, in Group B (double pipe pile), the displacement values are symmetrically distributed, with the centerline of two tie rods acting as the axis of symmetry.  
In Group A (single pipe pile), the anchoring action of the pipe pile leads to a significant reduction in displacement at the tie rod junction compared to peripheral displacement.  
Figure 15: Comparison between test results and numerical simulation results of horizontal displacement at top of sheet pile.  
Furthermore, positioning the pipe pile closer to the sheet pile diminishes the pressure exerted by the soil on the sheet pile due to the presence of the pipe pile, resulting in slightly smaller displacements of the sheet pile compared to the outer soil at the same height. On the contrary, in Group B (double tubular piles), it is notable that there is a smaller displacement of the sheet pile than in Group A. When within its influence range, spacing of tubular piles directly affects soil pressure acting on the sheet pile, and the overall increase in stiffness contributes positively to displacement control.  
The numerical simulation results exhibit a similar trend to the test results, although they are slightly larger. The displacement of the top pile in the horizontal direction of the sheet pile displays a centrosymmetric distribution, with the minimum displacement occurring at the position of the tie rods. The tie rods and tubular piles effectively constrain the deformation of the sheet pile. The displacement of the sheet pile between Group B's tubular piles (double tubular piles) is essentially identical due to superposition effects, further confirming that tubular pile spacing affects the support system. It also suggests a potential solution to minimize differences in displacement between tie rods and overall sheet pile deformation.  
Figure 16 illustrates the cloud diagrams depicting the overall horizontal displacement of test sheet piles for Groups A3 and B2 obtained through numerical simulation at an excavation depth of 50 cm. The overall horizontal displacement patterns of the sheet piles for Group A (single pipe pile) and Group B (double pipe pile) are found to be essentially identical. Upon comparing the displacement change of sheet piles at the tie rod node, it is observed that the displacement at the top of sheet piles is greatest at the beginning of excavation, while that at the bottom is minimal. With increasing excavation depth, it is noted that the sheet piles undergo bending, with their maximum displacement point gradually shifting downward to approximately 1/2\(\sim\)1/3 of the excavation depth. This observation indicates that factors such as length, stiffness, and other specifications of sheet piles also influence stability within this support system.