## 5 Results and Discussion
### Change Rule of Horizontal Displacement of Pipe Pile  
Figure 12 gives the horizontal displacements of the top of the pipe pile obtained using DIC. Although DIC monitoring provides real-time and continuous data, the accuracy of  
Figure 11: The variation in earth pressure. the excavation process for the model foundation may not be consistent at every depth, resulting in scattered results. The displacement at the top of the pile increases gradually as excavation deepens. Initially, with a shallow excavation depth, the displacement shows almost linear progression. Subsequently, despite a sudden change in horizontal displacement, there is still a certain level of bearing capacity and deformation resistance. This behavior generally follows the hyperbolic rule of change, with a correlation coefficient (\(R^{2}\)) exceeding 0.9. The fitting parameters in the numerator of the hyperbolic equation represent the limit excavation  
Figure 12: Measurement of displacement at the top of the tubular pile. depth, while those in the denominator indicate the rate of hyperbolic convergence towards the asymptote. The test findings reveal that the ultimate excavation depths are largely consistent within groups A1 and A4 as well as A2 and A3, respectively. Similarly, the ultimate excavation depths within groups B1 and B2 exhibit consistency and surpass those of single pipe piles (groups A2 and A3) under identical pipe pile and sheet pile spacing conditions. This suggests a correlation between ultimate excavation depths and the spacing of pipe piles and sheet piles. When the spacing between the two exceeds a certain threshold, the ultimate excavation depth diminishes. Moreover, under identical excavation depth conditions, greater spacing leads to reduced deformation of the support system. Furthermore, it is found that the ultimate excavation depth is inversely proportional to the spacing of tubular piles; smaller spacing results in larger ultimate excavation depths under equivalent conditions. Additionally, the horizontal displacement monitoring data at the top of the pipe pile indicate that the pipe pile tilts as a whole once the soil deforms to the point of failure. Figure 13 gives the comparison between the measured and numerical simulation values of the horizontal displacement of the top of the pipe pile in each group of tests. The displacement pattern during excavation is consistent across all groups of model tests. When the excavation depth falls within a certain range, the displacement of the top of the pipe pile changes slowly. However, when the excavation depth exceeds a certain range, the displacement of the top of the pile increases rapidly, indicating instability in the support system. The numerical simulation results align with the overall trend of the test results. It is noted that simulated values before instability are slightly larger than actual test values. Additionally, simulations for Group B (double tubular piles) are more closely aligned with the test results compared to those for Group A (single tubular piles). Nevertheless, it is important to note that existing model simulations do not effectively capture sudden changes in displacement after instability occurs. Figure 14 gives the overall horizontal displacement curves of each group of test piles obtained by numerical simulation. It is evident that the maximum displacement of the pile occurs at the top and gradually decreases towards the bottom. With increasing excavation depth, the pipe pile bends, and the bending position is correlated with the excavation depth. The minimum displacement is observed at the bottom of tubular piles, with overall  
Figure 13: Comparison between test results and numerical simulation results of horizontal displacement at the top of pipe pile. variation being minimal, particularly when there is a large spacing between tubular piles and sheet piles.