# A Novel Strutless Double-Row Structure for Deep Excavation: Working Mechanism Study and Analysis
## 3 Analysis of Experimental Results
### Deformation Analysis
#### 3.1.2 Horizontal Displacement of the Pile  
Figure 14 presents a comparative analysis between the measured pile lateral displacement curve and the numerical simulation curve above the excavation face upon completion of the excavation. The displacement trends predicted by the numerical simulation closely match the actual measured displacements. This similarity indicates the simulation model's accuracy and reliability. Moreover, the deformation characteristics of DRPW and ARPW are distinct from those of SPW. While SPW exhibits the maximum horizontal displacement at the top of the pile, the DRPW and ARPW structures show the maximum displacement at different locations along the pile body. For DRPW, the maximum displacement is approximately 50 mm below the pile top, whereas for ARPW, it is around 200 mm below the pile top. These differences suggest varying load distribution and stress patterns between the ARPW and DRPW structures. The horizontal displacement contour diagram (Figure 15) from the numerical simulation further highlights these differences. The figure also indicates that the ARPW structure has a lower overall lateral displacement compared to the DRPW structure, despite similarities in their displacement patterns. Figure 13: Pile top horizontal displacement (H = 500 mm). The measured results (Figure 12) reveal the maximum lateral displacement of the pile top for various supporting structures. Specifically, the SPW structure exhibits the highest maximum lateral displacement at 5.061 mm. For the DRPW structure, the maximum lateral displacement of the pile body at 2D, 4D, and 6D row spacings is 2.507 mm, 1.661 mm, and 2.724 mm, respectively. As the row spacing increases, the maximum lateral displacement of the pile body initially decreases, reaching a minimum at a 4D row spacing, before increasing again. This trend indicates that an optimal row spacing exists for minimizing the lateral displacement of the pile body; the reason for this will be discussed in the Section 5. At a 4D row spacing, the pile body's lateral displacement decreases by 33.7% compared to the 2D row spacing, while at a 6D row spacing, there is minimal difference from the displacement at a 2D row spacing. In the case of the ARPW structure, the maximum lateral displacement of the pile body is consistently lower across all row spacings, measuring 1.688 mm, 1.02 mm, and 0.72 mm at 2D, 4D, and 6D row spacings, respectively. Notably, the average lateral displacement reduction from a 2D to a 4D row spacing is significantly greater than the reduction from a 4D to a 6D row spacing, with percentages of 40.6% and 29.4%, respectively. This observation suggests that the effectiveness of reducing lateral displacement diminishes as the row spacing increases, potentially due to reduced interaction between the piles and the soil at wider spacings. Form the above analysis, it is evident that both ARPW and DRPW exhibit greater lateral displacement restriction capabilities compared to SPW. Additionally, under the same row spacing, the ARPW structure demonstrates significantly superior lateral displacement restriction abilities in comparison to DRPW. The maximum displacement point in the SPW structure is located at the top of the pile, whereas in the double-row structures, this point is observed lower down the pile body. In the ARPW structure, the maximum displacement point is even further down compared to the DRPW, indicating a more effective distribution of loads and a better control of deformation. The top of the SPW remains in a free state, whereas the double-row supporting structure coordinates the deformation of the front and back row supporting structures through the transfer of binding force via the crossbeam. This coordination is similar to the structure top subjected to a certain amount of horizontal thrust inside excavation, causing the maximum displacement point to move down from the structure top to the structure body.