# A Novel Strutless Double-Row Structure for Deep Excavation: Working Mechanism Study and Analysis
## 3 Analysis of Experimental Results
### Bending Moment  
Figure 23 illustrates the variations in bending moments of the SPW structure. The figure shows a gradual increase in the bending moment along the pile body, attributed to the earth pressure acting on the upper part of the pile. This pressure relies on the soil resistance of the embedded section to maintain equilibrium, leading to a bending moment curve that peaks in the middle and has lower values at the ends [(41; 34)].  
Figure 23: Bending moment of SPW.  
Figure 22: E\({}_{\text{rf}}\) (H = 500 mm) (**a**) model test results and (**b**) numerical simulation results.  
Figures 24-27 illustrate the variation in bending moment of the front-row pile as excavation depth increases. The connecting beams between the front and rear rows of piles (walls) in the DRPW and ARPW structures lead to a reverse bending in the upper section of the row pile. This bending is characterized by the excavation side acting as a pulled face, while the lower part of the pile continues to experience soil pressure, resulting in an S-shaped bending moment distribution with a zero point at the excavation's bottom. This observation aligns with the previous research [13; 34; 45; 46; 47]. Figure 27 presents a comparative illustration of how pile bending moments change with excavation depth for each structure. It shows that the SPW structure exhibits higher bending moment values compared to the DRPW and ARPW structures, primarily due to the larger lateral displacements generated by the SPW structure. Because the distance between the back wall and the front pile is too small, the bending moment value of the front pile does not change much under 2D row distance. As the row spacing increases, the maximum bending moment for both the ARPW and DRPW structures increases, with the DRPW structure showing maximum bending moments of 12.1 kN\(\cdot\)m and 15.5 kN\(\cdot\)m at 4D and 6D row spacings, respectively. The ARPW structure records maximum bending moments of 10.1 kN\(\cdot\)m and 7.2 kN\(\cdot\)m at the same row spacings, indicating a reduction in maximum bending moments by 17.3% and 53.5% compared to the DRPW structure.  
Figure 24: Comparison of 2D bending moment with excavation.  
Figure 25: Comparison of 4D bending moment with excavation.  
It is evident from the figure above that the supporting pile's distribution patterns for each structure are distinct. In the case of the SPW support, the supporting piles experience tension outside the excavation, with the maximum bending moment located below the excavation face. In contrast, the DRPW and the ARPW structures exhibit reverse bending points. Notably, the maximum bending moment points in the ARPW structure are positioned 100 mm to 200 mm higher compared to those in the DRPW structure. The maximum bending moment points and reverse bending points in these structures show little movement during excavation, indicating a stable response. The ARPW structure has a smaller axial force through the crossbeam compared to the DRPW structure because the soil stiffness between the piles is more pronounced in the ARPW structure. The moment distribution in double-row structures is superior to that in the SPW structure due to the coordinated spatial effects of both the front and back rows. The ARPW structure enhances the stiffness of its rear supporting structure and optimizes the utilization of soil stiffness between the piles, resulting in a more balanced and efficient bending moment distribution compared to both the SPW structure and the DRPW structures.