# A Novel Strutless Double-Row Structure for Deep Excavation: Working Mechanism Study and Analysis
## 4 Engineering Example
The point of maximum displacement for the single-row pile is located at the top of the pile, for the double-row pile at approximately \(-\)2.5 m, and for the irregular double-row pile at approximately \(-\)3.5 m. This distribution pattern of pile displacement is consistent with the results obtained from model tests. According to the Technical Code for Building Foundation Pit Support (JGJ120-2012), the maximum horizontal deformation limit for pile-supported foundation pits with safety levels 1 and 2, when there are no specific requirements, is 0.0025 \(h\) and 0.0050 \(h\), respectively (where \(h\) is the excavation depth of the foundation pit). Therefore, for this foundation pit, the maximum horizontal limit for safety levels 1 and 2 is 22.5 mm and 11.25 mm, respectively. It can be inferred that the SPW structure may not meet the deformation requirements for a level 1 foundation pit, and the DRPW structure may not meet the deformation requirements for a level 1 foundation pit, while the ARPW structure can satisfy the deformation requirements for a level 1 foundation pit. The bending moments of the piles in each structure are shown in the Figure 31. Similar to the model test results, the bending moment of the SPW structure increases gradually from the top, reaching a maximum near the excavation surface, and then decreases, forming a C-shaped distribution. In contrast, the DRPW and the ARPW structures exhibit bending moment distributions with inflection points, forming an S-shaped distribution. For the  
Figure 30: Layout of ARPW. DRPW structure, the inflection point is located approximately 5 m below the excavation surface, while for the ARPW structure, it is about 4 m below the excavation surface. In terms of bending moment values, the maximum bending moment for the SPW structure is 120.8 kN-m. For the DRPW and ARPW structures, the maximum bending moments are 97.6 kN-m and 62.6 kN-m, respectively, representing reductions of 19.2% and 48.2% compared to SPW structure. Overall, it can be observed that the bending moment distribution of the DRPW and ARPW structures is more reasonable, with distribution patterns consistent with those obtained from the tests. The cost per linear meter for each support structure is summarized in Figure 26:0 The unit costs used in the calculation are 1800 RMB/m\({}^{3}\) for piles, 1000 RMB/m\({}^{3}\) for cap beams and crossbeams, and 700 RMB/m\({}^{3}\) for soil mixed walls. The final project costs are shown in Figure 26:1 It is evident that the SPW structure has the lowest project cost. However, compared to the DRPW and ARPW structures, its support effectiveness is inferior and does not meet the support requirements of the foundation pit. The project cost for the DRPW structure is approximately 45% higher than that of the SPW structure. While the DRPW structure can meet the support requirements for a level 1 foundation pit, it cannot satisfy the requirements for a level 2 foundation pit. But, the overall cost of the ARPW structure is about 15% lower than that of the DRPW structure, yet it can meet the support requirements for a level 2 foundation pit. Therefore, adopting the ARPW structure can reduce costs while enhancing the support capacity of the foundation pit. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **Pile** & **Soil Mixed Wall** & **Cap Beam** & **Crossbeam** & **Total** \\ \hline SPW (RMB/m) & 4662 & 0 & 600 & 0 & 5662 \\ DRPW (RMB/m) & 4662 \(\times\) 2 & 0 & 600 & 440 & 10,324 \\ ARPW (RMB/m) & 4662 & 3080 & 600 & 440 & 8782 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of cost per linear meter for support structures. Figure 31: Bending moment of the front pile.