# Displacement Analyses of Main Structure of Parallel Pit Excavation and Analysis of Countermeasures
## 3 Parallel Pit Excavation Scheme
### Discussion
#### 4.3.2 Relative Stiffness Coefficient of the Main Structure  
The relative stiffness ratio of the retaining system proposed by [PERSON] [17] and [PERSON] [18] was used to evaluate the maximum disturbance of the diagram wall during excavation. The above study of the stiffness coefficient of the supporting structs focuses on the relative strength ratio of the soil\(-\)structure interaction and the relative stiffness ratio of the support to the retaining structure. Combined with the above simulation results, it can be seen that the stability of the main structure is also related to the distance from the pit edge and excavation depth. Therefore, based on this paper, the relative stiffness coefficient of the main structural system in the cover excavation area is proposed, which can comprehensively respond to the relative stiffness of the soil\(-\)structure interaction, the overall stiffness of the main structure, and the influence of factors such as the excavation depth and distance from the pit edge on the permanent structure system. Three dimensionless groups are used to express the relationship between the variables, among which: the relative stiffness resistance ratio, \(E_{y}\)/\(E\), indicates the interaction between the soil and structure; the relative flexural bearing capacity ratio, \(SoS_{h}\)/\(H\)/, indicates the ratio between the vertical support structure of the steel pipe column and the horizontal support structure of the beam and \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Excavation Schemes**} & \multicolumn{5}{c}{**Additional Deformation Rates**} \\ \cline{2-6}  & **The Retaining Walls** & **Struct 1** & **Struct 2** & **Struct 3** & **Struct 4** \\ \hline Case 2—Area A finished & 1.5 & 1.7 & 2.67 & 5.75 & 1.96 \\ Case 2—Area C finished & 1.1 & 1.1 & 1.4 & 3.45 & 0.64 \\ Case 3 & 1 & 1 & 1 & 1 & 0.87 \\ Case 4 & 0.72 & 0.68 & 0.95 & 1.35 & 0.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Additional deformation rates for different excavation schemes. slab; and the depth distance ratio, \(D/L\), reflects the ratio between the excavation depth of the foundation pit and the distance of the vertical structure from the edge of the foundation pit. The relative stiffness coefficient of the main structure is shown in Equation (5):  
\[R_{d}=\frac{E_{s}}{E}\bullet\frac{S_{h}S_{v}H}{I}\bullet\frac{D}{L} \tag{5}\]  
\(R_{d}\) is the relative stiffness coefficient of the main structure; \(E\) is Young's modulus of the supporting structure; \(I\) is the moment of inertia of the structure per unit length; \(E_{s}\) is the average Young's modulus of the soil; \(H\) is the total height of the supporting structure; \(D\) is the excavation depth; \(S_{v}\) is the average horizontal spacing of the main structure; \(S_{h}\) is the average vertical spacing of the main structure; and \(L\) is the distance of the vertical structure from the edge of the pit. The greater the excavation depth or the closer to the edge of the pit, and the more significant the impact of the adjacent pit excavation on the structure, the larger the value of \(R_{d}\). According to the physical parameters, spatial location relationship, and excavation depth of the main structure in the cover excavation area in the above four excavation cases, Table 4 calculates the relative stiffness of the main structure \(R_{d}\). It can be seen that the changing trend of the relative stiffness coefficient of the steel pile structs is consistent with the trend of horizontal deformation. The greater the stiffness of the main structural system, the smaller the relative stiffness coefficient. The value of \(E_{s}\) can be calculated by the following equation, Equation (6):  
\[E_{s}=\frac{\sum H_{i}E_{si}}{H} \tag{6}\]  
where \(H_{i}\) = thickness of each layer of soil within the enclosure; and \(E_{si}\) = modulus of elasticity of each layer of soil.