## 5 Discussions about the Control Parameter of the Complex Underground Structure System Design  
As the floor height and overburden thickness of the station are fixed values after the determination of the functional requirements of the subway station and the external environment, parameters \(q\), \(\beta\), and \(L\) are determined in Equation (38). Engineers can actively adjust the section sizes of the wall columns and the frame beams, that is, the stiffness ratio between the wall column and the frame beam \(\alpha\), which can be named as the column-beam stiffness ratio. A correct and comprehensive understanding of the influence law of the parameter \(\alpha\) is essential to improve the personal initiative of engineers in engineering design. Now, we will try to discuss \(\alpha\). (1) Let us suppose that the column-beam stiffness ratio \(\alpha\) approaches infinity, which means that the cross section of the frame beam of the side wall is so tiny that the stiffness \begin{table}
\begin{tabular}{c c c c} \hline
**The Thickness of** & **Analytical Solution** & **Simulation** & **The Error between** \\
**Earth Covering** & **Analytical Solution** & **Simulation** & **Them** \\ \hline
1.5 & 3717 & 3532.68 & 4.96\% \\ \hline
2 & 4032 & 3762.3 & 6.69\% \\ \hline
3 & 4645 & 4221.3 & 9.12\% \\ \hline
4 & 5268 & 4668.3 & 11.38\% \\ \hline
5 & 5886 & 5139 & 12.69\% \\ \hline
6 & 6494 & 5598.6 & 13.79\% \\ \hline \end{tabular}
\end{table} 
Table 4: The comparison between simulation and analytical solution within different thickness of earth covering. Figure 18: Relation curve of the column bottom bending moment with the thickness of earth covering. can be ignored compared with the column. Then, the limit of the analytical solution formula can be expressed as Equation (39) when \(\alpha\) approaches infinity. \[\lim_{\alpha\rightarrow\infty}M=-\frac{(\beta+3)qL^{2}}{6} \tag{39}\]  
If we let \(\beta=0\), that is, there is only uniform linear load applied, Equation (39) is simplified to Equation (40). \[M=-\frac{qL^{2}}{2} \tag{40}\]  
(2) On the contrary, if the opening is far away from the frame beam of the side wall, the cross section of the frame beam of the side wall is large enough to bear any deformation. The column-beam stiffness ratio \(\alpha\) decreases to infinitely small consequently, and Equation (38) can be expressed as Equation (41) by taking the limit \(\alpha\to 0\). \[\lim_{\alpha\to 0}M=-\frac{(31\beta+30)qL^{2}}{1680} \tag{41}\]  
Set \(\beta=0\), i.e., there are only uniform distributed linear loads applied, then Equation (40) can be simplified to Equation (42):  
\[M=-\frac{qL^{2}}{56} \tag{42}\]  
which agrees with the calculation of the hogging bending moment value at the root of the beam with the fixed support at one end, the hinged support at the other end, and the mid-span under the uniform distributed load. In addition, the correctness of the derivation in this paper is also verified from the perspective of the limit. (3) Taking the parameters in Section 3.1 as an example, let \(\beta=0\) and substitute different values \(\alpha\) into Equation (38). The relationship diagram between the column bottom bending moment of the wall column and the stiffness ratio between the wall column and the frame beam is obtained, as shown in Figure 19.  
The wall column's control bending moment increases remarkably with the increase of \(\alpha\) in the range of 1-64 from Figure 19, which means that there is a sensitive region of the column's control bending moment to the column-beam stiffness ratio \(\alpha\), and the change of the bending moment is not noticeable out of this region. Therefore, it is beneficial to reduce the concentration of the bending moment at the bottom of the wall column by taking the Track Panel Tunnel (TPT) openings a little closer to the middle longitudinal beam under the condition of meeting the functional requirements. However, the mechanical performance  
Figure 19: Relation curve of the column bottom bending moment with column-beam stiffness ratio.