## 6 Conclusions  
In this study, considering the subway tunnel project supported by the Jinan CBD Municipality, the impact of undercrossing non-circular tunnels on existing underground  
Figure 15: The influence of the horizontal spacing of the double-hole tunnel on the existing underground structure: (**a**) floor settlement curve, (**b**) variation curve of additional bending moment of floor, and (**c**) influence of tunnel spacing \(L\) on \(S_{\text{max}}\) and \(M_{\text{max}}\).  
structures was systematically analyzed using theoretical calculation and numerical simulation. The following conclusions were derived:  
1. By integrating the equivalent radius of non-circular caverns, the Park soil movement model, and the Verruijt formula, the analytical solution for stratum deformation from non-circular cavern excavation is derived. Compared to the measured results, the revised formula exhibits good predictive accuracy for stratum deformation.
2. By employing various equivalent methods, the stiffness of tubular or box hollow structures with different cross-sections and materials is determined and verified through numerical simulation. The results indicate that the deformation and additional bending moment of the foundation beam, equivalent to the wall thickness of the hollow structure, align with finite element findings.
3. During the construction of the new tunnel undercrossing the existing structure, the excavation face area of the new tunnel and the net distance between its vault and the existing structure must be tightly controlled. Additionally, considering the spatial relationship between the tunnel and the existing structure, an appropriate axis distance for the twin tunnels should be chosen to minimize any disturbance to the latter.
4. When analyzing the deformation of the existing structure in the crossing project using an elastic foundation beam, the sensitivity of the beam's deformation to the equivalent stiffness is low. However, when approaching a critical stiffness value (approximately \(1\times 10^{9}\) N\(\cdot\)m\({}^{-2}\)), small variations in the foundation beam's stiffness led to significant differences in the calculated deformation of the existing structure. Notably, the structural stress is highly sensitive to these stiffness changes, with even minor adjustments resulting in considerable differences.  
Conceptualization, Y.L. and Q.Z.; methodology, Y.L., M.L. and J.Y.; software, Q.Z. and J.Y.; validation, Y.L. and Q.Z.; formal analysis, Q.Z.; investigation, J.Y.; resources, M.L.; data curation, M.L. and J.Y.; writing--original draft preparation, Y.L.; writing--review and editing, J.Y.; visualization, M.L.; supervision, M.L. and Q.Z.; project administration, M.L.; funding acquisition, Y.L. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data presented in this study are available upon request from the corresponding author.  
Author [PERSON] was employed by Guangzhou Metro Design and Research Institute Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.