# A New Design Method of Shield Tunnel Based on the Concept of Minimum Bending Moment
## 5 Conclusions  
1. Given that the bending moment of the cross-section of the shield tunnel constructed in the soft soil area tends to easily lead to beyond-limit oval deformation of the cross-section and induce diseases and waterproof failure in terms of the segment joint structure, this article puts forward the concept of designing a zero bending moment shield tunnel for the first time.
2. Based on the characteristics of the surrounding rocks of the tunnel and rational assumption conditions, this article obtains the structural and mechanical calculation model of the rational axis for the zero bending moment shield tunnel and the expression of the rational axis. In addition, the internal force and key parameters calculating the equations of the zero bending moment shield tunnel are advised here in this article.
3. Taking the shield tunnel constructed in the Shanghai soft soil area as an example, we designed and analyzed the zero bending moment shield tunnel. The results indicate that if the vertical diameter \(a\) remains the same, as the lateral earth pressure coefficient \(k\) increases, the center horizontal diameter \(b\) and the maximum horizontal diameter \(c\) both increase, but still less than the vertical diameter \(a\); however, if the center horizontal diameter \(b\) remains the same, as the buried height of the tunnel increases, the vertical diameter \(a\) increases and the shear force of the zero bending moment shield tunnel is zero.
4. Normally, one metro line can only use one shield tunnel with one cross-section shape. Given this, the shield tunnel cross-section design methods and procedures based on the minimum bending moment are proposed here. We took the parameters of the soils that one metro line shield tunnel in Shanghai passes through as an example and used the weighted average to obtain the minimum bending moment tunnel cross-section of that metro line. The numerical simulation analysis indicates that the similar vertical elliptical cross-section shield tunnel features a significantly smaller bending moment compared to that of the circular shield tunnel.  
Investigation of the actual utilization for different shield tunnel cross-sections, D.H. and H.J.; the proposal of the concept of zero bending moment, D.H. and C.X.; the proposal of the concept of minimum bending moment, D.H. and H.J.; rational and feasible hypotheses about zero bending moment, W.T. and X.L.; theoretical analysis for structural mechanical model of zero bending moment shield tunnel, D.H. and C.X.; data analysis of zero bending moment shield tunnel, H.J. and W.W.; numerical simulation of Shanghai minimum bending moment shield tunnel, D.H. and H.J. All authors have read and agreed to the published version of the manuscript.  
This study was supported by the National Natural Science Foundation of China, grant number 52078213(the funder: [PERSON], [PERSON]), U1934208(the funder: [PERSON], [PERSON]) and 52178333(the funder: [PERSON], [PERSON]) and Natural Science Foundation of Jiangxi Province, grant number 20192 ACBL21003 (the funder: [PERSON], [PERSON]) and 20212 BAB204013(the funder: [PERSON], [PERSON]).  
Institutional Review Board Statement: Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** All data are available from the author.  
**Conflicts of Interest:** The authors declare no conflict of interest.