## 5 Conclusions  
This article mainly illustrates the connection and verification of the modified routine method and beam-spring model in the calculation of shield tunnel lining structure. The development software took into account the discontinuous displacement between the beam and the joint in the beam-spring model and verified on-site measurements to inversely calculate the stiffness reduction coefficient and equivalent foundation resistance factor in the modified routine method. Consequently, the accuracy and efficiency of the calculation of the segment structure were improved by using the method discussed above. The proposed scheme works, as the adopted load-structure method provides a solution for internal force calculation of shield tunnel structure under different engineering hydrogeological conditions, but the interaction analysis of the construction process of twin tunnels can not  
Figure 11: Field segment data measurement (The earth pressure cells and reinforcement stress gauges are embedded in the segment. The axial force and bending moment of the segment are derived from the measured data of the reinforcement stress gauges, and the measured internal force of the segment is obtained, which is shown in Table 2). (**a**) Indoor data measurement. (**b**) Field data measurement. (**c**) Diagram of layout of measuring points.  
Figure 12: Relationship curve of stiffness reduction factor.  
be considered, which needs further research. The details of the conclusions are concluded as follows:  
1. The calculation program based on the beam-spring method evaluating the joint effect between the segments and the discontinuous displacement between the beam and the joint can reasonably evaluate the staggered assembly of the shield tunnel segments, which is more reasonable than the beam-joint strain continuous assumption model in the mechanical behavior between segments. Through the development of the calculation program by setting analytical conditions, the joint spring stiffness can be determined reasonably, and the rationality and accuracy of the calculation of the segment structure are improved;
2. The reasonable value of the stiffness reduction coefficient in the modified routine method is obtained through the inversion of the field measured data and the calculation results of the beam-spring model. A large number of software calculation results were compared with the measured data, which shows that the modified routine method calculation module of the software has high accuracy in the calculation of segment bending moment;
3. The calculation parameters of shield tunnels with different cross-section diameters should be further studied with variables of hydrogeological parameters and the segment diameters. The current research shows that for shield tunnels with different segment diameters adopting recommended bending stiffness reduction coefficient for different parts of the lining ring could provide significant reference value in numerical calculation.  
Conceptualization, Q.H. and S.L.; methodology, S.L. and P.L.; software, Q.H.; validation, S.L., Y.L. and D.J.; investigation, S.L.; data curation, S.L.; writing--original draft preparation, Q.H. and P.L.; writing--review and editing, S.L. and P.L.; visualization, D.J. and P.L.; supervision, Y.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key R&D Program of China, grant number 2018 YFC0809600, the National Natural Science Foundation of China, grant number 51978019 and the Beijing Natural Science Foundation, grant number 8222004.  
Not applicable.  
The relevant data are all included in the paper.  
The authors declare no conflict of interest.