# Mechanical Properties of the Functionally Graded Lining for a Deep Buried Subway Tunnel
## 3 Conclusions  
This study aims to develop a new approach to design the functionally graded lining of subway tunnels. With two parameters of the elastic modulus function and lateral pressure coefficient, the mechanical properties of the functionally graded lining were studied, proving that the new lining shows great characteristics of economy and security.  
In the study, the mechanical properties of the functionally graded lining were researched and by analyzing theoretically and numerically, some conclusions are drawn as follows:  
1. The single factor test shows that the radial displacement of the lining axis decreases with the increase in \(a\) and \(b\), but the deformation mode remains the same, and the reduction in deformation is smaller and smaller. In addition, with the increase in \(a\) and \(b\), the distribution trend of moment remains the same. With the increase in \(a\), the positive section moment increases linearly and the negative bending moment decreases linearly. With the increase in \(b\), the negative moment increases linearly and the positive moment decreases linearly, which embodies the idea of \"flexible yielding\". The displacement of the lining axis and the section moment change linearly with the increase in \(\lambda\). With the increase in \(\lambda\), the shape of the lining changes significantly, which shows that the side with large lateral pressure deforms to the inside, and the side with small lateral pressure expands to the outside.
2. The orthogonal test shows that when the maximum deformation occurs at \(0^{\circ}\), the parameter \(a\) should be larger than \(b\). When the maximum deformation occurs at \(90^{\circ}\), the parameter \(b\) should be larger than \(a\), so as to save material costs on the premise of ensuring safety. In addition, the lateral pressure coefficient has a great impact on the safety of the structure, which exceeds the influence of structural parameters on the safety of the structure.
3. The numerical simulation shows that the calculation model of internal force and deformation is suitable for the cylinder with \(t/R\leq 0.2\). There is a certain gap between the theoretical analysis and numerical simulation, but the gap between the theoretical analysis and numerical simulation results is within \(8\%\) at \(0^{\circ}\) and \(90^{\circ}\) with large displacement. In addition, the conclusion of the theoretical analysis is verified. There is little difference in deformation between the two kinds of functional graded linings, but there is a big difference in circumferential stress. It can be observed that compared with Function I, Function II has some advantages in reducing the maximum deformation of the structure, but the advantages are relatively low.  
In further study, the solution model of internal force and the displacement of functionally graded lining under specific elastic function should be conducted based on the theory of elasticity.  
Conceptualization, D.-C.L. and X.-Q.X.; methodology, Z.-D.C.; software, T.-T.Z.; validation, Z.-D.C., T.-T.Z. and J.-M.C.; formal analysis, Z.-D.C.; investigation, C.X.; resources, Z.-W.Z.; data curation, G.S.; writing--original draft preparation, T.-T.Z.; writing--review and editing, Z.-D.C.; visualization, T.-T.Z.; supervision, Z.-D.C.; project administration, D.-C.L.; funding acquisition, D.-C.L. All authors have read and agreed to the published version of the manuscript.  
This work in this paper was funded by the national key research and development program (Grant No. 2016 YFC0600904).  
No applicable.  
All data, models, and codes generated or used during the study appear in the submitted article.  
The authors declare no conflict of interest.