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Number | Methods | Circular joints | Radial joints | Features |
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1 | Uniform rigidity ring method | Do not consider | Do not consider | It is widely used in Japan and is mostly used in sewer tunnels. Since the influence of the circular joints is not considered, it can be utilized to design segments with straight joints |
2 | Improved uniform rigidity ring method | Considered through reducing the lining stiffness | Do not consider | There may be problems in the calculation results of the axial force value calculated by this method in the range of 90∼180° with the vertical angle |
3 | Average uniform rigidity ring method | Considered through reducing the lining stiffness | Considered through increasing or decreasing the bending moment | It can be used to design linings for small tunnels and relatively large tunnels. It can be utilized to design staggered segments |
4 | Multihinge ring method | Considered through a hinge | Considered through a hinge | It can be used to design linings in hard rock, and it can be utilized to design segments with straight joints |
5 | Elastic hinge ring method | Considered through a rotating spring | Considered through a rotating spring | Compared with those of methods 1 and 3, the calculation results of method 5 are closer to the real value |
6 | Beam-spring method | Considered through a rotating spring | Considered through a shear spring | It can be used to design linings for large tunnels. It is suitable for large-scale tunnels |
7 | Shell-spring method | Considered through the discrete to joint units method | Considered through the discrete to joint units method | It considers the segment ring as a cylindrical shell. Theoretically, the internal force of the segment can be calculated more accurately, but it is difficult to determine the stiffness of the segment joint. If the unit is sufficiently small, it will lead to a sharp increase in the calculation amount |
8 | Plate shell-joint element-foundation system method | Considered through the block-to-block joint model | Considered through the ring seam model | It is a three-dimensional model, the segment ring is regarded as a flat shell, and the effect of the joint is considered by constructing the segment lining joint element model |
9 | Flat shell-elastic hinge-foundation system method | Considered through the elastic hinge model | Considered through the elastic hinge model | It is a three-dimensional model based on the Reissner–Mindlin plate element. The joint effects between each segment are considered through elastic hinge elements |
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