A beam-spring model with constant rotational stiffness is a practical tool for the prediction of the general deformations and bending moments in circular tunnel linings. However, in reality, the rotational stiffness of a segmental joint is not constant, due to nonlinear deformations and local yielding in the vicinity of the joint. These are a result of the specific geometry at the joint, which is related to water-tightness measures and buildability issues. For quasi-rectangular tunnels this nonlinearity should not be neglected, as the bending component in the lining is significantly larger compared to circular linings. To date, there are only few studies that have investigated a calculation method for consideration of the joint’s nonlinear moment-axial force and shear-axial force interaction behavior and its consequences on the calculated lining behavior. In this paper, an iterative incremental method is proposed to tackle this issue, based on rotational stiffness curves derived from 3D nonlinear finite element modelling of the joints, and substantiated by testing. The significance of the variable rotational stiffness is highlighted through a comparison with results based on a constant stiffness assumption. Further, using the proposed calculation method, the effects of the circumferential joints, the bending moment transmission and several other parameters on the full-ring behavior of quasi-rectangular tunnels are discussed for a wide interval of design parameters. The results provide some new insights into the behavior of this non-traditional tunnel type. Although the presented results are related to specific overall and local geometries, the presented method is considered to be useful for the design of other special tunnel geometries.

There are large bending moments in quasi-rectangular shield tunnels due to their deviation from the circular shape, and as for other types of shield tunnels, the longitudinal joints are the most critical parts in the lining structure. A new type of joint with ductile iron joint panels (DIJPs) was installed in quasi-rectangular tunnels to solve these problems. The distance from the bolts to the segment’s inner surface was improved for better performance under specific bending moment types. Both tests and finite element modeling (FEM) simulations were conducted to investigate the effect of the bolt position improvements. The resistances to crack appearance increased by 33.6% and 18.0% for positive and negative moment cases, respectively. The resistances to crack penetration increased by 13.8% and 18.4% for positive and negative cases. From the FEM approach, it was found that the behavior of the joint under the design bending moment range can be divided into three stages, whereby the bolts are only active from the second stage on. The effects of other optimizing methods, such as enhancement of concrete properties and increase of bolt diameters and numbers, are explored. Through comparison, it is believed that optimizing the joint section to increase the lever arm between bolts and the compression zone can improve the joint behavior most effectively. This optimization direction is recommended when designing a shield tunnel joint with DIJPs.

The modified routine modelling (MRM) and the beam spring modelling (BSM) are two of the classical design methods for circular shield tunnels, but a comparison between their applications in special-section shield tunnels (SSSTs) has not yet been conducted. In this study, these two methods are investigated and compared specifically for the case of quasi-rectangular shield tunnels (QRSTs). While the MRM gives acceptable results for axial force values, some critical bending moments in joint sections and segment sections can be overestimated or underestimated, not giving accurate values for design. It is demonstrated that the MRM cannot precisely predict the degree of bending moment transfer and convergence deformations of the studied SSST, and should only be used in preliminary design. On the other hand, deeper insights into the mechanical behaviour of the QRST lining structure can be gained through the analysis of the BSM. The staggered assembly pattern results in a bending moment transfer between rings and the relatively stiff area sustains the transferred moment from its neighbouring less stiff areas. For most of the longitudinal joints, 20% to 40% of bending moment is redistributed to its neighbouring segments. The transfer increases the nonsymmetric distribution of bending moments in the two halves of a QRST lining ring. This characteristic does not exist in a traditional circular shield tunnel but needs due attention to the types of shield tunnels with two compartments in one tube. Finally, the influences of different parameters related to the assumed pressures and soil reactions are discussed.

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