An algorithm for calculating the effective ratio of the transverse bending rigidity is established based on the segment longitudinal joint bending stiffness. With the knowledge of this effective ratio, the bending rigidity of a modified uniform rigidity ring is fully defined. To verify this developed algorithm, the effective ratios and convergence deformations of the modified uniform rigidity rings obtained with different methods are compared. Moreover, the responses of the modified uniform rigidity ring model under loading obtained from this algorithm are compared to those obtained with the existing generally accepted beam-spring model. The results show that although the bending moments obtained from these two models are different, the axial forces, horizontal convergent deformations, and vertical convergent deformations are quite consistent with each other. The modified uniform rigidity ring model built on the developed effective ratio algorithm is applicable for the analysis of the tunnel convergence deformation and the interaction between the tunnel structure and the ground during operation. This modified uniform rigidity ring model is simpler and easier to use than the beam-spring model; thus, the significance of the developed algorithm for the effective ratio of the transverse bending rigidity is demonstrated.

As the soil-resistance coefficient in a soft soil area is small, overlarge bending moment may cause exceeding transverse deformation for the shield tunnel and cause structural diseases and waterproof failure at the longitudinal segment joints. Hence, a new idea of cross-section design for a minimum bending moment shield tunnel was proposed. This article has first put forward the concept of a zero bending moment shield tunnel. Then, based on rational and feasible hypotheses, a structural mechanical model and an analytical expression of axis for the cross-section of the zero bending moment shield tunnel was obtained, and computational formulas of internal force and key geometry parameters were given. Based on the case of the metro shield tunnel constructed in the Shanghai soft soil area, the zero bending moment shield tunnel was designed, and its characteristics were analyzed. Considering only one cross-section of shield tunnel can be adopted in one metro line, the design method and procedure of the minimum bending moment shield tunnel were put forward. Finally, taking one of the Shanghai metro lines as an example, a cross-section of a minimum bending moment shield tunnel was designed, and its bending moment was compared with the bending moment of a circular section shield tunnel, which had the same horizontal diameter. The comparison revealed that the cross-section of the minimum bending moment can significantly reduce the bending moment of shield tunnel.

It is found that the coefficient of uniformity of coarse grained soil is very large, while its coefficient of curvature is relatively small by analyzing the filler from Gobi Desert area in Xinjiang Province which is used in the second double-line of Lanzhou-Xinjiang high-speed Railway. According to the current standard in China, the coarse grained soil is poorly graded since the coefficient of curvature is too small, which, however, may not necessarily cause poor grading for coarse grained soil. The limitation and inapplicability of the current standards on grading are figured out based on the analysis of particle composition of coarse grained soil, and a new method dividing the coarse grained soil into the coarse and fine part to value the grading is proposed in the paper. The coarse and fine fillers are distinctly segregated from each other in the conventional compaction test. In order to ascertain the optimum moisture content and maximum dry density, it is suggested in this paper to run a compaction test only on the fine grain fraction in the soil to measure its optimum moisture content and its porosity, and use the conversion method to control the density of the subgrade.