Recent tunnel shape optimization considers only the stress distribution in the soil around the tunnel or the lining's mechanical performance and frequently ignores the influence of the interaction between the lining and soil. Thus, this study presents a tunnel shape optimization method considering this interaction. First, the concept of a lining rational arch axis is employed to derive an analytical expression for the tunnel shape, which is subjected to earth pressure recommended by the International Tunneling Association (ITA). Further, the rationality of the obtained tunnel shape is verified using a finite element method (FEM) simulation, which considers the interaction between the lining and soil. Thus, an iterative FEM is further proposed to minimize the lining's eccentricity. The tunnel shape is gradually modified via the iterative FEM by offsetting the lining axis along the normal vector using the corresponding eccentricity to obtain the optimal tunnel shape. The results reveal that, with the optimal tunnel shape based on the rational arch axis, the tunnel lining is mainly subjected to axial compressive force and exhibits good performance in terms of deformation and bending moment.
The exploration of underground space has rapidly developed following socio-economic growth and increasing demand of humans for living space, as well as the design theory and construction methods of tunnels have also been fully developed. However, certain tunnel challenges are yet to be fully resolved. Some tunnel segments are subjected to excessive bending moments under earth pressure and other loadings, resulting in several issues such as lining cracking and segment damage, thus the tunnel's stability is severely affected [1-2]. However, these issues are usually associated with the tunnel shape to some extent. In tunnel engineering, various tunnel shapes are adopted [3], although the circular tunnel is usually preferred due to convenient construction and function layout requirements.
Currently, segment assembly technology is widely applied in the construction of circular tunnels, which has resulted in higher requirements for the bending resistance of the segments and their joints. Therefore, some scholars have conducted several experimental investigations on the tunnel lining structure's mechanical performance [4-7], which focus on the bending characteristics of the segments and their joints. The lining mechanical performance is closely related to the adopted tunnel shape. If the tunnel shape is unreasonable, an excessive bending moment may arise on the lining under earth pressure. In the tunnel design, the shape of the tunnel must be evaluated and optimized to minimize the bending moment on the lining, so that the optimum mechanical performance is achieved.