An analytical solution for internal forces of shallow circular low-to-vacuum tunnel linings in soft soils

This paper presents an analytical solution derived with force method for the internal forces in the ring lining of maglev train tunnels, which are typically in a circular section and shallowly buried with low vacuum air pressure in the lining. The model incorporates the vacuum pressure induced by the differences in air pressures outside and inside the lining, and the vacuum pressure is assumed to be the active load exerting to the outside of the lining. The model assumes the vertical overburden acting on the lining is proportional to the soil depth at every particular point along the tunnel lining circumference. The lining-ground interaction, represented by tangential and normal resistance to the lining, is combined into the model and is comprehensively evaluated. The Mohr-Coulomb theory is used to estimate the interaction between tangential and normal resistance. The comparison with other models and case histories implies that the proposed model fits well for the field measurement data and results predicted with other models. Analyses based on the proposed model indicated that the vacuum pressure has a negligible effect on the bending moments acting on the lining, but its effect on the normal forces is significant. Parametric studies show that a higher cohesion and internal angle of friction of soils can induce a lower maximum bending moment and higher normal force, indicating that the better the soil conditions the thinner the lining. The cover-to-diameter ratio C/D impacts the maximum bending moment and the optimum C/D is approximately 0.20 in this study, a generally soft soil case.