Abstract:As an important construction auxiliary method, tunnel pre-supporting technology not only effectively strengthens the surrounding rock, but also has good bearing and restraining deformation. To better simulate the real stress of the tunnel pre-supporting arch shed, firstly, the orthogonal curve coordinate system was established based on the shell characteristics of the grouting pipe shed and the horizontal jet grouting arch shed, and the control equation was solved by the displacement function. Then, the Pasternak foundation model was introduced, and the mechanical shell model of the arch shed on the Pasternak two-parameter foundation was established. Finally, the analytical solution expressions of the deflection, internal force, and foundation reaction force of the arch shed were derived. The proposed model was subjected to case calculation and numerical verification, and then the deformation, transverse and longitudinal forces, and foundation contact reaction force of the pre-supporting arch shed were analyzed. The influence of arch shed design parameters on the deformation of the jet grouting arch shed was discussed. Compared with the analysis methods in the existing literature, the proposed model considers the continuity of rock-soil mass and the integrity of the grouting reinforcement area, which is closer to the real stress state of arch shed pre-support in theory compared with the traditional method. The overall deflection curves obtained by the analytical method and the numerical method are all ‘spoon-shaped’ distributions, and the results are in good agreement. The mechanical analysis shows that in the longitudinal direction, the arch shed can adjust the pressure distribution well to a certain extent, and the internal surrounding rock is in a pressure-free state. Taking the excavation face as the boundary, the influence range of the longitudinal bending moment and shear force of the arch shed is about 5 times the excavation footage. Transversely, the shear stress at the arch foot plays a leading role, and the vault is mainly dominated by normal stress and prone to material damage. Different parameters have different effects on the deformation of the arch shed structure, and the impact degree decreases in the following order: initial deflection > excavation footage > pile diameter > excavation height.