Based on the self-weight effect and the displacement effect of grout, the penetration diffusion characteristics of the back-filled grouting of shield tunnel in sand gravel stratum at different locations were analyzed.First, the penetration diffusion motion equation for Bingham grout under gravity is analyzed.According to the continuity equation in the spherical diffusion process of the grout, the model of grout displacement diffusion was established, and then the analytical solution of the grout diffusion process was given for the diffusion process injected from top and bottom grouting holes.Calculation results show that when the displacement effect of the grout is considered, the effect of gravity on the diffusion distance of the grout is more significant.Based on the grout permeation diffusion model of displacement effect, the calculation shows that when low grout pressure is used in high permeability formation, as the grouting time increases, the gravity of the grout has a significant influence on the grout permeation and diffusion process. © 2020, Editorial Board of Journal of Huazhong University of Science and Technology. All right reserved.