Diffusion Model of Grouting behind Shield Wall Considering the Spatial Distribution of Consistency

After the shield tail is separated from the segment, an annular columnar gap is formed between the soil and the segment of the shield tunnel. Grouting behind the shield tail gap is an important means to control the stress release and formation deformation. The slurry injected into the soil will cause certain pressure on the segment, easily leading to dislocation and cracking of the segment. Based on the principle of hemispherical diffusion, considering the inhomogeneity of slurry in spatial distribution, the temporal and spatial distribution of consistency of power-law slurry is studied, and the calculation formula of slurry pressure distribution and slurry pressure on the segment are obtained. Through case analysis, the calculation results of whether the spatial distribution of slurry consistency is considered are compared. At the same diffusion radius, when the spatial distribution of slurry consistency is considered, the slurry pressure is large. When the spatial distribution of slurry consistency is considered, the force calculation result of slurry acting on the segment is twice that without consideration. The calculation result considering the spatial distribution of slurry consistency is safe for engineering. It is suggested that the calculation formula considering the spatial distribution of slurry consistency proposed in this paper should be used to calculate the pressure of power law flow slurry acting on the tube sheet.