Penetration diffusion model for backfill grouting through segments of shield tunnel considering weight of grout

In order to study the penetration diffusion model for backfill grouting through segments of shield tunnel, taking the Bingham fluid as research object, the formulae for calculating the backfill grouting through segments of shield tunnel are deduced based on the generalized Darcy's law (capillary group theory) by means of the theory of fluid mechanics and their application scopes and the determination methods for their parameters are analyzed. For a specific case, the influences of grouting parameters (grouting pressure and grouting time) and ground conditions (permeability coefficient) upon the radius of grout diffusion and the total pressure on segments are discussed. The results show that after considering the weight of grouts, the diffusion shape of the grouts looks like a spheroid. Under the same grouting pressure, the diffusion range of the grouts from the top grouting hole is smaller than that from the bottom grouting hole (the minimum diffusion radius appears at the top grouting hole and the maximum diffusion radius appears at the bottom grouting hole). The diffusion radius increases along with the increase of grouting pressure, grouting time and permeability coefficient of strata, but its growth rate decreases. The pressure on segments increases with the increase of grouting pressure, and the pressure on unit segment grows linearly. The grouting pressure on the upper unit segment is greater than that on the bottom one considering the weight of the grouts. The difference between the maximum and the minimum diffusion radiis will be larger if the pressure on segments is greater, the grouting time is longer and the permeability coefficient of strata is larger. That is to say, the weight of the grouts has a great impact on the diffusion radius of the grouts.