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Fractal theory demonstrates significant merit in the feature expression of forms of matter in nature. This study uses fractal theory to study the backfill grouting of a shield tunnel. The seepage path was considered as a seepage mesh inserted into the rock-soil mass. For the fractal features of the seepage mesh, the formulas for the diffusion distance and the pressure contribution of grout were derived. The results showed that the diffusion equations of different grout patterns (Newtonian fluid and Bingham fluid) were of a uniform form after calculation, and the equations for the pressure distribution of grout with a change in radius were identical. The diffusion distance of grout increased with increasing grouting time, and there was no indication that the development of diffusion distance tended to be gradual; the downward tendency of the grout diffusion velocity was not moderated. The segment pressure increased with an increase in the diffusion distance. With a constant diffusion distance, a greater grouting pressure produced a greater segment pressure. The favorable performance of grout was attributed to an appropriate mixture ratio. An improper mixture ratio resulted in a smaller reinforcement area in the stratum, which impaired the stability of the shield tunnel.

Model study on backfill grouting in shield tunnels based on fractal theory