Grouting in deep, loose layers are a complex process in which many modes such as infiltration, splitting, and compaction coexist. It is of great significance to establish a realistic, simplified physical model to study the law of slurry diffusion. Herein, a cylindrical diffusion model of radial tube flow is established, and the control differential equations of both the Bingham slurry diffusion velocity in a single tube and the diffusion velocity of the radial tube flow are deduced.

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... , the calculation formulas for the diffusion radius and slurry pressure distribution function are obtained. The rationality of the theory is verified by combining our results with those of the field grouting test of the Guotun coal mine. The results show that the cylindrical diffusion model of radial tube flow can successfully characterize the slurry diffusion law of grouting in a deep, loose layer. The slurry pressure attenuation shows distinguishable stages: within the first 30% of the diffusion radius, the slurry pressure decreased sharply by approximately 70%, and the slurry pressure decreases slowly in the later stages. Furthermore, the diffusion radius has a nonlinear, negative correlation with the height of the grouting section and the comprehensive injection rate of formation; the change rate is relatively more gradual, and there are no distinguishable stages. The research results provide a theoretical basis for reasonably determining the grouting parameters of deep, loose layers in the future.