Capillary Penetration Diffusion Model for Backfill Grouting of Shield Tunnel

In order to discuss the calculating method of diffusion radius and pressure on segments of backfill grouting, a mechanical model for penetration diffusion in surrounding soils was set up by simplifying grouting penetration as transfusion in soil capillary tubes with uneven bore diameters. Based on the cylinder diffusion theory and the assumption that grout is as Bingham fluid, under the premise of bring the equivalent porosity to replace the soil porosity, the calculation formula of the diffusion radius and the pressure on segments of backfill grouting were obtained through simulating the penetration process of grout in single capillary tube. Then, the relations between grouting pressure, time, and the diffusion radius, pressure on segments were discussed through a detail example. The result shows that the increase rate of the pressure on segments is bigger than that of the grouts diffusion radius under different grouting time and pressure, and the total capillary area on the grouts flowing frontal surface is in proportion to diffusion radius when keep the influence depth of tail gap and the soil equivalent porosity unchanged.