Displacement infiltration diffusion model of power-law grout as backfill grouting of a shield tunnel

Shield tunnel is widely adopted in the metro construction, and backfill grouting is the significant part. With power-law fluid grouts as the study object, a cylindrical infiltration diffusion model and spherical infiltration diffusion model are developed by applying the generalized Darcy law and theories of seepage mechanics based on the displacement effect of grout on groundwater. Through examples, the impact of factors including grouting pressure and formation permeability coefficient in the spherical displacement infiltration diffusion model on diffusion radius, flow rate, total pressure of grout in segments, and uniform equivalent pressure in grout diffusion area (grout pressure per unit area in a segment) is analyzed. The result shows that, the diffusion speed, injection flow rate and the pressure received in segments increase with an increase of the grouting pressure. Meanwhile, as the injection time increases, the flow rate of grout under conditions of different grouting pressure all decreases, and a sharp decrease exists. The diffusion speed and grouting pressure are positively correlated to the permeability coefficient, and with the increasement of the injection time, the diffusion displacement of grout in different permeability coefficient varies increasingly, the increase amplitude of the pressure acting on the segment by grout increases gradually.