A diffusion model for backfill grout behind shield tunnel lining

This paper presents an analytical model to investigate backfill grout diffusion behind tunnel segmental lining, in which the backfill grout is taken as a Bingham fluid. The analytical model of grout diffusion is derived based on force–equilibrium principle, Darcy's law, and the law of momentum conservation of the grout. Time-dependent grout diffusion pressure and distance are highlighted in the model. The proposed grout diffusion model is applied in two field cases: Metro Lines No. 9 and No. 4 in Shanghai City. The results show that the proposed model agrees well with the measured grout diffusion distance in the field. Parametric studies are then conducted, implying that grout diffusion distance along the radial direction of tunnel lining is proportional to either hydraulic conductivity or initial grout pressure, whereas it is in inverse proportion to the yield stress of backfill grout. The distributions of initial grout pressure exert key influences on the grout diffusion distance and grout diffusion pressure behind tunnel segment lining.