Compaction-fracture diffusion model for backfill grouting of shield tunnels in low permeability strata

Based on the calculation of annular grout pressure distribution and fracturing pressure distribution of shield tunnels, the grouting compaction-fracture diffusion model for shield tunnel segments in low permeability strata is established, the annular fracturing interval angle and its calculation method are proposed, and the formula for calculating the diffusion distance and channel width is given. The influences of lateral pressure coefficient of soils and buried depth of shield on the fracturing interval angle as well as those of elastic modulus of soils and grout viscosity on the maximum diffusion distance and channel width are analyzed. The results show that the grout diffuses in fracture mode in the fracture interval angle, and the grout diffuses in compaction mode in the other regions. The fracturing interval angle is negatively correlated with lateral pressure coefficient of soils and tunnel depth. The relationship between the maximum diffusion distance and the grouting pressure difference and that between the maximum channel width and the maximum diffusion distance are both exponential, and the indices are 4 and 0.25, respectively. Under the normal grouting parameters, the downward diffusion distance of the diffusion grout is much larger than the upward one. Based on the actual grouting parameters and stratum parameters of an inter-city railway shield tunnel, the causes for surface grout-oozing are analyzed, and the rationality of diffusion model is further verified.