In order to explore the slurry diffusion law of shield tail synchronous grouting in water-rich fine sand layer

start time of filter cake generation in the process of slurry diffusion is taken as the turning point of slurry permeation diffusion and compaction diffusion

and the theoretical formula of slurry permeation diffusion considering permeation effect and the theoretical formula of influence radius of slurry compaction diffusion are established. The similarity model test is carried out by the self-developed shield tail synchronous grouting system to verify the rationality of the theoretical formula. The results show that: (1) In the water-rich fine sand layer

different from the conventional single diffusion mode

the slurry is diffused in two stages of permeation-compaction. (2) The function of filter cake is to convert the slurry pressure in the form of pore pressure into effective stress acting on the soil skeleton

and after the filter cake begins to form

the slurry diffusion mode changes from permeation diffusion to compaction diffusion. (3) According to the change law of the effective stress conversion rate curve of the slurry pressure

the larger the grouting pressure

the shorter the time of filter cake formation

i.e. the shorter the duration of the slurry permeation diffusion. (4) With the increase in grouting pressure

the influence radius of slurry compaction diffusion stage also increases

e.g. the disturbance range of the stratum is about one times the tunnel excavation contour when the grouting pressure is 0.4 MPa through experiments and theoretical calculations

. The research results can provide theoretical support for synchronous grouting construction of shield tail in water-rich fine sand layer.