Calculation method for the formation time of dynamic filter cake in slurry shield tunneling

In slurry shield tunneling, the stability of tunnel face is closely related to the filter cake. The cutting of the cutterhead has negative impact on the formation of filter cake. This study focuses on the formation time of dynamic filter cake considering the filtration effect and rotation of cutterhead. Filtration effect is the key factor for slurry infiltration. A multilayer slurry infiltration experiment system is designed to investigate the variation of filtrate rheological property in infiltration process. Slurry mass concentration C_L, soil permeability coefficient k, the particle diameter ratio between soil equivalent grain size and representative diameter of slurry particles d₁₀/D₈₅ are selected as independent design variables to fit the computational formula of filtration coefficient. Based on the relative relation between the mass of deposited particles in soil pores and infiltration time, a mathematical model for calculating the formation time of dynamic filter cake is proposed by combining the formation criteria and formation rate of external filter cake. The accuracy of the proposed model is verified through existing experiment data. Analysis results show that filtration coefficient is positively correlated with slurry mass concentration, while negatively correlated with the soil permeability coefficient and the particle diameter ratio between soil and slurry. As infiltration distance increases, the adsorption capacity of soil skeleton to slurry particles gradually decreases. The formation time of external filter cake is significantly lower than internal filter cake and the ratio is approximately 3.9. Under the dynamic cutting of the cutterhead, the formation time is positively associated with the rotation speed of cutter head, while negatively with the phase angle difference between adjacent cutter arm. The formation rate of external filter cake is greater than 98% when d₁₀/D₈₅ ⩽ 6.1. Properly increasing the content or decreasing the diameter size of solid-phase particles in slurry can promote the formation of filter cake.