<p>Focusing on slurry penetration on slurry shield excavation face, this study proposes a two-step methodology. First, a fractal effective permeability of power-law slurry fluid flow in soil considering the effective radius of soil pores is established. Then, the governing equations for the power-law slurry grouting penetration in soil are established by considering the porosity attenuation induced by suspended slurry particle deposition, which reveals control laws of grouting pressure, slurry concentration, and penetration distance. The proposed models are verified by comparing with the available models, and then, the grouting penetration mechanism on slurry shield tunneling face is also analyzed. The results show that the low penetration speed shortens filter cake formation significantly; long rotation cycles increase slurry penetration distance. This study provides a theoretical basis for optimizing slurry shield operations, enhancing excavation face stability.</p>