FRACTAL ANALYSIS OF NON-NEWTON FLUID GROUTING IN SOIL COMPOSED OF ARBITRARY CROSS-SECTIONAL CAPILLARIES

The fractal theory has been applied to understand the transport law for the non-Newton Herschel–Bulkley (H-B) fluid grouting in fractal soil consisting of a bunch of arbitrary cross-sectional tortuous capillaries. The fractal models for the average flow velocity, starting pressure gradient and effective permeability are the functions of the cross-sectional geometric factors of capillaries, minimum and maximum cross-sectional area of capillaries, porosity, fractal dimensions and characteristic parameters of H-B fluid. The proposed models are verified by comparing with the available models, and then the effects of cross-sectional shapes of capillaries and the characteristic parameters of H-B fluid on the average flow velocity, starting pressure gradient and effective permeability are also analyzed. The results show that the present models relate the characteristics of H-B fluid to the microstructure of soil, and both are the most important factors in determining the grouting effect.