Fractals,fault-gouge,and friction

The particle-size distribution of a natural fault-gouge has been determined over the range from 5 m to 40 cm. The gouge is self-similar over the range from 5 m to 1 cm having a fractal dimension of 2.60±0.11. The lower and upper fractal limits were also determined. The lower fractal limit occurs at a dimension of about 1–10 m where mineral cleavage and intergranular porosity dominate the cataclasis. The upper fractal limit occurs at particle sizes on the order of 1 cm where the scaled particle density decreases abruptly by a factor of about three. By analogy to soil-mechanics shear box tests and laboratory rock friction experiments, it is argued that the upper fractal limit of the gouge determines the characteristic displacement parameter in stick-slip friction models. A characteristic displacement on the order of 1 cm is consistent with estimates based on numerical simulations of faulting.