Fractal dimension of molten surfaces as a possible parameter to infer the slip-weakening distance of faults from natural pseudotachylytes

High-velocity friction experiments on gabbro and monzodiorite, using a rotary-shear high-velocity friction apparatus, have revealed that frictional melting and progressive growth of a molten layer along a fault cause slip weakening, eventually reaching a nearly steady-state. The melting surface at the host rock/molten layer interface is initially very flat, but it becomes more complex and rounded in shape towards the steady state owing to the selective melting of minerals with lower melting points and the Gibbs–Thomson effect. This change in the melting-surface topography can be quantitatively expressed by the fractal dimension D, as determined by the divider method, from about 1.0 near the peak friction to around 1.1 near the steady-state friction. The ultimate fractal dimension at steady-state friction tends to decrease with increasing heat production rate presumably due to more rapid and uniform melting. A systematic correlation of D with mechanical behavior of the fault during frictional melting may provide a way of estimating slip-weakening distance and heat production rate at steady-state friction by measuring D for natural pseudotachylytes on slip surfaces with different displacements. The weakening distance is of vital significance in relation to fault instability and the heat production rate is related to the fault strength. The experimental studies point to ways to estimate these difficult quantities for natural faults.