APPLICATION AND EXPLORATION OF THE PERIMETER-AREA FRACTAL DIMENSION OF RECRYSTALLIZED QUARTZ GRAIN BOUNDARIES: A CASE STUDY FROM THE SANDHILL CORNER SHEAR ZONE

The microstructure of polycrystalline rocks strongly influences their mechanical properties. In metals, the characterization of dynamically recrystallized grains through fractal analysis has demonstrated relationships between the perimeter-area fractal dimension (D-value), deformation conditions (i.e., strain-rate and temperature), and physical properties such as creep rupture strength. Deformation experiments on monocrystalline quartz aggregates suggest a similar relationship between the D-value and strain rate. To explore the utility of the perimeter-area fractal dimension as a strain rate meter, we apply it to deformed and recrystallized quartz veins across the seismogenic Sandhill Corner shear zone, a well-documented mid-crustal dextral transpressive shear zone exhumed from the base of the frictional to viscous transition zone. The spatial pattern and range of strain rate estimates from D-values is remarkably similar to that of 9 published flow laws. Additional comparisons of the D-value with common measurements of shape properties (e.g., RMS grain size, aspect ratio, circularity, roundness) demonstrate an interdependence on aspect ratio and grain boundary irregularity, and a strong negative correlation with RMS grain size, suggesting its potential use as a flow-stress piezometer. Theoretical considerations and preliminary modeling also suggest the D-value contains information on deformation mechanisms during dynamic recrystallization. Future experimental work is required to constrain and verify these relationships.