Fractal and length analysis of fractures during brittle to ductile changes

Abstract

Linear Cantor's dust type fractal analysis of spacial distribution and fracture length analysis has been made on the fracture sets obtained in four deformation experiments performed at different confining pressures (0.5 to 5 kbar) using the Barre Granite. The fractures, mapped using petrographic microscope methods, were subsequently classed into those of shear, tension, and relaxation or decompression origin. Fracture lengths were found to have a distribution similar to a log normal frequency distribution for all sets. The difference between the mean lengths for the fractures of different orientations in a given experiment decreases with pressure, ie. the fracture lengths for all orientations (stress origins) tend to be more homogeneous as confining pressure increases. The fracture sets were also subjected to the linear Cantor's dust method of analysis. These analyses show that the fractal dimension for all of the fractures in a sample increases slightly as confining pressure increases. The difference in fractal dimension of individual fracture sets in a sample (shear, tension, decompression) tends to decrease with increased confining pressure. In the experiments with the lowest confining pressure, one finds the greatest contrasts in both fracture length and fractal dimension for fractures of different origin. These analyses show that one can describe the differences in fracture style in fracture fields using fractal measurements and length measurements. This follows the change from anisotropic stress fields to those more homogeneous through an increase of confining pressure. This shows that one can measure the change in fracture style in going from brittle rupture toward plastic deformation.