Self-similitude and fractal dimension of sand grains

Fractal theory postulates that geological materials possess a noninteger, fractal dimension describing length-surface-volume relations and particle-size distribution. We examined sand grains, composed largely of quartz, from several horizons of Wisconsin soils derived from glacial outwash for fractal dimension using image analysis of reflected light micrographs with NIH Image software. No evidence was found to support other than a Euclidean, i.e., regular dimension, relating the geometric properties of: (i) measured particle perimeter as a function of magnification or (ii) particle area and perimeter. In addition, particle-size distributions were better fit by lognormal distribution than by a fractal fragmentation dimension. Fractal theory would not appear to provide a useful description for these soil materials.