Analysis of Particle Shape Using Fractals

The static and dynamic behaviors of granular materials depend upon the shape of the grains. The shape includes form, roundness and surface texture. Form refers to the gross morphology. Roundness measures the sharpness of the particle corners. Surface texture refers to micro relief features. In this study a method based on the fractal dimension concept is used to determine separately the form, the roundness and the texture of granular materials. Straight pixel chains of different size are used to measure the length of a particle profile. The resulting number of pixel chains needed to cover the profile and the associated chain sizes are plotted on a log-log graph. The plot shows three distinctive straight line segments representing the fractal dimension of the form, roundness and texture of the particle respectively. The fractal dimension concept was found to be a powerful tool to measure these components of shape in granular materials.