Fractal Approach of Structuring by Fragmentation

Abstract

The paper addresses the problem of fingerprints of fragmentation processes, showing that structuring by fragmentation can be detected and investigated fruitfully if approached with a proper methodology, of which fractal instruments represent an important part. Studied aspects include fragments size distributions, fragments size-position relations, and long-range correlations in fracture profiles and fracture patterns. The choice of experiments (comminution of flat samples and fragmentation by desiccation cracking) was directed by the aim to complement existing studies from the point of view of fragmentation energy application, being also intended to provide data from processes where different mechanisms are at work. Power-law fragments size distributions were found, but also fragments clusters on dominant size intervals that point towards a fractal character of the size distribution from the point of view of the positions of the distribution maxima. The self-affine character of fractures and of fracture patterns could be emphasised on certain scale intervals, separated by thresholds that are important for studies concerning the implied mechanisms. Fragments size-position correlations indicate a high probability of neighbouring fragments to be of comparable size. The features highlighted for structuring by fragmentation were found in all the studied experiments, their generality pointing towards useful implications for geoscientific research.

Energy Partitioning, Dynamic Fragmentation, and Off‐Fault Damage in the Earthquake Source Volume

“…In the inner Sandhill Corner shear zone, B. R. found that the fragment size distribution defined two power-law trends (two slopes, or D-values, in a log-log plot) that intersect at a value of E s = ∼10 μm (Figure 4). Such "bifractal" distributions are observed in a wide range of different processes from drilling, brecciation, crushing, and milling of rock (Barnett, 2004;Carpinteri & Pugno, 2002;Farris & Paterson, 2007;Roy et al, 2012;Taşdemir, 2009) to rapid shock fragmentation of brick, glass, quartz, rock and ceramic (Barnett, 2004;Capaccioni et al, 1986;Davydova et al, 2014;Fujiwara et al, 1977;Hossain & Kruhl, 2015;Keulen et al, 2007;Roy et al, 2012;Suteanu et al, 2000). Bifractal distributions are sometimes interpreted as identifying a grinding limit (e.g., Keulen et al, 2007), but 10 μm is far too large for the grinding limit of garnet (∼0.26 μm for almandine-pyrope; B. R. .…”

Effect of sampling and linkage on fault length and length–displacement relationship

“…Turcotte and Anderson 1992;Yielding et al 1996). Although different data has been obtained in other experiments (Suteanu et al 2000), in this paper we adopted a value near the Sammis's model for fault length L distribution using the following equation…”

A Scale-Space Information Flux Approach to Natural Irregular Patterns: Methods and Applications

“…Figure 5 shows an example related to a crack pattern produced experimentally (axes are represented in base 2 logarithms). Starch suspension in water, poured on glass plates, was subject to dessication, and the resulting crack pattern was analyzed; details regarding the experimental conditions can be found in Suteanu et al, 2000. The points connected with a full line lead to v F = 1.58 ± 0.06.…”