A Network of Fractal Force Chains and Their Effect in Granular Materials under Compression

Abstract

Granular materials forming part of civil engineering structures such as rockfill dams and the granular base in pavement systems are subjected to large compressive stresses resulting from gravity and traffic loads respectively. As a result of these compressive stresses, the granular materials break into pieces of different sizes. The size distribution of the broken granular material has been found to be fractal in nature. However, there is no explanation to date about the mechanisms that cause the granular materials to develop a fractal size distribution. In the present study, a compression test designed to crush granular materials is presented. The tests used 5 mm glass beads and a plexiglass cylinder having an internal diameter equal to 5 cm. As a result of compression in the cylinder, the glass beads broke into pieces that had a fractal size distribution. The compression test was numerically simulated using the Discrete Element Method (DEM). The DEM simulation indicated that the particles developed a network of force chains in order to resist the compressive stress. These force chains did not have a uniform intensity but was found to vary widely through out the sample. Also, the distribution of the force chains in the sample did not involve all the grains but only a selective number of them. Thus, the force chains did not cover the whole sample. Using the box method, it was determined that the distribution of the force chains in the sample was fractal in nature. Also, the intensity of the force chains in the sample was found to be fractal in nature. Thus, the fractal nature of the intensity of the force chains and their distribution were found to be the main reason why granular material develop fractal fragments as a result of compression.

Breakage of an artificial crushable material under loading

“…: [34,38,40]) have also indicated that the predominant effect of particle crushing is to increase the proportion of fine material without significantly changing the size of the largest particles. To date, the mechanisms that cause the granular material to develop a fractal size distribution are not fully explained.…”

“…In other words, the larger coordination number for larger particles outweighs the effect of the strength of individual particles reducing with increasing particle size. However, DEM simulations of direct shear tests on mixtures having a limited number of oversized particles carried out by [39] have shown that the smaller particles exert large compressive forces on a small section of the perimeter of the large particles [40] explain the fractal size distribution of the broken grains by the fact that compression of granular materials, simulated by DEM analyses, results in a network of force chains that are fractal in their intensity and distribution. It may be noted, however, that the numerical experiments were conducted on uniform granular materials with permanent grains.…”

Otimização construtal de uma cavidade multi-bifurcada para dissipação de calor

“…2 para o cálculo de problemas de autovalores: (2) na seguinte forma matricial equivalente: (3) onde M é a matriz de massa e K é conhecida como a matriz de rigidez. Essa equação de autovalores é então resolvida por um algoritmo de Arnoldi até todos autovalores serem encontrados para um determinado intervalo.…”

“…O uso da teoria dos fractais abrange aplicações na área de física [2,3], engenharia química [4,5], finanças [6,5], tráfego de internet [7], processamento de imagens [8,9], dinâmica dos fluidos [10,11], ciência ambiental [12,13], análise de superfícies [14] dentre outros. O motivo dessa gama de aplicações da teoria fractal se deve particularmente a sua característica de descrever a auto-similaridade em diferentes escalas que é uma aproximação do que ocorre na natureza [15,16].…”

A fractal model of contact force distribution and the unified coordination distribution for crushable granular materials under confined compression

“…Additionally, the characteristics of the fabrics of contact forces during one-dimensional compression test are beyond the scope of this paper [14,51]. This study mainly aims to identify the features of the contact force distribution in detail using a fractal model, which is developed to analyze the normal contact force, shear contact force and total contact force in the granular packing [52]. This fractal model can also be used to explain the development of the fractal size distribution.…”