Chapter

Fractals in Engineering

pp 67-80

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

  • Luis E. VallejoAffiliated withDepartment of Civil and Environmental Engineering, University of Pittsburgh
  • , Sebastian Lobo-GuerreroAffiliated withDepartment of Civil and Environmental Engineering, University of Pittsburgh
  • , Zamri ChikAffiliated withDepartment of Civil and Environmental Engineering, University of Pittsburgh

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Summary

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.