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

• We propose a developed fractal formulation to describe the contact force distribution.
• The ultimate coordination number distribution shows a unified relationship.
• It is suggested to set the size ratio as 30 times to balance the efficiency and accuracy.
• Weibull modulus, interparticle frictional coefficient, and critical tensile strength are investigated.
• The ultimate fractal dimension of PSD and visualization of contact force network are studied.

The contact forces and coordination number distributions for granular materials under breakage during one-dimensional compression are investigated using the discrete element method (DEM). The fractal distribution of contact forces within the granular packing is the main factor that induces the progressive development of the particle fractal size distribution. A simple method is developed in the current study to reveal the fractal distribution of contact forces in comminuted granular materials. It can also be used to evaluate the structural feature of granular materials. Another interesting finding is that the coordination number distribution for each particle displays a unique distribution within the fractal size distribution of granular assemblages at the ultimate state. Furthermore, the numerical results also demonstrate that the Weibull modulus, inter-particle frictional coefficient and permitted tensile stress of the initial largest particle can affect the evolution of the contact force distribution and coordination number distribution.

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