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4 W H I T E P A P E R where S is the selection function coefficient, which is a material constant. Particles will break if the P(e cum ) value is higher than the initial strength attributed to the particle at the beginning of the simulation. If the particle is broken, then the fragments are generated following the Gaudin-Schumann or the Incomplete Beta size distributions. The Voronoi fracture algorithm will generate fragments by respecting the t 10 value, which specifies the percentage of particles passing a screen whose size is 10% of the original particle size, according to the expression: where M is the maximum t 10 value. where e* is the relative specific fracture energy, e 50 is the median fracture energy of the distribution, and σ 2 is the geometric variance of the distribution. The relative specific fracture energy is defined as: (4) (5) (6) 2.2 Tavares Breakage Model The Tavares Breakage Model is based on the doctoral work of Professor L. M. Tavares at the University of Utah and the further development with his research group at the Federal University of Rio de Janeiro, Brazil [6]. The model is based on a set of equations used to describe the behavior of brittle particles when subjected to stresses, and it also incorporates the Voronoi Fracture particle subdivision algorithm to predict particle fragmentation. The breakage probability is based on an upper-truncated log-normal distribution of the specific fracture energy, e. This distribution in its cumulative form is given by:

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