1938 v = Gas velocity α = Porosity Factor h = Crack depth μt = Viscosity Coefficient DEM MODEL Following rock mass fragmentation, the finite elements decouple from the continuous mesh, becoming independent of discrete entities. These elements acquire energy and speed, so they can cause damage from collision or pressure. The size of the Discrete Elements is variable, since the minimum size they can reach is the smallest size of the Finite Element. The method used for these models is based on the studies of Cundall (Cundall, 1980), which predicts the kinematic and dynamic behavior of bodies when they collide. For this, we use models such as those of Hertz-Mindlin (Hertz, 1882) (Mindlin, 1949), where the elements are considered solids with viscoelastic behavior. Illustration 3; Hertz-Mindlin contact model (Dem-Solution, 2010). As can be seen in Illustration 3, the Hertz-Mindlin viscoelastic model is basically represented by a system consisting of a spring and a dashpot (normal and tangential). The stiffness of the bodies is represented by a spring, while the property of absorbing the energy of the bodies is represented by the dashpot. The equation that governs this phenomenon is: U=> ∙ (+s äã äã>ã å +ïä>2 ã ä ãããã2( (6) Where: F = Force. k = Coefficient of Rigidity. C = Damping coefficient. m = Reduced system mass. x = Distance (overlap of particles). To avoid numerical problems in the models, it is necessary to consider a sufficiently small timestep, since, when a high overlap value is generated between particles, the damping does not absorb the energy necessary to soften the effect of the collision, producing an unwanted particle expulsion. A conservative model is to calculate the timestep, as described by Juan Mellado in his thesis (Mellado, 2005). ∆MD1)>)DC = ’ 2-5( çã1+Ô# −Ôé (7)
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