OFFICIAL CFD THEORETICAL MODEL This type of calculation is based on the finite difference method, which consists of evaluating the behavior of compressible fluids in a Euclidean domain, where the explosive and the objects with which it interacts (in this case the rock mass) must be represented. Alan Minchinton and Peter Lynch (Minchinton & Lynch, 1997) explain in their publication how gases behave along the blasthole. An adiabatic expansion is defined, so the effects of energy loss due to heat transfer are neglected. On the other hand, they also consider that the flow of gas is developed because it is turbulent flow and has a Reynolds number greater than 105. The equations used for a 2D model for conservation of mass and momentum are: ( )+ ( )+ ൫ ൯ =0 (3) =− ℎ 2 തതത 12 (4) =− ℎ 2 തതത 12 (5) Where: ρ = Gas density 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.
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