1937 The model for calculating fracture is based on a simplified plastic model of Rankine (1857), where each element is reviewed for each timestep. A fracture can occur if the stress of the element exceeds the tensile limit and then decays to zero. Y ) P =− 8> # 2ä3 ã}) (2) Where: σt = Tractive effort. Gf = It is the coefficient of energy release per fracture. Ai = It is the area of the element. The fracture energy (Equation 5) is the one that governs once the maximum tensile stress has been reached, that is, when the material begins its plastic deformation. Illustration 2; Fracture based on the Rankine model. 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: Ì Ì> (Œ–)+ Ì Ì( (Œ¡(–)+ Ì Ì' ÖŒ¡'–Ü=0 (3) ¡( =− ℎ(# 1 Í 2 ÍÍ 7> Ì Ì 1 ( (4) ¡' =− ℎ'# 1 Í 2 Í 7 Í> Ì Ì N 1 (5) Where: ρ = Gas density
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