Impulse-based discrete element modelling of rock impact and fragmentation, with applications to block cave mining

Impulse-based methods efficiently and accurately model high-frequency collisions of complex shapes based on the enforcement of non-penetrating constraints. It does not rely on penalty parameters nor requires the computation of penetration between bodies. This work presents a novel necessary condition for energy conservation in impulse-based methods. In previous versions of the impulse methods, such as sequential and simultaneous impulse methods, the relative velocity at the contact points after collision is directly derived from the relative velocity before collision, in a purely simultaneous or sequential manner. This work presents a novel energy tracking method (ETM), in which the relative velocities are iteratively but gradually adjusted, simultaneously modelling their interaction at each iteration. ETM ensures the energy conservation while capturing the propagation of forces during collision. The ETM is applied to model the dynamics of fragment collision in the context of fragmentation. Two approaches of fragmentation are proposed: a finite-discrete element approach, and a low cost, fragmentation pattern-based approach. The first approach models the growth of fractures using the finite element method (FEM) and advanced re-meshing technology. This finite-discrete element approach suffers from the drawback of massive computational cost. The low-cost, fragmentation pattern-based approach separate colliding bodies directly. The fragmentation pattern is generated using Weibull distribution equations, the patterns and size distributions computed using full finite/discrete element simulations and experimental results. This work investigates the influence of fragmentation on the frequency of hang-up events and on the gravity flow of rock fragments within a block caving system. Numerical results indicate that models that do not consider fragmentation tend to overestimate the frequency of hang-up accidents.