The application of debris and fragment throw models in risk assessment methodologies

The throw of debris and fragments is often a dominant effect in explosion events. Models to quantify this effect are therefore of great importance for consequence analysis and risk assessment methodologies. Recently much effort has been expended to develop throw models related to detonations in reinforced concrete ammunition magazines (Klotz Group Engineering Tool and Software), and stacks of ammunition shells (stack fragment throw model). These models are currently being further developed by using/including new test results and insights. At the same time attention is given to the implementation of these models in risk assessment methodologies. This is the subject of the current paper.
Model predictions typically involve large numbers of numerical trajectory calculations. The initial conditions for these calculations are related to the distributions of projectile mass, velocity and angle. For risk assessment purposes it is necessary to limit the calculation time for an explosive event, since many so-called ‘donors’ have to be taken into account.
Dependent on the regime various simplifications can be applied. One of these simplifications is the horizontal drag approximation, an approximation to the equations of motion which is valid for wall debris with up to moderate launch velocities. Besides possibilities for efficient calculation, this approximation also provides the physical explanation for the scaling of existing QD-relations. Results, using this simplification have been compared to experimental data.
The recently developed throw models predict the projectile density in a horizontal plane, to enable direct comparison with pick-up test data. For risk assessment however, the number of hits at persons and structures is relevant. Different approaches to quantify these numbers are discussed in the paper.