An empirical method for modelling the secondary shock from high explosives in the far-field

As the detonation product cloud from a high explosive detonation expands, an arresting flow is generated at the interface between these products and the surrounding air. Eventually this flow forms an inward-travelling shock wave which coalesces at the origin and reflects outwards as a secondary shock. Whilst this feature is well known and often reported, there remains no established method for predicting the form and magnitude of the secondary shock. This paper details an empirical superposition method for modelling the secondary shock, based on the physical analogy of the secondary loading pulse resembling the blast load from a smaller explosive relative to the original. This so-called dummy charge mass is determined from 58 experimental tests using PE4, PE8, and PE10, utilising Monte Carlo sampling to account for experimental uncertainty, and is found to range between 3.2–4.9% of the original charge mass. A further 18 “unseen” datapoints are used to rigorously assess the performance of the new model, and it is found that reductions in mean absolute error of up to 40%, and typically 20%, are achieved compared to the standard model which neglects the secondary shock. Accuracy of the model is demonstrated across a comprehensive range of far-field scaled distances, giving a high degree of confidence in the new empirical method for modelling the secondary shock from high explosives.