Spherical equivalence of cylindrical explosives: Effect of charge shape on deflection of blast-loaded plates

Quantification of near-field blast loading is a pressing issue for defence, transport security, and structural engineering. Realistic explosion scenarios often involve the detonation of non-spherical high explosive charges, rather than the idealised spherical/hemispherical explosives assumed in commonly employed semi-empirical approaches. Additionally, near-field effects are of great importance when assessing structural damage and injury risk from such an event. There is a need, therefore, to incorporate the effects of charge shape and the resulting loading distribution in simplified engineering-level tools using adjustments based on sound physical principles. This article details the development of an energy equivalent formulation to derive spherical equivalence factors, with the methodology illustrated for the scenario of a centrally detonated cylindrical explosive charge. A validated two-part numerical model is used to generate specific impulse distributions and quantify the resulting plate deformation , for a wide range of cylindrical aspect ratios (0.20 ≤ L/D ≤ 5), at a range of near-field scaled distances (0.108 ≤ Z ≤ 0.485 m/kg 1/3) for different sized structural targets. A series of verification examples are used to demonstrate the accuracy of the method, with the peak deflection under the equivalent spherical charge matching peak deflection under the cylindrical charge to within ∼4%. The method developed in this article could be extended to find equivalence between any two systems with complex distributed loading, allowing for a fast running engineering approximation in cases where detailed modelling is inappropriate or infeasible.