Dimensional analysis and scalability of a simplified hull girder subjected to underwater explosion shock loading

Conducting full-scale experiments on naval structures subjected to underwater explosions (UNDEX) is generally impractical, leading to the employment of small-scale models. This requires the existence of scaling laws that relate the behaviour of the full-scale structure to the prototype. However, the derivation of scaling laws for impact problems is hindered by the distortion induced by strain rate effects, and scholars in the last 20 years have focused on developing correction methodologies. However, their application to naval structures remains unexplored. This work examines the interaction between the primary shock of a UNDEX and the structural response, focusing on the scalability of a steel Simplified Hull Girder (SHG). The investigation is based on numerical simulations carried out using the Coupled Eulerian–Lagrangian framework, and is demonstrated against an experimentally validated case study. In the selected scenario, the SHG prototype undergoes hogging damage. The response of small-scale models with scaling factors of 1/2, 1/10, 1/20, 1/50, 1/80, and 1/100 is investigated, revealing distortions caused by strain rate effects. A correction strategy based on the joint or exclusive modification of the explosive mass and the material’s static yield strength is employed to compensate for these effects, yielding satisfactory results. Unlike existing studies, which often focus on single damaged configurations, this work emphasises the time-dependent structural response, analysing the hogging motion of the SHG and the influence of the correction strategy over time. The proposed approach demonstrates the effectiveness of the correction procedure in the largely unexplored naval domain and contributes to the development of general scaling laws for structural impact problems. • Scaling laws for underwater explosion shocks on hull girders are analysed. • Numerical small-scale models are developed using a validated numerical prototype. • Strain rate effects are corrected via explosive mass and material yield strength. • Structural response is studied over time, beyond single damage states. • Results extend scaling law corrections to naval structures under shock loads.