An improved method for calculating near-field shock wave loads of underwater explosions

To address the limitations of traditional segmented empirical formulas for underwater explosion shock wave loads, namely, insufficient near-field accuracy and physical discontinuities at partition boundaries, this paper establishes an improved unified continuous calculation model for near-field shock wave loads based on the Chapman-Jouguet (CJ) detonation model, post-shock approximate isentropic flow assumption, and Kirkwood-Bethe (K-B) theory. By introducing the K-B equation in the form of second-order Mach accuracy and an improved pressure attenuation time constant, the theoretical application range is extended to the dimensionless detonation distance of 2 to 20, eliminating the discontinuities inherent in conventional piecewise approximations. The model is validated against multi-scale spherical charge tests, unified bubble dynamics high-fidelity theory, Arbitrary Lagrangian-Eulerian (ALE) numerical simulation, and classical empirical formulas, with the peak pressure calculation error controlled within 10 % and the accuracy of impulse and energy flux significantly superior to Cole’s empirical formula. Calculation results show that the peak pressure and energy flux of the shock wave rapidly and nonlinearly decay in the near field, while the decay rate decreases markedly in the middle and far fields. In the near field (2-10 charge radii), geometric diffusion contributes approximately 89 % to the peak pressure attenuation, and the energy flux decay is almost entirely dominated by geometric diffusion. The impulse decays slowly with detonation distance at a rate much lower than that of the peak pressure. The systematic overestimation of impulse and energy flux by Cole’s formula in the middle and far fields stems from its constant time constant assumption, which neglects the unsteady nature of bubble expansion. The proposed model possesses both analytical efficiency and numerical accuracy, providing an effective theoretical tool for underwater weapon warhead design and ship anti-blast protection.