Abstract:
Objectives This study aims to calculate and analyze the capsizing probabilities of damaged vessels in beam seas under dead ship conditions with varying significant wave heights and wave characteristic periods based on direct counting method and dynamic model and then proceed to improving the current conservative estimation method based on residual stability parameters in damaged vessel stability assessment regulations. Methods The dynamic model incorporates the coupled "wave-ship-floodwater" interactions. Wave-ship coupling involves calculating nonlinear restoring forces and Froude-Krylov forces through instantaneous wet surface pressure integration. Radiation and diffraction forces are computed using the STF method combined with impulse response functions, while experimentally derived roll damping coefficients are incorporated to address viscous effects. The wave-floodwater coupling effect is taken into account through the modified Bernoulli equations that determine water inflow/outflow rates at damaged breaches. The ship-floodwater coupling effect is considered by employing the lumped mass method to simulate sloshing forces of floodwater. Hydrostatic pressure induced by flooding is evaluated via instantaneous wet surface pressure integration. The viscous dissipation effects are approximated using semi-empirical formulas. The direct counting method, adhering to International Maritime Organization (IMO) guidelines, quantifies capsizing probability through time-dependent marginal probability functions. Results The model is applied to the benchmark damaged vessel DTMB 5415 for roll motion response and capsizing probability calculations. Key findings include: 1) The dynamic model which predicts roll motion responses shows relative errors within 20% compared to experimental results in the vicinity of the period corresponding to the peak response. 2) The 30-minute capsizing probability increases with significant wave height, reaching the maximum value when the wave characteristic period approached the natural roll period of the damaged vessel. Conclusions The proposed methodology provides objective and accurate capsizing probability predictions for damaged vessels in beam seas, demonstrating significant improvements over conventional residual stability-based approaches.