Objectives  Ships may encounter accidents such as collisions, groundings, and reef impacts during navigation, which can lead to hull damage and flooding, thereby significantly reducing buoyancy and stability. Under wind and wave conditions, a damaged ship's resistance to sinking is a crucial to its survivability assessment. Traditional methods evaluate the dynamic stability of ships in wind and waves by analyzing resonance angles to quantify wave effects. These methods are limited in their ability to assess the survivability and resistance to sinking of damaged ships under real-world conditions. Therefore, this study aims to develop a more comprehensive and accurate method for evaluating the dynamic stability of damaged ships under wind and wave conditions, providing a reliable reference for enhancing their survivability and safety.

Methods Firstly, the DTMB 5415 standard ship model was selected as the test case, and its static stability parameters were calculated under typical damage conditions. Then, a single-degree-of-freedom roll motion equation for the damaged ship under the combined action of wind and waves was constructed. The CFD method was used to obtain the roll damping coefficient, which is of great significance for accurately calculating the roll motion response. Subsequently, a numerical method was employed to calculate the roll motion response of the damaged ship under wind and wave conditions. Finally, the Monte Carlo method and the Gumbel method were combined.

Results The results show that the proposed method takes into account the effects of wave parameters such as significant wave height and wave period on the dynamic stability of damaged ships. It was found that the wave period has a significant impact on the extreme roll motion response distribution. When the wave period approaches the natural roll period of the damaged ship, the roll motion response reaches its peak. In contrast, traditional methods based on the limiting dynamic heel angle fail to fully consider this factor. Calculations and comparisons reveal that the limiting dynamic heel angles under various wind and wave conditions are considerably greater than the extreme roll motion responses of damaged ships. This indicates that traditional methods may lead to conservative calculation results and underestimate the ability of damaged ships to withstand sudden wind-induced heeling.

Conclusions The study shows that the extreme roll motion response of damaged ships under the combined action of wind and waves follows a Gumbel distribution. The Gumbel method can effectively predict this distribution. The proposed dynamic stability assessment method, which incorporates wave parameters, offers a more comprehensive evaluation than traditional methods. It is applicable not only to the dynamic stability assessment of damaged ships but also to that of intact ships, providing an important reference for ship stability assessment, which helps to improve the accuracy of ship stability evaluation and enhance the ship safety in complex sea conditions.