Study on ultimate strength reliability and calibration of partial safety factors for CSR ships under new IACS Rec. 34 Rev. 2 wave environment

Objective This study investigates the impact of the updated ocean wave data, IACS Rec. 34 Rev. 2 (2022), on the reliability of hull girder ultimate strength and its corresponding partial safety factors.

Method A database comprising 36 CSR sample ships, including bulk carriers and oil tankers, was established. Based on the IACS Rec. No. 34 Rev. 2 wave data released in 2022, the statistical distributions of extreme significant wave heights and conditional periods were refitted to revise the extreme wave bending moment prediction formulas under the updated wave environment. On this basis, limit state equations were constructed within the hull girder ultimate strength reliability framework, establishing hull girder ultimate capacity, still-water bending moment, and vertical wave bending moment as key random variables, with their respective statistical characteristics derived from sample ship data. The Improved First-Order Second-Moment (IFOSM) method was then employed to compute and compare the failure probabilities (P_f) and reliability indices between the original and revised wave environments, thereby determining the target failure probability. Finally, based on the least-error indicator method and target reliability, the partial safety factor for vertical wave bending moment (γ_W) was optimized and calibrated across various operational conditions, followed by a comprehensive sensitivity analysis of the optimized values.

Results Compared with the original wave environment (Corr. 1), the sea state distribution under Rev. 2 is more centralized, with the overall mean of significant wave height increasing by 0.151 m, while the standard deviation shows a trend of initial increase followed by a decrease with respect to wave height. The failure probabilities of hull girders under Rev. 2 are consistently lower than those under Corr. 1, with an average reduction of 5×10⁻⁴ across both hogging and sagging conditions for all sample ships. Under Rev. 2, the rate of change in the partial safety factors for ultimate capacity (γ_R) and still-water bending moment (γ_S) is significantly smaller than that for vertical wave bending moment, with average percentage increases of 0.21% and 1.92% for γ_R and γ_S, respectively, whereas γ_W exhibits an average reduction of 10.13%. For oil tankers under the sagging condition and all sample ships across all operational conditions, the optimized values of γ_W under Rev. 2 are 1.243 and 1.113, representing decreases of 0.137 and 0.124 compared to Corr. 1, respectively. Furthermore, a strong linear correlation is observed between the optimized γ_W and the target reliability index across both wave environments (fitting slope k ≈ 0.38), displaying low sensitivity to variations in the target failure probability.

Conclusion These findings provide a quantitative reference for updating ship structural design standards and calibrating safety factors under the latest ocean wave environment.