Mooring System Calibration of the Damaged Condition, Accidental Limit State (ALS)
Authors: Hørte Torfinn , Okkenhaug Siril , Paulshus Øivind 
Published: October 2017

Structural reliability analysis (SRA) has been used to calculate the probability of two adjacent mooring line failures. The initial failure is caused by some exceptional causes which most likely is related to substandard strength, but could also be exceptionally high tension caused by mal operation. Empirical failure data are used to assess the probability of initial failure. The ALS in the context here should control the probability a second mooring line failure with ordinary strength, adjacent to the initial failure of a weak substandard line. This check is also called the ULS redundancy check in ISO 19901-7. A range of different units have been considered, comprising ship shaped units and semisubmersibles at different water depths from 100 m to 2200 m. Environmental conditions representative for the Norwegian continental shelf and the Gulf of Mexico are used in the analyses, and the characteristics of the results in the different environments are compared and discussed. Analyses for Brazilian environment are currently ongoing, but not included here.
Considerations for when the initial failure occurs have been made, and three different time intervals are considered: i) Failure of the second line during the transient motion after first failure, ii) failure of both lines in the same storm and iii) failure of the second line during stationary conditions after the initial failure. Time interval ii) is identified as most critical, when there is practically no time to implement mitigating actions. Detailed SRA analyses have been carried out, and include the concept of having a weak line in the system that represents the first failure. It was found that weak lines, with strength distributions that are consistent with the empirical probability of line failure, are too weak to contribute significantly to reduce the probability of the 2nd line failure of an ordinary line. The probability of the combined event of 2 line failure can therefore be simplified and set equal to the product of the probability of the presence of a weak line and the probability of 2nd line failure of an ordinary line in a system with one line missing.
Time domain analysis is applied to obtain the short-term, extreme value distribution of line tension in the most loaded line after one line is removed from the mooring system. A large number of different metocean conditions are considered. A response surface is used to interpolate on the distribution parameters to describe the tension response in varying conditions. Joint probabilistic models of the metocean environment corresponding to the different geographical locations have been applied, taking account of wind, wave and current and their respective heading angles. The mooring line component strength is based on strength data from break load tests. Conventional catenary chain-wire chain systems as well as polyester moorings are considered.
The probability of failure, conditional on the initial failure, is calculated using SRA. Calibration of safety factors are provided for different reliability levels, and for different assumptions for the probability of the presence of a weak line. It is demonstrated how the ALS criterion can be relaxed if the frequency of initial line failures due to exceptional causes is reduced. The final recommendations on target reliability level and on the probability of having a weak line in the mooring system are given in a companion paper at OMAE 2017, which comprises both the ULS and the ALS. It is demonstrated that alternative design formats can provide a more consistent safety level across the cases. A different design philosophy is needed the Gulf of Mexico to achieve acceptable risk, and options are discussed.
This paper is the second one in a series of three at OMAE 2017, where the first one deals with structural reliability analysis of the ULS and the third one provides summary and recommendations for safe mooring design in ULS and ALS.