Failure Probability Analysis Techniques for Long Mooring Lines

ABSTRACT This paper describes statistical techniques for analyzing failure probabilities of long mooring lines. The long line is treated as a series of segments, each as long as the break or fatigue test specimens. Termination failure statistics are treated separately. The analysis techniques are applicable to mooring lines comprised of chain, Wire, or fiber rope. They are also appropriate for long electrical and control cables, hoses, and umbilicals. Examples are given to illustrate the techniques. INTRODUCTION There is much interest in assessing the reliability of deepwater mooring systems.! Mooring lines are typically much longer than the short test specimens used in determining breakmg strength and fatigue life statistics. For example, each ofseveral mooring lines used on a floating platform in deep water might be over 1000 m (3000 ft) long, but the specimens used m break and fatigue testing might only be 10 m (30 ft) long., This paper addresses problems in relating break and fatigue test .data obtained from tests on short specimens to the reliability of the same type of line in very long lengths. It includes the effects of terminations with different statisticalproperties than the body of the line. . "A chain is. only as strong as it's weakest link". For simplicity chain will be used as a model in this paper. The technique s also apply to wire and fiber ropes, in which performance IS determined from tests on short specimens and the ropes used in service are much longer. "Short rope" can be substituted for 'link', and long rope" can be substituted for 'chain' throughout this paper. Here the word termination means any component or method used to connect parts of the mooring line together or to connect the entire mooring line to a vessel or an anchor. Examples include chain connector links shackles and splices in wire or fiber rope. " The probability of failure at any given load increases as the total line length and the number of terminations increase. Of course. It also depends on the mean strength and the strength variability of these components. If sufficient statistical data for the components are available, the analysis techniques described m this paper can be used to design a system with an acceptable risk of failure. The prediction of reliability for a length of chain based on the statistics of individual links is first considered. The effects of terminations on the reliability of this length of chain areintroduced later. STATISTICAL CONCEPTS The Chain Link Model A theoretical chain comprised of individual links is shown in Figure la. It is analogous to a long length of chain made upof shorter lengths equivalent to the test specimen length, as shown in Figure lb. It is also analogous to a long length of rope, again made up of shorter lengths equivalent to the test" specimen length, as shown in Figure lc. The breaking strength of the long chain can be determined from the strengths of individual links.