SS: Fiber Moorings, Recent Experiences and Research: Fiber Rope Mooring Assessment - Original API RP 2SM Piecewise Linear Stiffness versus Non-linear Stiffness with Integrated Permanent Rope Elongation
Authors: Zimmerman Evan H. , Garrity Robert 
Published: July 2010

Abstract
This paper provides a comparison of the performance of fiber rope mooring systems when assessed with the original API RP 2SM 1st Edition recommended method of modeling EA (Young's Modulus × Cross Sectional Area) with an upper and lower bound linear fiber rope stiffness as compared to modeling the true non-linear stiffness behavior exhibited by fiber ropes. API RP 2SM 1st Edition recommended modeling the stiffness of fiber ropes via an upper and lower bound method - a linear Post Installation stiffness and a linear Storm stiffness. The second edition of the document addresses stiffness behavior under near static loading, low frequency dynamic loads, and wave (high) frequency dynamic loads which provides information to capture the true non-linear stiffness behavior of fiber ropes with non-recoverable elongation. Both stiffness models are analyzed for a truss SPAR and the results are compared showing the difference between the two stiffness models.
Additionally, the assessment will capture permanent or non-recoverable rope elongation due to a hurricane event and its impact on mooring system performance. Accurate estimates of permanent elongation are also important for length management issues, especially for permanently moored facilities.

Introduction
Fiber mooring ropes have non-linear stiffness characteristics which generally increase based on their mean load. To most accurately analyze a mooring system it is important to model the fiber mooring rope with its true non-linear stiffness and separate out the permanent non-recoverable elongation. Considerable thought must be given to testing the fiber rope properly so that true stiffness values and accurate non-recoverable elongation based on mean loading can be captured.
Original fiber mooring designs utilized an upper and lower bound stiffness method which essentially linearized the stiffness of the rope in a mooring analysis. This practice allowed the designer to utilize commercial software with little or no modification to their analysis method. Prudent designers have been able to utilize high enough upper bound linear stiffness values to get a good estimate of peak mooring line tensions while also finding a suitable lower bound stiffness which can capture the maximum vessel offsets.
The analysis method described in this paper utilizes a true non-linear stiffness model that also accounts for the frequency of loading oscillations. The method also accounts for permanent non-recoverable elongation of the fiber rope which allows the designer to analyze how much longer each line would be after a given metocean event. It is common for permanently moored facilities with fiber mooring lines to have to re-tension after a significant storm event to get back to their design location and operating tensions. This is due to the fact that the storm event will permanently change the lengths of the fiber ropes dependant on what their individual loading was during the storm.
By modeling the true non-linear stiffness and being able to capture the permanent non-recoverable elongation of fiber mooring ropes in a mooring analysis, the designer can more accurately assess the vessel motions during a storm event and more effectively plan component lengths such that re-tensioning operations will not significantly impact the facility's ability to operate. Such accurate vessel motions and offsets from this analysis method would also aid greatly in the riser and other system designs that are integral parts of permanently moored facilities.