Table of Contents:

• INTRODUCTION
• METHOD OF ATTACK
• COMPARABLE SYSTEMS
• TWO-POINT MOORINGS
• MULTI-POINT MOORINGS
• EFFECT OF STIFFNESS
• POLYESTER ROPE

I. INTRODUCTION:

There are two primary conclusions which can be drawn from this study:

• An optimal Kevlar-chain mooring system will provide substantially more restoring force than a wire-chain system, and the difference in restoring force increases with water depth (from a factor of 1.28 at 1000 feet, to 1.64 at 3500 feet). The length of Kevlar required for the optimal system is substantially greater than the length of wire required for the optimal wire system.
• If a Kevlar-chain and a wire-chain mooring system produce the same restoring force, the Kevlar system will be shorter.

Thus, the use of Kevlar can be beneficial in two ways: either more Kevlar than wire can be used to obtain more restoring force than is possible with wire, or less Kevlar than wire can be used to obtain the same restoring force.

Below, in Section II, the basic approach of the study is outlined, while in Section III, the various systems considered are discussed. Section III contains the primary results of the study, the analysis of various two-point mooring systems. Section IV contains the results for some eight-point mooring systems.

II. METHOD OF ATTACK:

The criteria by which mooring system performance is, in general, measured is the ability to restrain the vessel in a given environment without any of the lines becoming overloaded. To be more specific, two cases must be considered: 1.) Operational and 2.) Survival. During the operational condition, the vessel is connected to the ocean floor by the riser, and hence the excursion must be limited. For the survival condition, the riser is disconnected, and thus, there is no limit on the allowable excursion. In both cases, the tension in the mooring lines should not become excessive, and the anchor should not slip.

As one can see from the above constraints, the design, or assessment of a mooring system depends on many variables, and hence, is quite complex. To further complicate the issue, the problem here is to compare the performance of Kevlar rope with wire rope over numerous water depths, and for numerous difference rope-chain combinations. To minimize the number of variables considered, the following strategy was adopted:

• Use water depth and chain length as independent variables.
• For fixed values of water depth and chain length, find the length of ropes required to produce a given horizontal force at the point when the anchor first experiences uplift.
• Find the restoring force vs. excursion curve for a two-point mooring system composed of both wire and Kevlar rope combinations, both pretensioned so that at an excursion of 6% of the water depth, the most heavily loaded line will have a tension of 1/2 the breaking strength.
• Design a wire rope-chain mooring system and a Kevlar rope-chain mooring system for the same vessel.
• Compare the performance of the two systems as the environment which acts on the vessel varies.

The primary idea behind the above strategy was to find steel rope and Kevlar rope combinations which were "comparable", i.e., both the Kevlar rope-chain system and the steel rope-chain system will fail at the same time. This explains the rather circuitous methods of finding the length of rope to use in the combinations and of choosing the pretensions. If equal lengths of Kevlar and steel were used, the Kevlar could not reach 1/2 of its breaking strength without pulling out the anchor. Also, if equal pretensions were used, the Kevlar system would reach 1/2 of its breaking strength with less excursion than the steel system.

III. COMPARABLE SYSTEMS:

The various systems considered were all composed of 3 1/2 inch Kevlar, 3 1/2 inch wire rope, or 4 1/4 inch wire rope and 3 inch chain. The 3 1/2 inch ropes were chosen because they have about the same breaking strength, approximately 1000 kips. This breaking strength is also a good match with 40 kip anchors, since it is commonly assumed that the holding power of these anchors is 400 kips. Thus, systems composed of 3 inch chain, 40 kip anchors, and either 3 1/2 inch wire rope or 3 1/2 inch Kevlar rope can sustain a tension of 400 kips (or 1/2 the breaking strength) without anchor slippage, provided there is no vertical pull on the anchor commenced at a horizontal force of 420 kips. The result is a mooring system which is consistently designed. Notice also that, for the systems chosen, the anchor will slip before it pulls out, and the anchor will pull out before the line breaks, which is the desired sequence.

Since the predominant difference between the 3 1/2 inch wire and 3 1/2 inch Kevlar ropes was weight, the 4 1/4 inch wire rope was considered so that the effect of weight could be more adequately assessed. Figures 1 - 6 show the lengths of rope which must be combined with 3 inch chain to have impending uplift on the anchor at 420 kips of horizontal force. Figures 1 - 3 are plots of length of rope vs length of chain for depths of 3500 feet, 2400 feet, and 1600 feet. Figures 4 - 6 are plots of rope length vs depth for chain lengths of 1400, 2000, and 3000 feet. For comparison, the dashed lines in Figures 4 - 6 show the amount of chain required to meet the criteria. Figures 4 - 6 are particularly interesting, since they show most explicitly the effect of the weight of the top segment of a combination. Notice that as the weight of the top segment is decreased, the curvature of the curves lessens. This shows that the catenary effect of the top segment becomes less important. In fact, since the curve for Kevlar is a line, these figures show that, for a Kevlar system, the Kevlar will be essentially straight down to the chain.

IV. TWO-POINT MOORINGS:

Since many of the features of a mooring system are exhibited by a simple two-point mooring system, a detailed investigation of the restoring force for two-point systems composed of various rope-chain combinations was carried out. For these results, it was assumed that this was an operational condition, and hence, the lines were pretensioned to limit the excursion to 6% of the water depth.

Figures 7 - 9 show the restoring force produced by the two-point systems, at an excursion equal to 6% of the water depth as a function of water depth. All the lines are comparable in that they all have length of rope so that vertical uplift on the anchor will start when the line has a horizontal force of 430 kips. The three figures correspond to lengths of chain of 1400, 2000, and 2600 feet respectively. These figures show that all the Kevlar systems produce greater restoring force than either of the wire systems, and that the difference increases with water depth. It can also be seen that the restoring force depends on the length of chain used.

A better idea of why the Kevlar lines produce a greater restoring force than the wire systems can be seen by comparing Figures 10 and 11. These figures show the Tension, Restoring Force, and Vertical Pull on the anchor for comparable Kevlar and wire systems. For the wire system (Figure 11), the tension increase gradually in comparison to the Kevlar system (Figure 10). Thus, the pretension required to produce a tension of 400 kips at an excursion of 6% of the water depth is substantially greater for the wire combinations. The important fact, however, is that the restoring force is obtained by the resultant of tightening one line and slackening another. Since the tension in the Kevlar system changes more rapidly, the restoring force will be greater. The result is that Kevlar-chain mooring systems can work at a lower pretension and produce a substantial increase in restoring force. This increase, however, was achieved by using Kevlar rope lengths which were substantially greater than the wire rope lengths.

Up until now, all the systems which have been considered have been comparable in that they all have vertical pull on the anchor at the same point. Since the Kevlar rope combinations produce greater restoring force at the same tension, it is reasonable to consider shorter lengths of Kevlar. Figure 12 shows the results for a two-point mooring system with 7300 feet of Kevlar and 1400 feet of chain in 3500 feet of water. Notice that the systems considered in Figures 10 and 11 have 12,000 feet of Kevlar and 8300 feet of wire respectively. For this system, the pretension condition is, however, different. Here, the pretensions were set so that there was vertical pull on the anchor at an excursion of 6% of the water depth. A comparison of the restoring force for these three systems is shown in Figure 13. Notice that even with a length of Kevlar shorter than the wire rope, the lines can be pretensioned so that the Kevlar system produces more restoring force.

The fact that a shorter length of Kevlar can safely produce a greater restoring force than the wire rope led to the question of what length of Kevlar is needed to produce a restoring force equal to the 3 1/2 inch wire rope. This question is addressed in Figures 14 - 16. As can be seen in these figures, the use of Kevlar instead of wire rope can result in up to 50% less rope being required to produce the same restoring force. Again, the beneficial effect of Kevlar increases with water depth.

V. MULTI-POINT MOORINGS:

To see how the results of the two-point mooring systems can be used to predict the behavior of an eight-point mooring system, a vessel with both Kevlar and wire mooring systems was analyzed for several cases. The vessel considered was 362 feet long, with a 70 foot beam, and a draft of 17 feet. The mooring system was an eight-point system with two breast lines and two quarter lines at 45 degrees on each side of the vessel. Both the Kevlar and the wire systems contained 2600 feet of chain, and rope lengths given by Figures 1 - 3.

These models were subjected to various environmental conditions, and the results for all weather abeam are shown in Figure 17, where the maximum line tension / 400 kips is plotted vs wave height. Again, the Kevlar system's performance is superior to that of the wire system's, and the difference increases with depth. While they are not plotted, the results for head and quartering weather follow similar patterns.

VI. EFFECT OF STIFFNESS:

In order to assess the effect of rope construction on mooring performance, a series of runs were made in which the AE of the rope was varied. In particular, a two-point Kevlar-chain system was considered for depths of 1600, 2400, and 3500 feet. The length of chain was 2600 feet and the lengths of Kevlar were chosen from Figure 6. Restoring Force vs Excursion curves were generated for the above systems with a longitudinal stiffness of 30 X 10\6 and 83 X 10\6. In all runs, the lines were pretensioned so that a tension of 400 kips was experienced at an excursion of 6% of the water depth. The results were:

       DEPTH           RESTORING FORCE         RESTORING FORCE
       (FEET)            AT 6% FOR               AT 6% FOR
       ------            AEE = 30E6               AE = 83E6
                    ---------------         ---------------
       1600              277 kips                  282 kips
       2400              314 kips                  323 kips
       3500              342 kips                  343 kips

As can be seen, this change in stiffness produces little change in mooring performance.

VII. POLYESTER ROPE:

A comparison of the mooring performance of polyester rope with Kevlar rope was also made. The particular comparison was for comparable rope-chain systems with 2600 feet of 3 inch chain. The length of 6 inch polyester rope required in addition to 2600 feet of chain was computed as a function of water depth. The restoring force in these systems as a function of depth is shown in Figure 18. Notice that for shallower water, the polyester behaves like wire, while for deeper water, it performs somewhat better. Since, however, its weight is over twice that of Kevlar, its performance is not as good.