Encyclopedia of Ocean Engineering

Living Edition
| Editors: Weicheng Cui, Shixiao Fu, Zhiqiang Hu

Catenary Mooring

  • Hongwei WangEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-981-10-6963-5_145-1
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Synonyms

Introduction

Mooring systems have been around just as long as man has felt the need for anchoring a floating structure at sea. These systems were used, and are still used, on ships and consisted of one or more lines connected to the bow or stern of the ship. Generally, the ships stay moored for a short duration of time (days). When the exploration and production of oil and gas started offshore, a need for more permanent mooring systems became apparent. Due to the demand for marine resource development, a large number of new floating structures have been designed and constructed, and various mooring systems have been emerged over the years; the catenary mooring system is a common and traditional way of locating floating structures, and several pretension mooring lines are arrayed around the structure to hold it in the desired location (Fig. 1).
Fig. 1

The catenary mooring system of a semisubmersible platform. (From anchor manual 2005)

Definition

It gets its name from the shape of the free hanging line, one end of the mooring line is connected to the floating structure, and the other end is fixed at the anchor point of the seabed; the part that is suspended in the seawater will take a catenary shape, which is similar to the rope that is fixed at both ends and freely placed under the uniform force. The catenary forms can be seen everywhere in nature; when you wake up in the morning to see spider webs covered with water drops, when you see the ropes on the suspension bridge, and when you see the wires between the two poles, you know what kind of shape are they? The answer is the catenary. As early as 1690, Jacobi Bernoulli proposed the famous “catenary problem,” but it was not until Newton and Leibniz invented the calculus to get the correct answer. The catenary is a magical curve that has been used extensively in buildings, bridges, ship, and ocean platform moorings (Wren et al. 1989).

In marine engineering, spread catenary mooring systems and single-point catenary mooring systems are two common arrangements (Skop 1988). Mono-hull ship and semisubmersible platforms have traditionally been moored using a spread catenary mooring system, and the points are connected to different positions on the platform so that the platform cannot rotate freely, and the orientation of the platform remains basically unchanged. In some cases, excessive displacement caused by environmental forces may cause large loads on the mooring system. In order to overcome this drawback, a single-point mooring system has been developed which is characterized in that a plurality of mooring lines are connected at a point on the longitudinal centerline of the platform. The platform will have a wind vane effect to reduce the environmental loads caused by wind, current, and waves. Single-point moorings are used primarily for ship-shaped vessels. They allow the vessel to weather vane. This is necessary to minimize environmental loads on the ship-shaped vessel by heading into the prevailing weather (API 2005).

As can be seen from the above (Fig. 1), the catenary mooring system occupies a large range on the seabed, that is, the radius of influence of the mooring point will be large. In actual ocean engineering, the collision problem has to be considered with other structures, such as risers, conveyor cables, etc. At the seabed, the catenary mooring line lies horizontally, in general, which has a minimum length of 50 m; thus the mooring line has to be longer than the water depth, and the anchor points in a catenary mooring system only bear horizontal forces and are not subject to vertical forces (Fig. 2); the nonlinear restoring force generated by the catenary mooring system provides the positioning function of the floating platform and balances the environmental load acting on the water platform (Samad 2009). Meanwhile, as the water depth increases, the length and weight of the mooring line also increase rapidly, which not only increases the tension in the chain but also increases the vertical load on the floating structure, further reducing the payload capacity of the floating structure. In that case, synthetic ropes are used because of conventional catenary systems become less and less economical (Banfield and Flory 2009). That is to say, the catenary mooring system is suitable for relatively shallow waters (<1000 m).
Fig. 2

The catenary mooring line

Theoretical Analysis Methods

For the mooring line of the general floating structure, it is not completely consistent with the theoretical catenary due to its own tensile, bending, and sea flow forces. However, for the convenience of calculation and analysis, the catenary theory is still used to describe its preliminary analysis and ignore the influence of sea current and wave, which is static analysis. Figure 3 shows catenary mooring line and its two-dimensional diagram of the force. The angle j is the angle between the mooring line at the fairlead and the horizontal; a segment of arc microelement is selected from the catenary mooring line.
Fig. 3

Static analysis of catenary mooring line

Depending on the water depth, the weight of the mooring line, and the force applied to the mooring line at the fairlead, the length of the suspended mooring line S in [m] can be calculated with:
$$ S=\sqrt{d}\cdot \left(\frac{2\cdot F}{w}-d\right) $$
with
  • d: the water depth plus the distance between sea level and the fairlead in [m]

  • F: the force applied to the mooring line at the fairlead in [t]

  • S: the unit weight of the mooring line in water in [t/m]

The horizontal distance X in [m] between the fairlead and the touchdown point of the mooring line on the seabed can be calculated with:
$$ X=\left(\frac{F}{w}-d\right)\cdot \ln \left(\frac{S+\frac{F}{w}}{\frac{F}{w}-d}\right) $$
The weight of the suspended chain V in [t] is given by:
$$ V=w\cdot S $$
The vertical distance of a catenary mooring line is given by the function:
$$ y=-\frac{T_0}{w}\left[\cosh \left(\frac{wS}{T_0}\right)-1\right] $$
According to the above formula based on single-component mooring line, the shape and force of the catenary mooring line can be preliminarily calculated. However, mooring lines are usually composed of materials with many different properties, the calculation principle is the same, but the equations of the individual components need to be integrated. As for the dynamic analysis of mooring lines, the lumped mass method (Fig. 4) and the slender rod theory (Fig. 5) are commonly used. The lumped mass method is equivalent to simulating the slender structure into a series of lumped mass node systems connected by springs (Kato 1982). The finite difference method is used to solve the dynamic problem, which can simplify the analysis of the structure without losing accuracy. It has been widely used. The slender rod theory applies the overall coordinates and slope and establishes the governing equations of the mooring line under tensile deformation and bending deformation (Webster et al. 2012; Ma et al. 2015). The finite element method is used to solve the dynamic problem. Its main advantage is that the nonlinear governing equations can be performed in the global coordinate system without coordinate system transformation. In comparison of the two methods, the equation computational speed of the former is faster, but the accuracy is smaller than the latter.
Fig. 4

The lumped mass method. (Image by MIT OpenCourseWare)

Fig. 5

The slender rod theory

Composition Materials

The abovementioned mooring line can be composed of a single component material or a combination of multiple components on the basis of different needs. The most common product used for mooring lines is chain which is available in different diameters and grades. Although the steel chain is resistant to abrasion and is not easily damaged, the quality is high and the cost is high. Since the deep water mooring system has strict weight restrictions, the full chain system is generally not used. When compared to chain, wire rope has a lower weight than chain, for the same breaking load and a higher elasticity. The most common combination method is three components: top chain + steel cable + bottom chain. The use of multicomponent mooring lines needs to focus on the length and diameter of each component and the choice of buoys or weights. In this way, the top and bottom chains prevent damage to the top mooring line from long-term friction of the fairlead and subsea portion as well as undulating collisions (Smith and Macfarlane 2001).

Selection of Anchors

The restoring force of the catenary mooring line is mainly caused by its own weight. The bottom of the mooring line usually has sufficient length to contact the sea floor even if the floating structure system is in the worst sea conditions. Therefore, the seabed anchor is only subjected to horizontal forces and does not bear vertical forces (Fig. 2). Drag embedment anchors (Fig. 6) are then employed to resist the horizontal loads, but not for large vertical loads; this is the most popular type of anchoring point available today. The drag embedment anchor has been designed to penetrate into the seabed, either partly or fully, and its holding capacity is generated by the resistance of the soil in front of the anchor (Ruinen and Degenkamp 2001).
Fig. 6

Drag embedment anchor. (From anchor manual 2005)

Development and Challenges

In general, the traditional catenary mooring positioning system occupies an important position in the mooring positioning system of the mobile platform. However, the influencing factors to be considered in deep-water mooring systems are more complicated than those in shallow water, and their research needs more attention and consideration. On the one hand, the traditional steel anchor chain and wire rope system, with the increase of water depth, its self-weight increases, and horizontal stiffness decreases sharply, while the weight increase leads to the increase of the cost, and it will also cause the multifaceted impact about deployment and recovery of the mooring system. On the other hand, the new concept and new materials for the deep-water mooring system are continuously developed. For example, polyester ropes with light weight and high strength and weight ratio have replaced steel cables in some cases. The application of the new material can not only reduce the weight of the mooring system, but also its mechanical properties are improved to suit deep water. The lightweight catenary mooring system developed in recent years overcomes many shortcomings of the traditional catenary mooring system in deep sea mooring, but neither the lightweight catenary line nor the traditional can’t overcome the excessive deviation of the horizontal level under sea conditions; the greater the water depth, the more obvious this shortcoming. In addition, the use of such mooring systems in deep water requires a large number of mooring lines of larger diameter, which can take up a lot of space on the installation vessel. There are many problems that need to be solved, and the effectiveness and economy of the multiple component systems also need further study.

Cross-References

References

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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Harbin Engineering UniversityHarbinChina

Section editors and affiliations

  • Liping Sun
    • 1
  1. 1.College of Shipbuilding and Ocean EngineeringHarbin Engineering UniversityHarbinChina