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A quasistatic analysis and sensitivity investigation of two different mooring configurations—a single anchor leg mooring (SALM) and a threelegged catenary anchor leg system (CALM)—is presented. The analysis aims to indicate what can be expected in terms of requirements for the mooring system size and stiffness. The two mooring systems were designed for the same reference load case, corresponding to a horizontal design load at the wave energy converter (WEC) of 2000 kN and a water depth of 30 m. This reference scenario seems to be representative for large WECs operating in intermediate water depths, such as Weptos, Wave Dragon and many others, including reasonable design safety factors. Around this reference scenario, the main influential parameters were modified in order to investigate their impact on the specifications of the mooring system, e.g. the water depth, the horizontal design load, and a mooring design parameter.
The mooring system is a vital part of offshore wave energy converters (WEC) as it is responsible for the stationkeeping of the WEC, but it counts as well for a significant part of the overall cost of the device [
This document presents a quasistatic analysis for an ultimate limit state (
An ultimate limit state (ULS) corresponds to the design criteria where the individual components of the mooring system have adequate strength to withstand the maximum environmental loads [
The design of the mooring system for wave energy converters can be performed under consequence class 1 [
In the case that a system does not provide any redundancy, the safety factor is multiplied by a factor of 1.2. Depending on the type of inspection, the corrosion allowance referring to the chain diameter of a suspended catenary chain is 0.2 or 0.3 mm/year.
The SALM system was first developed for the mooring and loading of large tankers offshore in severe environments and was first used in 1969 [
Spread moorings using catenary lines are commonly used for semisubmersible structures in shallow water. The restoring force from a catenary system comes from the suspended weight of the mooring lines, which changes in configuration with the excursion of the WEC. The mooring lines of the catenary system terminate at the seabed horizontally, which means that the anchor point is only subjected to horizontal forces. This results in relatively long mooring lines compared to the water depth.
This CALM system consists of three catenary mooring lines (spaced 120 degrees apart), three anchors, an intermediate buoy, and a hawser connecting the buoy to the WEC (see
Illustration of the threelegged catenary anchor leg mooring (CALM) system configuration.
Some design criteria are respected:
The length of the mooring lines was calculated such that the anchors are not exposed to vertical forces from the mooring lines.
The design load of all the mooring lines is set equal to the resulting tension in them under the design conditions.
The length of the hawser is 30 m.
The buoy volume was calculated so that its buoyancy force is equal to the combined force of its own weight, the vertical forces from the three mooring lines (combined
The horizontal pretension in the mooring lines was set to 20 kN, which corresponds to 1% of the maximum design load at the WEC.
The elasticity of the mooring lines is considered, while the following assumptions and approximations are made for the calculations:
There is no back mooring line considered.
The sea bed is horizontal.
There is no bending mooring stiffness in the chains.
Dynamic effects in the mooring lines are ignored.
Current forces resulting from the movement of the chains in the water and on the seabed are ignored.
Friction on the seabed is ignored.
Mooring lines have a constant weight per unit length.
The angle between the chains is assumed constant at 120 degrees (as the horizontal excursion is small relative to the length of the chains).
The environmental loads are in line with one of the three mooring lines.
The mooring lines are assumed to be connected to the buoy at mean water level.
The forces at the different locations and the length of the different components under different tensions, taking the elasticity of the mooring lines into account, can be derived from the following equations [8,9]. First, the horizontal design load (
The minimum unstretched length of the chain
From this, the maximum vertical force at the fairlead on the buoy can be found with
From here, the following steps need to be repeated to obtain the forcedisplacement curve. First, a value of
The resultant force at the fairlead is
Based on this, the length of the hanging part of the chain can be calculated by
The stretched length of
The stretched length of the lying part of the line (
Finally, the horizontal distance between the anchor and the buoy can be found using the stretched values of the lines with
The resulting distance between the buoy and the two other mooring lines can be obtained easily assuming that the angle between the lines remains at all times at 120 degrees. Thereby, the change in distance between the buoy and anchor B and C is half of the increase in distance between anchor A and the buoy.
The single anchor leg mooring (SALM) system, also referred to as a tension leg mooring system, consists of an anchor point, which in this case is a suction anchor, two mooring lines (a tether and a hawser) and a submerged buoy (see
Illustration of the single anchor leg mooring (SALM) system.
Some design criteria are respected:
The angle between the hawser and tether at maximum excursion of the WEC is equal to 160 degrees. Although angles up to 180 degrees are physically possible, the resulting horizontal force increases too exponentially after 160 degrees (illustrated in
The design load of the lines is set equal to the maximum resulting tension in them under the design condition.
The depth of the buoy at rest,
The length of the hawser is 30 m.
The volume of the buoy is calculated relative to the required buoyancy force to fulfill the specifications of the mooring system. The combined gravitational force of the system consists of the buoy’s own weight, the weight of the tether, half of the weight of the hawser and 250 kg for extra equipment.
The length of the tether is a result of the water depth, the submergence depth of the buoy at rest and the height of the connection on the seabed.
Some assumptions were taken into account:
There is no back mooring line considered.
Dynamic effects in the line are ignored.
Current forces resulting from the movement of the chain in the water and on the seabed are ignored.
The mooring line is assumed to be connected to the WEC at mean water level.
Overview of the force excursion and the mooring stiffness curve, together with the maximum admissible
The calculations related to the SALM system can be obtained through an iteration process and the various forces and angles in the system can mainly be obtained geometrically with the equations described below.
The elongation of the lines can be calculated with their elasticity (
The depth of the buoy, where
The force at the buoy is
The horizontal force at the WEC is
The angle between the second line and the mean water level (MWL) is
The overall tension at the WEC is
The environmental conditions and loads are chosen with the objective to be as generic as possible. Therefore, they were inspired from values that were obtained from tank testing of various large devices [10,11]. The parametric study will analyse some of the effect of these environmental conditions, around the reference load case, presented in
Overview of the specifications of the reference load case.
Unit  Symbol  Value  

Water depth  [m]  30  
Horizontal design load at the WEC  [kN]  2000 
Note that the mooring stiffness, also called the resulting horizontal compliance, indicates the rate of change in the horizontal mooring force for a given WEC excursion (similar to the derivative of the forcedisplacement curve). It evolves differently with the excursion of the WEC depending on the mooring characteristics and has thereby a high influence on the horizontal design load at the WEC. As the mooring stiffness over the permissible excursion of the WEC is different for both mooring systems, the resulting horizontal design load at the WEC of a dynamic or experimental analysis can be expected to be different as well. However, the configurations that are presented are believed to be representative of what would physically be required under these specifications. A dynamic or experimental analysis should provide better indications of the WEC motions and resulting mooring forces.
The maximum values are set against a possible 100year storm having a
The characteristics of the chain (diameter, dry and submerged weight
The characteristics of the six strand wire rope IWRC (diameter, dry and submerged weight
In this exercise, for the spread catenary mooring system FlipperDelta anchors were selected. The holding capacity of the anchor is set equal to the horizontal design load at the WEC and its weight can be calculated with the following equation for a range of anchor weights between 0.3 and 27.5 ton (3 and 270 kN) [
It was chosen to use
Suction anchors have been used to moor buoyant oil and gas facilities for the last 40 years [
A monolayer soil profile is assumed. The soil is medium soft clay with homogeneous strength profile, average undrained shear strength,
The mooring is connected to the suction anchor by means of a padeye placed on the foundation lid. The thickness of lid and wall of the anchor was chosen by taking existing similar foundations as reference.
The force calculated at the buoy,
It is worth noting that in the calculation of
Since
Seven different sizes of suction anchor were designed to fulfill the seven different loading cases. The dimensions of the suction anchors, including the thickness of lid and wall, are listed in annexed
Failure envelope of the suction anchor encompassing the reference design load point.
Main results from investigating the influence of the length of the hawser,
Reference  

length 
20  30  40 
Max excursion [m]  9.3  12.1  13.8 
Mooring stiffness at max excursion [kN/m]  465  460  469 
alpha [°]  33  42.6  47.9 
Beta [°]  37.0  27.4  22.1 
Buoy volume [m^{3}]  350  248  206 
Equivalent to a cylinder of height and diameter [m]  7.6  6.8  6.4 
Length 
20.1  20.5  20.7 
3086  2178  1808  
Max 
3677  2957  2696 
Max 
2505  2254  2159 
Suction anchor diameter [m]  4.25  3.75  3.55 
Suction anchor height [m]  8.5  7.5  7.1 
Suction anchor lid thickness [mm]  100  100  100 
Suction anchor wall thickness [mm]  30  26  25 
Suction anchor weight [ton]  37  27  23 
Total weight [ton]  82  59  50 
Main results from investigating the influence of water depth on a SALM system.
Water depth − 33%  Reference  Water depth + 33%  

Water depth [m]  20  30  40 
Max excursion [m]  7.0  12.1  16.7 
Mooring stiffness at max excursion [kN/m]  879  460  310 
Alpha [°]  47.1  42.6  39.2 
Beta [°]  22.9  27.4  30.8 
Buoy volume [m^{3}]  210.85  247.6  279.4 
Equivalent to a cylinder of height and diameter [m]  6.5  6.8  7.1 
Length 
10.7  20.5  30.4 
1856  2178  2457  
Max 
2728  2957  3168 
Max 
2171  2254  2330 
Suction anchor diameter [m]  3.6  3.75  3.9 
Suction anchor height [m]  7.2  7.5  7.8 
Suction anchor lid thickness [mm]  100  100  100 
Suction anchor wall thickness [mm]  25  26  27 
Suction anchor weight [ton]  24  27  30 
Total weight [ton]  51  59  66 
Main results from investigating the influence of horizontal design load at the WEC on a SALM system.
−50% 
Reference  +50% 


Horizontal design load

1000  2000  3000 
Max excursion [m]  12.6  12.1  11.7 
Mooring stiffness at max excursion [kN/m]  231  460  703 
Alpha [°]  43.2  42.6  42.2 
Beta [°]  26.7  27.4  27.8 
Buoy volume [m^{3}]  121  248  376 
Equivalent to a cylinder of height and diameter [m]  5.4  6.8  7.8 
Length 
21.2  20.5  20.0 
1063  2178  3308  
Max 
1459  2957  4466 
Max 
1119  2254  3393 
Suction anchor diameter [m]  2.75  3.75  4.5 
Suction anchor height [m]  5.5  7.5  9 
Suction anchor lid thickness [mm]  100  100  100 
Suction anchor wall thickness [mm]  19  26  31 
Suction anchor weight [ton]  12  27  44 
Total weight [ton]  28  59  92 
The buoys are assumed to have a weight density of 125 kg/m^{3} and to be of equal height as diameter. The volume of the buoy is calculated to provide the required buoyancy force, which is described in the section of the CALM and SALM systems.
Based on the specifications of the mooring system, the dimensioning of the components has been made by mainly following [
Overview of the forces in the CALM system and in its individual lines together with the mooring stiffness of the mooring system.
It can be seen that most of the compliance comes from the catenary mooring lines, as in this case, the hawser had a very low elasticity. The resulting forcedisplacement curve of the “active” mooring line is almost identical to the overall forcedisplacement curve, meaning that the other mooring lines have very little influence on the system. All the related values and details of the mooring configuration can be found in
Summary of the main details of the spread catenary mooring system for the reference load case.
Unit  Symbol  Value  

Pretension  [kN]  20  
Steel grade Q3  
Unstretched length  [m]  509  
Minimum breaking force *  [kN]  2014  
Diameter  [mm]  50.4  
Unit linear weight  [N/m]  521  
Submerged linear weight  [N/m] 

457  
Axial mooring stiffness per unit length AE  [N] 

2.28E+08  
Elasticity of the chain  [N^{−1}] 

4.38E−09  
Wire rope steel capacity 1770 N/mm2  
Length  [m]  30  
Minimum breaking force  [kN]  2000  
Diameter  [mm]  61.7  
Unit linear weight  [N/m]  130  
Submerged linear weight  [N/m]  113  
Elasticity of the wire rope  [N^{−1}] 

4.29E−09  
FlipperDelta anchor in sand  
Holding power  [kN]  2000  
Weight  [kN]  150  
Minimum buoyancy  [kN]  298  
Unit volume weight buoy  [kN/m^{3}]  1.2  
Weight  [kN]  43  
Volume  [m^{3}]  35  
Equivalent to a buoy of height and diameter of  [m]  3.5  
Minimum length mooring lines  [m]  509.1  
Maximum excursion WEC  [m]  14.2  
Horizontal distance anchor to WEC  [m]  498  
Tension at end of each line at the WEC at rest  [kN]  34  
Vertical force at connection with WEC at rest  [kN]  27  
Total mooring system weight  [ton]  132 
* The material of the hawser will probably be different, e.g., synthetic, as it is more elastic. The hawser should also be overdimensioned relative to the chains, if this part is not redundant.
The influence of the pretension is analysed as it is an independent design variable that can be modified, besides the hawser length. The weight of the mooring lines could also be adapted, but they are in this case dimensioned in accordance with their corresponding design load. The change in pretension has no influence on the length of the mooring lines or the weight of the whole system, as these depends mainly on the horizontal design load at the WEC and water depth, which remained the same (
Main results from investigating the influence of the pretension on a spread catenary mooring system.
Main results from investigating the influence of the pretension on a CALM system.
Pretension − 50%  Reference  Pretension + 50%  

Pretension [kN]  10  20  30 
Max excursion [m]  17.6  14.2  12.5 
Max 
2014  2014  2014 
Max 
2000  2000  2000 
234  234  234  
Length of the mooring line 
509  509  509 
495  498  500  
Nominal diameter of the chain [mm]  50.4  50.4  50.4 
Submerged weight of the chain [N/m]  461  461  461 
Buoy volume [m^{3}]  30  30  31 
Equivalent to a cylinder of height and diameter [m]  3.4  3.4  3.4 
Total system weight [ton]  114  114  114 
The resulting forcedisplacement curve together with the mooring stiffness curves are given in the next figure (
The resulting forceexcursion curves and mooring stiffness curves of the spread catenary mooring system for the reference situation (Reference) and the shortening (−50%) and extension (+50%) of the pretension.
Keeping the horizontal design load and the hawser length constant, the change in water depth affects the vertical force at the end of the mooring line, which affects the overall tension in the mooring lines and the minimum mooring line length (
Main results from investigating the influence of the water depth on a CALM system.
Note that a change in water depth (at a certain location) will change the characteristics of the waves (and especially of the extreme waves), and thereby it is very unlikely that the same WEC would be subjected to the same design loads at different water depths. However, these values intend to present what is to be expected in terms of mooring systems at a different water depth for the same design load.
An increase in water depth of 33% results in a decrease of the maximum mooring stiffness of 17%, an increase in mooring line length of 15% and an increase in total system weight of 12%. A decrease of 33% in water depth corresponds to an increase of the maximum mooring stiffness of 21%, a decrease in mooring line length of 18% and a decrease in total system weight of 14%. The excursion of the WEC is also strongly influenced by the change in water depth, as it is reduced to 9.2 m and extended to 19.6 m from 14.2 m. All the related values can be found in
Main results from investigating the influence of water depth on a spread catenary mooring system.
−33% Water Depth  Reference  +33% Water Depth  

Water depth [m]  20  30  40 
Max excursion [m]  9.2  14.2  19.6 
Max 
2009  2014  2018 
Max 
2000  2000  2000 
Max 
212  234  310 
Length of the mooring line l [m]  416  509  587 
410  498  571  
Nominal diameter of the chain [mm]  50.3  50.4  50.4 
Submerged weight of the chain [N/m]  459  461  462 
Buoy volume [m^{3}]  24  30  36 
Equivalent to a cylinder of height and diameter [m]  3.1  3.4  3.6 
Total system weight [ton]  98  114  128 
The resulting forcedisplacement curve together with the mooring stiffness curve are given in the next figure (
As the minimum breaking force of the chains is set equal to the resultant design load at the WEC, it directly affects also the diameter and the weight of the mooring lines. This will then have an influence on the minimum length of the mooring lines, as it is a function of their weight (
For an increase in horizontal design load at the WEC of 50%, the submerged weight of the chain increases by 58%, the chain length is reduced by 3%, the mooring stiffness at maximum WEC excursion increases by 48%, the maximum WEC excursion increases by only 13% and the total weight of the system increases by 57%.
While, for a decrease in horizontal design load at the WEC of 50%, the submerged weight of the chain decreases by 58%, the chain length is increased by 9%, the mooring stiffness at maximum WEC excursion decreases by 47%, the maximum WEC excursion decreases by 19% and the total weight of the system increases by 56%. All the related values can be found in
The resulting forceexcursion curves and mooring stiffness curves of the spread catenary mooring system for the reference situation (reference, 30 m) and the deeper (+50% or 40 m) and shallower (−33% or 20 m) of water depth.
Main results from investigating the influence of horizontal design load at the WEC on a spread catenary mooring system.
Main results from investigating the influence of horizontal design load at the WEC on a CALM system.
−50% 
Reference  +50% 


Horizontal design load at the WEC,

1000  2000  3000 
Max excursion [m]  11.5  14.2  16.1 
Max 
1006  2014  3022 
Max 
1000  2000  3000 
107  234  361  
Length of the mooring line

557  509  496 
550  498  481  
Nominal diameter of the chain [mm]  34.5  50.4  62.8 
Submerged weight of the chain [N/m]  192  461  729 
Buoy volume [m^{3}]  14  30  47 
Equivalent to a cylinder of height and diameter [m]  2.6  3.4  3.9 
Total system weight [ton]  50  114  179 
The resulting forcedisplacement curve together with the mooring stiffness curve are given in the next figure (
The resulting forceexcursion curves and mooring stiffness curves of the CALM system for the reference situation (
When the SALM system is close to be fully extended, the resulting horizontal mooring force starts to increase exponentially with the further excursion of the WEC (which is illustrated by “
In the figure (
Limiting the maximum angle between the hawser and tether limits also the maximum stiffness of the system. Up to this imposed maximum angle, the forcedisplacement curve increases almost linearly, while the mooring stiffness already begins to increase exponentially half way through the curve. All the related values and details of the mooring configuration can be found in
Summary of the main details of the SALM system for the reference load case.
SubSystem  Unit  Symbol  Value  

Depth of the buoy at rest  [m]  8.5  
Minimum buoyancy  [kN]  2178  
Unit volume weight buoy  [kN/m^{3}]  1.2  
Weight  [kN]  304  
Volume  [m^{3}]  247.6  
Equivalent to a cylinder ofequal height and diameter  [m]  6.8  
Wire rope steel capacity 1770 N/mm^{2}  
Length  [m]  20.5  
Minimum breaking force  [kN]  2957  
Diameter  [mm]  68  
Unit linear weight  [N/m]  193  
Submerged linear weight  [N/m]  168  
Elasticity of the wire rope  [N^{−1}]  4.1E−09  
Wire rope steel capacity 1770 N/mm^{2}  
Length  [m]  30  
Minimum breaking force  [kN]  2254  
Diameter  [mm]  59  
Unit linear weight  [N/m]  147  
Submerged linear weight  [N/m]  127  
Elasticity of the wire rope  [N^{−1}]  4.2E−09  
Suction anchor in medium soft clay  
Diameter  [m]  3.8  
height  [m]  7.6  
Lid thickness  [mm]  100  
wall thickness  [mm]  26  
Weight  [ton]  27  
Total mooring system weight  [ton]  59 
The main design variable that, in this case, can be adapted is the length of the hawser, as the length of the tether is a function of the water depth, and the volume of the buoy is calculated to fulfill the mooring requirements. The length of the hawser is however inversely proportional to the required buoyancy force, as a longer hawser demands a smaller buoy in order to maintain a similar compliant mooring system (
Main results from investigating the influence of the (unstretched) length of the hawser,
So, if the length of the hawser is increased by 33%, the required buoyancy force of the buoy drops (by 17%), which results in a lower maximum tension in the tether
The resulting forcedisplacement curve together with the mooring stiffness curve is given in the next figure (
An increase in water depth leads to an increase in length of the tether
Note that a change in water depth (at a certain location) will change the characteristics of the waves (and especially of the extreme waves), and thereby it is very unlikely that the same WEC would be subjected to the same design loads at different water depths. However, these values intend to present what is to be expected in terms of mooring systems at different water depths for the same design load.
The resulting forceexcursion curves and mooring stiffness curves of the SALM system for the reference situation (reference) and the shortening (−50%) and extension (+50%) of the hawser,
An increase in water depth (33%), and thereby an increase in tether length (48%), affects mainly the maximum excursion of the WEC (+37%) and reduces significantly the maximum mooring stiffness (by 32%) (
Main results from investigating the influence of the water depth on a SALM system.
The resulting forcedisplacement curve together with the mooring stiffness curve are given in the next figure (
The resulting forcedisplacement curves and mooring stiffness curves of the SALM system for the reference situation (reference, 30 m) and the increased (+50% or 40 m) and reduced (−50% or 30 m) water depth.
While the horizontal design load at the WEC has been changed, the water depth and the length of the hawser have been kept the same. This change in load was countered by an adjustment of the volume of the buoy, which affects slightly the length of the tether and thereby also the maximum excursion of the WEC (
As the maximum tension in the lines change according to the horizontal design load at the WEC, the dimensions of the suction anchor change as well, having a significant influence on the system weight (+57% and −53% for a variation of the horizontal design load at the WEC of +/−50%). All the values can be found in
The resulting forcedisplacement curve together with the mooring stiffness curve are given in the next figure (
These outcomes are a bit controversial, as less compliant systems (having a higher mooring stiffness) will result in a higher horizontal design load and
Main results from investigating the influence of horizontal design load at the WEC on a SALM system.
The resulting force excursion curves and mooring stiffness curves of the SALM system for the reference situation (reference, 2000 kN) and the increased (+50% or 3000 kN) and reduced (−50% or 1000 kN) horizontal design load at the WEC.
The two mooring configurations present very different forcedisplacement and mooring stiffness curves under the identical reference load case, as can be seen in the following figure (
The resulting force displacement and mooring stiffness curve for the CALM and SALM systems dimensioned for the same quasistatic load (2000 kN) and water depth (30 m).
Based on these curves, it is difficult to say, which mooring system is the most suitable or will actually result in the lowest mooring loads. A dynamical or experimental analysis should give a much better view on this.
The SALM system is the most sensitive to the change in water depth, as an increase in water depth (+33%) has a large effect on the maximum mooring stiffness of the SALM system (−32%), which can be seen in the following figure (
At a water depth of 40 m, both systems present approximately a similar maximum mooring stiffness (310 and 322 kN/m for the SALM and CALM), but the SALM system is much lighter than the CALM system (60 against 128 ton).
Comparison of the maximum mooring stiffness and weight of the CALM and SALM systems for different water depths.
The next figure (
Presentation of the resulting forcedisplacement and mooring stiffness curve for the CALM and SALM systems dimensioned for the same quasistatic horizontal design load at the WEC (2000 kN) and 40 m of water depth.
Note that although the CALM system appears to allow greater maximum WEC excursions, the forcedisplacement and mooring stiffness curve remain close to zero up to an excursion of the WEC of approximately 7 m.
For the SALM system, the increase in horizontal design load at the WEC (+50%) is mainly countered by an increase in buoy volume (+52%), while for the CALM system this is done by increasing the weight of the chains (+58%), which can be seen in the following figure (
Comparison of the maximum mooring stiffness and weight of the CALM and SALM systems for different horizontal design loads.
The next figure (
Presentation of the resulting force displacement and mooring stiffness curve for the CALM and SALM systems dimensioned for the same quasistatic horizontal design load at the WEC of 3000 kN and 30 m of water depth.
Note again that although the CALM system appears to allow greater maximum WEC excursions, the forcedisplacement and mooring stiffness curve remain close to zero up to an excursion of the WEC of approximately 6 m. Without this 6 m, which could be avoided by increasing the pretension, the maximum excursion of the WEC for both mooring systems would be approximately the same.
Quasistatic analyses on two different types of mooring systems have been performed for a reference load case and for three other cases, where an important environmental or design parameter has been modified. The mooring systems are a threelegged catenary anchor leg mooring (CALM) system and a single anchor leg mooring (SALM) system, also referred to as a tension leg mooring system. The reference case corresponds to a horizontal design load at the WEC of 2000 kN and a water depth of 30 m. Around this reference case, the influence of a main mooring design parameter was investigated, as well as the influence of the water depth and of the horizontal design load at the WEC on the design of the mooring systems.
The main observations for the CALM system are:
The reference case consists of chains that are each 509 m long and have a diameter of 50 mm, the maximum excursion of the WEC is 14.2 m and the total weight of the system is 132 ton.
The forcedisplacement curve remains very low up to half the excursion, as at an excursion of 7.0 m the resulting horizontal mooring force is still only of 178 kN, where it then starts to increase exponentially.
The pretension influences mainly the maximum excursion of the system, but not the mooring stiffness, as the forcedisplacement curve has the same shape and inclination, but is just translated. It might thereby not have an influence on the dynamic response of the system.
For greater water depths, the length of the same mooring lines needs to be increased, resulting in a larger maximum excursion of the WEC and a lower maximum mooring stiffness.
For larger horizontal mooring forces, the submerged weight and dimension of the chains need to be significantly increased; while their required length remains roughly the same. This results in an increase in maximum WEC excursion and maximum mooring stiffness.
The main observations of the SALM system are:
As the system is always under tension, the mooring stiffness is present from the smallest WEC excursion. The mooring stiffness increases almost linearly with the excursion of the WEC up to about 80% of the maximum excursion of the WEC (12.1 m), and then it increases exponentially. The total weight of the system is 60 ton.
The length of the hawser has a significant influence on the maximum excursion of the WEC, while it does not affect the mooring stiffness as the volume of the buoy changes inversely.
In this quasistatic analysis, the length of the tether was set in relationship with the water depth. A larger water depth mainly decreases the maximum mooring stiffness, while it increases slightly the volume of the buoy and the maximum excursion of the WEC.
The increase in horizontal design load is, in this case, compensated directly by an increase in the volume of the buoy. This influences the maximum mooring stiffness of the system and reduces slightly the maximum excursion of the WEC due to the increased size of the buoy and thereby reduction in length of the tether.
Both systems appear to have advantages and inconveniences. Some comparison can be made:
For the reference situation, the maximum mooring stiffness coming from this quasistatic analysis is larger for the SALM system. However, it is not sure that this would also result from a dynamic or experimental analysis, due to the slack initial distance of the CALM system.
The maximum mooring stiffness resulting from this quasistatic analysis is approximately the same for both mooring systems at a water depth of about 40 m.
The footprint of the SALM system is much more compact and light (60 ton), as it only requires the suction anchor on the seabed. The CALM system has a very large footprint as it is composed of three mooring lines of approximately 500 m and three anchors, so it is much heavier (up to 132 ton).
The CALM system presents more redundancy, as it is composed of three mooring lines, which each should be able to take the full mooring load. This of course requires the hawser to be stronger than the chains and possibly doubled to have full redundancy on the system. The SALM system does not present any obvious redundancy, unless the whole system would be doubled. In case no redundancy is provided, the system requires an additional safety factor (multiplication factor of 1.2).
The mooring stiffness increases very differently with the excursion of the WEC for both systems. The catenary mooring has a very low mooring stiffness of up to about 50% of its excursion after which it increase very steeply. The SALM system has a much more progressive mooring stiffness as it increases linearly up to 80% of its excursion, after which it increases steeply. So, it appears that the operational working range of the SALM mooring is greater than for the CALM system and this will have a very strong influence on the dynamic behaviour of the system and the resulting mooring loads.
The authors gratefully acknowledge the financial support from the Danish Council for Strategic Research under the Programme Commission on Sustainable Energy and Environment (Contract 09067257; Structural Design of Wave Energy Devices) and the ForskEL R&D programme administered by energinet.dk (Contracts 2013112057; Common prestudy and tests of wave power challenges; and 2013112039; Weptos WEC Hanstholm) which made this work possible.
The authors declare no conflict of interest.