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Practical method for calculating mooring chain wear for floating offshore installations
Mooring Integrity Joint Industry Project Phase 2
Prepared by the Joint Industry Project Steering Committee for the Health and Safety Executive
RR1092 Research Report
© Crown copyright 2017
Prepared 2010 First published 2017
You may reuse this information (not including logos) free of charge in any format or medium, under the terms of the Open Government Licence. To view the licence visit www.nationalarchives.gov.uk/doc/open-government-licence/, write to the Information Policy Team, The National Archives, Kew, London TW9 4DU, or email [email protected].
Some images and illustrations may not be owned by the Crown so cannot be reproduced without permission of the copyright owner. Enquiries should be sent to [email protected].
This report and the work it describes were funded by the Health and Safety Executive (HSE). Its contents, including any opinions and/or conclusions expressed, are those of the authors alone and do not necessarily reflect HSE policy.
Mooring integrity for floating offshore installations is an important safety issue for the offshore oil and gas industry. This report is one outcome from Phase 2 of the Joint Industry Project on Mooring Integrity. This work ran from 2008 to 2012 and had 35 industry participants. It followed the Phase 1 work described in HSE Research Report RR444 (2006). The Phase 2 work compiled research on good practice and is summarised in HSE Research Report RR1090 (2017).
Long lengths of steel chain links are used in the mooring lines of floating installations. As an installation moves, the tension and position of the upper ends of its mooring lines change producing rotational movement between adjacent chain links that results in wear. As part of ensuring that mooring chains to do not fail, it is important to have robust estimates of inter-link wear. This report describes the formulation of a practical analytical method to calculate inter-link wear. The report details: the relevant wear mechanisms (adhesion, corrosion, surface fatigue and erosion); how the links move under the influence of environmental forces including consideration of the influences of the manufacturing and proof testing processes; and the underlying theory and calibration approach used to develop the method.
For ease of use by practitioners applying the method, a summary is provided in Appendix A of the report.
HSE Books
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Lorem ipsum dolor sit amet consectetuer adipiscing elit
GL Noble Denton No 1 The Exchange 62 Market Street Aberdeen AB11 5JP
Practical method for calculating mooring chain wear for floating offshore installations
Mooring Integrity Joint Industry Project Phase 2
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CONTENTS
SECTION PAGE
1 PREFACE 7 2 DESCRIPTION OF PROBLEM 8
2.1 MOORING LINE SHAPE 8 2.2 GENERALISED WEAR 11 2.3 SURFACE ROUGHNESS 12 2.4 OVERALL PROBLEM 13 3 CHAIN LINK MOVEMENT 14
3.1 IDEALISED CONDITION 14 3.2 ACTUAL CHAIN CONDITION 18 4 CHAIN WEAR CALCULATION DEVELOPMENT 33
4.1 METHOD 33 4.2 GENERALISED WEAR EQUATION 33 4.3 GENERALISED CHAIN WEAR MODEL 39 4.4 DIAMETER LOSS TO VOLUME LOSS 43 4.5 CHAIN WEAR CALCULATION METHODOLOGY 50 5 CHAIN WEAR CALCULATION CALIBRATION 53
5.1 INTRODUCTION 53 5.2 ACTUAL WEAR VOLUME 54 5.3 REGULAR WAVE SCATTER DIAGRAM 55 5.4 CHAIN WEAR CALCULATION 59 5.5 SLIDING WEAR COEFFICIENT CALIBRATION 63 6 VALIDATION 65
6.1 PURPOSE 65 6.2 METHOD 65 6.3 RESULTS 66 6.4 CONCLUSION 68
70
72
73
75
75
76
80
82
REFERENCES
APPENDIX A CHAIN WEAR CALCULATION METHOD A.1 CALCULATION METHOD
A.1 FLOWCHART
A.2 TABLE OF EQUATIONS
APPENDIX B REGULAR WAVE SCATTER DIAGRAM CREATION FROM IRREGULAR SEA-STATE DATA MATHCAD SHEET
APPENDIX C ‘PRINGLE’ MODEL MATHCAD SHEET
APPENDIX D REGULAR WAVE SCATTER DIAGRAMS
4
Figure 2-1: Variation of Catenary shape with Depth at 1000kN constant Top Tension 9 Figure 2-2: Variation of Catenary shape with Top Tension at constant 100m Depth 9 Figure 2-3: Studless Link Chain 10 Figure 2-4: Inter-grip area 10 Figure 2-5: Open Polygon Shape taken up by Chain 11 Figure 2-6: Surface Roughness Measurement 12 Figure 3-1: Start Position 14 Figure 3-2: Rolled Up Position 15 Figure 3-3: Close up of Rolled Up Position 15 Figure 3-4: Final Position 17 Figure 3-5: Chain Link Measurement Locations 19 Figure 3-6: New chain with non-uniform cross-section 20 Figure 3-7: New studded chain with non-uniform cross-section 20 Figure 3-8: New studless chain with non-uniform cross-section 20 Figure 3-9: Minimum Break Loads curves for various grades of Offshore Mooring Chain 21 Figure 3-10: Studless Chain Link Inter-Grip area at Proof Load 22 Figure 3-11: Studless Chain Link Inter-Grip Area Residual Stressed after Proof Load 22 Figure 3-12: ‘Witness Mark’ on Chain that has been Proof Loaded 22 Figure 3-13: Pre-Proof Test 23 Figure 3-14: Proof Loaded Chain 24 Figure 3-15: Rotation Causing Initial Roll up with Chain Links that have started from an axially
loaded condition 25 Figure 3-16: Rotation at point of sliding at edge of witness mark of originally axially loaded chain 26 Figure 3-17: Final position after sliding of originally axially loaded chain 27 Figure 3-18: Link from axially loaded chain that has under gone wear and material lapping 28 Figure 3-19: Proof Loaded link in a Catenary before load is applied 29 Figure 3-20: Proof Loaded link in a Catenary after load is applied 30 Figure 3-21: Proof Loaded link in a Catenary after load is applied rolling up due to chain motion 31 Figure 3-22: Even wear due to rolling and sliding 32 Figure 4-1: Single Asperity 33 Figure 4-2: Plastically Deformed Asperity 34 Figure 4-3: Formation of Wear Particle from Plastically Deformed Asperity 34 Figure 4-4: Typical Steel Surface 36 Figure 4-5: Scanning Electron Microscope Surface Image 36 Figure 4-6: Idealised Normalised Surface 36 Figure 4-7: Relative Angle between Links in 5.25m Regular Wave 41 Figure 4-8: Tension between Links in 5.25m Regular Wave 41 Figure 4-9: Inter-grip Double Diameter Measurement 43 Figure 4-10: Light Narrow Wear 44 Figure 4-11: Heavy Narrow Wear 44
5
FIGURES
45 45 46 46 48 48 48 49 50 53 63
Figure 4-12: Light Broad Wear
Figure 4-13: Heavy Broad Wear
Figure 4-14: Chain Link Geometry
Figure 4-15: Cross-section of Worn Chain Link
Figure 4-16: Wear Zone Dimension Definition
Figure 4-17: Initial Wear Surface
Figure 4-18: Initial Broad Banded Wear Surface
Figure 4-19: Wear Depth versus Wear Volume for Calibration Mooring System
Figure 4-20: Chain Wear Calculation Methodology
Figure 5-1: Tri-Catenary Mooring System (TCMS)
Figure 5-2: Predicted versus Actual Links 2 & 3 Inter-grip Double Diameter
Figure 6-1: Absolute Actual Double Diameter Wear versus Predicted Double Diameter Wear
Figure 6-2: Absolute Actual Double Diameter Wear versus Predicted Double Diameter Wear
with Ks=0.0139 68
TABLES
Table 2-1: Classification of Type of Wear based on Environmental Interactions 11 Table 3-1: Chain Measurements from the SBM led Out of Plane Bending JIP 19 Table 3-2: Proof Load to Minimum Break Load Ratios 22 Table 5-1: Link 2/3 Chafe Chain Inter-grip Double Diameter Measurements 54 Table 5-2: Seastate data 55 Table 5-3: Irregular Wave Factors 57 Table 5-4: Calculated Regular Wave Scatter Diagram 58 Table 5-5: Basic Chain Data for Subject Unit 59 Table 5-6: Mean Tension (kN) 60 Table 5-7: Angle Change Range (degrees) 61 Table 5-8: Calculated Wear Volumes (mm3) per annum with Ks=1.0 62 Table 6-1: Predicted Volumetric Wear Rates 66 Table 6-2: Loss of Diameter Wear rates 66
6
67
1 PREFACE
This sub-report describes the formulation of a practical method for calculating interlink wear for chains that form part of a mooring system. To do this it first lays out the problem in Section 2 before going on to describe how chain links move due to the influence of environmental forces on the floating production unit in Section 3, including a discussion of the influences of the manufacturing process (Section 3.2.1) and the proof testing process (Section 3.2.2). Given these issues the development of the method and the theory behind it are described in detail in Section 4, before the methodology is calibrated using actual wear data in Section 5. The overall methodology and calibrated model is then tested against additional wear data in Section 6 in order to validate it.
The basic methodology, associated equations for standard geometry studded and studless chain, and associated calculation flowchart are summarised in Appendix A for ease of reference for practitioners that are applying the method to actual cases.
This methodology and sub-report has been produced under the auspices of Phase 2 of the Noble Denton led Mooring Integrity for Floating Offshore Installations Joint Industry Project, which has been sponsored by the following companies:
• Maersk Oil• Petrobras• BP• Chevron• Statoil ASA• Exxon Mobil• A/S Norske Shell• Conoco Philips• Husky Energy• 2H Offshore• Wood Group Engineering• Single Buoy Moorings Inc.• SOFEC• Bluewater Energy Services• Health and Safety Executive• BG Plc• Total• Franklin Offshore
• Lloyds Register EMEA• Det Norske Veritas• Bureau Veritas• ABS• Welaptega• Vicinay Cadenas S.A.• TSC Inspection Systems• Hamanaka Chain Mfg.Co., Ltd.• Imes Group• Sanmar Chain International Pte• Viking Moorings• International Mooring Systems• Ramnas Bruk AB• Mooring Systems Limited• Bruce Anchors Limited• Inpex• Delmar• Film Ocean Limited
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2 DESCRIPTION OF PROBLEM
2.1 MOORING LINE SHAPE
A continuous mooring line material such as wire rope, spiral strand or fibre rope will naturally form a catenary curve if, in a static condition, it is attached to an anchoring point on the seabed and a fixed point on a vessel. The shape of the catenary curve being governed, in Cartesian co-ordinates, by:
gTa
aaxay
λ0
cosh
=
−⎟⎠
⎞⎜⎝
⎛×=
Equation 2-1: Catenary Equation
Where:
gravity todueon Acceleratigchain oflength unit per Mass
Tension Top ofComponent Horizontalpointfixation from distance Verticaly
pointfixation from distance Horizontal
0
=
=
=
=
=
λ
T
x
The above equation, which assumes that the influence of the axial stiffness of the line on the shape of the curve is negligible, can be solved for any given Top Tension (T) and Depth (ymax) to find the shape of the catenary curve; where Depth is definedas the summation of the water depth and the height of the attachment point abovethe waterline of the vessel. Variation of either of these variables results in a changein shape of the Catenary Curve as shown in Figure 2-1 and Figure 2-2 where, as anexample the equation has been solved for a line mass of 130kg/m. By examinationit can be seen that the Top Angle (α) of the line, in relation to the horizontal axis,changes with any variation in Top Tension or Depth.
8
0
10
20
30
40
50
60
70
80
90
100
110
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400
Depth (m
etres)
Horizontal distance from anchor (metres)
Depth: 90m Depth: 100m Depth: 110m
Figure 2-1: Variation of Catenary shape with Depth at 1000kN constant Top Tension
0
10
20
30
40
50
60
70
80
90
100
110
0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400
Depth (m
etres)
Horizontal distance from anchor (metres)
Tension: 900kN Tension: 1000kN Tension: 1100kN
Figure 2-2: Variation of Catenary shape with Top Tension at constant 100m Depth
Mooring chain, however, is not continuous, as it consists of a number of discrete torus links, made from solid steel bar, that pass through similar links on either side, as shown in the figure below, to form a chain length.
9
Figure 2-3: Studless Link Chain
Where, when tension is applied to the chain length, the inter-linked links come into contact with each other in an area termed the inter-grip area, as shown in Figure 2-4. Within this area, the two links are nominally perpendicular to each other, inrelation to the longitudinal axis of the chain, although twist along or torque in thechain can affect this.
Figure 2-4: Inter-grip area
Inter-grip Area
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This means that fundamentally chain cannot form a continuous curve. Instead it forms an open ended polygon with vertices equal to the length between the inter-grip areas, as shown in the figure below:
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 2 4 6 8 10 12 14
Dep
th
Horizontal Distance
Chain Length Open Polygon versus Catenary Curve
Catenary Curve Chain Length Open Polygon
Figure 2-5: Open Polygon Shape taken up by Chain
Therefore, for the chain length to mimic the catenary curve, the individual links have to lie at varying angles to each other, as can be seen in the figure above. As a consequence, any change in the shape of the curve results in relative rotational movement between each pair of links, with this rotational movement taking place in the inter-grip area. Such interaction between links will, over time, lead to a loss of material and the mechanism of wear, as discussed in the following section.
2.2 GENERALISED WEAR
In general, where the interaction of a surface with its interfacing environment results in loss of material from the surface then the process leading to this is termed wear [1]. The standard DIN 50320 [2] classifies four wear mechanisms, namely: adhesion; abrasion; surface fatigue and tribological reaction. This classification system though, fails to distinguish between several types of wear such as erosion and corrosion [1]. Chattopadhyay [3] therefore proposes the following more comprehensive classification system:
Type Interacting Environment Adhesion Similar or dissimilar material Abrasion Solid particles Erosion Suspended particles in fluid medium Corrosion Reactive fluids Cavitation Collapsing of bubble carried in liquid on surface Thermal Fatigue Heat cycle Surface Fatigue Cyclic loading/stress
Table 2-1: Classification of Type of Wear based on Environmental Interactions
In respect of mooring chain, due to the definition of the interacting environments the only applicable wear mechanisms are: adhesion, corrosion and surface fatigue, and perhaps to a much lesser extent, erosion. Based in the main on DIN 50320 [2] these Wear Mechanisms can be defined as:
• Adhesion: formation of interfacial adhesion (“weld”) junctions between surfaceasperities by the action of molecular forces.
• Corrosion: loss of material due to electrochemical reactions between thesurface and the surrounding medium.
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• Surface Fatigue: cracking at the surface due to stresses or strains varying inmagnitude and direction.
• Erosion: grooving by scratching action or microcutting process by particlessuspended in the surrounding medium e.g. grit within lube oil.
Adhesion and Surface Fatigue are a result of two surfaces being in direct contact and moving relative to each other, such as in the inter-grip area of a chain, and are therefore principally mechanical processes that are to a certain extent dependent on surface roughness. Whereas Corrosion, and to a certain extent Erosion, depend on the surrounding medium. Erosion, though, can become a principally mechanical process if particles become trapped between two surfaces that are moving relative to each other.
2.3 SURFACE ROUGHNESS
All surfaces have texture and Surface Roughness is a measure of this texture. It is quantified by the vertical deviations of a surface from its ideal form. If these deviations are large, the surface is rough; if they are small the surface is smooth. Surface Roughness is typically considered to be the high frequency, short wavelength component of a measured surface and is typically measured by running a stylus across the surface, as shown in the following diagram:
Figure 2-6: Surface Roughness Measurement
The consequence of this, as can be seen by the red trace, is that the surface is measured as a series of rounded humps and valleys i.e. the traced surface is not a true representation of the surface. As a consequence, Surface Roughness tends to be expressed statistically where the distribution of peaks and valleys is taken as conforming to a Normal Distribution.
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2.4 OVERALL PROBLEM
As a floating production unit moves, it will cause changes in tension and the position of the upper ends of its mooring lines. This in turn will cause rotational movement between adjacent links as the overall catenary shape changes and this will result in individual links wearing. A method would therefore be useful to quantify the likely wear that a mooring system is likely to see, through a given period of time, taking into account line motion due to vessel motion, changes in line tension, material characteristics and surface roughness of the individual chain links.
Such a method has a number of potential uses:
• Design Life predictions at the initial design stage, rather than relying onnormalised wear/corrosion allowances as presently contained within mooringdesign standards;
• Input into material choices at the initial design stage (as different steel gradeswear at different rates);
• Input into an optimal choice of design pre-tension (for example a higher pre-tension may limit offsets, but it may also increase wear rates and reduce the lifeof the system);
• Prediction of remaining useful life following a set of in-place measurements,which could be used to justify leaving the chain in place for a longer period thanthe original design, or to justify why it should be changed out early.
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3 CHAIN LINK MOVEMENT
3.1 IDEALISED CONDITION
As discussed in Section 2.1, any variation in Top Tension or Depth or a horizontal translation will result in a change in the shape of the catenary and hence a change in the angle between adjacent chain links. If for the moment, a pair of adjacent idealised studless chain links is considered i.e. links of homogenous round cross-section throughout their torus shape, then the physical mechanism that allows the change in angle between the links to take place can be hypothesised.
First, consider the generalised condition, as shown in Figure 3-1 below, of a studless chain link under tension ‘T’ at an angle ‘β’, in relation to its adjacent link due to the shape of the catenary curve.
Figure 3-1: Start Position
If the tension in the chain length is increased by an amount ‘dT’ then the catenary curve will tend to straighten as illustrated by Figure 2-2. This will cause the angle between the two links to start to decrease by an angular increment ‘dβ’ ( note ‘dβ’ is taken as being in radians in the following equations), causing the link to rotate in a clockwise direction, in this case, as illustrated by the red link in.
14
Figure 3-2: Rolled Up Position
Due to friction, the rotation of the link will cause it to initially ride up the other link by an amount ‘dr’, as shown in the figure above, until such time as the tangential force ‘FT’ at the contact point, overcomes the friction force ‘FF’, due to the normal force ‘FN’ at the contact point, at which point the surfaces will then slide along each other. In order to calculate these forces, at the transition point between rolling and sliding, it is first necessary to determine the angle ‘ð’ in Figure 3-3, which determines the relationship between the Tension on the link ‘T+dT’ and both the tangential and normal forces at the contact point.
Figure 3-3: Close up of Rolled Up Position
Start Position Rolled Up Position
Start Position Rolled Up Position
15
From Figure 3-3 it can be seen that:
βββ d−+=+ ðþ
Equation 3-1: Angle balance
Where ‘þ’ is the angle between the two contact points. Based on the fact that the circumferential distance rolled by the moving link, must be equal to the circumferential distance rolled along the non-moving link, then the angle ‘þ’ is given by:
Rrdβ=þ
Equation 3-2: Angle between contact points due to rotation ‘dβ’
Thus reducing Equation 3-1 to:
⎟⎠
⎞⎜⎝
⎛+=
Rrd 1ð β
Equation 3-3: Angle between Tension ‘T+dT’ and the normal force at the contact point due to rotation ‘dβ’
Given the definition of ‘ð’ in Equation 3-3, the normal force ‘FN’, the tangential force ‘FT’, and the friction force ‘FF’, at the contact point can be determined:
( ) ( ) ( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛++=+=
RrddTTdTTFN 1cosðcos β
Equation 3-4: Contact Point Normal Force
( ) ( ) ( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛++=+=
RrddTTdTTFT 1sinðsin β
Equation 3-5: Contact Point Tangential Force
( ) ⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛++==
RrddTTFF NF 1cos βµµ
Equation 3-6: Contact Point Friction Force
where ‘µ’ is the coefficient of friction.
16
In order for the link to roll up the other link, then the Friction Force must exceed the Tangential Force. Similarly, for the link to slip, the Tangential Force must exceed the Friction Force. Hence, the following expression can be developed for the point at which slippage occurs:
( ) ( )
11tan1
1cos1sin
=⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛+
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛++=⎟⎟
⎠
⎞⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛++
=⇒=
Rrd
RrddTT
RrddTT
FFFF
Critical
CriticalCritical
NTFT
βµ
βµβ
µ
Equation 3-7: Roll Up Limit for Studless Chain
If the two radii and the coefficient of friction are taken as pseudo-static quantities, then the Roll Up Limit Angle, ‘dβCritical’, can be found by solving Equation 3-7 for ‘dβCritical’. This can then be related to a change in tension ‘dT’ from a starting tension ‘T’ via the Catenary Equation, see Equation 2-1. If T+dT > T’, where ‘T’’ is the final tension for a given tension change, then no slippage will occur and the chain link will simply roll up the adjacent link. If, however, T’ > T+dT then slippage will occur and the chain link will take up a new position as dictated by the Catenary Equation, with the link at an angle ‘Ø’ such that ‘Ø’ equals ‘β-dβ’, as shown by the green link in Figure 3-4 below.
Figure 3-4: Final Position
This means that if the change in angle ‘dβ’ is less than the Roll Up Limit Angle ‘dβCritical’, such that friction prevents the chain links from sliding over each other, then the total distance traversed by the chain links over each other will be given by:
onlyRollingdrd
rdrddFor Critical …… βπ
βπββ =×=<
22
Equation 3-8: Rolling only Distance for Studless Chain
Whereas if the change in angle ‘dβ’ is greater than the Roll Up Limit Angle ‘dβCritical’ then the chain links will roll-up before sliding to their final position. Therefore the total distance travelled of one link relative to the other will be the summation of the rolling ‘dr’ and sliding ‘ds’ distances given by:
17
SlidingdRdrdsdr
RollingdrdrddFor
Critical
Critical
Critical…
……
ββ
βββ
+=+
=>
Equation 3-9: Rolling and Sliding Distances for Studless Chain
The same process can also be used to find similar equations for studded chain, where it is assumed that the inside of a studded chain link can be represented by an ellipse with a semi-major axis length equal to half the inner length of the chain ‘b’ and a semi-minor axis length equal to half the inner width of the chain at its widest point ‘a’:
( ) ( )( )( ) ( )( )
µββββββ
=⎟⎟⎠
⎞⎜⎜⎝
⎛+−⎟⎟
⎠
⎞⎜⎜⎝
⎛
×××−×
×+×××−Critical
Critical
Critical ddrbab
bdraatantantantantantan 1
Equation 3-10: Roll Up Limit for Studded Chain
onlyRollingdrdrddFor Critical …… βββ =<
Equation 3-11: Rolling only Distance for Studded Chain
( ) ( ) Slidinga
ba
dbdrdsdr
Rollingdrdr
ddForCritical
Critical
Critical…
…
…⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛ ×−⎟⎠
⎞⎜⎝
⎛ −×+=+
=
>−− βββ
β
β
ββ tantantantan 11
Equation 3-12: Rolling and Sliding Distances for Studded Chain
If standard studded chain geometry is assumed then:
( ) ( )( )( ) ( )( )
µββββββ
=⎟⎟⎠
⎞⎜⎜⎝
⎛+−⎟⎟
⎠
⎞⎜⎜⎝
⎛
×××−
×+××−Critical
Critical
Critical ddr
drtantan28.0
tan8.0tan32.0tantan 1
Equation 3-13: Roll Up Limit for Standard Studded Chain
onlyRollingdrdrddFor Critical …… βββ =<
Equation 3-14: Rolling only Distance for Standard Studded Chain
( )( ) ( )( )( ) Slidingddrdsdr
RollingdrdrddFor
Critical
Critical
Critical…
……
ββββ
βββ
tan5.2tantan5.2tan 11 ×−−×+=+
=>
−−
Equation 3-15: Rolling and Sliding Distances for Standard Studded Chain
The above idealised condition makes a number of assumptions, particularly as regards the shape of the bar and the shape of the link. In reality chain links are not of uniform cross-section due to a variety of reasons, as will be examined in the following section, and this will affect the motion and wear regime of the chain.
3.2 ACTUAL CHAIN CONDITION
3.2.1 Manufacturing Issues
The bar used to make mooring chains starts off as homogenous round bar, which in some cases may be turned round bar, typically with a diameter one size larger than
18
the chain to be produced. This is because the manufacturing process of heating, bending, flash butt welding and in the case of studded chain stud insertion, means that chain links end up with a reduced and non-uniform cross-section, particularly where the bar is bent. This is illustrated by the normalised chain measurements below:
D1
D3D2
W1
L
W2
W3
D1
D3D2
W1
L
W2
W3
D1
D3D2
W1
L
W2
W3
Figure 3-5: Chain Link Measurement Locations
Diameter Measurements Length Measurements
Type Size (mm)
D1 D1 D2 D2 D3 D3 L W1 W2 W3 0° 90° 0° 90° 0° 90° R3
Studless 146 97.0% 101.8% 101.7% 102.8% 103.1% 103.2% 98.2% 96.6% 100.1% 95.6%
R3 Studless 127 97.4% 102.0% 100.9% 98.4% 106.0% 104.4% 98.8% 96.0% 98.4% 87.3%
R4 Studless 127 97.0% 103.8% 103.3% 98.1% 102.1% 102.5% 98.8% 95.8% 98.6% 93.5%
R3 Studless 84 96.7% 101.8% 101.9% 103.1% 102.3% 103.1% 99.5% 99.2% 100.0% 96.6%
R4 Studded 84 101.2% 103.6% 101.2% 98.8% 111.9% 110.7% 99.5% 95.0% 99.8% 97.5%
R4 Studless 84 98.6% 101.8% 102.5% 103.3% 102.3% 102.7% 98.8% 99.6% 100.5% 97.9%
R3 Studless 107 99.2% 104.4% 104.9% 100.6% 103.7% 103.0% 98.8% 99.9% 100.3% 95.1%
R4 Studless 84 98.3% 101.3% 102.6% 103.2% 117.4% 102.6% 99.8% 98.6% 101.3% 77.5%
R4 Studless 84 97.5% 101.3% 102.1% 103.3% 101.9% 102.3% 97.1% 100.5% 101.2% 100.1%
R4 Studless 84 97.7% 101.3% 102.9% 102.5% 102.1% 102.1% 99.7% 100.6% 101.8% 101.2%
R4 Studless 84 98.0% 101.3% 102.1% 102.4% 101.9% 102.3% 99.5% 99.6% 100.6% 98.6%
R3 Studless 107 99.0% 103.3% 101.9% 103.3% 102.8% 103.7% 98.8% 95.8% 101.0% 98.1%
R4 Studless 84 97.0% 100.8% 102.3% 101.3% 101.9% 103.1% 99.2% 99.8% 101.1% 99.9%
R4 Studded 84 101.9% 105.5% 104.3% 104.6% 110.0% 109.8% 100.2% 98.4% 99.4% 93.4%
R4 Studless 84 101.0% 103.7% 104.6% 104.5% 102.5% 104.0% 99.6% N/M N/M N/M
R3 Studless 146 101.6% 97.9% 103.5% 101.2% 102.7% 101.2% 100.6% 101.5% 102.0% 103.1%
R3 Studless 107 102.4% 99.5% 103.4% 100.7% 101.8% 101.3% 101.2% 102.2% 101.7% 101.9%
R3 Studless 84 101.3% 98.6% 95.8% 101.3% 93.0% 101.1% 99.7% 102.7% 102.0% 105.1%
Table 3-1: Chain Measurements from the SBM led Out of Plane Bending JIP
These measurements are clearly borne out by the following pictures of new un-used chain that illustrate the non-uniform cross-section of new chain. Hence account needs to be taken of this when considering chain motion and the wear that results from it.
19
Figure 3-6: New chain with non-uniform cross-section
Figure 3-7: New studded chain with non-uniform cross-section
Figure 3-8: New studless chain with non-uniform cross-section
20
3.2.2 Proof Testing
During the manufacturing process the chain links are batch tested to proof load. This is done in order to prove that the chain links are free of gross manufacturing defects, increase the probability that the chain links would meet the minimum break load requirements and to produce a permanent set in the links. Such testing of chains comes from Lloyd’s Register of Shipping, who augmented their rules in 1846 so that thereafter all chains for classed vessels were to be proof tested and stamped on each end to indicate the load applied. In 1853, Lloyd’s Rules made it mandatory that, before a vessel could be classed, a certificate should be produced as to the test of the chain cable, and in 1858 they issued rules as to length and size of chain cable. Lloyd’s Register then progressively added to their rules regarding methods of manufacture and testing, resulting in the "Anchors and Chain Cables Act of 1899"; which, with few amendments, is still the basis of the present day chain testing procedure.
This resulted in the well known formula for the minimum break load of chains, namely:
MBL = k d2 (44 – 0.08d)
Equation 3-16: Chain Minimum Break Load Equation
Where:
d = nominal chain diameter
and K is proportional to the minimum ultimate strength of the grade of material
0.08d takes into account the effect of thickness of the material on its mechanical properties. With the use of defined constants K, for each chain grade, this formula results in the following curves for the minimum break loads of various chain grades that appear in manufacturers’ and Class rules, and for which break tests are performed against.
0
1000
2000
3000
4000
5000
6000
0 50 100 150 200 250 300
Minim
um Break Load (ton
nes)
Nominal Chain Bar Diameter (mm)
Minimum Break Load versus Chain Diameter
R3
R3S
R4
R5
Chain Grade
Figure 3-9: Minimum Break Loads curves for various grades of Offshore Mooring Chain
21
The Proof Load requirements for chain, was originally based on Grade U3/K3 chain, and have been adapted to higher chain grades via the yield stress ratio to Grade U3/K3 chain, as shown in the table below:
Steel Grade Yield Stress Yield Stress Ratio K Factor Ratio PL / MBL R3 410 1.000 1.000 0.70
R3S 490 1.195 1.154 0.72 R4 580 1.414 1.385 0.78
R4S 700 1.707 1.538 0.78 R5 760 1.854 1.609 0.78
Table 3-2: Proof Load to Minimum Break Load Ratios
It should be noted, that because of the higher strength and hardness levels of Grades R4S and R5, these will have less plasticity than the lower grades, hence, the PL to MBL ratio has not been increased in line with the Yield Stress Ratio.
The practical effect of applying this proof load, is to produce a permanent set in the chain, resulting in residual stresses, as illustrated below for the inter-grip area, and to produce an area of plastic deformation, also known as a ‘witness mark’, as illustrated in Figure 3-12.
Figure 3-10: Studless Chain Link Inter-Grip area at Proof Load
Figure 3-11: Studless Chain Link Inter-Grip Area Residual Stressed
after Proof Load
Figure 3-12: ‘Witness Mark’ on Chain that has been Proof Loaded
As can be seen from Figure 3-12, the witness mark left by proof test is a permanent, although shallow, depression in the chain. The significance of this depression, is that it is thought to ‘trap’ the two links and so prevent the two links from being able to roll against each other, as described in Section 3.1, in certain circumstances, as described in the following sections.
Witness Mark
22
For the moment, the case of axially loaded chain is considered i.e. where the load is in line with the axis of the individual chain links, as is the case with proof loading. Then, as can be seen in Figure 3-13, the links will start off with nominally perfectly smooth surfaces and regular geometry.
Figure 3-13: Pre-Proof Test
23
When the proof load is applied, see Figure 3-14, this will result in the formation of a small plastic deformation in the contact zone of each link, causing the formation of the so called witness mark, which is denoted by the purple line for the left hand blue link and, in future figures, by a black line for the right hand red link.
Figure 3-14: Proof Loaded Chain
24
If the right hand link starts to rotate clock-wise, then it will initially roll-up, as described in Section 3.1, however, the roll up will literally be up the edge of the witness mark, as shown in Figure 3-15.
Figure 3-15: Rotation Causing Initial Roll up with Chain Links that have started from an axially loaded condition
25
As this happens, the small area of plasticity within the contact area will move towards the cusp of the witness mark resulting in an area of high plasticity as shown in Figure 3-16.
Figure 3-16: Rotation at point of sliding at edge of witness mark of originally axially loaded chain
26
Such a concentrated area of plasticity will have a low shear resistance and so the right hand link will slide to its final position back down the witness mark, see Figure 3-17, rather than riding further up the left hand link.
Figure 3-17: Final position after sliding of originally axially loaded chain
The effect of this will be two fold, firstly it will cause wear within the witness mark thus deepening it. Secondly, the shearing at the cusp of the contact zone will cause material to be lapped away from this zone, and in doing so will build up an edge to the zone. The combined effect of these two actions is likely to be to further ‘trap’ the links and so lead to a higher rate of wear. Figure 3-18 shows the effect of this type of movement on a plan view of a link that can be seen as representing the right hand link in the aforementioned figures.
27
Figure 3-18: Link from axially loaded chain that has under gone wear and material lapping
If on the other hand, the case of nominally perfect links within a chain catenary is considered, then the influence of the witness mark is somewhat altered. As before the two links, see Figure 3-13, will be subject to axial loading in the proof test condition, resulting in plastic deformation within the contact zone, resulting in the formation of a witness mark, see Figure 3-14. Unlike the axially loaded case though, the links in a catenary will naturally take up the shape of the catenary curve by relative angular movement to each other, see Figure 3-19, before further load is applied to them.
Extent of wearzone
Lapped Material
28
Figure 3-19: Proof Loaded link in a Catenary before load is applied
Application of a load will cause plastic deformation within the contact area, which up to relatively high angle between the links will include plastic deformation of the cusp at the edge of the witness mark, see Figure 3-20.
29
Figure 3-20: Proof Loaded link in a Catenary after load is applied
The effect of which will be to effectively flatten the edge of the witness mark, so leading to a smooth transition from the witness mark to the body of the chain. Hence, when clockwise motion is applied to the right hand link it is able to roll-up the left hand link, see Figure 3-21, to the point slippage due to friction i.e. the critical angle as per Section 3.1, as the witness mark is no longer trapping it.
30
Figure 3-21: Proof Loaded link in a Catenary after load is applied rolling up due to chain motion
This means that chain links within a catenary where the initial load point is on or around the cusp of the witness mark will undergo wear due to the combined effects of rolling and sliding as described in Section 3.1. Such action is likely to result in the type of even wear seen in the picture below:
31
Figure 3-22: Even wear due to rolling and sliding
Thus it can be seen that it is important when considering the motion of chain links to take into account their starting position, in order to determine whether they are likely to be subjected to rolling and sliding or sliding only motion.
Extent of wearzone
32
4 CHAIN WEAR CALCULATION DEVELOPMENT
4.1 METHOD
The following four steps have been taken in order to develop the proposed chain wear calculation method and are described in detail in the following sections:
1. Formulation of a generalised wear model (based on the general considerationsdescribed in Sections 2 and 3);
2. Development of a generalised chain wear model linked to chain motion;
3. Development of a model that links chain wear volume to diameter loss, takinginto account actual chain geometry;
4. Development of a methodology to apply the generalised chain wear model toactual mooring systems.
It should be noted, that the aim of the chain wear calculation method is to give designers and operators a practical tool for quantifying the likely loss of chain diameter over a given operating period, rather than trying to develop a model that captures all of the physiological aspects of chain wear.
4.2 GENERALISED WEAR EQUATION
4.2.1 Archard’s Wear Equation
The Archard Wear Equation [1][5], as shown below, is the most widely used wear model, and is a simple model used to describe sliding wear and is based around the theory of asperity contact:
HFKdV N
wear 3=
Equation 4-1: Archard’s Wear Equation
Where:
HardnessForce Normal
tCoefficienWear Distance Sliding
MaterialLost of Volume i.e. VolumeWear
=
=
=
=
=
HFKdV
N
wear
This equation can be derived by reference to a single asperity as shown in the figure below:
Figure 4-1: Single Asperity
33
If this single asperity supports an ideally smooth surface that exerts a normal force Fn on it, then the tip of the asperity will deform by a distance ‘δ’, see Figure 4-2 below, such that the pressure on the resulting contact area πr2 is equal to the yield pressure of the material; where the yield pressure of the material is close to the indentation Hardness ‘H’ of the material.
Figure 4-2: Plastically Deformed Asperity
Hence the equilibrium state can be described by:
HrFn2π=
Equation 4-2: Plastically Deformed Asperity Equilibrium State
If the ideal surface is then moved by a distance ‘dx’, equal to twice the contact radius, then Archard’s theorem states that there is a definite probability that a wear particle will be formed as per Figure 4-3. From experimental observations by Holm in 1946 it was found that these particles had roughly equal lengths in all three dimensions.
Figure 4-3: Formation of Wear Particle from Plastically Deformed Asperity
By assuming that the radius of the wear particles is proportional to the contact radius then the volume of the wear particles is given by:
332 rdV π=
Equation 4-3: Wear Particle Volume
34
If ‘Q’ is defined as the wear volume per unit movement then:
HF
rrr
dxdVQ
n
3
3
22
332
=
=
==
π
π
Equation 4-4: Derivation of Archard’s Idealised Wear Rate Equation
Given that not all of the asperities will produce wear particles then a wear coefficient ‘K’ is included in the final form of Archard’s Equation, as shown in Equation 4-1. As a consequence, the wear coefficient can be seen as the probability of an asperity producing a wear particle. The value of ‘K’ varies between 10-8 for mild wear up to 10-2 for severe wear with ‘K’ being generally less than 10-6 for fully immersedconditions.
4.2.2 Discussion
Although Archard’s equation forms the basis for a number of wear models including that put forward by Shoup and Mueller [4] for mooring chain, it contains a number of inconsistencies in its derivation and application.
The assumption that the deformation distance ‘δ’ will always be equal to the Contact Radius ‘r’ as illustrated in Figure 4-1 to Figure 4-3, appears to have no physical basis. The reality is that the deformation distance of the asperity ‘δ’ will be between zero and the asperity height ‘Ra’, see Figure 4-1, depending on the load applied and the yield pressure of the material.
It has been found that depending on which derivation of Archard’s model is reviewed the shape of the idealised asperity changes. The truncated circular cone with a hemi-spherical top (as illustrated in Figure 4-1) appears to be the closest to reality for steel as shown in Figure 4-4 and Figure 4-5 below. The single asperity concept can be extended to an idealised surface made up of multiple asperities, as shown in Figure 4-6, where ‘Ra’ is the arithmetic average of absolute values of asperity heights. Figure 4-6 also ties in well with the traced surface shown in Figure 2-6 and therefore is consistent with a number of data sources.
It should be noted, that although both ‘Ra’ (asperity height) and ‘Rb’ (base width of asperity) can be readily measured, the asperity radius r is not easy to measure, except through the use of specialist surface investigation tools such as Electron Scanning Microscopes. As a consequence, it could be seen as being more appropriate to approximate the surface by using pointed conical cones with a height of ‘Ra’ and a base diameter of ‘Rb’, given that these are measurable quantities.
35
Figure 4-4: Typical Steel Surface
Figure 4-5: Scanning Electron Microscope Surface Image
Figure 4-6: Idealised Normalised Surface
The fact that the value of ‘K’ in Archard’s Wear Equation (see Equation 4-1) varies between 10-8 for mild wear up to 10-2 for severe wear, a range of some 100million percent, would appear to show that the theory, although mathematically convenient and concise, may not be taking into account all physical aspects of wear. This, however, is outside the scope of this report. ‘K’ though, is usually interpreted as “the probability that transfer of a material fragment occurs or a wear particle is formed for a given asperity encounter” [5] and it is useful to think of it in these terms, as it forms the basis of the logic in Section 4.2.3.
36
4.2.3 Formulation of Modified Generalised Wear Model
Archard’s analysis suggests that there should be two simple rules of wear:
1. Wear is independent of the apparent area and is directly proportional to theapplied load.
2. The rate of wear is constant with sliding distance and is independent of thespeed of sliding.
As stated by Bhushan [5] there is, however, evidence that for some materials the wear rate may follow a typical bath tub curve with a high wear rate to begin with, followed by a period of steady wear, before failure of the surface results in rapid wear.
As discussed in Section 4.2.2, the assumption in Archard’s Wear Model that the vertical deformation distance ‘δ’ as the load is applied to the asperity will always be equal to the Contact Radius ‘r’ is questionable. In principle the asperity deformation distance ‘δ’ will vary between zero and the asperity height ‘Ra’ depending on the load applied and the yield pressure of the material. As a consequence, it was proposed in the aforementioned section that the asperity should be modelled as a truncated circular cone with a hemi-spherical top. It was also discussed that the hemi-spherical top radius of asperities is difficult to measure except through the use of specialist surface investigation tools such as Electron Scanning Microscopes. Due to this, it was discussed that it might be more appropriate to approximate the surface by pointed conical cones of a height ‘Ra’ and a base diameter ‘Rb’, given that these are measurable quantities. This would then lead to the following derivation of a modified Archard’s Wear Model.
From Equation 4-2, the Plastically Deformed Asperity Equilibrium State is:
HrFn2π=
Equation 4-2: Plastically Deformed Asperity Equilibrium State
Where ‘Fn’ is the normal force acting on the asperity, ‘r’ is the radius of the contact area and ‘H’ is the hardness of the material. This can be transformed to give an expression for the contact radius thus:
HFr n
π=
Equation 4-5: Contact Radius of Plastically Deformed Asperity at point of Equilibrium
If the asperity before contact is taken as a circular cone and after contact as a frustum of a circular cone, where the base diameter of the cone is ‘Rb’ (hence the base radius is Rb/2) and the starting cone height is ‘Ra’, then based on the linear relationship between the base radius of the cone and its height, the vertical deformation distance ‘δ’ will be linearly proportional to the contact radius ‘r’ and can be written as:
b
a
RrR2
=δ
Equation 4-6: Deformation Distance for Circular Cone Asperity
37
By combining Equation 4-5 with Equation 4-6, an expression for the deformation distance ‘δ’ can be developed in terms of the normal force on the asperity and the characteristics of the parent material, and its surface roughness, thus:
HF
RR n
b
a
πδ
2=
Equation 4-7: Deformation Distance in terms of normal force and material characteristics
The volumetric difference between the circular cone and frustum of the circular cone, before and after contact is:
231 rdV δπ=
Equation 4-8: Wear particle volume
Which, based on Equation 4-5 and Equation 4-7, can be re-written in terms of the normal force on the asperity and the characteristics of the parent material and its surface roughness, thus:
23
32
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HF
RRdV n
b
a
ππ
Equation 4-9: Wear particle volume in terms of normal force and material characteristics
If the ideal surface is then moved by a distance ‘dx’, equal to twice the contact radius, then there is a definite probability that a wear particle will be formed, as per Archard’s theorem (see Section 4.2.1), with a volume given by Equation 4-9. Based on Equation 4-5, the following expression can be derived for ‘dx’:
⎟⎟⎠
⎞⎜⎜⎝
⎛=
HFdx n
π2
Equation 4-10: Sliding distance to give a definite probability of a wear particle
If, as in Section 4.2.1, ‘Q’ is defined as the wear volume per unit movement then:
⎟⎠
⎞⎜⎝
⎛=
=
HF
RKR
dxdVKQ
n
b
a
3
Equation 4-11: Alternative Derivation of Wear Rate Equation
Where ‘K’, as before, is the wear coefficient and can be seen as the definite probability of an asperity producing a wear particle.
38
The wear volume ‘Vwear’, for a given sliding distance ‘d’, is therefore given by:
⎟⎠
⎞⎜⎝
⎛=
HF
RRKdV n
b
awear 3
Equation 4-12: Alternative Derivation of Wear Equation
If Equation 4-12 is compared with Equation 4-1, then the essential difference is the inclusion of the asperity height to width ratio. The inclusion of this term makes sense from a tribological point of view for at least two reasons:
• Firstly, the higher the asperity height, Ra, the higher the moment acting on itwhen the surfaces slide against each other, therefore the higher the probabilityof de-cohesion of material and the formation of wear particles. Thus Equation4-12 predicts this physical phenomenon over Archard’s original equation asstated in Equation 4-1.
• Secondly, the more slender the asperity, characterised by a low Rb, then thehigher the asperity deformation distance ‘δ’ will be as the two surfaces arepressed together until the point of equilibrium is reached as characterised byEquation 4-2. This increase in deformation distance will cause an increase indeformation volume. In turn, this will logically lead to a higher probability of awear particle being formed, and Equation 4-12 correctly predicts a higher wearvolume compared to Archard’s original equation as stated in Equation 4-1.
4.3 GENERALISED CHAIN WEAR MODEL
As with Archard’s original wear equation, see Equation 4-1, the alternative generalised wear equation, see Equation 4-12, is based on the sliding distance ‘d’. Similarly, Archard’s original wear equation has been applied to rolling contact situations through the use of a different wear coefficient ‘K’ [5].
Section 3.1 above derived the rolling and sliding distances for changes in relative angles between two idealised chain links, for angles less than or greater than the Roll Up Limit Angle ‘dβCritical’, see Equation 3-8 and Equation 3-9 respectively. The next step in the derivation of the Generalised Wear Model is to combine these distance equations, with the alternative proposed generalised wear equation.
However, the discussion in Section 3.2.2 with regard to the influence of Proof Loading and the consequential ‘witness mark’ on chain motion is relevant and a further equation is required to define whether the wear regime will be affected by the ‘witness mark’. As discussed in Section 3.2.2, if the initial adjacent link angle is within the ‘witness mark’ then it is likely that the wear regime will be sliding only, although it could be argued that is the angle change keeps the contact point within the ‘witness mark’ then the regime will be rolling only until the angle change is out with the witness mark. For simplicity and practicality though, chain motion within the ‘witness mark’ will be defined as sliding only; since wear results in effectively an increase in the dimensions of what is called a “witness mark” when new, and hence also decreases the roll up limiting angle and the amount of rolling. This assumption will lead to a marginally conservative model as sliding wear for a given load will generate a higher wear volume than rolling wear for the same load and angle change.
39
Hence, the change in wear regime can be defined based on whether the starting angle is within or out-with the witness mark. The witness mark can be no greater than the nominal chain bar diameter ‘D’ and will generally be significantly less, which gives rise to the following equation if ‘w’ is used as the theoretical witness mark width:
Chain Studded Standardfor
56.2164.0
tan
Chain Studless Standardfor 205625.0
5.0tan
2
2
1
2
1
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛−
⎟⎟⎠
⎞⎜⎜⎝
⎛
=−
−
DwD
w
Dw
markwitnessβ
Equation 4-13: Wear Regime Starting Angle ‘βwitness mark’
This then allows the
following equations to be stated for the three wear regimes for studless chain, namely: rolling only, rolling and sliding, and sliding only.
onlyRollingH
FFR
RKdrVddFor nn
b
aRollingwearRollingCriticalMarkWitness …… ⎟
⎠
⎞⎜⎝
⎛ Δ+=<>
5.03
& βββββ
Equation 4-14: Rolling only Wear Volume for change in angle ‘dβ’
( )
wearSlidingwearRollingwearSlidingRolling
nn
b
aSlidingCriticalwearSliding
nn
b
aRollingCriticalwearRolling
CriticalMarkWitness
VVV
SlidingH
FFR
RKdRdrV
RollingH
FFR
RKdrV
ddFor
+=
⎟⎠
⎞⎜⎝
⎛ Δ++=
⎟⎠
⎞⎜⎝
⎛ Δ+=
>>
&
5.03
5.03
& …
…
… ββ
β
ββββ
Equation 4-15: Studless Chain Rolling and Sliding Wear Volume for change in angle ‘dβ’
( ) onlySlidingH
FFR
RKdRVFor nn
b
aSlidingwearSlidingMarkWitness …… ⎟
⎠
⎞⎜⎝
⎛ Δ+=<
5.03
βββ
Equation 4-16: Studless Chain Sliding Wear Volume only for change in angle ‘dβ’
And similarly the following equations can be stated for standard geometry studded chain:
onlyRollingH
FFR
RKdrVddFor nn
b
aRollingwearRollingCriticalMarkWitness …… ⎟
⎠
⎞⎜⎝
⎛ Δ+=<>
5.03
& βββββ
Equation 4-17: Rolling only Wear for Standard Studded Chain
40
( )( )( )( )
wearSlidingwearRollingwearSlidingRolling
nn
b
aSliding
Critical
wearSliding
nn
b
aRollingCriticalwearRolling
CriticalMarkWitness
VVV
Sliding
HFF
RRK
ddr
V
RollingH
FFR
RKdrV
ddFor
+=
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
⎟⎠
⎞⎜⎝
⎛ Δ+×
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛
×−
−×+
=
⎟⎠
⎞⎜⎝
⎛ Δ+=
>>−
−
&
1
1
5.03
tan5.2tantan5.2tan
5.03
& …
…
…β
βββ
β
ββββ
Equation 4-18: Rolling and Sliding Wear for Standard Studded Chain
( )( )( )( )
SlidingH
FFR
RKdVFor nn
b
aSlidingwearSlidingMarkWitness ……
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡⎟⎠
⎞⎜⎝
⎛ Δ+⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛
×−
−×=<
−
− 5.03tan5.2tan
tan5.2tan1
1
β
ββββ
Equation 4-19: Sliding Wear only for Standard Studded Chain
Where ‘r’ is the chain bar radius and is nominally equal to ‘0.5D’ and ‘ΔFn’ is the change in tension from the start to the end of the angular change.
These equations are not easy to apply in practice, however, proving runs for the chafe chain of a tri-catenary mooring system (TCMS), in the time domain, for regular waves showed that once steady state motion is achieved then the angular motion and changes in line tension are generally of a sinusoidal nature, as illustrated in the following figures:
0.0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
200.0 210.0 220.0 230.0 240.0 250.0 260.0 270.0 280.0 290.0 300.0
Relativ
e An
gle (deg)
Time (s)
Relative Angle between Links in 5.25m Regular Wave
Figure 4-7: Relative Angle between Links in 5.25m Regular Wave
0500
10001500200025003000350040004500
200.0 210.0 220.0 230.0 240.0 250.0 260.0 270.0 280.0 290.0 300.0
Tension (kN)
Time (s)
Tension between Links in Regular Wave
Figure 4-8: Tension between Links in 5.25m Regular Wave
41
Where the small amount of deviation from the sine wave is caused by ‘numerical noise’ within the calculations rather than due to any physical effect. Given this, and the theory of Fourier Analysis that any irregular wave can be formed by superimposing a number of regular waves of varying wave height and period, then Equation 4-14 and Equation 4-15 can be reformulated for ‘n’ regular wave heights and ‘m’ regular wave periods i.e. a regular wave scatter diagram, to give an equation for idealised chain wear volume for studless chain:
( ) ( ){ }
∑∑= =
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
+<
⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
++>
<>
=m
j
n
i
ji
b
a
jiCrticalMarkWitnessji
jiCrticalSlidingCriticalRollingCriticalji
RollingjiCriticalji
Witnessji
Wear HT
RR
dRdr
dRdrKdrKddIf
KdrddIf
V1 1
,
,,
,,
,,
,
3ββββ
βββββ
βββββ
…
…
……
Equation 4-20: Total Wear Volume for Studless Chain
and similarly, for standard geometry studded chain:
( ) ( )( )( )( )
( )( ) ( )( )( )( ){ }
∑∑= =
−−
−
−
⎟⎟⎠
⎞⎜⎜⎝
⎛
⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
×−−×<
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
×−
−×++>
<
>=
m
j
n
i
ji
b
a
jijijiSlidingMarkWitnessji
ji
jiji
CriticalSlidingCriticalRollingCriticalji
RollingjiCriticalji
MarkWitnessji
Wear HT
RR
dK
ddrKdrKddIf
KdrddIf
V1 1
,
,1
,,1
,
,1
,,1
,
,,
,
3
tan5.2tantan5.2tan
tan5.2tan
tan5.2tan
βββββ
β
ββββββ
βββ
ββ
…
…
…
…
Equation 4-21: Total Wear for Standard Studded Chain
Where, ‘dβi,j’ is the angular change and ‘Ti,j’ is the mean tension due to the regular wave of height ‘i’ and period ‘j’. KRolling and KSliding being the wear coefficients for chain rolling and sliding respectively. These two coefficients can be found from analysing existing mooring systems where the actual wave conditions and chain wear volumes are known over time.
For a given wave condition (height and period) the angular change and mean tension can typically be found from a finite element time domain mooring analysis program, such as Orcaflex. When using these programs it is important that the finite element length within the catenary is set at the effective length of a chain link i.e. 4D.
42
4.4 DIAMETER LOSS TO VOLUME LOSS
Generally the wear volume is not a measurable parameter, but the inter-grip diameter can be measured; hence the need for a model that relates the two. The development of this is discussed below.
Typically on a mooring system the inter-grip double diameter is measured, as illustrated in the figure below:
Figure 4-9: Inter-grip Double Diameter Measurement
By comparison to previous measurement results, the diameter loss within the inter-grip area for the time period between surveys can be found. As discussed in Section 4.3, the wear models given above are designed to calculate the volume of the ‘lost’ material rather than the change in diameter. Hence a method is required to link the volume to diameter, something that is made slightly more complicated by the different wear patterns that can be found on mooring chains, as illustrated by the pictures overleaf.
43
Figure 4-10: Light Narrow Wear
Figure 4-11: Heavy Narrow Wear
44
Figure 4-12: Light Broad Wear
Figure 4-13: Heavy Broad Wear
45
In addition, as discussed in Section 3.2.1, the actual geometry of the links needs to be taken into account in the diameter loss versus volume loss relationship as well as the fundamental difference in geometry between a studded and studless link, as shown below:
Figure 4-14: Chain Link Geometry
These geometric restrictions are best represented through the use of ellipses or part ellipses. As when the semi-major and semi-minor axes of an ellipse are set equal to each other, then the resultant curve is a circle or arc that represents idealised geometry.
From examination of Figure 4-10 to Figure 4-13 it can be seen that the wear zone does not appear to extend past the tangent point, as shown below:
Figure 4-15: Cross-section of Worn Chain Link
46
Given that this means that the wear zone has a defined width across the bar, and the extent of the wear can be measured, see Figure 3-18 and Figure 3-22, then this effectively bounds the wear zone. Hertzian Contact theory, for two arbitrary curved bodies in contact [6] suggests that the contact zone will be elliptical in shape. There is therefore a logic in suggesting that the wear zone will have an elliptical boundary, with a major axis length equal to the wear extent and a minor axis length equal to the chain bar width, see Figure 4-15.
A bi-directional bounded elliptical surface can then be developed to describe the wear zone, as below where the dimensions are as shown in Figure 4-16:
( ) ( ) ( )
( )
( )
( )
( )
BarChain across Resolution Surface Wear ofExtent across Resolution SurfaceArea grip-Interin Depth HalfBar Chain
Area grip-Interin Bar Chain ofwidth -Half WearofExtent ofwidth -Half
DiameterChain Nominal1-n0j1-m0i
12
12
Chain Studded Standardfor 64.0
112
Chain Studless Standardfor 675.0675.0
1
1
:
10,
1,
2
2
22
2
22
2
2
22
1
2
2
2
2
2
2
2
2
21
,
=
=
=
=
=
=
=
=
−⎟⎠
⎞⎜⎝
⎛−
×=
−⎟⎠
⎞⎜⎝
⎛−
×=
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛−−
−−
=
⎟⎟⎠
⎞⎜⎜⎝
⎛−×=
⎟⎟⎠
⎞⎜⎜⎝
⎛−×=
>+∀=
≤+⇔−+==
nmcbaD
bn
bjY
am
aiX
DaD
aDD
d
aXdXf
bY
cYf
wherebY
aXYXf
bY
aXXfdYfYXf
Z
j
i
ii
jj
jiji
jiijji
ji
……
Equation 4-22: Initial Wear Zone Surface
47
Figure 4-16: Wear Zone Dimension Definition
The following plots show the resultant surface for a 100mm stud-less chain link with a wear extent of ‘D’, representing Narrow Banded Wear, and ‘1.346D’, representing Broad Banded Wear, where the chain bar half width and depth has been set to ‘0.5D’ i.e. nominally round chain bar.
Figure 4-17: Initial Narrow Banded Wear Surface Figure 4-18: Initial Broad Banded Wear Surface
Comparison of plots Figure 4-17 and Figure 4-18 with the narrow banded and broad banded wear pictures, see Figure 4-10 to Figure 4-13, show that the surface given by Equation 4-22 is a gives a good representation of the wear surface. In addition, given that the shape resembles that of a ‘Pringle’ crisp, then this has given rise to this being called the ‘Pringle’ model.
A similar surface can then be fitted to the wear zone for a change in Chain Bar Depth ‘Δc’, which represents the change in half the intergrip measurements between two different surveys, as shown below:
D
Δc
a
b
c
48
( ) ( ) ( )
( )
( ) ( )
( ) ( )
depth wear theasknown also Depth,Bar Chain in Change
1
1
:
10,
1,
2
22
2
2
22
1
2
2
2
2
2
2
2
2
21
,
=Δ
⎟⎟⎠
⎞⎜⎜⎝
⎛−×Δ+=
⎟⎟⎠
⎞⎜⎜⎝
⎛−×Δ−=
>+∀=
≤+⇔−Δ++==ʹ′
caXcdXf
bY
ccYf
wherebY
aXYXf
bY
aXXfcdYfYXf
Z
ii
jj
jiji
jiijji
ji
Equation 4-23: Worn Wear Zone Surface
This then allows the wear volume to be approximated by multiplying the area of each ‘i,j’ square cell by its associated height difference, between the initial and worn surface, as shown below. The accuracy of the approximation is dependent on the chosen Surface Resolutions ‘m’ and ‘n’.
( )∑∑−
=
−
=
ʹ′−⎟⎠
⎞⎜⎝
⎛−
⎟⎠
⎞⎜⎝
⎛−
=1
0
1
0,,1
21
2 n
j
m
ijijiWear ZZ
nb
maV
Equation 4-24: Calculated Wear Volume
If this calculation is undertaken for a range of wear depths for a specific chain link and wear extent, then a simple relationship can be found between the Volume wear, ‘Vwear’, and wear depth, ‘∆c’, as shown below for the chain data used to find the sliding wear coefficient, ‘Ksliding’ in Section 5.
y = 0.0001x -‐ 0.0002R² = 1
0
0.5
1
1.5
2
2.5
3
0.00E+00 5.00E+03 1.00E+04 1.50E+04 2.00E+04 2.50E+04
Wear D
epth (m
m)
Wear Volume (mm3)
Wear Depth versus Wear Volume
Figure 4-19: Wear Depth versus Wear Volume for Calibration Mooring System
49
4.5 CHAIN WEAR CALCULATION METHODOLOGY
By combining all of the issues discussed in Sections 4.2 to 4.4 a complete methodology can be put together to calculate chain wear, as illustrated in the following flow chart.
Create Regular Wave Scatter Matrix (W)Size mxn
Create Time Domain Model of Mooring System
Note: Line in way of links of interest must be modelled as individual links
For each wave height and period with occurrence data run time domain model to
achieve steady state motion
From each time domain analysis extract mean tension and angle change range for
inter-grip of interest
Create MeanTension Matrix (T)
Size mxn
Create Angle ChangeRange Matrix (dβ)
Size mxn
Sliding Only?Equation 4-30
Calculate Critical AngleβCritical
Equation 4-29
Is dβi,j < βCritical
No
Calculate rolling wear volume entry Vi,j for wave scatter entry i,j
Equation 4-25
Yes
Calculate rolling and sliding wear volume entry Vi,j for wave scatter entry i,j
Equation 4-26
No
Calculate sliding wear volume entry Vi,j for wave scatter entry i,j
Equation 4-27
Yes
Calculate overall wear volume for Wave Scatter Matrix Time
Span by summing Wear Volume Matrix DV
Calculate change in diameter from wear volume using
‘Pringle’ modelSee Section 4.4
Calculate Material Wear Constant (Cm)Equation 4-28
Calculate overall wear volume for each Wave Scatter Matrix Entry with Occurrence data:
DVi,j=Wi,j x Vi,j
Create Starting Angle Matrix (β)
Size mxn
Figure 4-20: Chain Wear Calculation Methodology
50
Where the equations referenced in Figure 4-20 are:
Chain Studdedor Studless,,, …jiRollingjimji TKdrCV β=
Equation 4-25: Rolling Only Wear Volume for Regular Wave ‘i,j’
( ) ( )( )( )
( )( )( )( )
ChainStuddedGeometryStandard
tan5.2tan
tan5.2tan
ChainStudless
,1
,,1
,
,,…
…
⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
×−
−×+
+
++
=
−
−
ji
jiji
Critical
Sliding
CriticalRolling
jiCrticalSlidingCriticalRolling
jimji
d
dr
K
drK
dRdrKdrK
TCV
β
ββ
β
β
βββ
Equation 4-26: Rolling and Sliding Wear for Regular Wave ‘i,j’
( )( )( )( )
( )( ) ChainStuddedGeometryStandardtan5.2tan
tan5.2tan
ChainStudless
,1
,,1
,
,,…
…
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
×−
−×=−
−
ji
jiji
Sliding
jiSliding
jimji dK
dRK
TCV
β
ββ
β
Equation 4-27: Sliding Only Wear for Regular Wave ‘i,j’
Where, ‘r’ is the chain bar radius and can be taken, in the absence of other data, as half the nominal diameter of the chain i.e. ‘0.5D’. Similarly, ‘R’ is the inner radius of a studless chain link and can be taken as ‘0.675D’ for standard geometry studless chain in the absence of other data.
The material constant ‘Cm’ is given by:
b
am HR
RC3
=
Equation 4-28: Material Constant
And the Roll up Limit Angle, ‘dβcritical’, is found by solving the following equation for ‘dβcritical’, for the relevant type of chain:
( ) ( )( )( ) ( )( ) Chain StuddedGeometry Standardtantan28.0
tan8.0tan32.0tantan
Chain Studless1tan
1
…
…
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
+−
⎟⎟⎠
⎞⎜⎜⎝
⎛
×××−
×+××
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛+
=−
Critical
Critical
Critical
Critical
ddr
dr
Rrd
ββ
ββββ
β
µ
Equation 4-29: Roll Up Limit Angle
And the wear regime is chosen by checking whether the starting angle is within or out with the ‘witness mark’ angle, ‘βWitness Mark’, which is given by:
51
Chain Studded Standardfor
2.31224
tan
Chain Studless Standardfor 205625.0
5.0tan
1
2
1
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎠
⎞⎜⎝
⎛−−
−⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
−
−
DD
D
DD
markwitnessβ
Equation 4-30: Wear Regime Starting Angle ‘βwitness mark’
This set of equations can then be used in combination with a Regular Wave Scatter Diagram Matrix, ‘W’, and a time domain mooring analysis model to calculate the wear volume using the method shown in Figure 4-20. Through the use of the ‘pringle’ model, see Section 4.4, the change in chain bar diameter, for the time period covered by the occurrence data in the wave scatter diagram, can then be calculated.
It should be noted, that the mooring line in the time domain model in the way of the inter-grip area of interest, should have a segment length equal to the inter-grip distance i.e. 4 x D for standard geometry studless or studded chain, and for some distance either side of it. This being required in order to ensure that the actual angle and angle change between the links is correctly modelled and recorded.
For practical application, Appendix A contains the above methodology in a step by step form for different types of chain. In order to be able to use this methodology, however, values of Krolling and Ksliding are required, the derivation of these is described is Section 5.
52
5 CHAIN WEAR CALCULATION CALIBRATION
5.1 INTRODUCTION
Examination of the proposed chain wear calculation method, and associated equations in Section 4.5, shows that all parameters except for the rolling and sliding wear coefficients, ‘KRolling’ and ‘KSliding’, are known, calculable, or measurable quantities. The wear coefficients, however, can only be found by running the proposed chain wear calculation method for a mooring system, where both the regular wave scatter diagram and wear loss is known.
To this end, a time domain mooring analysis model, sea-state occurrence data, and wear data, have been made available to the JIP for the chafe chain of a tri-catenary mooring system, as illustrated below:
Figure 5-1: Tri-Catenary Mooring System (TCMS)
Due to the fact that the Chafe Chain is always in tension it has a minimal catenary. Therefore the inter-grip contact point is always within the ‘witness mark’ of the chain links. Consequently, based on the methodology given in Figure 4-20, it can be assumed that the links will only ever be subject to sliding wear. Thus the system and associated data can be used to find a value for the sliding wear coefficient, ‘KSliding’, by using the following method:
1. Calculate actual Wear Volume, VActual, for the time period covered by the sea-state occurrence data, by using the ‘Pringle’ model, as per Section 4.4
2. Calculate regular wave scatter diagram from sea-state occurrence data
3. Run chain wear calculation method as per Figure 4-20 with KSliding=1.0 tocalculate Wear Volume, VCalculated, for the time period covered by the sea-stateoccurrence data
4. Compare Actual and Calculated Wear Volumes, and adjust the Sliding WearCoefficient ‘KSliding’ until VCalculated = VActual
These four steps are described in more detail in the following sections.
FPSO
Chafe Chain
3 Mooring Legs
4 Umbilicals
53
5.2 ACTUAL WEAR VOLUME
The chafe chain consists of a length of 130mm nominal diameter extra wide studless chain with an inner end radius of ‘0.775D’. Double Diameter inter-grip measurements, see Figure 4-9, were taken for each of the first 14 links of the chafe chain approximately every six weeks over a four year period, as detailed below for the link 2/3 interface for the first time period of anomaly free measurements:
Measurement Day
Previous Measurement Interval (days)
Double Diameter Measurement
(mm)
Change in diameter
(mm)
Diameter change rate per annum
(mm/year) 36 0 246
186 150 245 -0.5 -1.217234 48 245 0.0 0.000 267 33 245 0.0 0.000 307 40 243 -1.0 -9.125404 97 243 0.0 0.000 449 45 241 -1.0 -8.111484 35 241 0.0 0.000 514 30 241 0.0 0.000 562 48 241 0.0 0.000
Average -2.050
Table 5-1: Link 2/3 Chafe Chain Inter-grip Double Diameter Measurements
Given this average annual chain diameter loss rate of 2.050mm per year, what is required is the annual volume loss. From Section 4.4 the following equations for the initial and worn surface can be stated:
( )
( )
( ) ( ) ( )
( )
( )
BarChain across Resolution Surface201 Wear ofExtent across Resolution Surface201
depth wear theasknown also Depth,Bar Chain in Change050.2Area grip-Interin Depth HalfBar Chain 65
Area grip-Interin Bar Chain ofwidth -Half65 WearofExtent ofwidth -Half65
DiameterChain Nominal1301-n0j1-m0i
12
12
Chain Studless WideExtrafor 775.0775.0
:
10,
111,
10,
111,
22
2
2
2
2
2
2
2
2
2
22
2
22
,
2
2
2
2
2
2
2
2
2
22
2
22
,
==
==
==Δ
==
==
==
==
=
=
−⎟⎠
⎞⎜⎝
⎛−
×=
−⎟⎠
⎞⎜⎝
⎛−
×=
−−=
>+∀=
≤+⇔⎟⎟⎠
⎞⎜⎜⎝
⎛−×Δ+−Δ++⎟
⎟⎠
⎞⎜⎜⎝
⎛−×Δ−=
=ʹ′
>+∀=
≤+⇔⎟⎟⎠
⎞⎜⎜⎝
⎛−×−+⎟
⎟⎠
⎞⎜⎜⎝
⎛−×=
=
nm
mmcmmcmmbmma
mmD
bn
bjY
am
aiX
aDDd
wherebY
aXYXf
bY
aX
aXcdcd
bY
ccYXfZ
bY
aXYXf
bY
aX
aXdd
bY
cYXfZ
j
i
jiji
jiijji
ji
jiji
jiijji
ji
……
Equation 5-1: Initial and Worn Chafe Chain Wear Zone Surfaces
54
( )∑∑−
=
−
=
ʹ′−⎟⎠
⎞⎜⎝
⎛−
⎟⎠
⎞⎜⎝
⎛−
=1
0
1
0,,1
21
2 n
j
m
ijijiWear ZZ
nb
maV
Equation 5-2: Calculated Chafe Chain Wear Volume
Substitution of the data stated in Equation 5-1, and the results into Equation 5-2, with the stated resolution of 201 x 201, results in a calculated wear volume rate of 2.315 x 104 mm3 per annum. Use of a higher resolution of 401 x 401 results in an answer that is only 0.025% higher, and therefore the selected resolution can be seen as being high enough to minimise the calculation error.
5.3 REGULAR WAVE SCATTER DIAGRAM
5.3.1 Data
During the time that the unit was operating, a number of the deck crew members were specially trained to take sea-state observations, which they did and recorded every three hoursi. This information was supplied to the JIP in the form of occurrence data, along with associated Mean Zero Crossing and Wave Periods, as shown in Table 5-2 below. The Mean Zero Crossing (Tz) and Peak (Tp) Periods were derived based on a Jonswap Spectrum with a γ=3.0, which is known to be a good representation of the wave spectrum in the area that the unit was operating.
Significant Wave Height (m) Occurrence
Mean Zero Crossing Period (s)
Peak Period
(s)
Number of 3hour Storms
per Annum From To Mean 0.0 0.5 0.25 26.5% 4.61 5.98 773.80 0.5 1.0 0.75 18.2% 4.82 6.25 531.44 1.0 1.5 1.25 15.0% 5.20 6.74 438.00 1.5 2.0 1.75 11.3% 5.75 7.46 329.96 2.0 2.5 2.25 8.7% 6.23 8.08 254.04 2.5 3.0 2.75 6.5% 6.56 8.51 189.80 3.0 3.5 3.25 4.6% 6.79 8.81 134.32 3.5 4.0 3.75 3.1% 7.42 9.62 90.52 4.0 4.5 4.25 2.3% 7.51 9.74 67.16 4.5 5.0 4.75 1.6% 7.69 9.97 46.72 5.0 5.5 5.25 0.9% 8.36 10.84 26.28 5.5 6.0 5.75 0.6% 8.50 11.02 17.52 6.0 6.5 6.25 0.4% 8.50 11.02 11.68 6.5 7.0 6.75 0.2% 8.75 11.35 5.84 7.0 7.5 7.25 0.1% 9.50 12.32 2.92
Table 5-2: Seastate data
Given that the proposed Chain Wear Calculation Method described in Section 4.5 is reliant on a regular wave scatter diagram, a method was required to convert the sea-state data to such a diagram.
i. It is not often considered practicable to take visual observations of sea height as reliable readings, andhence why specific training was given. Additionally a sample of observations were tallied with a metoceanmodel for the applicable fetch distances based on the measured mean wind speeds in 3 hour periods andcorrelation was found to be within 6.5% of waveheight.
55
5.3.2 Method
Daemrich, Mai, Ohle, and Tautenhain described such a method in their paper to the 2nd Chinese-German Joint Symposium on Coastal and Ocean Engineering [7]. The basic methodology is:
• Solve Equation 5-3 for the given Significant Wave Height, ‘Hs’, and Peak Period,‘Tp’, pair to find α
• Assign Storm Length, ‘Ts’, in seconds
• Calculate the frequency bin width, ‘Δf’, using Equation 5-5
• Assign maximum spectral frequency ‘fmax’
• Calculate number of wave amplitudes, using Equation 5-6
• Calculate the wave amplitudes, using Equation 5-7
• Assign a random phase angle, ‘phasei’, to each wave amplitude
• Assign the number of points, ‘Ss’, to be created along the irregular wave timeseries over the storm period, ‘Ts’
• Calculate Time Series Wave Height at each time series point using Equation5-8
• Use a zero down crossing routine to count number of waves of each selectedwave height and wave period bin, thus returning the regular wave scatterdiagram
( )( )∫= dfffSHs04
Equation 5-3: Significant Wave Height
( )( )
( )
Tpf
ffff
ff
fgfS
p
p
p
pf
pff
p
1
09.007.0
45exp
2
222
2exp4
54
2
=
≥
<=
×⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟⎟⎠
⎞⎜⎜⎝
⎛−×=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛ −−−
…
…σ
γπα σ
Equation 5-4: Spectral Density Distribution Function
sTf 1
=Δ
Equation 5-5: Frequency Bin Width
Integerf
fn ⎟⎟⎠
⎞⎜⎜⎝
⎛
Δ= max
Equation 5-6: Number of Wave Amplitudes
56
( ) ( ) ffSfa Δ= 2
Equation 5-7: Spectral Density Distribution
( ) ( )
( )11
00
2sin
1
1
0
−=⇔+
=⇔
=
+−=
−
−
=∑
ss
sk
k
n
iikiik
SkSTT
kT
phaseTffaZ
…
π
Equation 5-8: Time Series Wave Height over Storm Period ‘Ts’
5.3.3 Results
Application of the methodology given in Section 5.3.2, to the sea-state data given in Table 5-2, with the additional parameters as stated in Table 5-3, resulted in the production of the fifteen regular wave scatter diagrams given in Appendix D.
Parameter Variable Value Peakedness Factor γ 3.0 Acceleration due to Gravity g 9.8065m/s2 Storm Length Ts 10,800s ≡ 3hour storm Maximum Spectral Frequency fmax 0.5Hz Number of Storm Creation Points Ss 108,000
Random Phase Vector Phasei Mathcad Function
runif(n,-2π,2π)
Table 5-3: Irregular Wave Factors
Each of the regular wave scatter diagrams given in Appendix D was calculated for a 3 hour storm, for the applicable mean significant wave height given in Table 5-2. Hence, the annual regular wave scatter diagram can be calculated by summing the multiplication of each of the fifteen individual wave scatter diagrams by the number of 3hour storms per annum associated with it. The result of this manipulation is given in Table 5-4.
57
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50 0.5 0.25 7.02E+03 8.75E+04 3.33E+05 4.78E+05 5.37E+05 6.88E+05 4.26E+05 1.16E+05 2.38E+04 5.41E+03 3.72E+03 3.79E+03 4.12E+03 4.45E+03 4.78E+03 5.11E+03
0.5 1 0.75 8.64E+02 9.57E+03 4.30E+04 1.13E+05 2.13E+05 3.19E+05 2.83E+05 1.15E+05 3.39E+04 8.20E+03 2.61E+03 1.04E+03 2.54E+02 0 0 01 1.5 1.25 6.13E+01 0.00E+00 4.10E+03 4.26E+04 1.02E+05 1.57E+05 1.61E+05 1.07E+05 5.20E+04 2.31E+04 7.95E+03 2.88E+03 2.95E+02 0 0 0
1.5 2 1.75 2.92E+00 0 0 3.37E+03 2.96E+04 7.00E+04 1.16E+05 1.05E+05 8.24E+04 3.55E+04 8.86E+03 2.89E+03 6.66E+02 2.34E+02 0 02 2.5 2.25 0 0 0 2.28E+02 5.36E+03 2.27E+04 6.58E+04 8.00E+04 6.13E+04 2.62E+04 1.12E+04 3.34E+03 1.53E+03 2.74E+02 3.21E+01 0
2.5 3 2.75 0 0 0 1.08E+02 5.11E+02 7.20E+03 3.93E+04 4.90E+04 3.44E+04 1.91E+04 9.14E+03 2.85E+03 1.76E+03 5.46E+02 1.55E+02 03 3.5 3.25 0 0 0 0 9.64E+01 9.23E+02 1.07E+04 2.23E+04 1.99E+04 1.49E+04 7.41E+03 2.67E+03 1.59E+03 3.77E+02 8.18E+01 0
3.5 4 3.75 0 0 0 0 0 3.10E+02 2.69E+03 1.36E+04 1.30E+04 1.09E+04 6.16E+03 1.96E+03 1.27E+03 4.15E+02 1.20E+02 04 4.5 4.25 0 0 0 0 0 4.67E+01 8.91E+02 6.39E+03 6.17E+03 6.46E+03 4.27E+03 1.59E+03 1.08E+03 4.15E+02 6.13E+01 0
4.5 5 4.75 0 0 0 0 0 0 1.14E+02 3.45E+03 4.85E+03 5.27E+03 3.29E+03 1.16E+03 6.10E+02 1.49E+02 6.42E+01 05 5.5 5.25 0 0 0 0 0 0 5.84E+01 1.28E+03 3.10E+03 3.47E+03 2.16E+03 9.81E+02 6.42E+02 1.02E+02 7.01E+01 0
5.5 6 5.75 0 0 0 0 0 0 2.92E+00 8.58E+02 1.73E+03 1.74E+03 1.73E+03 6.37E+02 4.50E+02 6.72E+01 1.46E+01 06 6.5 6.25 0 0 0 0 0 0 2.63E+01 2.10E+02 1.38E+03 1.35E+03 8.61E+02 4.41E+02 3.50E+02 3.80E+01 1.75E+01 0
6.5 7 6.75 0 0 0 0 0 0 1.75E+01 1.69E+02 7.07E+02 8.26E+02 6.13E+02 2.69E+02 1.43E+02 2.63E+01 5.84E+00 07 7.5 7.25 0 0 0 0 0 0 1.75E+01 0 6.95E+02 5.58E+02 4.53E+02 2.57E+02 1.58E+02 2.34E+01 2.92E+00 0
7.5 8 7.75 0 0 0 0 0 0 0 0 2.77E+02 4.15E+02 2.07E+02 1.90E+02 7.88E+01 2.92E+00 8.76E+00 08 8.5 8.25 0 0 0 0 0 0 0 0 1.37E+02 2.80E+02 1.64E+02 1.11E+02 4.67E+01 1.17E+01 0 0
8.5 9 8.75 0 0 0 0 0 0 0 0 1.17E+02 5.26E+01 1.26E+02 9.05E+01 2.63E+01 2.92E+00 0 09 9.5 9.25 0 0 0 0 0 0 0 0 1.17E+01 6.72E+01 4.96E+01 2.63E+01 2.92E+01 0 0 0
9.5 10 9.75 0 0 0 0 0 0 0 0 0 2.63E+01 3.50E+01 4.96E+01 5.84E+00 0 0 010 10.5 10.25 0 0 0 0 0 0 0 0 0 1.17E+01 3.50E+01 2.04E+01 1.46E+01 0 0 0
10.5 11 10.75 0 0 0 0 0 0 0 0 0 1.17E+01 2.04E+01 1.17E+01 2.92E+00 2.92E+00 0 011 11.5 11.25 0 0 0 0 0 0 0 0 0 0 2.92E+00 2.92E+00 0 2.92E+00 0 0
11.5 12 11.75 0 0 0 0 0 0 0 0 0 0 2.92E+00 0 0 0 0 012 12.5 12.25 0 0 0 0 0 0 0 0 0 0 5.84E+00 2.92E+00 2.92E+00 0 0 0
12.5 13 12.75 0 0 0 0 0 0 0 0 0 0 2.92E+00 0 0 0 0 013 13.5 13.25 0 0 0 0 0 0 0 0 0 0 0 0 2.92E+00 0 0 0
13.5 14 13.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 14.5 14.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14.5 15 14.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 15.5 15.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wave Period (Seconds)
Wav
e H
eigh
t (M
etre
s)
Table 5-4: Calculated Regular Wave Scatter Diagram
58
5.4 CHAIN WEAR CALCULATION
The time domain model of the mooring system of the subject unit was modified, so that the length of the segments within the chafe chain element was equal to ‘4D’, where ‘D’ is the nominal diameter of the chain, i.e. the distance between each inter-grip area. The model was then run for each of the regular wave height and period pairs, with occurrence data, shown in Table 5-4. The simulation period for each run was set such that five full waves would pass through the model in the build up period, before ten waves passed through the model in the measuring period. This number of waves was found to be suitable in early testing to ensure that steady state motion occurred during the measuring period. On completion of all of the runs, the mean tensions and angular change ranges, between links 2 and 3 were extracted, as shown in Table 5-6 and Table 5-7 respectively.
Given the discussion in Section 5.1 that the chafe chain will only be subject to sliding wear, then the governing wear equation is:
( )( )∑∑= =
=m
j
n
ijiSlidingjimWear dDKTCV
1 1,, 775.0 β
Equation 5-9: Sliding Only Wear for Regular Wave ‘i,j’
Where the material constant ‘Cm’ is given by:
b
am HR
RC3
=
Equation 5-10: Material Constant
The basic chain data for the subject unit is: Symbol Quantity Unit Description Source
Ra 6.20x10-06 metres Asperity Height From Corus for turned bar supplied by them for offshore chain
Rb 6.20x10-06 metres Asperity Width Guesstimate from examination of steel surface pictures
H 9.20x1008 pascals Hardness of material Measured Data for Chafe Chain of Subject Unit
r 0.065 metres Chain Bar Radius Nominal Chain Radius for Subject Unit
R 0.101 metres Chain Inner Radius Chafe Chain of Subject Unit is Extra Wide
Table 5-5: Basic Chain Data for Subject Unit
Application of the data in Table 5-5 to Equation 5-10, results in a material constant of 3.6232 x 10-4 mm2/N. With the sliding wear coefficient, ‘KSliding’, set to unity, the result of applying Equation 5-9 to the mean tension and angular change range data in Table 5-6 and Table 5-7 respectively resulted in a wear volume rate of 994,018 mm3 per annum. Given that the actual wear volume rate was calculated to be 2.315 x 104 mm3 per annum in Section 5.2, then it can be seen that the sliding wear coefficient, ‘KSliding’, requires calibration.
59
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50.25 0.00000 2,039.9 2,039.7 2,039.4 2,039.1 2,039.2 2,039.3 2,039.4 2,039.4 2,039.3 2,039.2 2,039.2 2,039.2 2,039.2 2,039.2 2,039.20.75 0.00000 2,039.9 2,039.9 2,039.9 2,039.9 2,040.4 2,040.8 2,040.8 2,040.8 2,042.8 2,044.9 2,044.4 2,043.91.25 0.00000 2,042.7 2,042.1 2,042.0 2,040.9 2,043.9 2,041.6 2,038.0 2,041.6 2,045.5 2,047.7 2,048.11.75 0.00000 2,046.9 2,046.9 2,046.2 2,049.5 2,042.2 2,034.8 2,038.1 2,041.4 2,046.3 2,051.1 2,051.12.25 2,054.7 2,054.7 2,052.6 2,056.6 2,044.1 2,035.6 2,037.3 2,039.0 2,045.8 2,052.7 2,055.6 2,058.52.75 2,064.0 2,064.0 2,060.5 2,063.1 2,047.0 2,037.0 2,037.7 2,038.4 2,046.0 2,053.5 2,058.3 2,063.13.25 2,071.6 2,066.3 2,069.0 2,051.9 2,042.8 2,041.2 2,039.7 2,047.3 2,055.0 2,061.2 2,067.53.75 2,057.3 2,077.9 2,051.3 2,052.8 2,051.0 2,050.5 2,053.6 2,060.3 2,069.0 2,075.74.25 2,060.6 2,090.7 2,082.4 2,074.0 2,069.9 2,065.9 2,083.3 2,073.5 2,092.5 2,088.14.75 2,110.6 2,109.0 2,107.3 2,100.6 2,093.9 2,113.0 2,092.3 2,115.9 2,106.75.25 2,133.7 2,136.9 2,140.2 2,134.3 2,128.4 2,142.7 2,113.8 2,139.4 2,129.05.75 2,161.2 2,170.8 2,180.4 2,174.2 2,167.9 2,172.3 2,143.0 2,162.8 2,157.76.25 2,199.5 2,215.3 2,233.8 2,244.0 2,222.3 2,202.0 2,186.4 2,186.3 2,196.06.75 2,252.8 2,279.9 2,307.0 2,346.4 2,282.7 2,296.3 2,248.2 2,247.5 2,246.87.25 2,333.6 2,410.8 2,448.8 2,391.3 2,390.7 2,333.6 2,331.5 2,329.57.75 2,515.9 2,551.2 2,485.9 2,485.0 2,429.8 2,421.1 2,412.58.25 2,627.4 2,653.7 2,589.6 2,579.3 2,527.1 2,527.18.75 2,748.5 2,756.1 2,714.8 2,673.7 2,641.6 2,626.89.25 2,892.2 2,894.9 2,843.7 2,821.0 2,765.69.75 3,036.1 2,980.3 2,968.2 2,900.5
10.25 3,188.3 3,141.7 3,115.5 3,055.210.75 3,356.7 3,323.7 3,262.8 3,221.2 3,183.211.25 3,504.8 3,439.8 3,353.711.75 3,693.012.25 3,871.1 3,810.7 3,760.012.75 4,076.813.25 4,164.4
Wave Period (Seconds)W
ave
Hei
ght (
Met
res)
Table 5-6: Mean Tension (kN)
60
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50.25 0.000 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.001 0.0010.75 0.000 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.0011.25 0.000 0.001 0.002 0.001 0.003 0.001 0.003 0.003 0.002 0.002 0.001 0.0011.75 0.000 0.002 0.001 0.004 0.002 0.003 0.004 0.003 0.003 0.002 0.002 0.0022.25 0.002 0.002 0.006 0.002 0.005 0.006 0.005 0.004 0.004 0.003 0.003 0.0022.75 0.003 0.002 0.007 0.002 0.007 0.009 0.008 0.006 0.006 0.004 0.004 0.0033.25 0.003 0.008 0.003 0.009 0.012 0.011 0.008 0.007 0.006 0.005 0.0043.75 0.009 0.004 0.014 0.018 0.017 0.012 0.009 0.007 0.006 0.0054.25 0.010 0.005 0.019 0.023 0.022 0.017 0.014 0.010 0.009 0.0064.75 0.006 0.024 0.029 0.028 0.020 0.019 0.013 0.011 0.0085.25 0.007 0.029 0.030 0.031 0.030 0.024 0.016 0.014 0.0105.75 0.008 0.034 0.041 0.039 0.039 0.029 0.021 0.017 0.0126.25 0.010 0.040 0.045 0.045 0.045 0.034 0.027 0.019 0.0146.75 0.011 0.045 0.058 0.050 0.051 0.042 0.033 0.025 0.0177.25 0.014 0.069 0.056 0.060 0.049 0.037 0.031 0.0207.75 0.073 0.061 0.072 0.057 0.044 0.037 0.0248.25 0.086 0.066 0.066 0.064 0.052 0.0428.75 0.094 0.071 0.079 0.071 0.061 0.0489.25 0.106 0.097 0.152 0.109 0.0679.75 0.184 0.184 0.147 0.068
10.25 0.198 0.259 0.184 0.08010.75 0.289 0.290 0.222 0.079 0.06111.25 0.379 0.217 0.05711.75 0.48212.25 0.466 0.345 0.14812.75 0.48913.25 0.183
Wave Period (Seconds)W
ave
Hei
ght (
Met
res)
Table 5-7: Angle Change Range (degrees)
61
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50.25 0 7511.892 28602.4888 40489.55 44838.43 54038.95 31327.39 7939.927 1499.497 277.1604 147.2366 135.4452 131.1389 157.249 185.673 198.47710.75 0 963.2537 4325.38796 11374.27 21446.86 27493.32 20314.29 10015.76 3476.913 683.3781 167.3689 65.39359 15.56687 0 0 01.25 0 0 397.537897 5797.22 10909.27 37990.5 13380.16 20793.71 11268.33 3499.124 975.1466 300.3837 28.94183 0 0 01.75 0 0 0 426.9512 2896.721 23089.34 13974.32 27017.04 27109.39 9150.668 1772.157 506.9364 103.3314 32.09494 0 02.25 0 0 0 35.16867 671.5856 9494.863 9637.457 28983.37 29264.52 10568.22 3507.755 910.6612 342.3513 55.21265 5.733262 02.75 0 0 0 21.62779 87.4044 3654.451 7222.939 24344.75 22805.15 11386.64 4322.619 1193.975 556.4619 151.3243 36.75774 03.25 0 0 0 0 20.18851 550.9295 2519.036 14955.25 17917.42 12292.6 4430.779 1477.177 658.2264 135.2608 24.74777 03.75 0 0 0 0 0 211.0975 797.2429 14101.4 17942.85 13735.54 5375.205 1326.997 682.1337 187.8927 46.29696 04.25 0 0 0 0 0 36.01096 327.8106 9228.647 10691.74 10976.92 5608.024 1701.459 826.5129 274.1176 29.93046 04.75 0 0 0 0 0 0 48.62163 6403.173 10999.41 11377.82 4972.952 1710.051 583.9564 130.0957 39.53164 05.25 0 0 0 0 0 0 31.45632 2914.076 7281.035 8380.774 5038.836 1859.827 771.119 111.4632 52.2371 05.75 0 0 0 0 0 0 1.882721 2341.004 5693.345 5461.343 5361.736 1478.936 727.72 88.12919 13.27926 06.25 0 0 0 0 0 0 21.29622 672.3732 5088.09 5009.241 3155.448 1217.822 755.2583 58.39625 19.18002 06.75 0 0 0 0 0 0 16.06984 629.8316 3463.52 3565.224 2613.439 940.116 390.2926 54.01657 8.049043 07.25 0 0 0 0 0 0 20.17024 0 4232.251 2772.262 2357.362 1101.832 498.7063 61.29735 5.028332 07.75 0 0 0 0 0 0 0 0 1858.931 2349.429 1355.006 973.1507 305.7071 9.447617 18.35978 08.25 0 0 0 0 0 0 0 0 1128.483 1794.278 1022.333 667.6918 222.2493 45.66913 0 08.75 0 0 0 0 0 0 0 0 1096.984 377.0969 976.8302 629.8793 154.8473 13.48539 0 09.25 0 0 0 0 0 0 0 0 130.4243 685.6585 784.2557 294.874 196.4599 0 0 09.75 0 0 0 0 0 0 0 0 0 535.3394 702.8126 788.655 41.74844 0 0 010.25 0 0 0 0 0 0 0 0 0 268.6686 1041.909 428.4124 129.7569 0 0 010.75 0 0 0 0 0 0 0 0 0 413.2844 718.6474 308.7787 26.9618 20.79016 0 011.25 0 0 0 0 0 0 0 0 0 0 141.5938 79.65573 0 20.30698 0 011.75 0 0 0 0 0 0 0 0 0 0 189.8415 0 0 0 0 012.25 0 0 0 0 0 0 0 0 0 0 384.7867 139.9381 59.27032 0 0 012.75 0 0 0 0 0 0 0 0 0 0 212.4972 0 0 0 0 013.25 0 0 0 0 0 0 0 0 0 0 0 0 81.03884 0 0 0
Wave Period (Seconds)W
ave
Hei
ght (
Met
res)
Table 5-8: Calculated Wear Volumes (mm3) per annum with Ks=1.0
62
5.5 SLIDING WEAR COEFFICIENT CALIBRATION
As discussed in the previous section, with the sliding wear coefficient, ‘KSliding’, set to unity resulted in a wear volume rate of 994,018 mm3 per annum versus the actual wear volume rate of 18,990 mm3 per annum. Given that the calculation described in Section 1.1 was undertaken in a spreadsheet once the results had been extracted from the time domain model, then sliding wear coefficient, ‘KSliding’, was found by using the solver function such that the calculated wear rate equalled the actual wear rate. This resulted in a sliding wear coefficient, ‘KSliding’, of 0.0191, which is somewhat higher than expected, although it is no doubt relevant that the chafe chain is not submerged and is subjected to ‘dry’ sliding. Such sliding traditionally results in a high rate of wear, hence the use of lubrication on traditional mechanical sliding systems, and therefore in all likelihood is correct. For submerged chains, a lower sliding wear coefficient might be expected although the use of the dry one would result in a conservative approach. Shoup & Mueller investigated this relationship as part of their investigation [4], however, they found that the ratio in their experiments between the wet and dry wear coefficients was in the range 1:2→1:150. Given this variation the conservative approach of using the dry coefficient, or no less than half the dry coefficient, might be seen as appropriate.
Application of the model to the full time range of chain measurements provided to the JIP for the subject unit, with the calculated wear volumes converted to diameter losses resulted in the following figure:
215
220
225
230
235
240
245
250
0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500
Doub
le In
ter-‐grip Diameter (m
m)
Cumulative Days
Links 2 & 3 Intergrip Double Diameter versus time
Predicted
Measured
Figure 5-2: Predicted versus Actual Links 2 & 3 Inter-grip Double Diameter
The above figure shows a good correlation between the calculated and measured wear, thus giving confidence that the calibration is correct. Particularly, given that the calibration itself only covers the first 562 days and the remaining days are predicted by the model. Some anomalous data is present on the graph, which is a function of the inter-grip double diameter measurements being taken by hand, and illustrates the need to look at such measurements over time rather than in isolation. For this particular example, for the first two years the same person took nearly all of
63
the measurements; when he left the variation in measurements is particularly notable until the Operators provided training to specific personnel.
It should be noted that the model has been calibrated for angle changes in degrees and mean tensions in kilonewtons. Given that the model is essentially linear then the use of degrees rather than radians is acceptable. It also means that the stated coefficient figures can be modified to any set of angle and tension units by simple manipulation.
64
6
6.1
6.2
9 10 11 12 13 14 1510 11 12 13 14 15 169.5 10.5 11.5 12.5 13.5 14.5 15.5
5.41E+03 3.72E+03 3.79E+03 4.12E+03 4.45E+03 4.78E+03 5.11E+038.20E+03 2.61E+03 1.04E+03 2.54E+02 0 0 02.31E+04 7.95E+03 2.88E+03 2.95E+02 0 0 03.55E+04 8.86E+03 2.89E+03 6.66E+02 2.34E+02 0 02.62E+04 1.12E+04 3.34E+03 1.53E+03 2.74E+02 3.21E+01 01.91E+04 9.14E+03 2.85E+03 1.76E+03 5.46E+02 1.55E+02 01.49E+04 7.41E+03 2.67E+03 1.59E+03 3.77E+02 8.18E+01 01.09E+04 6.16E+03 1.96E+03 1.27E+03 4.15E+02 1.20E+02 06.46E+03 4.27E+03 1.59E+03 1.08E+03 4.15E+02 6.13E+01 05.27E+03 3.29E+03 1.16E+03 6.10E+02 1.49E+02 6.42E+01 03.47E+03 2.16E+03 9.81E+02 6.42E+02 1.02E+02 7.01E+01 01.74E+03 1.73E+03 6.37E+02 4.50E+02 6.72E+01 1.46E+01 01.35E+03 8.61E+02 4.41E+02 3.50E+02 3.80E+01 1.75E+01 08.26E+02 6.13E+02 2.69E+02 1.43E+02 2.63E+01 5.84E+00 05.58E+02 4.53E+02 2.57E+02 1.58E+02 2.34E+01 2.92E+00 04.15E+02 2.07E+02 1.90E+02 7.88E+01 2.92E+00 8.76E+00 02.80E+02 1.64E+02 1.11E+02 4.67E+01 1.17E+01 0 05.26E+01 1.26E+02 9.05E+01 2.63E+01 2.92E+00 0 06.72E+01 4.96E+01 2.63E+01 2.92E+01 0 0 02.63E+01 3.50E+01 4.96E+01 5.84E+00 0 0 01.17E+01 3.50E+01 2.04E+01 1.46E+01 0 0 01.17E+01 2.04E+01 1.17E+01 2.92E+00 2.92E+00 0 0
0 2.92E+00 2.92E+00 0 2.92E+00 0 00 2.92E+00 0 0 0 0 00 5.84E+00 2.92E+00 2.92E+00 0 0 00 2.92E+00 0 0 0 0 00 0 0 2.92E+00 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 0
VALIDATION
PURPOSE
In Section 5, the sliding wear coefficient ‘Ks’ was calibrated and a suggested rolling wear coefficient ‘Kr’ was stated. This section applies the calculation methodology described in Section 4.5, and summarised in Appendix A, to a different section of the chafe chain of the TCMS system used in Section 5, in order to validate the methodology and sliding wear coefficient ‘Ks’.
METHOD
To validate the methodology the steps laid down in Appendix A were in essence followed, with the only exception being that the Overall Wear Volume Matrix (DV) was calculated when the Wear Volume Matrix (V) would have been calculated, in order to save calculation time.
This resulted in the following data during the validation process:
Step 1: The Regular Wave Scatter Diagram (W) was the same as for the calibration exercise in Section 5, as shown in Table 5-4.
Step 2: The time domain model was the same as used in Section 5 as the model had already been modified to model the chafe chain as individual links with a length of 4 x the nominal diameter of the chain.
Step 3: The time domain model was run and the results extracted into an excel spreadsheet for each regular wave height and period pair with occurrence data.
Step 4: The material coefficient was calculated as being: 3.65036 x 10-13 m3/N.
Step 5: The Witness Mark Angle ‘βWitness Mark’ was calculated as being: 47.8°
Step 6: As the chafe chain is always in tension the maximum starting angle ‘dβiMax’ was found to be zero. Hence the chain will always be in the sliding regime as the links will never escape the witness mark and steps 7, 8 & 9 can be omitted.
65
Inter-grip Links Predicted Wear Rate 21/22 19148.91 mm3/year 22/23 23397.76 mm3/year 23/24 28092.76 mm3/year
Table 6-1: Predicted Volumetric Wear Rates
Step 14: Application of the ‘pringle’ model to the volumetric wear rates shown in Table 6-1 lead to the following predicted loss of diameter wear rates, which seem reasonable:
Inter-grip Links Predicted Wear Rate 21/22 1.91 mm/year 22/23 2.34 mm/year 23/24 2.81 mm/year
6.3
Table 6-2: Loss of Diameter Wear rates
RESULTS
As with the link further up the chafe chain of the TCMS that was used in Section 5.5 to calibrate the sliding wear coefficient ‘Ks’, inter-grip double diameter measurements over a period of some four years were made available for the subject links. These measurements were taken by hand and for the first two years the same person took nearly all of the measurements. After this there was a period of variation in the measurements until the Operator provided training to specific personnel to avoid the sort of false readings seen in year three (750days to 1000days approximately). Figure 6-1 below, shows the time line of these measurements along with the predicted double diameter measurements for each inter-grip area based on the predicted diameter wear loss rates given in Table 6-2.
Step 10 to 12: The three total wear volume matrices (DV), one for each inter-grip area, were calculated and stored within a spreadsheet along with the wave scatter diagram (W), mean tensions (T) and angle change range (dβ) matrices for ease of calculation.
Step 13: Summing of the three total wear volume matrices (DV) lead to the following predicted annual wear rates:
66
210
220
230
240
250
260
270
0 250 500 750 1000 1250 1500
Intergrip
Diameter (m
m)
Time (days
Actual Wear Versus Predicted Wear
Actual 21/22
Predicted 21/22
Actual 22/23
Predicted 22/23
Actual 23/24
Predicted 23/24
Figure 6-1: Absolute Actual Double Diameter Wear versus Predicted Double Diameter Wear
67
6.4 CONCLUSION
At first glance, this figure appears to show a significant over prediction of the double diameter loss over time. In reality though, the over prediction at the end of the period is only 1.7%, 3.5% and 4.5% respectively for inter-grip links 21/22, 22/23 and 23/24. This is an acceptable error rate for such a calculation. The predicted diameter loss rates in given in Table 6-2 are also an improvement on those typically stated in mooring codes of up to 0.6mm/year, as these links would appear to have been seeing between 2 and 5mm per year wear depending on how the measured data is interpreted.
This error rate can be reduced to 0.001%, 1.405%, and 2.152% respectively for inter-grip links 21/22, 22/23 and 23/24 if the sliding wear coefficient ‘Ks’ is reduced to 0.0139, without the model under-predicting the wear, as shown in the figure overleaf. Consequently, it is believed that there is a good basis for utilising the methodology when predicting the wear on mooring systems. Further application of this method to other mooring systems will also act as a useful cross-check and will allow the further validation of the methodology and in particular the wear coefficients.
210
220
230
240
250
260
270
0 250 500 750 1000 1250 1500
Intergrip
Diameter (m
m)
Time (days
Actual Wear Versus Predicted Wear
Actual 21/22
Predicted 21/22
Actual 22/23
Predicted 22/23
Actual 23/24
Predicted 23/24
Figure 6-2: Absolute Actual Double Diameter Wear versus Predicted Double Diameter Wear with Ks=0.0139
68
This report is intended for the sole use of the person or
company to whom it is addressed and no liability of any
nature whatsoever shall be assumed to any other party
in respect of its contents.
GL NOBLE DENTON
Signed:
Eur Ing Andrew Comley, C Eng MRINA BEng (hons)
Countersigned: _________________________________________
Martin Brown, C Eng MRINA MSc MBA BSc (hons)
Dated: Aberdeen, 11 May 2010
69
REFERENCES
[1] Surface Wear: Analysis, Treatment and Prevention, R. Chattopadhyay, ASM International,June 2001, ISBN: 0-87170-702-0
[2] DIN 50320: Verschleiß“, Beuth Verlag, Berlin, December 1979
[3] National Seminar on Maintenance and Productivity, R. Chattopadhyay, NationalProductivity Council and Confederation of Engineering Industries, February 1990
[4] Failure Analysis of a CALM Buoy Anchor Chain System by G. J. Shoup and R. A. Mueller,Cities Service Oil & Gas Corp. - OTC 4764, 1984
[5] Introduction to Tribology, B. Bhushan, John Wiley and Sons, 2002, ISBN 0471158933
[6] Roark’s Formulas for Stress and Strain - Seventh Edition, Young, Budynas, McGraw Hill,2002, ISBN 0-07-072542-X
[7] Influence of Spectral Density Distribution on Wave Parameters and Simulation in TimeDomain, K.-F. Daemrich, S. Mai, N. Ohle , E. Tautenhain, 2nd Chinese - German JointSymposium on Coastal and Ocean Engineering, October 2004, Nanjing, China
70
APPENDICES
71
APPENDIX A CHAIN WEAR CALCULATION METHOD
72
A.1 CALCULATION METHOD To apply the chain wear calculation methodology described in this report to a mooring system, whether it be at the design stage or during the operational stage, the following steps need to be undertaken. These steps should be read and applied in conjunction with the flow diagram shown and the table of equations shown below:
1. Obtain or create Regular Wave Scatter Diagram (W) of size M x N, where M isthe number of regular wave heights and N is the number of regular waveperiods.
Note: If the regular wave scatter diagram needs to be created from irregularsea-state data then the MathCad sheet in Appendix B can be used to create aregular wave scatter diagram for each sea-state. If several sea-states are beingconsidered then the regular wave scatter diagrams can be produced using theMathCad sheet and then summed to give the full regular wave scatter diagram
2. Create or modify an existing time domain model (e.g. Orcaflex model) of themooring system including first and second order motions as appropriate. It is ofparamount importance that the element length in the area of mooring line(s) forwhich the wear model is to be applied has a length equal to the inter-grip lengthi.e. 4 x nominal diameter for standard geometry chain for the subject pair oflinks and a suitable number either side.
Note: It is suggested that as a minimum ten links either side of the subject pair of links are modelled with a length equal to the inter-grip length
3. Run the time domain model from step 2 for each of the regular wave height andperiod pairs from the Regular Wave Scatter Diagram (W) from step 1 that haveassociated occurrence data such that steady state motion is achieved andrecorded for the inter-grip(s) of interest:
• The mean tension, thus creating a Mean Tension Matrix (T)
• The angular range change, thus creating an Angular Change Range Matrix(dβ)
• The starting angle, thus creating a Starting Angle Matrix (dβi)
Note: During testing it was found that a build up period of 5 waves followed by a recording period of 10 waves was sufficient to achieve steady state conditions and so steady state results.
4. Calculate Material Constant using Equation 1
5. Calculate Witness Mark Angle (βWitness Mark) using Equation 2
6. Find Maximum Starting Angle (dβi Max) from Starting Angle Matrix (dβi) andcompare to Witness Mark Angle (βWitness Mark). If Maximum Starting Angle (dβi Max)
73
7. Is less than Witness Mark Angle (βWitness Mark) then all wear will be sliding only,therefore go to step 10, otherwise continue to step 7.
8. Calculate Critical Angle (βCritical) using Equation 3
9. For each of the regular wave height and period pairs, from the Regular WaveScatter Diagram (W) from step 1 that have associated occurrence data,compare associated Angular Change Range Matrix (dβ) entry against theCritical Angle (βCritical):
• If dβ < βCritical then calculate the associated Wear Volume Matrix (V) entryusing Equation 4
• If dβ > βCritical then calculate the associated Wear Volume Matrix (V) entryusing Equation 5
10. Go to Step 12
11. For each of the regular wave height and period pairs, from the Regular WaveScatter Diagram (W) from step 1 that have associated occurrence data,calculate the associated Wear Volume Matrix (V) entry using Equation 6
12. Go to step 12
13. Calculate Overall Wear Volume Matrix (DV) by multiplying each Wear VolumeMatrix (V) entry by its associated occurrence data from the Regular WaveScatter Diagram (W)
14. Sum the Overall Wear Volume Matrix (DV) to find the Wear Volume for the timeperiod covered by the Regular Wave Scatter Diagram (W)
15. Calculate change in diameter using the ‘Pringle’ Model given in Section 4.4.
Note: An example MathCad sheet for the ‘Pringle’ model is given in Appendix C.
74
A.1 FLOWCHART
Error! Objects cannot be created from editing field codes.
Where:
KR = 0.0013 → 0.0952
Ks = 0.0139 → 0.0191
A.2 TABLE OF EQUATIONS
Equation Number
Standard Studless Chain Standard Studless Chain
1 b
am HR
RC3
=
2
⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎠
⎞⎜⎝
⎛−−
= −
2.31224
tan 1
DD
Dmarkwitnessβ
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛= −
2
1
205625.05.0tan
DD
markwitnessβ
3
( ) ( )( )( ) ( )( )
Critical
Critical
Critical
Critical
dd
drdr
β
ββ
ββββ
µ
for Solve
tantan28.0tan8.0tan32.0
tantan
1
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
+−
⎟⎟⎠
⎞⎜⎜⎝
⎛
×××−
×+××
=−
Critical
Critical
dRrd
β
βµ
for Solve
1tan ⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠
⎞⎜⎝
⎛+=
4 jiRollingjimji TKdrCV ,,, β=
5
( )
( )( )( )( ) ⎥
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢
⎣
⎡
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
×−
−×+
+=
−
−
ji
jiji
Critical
Sliding
CriticalRolling
jimji d
dr
K
drK
TCV
,1
,,1,,
tan5.2tan
tan5.2tan
β
ββ
β
β
( )( )⎟
⎟
⎠
⎞
⎜⎜
⎝
⎛
++=
jiCrticalSliding
CriticalRolling
jimji dRdrK
drKTCV
,
,,ββ
β
6 ( )( )
( )( ) ⎥⎥
⎦
⎤
⎢⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
×−
−×=
−
−
ji
jiji
Slidingjimji
dKTCV
,1
,,1
,, tan5.2tan
tan5.2tan
β
ββ ( )( )jiSlidingjimji dRKTCV ,,, β=
75
APPENDIX B REGULAR WAVE SCATTER DIAGRAM CREATION FROM IRREGULAR SEA-STATE DATA MATHCAD SHEET
76
Sea-state input data
Hs 4m:= Significant Wave Height
γ 3.3:= Jonswap peakness factor
α 0.001:= H.s Correction Factor Guess
Time Series input data
T0 10800s:= Time Series length
Ts 10800s:= Storm Length
Ss 108000:= Number of storm creation points
Δf1
T0:= Frequency bin width
Maximum spectral frequencyfmax 0.26688Hz:=
Number of amplitudesn round
fmaxΔf
⎛⎜⎝
⎞⎟⎠
:=
fp 0.125Hz:= Peak Frequency (1/peak period)
Scatter diagram input data
height_bin 0.5m:= Height Bin Width
height_bins 20:= Number of height bins
period_bin 1s:= Period bin width
period_bins 12:= Number of period bins
Calculate a for selected sea-state
α root 4
0
fmaxfσ 0.07← f fp<if
σ 0.09← otherwise
α g2⋅
2 π⋅( )4 f5⋅e
5−
4
f
fp
⎛⎜⎝
⎞⎟⎠
4−⋅
⎡⎢⎢⎣
⎤⎥⎥⎦⋅ γ
e
f fp−( )2−
2 σ( )2⋅ fp2
⋅
⎡⎢⎢⎣
⎤⎥⎥⎦
⋅
f0⋅⌠⎮⎮⎮⎮⎮⎮⎮⎮⎮⌡
d Hs− α,
⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣
⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦
:=
α 0.013=
Calculate Spectrum for selected sea-state
S f( ) σ 0.07← f fp<if
σ 0.09← otherwise
α g2⋅
2 π⋅( )4 f5⋅e
5−
4
f
fp
⎛⎜⎝
⎞⎟⎠
4−⋅
⎡⎢⎢⎣
⎤⎥⎥⎦⋅ γ
e
f fp−( )2−
2 σ( )2⋅ fp2
⋅
⎡⎢⎢⎣
⎤⎥⎥⎦
⋅
:=
Check Spectrum is calculating correct sea-state
m00
fmaxfS f( ) f0⋅
⌠⎮⌡
d:=
Hs 4 m0:=
Calculated sea-state: Hs 4m= Selected Ses-state: Hs 4m=
77
Calculate Amplitudes for selected sea-state
i 0 n 1−..:= Amplitude index
k 1 Ss..:= Storm creation point index
fi Δf i Δf⋅+:= Frequency Vector
Time0 0:= Start Time
Timek Timek 1−
TsSs
+:= Storm time vector
a f( ) 2S f( ) Δf⋅:= Amplitude Equation
Amplitudesi a fi( ):= Create Amplitude Vector for selected sea-state
0 0.05 0.1 0.15 0.2 0.25 0.30
5 10 3−×
0.010.0150.02
0.0250.03
0.0350.04
0.0450.05
0.0550.06
0.0650.07
Amplitudesi
f i
Create time series for storm with selected sea-state
phase runif n 2− π, 2π, ( ):= Assign a random phase to each amplitude
Zk0
n 1−
i
Amplitudesi sin 2π fi− Timek⋅ phase i+( )⋅( )∑=
:= Calculate time series
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 1004−
2−
0
2
4
6First 100seconds of Time Series
Z
Time0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 1004−
2−
0
2
4
6First 100seconds of Time Series
Z
Time
Calculate number of waves using a zero down crossing routine
TMarkk B Zk 1−←
F Zk←
1 B 0≥ F 0<∧ k Ss 1−∨if
0 otherwise
return
:=
Num_wave TMark∑:= Num_wave 1.582 103×= Calculate number of waves
num 0 Num_wave 1−..:= Create wave index
78
Create a vector marking the end point of each wave
Waves_index num 0←
Indexnum 1+k←
num num 1+←
TMarkk 1if
k 0 Ss 1−..∈for
Indexreturn
:=
Create a vector of wave periods
Periodnum Time Waves_indexnum 1+( ) TimeWaves_indexnum−:=
Create vector of wave heights
Height num 0←
min 0←
max 0←
min Zj← Zj min<if
max Zj← Zj max>if
j Waves_index num Waves_index num 1+..∈for
heightnum max min−←
num 0 Num_wave 1−..∈for
heightreturn
:=
Create regular wave scatter diagram
Scatter num 0←
Scatterheight_bins period_bins, 0←
Scatteri j, Scatteri j,
1+← i height_bin⋅ Heightnum≤ i 1+( ) height_bin⋅< j period_bin⋅ Periodnum≤ j 1+( ) period_bin⋅<∧if
j 0 period_bins 1−..∈for
i 0 height_bins 1−..∈for
num 0 Num_wave 1−..∈for
Scatterreturn
:=
Regular Wave Scatter diagram for selected sea-state
Scatter
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
19
52
13
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
41
62
32
12
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
23
39
56
34
27
20
6
5
3
0
0
0
0
0
0
0
0
0
0
0
0
10
24
48
52
41
36
36
21
8
7
1
0
1
1
0
0
0
0
0
0
0
6
26
43
50
62
59
46
36
28
23
6
7
4
2
0
0
0
0
0
0
0
5
23
29
62
52
43
37
15
6
4
2
0
0
0
0
0
0
0
0
0
0
2
11
19
28
23
13
9
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
8
7
5
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
⎛⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎜⎝
⎞⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎟⎠
=
79
APPENDIX C ‘PRINGLE’ MODEL MATHCAD SHEET
80
Basic Chain data and wear depth
D 130:= Chain diameter in mm
idf 0.675:= Inner diameter factor (1.35/2 for standard studless and 1.6/2 for standard studded links)
Δe 2.5:= Wear Depth in millimetres
aD2
:= Major Axis Half Length / Half width of wear
bD2
:= Minor Axis Half Length / Bar Radius
eD2
:= Maximum Wear Depth / Bar Radius
d idf D⋅ idf D⋅( )2 a( )2−⎡⎣ ⎤⎦−:= Part of Inner Diameter that defines the starting depth of the wear zone
itotal 201:= Major Axis Resolution
jtotal 201:= Minor Axis Resolution
z 1:= Guess Value for Z-cordinates
i 0 itotal 1−..:= X axis index
j 0 jtotal 1−..:= Y axis index
Xi i2a
itotal 1−⎛⎜⎝
⎞⎟⎠
⋅ a( )−:= X cordinates for grid
Yj j2 b⋅
jtotal 1−⎛⎜⎝
⎞⎟⎠
⋅ b( )−:= Y coordinates for grid
Create Starting Surface
Z1i j, root
Yj( )2
b2
z2
e( )2+ 1− z,
⎡⎢⎢⎣
⎤⎥⎥⎦
d+ rootXi( )2
a2
z2
d( )2+ 1− z,
⎡⎢⎢⎣
⎤⎥⎥⎦
−Xi( )2
a2
Yj( )2
b2+ 1≤if
0 otherwise
:=
Create Worn Surface
Z2i j, root
Yj( )2
b2
z2
e Δe−( )2+ 1− z,
⎡⎢⎢⎣
⎤⎥⎥⎦
d+ Δe+ rootXi( )2
a2
z2
d Δe+( )2+ 1− z,
⎡⎢⎢⎣
⎤⎥⎥⎦
−Xi( )2
a2
Yj( )2
b2+ 1≤if
0 otherwise
:=
Calculate Wear Volume
Volume2a
itotal 1−⎛⎜⎝
⎞⎟⎠
2 b⋅jtotal 1−
⎛⎜⎝
⎞⎟⎠
⋅
0
jtotal 1−
yj 0
itotal 1−
xi
Z1xi yj, Z2xi yj,
−( )∑=
⎡⎢⎢⎣
⎤⎥⎥⎦
∑=
⋅:=
Volume 23154.658=
81
APPENDIX D REGULAR WAVE SCATTER DIAGRAMS
82
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50 0.5 0.25 2 48 190 314 450 680 408 87 12 1 0 0 0 0 0 0
0.5 1 0.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 01 1.5 1.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1.5 2 1.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 02 2.5 2.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2.5 3 2.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 03 3.5 3.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3.5 4 3.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 04 4.5 4.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4.5 5 4.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 05 5.5 5.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5.5 6 5.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 06 6.5 6.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6.5 7 6.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 07 7.5 7.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7.5 8 7.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 08 8.5 8.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8.5 9 8.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 09 9.5 9.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9.5 10 9.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 010 10.5 10.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10.5 11 10.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 011 11.5 11.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11.5 12 11.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 12.5 12.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12.5 13 12.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 13.5 13.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.5 14 13.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 14.5 14.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14.5 15 14.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 15.5 15.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wave Period (Seconds)
Wav
e Hei
ght (
Met
res)
Table A-1: 0.0m to 0.5m Significant Wave Height Regular Wave Scatter Diagram
83
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50 0.5 0.25 2 39 174 278 258 230 177 76 18 2 0 0 0 0 0 0
0.5 1 0.75 0 0 0 11 142 345 278 60 1 0 0 0 0 0 0 01 1.5 1.25 0 0 0 0 1 24 10 0 0 0 0 0 0 0 0 0
1.5 2 1.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 02 2.5 2.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2.5 3 2.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 03 3.5 3.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3.5 4 3.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 04 4.5 4.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4.5 5 4.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 05 5.5 5.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5.5 6 5.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 06 6.5 6.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6.5 7 6.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 07 7.5 7.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7.5 8 7.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 08 8.5 8.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8.5 9 8.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 09 9.5 9.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9.5 10 9.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 010 10.5 10.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10.5 11 10.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 011 11.5 11.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11.5 12 11.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 12.5 12.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12.5 13 12.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 13.5 13.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.5 14 13.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 14.5 14.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14.5 15 14.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 15.5 15.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wave Period (Seconds)
Wav
e Hei
ght (
Met
res)
Table A-2: 0.5m to 1.0m Significant Wave Height Regular Wave Scatter Diagram
84
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50 0.5 0.25 5 35 128 149 94 76 29 13 5 1 0 0 0 0 0 0
0.5 1 0.75 0 0 7 71 160 220 249 159 56 9 0 0 0 0 0 01 1.5 1.25 0 0 0 1 39 123 176 75 8 0 0 0 0 0 0 0
1.5 2 1.75 0 0 0 0 0 23 51 6 0 0 0 0 0 0 0 02 2.5 2.25 0 0 0 0 0 1 6 1 0 0 0 0 0 0 0 0
2.5 3 2.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 03 3.5 3.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3.5 4 3.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 04 4.5 4.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4.5 5 4.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 05 5.5 5.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5.5 6 5.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 06 6.5 6.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6.5 7 6.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 07 7.5 7.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7.5 8 7.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 08 8.5 8.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8.5 9 8.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 09 9.5 9.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9.5 10 9.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 010 10.5 10.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10.5 11 10.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 011 11.5 11.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11.5 12 11.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 12.5 12.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12.5 13 12.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 13.5 13.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.5 14 13.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 14.5 14.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14.5 15 14.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 15.5 15.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wave Period (Seconds)
Wav
e Hei
ght (
Met
res)
Table A-3: 1.0m to 1.5m Significant Wave Height Regular Wave Scatter Diagram
85
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50 0.5 0.25 2 29 89 66 47 23 11 1 2 1 0 0 0 0 0 0
0.5 1 0.75 0 0 11 88 135 125 94 96 47 14 2 1 0 0 0 01 1.5 1.25 0 0 0 5 51 91 147 143 83 21 1 0 0 0 0 0
1.5 2 1.75 0 0 0 0 6 34 92 102 37 2 0 0 0 0 0 02 2.5 2.25 0 0 0 0 0 7 50 39 2 0 0 0 0 0 0 0
2.5 3 2.75 0 0 0 0 0 0 6 6 0 0 0 0 0 0 0 03 3.5 3.25 0 0 0 0 0 0 2 1 0 0 0 0 0 0 0 0
3.5 4 3.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 04 4.5 4.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4.5 5 4.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 05 5.5 5.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5.5 6 5.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 06 6.5 6.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6.5 7 6.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 07 7.5 7.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7.5 8 7.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 08 8.5 8.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8.5 9 8.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 09 9.5 9.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9.5 10 9.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 010 10.5 10.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10.5 11 10.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 011 11.5 11.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11.5 12 11.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 12.5 12.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12.5 13 12.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 13.5 13.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.5 14 13.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 14.5 14.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14.5 15 14.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 15.5 15.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wave Period (Seconds)
Wav
e Hei
ght (
Met
res)
Table A-4: 1.5m to 2.0m Significant Wave Height Regular Wave Scatter Diagram
86
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50 0.5 0.25 3 20 63 43 14 11 1 1 0 0 1 0 0 0 0 0
0.5 1 0.75 0 0 9 86 92 58 51 29 22 9 7 3 1 0 0 01 1.5 1.25 0 0 0 11 52 87 94 102 74 41 10 0 0 0 0 0
1.5 2 1.75 0 0 0 0 9 34 76 102 102 31 7 0 0 0 0 02 2.5 2.25 0 0 0 0 2 7 47 69 53 11 1 0 0 0 0 0
2.5 3 2.75 0 0 0 0 0 3 28 49 16 0 1 0 0 0 0 03 3.5 3.25 0 0 0 0 0 0 3 14 4 0 0 0 0 0 0 0
3.5 4 3.75 0 0 0 0 0 0 1 6 0 0 0 0 0 0 0 04 4.5 4.25 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
4.5 5 4.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 05 5.5 5.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
5.5 6 5.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 06 6.5 6.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6.5 7 6.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 07 7.5 7.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7.5 8 7.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 08 8.5 8.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8.5 9 8.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 09 9.5 9.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9.5 10 9.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 010 10.5 10.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10.5 11 10.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 011 11.5 11.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11.5 12 11.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 12.5 12.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12.5 13 12.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 13.5 13.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.5 14 13.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 14.5 14.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14.5 15 14.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 15.5 15.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wave Period (Seconds)
Wav
e Hei
ght (
Met
res)
Table A-5: 2.0m to 2.5m Significant Wave Height Regular Wave Scatter Diagram
87
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50 0.5 0.25 3 21 54 32 11 5 1 1 0 0 0 0 0 0 0 0
0.5 1 0.75 0 0 15 79 80 43 20 16 8 6 2 1 0 0 0 01 1.5 1.25 0 0 0 16 50 62 61 52 49 26 12 7 0 0 0 0
1.5 2 1.75 0 0 0 2 12 39 61 83 73 58 8 1 0 0 0 02 2.5 2.25 0 0 0 0 3 10 43 65 90 42 13 1 0 0 0 0
2.5 3 2.75 0 0 0 0 0 5 32 46 50 13 0 0 0 0 0 03 3.5 3.25 0 0 0 0 0 0 10 40 28 7 1 0 0 0 0 0
3.5 4 3.75 0 0 0 0 0 0 0 19 10 1 1 0 0 0 0 04 4.5 4.25 0 0 0 0 0 0 1 5 3 0 0 0 0 0 0 0
4.5 5 4.75 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 05 5.5 5.25 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
5.5 6 5.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 06 6.5 6.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6.5 7 6.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 07 7.5 7.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7.5 8 7.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 08 8.5 8.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8.5 9 8.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 09 9.5 9.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9.5 10 9.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 010 10.5 10.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10.5 11 10.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 011 11.5 11.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11.5 12 11.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 12.5 12.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12.5 13 12.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 13.5 13.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.5 14 13.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 14.5 14.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14.5 15 14.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 15.5 15.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wave Period (Seconds)
Wav
e Hei
ght (
Met
res)
Table A-6: 2.5m to 3.0m Significant Wave Height Regular Wave Scatter Diagram
88
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50 0.5 0.25 3 22 35 19 12 4 1 0 0 0 0 0 0 0 0 0
0.5 1 0.75 0 0 18 68 43 37 17 10 3 2 2 0 0 0 0 01 1.5 1.25 0 0 1 20 62 43 41 26 22 10 10 4 0 0 0 0
1.5 2 1.75 0 0 0 2 22 48 51 57 61 42 17 7 2 0 0 02 2.5 2.25 0 0 0 0 3 15 40 59 69 53 16 2 1 0 0 0
2.5 3 2.75 0 0 0 0 1 5 29 51 71 46 12 2 0 0 0 03 3.5 3.25 0 0 0 0 0 2 18 31 33 20 2 0 0 0 0 0
3.5 4 3.75 0 0 0 0 0 0 5 29 33 11 0 0 0 0 0 04 4.5 4.25 0 0 0 0 0 0 0 15 7 3 1 0 0 0 0 0
4.5 5 4.75 0 0 0 0 0 0 0 7 6 3 1 0 0 0 0 05 5.5 5.25 0 0 0 0 0 0 0 1 3 2 0 0 0 0 0 0
5.5 6 5.75 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 06 6.5 6.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
6.5 7 6.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 07 7.5 7.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7.5 8 7.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 08 8.5 8.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8.5 9 8.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 09 9.5 9.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9.5 10 9.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 010 10.5 10.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10.5 11 10.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 011 11.5 11.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11.5 12 11.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 12.5 12.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12.5 13 12.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 13.5 13.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.5 14 13.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 14.5 14.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14.5 15 14.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 15.5 15.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wave Period (Seconds)
Wav
e Hei
ght (
Met
res)
Table A-7: 3.0m to 3.5m Significant Wave Height Regular Wave Scatter Diagram
89
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50 0.5 0.25 2 8 29 9 14 1 4 0 0 0 0 0 0 0 0 0
0.5 1 0.75 1 0 9 40 36 19 16 9 3 1 2 1 0 0 0 01 1.5 1.25 0 0 1 17 38 42 30 17 13 13 5 4 2 0 0 0
1.5 2 1.75 0 0 0 3 14 30 34 34 42 24 18 10 2 1 0 02 2.5 2.25 0 0 0 1 4 15 33 36 46 48 38 13 7 1 0 0
2.5 3 2.75 0 0 0 0 0 7 21 33 56 56 30 6 4 1 0 03 3.5 3.25 0 0 0 0 0 1 8 19 35 42 25 7 4 0 0 0
3.5 4 3.75 0 0 0 0 0 0 1 19 26 36 13 2 0 0 0 04 4.5 4.25 0 0 0 0 0 0 0 10 18 17 5 1 0 0 0 0
4.5 5 4.75 0 0 0 0 0 0 0 4 13 11 4 0 0 0 0 05 5.5 5.25 0 0 0 0 0 0 0 4 8 4 1 0 0 0 0 0
5.5 6 5.75 0 0 0 0 0 0 0 2 4 6 1 0 0 0 0 06 6.5 6.25 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0
6.5 7 6.75 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 07 7.5 7.25 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
7.5 8 7.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 08 8.5 8.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8.5 9 8.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 09 9.5 9.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9.5 10 9.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 010 10.5 10.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10.5 11 10.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 011 11.5 11.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11.5 12 11.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 12.5 12.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12.5 13 12.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 13.5 13.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.5 14 13.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 14.5 14.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14.5 15 14.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 15.5 15.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wave Period (Seconds)
Wav
e Hei
ght (
Met
res)
Table A-8: 3.5m to 4.0m Significant Wave Height Regular Wave Scatter Diagram
90
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50 0.5 0.25 2 4 21 9 7 3 1 0 0 0 0 0 0 0 0 0
0.5 1 0.75 1 0 20 31 32 14 15 2 3 1 0 0 0 0 0 01 1.5 1.25 0 0 1 17 34 36 29 16 4 6 7 3 1 0 0 0
1.5 2 1.75 0 0 0 4 23 31 31 20 27 14 8 6 1 1 0 02 2.5 2.25 0 0 0 2 6 24 28 31 38 29 28 12 5 0 0 0
2.5 3 2.75 0 0 0 0 1 8 22 39 45 41 34 12 7 3 0 03 3.5 3.25 0 0 0 0 0 1 18 19 38 56 25 7 6 0 0 0
3.5 4 3.75 0 0 0 0 0 1 4 15 27 37 25 6 4 0 0 04 4.5 4.25 0 0 0 0 0 0 2 18 19 28 13 3 0 1 0 0
4.5 5 4.75 0 0 0 0 0 0 0 5 19 19 6 1 0 0 0 05 5.5 5.25 0 0 0 0 0 0 0 4 11 12 6 0 0 0 0 0
5.5 6 5.75 0 0 0 0 0 0 0 1 9 2 2 0 0 0 0 06 6.5 6.25 0 0 0 0 0 0 0 2 3 5 1 0 0 0 0 0
6.5 7 6.75 0 0 0 0 0 0 0 1 4 3 0 0 0 0 0 07 7.5 7.25 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0 0
7.5 8 7.75 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 08 8.5 8.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
8.5 9 8.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 09 9.5 9.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9.5 10 9.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 010 10.5 10.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10.5 11 10.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 011 11.5 11.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11.5 12 11.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 12.5 12.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12.5 13 12.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 13.5 13.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.5 14 13.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 14.5 14.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14.5 15 14.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 15.5 15.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wave Period (Seconds)
Wav
e Hei
ght (
Met
res)
Table A-9: 4.0m to 4.5m Significant Wave Height Regular Wave Scatter Diagram
91
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50 0.5 0.25 0 9 23 4 4 1 0 0 0 0 0 0 0 0 0 0
0.5 1 0.75 1 0 12 26 26 11 7 2 3 1 0 0 0 0 0 01 1.5 1.25 0 0 2 24 31 32 20 9 4 4 3 2 1 0 0 0
1.5 2 1.75 0 0 0 6 25 27 28 15 16 12 7 6 1 0 0 02 2.5 2.25 0 0 0 0 11 23 26 27 36 18 15 10 2 0 0 0
2.5 3 2.75 0 0 0 1 2 8 26 27 27 35 27 11 9 1 1 03 3.5 3.25 0 0 0 0 0 5 18 23 35 42 37 12 5 1 0 0
3.5 4 3.75 0 0 0 0 0 2 8 14 29 46 29 6 6 0 0 04 4.5 4.25 0 0 0 0 0 0 2 15 19 29 22 6 8 0 0 0
4.5 5 4.75 0 0 0 0 0 0 1 13 18 27 15 2 2 0 0 05 5.5 5.25 0 0 0 0 0 0 0 3 12 21 6 4 1 0 0 0
5.5 6 5.75 0 0 0 0 0 0 0 2 6 6 7 1 0 0 0 06 6.5 6.25 0 0 0 0 0 0 0 1 12 9 4 0 0 0 0 0
6.5 7 6.75 0 0 0 0 0 0 0 2 4 3 2 0 0 0 0 07 7.5 7.25 0 0 0 0 0 0 0 0 5 3 1 0 0 0 0 0
7.5 8 7.75 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 08 8.5 8.25 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0
8.5 9 8.75 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 09 9.5 9.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9.5 10 9.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 010 10.5 10.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10.5 11 10.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 011 11.5 11.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11.5 12 11.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 12.5 12.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12.5 13 12.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 13.5 13.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.5 14 13.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 14.5 14.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14.5 15 14.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 15.5 15.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wave Period (Seconds)
Wav
e Hei
ght (
Met
res)
Table A-10: 4.5m to 5.0m Significant Wave Height Regular Wave Scatter Diagram
92
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50 0.5 0.25 0 4 19 5 2 1 0 1 0 0 0 0 0 0 0 0
0.5 1 0.75 0 0 4 28 21 9 6 4 2 1 0 0 0 0 0 01 1.5 1.25 1 0 1 13 25 29 11 9 5 0 2 1 0 0 0 0
1.5 2 1.75 0 0 0 3 21 21 19 21 13 7 11 5 3 2 0 02 2.5 2.25 0 0 0 0 8 21 20 31 18 10 5 7 7 2 1 0
2.5 3 2.75 0 0 0 1 3 13 19 18 23 20 22 19 10 3 3 03 3.5 3.25 0 0 0 0 0 2 14 15 33 25 28 13 8 6 0 0
3.5 4 3.75 0 0 0 0 0 2 2 14 20 20 34 21 13 7 2 04 4.5 4.25 0 0 0 0 0 0 3 9 13 20 35 13 8 3 1 0
4.5 5 4.75 0 0 0 0 0 0 0 8 14 23 23 18 5 0 0 05 5.5 5.25 0 0 0 0 0 0 0 0 13 14 19 10 9 0 0 0
5.5 6 5.75 0 0 0 0 0 0 0 1 5 12 17 4 4 1 0 06 6.5 6.25 0 0 0 0 0 0 1 0 6 5 3 5 3 0 0 0
6.5 7 6.75 0 0 0 0 0 0 0 0 3 6 6 3 0 0 0 07 7.5 7.25 0 0 0 0 0 0 0 0 5 4 7 1 1 0 0 0
7.5 8 7.75 0 0 0 0 0 0 0 0 2 3 1 1 0 0 0 08 8.5 8.25 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0
8.5 9 8.75 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 09 9.5 9.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9.5 10 9.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 010 10.5 10.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
10.5 11 10.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 011 11.5 11.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11.5 12 11.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 12.5 12.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12.5 13 12.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 13.5 13.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.5 14 13.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 14.5 14.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14.5 15 14.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 15.5 15.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wave Period (Seconds)
Wav
e Hei
ght (
Met
res)
Table A-11: 5.0m to 5.5m Significant Wave Height Regular Wave Scatter Diagram
93
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50 0.5 0.25 0 10 14 2 3 0 0 0 0 0 0 0 0 0 0 0
0.5 1 0.75 0 0 3 21 20 6 5 3 1 0 0 0 0 0 0 01 1.5 1.25 1 0 2 12 21 26 7 9 5 0 1 0 0 0 0 0
1.5 2 1.75 0 0 0 3 20 18 17 16 12 5 6 1 1 1 0 02 2.5 2.25 0 0 0 0 9 21 23 20 15 8 5 8 5 4 0 0
2.5 3 2.75 0 0 0 1 5 16 17 18 20 14 16 7 7 4 1 03 3.5 3.25 0 0 0 0 1 3 13 18 29 23 18 24 12 4 3 0
3.5 4 3.75 0 0 0 0 0 2 8 8 14 21 28 12 12 5 0 04 4.5 4.25 0 0 0 0 0 1 2 12 16 24 23 21 13 9 1 0
4.5 5 4.75 0 0 0 0 0 0 2 3 7 23 33 11 8 1 2 05 5.5 5.25 0 0 0 0 0 0 1 6 13 14 23 16 9 1 1 0
5.5 6 5.75 0 0 0 0 0 0 0 1 8 13 19 11 9 0 0 06 6.5 6.25 0 0 0 0 0 0 0 0 8 7 12 5 5 0 0 0
6.5 7 6.75 0 0 0 0 0 0 1 0 3 5 6 2 2 1 0 07 7.5 7.25 0 0 0 0 0 0 0 0 2 8 4 6 2 0 0 0
7.5 8 7.75 0 0 0 0 0 0 0 0 3 3 5 2 0 0 0 08 8.5 8.25 0 0 0 0 0 0 0 0 3 2 6 1 1 0 0 0
8.5 9 8.75 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 09 9.5 9.25 0 0 0 0 0 0 0 0 0 2 1 0 0 0 0 0
9.5 10 9.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 010 10.5 10.25 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
10.5 11 10.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 011 11.5 11.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11.5 12 11.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 12.5 12.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12.5 13 12.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 13.5 13.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.5 14 13.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 14.5 14.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14.5 15 14.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 15.5 15.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wave Period (Seconds)
Wav
e Hei
ght (
Met
res)
Table A-12: 5.5m to 6.0m Significant Wave Height Regular Wave Scatter Diagram
94
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50 0.5 0.25 0 10 11 1 3 0 0 0 0 0 0 0 0 0 0 0
0.5 1 0.75 0 0 6 18 15 5 3 3 0 0 0 0 0 0 0 01 1.5 1.25 1 0 2 15 21 17 7 6 5 0 0 0 0 0 0 0
1.5 2 1.75 0 0 0 4 19 24 14 14 10 2 4 1 0 0 0 02 2.5 2.25 0 0 0 0 14 17 18 15 11 8 7 6 3 4 0 0
2.5 3 2.75 0 0 0 1 2 17 18 22 17 8 8 5 7 2 0 03 3.5 3.25 0 0 0 0 5 8 16 10 21 20 13 14 11 5 2 0
3.5 4 3.75 0 0 0 0 0 3 8 18 23 24 22 17 8 5 2 04 4.5 4.25 0 0 0 0 0 2 7 8 13 17 26 15 11 4 0 0
4.5 5 4.75 0 0 0 0 0 0 2 10 14 18 27 17 11 7 1 05 5.5 5.25 0 0 0 0 0 0 2 3 6 23 29 11 8 2 3 0
5.5 6 5.75 0 0 0 0 0 0 0 4 12 12 18 14 8 0 0 06 6.5 6.25 0 0 0 0 0 0 0 1 8 12 18 11 8 0 0 0
6.5 7 6.75 0 0 0 0 0 0 0 0 5 7 11 3 4 0 0 07 7.5 7.25 0 0 0 0 0 0 1 0 4 5 6 4 3 1 0 0
7.5 8 7.75 0 0 0 0 0 0 0 0 3 7 5 6 3 0 0 08 8.5 8.25 0 0 0 0 0 0 0 0 2 5 4 1 0 0 0 0
8.5 9 8.75 0 0 0 0 0 0 0 0 5 2 5 1 0 0 0 09 9.5 9.25 0 0 0 0 0 0 0 0 0 1 2 1 1 0 0 0
9.5 10 9.75 0 0 0 0 0 0 0 0 0 1 0 2 0 0 0 010 10.5 10.25 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0
10.5 11 10.75 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 011 11.5 11.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11.5 12 11.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 12.5 12.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12.5 13 12.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 13.5 13.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.5 14 13.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 14.5 14.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14.5 15 14.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 15.5 15.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wave Period (Seconds)
Wav
e Hei
ght (
Met
res)
Table A-13: 6.0m to 6.5m Significant Wave Height Regular Wave Scatter Diagram
95
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50 0.5 0.25 0 3 8 1 2 0 0 0 0 0 0 0 0 0 0 0
0.5 1 0.75 0 1 7 15 12 2 6 1 0 0 0 0 0 0 0 01 1.5 1.25 1 0 0 12 16 11 8 5 4 0 0 0 0 0 0 0
1.5 2 1.75 0 0 0 8 16 23 11 7 8 5 1 1 1 1 0 02 2.5 2.25 0 0 0 0 11 22 9 21 8 5 4 5 3 2 0 0
2.5 3 2.75 0 0 0 1 4 19 11 18 13 11 8 4 4 5 2 03 3.5 3.25 0 0 0 0 3 8 16 15 22 9 10 10 5 6 1 0
3.5 4 3.75 0 0 0 0 0 3 11 18 15 20 15 17 9 7 5 04 4.5 4.25 0 0 0 0 0 1 3 6 12 16 19 13 17 7 1 0
4.5 5 4.75 0 0 0 0 0 0 1 8 13 12 26 18 10 4 0 05 5.5 5.25 0 0 0 0 0 0 2 6 4 25 18 16 11 6 2 0
5.5 6 5.75 0 0 0 0 0 0 0 3 11 10 28 12 9 2 2 06 6.5 6.25 0 0 0 0 0 0 0 3 5 15 13 10 11 3 1 0
6.5 7 6.75 0 0 0 0 0 0 0 1 8 10 16 15 5 0 0 07 7.5 7.25 0 0 0 0 0 0 1 0 3 4 9 9 5 0 0 0
7.5 8 7.75 0 0 0 0 0 0 0 0 3 5 4 4 4 0 0 08 8.5 8.25 0 0 0 0 0 0 0 0 2 8 1 5 3 1 0 0
8.5 9 8.75 0 0 0 0 0 0 0 0 2 1 6 5 2 0 0 09 9.5 9.25 0 0 0 0 0 0 0 0 2 3 1 1 1 0 0 0
9.5 10 9.75 0 0 0 0 0 0 0 0 0 2 5 1 0 0 0 010 10.5 10.25 0 0 0 0 0 0 0 0 0 0 1 2 2 0 0 0
10.5 11 10.75 0 0 0 0 0 0 0 0 0 2 1 1 0 0 0 011 11.5 11.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11.5 12 11.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 012 12.5 12.25 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
12.5 13 12.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 013 13.5 13.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13.5 14 13.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 14.5 14.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14.5 15 14.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 15.5 15.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wave Period (Seconds)
Wav
e Hei
ght (
Met
res)
Table A-14: 6.5m to 7.0m Significant Wave Height Regular Wave Scatter Diagram
96
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.50 0.5 0.25 0 1 6 2 0 0 0 0 0 0 0 0 0 0 0 0
0.5 1 0.75 0 0 8 15 9 5 3 1 0 0 0 0 0 0 0 01 1.5 1.25 0 0 0 12 23 12 3 5 5 2 0 0 0 0 0 0
1.5 2 1.75 1 0 0 8 13 10 15 13 3 4 4 2 0 0 0 02 2.5 2.25 0 0 0 1 7 18 10 14 6 4 2 2 3 1 2 0
2.5 3 2.75 0 0 0 0 1 10 9 14 13 15 5 5 5 2 0 03 3.5 3.25 0 0 0 0 1 6 9 25 13 10 7 7 3 3 0 0
3.5 4 3.75 0 0 0 0 0 3 7 7 7 17 12 11 8 15 5 04 4.5 4.25 0 0 0 0 0 0 2 12 7 15 17 18 15 8 4 0
4.5 5 4.75 0 0 0 0 0 0 1 5 8 16 15 9 20 9 6 05 5.5 5.25 0 0 0 0 0 0 2 2 3 9 15 10 15 9 2 0
5.5 6 5.75 0 0 0 0 0 0 1 2 4 15 8 20 14 10 1 06 6.5 6.25 0 0 0 0 0 0 0 0 5 9 11 12 9 7 4 0
6.5 7 6.75 0 0 0 0 0 0 0 1 5 3 12 11 11 3 2 07 7.5 7.25 0 0 0 0 0 0 0 0 2 8 10 9 11 4 1 0
7.5 8 7.75 0 0 0 0 0 0 0 0 2 4 4 12 7 1 3 08 8.5 8.25 0 0 0 0 0 0 0 0 1 5 2 9 4 2 0 0
8.5 9 8.75 0 0 0 0 0 0 0 0 0 2 2 5 5 1 0 09 9.5 9.25 0 0 0 0 0 0 0 0 0 1 1 3 4 0 0 0
9.5 10 9.75 0 0 0 0 0 0 0 0 0 1 2 7 2 0 0 010 10.5 10.25 0 0 0 0 0 0 0 0 0 0 0 3 1 0 0 0
10.5 11 10.75 0 0 0 0 0 0 0 0 0 0 1 2 1 1 0 011 11.5 11.25 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0
11.5 12 11.75 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 012 12.5 12.25 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0
12.5 13 12.75 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 013 13.5 13.25 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
13.5 14 13.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 014 14.5 14.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
14.5 15 14.75 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 015 15.5 15.25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Wave Period (Seconds)
Wav
e Hei
ght (
Met
res)
Table A-15: 7.0m to 7.5m Significant Wave Height Regular Wave Scatter Diagram
97
98
Published by the Health & Safety Executive 07/17
Practical method for calculating mooring chain wear for floating offshore installations
Mooring Integrity Joint Industry Project Phase 2
RR1092
www.hse.gov.uk
Mooring integrity for floating offshore installations is an important safety issue for the offshore oil and gas industry. This report is one outcome from Phase 2 of the Joint Industry Project on Mooring Integrity. This work ran from 2008 to 2012 and had 35 industry participants. It followed the Phase 1 work described in HSE Research Report RR444 (2006). The Phase 2 work compiled research on good practice and is summarised in HSE Research Report RR1090 (2017).
Long lengths of steel chain links are used in the mooring lines of floating installations. As an installation moves, the tension and position of the upper ends of its mooring lines change producing rotational movement between adjacent chain links that results in wear. As part of ensuring that mooring chains to do not fail, it is important to have robust estimates of inter-link wear. This report describes the formulation of a practical analytical method to calculate inter-link wear. The report details: the relevant wear mechanisms (adhesion, corrosion, surface fatigue and erosion); how the links move under the influence of environmental forces including consideration of the influences of the manufacturing and proof testing processes; and the underlying theory and calibration approach used to develop the method.
For ease of use by practitioners applying the method, a summary is provided in Appendix A of the report.
This report and the work it describes were funded by the Health and Safety Executive (HSE). Its contents, including any opinions and/or conclusions expressed, are those of the authors alone and do not necessarily reflect HSE policy.
