Mooring System Analysis: Theory and practice of riser and mooring dynamics

Theory and practice of riser and mooring dynamics

Mooring System Analysis Mooring System Design          

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Layout and geometry Line type -- catenary, semi-taut and taut-leg Properties – selection of chain, wire and synthetic rope or combination Anchor/pile selection Load-elongation curve for each line Offset curves for the layout Static, quasi-static and dynamic mooring system analyses Loading on lines vs. line breaking strengths FOS vs. Guidelines Mooring line fatigue assessment

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In the process of design of the offshore system, For the mooring lines, first select

♦

layout

♦

geometry

♦

mechanical and structural properties (initial)

Layout of Mooring Lines

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Mooring Configuration

Taut vs catenary mooring spread (symmetric)

Taut mooring system: restoring force primarily from line stretch Conventional catenary system: restoring force primarily from changes in catenary shape

Riser corridors between non-symmetric spread

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Geometry of mooring lines Mooring Hardware Components Typical Chain geometry (a) Stud-Link

(b) Studless Chain

•

Wire or Rope Geometry (unsheathed or sheathed)

six strand

multi strand

s iral strand

Note: Sheathed wire ropes are of smooth cylindrical shape

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Design of Mooring Lines Three possible methods: Static design Quasi-static design Dynamic design

Static Design Uses only the static environmental loads ignoring dynamic forces. Steps Input line end-point coordinates, lengths and unit weight of line. Sum forces for all lines in the mooring spread. Determine design wind, current, and wave data for site Find displacement of vessel for the load from the offset curve Line length is insufficient or the line becomes taut. Compute the safety factor (FOS) for the most heavily loaded line based on the breaking strength. FOS is too low.

Assume that the most loaded line is broken.

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     





Outcome Line forces vs. displacement for each catenary line. Net horizontal and vertical restoring forces (offset curves) for the vessel. Compute steady forces on the vessel due to design environment Compute the tension of the most loaded line in the mooring spread. Increase the line length and repeat the above steps. Compare with design guides.

adjust suitable parameters in line pre-tension, material specification, line end co-ordinates or number of lines and repeat the above steps. Carry out the above steps and check FOS on heavily loaded line.

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Quasi-Static Design Uses maximum dynamic loads as well as static, assuming all as static load.

Follow static steps. In addition

compute max wave loads and vessel motion at wave and slow-drift frequency

Compute maximum excursion and peak line tensions

Compare maximum line tensions vs. allowable safety factor (generally 2)

Use separate safety factors for the mean and dynamic loads (DNV)

If it fails the safety factor test, then try a new specification

Recalculate maximum peak line loads with one line broken NO

Acceptable Design? YES

Note: Mean loads are more reliably predictable separate FOS avoids excess conservatism. Morning

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Dynamic Design In addition to steady loads, includes, the time-varying environmental loads on the mooring lines themselves

Establish a static configuration

Calculate platform motions independent of line dynamics

Include line top-end oscillation

Apply numerical scheme (lumped mass, FE or FD) to model line segments

De-compose line into straight elements (bars) with linear shape function

Lump distributed mass with added mass at end nodes

Include relative motion hydrodynamic damping

Include inertial effects between the line and fluid

NO

Acceptable Design? YES

Note:

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A time domain analysis is sought Damping levels vary significantly depending on water depth, line make up, offsets and top-end excitation. The influence of the last item is generally small. 56


Loading Mechanisms on Floater and Mooring Lines

Loads on Floater ♦ Steady and fluctuating wind ♦ Wave and wave drift ♦ Current

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Loads on Mooring Lines ♦ Top end surge motion (small heave) ♦ Wave ♦ Current ♦ Seabed friction

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Static Catenary Equation Definition of the single component catenary line Tv T (tension)

water line

φ (angle)

fairlead

TH

d scope, s

Single component line

chain Anchor

TDP xB

ocean floor x

h

Six (plus one) independent variables are: w = weight of line per unit length ≈ 0.87x (weight in air) for steel T = pretension at fairlead φ = fairlead angle h = horizontal component of catenary length (not including x B) d = vertical component of catenary length s = length of catenary called scope plus x B = component of line on bottom Also, (the following two items depend on T and φ ): T H = horizontal component of tension at fairlead T V = vertical component of tension at fairlead ASSUMPTIONS: (1) Seafloor is assumed flat; (2) Line segments are non-buoyant; and (3) Stretching of line is linear and follows Hooke’s law Two possible cases: Catenary: line resting on seafloor x B > 0, TBV = 0, xB = length of line on bottom Taut: line off the seafloor x B = 0, T BV > 0, TBV = vertical reaction at the anchor Morning

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Single line (no stretching ) Consider the following free-body diagram Free body diagram Ti xi, yi

θ ι

s0 0

current

, Fairlead angle

weight xi+1, yi+1

θ ι+1

Ti+1

For a static analysis in the absence of any external force, the two equilibrium equations (based on the notation in Fig. 10 become: Horizontal:

T i cosθ i

− T i +1 cosθ i +1 = 0

Vertical:

T i sin θ i

− T i +1 sin θ i +1 + wi = 0

which may be solved for tension and angles of subsequent elements as follows:

T i +1

= [(T i cosθ i ) 2 + (T i sin θ i − wi ) 2 ]

1/ 2

and

tan θ i +1 =

T i sin θ i

− wi

T i cos θ i

=

T V i

− wi

T Hi

Then, knowing the coordinates of the upper end of the element ( xi ,yi), the corresponding coordinates for the lower end becomes Morning

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xi +1 = xi

yi +1

l

− i [cos θ i + cos θ i +1 ] 2

l

= yi − i [sin θ i + sin θ i +1 ] 2

This calculation continues with the subsequent element until yi+1 just exceeds - d , where the d is the supplied depth of the line.

For a catenary line with portions on the bottom, the solution can be obtained in closed form using catenary equations. Basic catenary equation:

y = y0 cosh( x / y0 ) y0

= elevation at x = 0 s ( x) = (T H / w) sinh( wx / T H )

suspended line length along catenary s(x)

d ( x ) = (T H / w)[cosh( wx / T H ) − 1]

vertical line dimension along catenary d(x) for total lengths, use x = h in above equations

T H =

top tension of the line

or

T =

w( s 2

− d 2 )

2d w( s 2 + d 2 ) 2d T − T H

which reduce to

d =

horizontal component of line tension

T H = T cosφ

(2)

vertical component of line tension at top

T V = T sin φ = ws

(3)

Horizontal span of the suspended portion of line

h=

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w

T H w

log

T A

(1)

− T VA T H

(4)


6 (or 7) unknowns and 3 equations; need 3 (or 4) input variables, e.g., w = weight of line per unit length T 0= initial tension at fairlead, and d = mooring line depth L = total line length or x B = line length on bottom Note that Eqs. 2 and 3 are dependent equations, but easier to use separately for the solutions. For solution, follow the steps below: Use Eq. 1 to compute T H Note: T H is constant at any point along the catenary, while T v varies. Use Eq. 2 to compute the initial fairlead angle φ A Use Eq. 3 to compute the initial suspended line length s Use Eq. 4 to compute the horizontal span h Compute xB, the line laying on the bottom, using s and L. Increment T H and repeat the above steps. Compute the excursion based on the initial configuration. Plot load vs. excursion (line stiffness curve)

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Typical Example of a Single Catenary variable input unit weight of chain w pretension T 0 depth of line from fairlead d anchor line on bottom xB0

values 1.5 1300 450 700

units kN/m kN m m

The initial catenary will have the following properties: T H 0 T V0 φ 0 s0 h0 s0+ xB0

625.0 1139.9 61.3 759.9 567.5 1459.9

kN kN deg m m m

Horz. Tension Vert. Tension Fairlead Angle Length (scope) Horz. Span Total chain length

The sample output values for the catenary are obtained by setting the horizontal fairlead tension and determining the line excursion and the remaining line length on the bottom. TH kN 625.0 650 750 850 950 1050 1150 1250 1350 1450 1550 1650 1750 1850 1950 2050 2150 2250 Morning

T kN 1300 1325.0 1425.0 1525.0 1625.0 1725.0 1825.0 1925.0 2025.0 2125.0 2225.0 2325.0 2425.0 2525.0 2625.0 2725.0 2825.0 2925.0

TV kN 1139.9 1154.6 1211.7 1266.1 1318.4 1368.6 1417.1 1463.9 1509.3 1553.4 1596.3 1638.0 1678.7 1718.5 1757.3 1795.3 1832.5 1869.0

φ deg 61.3 60.6 58.2 56.1 54.2 52.5 50.9 49.5 48.2 47.0 45.8 44.8 43.8 42.9 42.0 41.2 40.4 39.7

s m 759.9 769.7 807.8 844.1 878.9 912.4 944.7 976.0 1006.2 1035.6 1064.2 1092.0 1119.2 1145.6 1171.5 1196.9 1221.7 1246.0 62

h Excursion xB m m m 567.5 0.0 700.0 580.2 2.9 690.2 628.6 13.3 652.2 673.8 22.1 615.8 716.2 29.7 581.0 756.4 36.4 547.5 794.6 42.3 515.2 831.1 47.6 484.0 866.2 52.4 453.7 899.9 56.7 424.3 932.4 60.7 395.7 963.9 64.3 367.9 994.3 67.6 340.8 1023.9 70.7 314.3 1052.7 73.6 288.4 1080.7 76.3 263.1 1108.0 78.8 238.3 1134.6 81.1 213.9


2350 2450 2550 2650 2750 2850 2950 3050

3025.0 3125.0 3225.0 3325.0 3425.0 3525.0 3625.0 3725.0

1904.8 1939.9 1974.4 2008.3 2041.6 2074.4 2106.7 2138.5

39.0 38.4 37.8 37.2 36.6 36.1 35.5 35.0

1269.8 1293.3 1316.2 1338.8 1361.1 1382.9 1404.5 1425.7

1160.7 1186.2 1211.2 1235.6 1259.6 1283.1 1306.3 1329.0

83.3 85.4 87.4 89.2 91.0 92.7 94.3 95.8

190.1 166.7 143.7 121.1 98.9 77.0 55.5 34.3

The load-excursion curve for the catenary line is shown in Fig. 11. Note that the curve is nonlinear. It is assumed in the curve that the line is catenary and a portion of line remains on the bottom throughout its range. 3500.0

2800.0

k , d a o L

2100.0

1400.0

700.0

0.0 0.0

20.0

40.0

60.0

80.0

Excursion, m

Figure 11. Load-excursion curve for a single catenary line

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100.0


Two line catenary

Three component line

Definitions: See preceding figure for multiple lines α = angle at the top of second line segment w1 = unit submerged weight of top line segment w2 = unit submerged weight of bottom line segment

total line length s

s = s1 + s2 line 1 –Top line

tensions T H and T V

T H = T cos φ ; TV

= T sin φ

(5)

line length s1

T H 

w1 x1 + w2 x2  w2 x2     s1 = sinh  − sinh     w1  T T H H    

(11)

vertical dimension d1

d 1

=

T H  w1

 w1 x1 + w2 x2  − cosh  w2 x2     T H   T H    

cosh  

angle Morning

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(10)


tan θ

w1 x1 + w2 x2   = sinh  − tan α  T H  

line 2 Bottom line (same as single caternary)

vertical tension at fairlead T V

TV

= w1s1 + w2 s2

(6)

line length s2

s2

=

T H w2

sinh(

w2 x2

)

(7)

 w2 x2    T H 

(8)

T H

angle

tan α = sinh  vertical dimension d2

d 2

=

T H  w2

cosh( 

w2 x2 T H

 

) − 1

(9)

NOTE: Clump weight or buoy may be added at the junction of the two lines giving an added vertical load at the joint.

Inputs:

w1 = unit weight of line 1 w2 = unit weight of line 2 T = Pretension at fairlead point (top of segment no. 1) φ = fairlead angle to x-axis s1 = segment 1 length L = total line length or x B = line length on bottom

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Calculations for Two Line Catenary Steps: Compute T H , same for both lines (Eq. 5) Compute T V, vertical tension at fairlead (Eq. 5) Compute s2 = segment 2 length (Eq. 6) Compute x2 = segment 2 span (Eq. 7) Compute α = segment 2 top angle (Eq. 8) Compute d 2 = segment 2 depth (Eq. 9) Compute d 1 = segment 1 depth (Eq. 10) Compute x1 = segment 1 span (Eq. 11)

INPUT Unit weight, w1 Unit weight, w2 Pretension at fairlead (line 1) Fairlead angle to x-axis Line length, s1 Total catenary length

Ex. do not UNIT change 0.104 0.10 kips/ft 0.104 0.04 kips/ft 300 300.0 kips 61.3 60 deg 2530.1 2000.0 ft 5030.6

4000.0

ft

Horiz. tension, TH Vert. tension, Tv at fairlead Line length, s2 Total scope, s Bottom length, xB Horiz. span line 2, x2 w2*x2/TH tan (a) Top angle line 2, a Horiz. span line 1, x1 w1*x1/TH

144.1 263.1 0.1 2530.2 2500.4 0.1 0.000 0.00 0.0 1888.4 1.363

150.0 259.8 1295.2 3295.2 704.8 1270.7 0.339 0.35 19.1 1635.6 1.134

kips kips ft ft ft ft

Total span, h Line 2 depth, d2 Line 1 depth, d1 Total depth, d

1888.5 0.0 1499.5 1499.5

2906.3 217.4 1784.9 2002.3

check

61.3

Initial Catenary Properties

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144 263.2 2530.4 2500

deg ft 1888.3 ft ft ft

1500


Single semi-taut line (no stretching ) Nine independent variables are: w = weight of line per unit length T = tension at fairlead T H = horizontal tension at fairlead T V = vertical tension at fairlead h = horizontal component of line length d = vertical component of line length s = curved length of line θ A = fairlead angle θ B = anchor angle Properties of semi-taut line: B = anchor point;

A = fairlead point;

s =

Scope

Horizontal fairlead tension

T H

T AV

Vertical fairlead tension

T BV

Vertical anchor tension

θ A

T AV − T BV

d =

Depth

Angles satisfy

=

w

T A − T B w s 2

− d 2

2 s

=

2dT A

=

2dT A

(2T A − wd )2 − w 2 s 2

+ w( s 2 − d 2 ) 2 s

− w( s 2 + d 2 ) 2 s

Horizontal component of tension

T AH Morning

= T A cos θ A ;

T BH 67

= T B cos θ B

> θ B ;


Vertical component of tension

T AV

= T AH tan θ A ;

T BV

= T BH tan θ B

9 unknowns and 5 independent equations; 4 input variables: w = weight of line per unit length θ A = fairlead angle s = line length d = vertical component of line length NOTES:

♦

The two cases of catenary and semi-taut line may switch back and forth under dynamic loads as the chain is picked up completely from the floor or settles down on floor.

♦

Semi-taut line with negligible stretch will move both in the horizontal and vertical direction with the vessel movement.

♦

When the line is completely taut, stretching will be needed to move it. In this case the angle throughout the line may be taken as the same.

Since stretching takes place along the entire shape of the mooring line under loading, and the stretched length or the shape of the line is not known apriori, a numerical procedure similar to the above may be adopted. In this case the stretching of a segment will occur based on the tensions at the two ends of the segment. Hooke’s law may be applied to obtain the stretch.

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TYPICAL SINGLE SEMI-TAUT LINE (NO STRETCH) NOTE: Horizontal excursion of line will require a simultaneous vertical excursion

Sample input values unit weight of chain vertical depth of chain length (scope) initial tension at fairlead

w d s 0 TA

Initial Semi-taut Lines initial tension at anchor initial horizontal tension initial fairlead angle initial anchor angle

0.0489 170 1000.0 175.0

TB TH

θA θB

kips/ft or kN/m ft/m ft/m kips/kN

166.69 166.62 17.8 1.6

kips/kN kips/kN deg deg

2.0

2.5

400.0

350.0 p i k , n 300.0 o i s n e T 250.0 p o T

200.0

150.0 0.0

0.5

1.0

1.5

Excursion, ft

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3.0


Offset Tension Curves of Mooring Lines Example Nansen SPAR in 3,678ft water depth The curve gives the top tension of the mooring line versus the horizontal offset of the fairlead point. Nansen SCR Case A, Offset-Tension Curves Lines 1, 4 and 7 3600 3200 ) s p i k ( n o i s n e T

2800

LINE NO. 1

2400

LINE NO. 4 LINE NO. 7

2000 1600 1200 800 400 0

-100 -75 -50 -25

0

25

50

75 100 125 150 175 200 225 250 275 300

Distance From Pretension Position (ft)

The curve gives the restoring force of the mooring line versus the horizontal offset of the fairlead point.

Restoring Characteristic of Mooring Lines Restoring Characteristic SCR Case A, Offset Direction Relative to Platform East

0 -4000 ) s p i k (

-8000

270° 315° 0° 45° 90° 180°

e -12000 c r o F -16000

-20000 -24000 0

25

50

75

100

125

150

175

200 2 25

250

275

Offset (ft)

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300 3 25

350


Example Quasi-static Mooring System Design Example 1

Consider an 8-point catenary spread mooring system for a semisubmersible [adopted from Offshore Moorings, p.104]. Use a typical 1-year storm for the North Sea environment. 4

5 Catenary lines

3

6

Wave

Semi

2

7

1

8

Input data: Semi: 22000 T displacement Water depth = 155 m Survival draft Fairlead point 5m below SWL Two component lines – chain and wire 8 catenary lines of same geometry chain on top: 3” ORQ w (submerged weight) = 117 kg/m Breaking strength = 472 T Proof load = 313 T s1 length from fairlead to wire top = 850m wire at the bottom end: 3-1/2” 6x41 Breaking strength = 498 T 2 Elastic modulus on nominal CSA = 7000 kg/mm Elasticity of chain-wire combination = 32.7 T/m s2 length from chain bottom to anchor = 800m Morning

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Environment: Wind: 1 hr mean = 34.0 m/s 1 min mean = 39.0 m/s Wave: HS = 12.1 m Hmax = 22.4 m TS = 13.3 s Current: Surface = 1.10 m/s 15 m depth = 0.84 m/s based on these environmental data, the mean environmental forces on the semi are computed at its nominal survival draft. The mean forces in a head sea case: load due to mean wind: hourly load due to mean wind: 1 min gust load due to mean wave drift load due to mean current

= 88 T = 114 T = 27 T = 46 T

Total (mean wind) = 161 T Total (1 min gust) = 187 T Mean steady displacement (1 min gust) = 24.2 m Compute the high frequency motions in surge for the head seas for the given wave spectrum as follows: Transfer function Response spectrum Most probable maximum surge amplitude = 8.4 m Mean static displacement (1 min gust) = 24.2 m Total displacement = 32.6 m Mooring line force (chain) = 210 T Safety factor (chain) = 2.25 Similar computation should be carried for other wave angles, e.g., beam and quartering seas, since the setup is not symmetric. Also, the analysis should be repeated for one broken line for the worst case from the above to check the safety factor. Morning

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Example 2

Mooring arrangement for the floater in shallow water

Buoy Mooring System

Auxiliary surface buoy

Spar

Environment

Float Flounder plate Catenary

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Choose a typical mooring line as a starting point: Stud Link Chain diameter = 1.25 inch Chain angle at the buoy = 45 degrees Vertical length = 5 meters (from buoy to the flounder plate) Catenary length = 132 meters (from the flounder plate to the foundation anchor) Chain virtual diameter = 3 x chain wire size CDN (normal)= 1.0 CDT (tangential) = 0.02 Environment Wind speed Wave Height Wave Period Surface current Bottom current Water Depth

Survival 80 knots 13.8 meter 12 seconds 3 knots 1 knots 40 meters

Maximum loading on the upstream leg Wind drag force Maximum hydrodynamic drag force Pull of the two downstream legs Total tension in the tether

1,400 lbs 48,000 lbs 12,000 lbs 61,000 lbs

Static Catenary solution (zero load): At the buoy end vertical tension = 1950 kg horizontal tension = 1950 kg and At the anchor end vertical tension = 0.0 kg horizontal tension = 1950 kg.

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700 kg 21,800 kg 5,500 kg 28,000 kg


Computed tensions from the load: Location Buoy Flounder plate Anchor

Tension, kg 23472 27689 27267

Angle, degrees 35.49 69.05 75.34

Horizontal distance between anchor and buoy =128.3 meters.

Total tensions Location Vertical, kg Horizontal, kg Buoy 19,111 + 1,950 = 21,061 3,626 + 1,950 = 15 576 Flounder plate 9,900 + 1,850 = 11,750 25,858 +1,950= 27 808 Anchor 6,900 + 0.0 = 6,900 6,379 + 1,950 = 28 329

Choice of chain. The chain strength = 3 x tether tension = 183,700 lbs. Choose 1.25 inch, grade 3, stud link chain The immersed weight = 19.4 kg/m. Rated breaking strength of 184,000 lbs. (83 258 kg) Safety factor Highest tension occurs at the flounder plate = 30,000 kg. Breaking strength of the chain = 83,000 kg. Safety factor = 83,000/30,000= 2.75

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Total, kg 26,194 30,271 29,157


Dynamic Mooring System Design Two step procedure Step 1: Vessel Motion Analysis For floating structure, mooring/ riser system is an external nonlinear stiffness term.

Step 2: Mooring & Riser Analysis For the flexible elements, motions of the floating structure are added to the attachment point as an externally defined oscillation.

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Numerical Model for a Mooring Line partially on the seabed

♦ ♦ ♦ ♦ ♦ ♦ ♦ ♦

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Mooring line divided into N segments (lumped mass system) Mass of each segment is lumped at the intersection point Line between the masses is massless elastic element. All forces at each mass are equated to the mass inertia Boundaries between masses are matched to the mooring line displacement Seabed supporting mooring line is a series of linear springs with dashpot The touchdown point is a variable during the oscillating excitation Flexural rigidity is negligible

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Matrix equation for lumped mass

Inertia Force Matrix + Damping Force Matrix (includes hydrodynamic and soil damping) + Stiffness Force Matrix (includes tension, hydrodynamic and soil stiffness) = External Force Matrix External forces (considering only the fluid drag term):

f nj

=

1 ρ C Dnj D j u nj u nj 2

Example problem (Inoue and Surendran) Consider a chain in a catenary form with a portion on the bottom foundation soil. The catenary is subjected to a harmonic oscillation. The following input values for the experiment was chosen: Chain weight = 0.127 kg/m Chain equivalent diameter = 0.0059 m Chain length = 15 m Initial length of chain on seabed = 5.19 m Initial tension = 1.84 kgf Added mass = 1.98(normal) Added mass = 0.2(tangential) Top harmonic displacement amplitude = 0.04 m Properties of chain in different media Medium

Vert. stiffness Mass density Drag coeff. Drag coeff. 6 kgf/m (x 10 ) Kg/m^3 normal tangential water 0 1025 2.18 0.17 clay 2.25 1428 3.04 0.24 mud w/ sand 8.01 1538 3.27 0.26 mud 10.79 2000 4.25 0.33 Note: Modified drag coeff. = C Dwater *(medium density/ water density) Morning

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Reduction in dynamic amplitudes w/ partial chain on seabed

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A finite element approach: Free-body diagram of the line segment, i Ti θ ι

wave

FE free body diagram

current

weight

θ 0, Fairlead angle

θ ι+1

Ti+1

BE free body diagram

The equation of motion: inertia force + linear damping force + nonlinear damping force + soil damping + restoring force + soil restoring force = line tensions + mooring line weight + current force + wave force + soil force finite line element equation in the horizontal direction, x:

&&i mi x

+ c1i x&i + c2i x&i x&i + c soil x&i + k x i i + k soil xi = T i cosθ i − T i +1 cos θ i +1 + f ci+ f wi+ f soili

vertical direction, y:

&&i mi y

+ c1i y& i + c2i y& i y& i + c soil y& i + k y i i + k soil yi = T i sin θ i − T i +1 sin θ i +1 + wi + f ci+ f wi+ f soili

These equations are written in a matrix form and solved for the values for xi and yi. Morning

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Mooring Line Fatigue Analysis Mooring line fatigue is based on long term cycle of dynamic tension due to time varying current and wave forces. Fatigue life estimates are made by comparing the loading in a mooring component with the resistance of that component to fatigue damage. 

Choose appropriate T-N (tension vs. allowable number of cycles) design curves e.g., API RP 2SK:

= K

N R M Fatigue Design Parameters Component Common chain link Spiral strand rope

M 3.36 5.05

K 370 166

Fatigue Design Curves (API RP 2SK) 10000 s p i k , e g n a R n o i s n e T

1000

100

10 1.E+03

1.E+05

1.E+07

1.E+09

1.E+11

Number of Cycles Chain DIA=3.75

Chain DIA=4.00

Wire DIA=3.50

Miner’s Rule for cumulative damage ratio, D:

D

=∑

ni

N i

< 1.0

ni = number of cycles applied at each tension range N i = number of cycles allowed at the corresponding tension range Morning

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Assume short-term tension peaks are represented by the Rayleigh distribution

p( s) 

 

σ

2

exp ( −

s 2 2σ

2

)

compute damage for each load case:

D j 

=

s

= N j ( 2

σ j

) M Γ(1 + M / 2) / K BS

Repeat calculations are for each fatigue load case Accumulated damage to obtain the total damage. The fatigue life is obtained from the inverse of the total damage.

Factors of Safety Dynamic Analysis Break Strength ABS BV DNV

FOS

Fatigue Life

1.82 2.0 1.82

Inspectable lines Un-inspectable lines Polyester rope

FOS 3 10 60

Variables: BS = breaking strength of line segment K = intercept of T-N curve M = slope of T-N curve ni = number of cycles within the tension range interval ‘i’, N = number of cycles N i = number of cycles to failure at the tension range ‘i’ as given by the appropriate T-N curve. N j = number of cycles for load case ‘j’ for a duration of 1 year R = ratio of tension range (double amplitude) to nominal breaking strength s = tension range Г = Gamma function σ = standard deviation of the tension range = 2 times the standard deviation of tension time history σ j = standard deviation of effective tension range for load case ‘j’

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Dynamics of floating structure and model testing

References Statistics

1. Borgman, L. E., Ocean wave simulation for engineering design, Journal of Waterways and Harbors Division, ASCE, November 1969,557-583. 2. Bretschneider, C.L., Wave variability and Wave Spectra for Wind-Generated Gravity Waves”, Technical memorandum No. 118, Beach Erosion Board, US Army Corps of Engineers, Washington, DC, 1959. 3. Chakrabarti, S.K., Hydrodynamics of Offshore Structures, Computational Mechanics Publication, Southampton, U.K., 1987. 4. Hasselman, K.,”A Parametric Wave Prediction Model”, Journal of Physical Oceanography, Vol. 6, 1976, pp. 200-228. th

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5. ITTC, Recommendations of the 11 International Towing Tank Conference, Proceedings 11 ITTC, Tokyo, 1966.

6. Longuet-Higgins, M.S., “On the Statistical Distribution of of the Heights of Sea Waves”, Journal of Marine Research, Vol. 11, 1952, pp. 245-266. 7. Ochi M.K., and Hubble, E.N., “Six Parameter Wave Spectra”, Proceedings of the Fifteenth Coastal Engineering Conference, Vancouver, BC, ASCE, 1972, pp. 301-328. 8. Ochi, M. K., Wave statistics for the design of ships and ocean structures, Transactions of the Society of Naval Architects and Marine Engineers 1978, 86, 47-76. 9. Pierson, W.J., and Moskowitz, L., “A Proposed Spectral Form for Fully Developed Wind Seas Based on the Similarity theory of Kitaigorodskii”, Journal of Geophysical Research, Vol. 69, No. 24, December, 1964, pp.5181-5203. 10. Proceedings of Second International Ship Structures Congress, Delft, Netherlands, 1964. 11. Walden, H., Comparison of one-dimensional wave spectra recorded in the German Bight with various "theoretical" spectra, Ocean Wave Spectra, National Academy of Sciences, Prentice-Hall, New Jersey, 1963, pp. 67-98. Mooring

1. ABS “Guidance Notes on The Application of Synthetic Ropes for Offshore Mooring”, American Bureau of Shipping, New York, Houston, 1999. 2. API, “Recommended Practice for Design and Analysis of Station Keeping Systems for Floating Structures, API RP 2SK, 2nd Edition, American Petroleum Institute, Washington, DC, 1996. 3. API, Recommended Practice for Design, Analysis and Testing of Synthetic Fiber Ropes in Offshore Mooring Applications, API RP 2SM, Fourth Draft, August, 1999. 4. Asaland, M and B.E. Sogstad, “Certification of Fibre Ropes for Offshore Mooring”, 1999 Offshore Technology Conference Proceedings, OTC 10911, Offshore Technology Conference, Richardson, TX, 1999. Day1PM

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Dynamics of floating structure and model testing

5. Banfield, S.J., J.F. Flory, J.W.S. Hearle and M.S. Overington, “Comparison of Fatigue Data for Polyester and Wire Ropes Relevant to Deepwater Moorings”, Proceedings of 1999 OMAE Conference”, ASME, New York, 1999. 6. BV, “Guidance Note, Certification of Synthetic Fibre Ropes for Mooring Systems”, NI 432 DTO R00E, Bureau Veritas, Paris, 1997. 7. Cupertino, CA, 1999. TTI/ND “Deepwater Fibre Moorings – An Engineer’s Design Guide”, Oilfield Publications Ltd., Herefordshire, UK, 1999. 8. De Pellegrin, Ivan, “Manmade Fiber Ropes in Deepwater Mooring Applications”, 1999 Offshore Technology Conference Proceedings, OTC 10907, Offshore Technology Conference, Richardson, TX, 1999. 9. Det Norske Veritas, Offshore Standard Position Mooring, DNV-OS-E301, June 2001. 10. DNV, “Standard for Certification of Offshore Mooring Fibre Ropes”, Det Norske Veritas, Hovik, Norway, 1998. 11. Flory, J.F., H.A. McKenna and M.R. Parsey, “Fiber Ropes For Ocean Engineering In the 21st Century”, Civil Engineering In the Oceans V Conference Proceedings, American Society of Civil Engineers, New York, 1992. 12. Francios, M, “Experience and Developments in Fibre Rope Mooring Certification”, Proceedings of 1999 ISOPE Conference, International Society of Offshore and Polar Engineering, Cupertino, CA, 1999. 13. Goldsmith, B., Burns, D., Das, S. (KBR), 2002 spread mooring systems and components for floating units, Poster, Offshore Magazine, Oct., 2002. 14. Huse, E., 1986, ‘‘Influence of Mooring Line Damping Upon Rig Motions,’’ Proc., 18th OTC Conference. 15. Inoue, Y., and Surendran, S., “Dynamics of the interaction of mooring line with the seabed”, th Proceedings of the 4 International Offshore and Polar Engineering Conference, Osaka, Japan, 1994, pp. 317-323. 16. Koralek, A.S. and J.K. Barton, “Performance of a Lightweight Aramid Mooring Line”, 1987 Offshore Technology Conference Proceedings, OTC 5381, Offshore Technology Conference, Richardson, TX, 1987. 17. Lee, M-Y, J.F. Flory and R. Yam, “ABS Guide for Synthetic Ropes in Offshore Mooring Applications”, 1999 Offshore Technology Conference Proceedings, OTC 10910, Offshore Technology Conference, Richardson, TX, 1999. 18. Lloyd’s “Fibre Ropes in Offshore Mooring Systems”, LR Report OS/TR/97008 (draft), Lloyd’s Register Offshore Services, London,, 1999. 19. OCIMF “Guide to Purchasing Hawsers”, “Procedures for Quality Control and Inspection during the Production of Hawsers”, and “Guide to Prototype Rope Testing”, Oil Companies International Marine Forum, Witherby & Co., London, 1987. 20. OCIMF, “Hawser Standards Development Program, Trial Prototype Rope Tests, Draft Final Report, Oil Companies International Marine Forum, London, 1983. 21. OCIMF, Hawser Test Report, Data on Large Synthetic Ropes in the Used Condition, Oil Companies International Marine Forum, Witherby & Co., London, 1982. Day1PM

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Mooring System Analysis: Theory and practice of riser and mooring dynamics

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