omae2010-20040

1 Copyright © 2010 by ASME

APPLICATION OF A VISCOELASTIC MODEL FOR POLYESTER MOORING

J. W. Kim Technip

Houston, Texas, U. S. A.

J. H. Kyoung Technip

Houston, Texas, U. S. A. A. Sablok

Technip

Houston, Texas, U. S. A.

ABSTRACT

A new practical method to simulate time-dependent material

properties of polyester mooring line is proposed. The time-

dependent material properties of polyester rope are modeled

with a standard linear solid (SLS) model, which is one of the

simplest forms of a linear viscoelastic model. The viscoelastic

model simulates most of the mechanical properties of polyester

rope such as creep, strain-stress hysteresis and excitation

period-dependent stiffness. The strain rate-stress relation of the

SLS model has been re-formulated to a stretch-tension relation,

which is more suitable for implementation into global

performance and mooring analyses tools for floating platforms.

The new model has been implemented to a time-domain global

performance analysis software and applied to simulate motion

of a spar platform with chain-polyester-chain mooring system.

The new model provides accurate platform offset without any

approximation on the mean environmental load and can

simulate the transient effect due to the loss of a mooring line

during storm conditions, which has not been possible to

simulate using existing dual-stiffness models.

INTRODUCTION

Since the first offshore application to P-19 semi-submersible

production unit, installed in 1997 by Petrobras, polyester rope

has been widely used for mooring lines of offshore floating

platforms [1]. The low weight to strength ratio of the polyester

rope, compared to steel strand, makes this synthetic rope more

attractive for deep water exploration and production. In 2004,

Technip introduced polyester mooring lines to BP’s Mad Dog

Spar (4,500 ft WD) in the Gulf of Mexico [2]. Since then,

polyester mooring lines have been widely used for deep- and

ultra deep water platforms, such as Anadarko’s Red Hawk Cell

Spar (5,300 ft WD, [3]), Chevron’s Tahiti Truss Spar (4,200 ft

WD) and Shell’s Perdido Truss Spar (7817 ft).

Design, installation and maintenance of offshore platforms with

polyester mooring line require good understanding of the

mechanical behavior of polyester mooring line. Polyester ropes

show significant nonlinear and time-dependent elongation-

tension properties. On-going efforts to identify the material

properties of polyester rope have been made since the early

stage of their offshore application. Del Vecchio [4] measured

the stiffness of polyester ropes under various loads with

different mean value, range and period. He concluded that the

stiffness of polyester rope increases with increased mean

tension, yet decreases with increased tension range and

increased loading period. More systematic tests both on yarn

and full polyester ropes have been performed by many others

and similar conclusions have been made [5-10]. Among the

three factors that govern the polyester rope stiffness, the mean

load level is the most dominant factor. The decrease in stiffness

for higher tension range is obvious in the case of sinusoidal

loading, but is less conclusive in the case of random loading

[8]. The dependency of stiffness on loading period is weak. The

stiffness change is less than 10% for a loading period range

from 10 to 2000 sec, which covers most of the period range of

extreme wave and wind-gust loads for offshore platforms.

Parallel to the experimental work, analytical efforts to simulate

the mechanical behavior of polyester mooring lines have been

made ([11]-[13]). Sophisticated mathematical models such as

the nonlinear viscoelastic-viscoplastic model based on the

Schapery model can simulate the nonlinear and time-dependent

properties of polyester rope [11]. However, implementation of

such a complicated model in the global performance analysis

tools has not yet been made. For practical applications, a

simplified linearized approach has been used. API RP-2SM

[14] recommends sensitivity study using dynamic storm

stiffness and static, lower, post-installation stiffness to estimate

maximum mooring loads and vessel offsets.

Proceedings of the ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering OMAE2010

June 6-11, 2010, Shanghai, China

OMAE2010-20040


Currently, Technip uses a dual-stiffness model to consider the

viscoelasticity of polyester rope. In this model, the stretch of

the polyester is given as a combination of:

1. Quasi-static stretch driven by mean current, mean wind

and mean wave drift force which follows Hooke’s law

based on low stiffness AE∞.

2. Dynamic stretch due to gust, wave and VIV that follows

Hooke’s law based on high stiffness E0A.

Global performance (or seakeeping) simulation of a floating

platform is performed in the time domain with mooring line

stiffness given by the dynamic stiffness (or storm stiffness),

E0A. The quasi-static stretch due to mean load is considered by

an increase in the length of the polyester rope equal to the

difference between stretches due to high and low stiffness of

the polyester rope. The storm and quasi-static stiffness of

polyester ropes vary for different environments and

manufacturer and are normally obtained from test data for each

project [14]. Typical values of E0 A and AE∞ applied for 100-

yr Hurricane condition in Gulf of Mexico are:

E0 A = 30 x MBL, AE∞= 13 x MBL

where MBL is the minimum breaking load of the polyester

rope.

Alternatively, two separate independent global performance

analyses for each design environment are performed with single

stiffness E0 A and AE∞ and the more conservative response of

the two analyses results is used for mooring line and platform

design.

The dual-stiffness model works well for most cases but it has

the following shortcomings and disadvantages:

1. The mean load on the platform needs to be accurately

estimated a priori to determine the mean stretch of the

polyester rope. If there is a drift force component that is

not accounted for theoretically, the platform offset may be

underestimated.

2. The broken line case has to be simulated with the broken

mooring line removed from the beginning of the simulation.

The transient effect due to a mooring line breaking during

the storm cannot be simulated.

3. The nonlinear relation between the platform offset and the

mooring line tension is tabulated before the simulation and

then interpolated during the time-domain simulation to

save computational time. This offset table has to be re-

evaluated each time a different environment is applied

even when the same mooring line system is used.

A new approach, based on the standard linear solid (SLS, [15])

model, is proposed in this paper. SLS is one of the simplest

theoretical models for linear viscoelastic material. The model

accommodates basic properties of polyester rope such as

relaxation, creep, strain-stress hysteresis and frequency

dependent stiffness. The SLS model is defined with three

parameters: E0A , AE∞and τ. The first two parameter, E0A and

AE∞, have the same definition as in the dual-stiffness model.

The new parameter τ, which is called relaxation time, controls

the transient time that the polyester rope requires to reach

quasi-static stiffness AE∞. The SLS model is equivalent to the

spring-dashpot systems that have been proposed by the industry

to simulate time-dependent material properties of polyester

rope ([12], [13]).

The SLS model has been implemented into an existing quasi-

static mooring line analysis routine. The quasi-static mooring

line tension, which is dependent on the instantaneous offset of

the platform, is corrected to the dynamic tension value by

considering the time history of the platform motion. The new

mooring line analysis method has the following advantages

against the existing dual-stiffness model:

1. The mean stretch is correctly and adaptively simulated

directly from the applied load time history, without

requiring a priori estimation of drift force.

2. The broken mooring line case can be simulated considering

the transient effect after a mooring line loss.

3. The same interpolation table for offset-tension relation can

be used regardless of changes in environmental conditions.

This saves considerable amount of computational time

when computing a large number of realizations during

detail design.

In the following sections, the mathematical formulation and

characteristics of the SLS model are introduced and then the

implementation of the SLS model in a time-domain global

performance analysis is presented.

LINEAR VISCOELASTIC MODEL

The expression for the stress-strain relation for a linear

viscoelastic material can be given by the following time

convolution integral [15]:

( ) ( ) *

0

** )( dttttEt

t

∫ −= εσ & (1)

where the kernel E(t) is the time-dependent elastic modulus,

which provides the relation between time-dependent strain ε(t) and stress σ(t).


One of the simplest forms for the time-dependent elastic

modulus is given by

( ) ( ) ( )τtEEEtE −−+= ∞∞ exp0 (2)

where E0 is the instantaneous elastic modulus at high rate

loading which corresponds to storm stiffness for the polyester

mooring line; E∞ is the static modulus; and τ is the relaxation

time [15]. The idealized material that is governed by Eq. (2) is

called the Standard Linear Solid (SLS). The mechanical

properties of the SLS are equivalent to the spring-dashpot

system shown in Figure 1 ([15]).

Figure 1 Spring-damper system equivalent to SLS

Combining Eq. (1) and Eq. (2) gives

( ) ( ) ( )[ ]{ } ( ) *

0

**0 /exp dttttEEEt

t

∫ −−−+= ∞∞ ετσ & (3)

The above time-dependent strain-stress relation involves

convolution integration of the strain rate, ( )tε& . For mooring

line analysis it is advantageous to reformulate the relation in

terms of strain, ( )tε . Integrating Eq. (3) by parts and assuming

( ) 00 =ε gives

( ) ( ) ( ) ( )[ ] ( ) *

0

**0

0 /exp dttttEE

tEt

t

∫ ετ−−τ

−−ε=σ ∞

(4)

Eq. (4) is more convenient for numerical application since it

does not involve the time derivative of strain. Eq.(4) is also

useful to explain relaxation1 of viscoelastic material.

The inverse relation of Eq.(4) can be given by

( ) ( ) ( ) ( )[ ] ( ) *

0

*

0

*

2

0

0

0

/exp dttEttEE

EE

E

tt

t

∫ στ−−τ

−+

σ=ε ∞

∞

(5)

Eq. (5) is suitable to explain the creep2 behavior of viscoelastic

material.

1 Retarded response of stress to a sudden application of strain 2 Retarded response of strain to a sudden application of stress

CHARACTERISTICS OF VISCOELASTIC MODEL

The characteristics of the SLS model are illustrated below. The

properties presented here are for a specific case when static

stiffness is 50% of storm stiffness. The time-dependent elastic

modulus, E(t), for this specific SLS model is shown in Figure 2.

In the following paragraphs, four characteristics of the SLS

model, stress relaxation, creep, strain-stress hysteresis and

period-dependent stiffness and damping are explained for this

specific model.

Relaxation Modulus ( E_infinity = 0.5 E0)

0

0.5

1

1.5

0 2 4 6 8 10

t / ττττ

E(t) / E0

Figure 2 Relaxation Modulus of a SLS with 05.0 EE =∞

Stress Relaxation

0

0.5

1

1.5

0 2 4 6 8 10

t / ττττ

Str

ain

, S

tress / E

0

Strain

Stress / E0

Figure 3 Stress response to a sudden loading of uniform

strain

Under sudden application of strain:

( )

≥

<=ε

0,1

0,0

t

tt (6)

The stress response is obtained from Eq.(4) as

∞= Ek1

∞−= EEk 02 τ= 2kc

( )tσ ( )tx ε=


( ) ( ){ },exp12

0 τ−+=σ tE

t (7)

where 2/0EE =∞ is assumed. Instantaneous stiffness E0 is

applied at the beginning of the loading and then stiffness

gradually decreases to E0 /2 or ∞E , as shown in Figure 3.

Creep

0

0.5

1

1.5

2

2.5

0 2 4 6 8 10

t / ττττ

Str

ain

/ (σσ σσ

0 / E

0), S

tress / E

0

Strain / (s0/E0)

Stress / E0

Figure 4 Strain response to a sudden loading of uniform

stress

Under sudden application of stress:

( )

≥

<=

0,

0,0

0 t

tt

σσ (8)

The strain response is obtained from Eq. (5) as

( ) ( )

−−= τσ

ε 2exp2

11

2

0

0 tE

t (9)

Strain is initially 0

0

E

σ and then gradually increases to∞E

0σ , as

shown in Figure 4. Note that it takes about 10 τ for the strain to

reach its steady limit.

Strain-Stress Hysteresis

Because of the time delay in response, viscoelastic material

shows strain-stress hysteresis during the loading and unloading

process. For a step loading as shown in Figure 5, strain

response can be obtained using Eq. (5), as depicted in Figure 6.

When the same strain response is plotted in the strain-stress

plane, as shown in Figure 7, it can be seen that the strain-stress

relation does not follow Hooke’s law and shows a different path

for loading and unloading. This strain-stress hysteresis also

implies energy loss during the loading and unloading. The area

enclosed by the hysteresis loop is work done by the applied

load, or energy loss due to the viscosity of the polyester rope.

Figure 5 Time history of applied stress

Figure 6 Time history of strain response

Figure 7 Strain-Stress diagram

0

0.5

1

1.5

0 0.5 1 1.5 2 2.5

Strain

Str

ess

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300 t / τ

Str

ain

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200 250 300 t / τ

Str

ess

σ0


Period-Dependent Stiffness and Damping

Figure 8 A mass-spring-damper system

A platform moored by an idealized synthetic rope that behaves

as SLS can be modeled by a mass-spring damper system shown

in Figure 8. Here m is the virtual mass of the platform in x

direction. Dynamic mooring force on the platform in a surge

motion with amplitude X0 and period T can be obtained by

substituting sinusoidal motion

( )T

tXtX

π=

2sin0

(10)

into Eq.(4) to obtain sinusoidal mooring force as

( ) ( )

( )( )( )

( ) T

tX

TT

TEE

T

tX

T

TEEtfmoor

π

π

τ+π

τ−+

π

τ+π

τ+π=

∞

∞

2cos

2

/4

/

2sin

/4

/4

022

2

0

022

2

0

2

(11)

Eq.(11) provides period-dependent stiffness and damping:

Stiffness = ( )( )22

2

0

2

/4

/4

τ+π

τ+π ∞

T

TAEAE (12)

Damping = ( )( )( )22

2

0

/4

/

τ+π

τ− ∞

T

TAEAE (13)

From the period-dependent stiffness given by Eq. (12), natural

period TN of the platform is given by the following relation:

( )( )

mT

T

TAEAE N

N

N =

πτ+π

τ+π ∞

2

22

2

0

2

2/4

/4 (14)

Damping ratio of the surge motion of the platform is then given

by

( )( )( )2

0

2

0

/4

/

Stiffness2

DampingRatioDamping

τ+π

τ−π=

×=

∞

∞

N

N

TAEAE

TAEAE

m (15)

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100

T / ττττ

Stiff

ness / E

0A

(a)

0.95

0.96

0.97

0.98

0.99

1

0 0.5 1 1.5 2

T / ττττ

Stiff

ness / E

0A

(b)

Figure 9 Dynamic Stiffness of SLS Model ( ∞= EE 20)

0%

1%

2%

3%

4%

5%

6%

7%

8%

9%

10%

0 0.5 1 1.5 2

TN / ττττ

Dam

pin

g R

atio (%

)

Figure 10 Damping Ratio of SLS Model

AEk ∞=1

AEAEk ∞−= 02 τ= 2kc

( )tf ( )tXx =

m


Figure 9 shows the theoretical stiffness of the dynamic system

when ∞= EE 20for the different period ranges. When the

motion period is less than the relaxation time, τ, the stiffness

decreases less than 2% from E0A. As the motion period

increases, the stiffness decreases to its asymptotic static value.

Figure 10 shows the theoretical damping ratio plotted against

ratio between platform natural period and relaxation time.

When the natural period of the platform is less than the

relaxation time the damping ratio is less than 4%. The damping

ratio presented here can also be applied to the damping ratio for

the surge and sway motion of a floating body, which has no

restoring mechanism other than mooring line tension.

OPTIMAL SLS MODEL

Dynamic stiffness of the SLS model is compared with the

available polyester rope test data. The static and storm stiffness

of the SLS model is chosen as typical value used for the global

performance and mooring analyses for 100-yr storm condition

in the Gulf of Mexico:

E0 A = 30 x MBL, AE∞= 13 x MBL

The relaxation time, τ, is varied from 60 s to 240 s.

Since the most of the polyester rope test has focused on the

influence of mean load and load amplitude on the rope

stiffness, there are only few data available to compare period-

dependency of dynamic stiffness. Table 1 shows number of

polyester rope test data taken from [2], [4] and [10]. Test data

with mean load of 40% MBL and load amplitude of 10% MBL,

which is a typical design response of polyester rope in extreme

condition, are used for the comparison. For the test data

provided in Casey & Banfield [10], only the lower mean load

data (20% MBL) were available. The normalized rope stiffness,

EA/EA0, has been calculated from the dynamic stiffness divided

by the stiffness at the shortest loading period among each set of

data.

Figure 11 shows dynamic stiffness of SLS model for three

different relaxation times, τ = 60, 120 and 240 s, and

normalized rope stiffness obtained from the test data. The

dynamic stiffness of SLS model with τ = 60 fits well with the

test data for loading period shorter than 100 s but

underestimates dynamic stiffness for longer loading period. The

SLS models with τ = 120 s and 240 s provides higher EA/EA0

than the test data for the load period shorter than 200 s. In case

of Spar platform in deep water, which has typical surge/sway

natural period around 120 seconds, the SLS model with

τ higher than 120 s will provide conservative mooring-line

tension response.

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1 10 100 1,000 10,000

Loading Period (s)

Stiffness / E

0A

SLS, Tau = 60 s

SLS, Tau = 120 s

SLS, Tau = 240 s

Del Vecchio [4] - Marlow

Del Vecchio [4] - Brascorda

Petruska et al. [2]

Casey & Banfield [10]

Figure 11 Dynamic Stiffness of SLS Model and Test Data

Table 1 Dynamic Stiffness Ratio (EA/EA0) from Test Data

Ref.Mean Load

(% MBL)

Load Amp.

(% MBL)

No. of

Cycle

Loading

Period (s)

EA ( x

MBL)EA / EA0

Del Vacchio [4], Marlow Superline (Empirical Formula)

40 10 100 8 14.17 1.00

40 10 100 15 14.04 0.99

40 10 100 100 13.68 0.97

40 10 100 200 13.54 0.96

Del Vacchio [4], Brascorda Prallel (Empirical Formula)

40 10 100 8 15.71 1.00

40 10 100 15 15.57 0.99

40 10 100 100 15.18 0.97

40 10 100 200 15.04 0.96

Petruska et al. [2]

40 10 100 20 31.52 1.00

40 15 100 30 29.65 0.94

40 15 100 32 30.33 0.96

40 10 100 100 30.26 0.96

43 5 1 3,600 19.89 0.63

Casey & Banfield [10]

20 10 20 3 24.62 1.00

20 10 20 12 24.28 0.99

20 10 20 200 23.60 0.96

20 10 1 77,400 22.78 0.93

The comparison shown in Figure 11 indicates that fitting

dynamic stiffness of test data by a single SLS model for overall

loading period range is not practical, because the period-

dependency of SLS model is governed by a single parameter, τ. More precise description of dynamic stiffness of actual

polyester rope needs more advanced viscoelastic model with

multiple relaxation time such as Wiechert model [15]. A rather

practical approach is pursued in this paper by adopting SLS

model with the relaxation time, τ, tuned for the optimal

accuracy and numerical efficiency. As shown in the previous

section, higher τ results in higher stiffness and smaller

damping, which will provide conservative dynamic mooring

line tension. On the other hand, global performance simulation

with higher τ requires longer simulation time since it takes

longer transient time before the mean offset of the platform

reaches steady state. Creep behavior of SLS model shown in


Figure 4 indicates that the required transient time is in the order

of 10 τ. The relaxation time, τ, is determined based on the

following criteria:

1. Dynamic stiffness of SLS should be higher than the

real polyester rope for the short loading period range

shorter than platform motion natural period for

conservative mooring-line tension response.

2. Dynamic stiffness of SLS should be lower than the

real polyester rope for the period range sufficiently

longer than platform natural period for conservative

platform offset.

3. Minimize transient time required for steady state.

Considering comparison with the test data and the above three

criteria, relaxation time, τ, is taken as 120 s. In this case,

damping ratio is 4% when platform surge/sway natural period

is 120 s and 2% when platform surge/sway natural period is 60

s. The transient time required for the steady response is

estimated as 20 minutes.

IMPLEMENTATION OF LINEAR VISCOELASTIC MODEL

Assuming polyester rope behaves like a standard linear solid

and has uniform stress and strain along its whole length, except

for the static stress and strain components due to gravity and

buoyancy force, the mooring tension along a polyester line can

be given as

( ) ( )( ) ( )[ ] ( ) ,/exp

0

**0

0

dttttAEE

tAEtT

t

polyester

∫ ετ−−τ

−−

ε=

∞ (16)

which can be obtained from Eq. (4) after multiplying cross

section area of the polyester rope, A. The first term on the right

hand side of Eq. (16) is the tension force due to the polyester

rope when storm stiffness is applied. The second term can be

interpreted as the tension relaxation due to viscoelasticity.

Generally, the polyester mooring line does not simply consist of

a continuous polyester rope. It has upper and lower mooring

chain sections, connectors made of steel and multiple segments

of polyester rope in between. Separate modeling of each

polyester segment is time consuming and complicates

implementation of the SLS model. A simplified approach,

where the whole mooring line system is lumped into one

viscoelastic line element, is adopted. The following

assumptions are made in this approach:

1. The catenary shape of the mooring line is close to the

geometry of the mooring line with quasi-static stiffness,

E∞A.

2. Stretch in steel chains and connectors are negligible

compared to the stretch in polyester ropes.

3. When there is more than one polyester rope segment in one

mooring line, relaxation time of all segments is the same.

The above scheme is implemented into the Technip in-house

computer code MLTSIM. MLTSIM performs time-domain

global motion simulation for floating bodies. Mooring force at

a given platform location is interpolated from look-up tables

generated by an internal subroutine FMOOR, which solves the

catenary equation considering elastic elongation using static

stiffness and force equilibrium of each segment.

APPLICATIONS

Global Performance of a Spar Platform with Intact

Mooring Lines

The new model has been applied to a conceptual Spar designed

as a dry-tree unit operating in 7,200 ft of water depth. Table 2

shows particulars of the Spar. The Spar is moored with 9

mooring lines. Each mooring line has three segments consisting

of upper and lower chain and a polyester rope segment in the

middle. The properties of each segment are given in Table 3.

Viscoelastic properties of polyester segment are given as

E0 A = 30 x MBL, AE∞= 13 x MBL , τ = 120 s

The mooring line layout is shown in Figure 12. Mooring lines

are grouped into 3 groups. Each group is separated by 120 deg

and each mooring line in a group is separated by 5 deg.

Table 4 shows the applied environment. Long-crested waves

with JONSWAP spectrum are used for the random wave model

and an NPD spectrum is used for the wind-gust model. Wind,

wave and current directions are collinear and towards negative

x-axis, as shown in Figure 12. Time simulation for 3 hours is

performed.

Analysis has been performed for the following four different

models of polyester rope:

1. Single stiffness model with quasi-static stiffness ( )AE∞

2. Single stiffness model with storm stiffness ( )AE0

3. Dual stiffness model

4. Viscoelastic model

Figure 13 shows the time history of platform surge for the first

100 minutes of simulation. Surge response using the

viscoelastic model is compared with the single-stiffness

models. The mean surge response from the viscoelastic model

agrees well with the static-stiffness model, whereas the

dynamic response due to wave and wind gust is closer to the

storm-stiffness model. Figure 14 shows the comparison of


tension of the most loaded mooring line. The mean tension

from the viscoelastic model follows the static-stiffness model

and the dynamic tension follows more closely to the storm-

stiffness model.

Figure 15 and Figure 16 show platform surge and mooring-line

tension around t = 2,500 s, respectively. Comparisons between

the viscoelastic and dual-stiffness models are made. The two

models agree well with each other. The dual-stiffness model

under-predicts mean surge slightly, which means that the

estimated mean environmental force and mean stretch of the

polyester rope is slightly lower than the actual value. Both

models agree well with each other on mooring line tension.

Table 2 Spar Particulars

Platform Properties

Displacement kips 300,000

Diameter ft 150

Hull Length ft 615

Hull Draft ft 570

Table 3 Mooring line properties

Diameter Length

Segment Type in ft

Platform

Chain

R5

Studless 5 600

Middle

Line Polyester 10 10,427

Anchor

Chain

R5

Studless 5 161

Table 4 Applied environments

Wave Spectrum JONSWAP

Hs(ft) 36.4

Tp(sec) 15.5

Shape γ 1.67

Wind

Spectrum Vw(knots)

NPD

78.5

Current

Depth (ft) Vel. (ft/s)

0 4.5

120 4.5

212 3.9

317 3.3

1640 2.1

1

2

3 4

5

6 7

8

9

Wind, Wave & Current

Figure 12 Mooring line layout

-250

-200

-150

-100

-50

0

0 1000 2000 3000 4000 5000 6000

t (s)

Surg

e (ft

)

Viscoelastic Model

Static-Stiffness Model

Storm-Stiffness Model

Figure 13 Platform surge compared with single-stiffness

models

8.0E+05

1.0E+06

1.2E+06

1.4E+06

1.6E+06

1.8E+06

0 1000 2000 3000 4000 5000 6000

t (s)

Tensio

n (lb

)

Viscoelastic Model



Figure 14 Mooring line tension at fairlead (Line #1)

compared with single-stiffness models


-240

-230

-220

-210

-200

-190

-180

-170

-160

2300 2400 2500 2600 2700 2800

t (s)

Surg

e (ft

)

Viscoelastic Model

Dual-Stiffness Model


Figure 15 Platform surge compared with dual- and single-

stiffness models

1.2E+06

1.3E+06

1.4E+06

1.5E+06

1.6E+06

1.7E+06

2300 2400 2500 2600 2700 2800

t (s)

Tensio

n (lb

)

Viscoelastic Model



Figure 16 Mooring line tension at fairlead (Line #1)

compared with dual- and single-stiffness models

-2.00E+06

-1.00E+06

0.00E+00

1.00E+06

2.00E+06

3.00E+06

4.00E+06

-250-200-150-100-500

Surge (ft)

Fx (lb

)

Viscoelastic Model

Dual-stiffness Model



Figure 17 Surge-Mooring Force Diagram

0

50

100

150

200

250

Max Min Mean STD x 10

Surg

e (ft

)

Viscoelastic Model




Figure 18 Statistics of Platform Surge

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Max Min Mean STD x 10

Tensio

n (kip

s)

Viscoelastic Model




Figure 19 Statistics of Tension at Mooring Line #1

The global characteristics of each mooring line model can be

clearly shown by the surge-mooring force curve shown in

Figure 17. The slope of each curve can be interpreted as global

mooring stiffness. The slope of the storm-stiffness model is

about 2.3 times that of the static-stiffness model. The

viscoelastic model shows a slope parallel to the storm-stiffness

model but it is creeping to the same mean offset as the static-

stiffness model.

Statistical values of platform surge and mooring line tensions

from the four different models are compared in Figure 18 and

Figure 19, respectively. The viscoelastic model provides the

same mean surge and mooring line tension as the static-

stiffness model, whereas the standard deviation is closer to the

storm-stiffness model. Comparing with the dual-stiffness

model, the viscoelastic model provides slightly higher (1.5%)

surge and slightly lower (0.09%) mooring line tension.

Transient Mooring Tension when a Mooring Line is Broken

The viscoelastic model is used to simulate transient mooring

line tension when a mooring line is broken during a severe

storm. The existing dual-stiffness model can simulate the


broken mooring line case only when the mooring line is

removed from the beginning of the simulation and cannot

simulate the transient response created by a broken mooring

line.

The time history of mooring line tension for the intact case,

shown in Figure 16, indicates that mooring line tension of #1

mooring line reaches maximum at around t = 2,470 s. To

determine the maximum transient tension, mooring line #9 (see

Figure 12) is removed at several different times and the tension

on mooring line #1 is compared with the base case when the

mooring line is removed at t = 0. Figure 20 shows the time

history of #1 mooring line tension. It can be seen that mooring

line tension reaches maximum value when the mooring line is

removed at t = 2,350 s. The maximum mooring tension is about

5% higher than the base case where the broken mooring line is

removed from the beginning of the simulation. Figure 21 shows

the platform surge response. It can be seen that the maximum

surge reduces when the transient effect is considered.

5.0E+05

7.0E+05

9.0E+05

1.1E+06

1.3E+06

1.5E+06

1.7E+06

1.9E+06

2.1E+06

2.3E+06

0 1000 2000 3000 4000 5000 6000

t (s)

Tensio

n (lb

)

Intact

Brkn at t = 0 s

Brkn at t = 2350 s

Brkn at t = 2400 s

Brkn at t = 2450 s

(a) t = 0 ~ 6,000 s

1.2E+06

1.3E+06

1.4E+06

1.5E+06

1.6E+06

1.7E+06

1.8E+06

1.9E+06

2.0E+06

2.1E+06

2000 2100 2200 2300 2400 2500 2600 2700 2800

t (s)

Tensio

n (lb

)

Intact

Brkn at t = 0 s

Brkn at t = 2350 s

Brkn at t = 2400 s

Brkn at t = 2450 s

(b) t = 2,000 s ~ 2,800 s

Figure 20 Mooring Line Tension at line #1

-350

-300

-250

-200

-150

-100

-50

0

0 1000 2000 3000 4000 5000 6000

t (s)

Surg

e (ft)

Surge (Intact)

Surge (Brkn at t = 0 s)

Surge (Brkn at t = 2350 s)

Figure 21 Platform Surge for Intact and Broken Mooring

Line Cases

CONCLUSIONS

1. A new numerical model for polyester mooring line analysis

based on a linear viscoelastic model, the standard linear

solid (SLS) model, has been successfully implemented to a

time-domain global performance and mooring analyses

tool.

2. The new model provides a more robust and accurate

engineering method to simulate global performance of

floating platform and mooring performance with polyester

mooring line compared with the existing models.

3. The new model requires less computational time and

manual intervention during the global performance and

mooring analyses.

4. The new model can calculate the transient effect of a

broken mooring line, which could not be simulated by the

existing dual-stiffness model.

ACKNOWLEDGMENTS

The authors would like to thank Technip for permitting

publication of this paper.

REFERENCES

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Schulz, N., 2005, “Polyester Mooring for the Mad Dog Spar-


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[4] Del Vecchio CJM, 1992, “Light Weight Materials for Deep

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[12] Flory, J.F., Leech, C.M., Banfield, S.J., Petruska, D.J.,

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[13] Flory, J.F., Ahjem, V., Banfield, S.J., 2007, “A New

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[14] API, 2007 “Recommended Practice for Design,

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