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Contract No. DE-AC36-08GO28308

Conference Paper

NREL/CP-5000-76015

September 2020

Umbilical Fatigue Analysis for a Wave 

Energy Converter

Preprint

Billy Ballard,1 Yi-Hsiang Yu,2 Jennifer Van Rij,2 and 

Frederick Driscoll2

1 Delmar Systems

2 National Renewable Energy Laboratory

Presented at the ASME 2020 39th International Conference on Ocean, 

Offshore and Arctic Engineering 

August 3–7, 2020 
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Conference Paper

NREL/CP-5000-76015

September 2020

Umbilical Fatigue Analysis for a Wave 

Energy Converter

Preprint

Billy Ballard,1 Yi-Hsiang Yu,2 Jennifer Van Rij,2 and 

Frederick Driscoll2

1 Delmar Systems

2 National Renewable Energy Laboratory

Suggested Citation

Ballard, Billy, Yi-Hsiang Yu, Jennifer Van Rij, and Frederick Driscoll. 2020. Umbilical 

Fatigue Analysis for a Wave Energy Converter: Preprint. Golden, CO: National 

Renewable Energy Laboratory. NREL/CP-5000-76015.

https://www.nrel.gov/docs/fy20osti/76015.pdf. 
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UMBILICAL FATIGUE ANALYSIS FOR A WAVE ENERGY CONVERTER

Billy Ballard

Delmar Systems

Houston TX, USA

Email: Billy.Ballard@delmarsystems.com

Yi-Hsiang Yu∗

National Renewable Energy Laboratory

Golden, CO, USA

Email: yi-hsiang.yu@nrel.gov

Jennifer Van Rij

National Renewable Energy Laboratory

Golden, CO, USA

Email: jennifer.vanrij@nrel.gov

Frederick Driscoll

National Renewable Energy Laboratory

Golden, CO, USA

Email: Frederick.Driscoll@nrel.gov

ABSTRACT

Unique umbilical designs for wave energy converters

(WECs), including the ability to handle significantly larger motions and loads over long deployments, are often required when

conventional marine umbilical designs for offshore oil and gas

and offshore wind may not meet the design and cost needs of

wave energy technologies. This study details a fatigue analysis

of a dynamic power umbilical attached to a two-body floating

point absorber WEC system, using the sea states provided for

the PacWave testing facilities. The 6 degrees of freedom motion time history for the WEC was simulated, and the motions of

the attachment point for the umbilical on the WEC and respective sea states were used to analyze the dynamic motions and

fatigue of the connected power umbilical to predict the fatigue

life. The results show that the fatigue damage observed is more

significant in shallow water, and extensive fatigue damage may

occur because of the larger curvature response of the umbilical.

The umbilical configurations departing at 90 deg off incoming

waves were found to have the highest fatigue life attributed to

less extension or compression of the umbilical. However, additional bend stiffener/limiter features may need to be incorporated

into the buoyancy section and touchdown regions to minimize

curvature-induced fatigue.

KEYWORDS

Wave energy converter; umbilical; fatigue analysis

∗Address all correspondence to this author.

NOMENCLATURE

A∞ Added mass matrix at infinite frequency

X Translational and rotational displacement vector

M Mass matrix

K Matrix of impulse response function

Fext Wave-excitation force vector

FMD Mean drift force vector

FPTO Power-take-off force vector

Fmo Mooring force vector

Fvis Quadratic viscous force vector

Fres Net buoyancy restoring force

TD Design tension

RD Design radius curvature

Els Bend stiffness along the bend stiffener

Elr Bend stiffness of the umbilical

INTRODUCTION

The umbilical is an essential part of the overall design for

a wave energy converter (WEC). Conventional marine umbilical

designs for offshore oil and gas and offshore wind are often applied (e.g., [1]). However, it may not meet the design and cost

needs of wave energy technologies, where unique requirements

for WEC designs, including the ability to handle significantly

larger motions and loads over long deployment duration, are often needed. As a result, poorly designed umbilical cables can fail

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early and/or increase project costs. Premature umbilical failure

can be catastrophic because umbilical cables are in the critical

path to delivering power and are difficult and expensive to swap

out. To our knowledge, no umbilical product line exists that is

specifically designed or able to meet the operational, functional,

and cost requirements of being connected to a WEC. The design

of robust and cost-effective umbilical cables for WECs requires

accurate estimates of motions, loads, vibration, bending, pressure, abrasion, fatigue, failure modes, corrosion, heating, resistance, dielectric strength, and possibly more factors, which may

be experienced by a range of expected WEC device types under

extreme and regular operating conditions, over the lifetime of the

project.

The design and utilization of robust and cost-effective

medium-voltage power and communication umbilicals that connect WECs to subsea transmission lines are essential for the success of the development of WEC technology and for the reduction of levelized cost of energy for commercial wave energy systems. This study details a fatigue analysis of a dynamic power

umbilical attached to a two-body floating point absorber (FPA)

type of WECs system using sea states for the PacWave testing

facilities. The 6 degrees of freedom motion time history for the

WEC was obtained through the use of WEC-Sim [2]. The motions of the attachment point for the umbilical on the WEC and

respective sea states were used to analyze the dynamic motions

and fatigue of the connected power umbilical. The cable dynamic simulations were carried out using OrcaFlex [3]. In the

paper, the methodology of the two numerical models is briefly

reviewed, followed by the approach to determine the size of the

bend stiffener. Finally, the results of the fatigue life analysis on a

lazy wave umbilical configuration with and without the consideration of mean drift force and for water depths of 50 m and 100

m are presented.

METHODOLOGY

A summary of the site location and wave environment, numerical methods, device and cable properties, bend stiffener sizing, and fatigue analysis are described in this section.

Site Location and Wave Environment

This analysis used the wave scatter diagram (Table 1) to represent the joint probability distribution of significant wave height

and energy period described for the PacWave test site. PacWave

is formerly known as the Pacific Marine Energy Center South

Energy Test Site (Fig. 1), which is located in the Pacific Northwest region near the city of Newport, Oregon, and Yaquina Bay.

PacWave is a grid-connected testing facility for WECs, funded

by the U.S. Department of Energy, which is expected to begin

operation in 2021 [4].

The joint probability distribution of the sea states over an

annual year for the PacWave location [5] was used to develop

the case matrix for analyzing the umbilical, as shown in 1. The

wave scatter table provided includes sea states ranging from 0.5

TABLE 1. WAVE SCATTER DIAGRAM FOR PACWAVE

FIGURE 1. PACWAVE TEST SITE LOCATION

m to 9.0 m, with corresponding peak spectral periods from 5.0 s

to 22.0 s. The PacWave data show that the most frequently occurring sea state is within the range of 1.5 m to 2.0 m, with peak

energy periods of 9.0 s to 10.0 s. The total occurrence for each

wave frequency and for each significant wave height are shown

at the bottom and to the right of the table, respectively, depicting

the majority of sea states ranging from 0.5 m to 3.5 m and peak

periods ranging from 8.0 s to 13.0 s. The frequencies of occurrence of less than 0.01% were considered negligible and were

not shown in Table 1. However, it should be noted that extreme

sea states with very low probabilities of occurrence can result in

very large fatigue damage (low cycle fatigue), should they occur

while deployed. As such, in practice it is recommended to conservatively account for the low-probability events in the fatigue

assessment.

As shown in Fig. 2, the waves for the PacWave location predominantly come from the west toward the shore, and one environmental heading was used throughout all analyses. To account

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FIGURE 2. ANNUAL WAVE ROSE OF SIGNIFICANT WAVE

HEIGHT AND DIRECTION

for different umbilical install azimuths, five line azimuths were

analyzed every 45 deg from 0 deg (west, into the environment)

to 180 deg (east, away from the environment).

Hydrodynamics Modeling

To estimate loads and fatigue damage for WEC umbilical

cables, the dynamic response of the two-body FPA (Fig. 3) was

obtained using WEC-Sim. [2]. WEC-Sim is a radiation-anddiffraction-method-based numerical model that has been developed to solve the system dynamics of WECs comprising multiple

bodies, joints, power-take-off systems, and mooring systems [6].

The dynamic response in WEC-Sim is calculated by solving the

equation of motion in the time domain for each body about its

center of gravity, based on Cummins’ equation [7],

(M+A∞)X ̈ =−

Zt

0

K(t −τ)X ̇ (τ)dτ

+Fext +Fvis +Fres +FPTO +Fmo +FMD

(1)

In this study, we used WAMIT [8], which is a boundary-elementmethod-based frequency-domain potential flow solver, to obtain

the added mass, wave excitation, impulse response function, and

restoring stiffness terms. To account for the influence of the drift

on the cable loading, the calculation of the mean drift force and

moment was also included, based on the momentum conservation principle.

The dimensions and mass properties for the WEC are presented in Fig. 3 and Table 2, respectively. The mass for

each body was equal to its displaced mass, and both the float

and spar/plate were located at their equilibrium positions. The

PacWave site has water depths ranging from 58 m to 75 m [5].

Therefore, the simulations were carried out in two water depths

of 50 m and 100 m in this study to account for the water depth

FIGURE 3. THE SCHEMATIC (SIDE VIEW) OF THE FPA DESIGN (LEFT) AND THE WEC-SIM MODEL (RIGHT)

TABLE 2. TWO-BODY FLOATING POINT ABSORBER WEC

MODEL SPECIFICATIONS

Center of Mass Moment of Inertia

Gravity (m) (103kg) (103kg-m2)

20,900 0 0

Float [0, 0, -0.72] 727.01 0 21,300 4.30

0 4.30 31,700

Spar/ 137,000 0 0

Plate [0, 0, -21.29] 878.30 0 137,000 218

0 218 28,500

variation. The WEC was connected to three mooring chains,

and WEC-Sim was coupled with MoorDyn [9] for simulating

the mooring dynamics. To represent the effect of viscosity, a

quadratic damping coefficient of 1 was used in surge for both the

float and the spar/plate. For heave and pitch, the values were set

to 1.1 and 3.7 for the float and spar/plate, respectively.

The WEC-Sim simulations were carried out based on the

joint probability distribution of the sea states given in Table 1,

with passive damping tuned to maximize the power output for

each sea state. The time history of the attachment point of the

umbilical and the WEC was recorded in WEC-Sim, with and

without the influence of mean drift force on the device, to analyze

the layout and dynamic load effect of the umbilical cables.

Note that, based on the given water depth in the case studies, the WEC is operated in intermediate depth and deep water.

For simplicity, a deep-water assumption was made for the analysis. Since the study is focusing on the fatigue analysis of the

umbilical design, we assumed WEC-Sim and OrcaFlex model

is one-way coupled and the influence of the umbilical cable dynamics on the WEC response is negligible, which can be overly

simplified for practical applications. However, the modeling of

fully coupled interaction between the WEC and the umbilical is

beyond the scope of this study. Nevertheless, a model to include

the bending stiffness calculation is currently being developed in

moorDyn and will be fully coupled to WEC-Sim for a more detailed study in the future.

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FIGURE 4. THE ORCAFLEX MODEL (50-M WATER DEPTH)

Cable Dynamics Modeling

The dynamic motions and fatigue of the connected power

umbilical were simulated using a commercial offshore dynamic

analysis and marine system modeling tool (OrcaFlex) [3]. This

analysis used the exact same sea states simulated in WEC-Sim.

The fatigue analysis is performed on a lazy wave umbilical configuration, as shown in Fig. 4, with the surface float of the WEC

as solid orange and the remaining vertical column with the reaction plate in blue.

For the 50-m water depth case, the total length of the umbilical used is 137 m from the WEC connection to the seabed connection past the touchdown location. This includes additional

length of the umbilical to sufficiently reduce the impact of the

anchored location, and the first 4 m of the umbilical is inside

the bend stiffener. It also has a 25-m buoyancy section, which

is 57 m from the WEC connection. The umbilical modeled has

an average pretension of 2.4 mT with a mean hang-off angle of

11.8 deg. For the 100-m water depth case, the length is 310 m,

with a 42-m buoyancy section that is 108 m from the WEC connection. The umbilical modeled has an average pretension of

4.7 mT with a mean hang-off angle of 10.0 deg. For simplicity,

the connection point of the umbilical is assumed to be attached

to the vertical column, such that the surface float does not clash

with the umbilical at the maximum range-of-surface float motion. The umbilical catenary assumes the reaction plate of the

WEC is designed to provide sufficient clearance.

Bend Stiffener Sizing

A bend stiffener limits the stresses in the umbilical during

the dynamic motions of the WEC. The bend stiffener gradually

increases the bending stiffness of the umbilical to a significantly

larger value that can be rigidly connected to the WEC. The preliminary bend stiffener used in the analysis followed the study

presented in [10]. To develop the preliminary bend stiffener,

each bin was first run without a bend stiffener, with the umbilical pinned at the connection location on the WEC. From each

bin, the maximum and minimum line tensions with the maximum

magnitude of declination or azimuth were used to determine the

sizing of the bend stiffener.

FIGURE 5. BEND STIFFNESS DESIGN

The design tension, TD, and design radius curvature, RD, are

based on nondimensional values referenced from the nondimensional bend stiffener design curves [10]. These values are then

used to determine the bend stiffness along the bend stiffener. The

shortest length of the bend stiffener is about 4 m, based on the

minimum bend radius.

Els = Elr +2TDR

2

DSin2

(

s

2RD

),0 ≤ s ≤ RDαR. (2)

Figure 5 shows the bend stiffness along the length of the

bend stiffener. The blue line represents the bend stiffness, as

described in Eq. 2, using the design tension and radius curvature.

The red lines indicate the bend stiffness using the varied root

radius. The solid red line shows the root radius of 0.21 m was

used in the analysis.

Fatigue Analysis

The fatigue life of the umbilical was calculated using the

fatigue analysis module within OrcaFlex. The module uses a

cycle-counting technique to break down each random wave case

into a series of half cycles, and then sums the damage. This

damage value for each load case is then scaled, based on the

specified total exposure time and summed to give the overall total

damage. The exposure time is determined by the frequency of

occurrence for each bin, as shown in Table 1. The conductors

in the umbilical are designed to meet the requirements set by

International Organization for Standardization standard [1]. It is

assumed that the individual elements within the umbilical move

freely in longitudinal direction against each other, but there is no

relative movement between the strands within the conductors.

The stresses associated with the cyclic tensile and bending

loads are determined for each of the simulated environmental

bins, for 16 evenly spaced intervals around the umbilical circumference. Using the rain flow counting method, the number of half

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FIGURE 6. S-N CURVE FOR THE HIGH-VOLTAGE COPPER

CONDUCTORS

cycles occurring in each simulation run were determined. The SN curve, shown in Fig. 6, was used to calculate the resulting

damage caused by each half cycle. The proposed S-N curve was

defined for stress amplitudes above 50 MPa, following Murphy’s

suggestion [11]. The Palmgren-Miner rule was used to sum the

damage caused by each of the half cycles to determine the damage value for the load case. The % occurrence from the wave

scatter diagram was incorporated via the exposure time factors,

with the scaled result reflective of the total overall annual damage

to the umbilical. Overall, the fatigue life is inversely proportional

to the total annual damage.

RESULTS

The analysis of the fatigue life for the umbilical of the WEC

system is presented in this section, including the influence of the

mean drift force and moment, bend stiffener, and water depth.

Fatigue Life Analysis

Figure 7 plots fatigue results for the bend stiffener and buoyancy sections of the umbilical, with and without considering the

mean wave drift force for the case of 50-m water depth. As

shown in the figure, most of the fatigue damage occurs in the

buoyancy section for the 0-deg azimuth with a 0.07-year (25

days) fatigue life. This is because the WEC surges back and

forth, which results in a pinching motion along the buoyancy

section. The second most damage-producing section is located

at the touchdown point for the 180-deg azimuth with a 0.39-year

(142 days) fatigue life. The least damage produced occurs with

the 90-deg azimuth with a 461-year fatigue life, which assumes

the umbilical at the touchdown is allowed to move freely along

the seabed without trenching. Additional abrasion protection at

the touchdown is also recommended because of the resulting motions and clashing that will be present with the sandy bottom.

The results also show that not accounting for mean wave drift

FIGURE 7. FATIGUE RESULTS COMPARISON WITH AND

WITHOUT ACCOUNTING FOR MEAN DRIFT FORCE

FIGURE 8. BEND STIFFENER SECTION FATIGUE RESULTS

COMPARISON WITH ACCOUNTING MEAN WAVE DRIFT

when simulating the WEC system could underestimate the fatigue life in some cases (e.g., the 0-deg and 45-deg umbilical

azimuths).

Figure 8 plots the fatigue results for the bend stiffener section from the previously shown fatigue results found in Figure

7. Overall, the accounting for the mean wave drift produces a

reduced fatigue life in the section, and the umbilical sustains an

extreme amount of fatigue damage for all installation azimuths

without a bend stiffener.

Influence of Water Depth

Figure 9 shows the curvature time history of the node showing the peak curvature at the sea state of 8.25 m with a peak

period of 14.5 s for both the 50-m and 100-m water depth configurations. The red dashed line depicts the umbilicals minimum

bend radius of 2.64 m, and the umbilical configuration in the

100-m water depth shows minimal fatigue damage.

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FIGURE 9. CURVATURE TIME HISTORY AT NODEPRODUCING PEAK CURVATURE

FIGURE 10. MAXIMUM DAMAGE OVER EXPOSURE AT INDIVIDUAL ARC POINTS (WATER DEPTH OF 50 M)

Umbilical Configuration Sensitivity

The fatigue results of the umbilical configuration for the 50-

m water depth showed a fatigue life of 0.07 years in the 0-deg

azimuth. A sensitivity of varying the length of the buoyancy

section and the length of the top section of the umbilical was

performed. The sea state load case that contributed the most to

the overall damage was selected. Figure 10 shows the maximum

damage scaled with the associated exposure, as determined from

the sea states, 3.75 m to 8.75 m. The majority of the damage is

accumulated from the sea state of 8.25 m with a peak period of

14.5 s.

The case was then used to perform a sensitivity on the umbilical length and the buoyancy section length. Figure 11 shows

the sensitivity fatigue results with the combined section (buoyancy with topside umbilical) lengths. As shown in the figure,

reducing the length of the buoyancy section and topside section

from 13.7 m ft to 12.5 m reduced the fatigue damage for this case

from 1.60 to 0.71. This could potentially reduce the other cases

by 56%, improving the fatigue life of the umbilical.

FIGURE 11. DAMAGE SENSITIVITY OVER ASSOCIATED EXPOSURE FOR VARYING SECTION LENGTHS

CONCLUSIONS

The fatigue life for a dynamic power umbilical attached to

a two-body floating WEC device was analyzed, including the

influence of the mean drift force and moment, bend stiffener,

and water depth. WEC-Sim simulations were carried out using

WEC-Sim to obtain the dynamic motion of the device. These

motions and respective sea states were used to analyze the dynamic motions and fatigue of the connected power umbilical using OrcaFlex. The results show that the fatigue damage observed

is more significant in the 50-m water depth than the 100-m water depth. For the 100-m water depth umbilical configuration,

minimal fatigue damage for all line azimuths was observed once

a bend stiffener was incorporated. For the 50-m water depth

umbilical configuration, extensive fatigue damage was observed,

because of the larger curvature response of the umbilical. The

umbilical configurations departing at 90 deg off incoming waves

were found to have the highest fatigue life attributed to less extension or compression of the lazy wave (assuming the umbilical

cable does not trench and has adequate cladding to prevent wear).

However, additional bend stiffener/limiter features may be required to be incorporated into the buoyancy section and touchdown regions to minimize curvature-induced fatigue. It was also

found that incorporation of a bend stiffener at the connection of

the umbilical cable to the WEC is essential to limiting bending

strain in this region for the given water depths. Finally, a lazy

S arrangement tuned for the device response envelope and sitespecific water depth is key to increasing compliance to prevent

snap loading and reduce the resulting extreme bending fatigue in

the touchdown region.

For future work, a preliminary bend stiffener was determined for use in the analysis to estimate fatigue damage at the

connection point on the WEC. This bend stiffener was developed

using the recommendations of the bend stiffener design standard

for umbilicals. This could be further expanded upon to incorporate actual bend stiffener manufacturer data into the design. For

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this analysis, the WEC motions in the 100-m water depth were

very similar to the 50-m water depth motions. Depending on the

mooring system design, the 100-m water depth WEC motions

may see greater surge extremes that could potentially decrease

the fatigue life, increasing the fatigue damage caused by the decreased stiffness of the associated mooring system. Finally, the

same umbilical configuration was used for all azimuths analyzed.

A sensitivity was performed on the 0-deg azimuth, showing that

reducing the buoyancy section and the umbilical section may increase the fatigue life, decreasing the fatigue damage. This may

lead to different umbilical configurations, depending on line installation headings based on the incoming waves.

ACKNOWLEDGMENT

This work was authored [in part] by the National Renewable

Energy Laboratory, operated by Alliance for Sustainable Energy,

LLC, for the U.S. Department of Energy (DOE) under Contract

No. DE-AC36-08GO28308. Funding provided by the U.S. Department of Energy Office of Energy Efficiency and Renewable

Energy Water Power Technologies Office. The views expressed

in the article do not necessarily represent the views of the DOE

or the U.S. Government. The U.S. Government retains and the

publisher, by accepting the article for publication, acknowledges

that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published

form of this work, or allow others to do so, for U.S. Government

purposes.

REFERENCES

[1] British Standard, 2009. Petroleum and Natural Gas Industies Design and Operation of Subsea Production System

Part 5: Subsea Umbilicals, International Standard. Tech.

rep.

[2] WEC-Sim (Wave Energy Converter SIMulator).

[3] OrcaFlex, 2015. OrcaFlex Manual. Orcina Ltd., Daltongate

Ulverston Cumbria, UK.

[4] PacWave Test Site.

[5] Dallman, A. R., and Neary, V. S., 2014. Characterization

of U.S. Wave Energy Converter (WEC) Test Sites: A Catalogue of Met-Ocean Data. Tech. Rep. September, Sandia

National Laboratories, Albuquerque, NM.

[6] Yu, Y.-H., Lawson, M., Ruehl, K., and Michelen, C., 2014.

“Development and Demonstration of the WEC-Sim Wave

Energy Converter Simulation Tool”. In 2nd Marine Energy

Technology Symposium.

[7] Cummins, W., 1962. The Impulse Response Function

and Ship Motions. Tech. rep., David Taylor Model Dasin

(DTNSRDC).

[8] Lee, C., and Newman, J., 2015. WAMIT User Manual Version 7.1. Chestnut Hill, MA, USA.

[9] Hall, M., 2015. MoorDyn User’s Guide.

[10] Sodahl, N., and Ottesen, T., 2011. “Bend stiffener design

for umbilicals”. pp. 449–460.

[11] Murphy, M. C., 1981. “The engineering fatigue properties

of wrought copper”. Fatigue & Fracture of Engineering

Materials & Structures, 4(3), pp. 199–234.

This report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications. 7