1

Fatigue Analyses in Fixed Offshore Jackets using Spectral Method

Peyman. Moazen1, Mohammad Javad Ketabdari

2

1-Hormozgan University, Department of Civil Engineering

2-AmirKabir University of Technology, Faculty of Marine Technology

Abstract

Fatigue, is defined as structural failure under alternative load cycles in a long period

of time. This experience is important when cyclic loads exert to the structures. In this

study a model was developed to estimate fatigue life under irregular waves for fixed

offshore jackets using S-N curves and Palmergen-Miner method. In this study valid

codes and most authentic international regulations, such as ABS and API codes of

practices were employed. The inputs to the model are wind velocity, wave spectral

density and structural details including S-N curves, type of connections and welding

situation in different joints. The model can estimate the fatigue life of the structure

based on the worst environmental condition. A case study carried out for a typical

jacket in Persian Gulf. A dynamic analysis using SAP2000 was undertaken with an

exciting force extracted from a proposed spectrum for sea state of the study area. The

results showed that the spectral analysis of fatigue life is more accurate than time

domain analysis using zero- up crossing technique. The result of the model also

shows promise for optimum design of steel offshore jacket type platforms choosing

proper type of connections and high quality welding in joints.

Keywords: Fatigue life, Spectral analysis, Jacket type platforms, Palmergen-Miner

rule, welded connections

1 Introduction

Wave is the most important phenomenon in the sea environment inducing

considerable forces to marine structures. In fact this is the main source of structural

cyclic stresses leading to fatigue fracture. Therefore, estimating fatigue life for such

structures, have a particular importance for marine engineers. To estimate the fatigue

life it is required to determine several transfer functions. First one is a transform from

wave profile to force in time or frequency domain. Second one is a transform of

dynamic forces to stresses in structural elements. Finally a transform is required to

give fatigue life using concentrated stresses.

2 Wave loading

To determine the fatigue life in a marine structure it is required to estimate the wave

loading to the structure. Therefore providing realistic information about the waves

properties in the desired location is the first stage in this study. Wave spectrum is a

useful tool to simulate the free surface profile for seas and oceans. Different research

groups tried to propose wave spectrums for different seas based on long term field

studies using wave buoys. some of these standard wave spectra are JONSWAP,

Pierson Moskowits and Bretshnieder Spectra. For Persian Gulf in south part of Iran

the available field measurements are not adequate to be able to propose an original

wave spectrum. However a few researchers tried to propose a modified spectrum to

above mentioned spectra using limited available data. A modified model to

1 M.Sc. Graduated in Marine structures

2 Assistant Professor

2

JONSWAP spectrum was proposed for north part of Persian Gulf [1]. This study

suggests the following relation for Persian gulf :

)2

)(exp{

454222

2

).)(4

5exp()2(.)(

f

ff

mf

ffgfE

λγπα

−−

−−− −= (1)

Where

����� 2.68 ,� =mf 0.2 , �=0.07 ( for ≤f 0.2) , �=0.09 ( for �f 0.2)

Using this spectrum the wave amplitude can some how be found using inverse Fourier

transform. This leads to a series of monochromatic waves with different amplitudes

and frequencies. In this study using the inverse Fourier transform on relevant

spectrum a series of monochromatic waves with different periods and amplitudes was

generated. Then superposition of these individual waves each of which has an

amplitude consistent with the energy in the target spectrum and a random phase Φ as

follows:

η ω( ) cos( )t c k x tn n n n

n

N

= − +=

� Φ1

(2)

where: c S f dfn n= 2 ( ) and ω πn nf= 2 .

The next stage is transform of free surface profile to force on members of the jacket

platforms. This can be performed using Morison Equatin as:

22

2

..

4

...u

DC

t

uDCF dm ρπρ

+∂

∂= (3)

Where D is the member diameter, � is the sea water density, u t∂ ∂ is the horizontal

acceleration of the water particles and Cm�and Cd are the inertia coefficient and drag

coefficient respectively. Different Standards suggested some values for these

coefficients [2].

The next step is calculating the stress concentration in particular elements of the

jacket due to wave attach. Finally considering Palmergen-miner rule and S-N curves,

we are able to calculating the fatigue life for members or connections of the jacket

leading to a fatigue life for whole structure. In this project ABS Standard has been

widely used to calculate fatigue life in structural connections [3]. The out put are

shown by plotting some curves which can display the variation of fatigue with the

kind of connection and welding details. Curve 1 shows the effect of connection class

on fatigue life. This curve can be used as a guide line to select proper connections for

particular parts of the jacket based on the fatigue analysis results. Some tests

performed on the effect of water depth on fatigue life of the jacket. The results are

presented in Curve 2. This curve shows that an increase in water depth around the

marine structure, resulted to an increase in stress leading to a decrease in fatigue.

Similarly, corrosion condition is another parameter which has a significant effect on

the fatigue life and will be considered in calculations. Stress concentration factors 3

and its method of calculation in a welded profile is an important parameter in this

process [4]. Existence of any kind of defect in a welded profile, categorize it in a

lower level of connection classification. This evaluation were set up in ABS standard

but could be developed in related studies. The fatigue life for a sample Jacket type

platform in Forouzan region of Persian gulf was studied. This Jacket is shown in fig.

1. To get a better results the height and the number of the stories of the structure were

3 SCF

3

increased based on assumptions that the water depth is 80m and dimensions of deck

were 10x20 m2. Using the available hydrodynamic and structural softwares. The

wave loading is dynamic (see fig. 2) and therefore stresses varies in the structure as

the wave troughs and crests pass the jacket elements. Curve 4 shows the time histories

of stress in a typical jacket element. The most common shape for marine structures

members is pipe element.. The connection of the legs to the sea bed is assumed to be

rigid 2 meters deep under the sea bed. All the bracings have a pinned connection to

the main legs. Therefore they don’t induce considerable moment in the jacket leading

to no significant flexural moment in these elements [5]. The output of stress analyzer

software then fed to a developed program in MATLAB to estimate the fatigue. To do

this several S-N cures in different situation based on ABS standard was introduced to

the developed model. In the tubular welded connections, because of the local flexural

moment in the pipe wall, the geometric stress is raised up. This increscent usually

occurs due to fabrication errors , edge deflection in joints and inconsistency between

ring stiffness of pipes [6]. SCF can be determine using table 1 for the worst condition

(larger value for this parameter) [2]. In the marine structures, deterioration starts with

initiation of a crack in a defect or unsymmetrical connection leading to stress

concentration. These cracks will propagation in the elastic materials by the local

plastic strains. Concept of damage accumulation is widely used in assessment of

fatigue and fracture mechanics methods.

3 Fatigue assessment

Fatigue assessment1 denotes a process where the fatigue demand on a structural

element or a connection detail is established and compared to the predicted fatigue

strength of that element. One way to categorize a fatigue assessment technique is to

say that it is based on a direct calculation of fatigue damage or expected fatigue life.

Three important methods of assessment are called the Simplified Method, the Spectral

Method and the Deterministic Method. Alternatively, an indirect fatigue assessment

may be performed by the Simplified Method, based on limiting a predicted

(probabilistically defined) stress range to be at or below a permissible stress range.

There are also assessment techniques that are based on time domain analysis methods

that are especially useful for structural systems that are subjected to non-linear

structural response or non-linear loading. Fatigue Demand is stated in terms of stress

ranges that are produced by the variable loads imposed on the structure. (A stress

range is the absolute sum of stress amplitudes on either side of a ‘steady state’ mean

stress). The term ‘variable load’ may be used in preference to ‘cyclic load’ since the

latter may be taken to imply a uniform frequency content of the load, which may not

be the case. The fatigue inducing loads are the results of actions producing variable

load effects. Most commonly, for ocean based structures, the most influential actions

producing the higher magnitude variable loadings are waves and combinations of

waves with other variable actions such as ocean current, and equipment induced

variable loads. Since the loads being considered are variable with time, it is possible

that they could excite dynamic response in the structure; this in turn will amplify the

acting fatigue inducing stresses. The determination of fatigue demand should be

accomplished by an appropriate structural analysis. The level of sophistication

required in the analysis in terms of structural modeling and boundary conditions (such

as. soil-structure interaction or mooring system restraint), and the considered loads

and load combinations are typically specified in the individual Rules and Guides for

Classification of particular types of Mobile Units and offshore structures. When

considering fatigue inducing stress ranges, one also needs to consider the possible

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influences of stress concentrations and how these modify the predicted values of the

acting stress (see fig. 3). The model used to analyze the structure may not adequately

account for local conditions that will modify the stress range near the location of the

structural detail subject to the fatigue assessment. In practice this issue is dealt with by

modifying the results of the stress analysis by the application of a stress concentration

factor. The selection of an appropriate ‘geometric’ SCF may be obtained from

standard references, or by the performance of Finite Element Analysis that will

explicitly compute the geometric SCF [7]. Two often mentioned examples of

geometric SCFs are a circular hole in a flat plate structure, which nominally has the

effect of introducing an SCF of 3.0 at the location on the circle where the direction of

acting longitudinal membrane stress is tangent to the circular hole. The other example

is the case of a transverse ring stiffener on a tubular member where the SCF to be

applied to the tube’s axial stress can be less than 1.0.

4 Conclusions

Whatever will differs this study from the other is using the spectral analyze instead of

the usual fatigue assessment. In statistical analysis of fatigue just using the minimum

and maximum of the design wave in an irregular wave the fatigue life is estimated.

Hence this metod is not accurate enough in fatigue assessments and the theorem of

reliability of fatigue surveying is often proposed [8]. This method is not able to

generate irregular waves through out an inverse process, whereas all the waves with

their own height and period are participant in creating cyclic stress in a structural

element. As the basic rules in fatigue assessment, the small stresses which cause the

tiny crack or damage in an element are added together making the final deterioration

in an structure , and this is the Palmergen-Miner rule which is directly used in this

study instead of any secondary relation which are suggested in the regulations or

similar papers.

As a conclusion, we may say that adopting the above process to estimate fatigue life

of a marine structure is accurate enough to be used in engineering projects of larger

scale and real modules of jacket structures.

References

[1] Shafeifar, M., Hamedi, A., (2002): "A spectral model for north part of Percian

Gulf using available data", Icopmas 2002,

[2] API "Recommended Practice 2A-WSD ( RP 2A-WSD )", Recommended Practice

for planning , Desigining and Constructing Fixed, Offshore Platforms-Working

Stress Design, 21st edition December 2000

[3] ABS, "Guide for the Fatigue Assessment of Offshore Structures", April 2003,

American Bureau of Shiping , Incorporated by Act of Legislature of the State of New

York 1862.

[4] Martinsson.J., (2004): Fatigue Assessment of Complex Welded Steel

Structure, Division of Lightweight Structures, Department Aeronautical and

Vehicle Engineering, Royal Institute of Technology, SE-100 44 Stockholm.

[5] Dal, K., (1997): "Innovative Tubular Connection", Department of Civil

Engineering, Monash University, Melbourne, 7th

international offshore & Polar

Engineering conference, Honolulu,USA,1997.

5

[6] Jang C. D., Song, H.C. & Jo, Y.C., (2004): "Fatigue Life Assessment of Fillet

Welded Joint Considering Stress Concentration", Seoul National University, Korea,

Proceedings of OMAE 2004

23rd International Conference on Offshore Mechanics and Arctic Engineering, June

20-25, 2004, Vancouver, British Columbia, Canada.

[7]-Halfpenny, A., (1999): "A Frequency domain approach for fatigue life estimation

from Finite Element Analyses", nCode International Ltd., Sheffield UK, International

Conference on Damage Assessment of Structures (DAMAS 99) Dublin.

[8] Assakkaf, I.A. & Ayyub, B. M., (2004): "Reliability-Based Design for Fatigue

of Marine Structure"

University of Maryland , College Park, Proceedings of OMAE 2004, 23rd

International Conference on Offshore Mechanics and Arctic Engineering June 20-25,

2004, Vancouver, British Columbia, Canada.

Table 1 Estimation of Stress Concentration Factor (SCF)

Comments��Equation��Status��Safety

Factor��

1

31

T

eSCF +=

Tube-A High�� T: member thickness

21 TT ≤��

e: Distance between midline

Tube 1 to Tube 2

�����

�

�

�����

�

�

��

���

+

+=5.1

1

21

1

161

T

TT

eSCF

��

Tube-B��Low��

6

7