Deterministic Fatigue Analysis

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Engineering & Construction Sector

DESIGN REFERENCE

OFFSHORE STRUCTURESDETERMINISTIC FATIGUE ANALYSIS

DR 361 Rev 0 L SEPTEMBER 1991

John Brown Engineers & Constructors Limited20 Eastbourne Terrace, London W2 6LE



DESIGN REFERENCE DR 361/0 L


CONTENTS

1. OBJECTIVE

2. DEFINITION

3. OUTLINE OF THE METHOD

4. COMPUTER MODEL4.1 STRUCTURAL MODEL4.2 TOP BRACING LEVEL4.3 PILE SLEEVES AND FOUNDATION

5. WAVE FORCE ANALYSIS5.1 WAVE FORCE COEFFICIENTS5.2 MARINE GROWTH5.3 WAVE THEORY5.4 WAVE FORCES AT ELEMENT LEVEL5.5 SURGE, TIDE, CURENT AND WATERDEPTH5.6 WAVE HEIGHT DISTRIBUTION5.7 ASSOCIATED PERIODS5.8 SELECTION OF WAVES FOR THE ANALYSIS5.9 SELECTION OF FATIGUE DESIGN WAVE FOR THE FOUNDATION

6. DYNAMIC AMPLIFICATION FACTORS6.1 CHOICE OF NATURAL PERIOD6.2 CHOICE OF DAMPING COEFFICIENT6.3 OBSERVATION ON NATURAL PERIODS6.4 THE PERIOD RANGE6.5 IGNORING DYNAMIC AMPLIFICATION

7. RELATED PROCEDURES

8. REFERENCES

FIGURESTABLES

APPENDIX A:HYDRODYNAMIC COEFFICIENTS FOR CONDUCTOR GUIDES

APPENDIX B: WAVE FORCE ANALYSIS - TWO COMPONENT REPRESENTATION





REV 0 ISSUED SEPTEMBER 1991

PREPARED BY: OFFSHORE STRUCTURES

APPROVED BY: ..........................K LOGENDRA,ASSOCIATE DIRECTOR,OFFSHORE STRUCTURES

AUTHORISED BY: ..........................H. THIRKELL,DIRECTOR OF ENGINEERING




OFFSHORE STRUCTURES PAGE 1 OF 14DETERMINISTIC FATIGUE ANALYSIS

1 OBJECTIVES

The two objectives of this Design Reference on the deterministic fatigue analysis are

- to capture current design practices as applied to recent John Brown projects

- to clarify certain elements in these practices

This is achieved by taking the Bruce deterministic fatigue analysis (Ref. 1) as a basis forthis Design Reference.

2 DEFINITION

Fatigue analyses are carried out to establish the adequacy of tubular joints and otherstructural details in jacket structures against wave loading.

The deterministic fatigue analysis is characterised by analysing the jacket for a series ofdeterministic waves thus taking full account of the non-linear part in the drag-fluid loading.

This analysis method is only able to address dynamics in an elementary fashion. Therefore,for jackets with natural periods greater than four seconds, a spectral analysis is essential.

3 OUTLINE OF THE METHOD

The deterministic fatigue analysis of a jacket structure is closely linked to a normal designwave jacket analysis. It repeats the same analysis for a series of waveheights andassociated periods from a number of directions.

An outline of the procedure is given in Fig.1. In principle it consists of two parts: part 1 isindependent of the local joint geometry and establishes the member end forces andmoments and their annual frequency of occurrence. It is also in this part that dynamicamplification will be addressed.

Part 2 is related to the local joint geometry. It requires the selection of appropriate stressconcentration factors (SCFs) and SN curves information on which has been collected inDR363.

The descriptions in Chapters 4,5 and 6 on modelling, wave force analysis and dynamicamplification should be self-explanatory. An exception has to be made for Section 5.7 onassociated periods; their selection may be Client specific and a particular warning is raisedfor the part of the curve representing the relationship between wave height and wave periodwhich is to be associated with dynamic amplification.

4 COMPUTER MODEL

The analysis will be performed on a 3D structural model which is based on the in-place





analysis model. The procedure adopted for the analysis is shown in Figure 1.

The computer model will have to address both the structural and the hydrodynamiccharacteristics of the platform.

4.1 STRUCTURAL MODEL

The structural model consists of the following elements:

a) Jacket, appurtenances and deckb) Pile Clustersc) Foundations

All structural members of the jacket will be included in the models and member sizes willbe based on uncorroded sections for stiffness analysis purposes only.

Non-structural members, such as risers and conductors, will be modelled as equivalenttubes for the evaluation of wave loads but are generally excluded from the stiffnessanalysis. It is good practice to model one or two platform conductors in detail for theevaluation of fatigue life of these components. Because of the distances betweenconductors the effect of shielding will be small and can in practice be ignored.

4.2 TOP-BRACING LEVELS

Specific attention should be given to the fatigue strength of the bracing level above thewater and the first bracing level below the water particularly for drilling platforms.

Nowadays the top bracing is often taken so high (i.e. 10m above MSL) to eliminate shipimpact on these members. As a consequnce the frequency of impact of these braces for afatigue analysis will also be small. On the other hand for older installation this level canwell be between 6-10 m above MSL and therefore this level will see regular wave loadingas follows:

- wave slamming (see DR365)- direct wave loading- buoyancy

The effects should be properly modelled in the fatigue analysis unless it can bedemonstrated by inspection and simplified analysis that fatigue at this level is of noconcern.

In order to examine the first plan level below MSL for its fatigue strength it isrecommended to make a rather detailed model of this bracing level (particularly of theconductor guide framing) so that the vertical loading and its effect on the structure will befully assessed.

4.3 PILE SLEEVES AND FOUNDATION





A pile cluster model, including sleeves and shear plates, will be included in the stiffnessmodel as a separate component using the substructuring technique in 'ASASH'.

The piled foundations will be represented in the fatigue analysis by an equivalent beamspring model at each pile location. The model will be developed for the centre of damagewave, which will be calculated using an S-Curve approach as explained in Section 5.9.

A short tubular representing the pile section properties will be included as well andbetween the top of packer can and scourline will facilitate the computation of pile fatiguedamage in the fatigue analysis.

5 WAVE FORCE ANALYSIS

The wave force analysis will be carried out using the ASASWAVE program.

5.1 WAVE FORCE COEFFICIENTS

The model used in the ASASWAVE load generation analysis will be adapted from themain structural stiffness model with diameters and/or CD and CM values adjusted to reflect

the waveload on the structure as explained below.

Various values of CD and CM have been used in the past but in the future the Fourth

Edition of the Guidance Notes will be adopted as follows:

CD = 0.6 for members without marine growth

CD = 0.7 for members with marine growth

CM = 2.0

Anodes can be taken into account by increasing CD by 5%.

For members supporting conductor guides CD and CM values can be calculated using the

method described in Appendix A.

5.2 MARINE GROWTH

To allow for the extra wave loading caused by the presence of marine growth on jacketmembers, conductors, risers, and caissons, their effective radii will be increased inaccordance with the Clients specification. The increase in Cd due to marine growth willhave been incorporated in the analysis if the force coefficients mentioned in Sect.5.1 aboveare used.

5.3 WAVE THEORY





Wave theories will be chosen in accordance with the criteria shown in Figure 2.

5.4 WAVE FORCES AT ELEMENT LEVEL

Forces will be calculated at a minimum of three points along each member and then appliedto the member.

The process is repeated for ten time-steps equally spaced at 36° phase angles. In this waywave loads are available for discrete time-steps as the wave passes through the structure.

For each wave of frequency w, the program scans the time history to locate the maximumand minimum for each force component and determines the amplitude (a) and phase angle(Ö) for an equivalent sinusoidal force which best fits the element loads. This sinusoidalforce is represented by a vector of real and imaginary components.

F(t) = aei(wt+Ö)

By this method the amplitude and phase of an individual applied force, displacement ormember stress can be retained more correctly than relating them to such globalcharacteristics as base shear (See Appendix B).

The real and imaginary components of force for all members for any one wave from anydirection are stored as two separate load cases which are then input to a stiffness analysis isASASH.

5.5 SURGE, TIDE, CURRENT AND WATERDEPTH

In line with the recommendation of the Fourth Edition of the Guidance Notes (Ref. 2) theeffects of surge, tide and current can be disregarded in a fatigue analysis.

The waterdepth for the fatigue analysis should be taken as mean sea level (MSL) which isthe mean between the high and the low astronomical tide (HAT and LAT).

5.6 WAVE HEIGHT DISTRIBUTION

The wave height distribution is to be provided by the Client. It is derived from the wavescatter diagram using a Rayleigh distribution of wave heights. By combining the scatterdiagram with a wind directionality table it is possible to derive a direction dependent waveheight distribution. An example is given in Fig. 3 which was used for Bruce.

5.7 ASSOCIATED PERIODS

In line with the common design wave approach it is good practice to assume waves ofconstant steepness for the individual fatigue waves. For dynamic structures (T> 35) it issometimes proposed to take a range of periods (Marshall) but the necessity of thisrefinement is questioned.





For the Bruce development BP adopted a different philosophy which is reflected in Fig. 3. It is noticeable that BP's assumption for wave heights between 3-4 seconds is an order ofmagnitude smaller than when applying constant wave steepness. This could result in anunderestimation of the amplitudes of the waves with a period in this range and thereforealso in the contribution of dynamics in the fatigue problem. This procedure should not beused in future projects.

5.8 SELECTION OF WAVES FOR THE ANLAYSIS

The basis of the deterministic fatigue analysis is to calculate the stress ranged for a selectednumber of wave heights. In order to achieve an acceptable degree of accuracy in theanalysis, wave heights should first be divided into 1m waveheight intervals. Subsequently,in order to optimise on computing, this analysis is further modified and will use as aminimum five waves from each direction, which will be representative of the whole waveheight range.

The five representative wave heights will be chosen to simulate five equal damageintervals. The relationship between the representative wave heights and damage isestablished by the following procedure.

a) First it is assumed that the stress range (S) is proportional to the waveheight (H)by the power 1.8 or

S:: H 1.8

This value has historically been established (probably by Shell). For lowerwaves the damage thus established can be either over or underestimated whenthe platform dimension become odd multiples of half the wave length. This willbe more pronounced for large jacket structures than for liftable jackets of a topdimension of the order of 30m.

The above relation between stress range and wave height ignores the effect ofdynamic amplification.

An independent study showed that for larger waves the power of 1.8 couldactually be greater than 2.0. Hence 1.8 could be a reasonable balance betweenover- and under-estimation.

b) The number of cycles to failure (N) is proportional to S-m where m is (thereciprocal of) the negative slope of the SN curve on a log-log scale (See Fig. 6)and S the stress range. A first and conservative assumption is to use m = 3. Therefore

N :: S-3 :: H-5.4





The kink in the SN curve at 107 cycles will result in a reduction of the effect ofthe smaller waves; this effect is incorporated in the ASAS suite.

c) Finally the damage (D) is proportional to

D :: n/N :: n.H5.4

where n is the number of occurrences of the waveheight H.

This is a sufficient condition to plot the S-curve as presented in Fig.4 for eachdirection provided a wave height table similar to Table 1 is available.

The S-curve is divided into at least five equal damage intervals of 20% each withcorresponding wave heights in the centre of each interval and the corresponding stresses forthese wave height is established. In addition for the zero wave height the stress are zero. Subsequently the stress ranges are calculated for each wave height by linear interpolationbetween the appropriate stress ranges.

It is noted that the accuracy of the upper tail of the S-curve (to be associated with largewave heights) in the fatigue damage of the tubular joints is not to significant. On the otherhand the effects of the lower tail of the S-curve (to be associated with small wave heights)will be exacerbated due to dynamic amplification. Therefore it is justified to improve therepresentation of this lower tail by increasing the number of points in that region.

5.9 SELECTION OF FATIGUE DESIGN WAVES FOR THE FOUNDATION

The foundation behaviour (particularly in the lateral direction) is also non-linear. It istherefore recommended to retain this non-linear behaviour and calculate the jacket andfoundation response for each of the wave heights from the S curve as discussed in Section5.8.

Alternatively the piled foundation can be represented by an equivalent beam spring modelat each pile location using the properties of the soil for the wave height in the centre of theS-curve.

The advantage of linearisation should be weighed against a small loss in accuracy in theanswer. In the end it will be the convenience of the user which will decide between the twooptions.

6 DYNAMIC AMPLIFICATION FACTORS

The dynamic amplification factor (DAF) will be calculated for selected waves from alldirections using the following formula and applied to stresses due to wave loads in thefatigue analysis to allow for dynamic effects of waves on the structure.

DAF = 1 / √ [ {1 - (fw/fn)²}² + {2 ksi fw/fn}²]





where

fn = fundamental frequency of the jacket

fw = wave frequency

ksi = damping ratio (inclusive of hydrodynamic andstructural damping)

6.1 CHOICE OF NATURAL PERIOD

The DAF to be used for the fatigue analysis is calculated for a one degree of freedomsystem. Since the natural period will be different for the two axes of the platform it isconservative to take the larger natural period as a basis for calculating the DAF.

6.2 CHOICE OF DAMPING

The value of damping is critical. For high frequency, low amplitude waves the forces onthe jacket are small but, for small damping values, the DAF can be quite large. Therecommended damping in line with current North Sea practices is 2%. Data fromdeepwater platforms in the Gulf of Mexico indicates a value of 4% but this may well be aconsequence of the soft soil in the Gulf.

6.3 OBSERVATIONS ON NATURAL PERIODS

Fatigue analysis will be carried out based on calculated natural periods. Fieldmeasurements on natural periods of platform highlight that measured periods will ingeneral be smaller than calculated periods resulting in a possible other source ofconservatism in a dynamic fatigue analysis.

6.4 THE PERIOD RANGE

It is essential for a simplified (semi-dynamic) deterministic fatigue analysis to divide thefrequency range near the natural period in a number of intervals and use a mean frequencyfor each interval. One of these frequencies should preferably coincide with the naturalfrequency of the platform. Since the DAF will decline sharply for small deviations fromthe natural period a practical semi-static fatigue analysis will give lower fatigue lives thanthe more comprehensive analysis using very small period increments. This rapid decline isillustrated by the following example:

for Tn = 4s and a damping of 2% the following values for the DAF are found:

T = 3 s DAF = 2.33.5 s 4.24 s 25.04.5 s 3.75 s 1.8





Therefore a closed form integration in the vicinity of the natural frequency is worthconsidering.

6.5 IGNORING DYNAMIC AMPLIFICATION

In accordance with the Guidance Notes (Ref.3 Sect. 21.2.10d) dynamic amplification in afatigue analysis should only be considered for structures with a natural period greater than 3seconds.

7 RELATED PROCEDURES

DR 362 Spectral Fatigue Analysis

DR 363 Stress Concentration Factors and SN Curves

DR 364 Vortex Induced Vibrations

DR 365 Wave slamming

8 REFERENCES

a) BP Bruce Jacket Design. Preamble to Design Brief for Deterministic fatigueanalysis BRU2-J00-70-SJ-1107, 1990.

b) Dynamic of Marine Structures Report UR8, Second edition Atkins Research &Development, 1978.

c) Department of Energy, Offshore Installations : Guidance on Design Constructionand Certification, 4th Edition, 1990.

d) Analysis Methods and Inspection Procedures for Single Sided Closure Welds inOffshore Structures. E Hesmati, R. Guy, I. Livett, G. Lewis OTC 5351, Houston1986.

e) UEG Report UR33, Design of Tubular joints for offshore structures, 1985.





STANDARDS\DR\DR361\FIG-1.WPG





FIGURE 2REGULAR WAVE THEORY SELECTION DIAGRAM (LOG SCALES)






FIGURE 3PROBABLE PERIOD VS. WAVE HEIGHT






FIGURE 4TYPICAL DAMAGE VS WAVE HEIGHT (S CURVE)






TABLE 1NUMBER OF INDIVIDUAL WAVES BY DIRECTION (BRUCE PUQ)






TABLE 2WAVE DISTRIBUTION BY HEIGHT FOR A 30 YEAR PERIOD

(GANNET)




DESIGN REFERENCE DR 361/0 LAPPENDIX A


APPENDIX AHYDRODYNAMIC COEFFICIENTS FOR CONDUCTOR GUIDES



DESIGN REFERENCE DR 361/0 LAPPENDIX 1


APPENDIX AHYDRODYNAMIC COEFFICIENTS FOR CONDUCTOR GUIDES

In order to allow for wave/current loading on non-modelled conductor/tieback guides, thefollowing adjustments to the model are made:

9 AXIAL/INPLANE LOADING OF SUPPORTING MEMBERS

Conductors/tiebacks are segmented and member sizes are increased in diameter toencompass the guides and associated plates at each plan level and guide location.

Appropriate CD and CM values will be used in conjunction with the increased diameter.

10 OUT OF PLANE LOADING ON SUPPORTING MEMBERS

CD and CM values for out of plane loading are calculated based on the following

equations:

CDe = ( CDtube.D.L + CDplate.a.b.N ) / (D.L)

CMe = ( Cmtube.(ð D²/4).L + Cmplate.Vplate.N )/(ð.L.D²/4)

where:

CDe, CMe = equivalent hydrodynamic coefficients

CDtube = 0.6 or 0.7 as appropriate (see Sect.5.1)

CDplate = 2.0

D, L = diameter and length of the supporting membera, b = approx. rectangular plate dimensions (a>b)N = number of supported guides on the memberCmplate = refer to following table.

Cmtube = added mass coefficients for tubes (Cm=2.0)

Vplate = ð/4 a b²



DESIGN REFERENCE DR 361/0 LAPPENDIX 1


TABLE A1: Added Mass Coefficients for rectangular flat plates

(Ref: DNV - APPENDIX B - 1982)

a/b Cmplate Vplate

1.01.52.03.0∞

0.580.690.760.831.00

ð a.b2/4



DESIGN REFERENCE DR 361/0 LAPPENDIX B


APPENDIX BWAVE FORCE ANALYSIS - TWO COMPONENT REPRESENTATION





APPENDIX BWAVE FORCE ANALYSIS - TWO COMPONENT REPRESENTATION

11 HARMONIC REPRESENTATION

Consider a long crested periodic wave acting on an offshore jacket as shown in Figure B1. The state of the jacket at any time may be described by any of a number of sets of physicalvariables:

a) The displacements and rotations (xi) associated with each degree of freedom i of

the computer model.

b) The member end loads or nominal stresses (fi) associated with each member

endpoint i.

c) The parameters defining environmental (wave) load distributions along eachmember (ái).

In this context as we are only considering the oscillatory periodic component of loadingthen static loads may be disregarded for the purposes of this discussion. It must be borne inmind that the analysis tools available assume a linear relationship between loads anddisplacements and that all physical variables considered have a periodic behaviour withtime and a period which is equal for all variables and equal to the period of the wave. Thisis also true for members in the splash zone.

A time history for a typical physical variable is illustrated in Figure B2. This time historyas obtained by "stepping the wave through the structure" in ASASWAVE, it is then fittedto a sine curve as shown by minimising the sum of the squares of the deviation from aharmonic function (sine or cosine). The functional representation for each physical variablewill then be of the form:-

xi(t) _ Xi(t) = Xi,osc cos (wt +Öi) + Xi,mean

where Xi(t) = the harmonic approximation to xi(t).

Xi,osc = the amplitude of the oscillation.

Öi = the phase angle associated with the variable xi with respect to a

reference position in time

Xi,mean = the mean value of xi(t); this mean value reflects the non-linearity

in the loading and is neglected in the analysis performed usingASASWAVE.





w = the angular frequency corresponding to the period T of the waveloading and is given by: w = 2ð / T

Hence Xi(t) = Xi,osc cos(2ðt/T + Öi)

12 COMPLEX REPRESENTATION

This expression for Xi can be expressed in its real and imaginary part by calculating the

phase angle Öi with respect to its chosen time-frame of reference or:-

Xi(t) = Xi,osc exp{2ðt/T +Öi} =

= Xi,osc cos(2ðt/T) cos(Öi) + + Xi,osc sin(2ðt/T) sin(Öi)

Using another notation, the real and imaginary part of the response results Xi,osc are

respectively:-

Re{Xi(t)} = X i,osc cos(Öi)

Im{X i(t)} = X i,osc sin(Öi)

and vice versa:-

Xi,osc = √[Re{Xi(t)}2 + Im{Xi(t)}

2]

Öi = atan[Im{Xi(t)} / Re{Xi(t)}]

Similar expressions to those derived in Appendix B1 and B2 hold for the memeber endloads and nominal stresses (fi) and the parameters defining environmental wave load

distributions (ái).

Deterministic Fatigue Analysis

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