Deterministic Fatigue Analysis

Engineering & Construction Sector

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OFFSHORE STRUCTURES DETERMINISTIC FATIGUE ANALYSIS DR 361

Rev 0 L

SEPTEMBER 1991

John Brown Engineers & Constructors Limited 20 Eastbourne Terrace, London W2 6LE


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OFFSHORE STRUCTURES DETERMINISTIC FATIGUE ANALYSIS

CONTENTS

1.

OBJECTIVE

2.

DEFINITION

3.

OUTLINE OF THE METHOD

4. 4.1 4.2 4.3

COMPUTER MODEL STRUCTURAL MODEL TOP BRACING LEVEL PILE SLEEVES AND FOUNDATION

5. 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9

WAVE FORCE ANALYSIS WAVE FORCE COEFFICIENTS MARINE GROWTH WAVE THEORY WAVE FORCES AT ELEMENT LEVEL SURGE, TIDE, CURENT AND WATERDEPTH WAVE HEIGHT DISTRIBUTION ASSOCIATED PERIODS SELECTION OF WAVES FOR THE ANALYSIS SEL SELECTI CTION OF FAT FATIGUE GUE DESI DESIGN GN WAV WAVE FOR THE FOU FOUNDA NDATION TION

6. 6.1 6.2 6.3 6.4 6.5

DYNAMIC AMPLIFICATION FACTORS CHOICE OF NATURAL PERIOD CHOICE OF DAMPING COEFFICIENT OBSERVATION ON NATURAL PERIODS THE PERIOD RANGE IGNORING DYNAMIC AMPLIFICATION

7.

RELATED PROCEDURES

8.

REFERENCES

FIGURES TABLES APPENDIX A: HYDRODYNAMIC COEFFICIENTS FOR CONDUCTOR GUIDES APPENDIX B: WAVE FORCE ANALYSIS - TWO COMPONENT REPRESENTATION


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REV 0

ISSUED

PREPARED BY:

OFFSHORE STRUCTURES

APPROVED BY:

.......................... K LOGENDRA, ASSOCIATE DIRECTOR, OFFSHORE STRUCTURES

AUTHORISED BY:

.......................... H. THIRKELL, DIRECTOR OF ENGINEERING

SEPTEMBER 1991


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1

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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 for this Design Reference. 2

DEFINITION

Fatigue analyses are carried out to establish the adequacy of tubular joints and other structural details in jacket structures against wave loading. The deterministic fatigue analysis is characterised by analysing the jacket for a series of deterministic 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 design wave jacket analysis. It repeats the same analysis for a series of waveheights and associated 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 is independent of the local joint geometry and establishes the member end forces and moments and their annual frequency of occurrence. It is also in this part that dynamic amplification will be addressed. Part 2 is related to the local joint geometry. It requires the selection of appropriate stress concentration factors (SCFs) and SN curves information on which has been collected in DR363. The descriptions in Chapters 4,5 and 6 on modelling, wave force analysis and dynamic amplification should be self-explanatory. An exception has to be made for Section 5.7 on associated periods; their selection may be Client specific and a particular warning is raised for the part of the curve representing the relationship between wave height and wave period which 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


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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 hydrodynamic characteristics of the platform. 4.1

STRUCTURAL MODEL The structural model consists of the following elements: a) b) c)

Jacket, appurtenances and deck Pile Clusters Foundations

All structural members of the jacket will be included in the models and member sizes will be based on uncorroded sections for stiffness analysis purposes only. Non-structural members, such as risers and conductors, will be modelled as equivalent tubes for the evaluation of wave loads but are generally excluded from the stiffness analysis. It is good practice to model one or two platform conductors in detail for the evaluation of fatigue life of these components. Because of the distances between conductors 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 the water 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 ship impact on these members. As a consequnce the frequency of impact of these braces for a fatigue analysis will also be small. On the other hand for older installation this level can well be between 6-10 m above MSL and therefore this level will see regular wave loading as follows: -

wave slamming (see DR365) direct wave loading buoyancy

The effects should be properly modelled in the fatigue analysis unless it can be demonstrated by inspection and simplified analysis that fatigue at this level is of no concern. In order to examine the first plan level below MSL for its fatigue strength it is recommended to make a rather detailed model of this bracing level (particularly of the conductor guide framing) so that the vertical loading and its effect on the structure will be fully assessed. 4.3

PILE SLEEVES AND FOUNDATION


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A pile cluster model, including sleeves and shear plates, will be included in the stiffness model as a separate component using the substructuring technique in 'ASASH'. The piled foundations will be represented in the fatigue analysis by an equivalent beam spring model at each pile location. The model will be developed for the centre of damage wave, 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 and between the top of packer can and scourline will facilitate the computation of pile fatigue damage 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 the main structural stiffness model with diameters and/or C and C values adjusted to reflect D M the waveload on the structure as explained below. Various values of C and C have been used in the past but in the future the Fourth D M Edition of the Guidance Notes will be adopted as follows: C = 0.6 for members without marine growth D C = 0.7 for members with marine growth D C = 2.0 M Anodes can be taken into account by increasing C by 5%. D For members supporting conductor guides C and C values can be calculated using the D M method described in Appendix A.

5.2

MARINE GROWTH To allow for the extra wave loading caused by the presence of marine growth on jacket members, conductors, risers, and caissons, their effective radii will be increased in accordance with the Clients specification. The increase in Cd due to marine growth will have been incorporated in the analysis if the force coefficients mentioned in Sect.5.1 above are used.

5.3

WAVE THEORY


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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 applied to the member. The process is repeated for ten time-steps equally spaced at 36 ° phase angles. In this way wave 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 maximum and 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 sinusoidal force is represented by a vector of real and imaginary components. i(wt+Ö) F(t) = ae By this method the amplitude and phase of an individual applied force, displacement or member stress can be retained more correctly than relating them to such global characteristics as base shear (See Appendix B). The real and imaginary components of force for all members for any one wave from any direction are stored as two separate load cases which are then input to a stiffness analysis is ASASH.

5.5

SURGE, TIDE, CURRENT AND WATERDEPTH In line with the recommendation of the Fourth Edition of the Guidance Notes (Ref. 2) the effects 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 is the 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 wave scatter diagram using a Rayleigh distribution of wave heights. By combining the scatter diagram with a wind directionality table it is possible to derive a direction dependent wave height 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 of constant steepness for the individual fatigue waves. For dynamic structures (T> 35) it is sometimes proposed to take a range of periods (Marshall) but the necessity of this refinement is questioned.


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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 of magnitude smaller than when applying constant wave steepness. This could result in an underestimation of the amplitudes of the waves with a period in this range and therefore also in the contribution of dynamics in the fatigue problem. This procedure should not be used 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 selected number of wave heights. In order to achieve an acceptable degree of accuracy in the analysis, 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 a minimum five waves from each direction, which will be representative of the whole wave height range. The five representative wave heights will be chosen to simulate five equal damage intervals. The relationship between the representative wave heights and damage is established 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 lower waves the damage thus established can be either over or underestimated when the platform dimension become odd multiples of half the wave length. This will be more pronounced for large jacket structures than for liftable jackets of a top dimension of the order of 30m. The above relation between stress range and wave height ignores the effect of dynamic amplification. An independent study showed that for larger waves the power of 1.8 could actually be greater than 2.0. Hence 1.8 could be a reasonable balance between over- and under-estimation. b)

-m The number of cycles to failure (N) is proportional to S where m is (the reciprocal 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 -3 -5.4 N :: S :: H


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7 The kink in the SN curve at 10 cycles will result in a reduction of the effect of the smaller waves; this effect is incorporated in the ASAS suite. c)

Finally the damage (D) is proportional to 5.4 D :: n/N :: n.H 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 each direction 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 with corresponding wave heights in the centre of each interval and the corresponding stresses for these 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 interpolation between the appropriate stress ranges. It is noted that the accuracy of the upper tail of the S-curve (to be associated with large wave heights) in the fatigue damage of the tubular joints is not to significant. On the other hand 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 the representation 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 is therefore recommended to retain this non-linear behaviour and calculate the jacket and foundation response for each of the wave heights from the S curve as discussed in Section 5.8. Alternatively the piled foundation can be represented by an equivalent beam spring model at each pile location using the properties of the soil for the wave height in the centre of the S-curve. The advantage of linearisation should be weighed against a small loss in accuracy in the answer. In the end it will be the convenience of the user which will decide between the two options.

6

DYNAMIC AMPLIFICATION FACTORS

The dynamic amplification factor (DAF) will be calculated for selected waves from all directions using the following formula and applied to stresses due to wave loads in the fatigue analysis to allow for dynamic effects of waves on the structure. DAF = 1 / √ [ {1 - (f /f )²}² + {2 ksi f /f }²] w n w n


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where f = fundamental frequency of the jacket n f = wave frequency w ksi = damping ratio (inclusive of hydrodynamic and structural damping) 6.1

CHOICE OF NATURAL PERIOD The DAF to be used for the fatigue analysis is calculated for a one degree of freedom system. Since the natural period will be different for the two axes of the platform it is conservative 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 on the jacket are small but, for small damping values, the DAF can be quite large. The recommended damping in line with current North Sea practices is 2%. Data from deepwater platforms in the Gulf of Mexico indicates a value of 4% but this may well be a consequence of the soft soil in the Gulf.

6.3

OBSERVATIONS ON NATURAL PERIODS Fatigue analysis will be carried out based on calculated natural periods. Field measurements on natural periods of platform highlight that measured periods will in general be smaller than calculated periods resulting in a possible other source of conservatism in a dynamic fatigue analysis.

6.4

THE PERIOD RANGE It is essential for a simplified (semi-dynamic) deterministic fatigue analysis to divide the frequency range near the natural period in a number of intervals and use a mean frequency for each interval. One of these frequencies should preferably coincide with the natural frequency of the platform. Since the DAF will decline sharply for small deviations from the natural period a practical semi-static fatigue analysis will give lower fatigue lives than the more comprehensive analysis using very small period increments. This rapid decline is illustrated by the following example: for T = 4s and a damping of 2% the following values for the DAF are found: n T=

3 3.5 4 4.5 5

s s s s s

DAF =

2.3 4.2 25.0 3.7 1.8


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Therefore a closed form integration in the vicinity of the natural frequency is worth considering. 6.5

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

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 fatigue analysis 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 Construction and Certification, 4th Edition, 1990.

d)

Analysis Methods and Inspection Procedures for Single Sided Closure Welds in Offshore Structures. E Hesmati, R. Guy, I. Livett, G. Lewis OTC 5351, Houston 1986.

e)

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


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FIGURE 2 REGULAR WAVE THEORY SELECTION DIAGRAM (LOG SCALES)



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FIGURE 3 PROBABLE PERIOD VS. WAVE HEIGHT


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FIGURE 4 TYPICAL DAMAGE VS WAVE HEIGHT (S CURVE)


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



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TABLE 2 WAVE DISTRIBUTION BY HEIGHT FOR A 30 YEAR PERIOD (GANNET)



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APPENDIX A HYDRODYNAMIC COEFFICIENTS FOR CONDUCTOR GUIDES

DR 361/0 L APPENDIX A


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APPENDIX A HYDRODYNAMIC COEFFICIENTS FOR CONDUCTOR GUIDES

In order to allow for wave/current loading on non-modelled conductor/tieback guides, the following adjustments to the model are made: 9

AXIAL/INPLANE LOADING OF SUPPORTING MEMBERS

Conductors/tiebacks are segmented and member sizes are increased in diameter to encompass the guides and associated plates at each plan level and guide location. Appropriate C and C values will be used in conjunction with the increased diameter. D M 10

OUT OF PLANE LOADING ON SUPPORTING MEMBERS

C and C values for out of plane loading are calculated based on the following D M equations: C = ( C .D.L + C .a.b.N ) / (D.L) De Dtube Dplate C = ( Cm .(ð D²/4).L + Cm .V .N )/(ð.L.D²/4) Me tube plate plate where: C ,C De Me C Dtube C Dplate D, L a, b N Cm plate Cm tube V plate

= equivalent hydrodynamic coefficients = 0.6 or 0.7 as appropriate (see Sect.5.1) = 2.0 = diameter and length of the supporting member = approx. rectangular plate dimensions (a>b) = number of supported guides on the member = refer to following table. = added mass coefficients for tubes (C =2.0) m = ð /4 a b²


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TABLE A1: Added Mass Coefficients for rectangular flat plates (Ref: DNV - APPENDIX B - 1982)

a/b

Cmplate

1.0 1.5 2.0 3.0 ∞

0.58 0.69 0.76 0.83 1.00

Vplate

ð a.b2 /4


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DR 361/0 L APPENDIX B


APPENDIX B WAVE FORCE ANALYSIS - TWO COMPONENT REPRESENTATION


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APPENDIX B WAVE 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 physical variables: a)

The displacements and rotations (x ) associated with each degree of freedom i of i the computer model.

b)

The member end loads or nominal stresses (f ) associated with each member i endpoint i.

c)

The parameters defining environmental (wave) load distributions along each member (á ). i

In this context as we are only considering the oscillatory periodic component of loading then static loads may be disregarded for the purposes of this discussion. It must be borne in mind that the analysis tools available assume a linear relationship between loads and displacements and that all physical variables considered have a periodic behaviour with time and a period which is equal for all variables and equal to the period of the wave. This is also true for members in the splash zone. A time history for a typical physical variable is illustrated in Figure B2. This time history as obtained by "stepping the wave through the structure" in ASASWAVE, it is then fitted to a sine curve as shown by minimising the sum of the squares of the deviation from a harmonic function (sine or cosine). The functional representation for each physical variable will then be of the form:x (t) _ X (t) i i

=

X cos (wt +Ö ) + X i,osc i i,mean

where

X (t) i

=

the harmonic approximation to x (t). i

X i,osc

=

the amplitude of the oscillation.

Ö i

=

the phase angle associated with the variable x with respect to a i reference position in time

=

the mean value of x (t); this mean value reflects the non-linearity i in the loading and is neglected in the analysis performed using ASASWAVE.

X i,mean


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w

Hence 12

X (t) i


=

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

=

X cos(2ðt/T + Ö ) i,osc i

COMPLEX REPRESENTATION

This expression for X can be expressed in its real and imaginary part by calculating the i phase angle Ö with respect to its chosen time-frame of reference or:i X (t) = X exp{2ðt/T +Ö } = i i,osc i = X cos(2ðt/T) cos(Ö ) + + X sin(2ðt/T) sin(Ö ) i,osc i i,osc i Using another notation, the real and imaginary part of the response results X

i,osc

are

respectively:Re{X (t)} = i

X cos(Ö ) i,osc i

Im{X (t)} = i

X sin(Ö ) i,osc i

and vice versa:X i,osc

=

2 2 √[Re{Xi(t)} + Im{Xi(t)} ]

Ö i

=

atan[Im{X (t)} / Re{X (t)}] i i

Similar expressions to those derived in Appendix B1 and B2 hold for the memeber end loads and nominal stresses (f ) and the parameters defining environmental wave load i distributions (á ). i


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Deterministic Fatigue Analysis

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