1. VALIDATION OF SPECTRAL FATIGUE ANALYSIS OF STRUCTURES IN MUMBAI HIGH FIELDBY
S.Nallayarasu, S.Goswami, J.S.Manral, R.M.Kotresh
Presenter: S.K. Bhattacharyya
Dept. of Ocean Engineering
IIT Madras

2. Mumbai high field location
Historically, Bombay High Field of ONGC has several offshore platforms in the shallow water region of 50 to 80m water depth.
Most of these platforms are fixed template type structures with either main or skirt piles.
Many of these structures are as old as 20 to 30 years & have been designed as per API RP 2A guidelines.
These structures mostly produce oil & Gas and have both process & well head platforms.
These platforms have been designed against fatigue from cyclic wave loads.

3. DIRECTIONAL DISTRIBUTION OF WAVES
The field is located on the west coast of India and the wave approach is from south to north-west directions and the other directions are shielded from land.
Generally waves are approaching the platforms only from South, South-West, West and North-West. The directional distribution of waves used in the deterministic and spectral methods is shown in Figure

4. FATIGUE RESPONSE ANALYSIS
Deterministic method of analysis
Seastate is discretised in discrete (deterministic) waves
the scatter data based sea state specific information is used.
Structural response to these discrete waves is then calculated either with or without dynamic effects depending on natural period.
Spectral method of analysis
Seastate is characterised by the spectral energy.
Further, the scatter data for different directions and wave heights are used to simulate the seastate.
The structural response is then calculated using stochastic method of structural analysis.
Dynamic analysis is performed to generate the dynamic characteristics such as mode shapes and mass characteristics.

5. WAVE SCATTER DATA
Wave scatter data and exceedance information used for the deterministic fatigue analysis is shown in Table 1 and 2.
The exceedance data has been converted to occurrence cyclic data with intermediate data range by interpolation
It has been summarised in Table 3.

7. WAVE SCATTER DATA – Deterministic Table - 1
WAVE HEIGHT
(M)
PERIOD (SEC) S SW W NW
8.7
9.6
8.3
6.6
9.2
10.1
7.4
3.048 – 4.571
9.5
10.3
7.9
4.572 – 6.095
9.7
10.4
8.4
6.096 – 7.619
9.9
10.5
10.0
8.9
10.6 --
9.144 –
10.8 –
11.0
10.9

8. Number of Waves Exceeding Specified Height
WAVE SCATTER DATA – Deterministic Table - 2
Wave Height (m)
Number of Waves Exceeding Specified Height
In One Year
S DIR
SW DIR
W DIR
NW DIR
CUMULATIVE
770535
1.524
61704
219347
220985
69788
571824
3.048
3132
37929
31902
3764
76727
4.572
167
5878
4073
177
10295
6.096 11
869
493 8
1381
7.620
126 59
185
9.144 - 18 7 25
10.668 2 1 3
12.192

9. WAVE SCATTER DATA – Deterministic Table - 3
Wave Height (m) W SW S NW
0.381
541944
359421
995444
928660
1.143
252784
191767
218897
222063
1.905
137022
128135
47802
53581
2.667
52061
53283
10770
12443
3.429
20503
22998
2409
2948
4.191
7326
9053
556
639
4.953
2656
3618
124
139
5.715
924
1391 32 30
6.447
322
538 11 8
7.239
112
205
8.001 39 78
8.763 13

10. WAVE SCATTER DATA – Spectral
The wave scatter data for spectral analysis obtained from National Institute of Oceanography is summarized in Tables 4 to 8 for south, south-west, west and north-west directions respectively.
The percentage distribution for each combination of wave period and height will be used for the spectral representation of the seastate using JONSWAP spectra Table-4 ( South) Hs
(m)
Mean wave period (s)
3-4
4-5
5-6
6-7
7-8
8-9
9-10
10-11
Total
0.38
0.77
0.00
1.15
5.00
17.31
18.85
11.54
53.85
2.69
10.77
15.00
1.92
2.31
32.69
3.85
12.31
8.46
30.38
36.15
15.77
7.31
100.00

11. WAVE SCATTER DATA – SpectralHs
(m)
Mean wave period (s)
3-4
4-5
5-6
6-7
7-8
8-9
9-10
10-11
Total
0.00
0.21
2.92
5.22
1.67
0.84
10.86
11.90
9.81
2.71
25.47
4.59
16.08
9.60
2.09
32.36
3.97
2.30
11.48
3.55
2.51
0.42
6.47
1.88
4.38
0.63
3.34
1.25
3.76
21.71
37.58
29.02
7.72
100.00

12. WAVE SCATTER DATA – SpectralHs
(m)
Mean wave period (s)
3-4
4-5
5-6
6-7
7-8
8-9
9-10
10-11
Total
0.00
0.28
1.83
3.94
1.69
4.22
0.70
6.61
0.42
9.00
2.81
12.24
6.05
5.63
0.56
2.39
12.80
0.84
0.14
16.17
3.66
3.52
6.33
9.99
9.85
8.30
2.53
3.38
5.91
1.27
1.41
23.63
34.60
30.52
7.03
100.00

13. WAVE SCATTER DATA – SpectralHs
(m)
Mean wave period (s)
3-4
4-5
5-6
6-7
7-8
8-9
9-10
10-11
Total
0.00
4.35
34.78
19.57
58.70
17.39
2.17
41.30
52.17
39.13
100.00

14. RS-14 WELLHEAD PLATFORM SELECTED STRUCTURES
4 LEGGED PRODUCTION CUM DRILLING PLATFORM
WATER DEPTH M
0 MAIN & 8 SKIRT PILES
16 WELL SLOTS & CONDUCTORS
MODULAR DRILLING RIG HAVING RIG MAST, RIG SUPPORT & LQ MODULE
TOPSIDE WEIGHT MT
JACKET WEIGHT-3300 MT (GROSS)

15. SELECTED STRUCTURE MNP PROCESS PLATFORM EIGHT LEGGED 4 LEVEL TOPSIDES
WATER DEPTH-72 M
16 SKIRT PILES
20 PRE-INSTALLED RISERS
LAUNCH JACKET WEIGHT-7200 MT
PROCESS HUB-
TOTAL TOPSIDE WEIGHT MT
3 PROCESS GAS COMPRESSORS, 1 BOOSTER GAS COMPRESSOR.
SUBSTRUCTURE SUPPORTS FOR 3 BRIDGES

16. DETERMINISTIC ANALYSIS
The calculation of cyclic stresses on the tubular joints shall include dynamic amplification. The effects of dynamic amplification can be ignored when the natural period of the structure is below 3 seconds as stated in API RP 2 A. This is due to the fact that most of the wave period inducing cyclic loads will be in range of 4 to 12 seconds.
The dynamic amplification factor (DAF) can be calculated using the following formula assuming a single degree of freedom system for the fixed type jacket structures.
where Tn is the natural period of the structure, T is the wave period and  is the damping ratio( 2%). It can be shown that the the response and cyclic stress ranges can be linearly multiplied by the DAF and hence the total response can be calculated without going into the full fledged dynamic response of the structure against waves. However, the accuracy of the analysis depends highly on the descretization of the seastate and any simplification will lead to erroneous estimation of response and fatigue damage.
Where [K] is the stiffness matrix, {X} and {F} are the displacement and force vectors respectively. The above approach indicates a simplified method and is very easy to implement for practice. This method has been in use for several years for the prediction response of offshore structures.

17. SPECTRAL ANALYSIS
Alternatively, the response and the cyclic stresses can be calculated using dynamic wave response including dynamic effects due to the above. This method of calculation involves procedures involving dynamic characteristics of the structure and performing the analysis in close intervals of frequency / wave period. However, the method of calculation involved several approximations and the discussion on these issues is outside the scope of this paper and can be found elsewhere. (3) Solution to the following equation will lead to Eigen modes and vectors. The dynamic analysis is performed to obtain the dynamic characteristics such as mode shapes and frequencies.

18. Where X” is the Eigen frequencies and X is the displacements
Where X” is the Eigen frequencies and X is the displacements. The mode shapes and frequencies are then used in the subsequent wave response calculation in which the following equation is solved including the dynamic response of the system.
( 4)
The response is calculated as a transfer function to facilitate the computation of the fatigue damage for various waves in different directions. Typical wave response stress transfer function for base shear and overturning moment is shown in Figure 1 and 2 respectively

19. SPECTRAL ANALYSIS FIG-1
TRANSFER FUNCTION FOR BASE SHEAR

20. SPECTRAL ANALYSIS FIG-2
TRANSFER FUNCTION FOR OVERTUNING MOMENT

21. SPECTRAL ANALYSIS
Selection of frequencies for the generation of transfer function is an important task such that the peaks and valleys of the response is not missed. Following the guidelines given API RP 2A, the frequencies near the natural period of the structure and its multiples shall be selected. The transfer function has been generated for various frequencies from 0.1 Hz to 0.5Hz (Typically from wave periods in the range of 2 to 10 seconds). The frequency interval is selected such that more number of points is generated near the natural period,
The transfer function and the response are generated for both maximum base shear and maximum overturning moment cases and the worst case is used for the calculation of fatigue damage.
A wave steepness of 1/20 is used for the all the waves as recommended by API RP 2A for the calculation of wave height for each frequency. This has been used for the generation of the transfer function.
It can be observed from Figure 1 and 2 that the maximum values of transfer function occurs near the frequency of 0.4 which corresponds to a period of 2.5 sec. The natural period of the structures for MNP and RS14 is noted to be between 2.5 sec and 3 sec.

22. ESTIMATION OF FATIGUE DAMAGE
Fatigue damage has been calculated for all the tubular connections using Miner’s rule using cumulative fatigue damage model stated as below.
(5) 
(6) 

23. ESTIMATION OF FATIGUE DAMAGE – (Contd.)
where σ is the RMS (Root mean square value) of the stress calculated from the transfer function for a given Seastate, H is the transfer function and S is the spectral density of the seastate.
(7)
where n(s) is the number of applied cycles, L is the design life and Tz is the spectral mean period calculated above.
Fatigue damage
(8) 
where N(s) is the allowable cycles from the S-N curve and S is the stress range. Stress concentration factor (SCF) for the tubular joints has been calculated as per Effthimiou formulas as recommended by API RP 2A for tubular joints and the S-N curve has been adopted as per API RP 2A for tubular joints. 

24. FACTOR OF SAFETY FAILURE CRITICAL API RP 2A ONGC INSPECTABLE
NON-INSPECTABLE NO 2 5
YES 10 4
ONGC USE A FOS OF 4.0 FOR JOINTS BELOW TOW LEVELS OF JACKET FRAMING TO COVER FOR FATIGUE DUE TO WAVE LOADS

25. RESULTS AND DISCUSSIONS
MHN (Mumbai High North) field has been presented in Table 8 and 9 respectively. The fatigue life of major tubular joints along the jacket legs and X braces is presented. Fatigue life greater than 1000 years is marked as * since it is very high compared to the required design fatigue life of 50 years.
The fatigue life predicted by deterministic analysis for RS 14 well platforms seems to be on a higher side compared to the spectral fatigue analysis. In the case of MNP Process platform deterministic results are lower than spectral for lower three levels and reverse is the case for 4th and 5th level.
This is due to the fact that the Seastate has been condensed to discrete waves and the DAF has been treated approximately.

26. Table 8. RS-14 Well platform Comparison of results of deterministic & spectral fatigue on selected joints
JOINT NO.
FATIGUE LIFE
DIFFERENCE
(D-S)
DETERMINISTIC
SPECTRAL
203L
74.71
17.84
56.87
217L
31.17
31.79
283L
968.58
473.76
494
297L *
400
201X
303L
224.9
83.01
142
317L
215.84
824
383L
245.01
750
397L
456.34
187.75
269
301X
302X
287.44
172.09
115
303X
416.70
241.13
175
303
304
305
403L
307.89
844.62 -
417L
1287.7
483L
369.62
90.76
278.86
497L
118.87
32.14
86.73
401X
23.18
5.32
17.86
402X
4.11
0.87
3.24

27. Table 8. Continued JOINT NO. FATIGUE LIFE DIFFERENCE (D-S)
DETERMINISTIC
SPECTRAL
403X *
404X
503L
255.38
252.72
2.66
517L
541.82
432.30
109.52
583L
78.56
14.58
63.98
597L
67.82
25.80
42.02
501X
49.13
3.86
45.27
502X
18.42
1.91
16.51
503X
655.58
345
504X
603L
145.32
141.13
131.19
617L
273.35
12.08
261.27
683L
160.99
19.34
141.65
697L
28.88
7.21
21.67
601X
399.95
600
602X
398.85
603X
23.92
976
604X
24.27
703L
6.60
994
717L
6.055
783L
6.099
797L
5.54

28. Table 8. Continued JOINT NO. FATIGUE LIFE DIFFERENCE (D-S)
DETERMINISTIC
SPECTRAL
404X *
503L
255.38
252.72
2.66
517L
541.82
432.30
109.52
583L
78.56
14.58
63.98
597L
67.82
25.80
42.02
501X
49.13
3.86
45.27
502X
18.42
1.91
16.51
503X
655.58
345
504X
603L
145.32
141.13
131.19
617L
273.35
12.08
261.27
683L
160.99
19.34
141.65
697L
28.88
7.21
21.67
601X
399.95
600
602X
398.85
603X
23.92
976
604X
24.27
703L
6.60
994
717L
6.055
783L
6.099
797L
5.54

29. Table 9. MNP Process platform Comparison of results of deterministic & spectral fatigue on selected joints
JOINT NO.
FATIGUE LIFE
DIFFERENCE
(D-S)
DETERMINISTIC
SPECTRAL
203L
52.41
108.38
-56
207L
9.47
34.14
-24
213L
9.26
21.43
-12
217L
78.80
127.34
-49
283L
52.93
129.05
-77
287L
11.55
81.14
-70
293L
11.14
69.06
-58
297L
43.65
88.38
-45
204X *
205X
206X
207X
208X
209X
210X
211X
212X
213X

30. Table 9. Continued JOINT NO. FATIGUE LIFE DIFFERENCE (D-S)
DETERMINISTIC
SPECTRAL
303L
20.89
202.21
-182
307L
70.45
508.03
-438
313L
69.36
806.51
-737
317L
18.49
302.99
-284
383L
19.56
267.49
-248
387L
197.60
485.68
-288
393L
253.92
783.73
-530
397L
18.97
358.24
-339
304X *
305X
306X
307X
308X
309X
310X
311X
312X
313X
403L
149.07
-851
407L
20.62
200.44
-180

31. Table 9. Continued JOINT NO. DIFFERENCE (D-S) DETERMINISTIC SPECTRAL
156.09
72.32 84
483L
185.24
163.23 22
487L
168.31
147.37 21
493L
140.70
132.46 8
497L
135.05
118.97 16
404X *
405X
406X
407X
408X
409X
410X
96.67
903
411X
513.86
486
412X
125.03
875
413X
429.95
21.49
409
503L
104.71
0.88
104
507L
24.17
0.06 24
513L
23.69
1.07
517L
153.88
0.85
153
583L
301.03
0.87
300

32. Table 9. Continued JOINT NO. DIFFERENCE (D-S) DETERMINISTIC SPECTRAL
73.39
0.89 72
593L
156.72
1.01
155
597L
181.49
0.69
180
501X *
127.26
873
502X
136.83
864
503X
234.38
760
504X
115.94
884
505X
108.49
892
506X
233.61
767
507X
1.42
999
508X
1.57
509X
510X
0.21
603L
151.58
0.57
151
607L
99.52
1.18 98
613L
184.74
1.21
183
617L
370.08
0.56
369
683L
206.42
0.70
205
687L
105.74
1.20
104
693L
180.44
1.13
179

33. CONCLUSIONS
Based on the results obtained from the fatigue analysis of platforms in Mumbai High North and South platforms, following observations are made.   
Generally both methods predict fatigue life reasonably well for most of the joints except for some joints at the bottom of the jacket, the deterministic method predicts the fatigue life lower than the spectral methods. This is due to the fact that the dynamic response of the structure over-predicted by deterministic method by approximate calculations of DAF due to course discretisation of wave periods.
However, the joints near the top of the jacket, the predicted fatigue life using deterministic methods seems to be higher than the spectral methods. This is due to the fact that the wave load and associated cyclic stresses are only due to the local wave loads rather than the dynamic response.
It is recommended that spectral fatigue analysis be used for large platforms to assess the fatigue life since the inaccuracy introduced due to the treatment of dynamic amplification factor.

34. References
API RP 2A Recommended Practice for the Design and Construction of fixed offshore platforms, working stress design.
Fatigue User Manual, SACS Software, EDI
Identification of wave spectra for Mumbai offshore region, National Institute of Oceanography, December 2007.