1999/059 OFFSHORE TECHNOLOGY REPORT Validation of inspection planning methods

HSE
Health & Safety
Executive
Validation of inspection
planning methods
Summary report
Prepared by Aker Offshore Partner AS
for the Health and Safety Executive
OFFSHORE TECHNOLOGY REPORT
1999/059
HSE
Health & Safety
Executive
Validation of inspection
planning methods
Summary report
Aker Offshore Partner AS
PO Box 1
Sandslimarka 251
N-5049
Norway
HSE BOOKS
© Crown copyright 2002
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First published 2002
ISBN 0 7176 2305 X
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assume any liability for the reports nor do they
necessarily reflect the views or policy of the Executive.
ii
SUMMARY
1.
INTRODUCTION......................................................................................................................... 1
2.
THE IN-SERVICE OBSERVATION DATA COLLECTED.................................................... 3
2.1
2.2
2.3
3.
THE COLLECTION AND CRACK CLASSIFICATION ........................................................................... 3
THE DATA COLLECTED ................................................................................................................ 3
FATIGUE CRACKS VS. FABRICATION DEFECTS ............................................................................ 5
CALCULATION OF THE RELIABILITY ESTIMATE OF OBSERVED EVENTS.......... 10
3.1
INTRODUCTION.......................................................................................................................... 10
3.2
METHOD USED FOR CALCULATION OF FATIGUE POTENTIAL ....................................................... 10
3.3
RESULTS FROM THE QUALITATIVE COMPARISON ...................................................................... 11
3.3.1
Overprediction Ratio ...................................................................................................... 11
3.3.2
Cracks Detected Prior Recommended Time of Inspection ............................................. 12
3.3.3
Cracks Not Detected by the Method of Target Inspection Planning .............................. 15
3.3.4
Discussion of the Results from the Qualitative Comparison........................................... 19
4.
QUANTITATIVE COMPARISON OF THE THEORETICAL PREDICTIONS AND INSERVICE OBSERVATIONS. .................................................................................................... 21
4.1
4.2
INTRODUCTION.......................................................................................................................... 21
THE QUANTITATIVE MEASURES OF DEVIATION BETWEEN THEORETICAL PREDICTION AND
OBSERVATION, REGRESSION ANALYSIS. ................................................................................................... 23
4.2.1
Method ............................................................................................................................ 23
4.2.2
The Results of the Regression Analysis........................................................................... 24
4.2.3
Comments Related to the Regression Analysis Results................................................... 27
5.
5.1
5.2
5.3
5.4
6.
6.1
6.2
6.3
6.4
6.5
6.6
6.7
7.
7.1
7.2
7.3
8.
THE CONCEPT OF ADJUSTMENT FACTORS ................................................................... 29
INTRODUCTION.......................................................................................................................... 29
METHOD FOR CALCULATION OF THE SENSITIVITY MEASURES................................................... 29
RESULTS OF THE SENSITIVITY ANALYSIS.................................................................................... 32
ADJUSTMENT BASED ON A LIMITED NUMBER OF VARIABLE ....................................................... 33
CONSEQUENCES OF THE RESULTS................................................................................... 37
INTRODUCTION.......................................................................................................................... 37
RELIABILITY OF COMPONENTS ESTIMATED TO HAVE LIMITED POTENTIAL FOR FATIGUE CRACK
GROWTH .................................................................................................................................... 37
IMPLEMENTATION OF THE OBSERVED CONSERVATISM .............................................................. 39
POTENTIAL EFFECT ON DESIGN .................................................................................................. 39
EFFECT ON INSPECTION PLANNING............................................................................................. 40
EFFECT ON STRUCTURE ASSESSMENT FOR LIFE TIME EXTENSION ............................................... 40
IMPROVEMENT OF FLS ANALYSIS PROCEDURES ........................................................................ 41
RECOMMENDATIONS FOR FURTHER WORK ................................................................ 42
INDUSTRIAL CONSENSUS ........................................................................................................... 42
RECOMMENDED PRACTICE ........................................................................................................ 42
AVAILABILITY OF IN-SERVICE EXPERIENCE................................................................................ 43
REFERENCES............................................................................................................................ 44
iii
iv
1. Introduction
Fatigue is of significant concern for load bearing offshore structures in the North Sea. The
present tools for predicting fatigue life or crack growth imply highly scattered estimates. There
is a need for more reliable fatigue life and defect assessment procedure for the most frequent
failure observed. The availability of a database of inspection data to correlate actual with
predicted performance will assist the development of fatigue assessment procedures
representing the observed crack growth.
A comparison was performed of in-service fatigue performance and the corresponding
theoretical predictions. The results are mainly measures of the deviation between theory and
observations and the observed correlation were used to recommend enhancements to existing
analytical methods. The results indicate the need for a major modification of the procedure used
for the theoretical prediction of the fatigue crack growth and consequently the need for the
conservative utilisation of the results. Further refinement and external confirmation of the
results is recommended before the safety margins are reduced to the allowable minima.
The results give the theoretical predictions of fatigue potential as a frequency of occurrence.
Figure 1 gives a summary of the relationship between predicted fatigue life by traditional
procedure and procedure adjusted by observed crack growth. Generally the present theoretical
predictions are conservative. However, between 10 and 40 per cent of the observed fatigue
cracks are not identified by the FLS analysis. A major challenge will be to identify why these
fatigue cracks not are predicted. The percentage of fatigue crack detection for the scheduled
inspections is 15% and of the order of 2% for the component normally not scheduled for
inspection by the inspection-planning tool.
For the brace to chord intersections with an initial estimated fatigue life of more than 800 years,
a fatigue crack occurrence rate of the order 1.2 to 1.8 per cent is estimated based on
observations. For the intersections with an initial fatigue life less than 40 years, the estimated
crack occurrence rate of the order 14 to 16 is estimated based on observations.
The present “standard” procedure for design and construction has an upper bound value for
documentation of reliability against fatigue crack growth. To achieve a reliability index above 4
additional information needs to be used in combination with the FLS analysis. Additional
information that may be required includes the results of a refined fatigue analysis, fabrication
inspection data, the use of weld improvements for enhanced fatigue capacity or in-service
observations.
The observed shortcomings in the present procedure will have a major impact on the condition
assessment performed during design, operation, modification and for the evaluation of life time
extension.
1
Observed Fatigue Life vs. Predicted Fatigue Life
125
Mean
10% percentile
105
85
90% percentile
65
45
25
5
100
200
300
400
500
600
Predicted fatigue life based on observations.
Figure 1
The fatigue life adjustment is based on more than 3000 observations. The adjustment is valid for
predicted fatigue life between 1 and 250 year by the SN-curve approach. The data is
representative for structures having been in operation for approximately 20years.
Section 2 presents the data collected. Section 3 contains the reliability estimate for the observed
events and gives a qualitative presentation of the observed deviation between theoretical
predictions and observations. Section 4 gives a description of regression analysis for a
quantitative comparison.
Section 5 present the concept of adjustment factors, a method for utilisation of the observed
correlation between theory and observation to improve the procedures and methods to predict
the fatigue potential. The consequences of the results are discussed in section 6. Section 7
contains recommendations for further work.
2
2. The In-Service Observation Data Collected
2.1 THE COLLECTION AND CRACK CLASSIFICATION
The inspection history was collected from original field inspection reports. For the cracks
reported, a careful examination was performed. A judgement on whether the cracks were nonpropagating (denoted fabrication cracks) or propagating was based on expert opinion,
represented by knowledge of metallurgy, structural analyses and inspection engineering. The
experience from evaluating more than 550 cracks and 4000 EC/MPI inspections has been
utilised in the classification process. Different groups of engineers have independently
performed the classification, i.e. given a percentage belief in the crack to be propagating
(fatigue crack). The uncertainty in the classification of cracks as propagating and nonpropagating is high for joints that only have been inspected once. The cracks with a highly
scattered judgement have been given less weight in the study, ref. /1/.
Upon the review of all inspection reports, structural drawings, fatigue analyses and crack
classification, a database containing all data required for statistical evaluation and calibration
was created. Criteria for arranging these data by structure, type of structure and/or position in
structure were specified, ref. /1/ and /2/.
2.2 The data collected
Table A.1 in appendix gives a summary of in-service observations collected. The data is
collected from a total of 30 Jacket structures located in the Norwegian North Sea. The water
depth is 70 metres or deeper with exemption of two booster structures. These are respectively
located in the British and German sectors. All jacket structures have 4, 8 or 12 legs. 17 tripod
structures are also used in the Norwegian North Sea for bridge and flare supports, but is not
included in the database. The tripod structures, which were installed in the period 1972 to 1977
at a minimum water depth of 70 metres, could provide approximately 1000 additional in-service
observations.
Tables 2.1 and 2.2 summarise number of observations for the three different groups of
structures. The structures were grouped according to whether they were installed before 1975,
in the period of 1975 to 1978 and structures installed after 1978.
Figure 2.1 gives the number of inspections, flaws detected and fatigue cracks detected as a
function of year of inspection. In figure 2.1 the number of fatigue cracks represents cracks for
which it is considered that there is a greater than 50 per cent probability that propagation is
occurring. (The used sorting criteria of 50 per cent or higher belief, is an example. Conclusions
require sensitivity studies related to the sorting criteria.) Figure 2.2 present the same results as
figure 2.1 but the focus is related to the ratio between the number of fabrication cracks vs.
fatigue cracks.
3
Table 2.1
Observations as a function of installation year.
# of effective observations is the sum of weight index for the given observations.
2
(The weight index is defined as 4*(S-0.5) , where S is the percentage belief that the flaw is a
fatigue crack. S is 1.0 for the inspections given a result “No Finding”, i.e. no indication
observed by use of EC or MPI.)
# of fatigue cracks 50% is the number of detected cracks given the belief that more than 50%
are due to fatigue i.e. propagating crack.
Installation
Year
Before 1975
1975- 1978
After 1978
Summary
# of
structures
8
14
8
30
# fatigue
cracks 50%
167
48
6
221
# of
cracks
309
178
24
511
# of
observations
1943
1732
299
3974
# of effective
observations
1677
1582
278
3537
Table 2.2
Observations as a function of installation year. Numbers in brackets are the numbers excluding
tertial structural members.
# of new inspections, i.e. number of inspections performed on intersections where cracks have
not been detected before. Hence, a new inspection is not necessarily a first time inspection for a
joint
1. fatigue cracks 30%, i.e. ≥ 30 % belief of propagating crack
2. fatigue cracks 50%, i.e. ≥ 50 % belief of propagating crack
3. fatigue cracks 70%, i.e. ≥ 70 % belief of propagating crack
4. fatigue cracks 90%, i.e. ≥ 90 % belief of propagating crack
Installation
Year
Before 1975
1975- 1978
After 1978
Summary
# of new
inspections
1536 (1415)
1555 (1538)
278 (277)
3366
# of
cracks
309(246)
178
(176)
24(24)
511
# fatigue
cracks 30%
202(143)
73(73)
# fatigue
cracks 50%
167(113)
48(48)
# fatigue
cracks 70%
128(80)
29(29)
# fatigue
cracks 90%
65(42)
15(15)
8(8)
283
6(6)
221
2(2)
159
0(0)
80
New fatigue analysis and inspection philosophy based on PIA was introduced in the period of
1989 to 1992. A critical group of intersections that according to PIA should have been
inspected for some years ago were inspected in the period 1989 to 1993. After 1993 the
inspections have mainly been performed at recommended time. This may be one explanation
for the increased detection of fatigue cracks for the period 1989 to 1993 and following
reduction in 1994 and 1995, ref. /10/.
4
Number of Inspections, Cracks and
Fatigue Cracks
700
Number of
Cracks
600
500
400
Number
Inspections
Number of Cracks
Number of Fatigue
Cracks
300
200
100
0
74/75
76/77
78/79
80/81
82/83 84,/85
86/87
88/89
90/91
92/93
94/95
Year of Inspection
Figure 2.1
Number of in-service observations, fabrication and fatigue cracks detected as a function of year
of inspection. A fatigue crack is defined as a flaw for which it is considered that there is a
minimum probability of 50% that propagation is occurring.
Number of Cracks, Fatigue Cracks
and Ratio of Fatigue Cracks
200
160
140
90,00
80,00
Number of Cracks
Number of Fatigue Cracks
%Fatigue Cracks
70,00
60,00
120
50,00
100
% Fatigue
cracks
Number of
cracks
180
40,00
80
30,00
60
40
20,00
20
10,00
0
0,00
74/75 76/77 78/79 80/81 82/83 84/85 86/87 88/89 90/91 92/93 94/95
Year of Inspection
Figure 2.2
Number of fabrication and fatigue cracks detected and ratio between fabrication and fatigue
cracks as a function of year of inspection. A fatigue crack is defined as a flaw for which it is
considered that there is a minimum probability of 50% that propagation is occurring.
2.3 FATIGUE CRACKS VS. FABRICATION DEFECTS
Figure 2.3 gives the ratio between fatigue cracks and total number of cracks detected as
a function of time in service according to different criteria for fatigue crack
classification for all the structures. FAT 90% corresponds to cracks classified as fatigue
cracks given a 90% belief that propagation is occurring.
5
Ratio of Fatigue Cracks and Number of Detected Cracks
R. FAT 30%
R. FAT 50%
R. FAT 70%
R. FAT 90%
0-3
4-7
8-11
12-15
16-19
0,9
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
20-23
Years in service
Figure 2.3
Ratio of cracks classified as fatigue crack related to total number of cracks detected as a
function of time in service when the crack was detected for all structures.
0,25
0,2
0,15
0,1
FAT 90%
FAT 70%
0,05
FAT 50%
0
0-3
FAT 30%
4-7
8-11
12-15
16-19
20-23
Years in service
Figure 2.4
Ratio of joints inspected containing fabrication cracks related to number of first time inspection
of intersection, for all structures. The ratio is given as function of time in service when the
inspections were performed.
Fatigue cracks will require certain crack lengths and growth rates before they are detected by
inspection. Figure 2.3 indicates the dramatic change in the percentage of detected cracks that
become fatigue cracks after 15 years in service. Improved methods to predict where and when
fatigue cracks occur may also have contributed to this increased crack growth detection. Ref.
figure 2.2 and comments related to new fatigue analysis and inspection planning by use of PIA.
If the in-service observations were performed on randomly selected brace to chord
intersections, the ratio between the number of fabrication cracks/defects and number of new
intersections to be inspected would have been independent of time in service, i.e. a constant
value. The curves in Figure 2.4 would therefore represent a statistical variation around a
horizontal line. Figure 2.4 has an increased ratio of detection in the period 7-11 years in service.
The experience from the first year’s inspection may have improved the knowledge of where the
fabrication defects have their highest frequency of occurrence. Since 1989 the inspection
6
planning has focused on fatigue failure potential, ref. /10/. A reduced detection of fabrication
flaws may therefore be assumed after 1989, i.e. 14 to 17 years in service.
Figure 2.5 presents the data in Figure 2.4 for different subsets of structure installation.
R a t i o o f F a b r i c a t i o n D e f e c t s o f F i r s t T im e In s p e c tio n , S t r u c t u r e s In s t a lle d B e f o r e
1975
0 ,3
0 ,2 5
0 ,2
FAT 30%
FAT 50%
0 ,1 5
FAT 70%
FAT 90%
0 ,1
0 ,0 5
0
0 -3
4 -7
8 -1 1
1 2 -1 5
1 6 -1 9
2 0 -2 3
Y e a r s in s e r v ic e
R a tio o f F a b r ic a tio n D e f e c t s o f F i r s t T im e In s p e c tio n , S t r u c t u r e s In s t a lle d
B e tw e e n 1 9 7 5 to 1 9 7 8
0 ,2 5
0 ,2
FAT
FAT
FAT
FAT
0 ,1 5
0 ,1
90%
70%
50%
30%
0 ,0 5
0
0 -3
4 -7
8 -1 1
1 2 -1 5
1 6 -1 9
Y e a r s in s e r v ic e
R a tio o f F a b ric a tio n D e fe c ts o f F irs t In s p e c tio n , S tru c tu r e s A fte r 1 9 7 8
0 ,2
0 ,1 5
FAT 90%
FAT 70%
FAT 50%
0 ,1
FAT 30%
0 ,0 5
0
0 -3
4 -7
8 -1 1
Y e a r s in s e r v ic e
Figure 2.5
Ratio of fabrication cracks detected related to number of first time inspection as function of time
in service when the inspections were performed. The subsets are defined according to time of
installation, i.e.:
−
structures installed before 1975
−
structures installed the period 1975 to 1978.
−
structures installed after 1978
Figure 2.6 gives the ratio of fabrication and fatigue cracks detected related to number of first
time inspections. A first time inspection is an inspection performed on a brace to chord
intersection which has previously not been inspected.
7
Figure 2.6 is a summary of all data collected. The ratios are presented for different criteria of
crack classification, i.e. a fatigue or fabrication crack. The horizontal axes give the number of
years in service before the inspections were performed. The uncertainty of the given percentage
of belief in fatigue cracks is high for the intersections, which only have been inspected once.
Cracks detected before 1988 have normally been issued for re-inspection. Based on the
information from re-inspection the uncertainty of crack classification will normally be reduced.
The inspections performed after more than 18 years in service will therefore have a higher
sensitivity related to crack classification criteria, i.e. very few of the detected cracks after 18
years in service have been re-inspected, ref. /10/.
Independent of crack classification criteria, Figure 2.6 shows an increased rate of fatigue crack
detection with platform age. If the intersections inspected had been selected randomly, Figure
2.6 would probably have documented the ratio of fatigue crack growth. The increased number
of fatigue cracks may also partly be related to improved prediction of where and when fatigue
crack growth occurs. Appendix A presents the data in Figure 2.6 for different sub sets of data
according to the structures time of installation.
Section 3 introduces the predicted potential for fatigue crack growth and gives a qualitative
discussion based on this additional information.
8
R a tio of Fabrication a n d F a tigue Crack Detections,
50 % confide n c e a p p l i e d for the fa tigue crack classifica tion
R a tio of Fa b r i c a tion a n d F a tigue Crack De te c tions,
( 90 % confide n c e r e l a ted to fatigue classifica tion)
0,25
0,25
0,2
0,2
0,15
0,15
FA T 50%
FA T 90%
Fab-cra 90%
0,1
Fab-cra 50%
0,1
0,05
0,05
0
0
0-2
3-5
6-8
9-11
12-14
15-17
18-20
0-2
21-23
3-5
6-8
9-11
12-14
15-17
18-20
21-23
Y e a r s in s e r vice
Years in service
R a tion of Fa b rica tion a n d F a tigue Crack Detections, 70 % confide n c e
for the fa tigue crack classifica tion
R a tio of Fa b rica t i o n a n d F a tigue Crack Detections,
30 % confide n c e r e l a te d to the fa tigue crack classifica tion
0,25
0,25
0,2
0,2
0,15
0,15
FA T 70%
FA T 30%
Fab-cra 70%
0,1
Fab-cra 30%
0,1
0,05
0,05
0
0
0-2
3-5
6-8
9-11
12-14
15-17
18-20
21-23
0-2
Years in service
3-5
6-8
9-11
12-14
15-17
18-20
21-23
Y e a r s in service
Figure 2.6
The ratio of fabrication and fatigue cracks related to the number of inspections of intersections which previously has not been inspected or
reported any findings. Ref. Appendix 1 for information related to sub set of data defined by the structures time of installation.
9
3. Calculation of the Reliability Estimate of Observed Events
3.1 INTRODUCTION
An increased rate of detection of cracks classified as fatigue cracks is observed. One important
question is whether the detected fatigue cracks are located in the area given a high fatigue potential
using fatigue and probabilistic inspection analysis.
This chapter presents the observed inspection results according to estimated potential for fatigue crack
growth for different subsets of data. The subsets of data will be defined by sorting criteria related to
the inspected intersection characteristics as:
−
−
−
−
located in structures installed before 1975, in the period 1975 to 1978 or after 1978
elevation in structure where intersection is located
number of years in service before the inspection was performed
the importance of brace to chord intersection, i.e. main, secondary or tertiary structural
components
3.2 METHOD USED FOR CALCULATION OF FATIGUE POTENTIAL
The different structures were originally assessed using different fatigue analysis procedures for
estimation of the long-term distribution of the stress range. To enable meaningful comparison of the
fatigue data a qualitative review of the fatigue analysis procedures has been performed, ref. /1/.
Approximately 70 per cent of the inspection histories have been analysed according to the same
procedure. This procedure is denoted as the reference procedure. The remaining 30% had their load
effect estimated by procedures resulting in systematic deviations compared to results from the
reference procedure. Based on qualitative evaluations and minor calculations, 30% of the estimated
long-term distribution of stress ranges were adjusted. An adjustment implemented to achieve the
theoretical predictions to be based on comparable fatigue analysis procedure results, i.e. fatigue life
estimate.
For comparison between in-service observations and predictions the event fatigue crack detection was
selected. The probability of the defined event for each inspection have been calculated using PIA, ref.
/4/ and /5/. PIA is a probabilistic fracture mechanic crack growth model developed by Aker as an
application of PROBAN, ref./6/ and /7/. PROBAN is a probabilistic analysis program developed by
DNV. PIA is the most used inspection-planning tool for the frame structures installed in the
Norwegian North Sea.
For this study PIA was used to estimate the probability of the result of fatigue crack detection upon a
given inspection. The PIA predicted probability was compared with the percentage belief in a detected
crack being due to fatigue.
10
3.3 RESULTS FROM THE QUALITATIVE COMPARISON
3.3.1 Overprediction ratio
Table 3.1 gives the overprediction ratio for all data collected and different subsets of data. The
overprediction ratio is defined as the ratio between the number predicted fatigue cracks and the
number of fatigue cracks actually detected. The number of fatigue cracks detected will depend on the
crack classification criteria used.
Table 3.1
Overprediction ratio, i.e. # of predicted fatigue cracks related to # of detected fatigue cracks.
−
fatigue cracks 50% i.e. 50 % or higher believe of propagating crack
−
fatigue cracks 70% i.e. 70 % or higher believe of propagating crack
−
fatigue cracks 90% i.e. 90 % or higher believe of propagating crack
Installation
# of fatigue
Overprediction
Overprediction ratio
Overprediction ratio
Year
cracks
ratio fatigue cracks fatigue cracks 70%
fatigue cracks 90%
predicted
50%
Before 1975
449
2.7
3.5
6.9
1975- 1978
284
5.9
9.8
18.9
After 1978
56
9.3
27.8
∞
Total
789
3.6
5.0
9.9
Table 3.2 gives the overprediction ratio as function of elevation in structure for the following
comparison criteria: fatigue crack detection (as earlier), crack 5 mm, and through thickness crack. The
used fatigue classification criterion is “fatigue crack 50%”.
Table 3.2
Overprediction ratio, i.e. # of predicted fatigue cracks related to # of detected fatigue cracks as function
of elevation in structure and following comparison criteria:
Fat. crack detection
detection of fatigue crack
Crack > 5mm
fatigue crack with depth more than 5mm
through thick.
through thickness fatigue crack
# of Observations
Description
All
+20’
-20’
-65’
< -65’
Total
890
303
400
344
3230
Fat.
crack
194
13
37
5
260
crack
> 5mm
65
4
7
6
94
Overprediction ratio
thru.
thick.
14
0
2
0
19
11
Fat. crack
detection
1.5
6.0
4.0
11.4
2.9
crack
> 5mm
2.7
12.5
15.6
5.3
5.0
thru.
thick.
10.2
∞
47.5
∞
20.3
3.3.2 Cracks Detected Prior Recommended Time of Inspection
Table 3.3, 3.4 and 3.5 give the number and percentage of cracks, which are detected prior to the
recommended time of inspection. The data are given for different combinations of fatigue crack
classification criteria and reliability target values β t i.e. β i > β t = 0.5, 2.0 and 3.7 where β i is the
reliability for through thickness cracks at the given time of inspection. The reliability index of 0.5, 2.0
and 3.7 corresponds to the probabilities 3.1E-01, 2.2E-02 and 1.1E-04.
Table 3.3
# of observed fatigue cracks which are detected prior to time of inspection defined by the target
reliability index inspection planning method. The numbers in brackets are related to a target reliability
index value of 5.0.
# of fatigue cracks observed by inspections performed prior to recommended time of
inspection
Year
fatigue 30 %
fatigue 50 %
fatigue 70 %
fatigue 90 %
283 f. cracks
221 f. cracks
159 f. cracks
80 f.cracks
of
βi >
βi >
βi >
βi >
βi >
βi >
βi >
βi >
βi >
βi >
βi > βi >
Instal.
0.5
2.0
3.7
0.5
2.0
3.7
0.5
2.0
3.7
0.5
2.0
3.7
<75
126
67
41
100
47
27
71
30
15
32
8
3
(19)
(10)
(5)
(1)
75-78
53
49
37
31
29
18
14
13
8 (6)
2
1
1
(21)
(11)
(1)
>78
8
7
3 (2)
6
5
1 (1)
2
2
1 (1)
0
0
0
All
187
123
81
137
81
46
87
45
24
34
9
4
Table 3.4
Percentage of observed fatigue cracks that are detected prior to time of inspection defined by the target
reliability inspection planning method.
% of the fatigue cracks observed by inspections performed prior to recommended
time of inspection
Year
fatigue 30 %
fatigue 50 %
fatigue 70 %
fatigue 90 %
of
βi >
βi >
βi >
βi >
βi >
βi >
βi >
βi >
βi >
βi >
βi > βi >
Instal.
0.5
2.0
3.7
0.5
2.0
3.7
0.5
2.0
3.7
0.5
2.0
3.7
<75
62
33
21
60
28
16
55
23
12
49
12
5
75-78
73
67
51
65
60
38
48
45
28
13
7
7
>78
100
88
38
100
83
17
100
100
50
0
0
0
All
66
43
29
62
37
21
55
28
15
43
11
5
The theoretical predictions in ref. /9/ have a negative correlation with the predictions for the tertiary
structural components. If the tertiary components are excluded from the data presented in table 3.3 and
3.4, the data for the structures installed after 1975 do not change. For the structures installed before
1975 the altered results are given in table 3.5. The target reliability values used for inspection
planning are the reliability related to through thickness cracks. Depending on the structural
redundancy, the required member reliability with respect to fatigue failure is in the rate 0.5 to 3.7
according to ref. /5/. However, the figures in the table are related to the event fatigue crack detection.
The percentage values in table 3.4 and 3.5 represent the percentage of fatigue cracks that could be
detected before the recommended time of inspection.
12
Table 3.5
# of observed fatigue cracks which are detected prior to time of inspection defined by the target
reliability inspection planning. The inspection history related to tertiary structural components is
excluded.
# and % of fatigue cracks observed by inspections performed prior to recommended
time of inspection
Year
fatigue 30 %
fatigue 50 %
fatigue 70 %
fatigue 90 %
of Instal. βi >
βi >
βi >
βi >
βi >
βi >
βi >
βi >
βi >
βi >
βi >
βi >
0.5
2.0
3.7
0,5
2.0
3.7
0,5
2.0
3.7
0,5
2.0
3.7
<75
85
56
32
63
39
21
39
22
9
17
6
2
as #
<75
59
39
22
56
35
19
49
28
11
40
14
5
as %
All
146
112
72
100
73
40
55
37
18
19
7
3
as #
All %
65
50
32
60
44
24
50
33
16
33
12
5
To obtain a measure of the number of fatigue cracks not detected by a target reliability inspection
planning procedure, the number of detected fatigue cracks need to be related to the number of
inspections. Table 3.6 gives the number of new inspections on components as a function of the
reliability level at the time of inspection (new inspection = inspection of component where no crack
have been observed previously, see Table 2.2).
Table 3.6
Number of new inspections as a function of reliability of through thickness crack upon time of
inspection. Numbers in brackets include inspection on tertiary structural components.
Year of
# of new inspections performed
installation
βi < 0.5
βi > 0.5
βi > 2.0
βi > 3.7
< 75
246 (297)
1169 (1239)
961 (989)
678 (693)
75-78
172(182)
1366(1373)
1256(1257)
1036(1036)
> 78
1(1)
276(277)
249(250)
143(144)
All
425
2819
2468
1858
Table 3.7
Percentage of new inspections in which fatigue cracks were detected as a function of the reliability at
the inspection time with respect to through thickness crack. A fatigue crack is defined as a detected
crack given a 30 % belief to be a fatigue crack. Numbers in brackets include inspections on tertiary
structural components.
% of inspections with the result fatigue crack detection, crack classification
Year of
FAT30%
installation
βi < 0.5
βi > 0.5
βi > 2.0
βi > 3.7
< 75
24.0 (25.6)
7.3 (10.2)
5.8 (6.8)
4.7 (5.9)
75-78
11.0
3.9
3.9
3.6
> 78
0.0
2.9
2.8
2.1
All
18.4
5.2
4.5
3.9
13
Table 3.8
Analogous to table 3.7 with 50 % belief of detected crack being a fatigue crack.
% of inspections with the result fatigue crack detection, crack classification
Year of
FAT50%
installation
βi < 0.5
βi > 0.5
βi > 2.0
βi > 3.7
< 75
20.7 (22.6)
5.4 (8.1)
4.1 (4.8)
3.1 (3.9)
75-78
9.3
2.3
2.3
1.7
> 78
0.0
2.2
2.0
0.7
All
15.8
3.5
3.0
2.2
Table 3.9
Analogous to table 3.7 with 70 % belief of detected crack being a fatigue crack.
% of inspections with the result fatigue crack detection, crack classification
Year of
FAT70%
installation
βi < 0.5
βi > 0.5
βi > 2.0
βi > 3.7
< 75
16.9 (19.2)
3.3 (5.7)
2.3 (3.0)
1.3 (2.2)
75-78
8.2
1.0
1.0
0.8
> 78
0.0
0.7
0.8
0.7
All
13.2
2.0
1.5
1.0
Table 3.10
Analogous to table 3.7 with 90 % belief of detected crack being a fatigue crack.
Year of
installation
< 75
75-78
> 78
All
% of inspections with the result fatigue crack detection, crack classification
FAT90%
βi < 0.5
βi > 0.5
βi > 2.0
βi > 3.7
10.3 (11.1)
1.5 (2.6)
0.6 (0.8)
0.3 (0.4)
7.1
0.1
0.1
0.1
0.0
0.0
0.0
0.0
8.9
0.7
0.3
0.2
Tables 3.3 to 3.10 contain results of inspections performed over a number of years in service. Some of
the cracks detected prior to the recommended time of inspection will be scheduled for inspection
before the cracks have grown critical. The results presented in tables 3.3 to 3.10 may therefore be
suggested as an upper bound on the percentage of joints not recommended for inspection which
subsequently develop fatigue crack growth.
The predicted reliability curve will generally decrease with time in service. The results presented in
table 3.3 to 3.10 are mainly related to inspections performed after a limited number of years in service.
If the predicted reliability is generally less conservative for the first years in service, the results given
in table 3.3 to 3.10 may not be upper bound values.
In ref. /8/, the value used for the initial crack depth a0 (i.e. E[A0=0.11mm) was considered to be nonconservative. Introduction of the new value of initial crack depth a0 (i.e. E[A0=0.36mm) will give
reduced reliability values. The reduction will decrease with time in service, i.e. due to the shortcoming
of the current value of initial crack depth a0, the reliability curve is less conservative for the first years
in service. As discussed above it is uncertain whether the results in table 3.3 to 3.10 will be upper
bound values.
14
3.3.3 Cracks Not Detected by the Method of Target Inspection Planning
Figure 3.1 gives the typical shape of a reliability curve, ref. /4/, /5/. The curves have approximately
asymptotic development towards a minimum value. The joints with the “asymptotic” reliability level
above the reliability target value will not be scheduled for inspection. The number and percentage of
detected fatigue cracks located on joints with the “asymptotic” reliability level above the target values
are given in table 3.11 and 3.12.
βReliability
βA - asymptotic
reliability value
30
Y e a r s in S e r v i c e
Figure 3.1
A typical curve of reliability of through thickness crack as a function of time in service, no inspection
history included.
The asymptotic minimum reliability value may be approximated by the reliability value related to
through thickness crack given upon 30 years in operation. The function between fatigue life estimate
and reliability level upon 30 years in operation is calculated, see figure 3.2. Based on the results
presented in figure 3.2 the following are used:
β t = 0.5 correspond to an initial fatigue life of 41 years
β t = 2.0 correspond to an initial fatigue life of 165 years
β t = 3.7 correspond to an initial fatigue life of 800 years
Reliability Index Upon 30 Years in Operation,
No Inspection Performed
4
3,5
Reliability
3
2,5
2
1,5
1
0,5
0
-0,5
-1
0
100
200
300
400
500
600
700
800
900
Initial Estimated Life Time
-1,5
Figure 3.2
Relationship for a test case between estimated fatigue life and reliability for a through thickness crack
after 30 years in operation.
15
Table 3.11
# of observed fatigue cracks located on joints classified as non-critical with respect to fatigue crack
growth by the theoretical analysis. Numbers in brackets include inspections on tertiary structural
components.
# of fatigue cracks observed on not recommanded inspections according to target
inspection planning methods
fatigue 30 %
fatigue 50 %
fatigue 70 %
fatigue 90 %
Year
283 f. cracks
221 f. cracks
159 f. cracks
80 f.cracks
of
βt =
βt =
βt =
βt =
βt =
βt =
βt =
βt =
βt =
βt =
βt =
βt =
Instal.
0.5
2.0
3.7
0.5
2.0
3.7
0.5
2.0
3.7
0.5
2.0
3.7
<75
67
39
27
48
24
15
26
13
7
8
2
1
(104) (49)
(36)
(81)
(31)
(21)
(54)
(20)
(13)
(19)
(3)
(2)
75-78
42
37
25
22
17
8
9
7
5
1
1
1
>78
6
5
3
4
3
1
1
1
1
0
0
0
All
115
81
55
74
44
24
36
21
13
9
3
2
Table 3.12
Percentage of observed fatigue cracks located on joints classified as non-critical with respect to fatigue
crack growth by the theoretical analysis. The percentage in brackets includes also tertiary structural
components.
% of fatigue cracks observed which is located on joints were inspection would not have
been recommended by PIA
Year
fatigue 30 %
fatigue 50 %
fatigue 70 %
fatigue 90 %
of
βt =
βt =
βt =
βt =
βt =
βt =
βt =
βt =
βt =
βt =
βt =
βt =
Instal.
0.5
2.0
3.7
0.5
2.0
3.7
0.5
2.0
3.7
0.5
2.0
3.7
<75
0.47 0.27 0.19 0.42 0.21 0.13 0.33 0.16 0.09 0.19 0.05 0.02
(.51) (.24) (.18) (.49) (.19) (.13) (.42) (.16) (.10) (.20) .05) (.03)
75-78
0.58 0.51 0.34 0.46 0.35 0.17 0.31 0.24 0.17 0.07 0.07 0.07
>78
0.75 0.63 0.38 0.67 0.50 0.17 0.50 0.50 0.50
All
0.51 0.36 0.24 0.44 0.26 0.14 0.32 0.19 0.12 0.16 0.05 0.04
To obtain a measure of the fatigue cracks not detected by a target reliability inspection planning
procedure, the number of detected fatigue cracks need to be related to the number of inspections.
Table 3.13 gives the number of new inspections, i.e. no crack observed previously on joint, as a
function of asymptotic reliability level β a. It is noted that table 3.13 is only marginally different from
table 3.6.
Table 3.13
Number of new inspections as a function of asymptotic reliability of through thickness crack. Numbers
in brackets include inspection on tertiary structural components
# of new inspections performed
Year of
βa < 0.5
βa > 0.5
βa > 2.0
βa > 3.7
installation
355 (413)
1060 (1123)
840 (863)
645 (659)
< 75
240 (252)
1298 (1303)
1161 (1162)
924 (924)
75-78
18 (18)
259 (260)
167 (168)
62 (62)
> 78
613 (683)
2617 (2686)
2168 (2193)
1631 (1645)
All
Tables 3.14 to 3.17 give the percentage of inspections performed with resultant fatigue crack
detection. The data are sorted according to asymptotic target values. Tables 3.14 to 3.17 give the
percentage for different classification criteria of fatigue crack.
16
The tables 3.14 to 3.17 document a correlation between low asymptotic reliability levels and
percentage of inspections with fatigue crack detection. The inspections performed on joints identified
by PIA for inspection resulted in 4 to 7 times as many fatigue cracks being detected as in the joints not
recommended for inspection. It is noted that tables 3.14 to 3.17 are only marginally different from
tables 3.7 to 3.10. Tables 3.18 to 3.21 correspond to tables 3.14 to 3.17 with tertiary structural
members excluded. Only minor changes are observed.
Table 3.14
Percentage of new inspections as defined in table 2.2 with the results fatigue crack detection as a
function of asymptotic reliability of through thickness crack. A fatigue crack is defined as a detected
crack with a 30 % belief of being a fatigue crack.
% of inspections with the result fatigue crack detection, crack classification
Year of
FAT30%
installation
βa < 0.5
βa > 0.5
βa > 2.0
βa > 3.7
9.3
5.7
5.5
23.7
< 75
12.3
3.2
3.2
2.7
75-78
11.1
2.3
3.0
4.8
> 78
5.7
4.1
3.9
19.2
All
Table 3.15
Analogous to table 3.14 with 50 % belief of detected crack to be a fatigue crack.
% of inspections with the result fatigue crack detection, crack classification
Year of
FAT50%
installation
βa < 0.5
βa > 0.5
βa > 2.0
βa > 3.7
20.8
7.2
3.6
3.2
< 75
10.3
1.7
1.5
0.9
75-78
11.1
1.5
1.8
1.6
> 78
16.7
4.0
2.3
1.8
All
Table 3.16
Analogous to table 3.14 with 70 % belief of detected crack to be a fatigue crack.
% of inspections with the result fatigue crack detection, crack classification
Year of
FAT70%
installation
βa < 0.5
βa > 0.5
βa > 2.0
βa > 3.7
17.9
4.8
2.3
2.0
< 75
7.9
0.7
0.6
0.5
75-78
5.6
0.4
0.6
1.6
> 78
13.9
2.4
1.3
1.2
All
Table 3.17
Analogous to table 3.14 with 90 % belief of detected crack being a fatigue crack.
% of inspections with the result fatigue crack detection, crack classification
Year of
FAT90%
installation
βa < 0,5
βa > 0.5
βa > 2.0
βa > 3.7
11,1
1,7
0,3
0,3
< 75
5,6
0,1
0,1
0,1
75-78
0,0
0,0
0,0
0,0
> 78
8,8
0,7
0,2
0,2
All
17
Table 3.18
Percentage of new inspections with the result fatigue crack detection as a function of asymptotic
reliability of through thickness crack. A fatigue crack is defined as a detected crack with a 30% belief of
being a fatigue crack. The observations on tertiary structural components are not included.
% of inspections with the result fatigue crack detection, crack classification
Year of
FAT30%
installation
βa < 0.5
βa > 0.5
βa > 2.0
βa > 3.7
21.4
6.3
4.6
4.2
< 75
12.9
3.2
3.2
2.7
75-78
11.1
2.3
3.0
4.8
> 78
17.8
4.4
3.7
3.4
All
Table 3.19
Analogous to table 3.18 with 50 % belief of detected crack being a fatigue crack.
% of inspections with the result fatigue crack detection, crack classification
Year of
FAT50%
installation
βa < 0.5
βa > 0.5
βa > 2.0
βa > 3.7
18.3
4.5
2.9
2.3
< 75
10.8
1.7
1.5
0.9
75-78
11.1
1.5
1.8
1.6
> 78
15.2
2.8
2.0
1.5
All
Table 3.20
Analogous to table 3.18 with 70 % belief of detected crack being a fatigue crack.
% of inspections with the result fatigue crack detection, crack classification
Year of
FAT70%
installation
βa < 0.5
βa > 0.5
βa > 2.0
βa > 3.7
15.2
2.5
1.5
1.1
< 75
8.3
0.7
0.6
0.5
75-78
5.6
0.4
0.6
1.6
> 78
12.2
1.4
1.0
0.8
All
Table 3.21
Analogous to table 3.18 with 90 % belief of detected crack being a fatigue crack.
Year of
installation
< 75
75-78
> 78
All
% of inspections with the result fatigue crack detection, crack
classification FAT90%
βa <
0,5
9,6
5,8
0,0
7,8
β a > 0.5
βa >
0,8
0,1
0,0
0,3
2.0
0,2
0,1
0,0
0,1
β a > 3.7
0,2
0,1
0,0
0,1
The inspections, which gave the results in table 3.14 to 3.17, were mainly performed upon structures
with 1 to 18 years in service. Since fatigue crack growth is a cumulative process, the number of
detectable fatigue cracks would be expected to increase with years in service. If the results in table
3.14 to 3.17 had been based on inspections performed upon 20 to 30 years in service, the percentages
would be higher.
18
3.3.4 Discussion of the Results from the Qualitative Comparison
To summarise:
−
Tables 3.1 and 3.2 show the theory to be conservative. The number of predicted fatigue cracks
are between 3 and 20 times too high.
−
Tables 3.3, 3.4 and 3.5 show that between 10 to 50 % of the detected fatigue cracks could be
detected prior to the recommended time of inspection.
−
Table 3.12 shows that between 10 and 40 % of the detected fatigue cracks would not have been
detected if the inspections were limited to the recommendations given from the target inspection
planning procedure.
−
Tables 3.7 to 3.10 show that up to 4 % of the intersections have developed detectable fatigue
cracks before the intersections are scheduled for inspection.
−
Tables 3.14 to 3.21 indicate that 1 to 5 % of the intersections, which would never be scheduled
for inspection, have fatigue crack growth.
−
Table 3.7 to 3.10 and 3.14 to 3.21 indicate the percentage of intersections with fatigue cracks
are 5 to 10 times higher for the joints recommended for inspection by the target reliability
inspection planning methods than for the joints not scheduled for inspection.
For evaluation of the results presented above, the following two items should be taken into
consideration:
1. The inspections performed are not randomly selected although they are not recommended by
theoretical analysis, ref. /10/.
2. The inspections are performed after a limited time in service. The inspected joint may have
developed a small fatigue crack which has not been discovered, i.e. for random selected inspection
item, the percentage of fatigue crack detection will increase with time in service.
Effect of point 1
The inspections performed which are not in accordance with the recommendations of PIA may be
scheduled due to, ref. /10/:
−
−
−
−
low fatigue life estimate given from an old fatigue analysis
a high static stress level
identified poor detail design or workmanship
suspicion based on visual inspection
The effect of point 1 above indicates the percentage of inspections with fatigue crack detection given
in table 3.7 to 3.10 and 3.14 to 3.21 to be higher than the percentage given from a random selection of
inspection on the joints not scheduled for inspection by the target reliability inspection planning
procedure. The percentages of inspections with the resultant fatigue crack detection are therefore
higher for inspection based on these criteria than random inspection. The percentage of inspections not
scheduled by the target reliability inspection planning procedure with the resultant fatigue crack
detection given in table 3.14 to 3.21 may not be used as a lower bound value. A lower bound value of
19
the percentage of intersections classified as low fatigue potential joints, which are to develop fatigue
crack growth.
Effect of point 2
Since the inspections are performed on structures with 1 to 18 years in service, there have been very
few years for potential fatigue cracks to develop. If the results in tables 3.7 to 3.10 and 3.14 to 3.21
had been based on inspections performed upon 20 to 30 years in service, it is likely that the
percentages would have been higher. The percentage of inspections not scheduled by the target
reliability inspection planning procedure with the result fatigue crack detection given in table 3.7 to
3.10 may therefore be uncertain, but may be used as an upper bound value.
However, the results given in tables 3.7 to 3.10 are assumed to be practical upper bound values. The
effect of point 1 above in addition to use of the reliability level at the time of inspection as the
classification criteria, is more likely to have a higher impact on the results than the effect of point 2.
For a North Sea Jacket, typically 20 % of the brace to chord intersections should be inspected by EC
or MPI during the structure’s lifetime.
Based on the results presented above, the target reliability inspection planning procedure will detect
approximately 30-40 % of the fatigue cracks present.
To increase the per cent of detection, the target reliability inspection planning procedure should be
improved or the required amount of inspection should be increased. Section 4 presents a method and
results from a more quantitative comparison between theoretical predictions and in-service
observations. A quantification of the deviations could be used for improvement of the target reliability
inspection planning procedure.
20
4. Quantitative Comparison of the theoretical predictions
and in-Service Observations.
4.1 INTRODUCTION
For the in-service observations collected, the majority of inspections have not been performed
according to the recommendations from the probabilistic inspection-planning tool PIA. The reliability
level against fatigue crack growth varies from joint to joint and upon time in service. The inspections
as indicated in figure 4.1 have been performed using a scattered level of reliability for fatigue crack
growth. To compare the reliability indices given by the theory and observations collected, the first step
has been to sort the observations according to the joint’s reliability level when the inspections were
performed.
Inspection
Item
β4
β
β3
t i4
β2
t i3
β1
t i2
t i1
Time In Service
Figure 4.1
The joints inspected have a scatter of reliability level against fatigue crack when the inspections were
performed.
Table 4.1 presents the number of inspections and fatigue crack detection as a function of the joints
reliability against fatigue crack growth when the joint was inspected.
21
Table 4.1
Observations as function of calculated reliability for fatigue crack detection. The table contains the
inspection history of the structures installed before 1975.
# of obser-vations # of fatigue cracks
Observed frequency of Φ(−β) Theory/
β
fatigue cracks
Prediction
-3.5
60
16.45
0.27
0.9997
-2.5
60
16.28
0.27
0.9938
-1.5
94
14.85
0.16
0.9332
-0.5
184
30.24
0.16
0.6915
0.5
289
47.36
0.16
0.3085
1.5
374
18.42
0.05
0.0668
2.5
402
17.36
0.04
0.0062
3.5
73
6.68
0.09
0.0002
Figure 4.2 is a plot of the data in table 4.1. The first column in table 4.1 contains the calculated
reliability for fatigue crack detection, i.e. the horizontal line in figure 4.2. The second column gives
the number of inspections performed for the different reliability classes, i.e. the reliability of inspected
joint at time of inspection. Column 3 gives the number of the inspections from column 2 with result in
the detection of a fatigue crack. Column 3 is the sum of the given percentage belief that the detected
cracks are due to fatigue.
Column 4 in table 4.1 is the ratio between column 3 and 2 and represents the frequency of occurrence
for the event fatigue crack detection, i.e. the bars given in figure 4.1. Column 5 is the theoretical
predicted probability of frequency of occurrence for the event fatigue crack detection, i.e. the upper
curve in figure 4.1. The curve fit to the bars values is the adjusted frequency of occurrence for the
event investigated. The deviation between the adjusted curve and the theoretical predictions give a
quantitative measure of the deviation between in-service observations and theoretical predictions.
Section 4.2 gives a description of how to measure the deviation between the theoretical prediction and
adjusted curve, i.e. curve fit to the observed frequency, ref. /1/.
1
0,9
0,8
0,7
0,6
Frequency
0,5
Adjusted
Theory
0,4
0,3
0,2
0,1
0
-3,5
-1,5
0,5
2,5
Figure 4.2
Observed frequency and calculated probability of fatigue crack detection as function of calculated
reliability.
22
4.2 THE quantitative measures of deviation between theoretical prediction and
observation, regression analysis.
4.2.1 Method
The probability and the corresponding reliability index for observed events were calculated. Each
observation was either true or false related to the event. A comparison between the observed results
and the reliability index was done by a binumerical regression, ref. /1/, /11/:
µ = Φ(c0 + c1 β (T))
where :
µ
c0
c1
Φ(-)
β (T)
-
the parameter compared with the observed frequency of event
constant adjustment parameter
adjustment factor related to the reliability index from PIA
is the standard normal distribution function
the reliability index calculated by PIA
The estimates of the parameters c0 and c1 were obtained by using a maximum likelihood estimator, i.e.
the estimate which minimises the discrepancy between the y-values (the observed frequency of event)
and µ -values (curve fitted value for the event frequency), see figure 4.3, ref. /1/. The format of figure
4.3 is comparable to format of figure 4.2.
If a perfect relation between predictions by PIA and experienced crack occurrence existed, c0 and c1
would be 0 and -1, respectively. The c0 and c1 estimates are described by mean value and standard
deviation. A simple measure for the correspondence between predicted and experienced fatigue
cracks, is the significance parameter (Z) given by the ratio between the mean value and the standard
deviation of the parameter c1, i.e. Z=c1/st.dev.c1, ref. /11/.
A high negative ratio indicates confidence in the trend obtained, i.e. a significance parameter z
= -3.7 will indicate a probability of Φ(z) = Φ(-3.7) = 0.999 related to a positive correlation
between the theoretical estimates and observations.
Φ(⋅)
Observed frequency of
occurrence, y-value
1.0
Absolute value of c0/c1
Theoretical value
0.8
Binumerical regression = µ
0.6
Φ(c0+c1)
β(Τ))
Φ(-β(Τ))
0.4
-8.00
-4.00
0.00
4.00
8.00
Figure 4.3.
Curve fitted frequency and the theoretical prediction.
23
β(T)
4.2.2 The Results of the Regression Analysis
To identify the deviation between theoretical predictions and in-service observations, combinations of
events for comparison and different sub-sets of data were used. For the event fatigue crack detection,
table 4.2 contains a presentation of different subsets of data analysed. Tables 4.2 and 4.3 contain
summaries of the results given in figure 4.4 to 4.8.
Tables 4.4 and 4.5 show the regression analyses results for the event crack detection with crack depths
of more than 5 mm and detection of through thickness crack respectively. Tables 4.4 and 4.5 have
equal subsets of data definition as table 4.2.
Table 4.2
Results of regression analyses.
Terminology:
All structures
: The inspection history from 27 jacket structures
Gr. 1
: The inspection history from platforms installed before 1977
Gr. 2
: The inspection history from platforms installed after 1977
Primary
: The inspection history from primary structural components.
Secondary
: The inspection history from secondary structural components.
Tertiary
: The inspection history from tertiary structural components.
El. 20’
: The inspection history from structural components located above water.
El. -20’
: The inspection history from components located 15’ to 40’ below water.
El. -65’
: The inspection history from components located 41’ to 70’ below water.
El. > -70’
: The inspection history from components located more than 70’ below water.
All inspections : Include first, second and repair inspection.
First inspect.
: Inspection events without previous inspection.
Second inspect. : Inspection events when previous inspection has been performed.
Repair inspect. : Inspection events when previous inspection and repair have been performed.
Regression
Figure
Structures /
# Observ.
# Fat.
Inspection Sequence
Components
crack
1
4
All structures
3230
260
All inspections
2
4
Gr. 1
1937
249
All inspections
3
4
Gr. 2
1293
11
All inspections
4
3 and 5
All structures
2741
180
First inspection
5
5
All structures
628
42
Second inspection
6
5
All structures
374
91
Inspection upon repair
7
6
Primary
1976
53
First inspection
8
6
Secondary
628
72
First inspection
9
6
Tertiary
137
54
First inspection
10
7
Elev. 20’
890
194
First inspection
11
7
Elev. -20’
303
13
First inspection
12
7
Elev. -65’
400
37
First inspection
13
7
Elev. > -70’
344
5
First inspection
24
inspected
finding
frequency
regression line
50 %
900
theoretical
value
800
number
600
30 %
500
400
frequency
40 %
700
300
200
100
0
0%
-4.5
-3.5
-2.5
-1.5
-0.5
2.5
3.5
4.5
5.5
6.5
β - value related to fatigue crack detection
Figure 4.4
All structures - First inspection- Event fatigue crack detection, regression 4 in Table 4.2.
0,7
Frequency of
occurrence
Frequency of
occurrence
0,7
0,6
0,6
0,5
Predicted
Gr. 1
0,4
Gr. 2
0,3
-4
-2
Predicted
0,4
Second Insp.
Insp. upon repair
0,3
All struct.
First Insp.
0,2
0,2
0,1
0,1
0
0
-6
0,5
0
2
4
6
-6
8
-4
-2
0
2
β - value related to fatigue crack detection
Figure 4.5 Regression organised upon installation year.
Regression 1, 2 and 3 in Table 4.2.
0,7
4
6
8
β - value related to fatigue crack detection
Figure 4.6 Regression organised upon inspection history
included. Regression 4, 5 and 6 in Table 4.2.
0,7
Frequency of
occurrence
0,6
Frequency of
occurrence
Predicted
0,6
El. 20'
0,5
Predicted
0,5
El. -20'
0,4
Primary
0,4
El. -65'
Secondary
0,3
0,3
El. >-65'
Tertiary
0,2
0,2
0,1
0,1
0
0
-6
-4
-2
0
2
4
6
8
-6
-4
0
2
4
6
8
β - value related to fatigue crack detection
β - value related to fatigue crack detection
Figure 4.7 Regression organised upon member importance
included. Regression 7, 8 and 9 in Table 4.2.
-2
Figure 4.8 Regression organised upon location in structure.
Regression 10,11, 12 and 13 in Table 4.2.
The quantified deviation is given by the regression parameters defined in section 4.1. Table 4.3
contains the regression parameter values for the analysis defined in table 4.2.
25
Table 4.3
The regression parameters for the regression analysis defined in table 4.2 for the event fatigue crack
detection. It is noted that the Z value is significance test parameter, se Section 4.2.1.
Regression
C0
C1
Z - value
# of
# Fat. crack
observ.
detections
1
-1.42
-0.17
-11.4
3230
260
2
-1.2
-0.15
-8.1
1937
249
3
-2.84
-0.01
-0.09
1293
11
4
-1.62
-0.23
-14.7
2741
180
5
-1.48
-0.61
-6.8
628
42
6
-0.57
-0.20
-2.4
374
91
7
-1.97
-0.20
-7.6
1976
53
8
-1.86
-0.32
-8.0
628
72
9
-0.43
0.10
1.4
137
54
10
-0.85
-0.13
-4.6
890
194
11
-2.02
-0.20
-2.8
303
13
12
-1.53
-0.17
-4.4
400
37
13
-2.36
-0.37
-4.7
344
5
Regression
1
2
3
4
5
6
7
8
9
10
11
12
13
C0
-1.7
-1.6
-2.3
-1.67
-1.70
-1.26
-1.80
-3.22
-1.01
-1.3
-1.9
-4.4
-1.9
Table 4.4
Analogous to table 4.3 for the event crack > 5 mm.
# of observ. Crack > 5mm
C1
Z - value
-0.08
-5.4
3230
94
-0.07
-4.0
1937
82
-0.01
-0.2
1293
12
-0.19
-10.5
2741
96
-0.20
-2.5
628
9
-0.05
-0.8
374
34
-0.07
-3.1
1976
44
-0.59
-7.5
628
29
0.06
1.0
137
23
-0.06
-2.5
890
65
-0.15
-2.2
303
4
-0.72
-4.6
400
7
-0.07
-1.1
344
6
26
Table 4.5
Analogous to table 4.3 for the event through thickness cracks (na = not applicable since the event
“through thickness crack” has not occurred).
Regression
# of observ. Through
C0
C1
Z - value
thickness
cracks
1
-2.3
-0.09
-3.9
3230
19
2
-2.2
-0.09
-3.1
1937
16
3
-2.7
-0.02
-0.3
1293
3
4
-2.4
-0.12
-5.2
2741
12
5
na
na
na
628
0
6
-1.8
-0.12
-1.7
374
6
7
-2.5
-0.16
-4.9
1976
2
8
-2.4
-0.17
-3.4
628
6
9
-1.9
-0.01
-0.1
137
4
10
-1.9
-0.12
-3.6
890
14
11
na
na
na
303
0
12
-3.0
0.12
1.4
400
2
13
na
na
na
344
0
4.2.3 Comments Related to the Regression Analysis Results
The results identify the application area of the theoretical method. The results presented in figure 4.7
show that the FLS procedure investigated does not describe the fatigue crack growth for tertiary
structural components i.e. conductor ladder, walkways, support arrangement of attachment structures
etc. Structural components used as support of inlet/outlet piping or risers may also be classified within
this category.
The results for the main structure and the main horizontal frame components reveal a correlation
between theory and observation. A 95 per cent confidence interval for the inclination parameter c1 is <
0.275, 0.324> for the comparison event fatigue crack detection. The correlation for the group 2
structures, i.e. structures installed after 1977, is not significant, see figure 4.5. The number of observed
fatigue cracks may be too low for statistical treatment. Other explanations may be errors or an
excessive uncertainty in the crack classification, i.e. fabrication cracks may have been classified as
fatigue cracks.
Figure 4.5 shows that the regression curve is unconservative for β higher than 1.5. An explanation
may be partly due to the uncertainties associated with the crack classification procedure. Each crack
was given a probability as being a fatigue crack. Since the crack evaluation is uncertain, one or several
fabrication cracks may have been classified as fatigue cracks. Gross errors for β > 1.5 and β < -1.5
will have a major impact on the regression curve. Gross errors may be related to the FLS analysis,
inspection work and crack classification. Finally the small number of cracks for high β‘s make the
observations uncertain in this range.
The theory may therefore generally be evaluated to be conservative although the observation of
regression curves to be unconservative for β higher than 1.5.
The present procedure is concluded to generally be applicable for the main structure and horizontal
frame components. The theory applied may not identify the improvements of the second-generation
North Sea structures, i.e. structures installed after 1977.
27
The discussion above is mainly related to the comparison based on the event fatigue crack detection.
The correlation between observations and predictions is reduced for the comparison events crack > 5
mm and through thickness crack, ref. Table 4.4 and 4.5. The limited number of observations may only
partly be the reason for this reduction. An increased degree of over-prediction and reduced value of
the inclination parameter c1 may also indicate limitations in the fracture mechanics crack growth
model. The predicted crack growth rate may be more conservative than the fatigue crack occurrence
rate.
The results presented in ref./8/ find that the initial crack size is 0.36 mm instead of 0.11mm, which is
used for this analysis. A combination of reduced hot spot stresses and the new data for initial crack
depth will most likely improve the correlation. The improvements are assumed to have higher impact
on the comparison criteria related to deeper crack depth i.e. “crack depth > 5mm” and “through
thickness crack”.
As mentioned above it is desirable that the uncertainty and possibility for cross errors in the fatigue
crack classification are further investigated. The comparison results could be very sensitive to the
crack classification quality, see Section 3 and the use of different crack classification criteria and ref.
/1/.
The observed reduction in correlation as function of comparison criteria may also be explained by
small fabrication defects believed to be fatigue cracks, i.e. defects located in joints evaluated to have a
high potential for fatigue crack growth. For the comparison criteria of deeper cracks, the classification
uncertainty is assumed to be reduced due to more information available during the classification
process. Further investigation is recommended.
The uncertainty of the variable used in the theoretical model represented by the parameters standard
deviations may be to low. Increased uncertainty for the theoretical predictions changes the slope of the
curve of theory or prediction given in Figure 4.2 to 4.8. The predicted frequency of occurrence will be
reduced for the low reliability values and the predicted frequency will increase for high reliability
values. The over prediction ratio will be reduced and the issue of unconservative predictions may be
removed or limited.
28
5. The Concept of Adjustment Factors
5.1 INTRODUCTION
An improvement of the theoretical predictions requires a physical interpretation of the observed
deviations. All potential areas for deviation are identified through a systematic description of the
process of the predictions i.e. the theoretical analyses required to estimate the fatigue potential and the
probability for fatigue crack growth, ref. /1/ /3/.
The systematic identification of where and how the prediction process has a potential for systematic
deviations and/or introduction of uncertainties are pin-pointed through a definition of an adjustment
factor Λi, for the uncertainty element i, ref. /1/ /3/. A presentation of the uncertainty elements is given
in ref. /3/.
The aim of this section is to present a summary description of the method applied and the results from
the sensitivity calculations of the regression parameters defined in Section 4 related to the adjustment
factors Λi. An approach for adjustment of the theoretical predictions to improve the correlation
between the predictions and observations will also be presented and discussed.
5.2 METHOD FOR CALCULATION OF THE SENSITIVITY MEASURES.
The deviation between theory and observation is given by the regression analysis results as the
parameter values c0, c1 and Z defined in chapter 4 and ref. /3/. The sensitivity measures
∂c0
,
∂Λ i
∂c1
∂Z
and
is deduced through three steps. The three steps or level of sensitivity measure related
∂Λ i
∂Λ i
to the adjustment factor as a function of the adjustment factorΛi, are:
−
−
−
the sensitivity of the basic variable θk used for input to PIA
the sensitivity of the reliability estimate β for given comparison event
the sensitivity of the regression parameters c0, c1 and Z
The first two steps are related to the sensitivity of the reliability indexes
∂β
, see eq. (5.1).
∂Λ i
∂β
∂β ∂θ k
=
•
∂Λ i ∂θ k ∂Λ i
(5.1)
where
β
θk
Λi
−
−
−
The reliability index for a given observation related to selected event
The basic variable k used as input to the PIA analysis program
The given adjustment factor i
29
The terms
δβ
δθ k
are given as a result from the PIA analysis. The terms
are deduced according to
δθ k
δΛ i
one procedure related to the adjustment factors for the FLS analyses uncertainty elements, and one
procedure for the adjustment factors related to the PIA uncertainty elements, ref. /1/.
The aim is to identify the regression parameter’s sensitivity related to the defined adjustment factors i.e.
calculate the sensitivity of the regression control parameters (c0, c1 and Z) :
∂Z
∂Λ i
∂c0
∂c1
for i=1,n
(5.2)
∂Λ i
for i=1,n
(5.3)
∂Λ i
for i=1,n
(5.4)
where n is the number of uncertainty parameters.
Based on the identified sensitivity measures, the aim is to establish an optimal set of adjustment
parameters by tuning the adjustment factor values to give c0 = 0 and c1 = -1.0 with a Z-value above a
given required value. The sensitivity measures are calculated by an incremental 10 % increase of the
adjustment factors. The regression parameters are calculated for the adjustment factors equal to 1.0 and
1.1, i.e. the initial values c00, c10, Z0 and the incremental values c0i, c1i and Zi. The sensitivity measures
are given as :
∂Z
∂c0
∂c1
(
) (01.⋅ Λ )
= ( c − c ) ( 01
. ⋅Λ )
= ( c − c ) ( 01
. ⋅Λ )
i
0
∂Λ i = Z − Z
∂Λ i
∂Λ i
i
for i=1,n
(5.5)
i
0
0
0
i
for i=1,n
(5.6)
i
1
0
1
i
for i=1,n
(5.7)
The first regression analysis as presented in Section 4 and ref. /1/, quantifies the initial values c00, c10
and Z0. The incremental regression analysis parameters c0i, c1i and Zi are for each adjustment parameter
calculated from a new regression analysis where the reliability index for each observation is adjusted
by :
β new = β old + (∂β ∂Λ i ) ⋅ 01
. ⋅ Λi
(5.8)
where ∂β/∂ Λi is given as described above.
A total of n regression analyses where the n adjustment factors are successively given an increment of
10% define the incremental values c0i, c1i and Zi. The established sensitivity factors ∂Z/∂Λi , ∂c0 /∂Λi
and ∂c1 /∂Λi are used to estimate new regression parameter values based on the suggested values of
adjustment factors, i.e.
Z new = Z 0 + ∂Z ∂Λ i ⋅ ( Λ i − 1)
(5.9)
c0,new = c00 + ∂c0 ∂Λ i ⋅ ( Λ i − 1)
(5.10)
c1,new = c10 + ∂c1 ∂Λ i ⋅ ( Λ i − 1)
(5.11)
30
A flow chart of the regression process is presented in Figure 5.1.
The different adjustment factors Λi will have a scatter or sensitivity related to the different predicted
potential for fatigue crack growth for the individual joints. A change in the adjustment factor Λi may
only have effect on the predicted fatigue potential for a subset of observed intersections, ref. /3/.
Quantify the PIA system’s ability to predict the occurrence of
fatigue cracks by initial regression analyses.
Identify the uncertainty elements in the prediction process.
To each uncertainty element define an adjustment factor for
systematic deviation Λb,i and one for uncertainty adjustment
Λu,i. It will be a subjectively selected start point for an iteration
to achieve adjustment values for a best fit between
theoretical simulations and in-service observations.
Calculate updated reliability index’s :
β new = β old + (∂β ∂Λ i ) ⋅ ∆Λ i
The different brace/chord intersections will only be affected
by a subset of uncertainty elements. Which uncertainty
elements affecting will change for the different intersections.
Perform regression analyses based on theadjusted reliability
index i.e. βnew . Calculate the sensitivity of the regression
control parameters (c0, c1 and Z), i.e.
∂Z
for i=1,n
∂Λ i
∂c0
for i=1,n
∂Λ i
∂c1
for i=1,n
∂Λ i
Establish an optimal set of adjustment parameters by tuning
the bias values to give c0 = 0 and c1 = -1.0 with as high Zvalue as possible.
Perform a physical interpretation of the selected adjustment
values and modify the selections.
Figure 5.1
Flow chart for interative calibration of PIA.
31
5.3 RESULTS OF THE SENSITIVITY ANALYSIS.
An increment in parameter Λi, was used to find the curve inclination used as an estimate for the
derivative i.e. calculate the sensitivity of the regression control parameters (c0, c1 and Z) :
∂Z/∂Λi
∂c0 /∂Λi
∂c1 /∂Λi
,
,
,
for i= 1, 66
for i= 1, 66
for i= 1, 66
Derivative estimates for an increment of +10% and -20% of the adjustment factor i = 1 to 66 were
calculated, ref. /3/. To evaluate the application area of the derivative the two estimates are compared.
The functional relationship between the regression parameter (C0, C1, Z) and some of the adjustment
factors Λi are also given by a second order curve fitting. The curve fitting was first done for the
adjustment factor values Λi = {0.8, 1.0, 1.1} and secondly for the values Λi = {0.6, 0.8, 1.0, 1.1, 1.4}.
Appendix A in ref. /3/ gives a description of the adjustment parameters and discusses the adjustment
factors effect on the regression parameters.
The process to identify a vector of adjustment factors which optimises the regression
parameter c0 = 0.0, c1 = -1.0 and Z as negative as possible was assumed to be performed by
use of the sensitivity parameter. The regression sensitivity parameters are based on the
assumption of independence among the adjustment parameters. This assumption may not be
possible to use. A separate computer program was developed for more effective calculation of
new regression parameters based on the sensitivity of the reliability index, as a function of a
change in the adjustment parameters. Ref. /3/ presents the adjustment factor vectors used for
calculation of new regression parameters.
To validate the adjustment parameter selected from the sensitivity study, new PIA analyses were
performed. The selected case was test vector 53 ref. /3/ and the structure 1 inspection history (263
NDT inspections, 55 cracks and 30 were assumed to be fatigue cracks). Tables 5.1 to 5.3 contain the
regression parameter values for the initial PIA calculation, the adjustment based on sensitivity values,
and the new PIA calculations.
Table 5.1
The regression parameters for comparison criteria “fatigue crack detection”
Analysis
C0 – value st.err. C0
C1 -value
st.err. C1
Z-val.
Initial analysis
-1.51
0.16
-0.16
0.05
-3.4
Adjusted by sensitivity
-0.14
0.17
-0.86
0.18
-4.8
New PIA analysis
-3.21
1.095
-0.98
0.48
-2.1
Pr(C1<0)
100.0%
100.0%
98.0%
Table 5.2
The regression parameters for comparison criteria “crack > 5mm deep”
Analysis
C0 – value st.err. C0
C1 -value
st.err. C1
Z-val.
Initial analysis
-1.63
0.17
-0.13
0.05
-2.6
Adjusted by sensitivity
-0.28
0.23
-0.82
0.21
-3.8
New PIA analysis
-2.00
0.49
-0.29
0.22
-1.3
Pr(C1<0)
99.5%
100.0%
91.1%
Table 5.3
The regression parameters for comparison criteria “through thickness crack”
Analysis
C0 - value
st.err. C0
C1 -value
st.err. C1
Z-val.
Initial analysis
-2.3
0.26
-0.07
0.08
-0.8
Adjusted by sensitivity
-1.3
0.33
-0.84
0.45
-1.9
New PIA analysis
-2.9
1.14
-0.33
0.49
-0.7
Pr(C1<0)
78.9%
97.8%
75.1%
32
The selected set of adjustment parameters based on the sensitivity study does not seem to give the
desired result. Based on the system developed the analyses are very time consuming and further
investigation may require new developments (on the given test set the PIA analyses required 2 - 3 days
work. For a change of order 5 % in one of the 66 adjustment factors, new PIA analyses are required. A
calibration based on the present procedure and analyses tool will therefore require approximately
m.hrs. 3-5000 to identify a limited numbers of alternative vectors of adjustment factor values and
concludes with a firm recommendation). The analyses computer programs, the electronic database and
the procedure for sensitivity analyses will from a practical point of view require modification before
reasonable results are obtained.
The separate study on the initial crack size ref. /8/ recommends a model change in PIA. The
calibration or optimisation of the adjustment parameter was performed on the present model. An
optimisation may require the PIA model to develop a new model for description of initial crack depth.
5.4 ADJUSTMENT BASED ON A LIMITED NUMBER OF VARIABLE
The sensitivity values have internal dependency and provide a fuzzy picture. As a first step, a
simplified adjustment was performed. The adjustment was based on a reduced number of adjustment
factors.
The total number of 66 adjustment factors is related to both the FLS and PIA analysis. The uncertainty
elements of the FLS analyses are summarised and transformed into the PIA analysis through the
variable representing the long-term hot spot stresses. A major simplification was to limit the
evaluation of the FLS uncertainties to the adjustment of the Weibull scale parameter lnA in the longterm distribution of the hot spot stresses.
A separate study of the basic variable a0 for the initial crack depth and the POD value of the inspection
methods used ref. /8/, indicated a need for major adjustments of these variables. Based on sensitivity
studies and evaluation of the potential for improvements, the compliance function Y and the material
parameter m were also included for adjustment, ref. Table 5.6.
Table 5.6
Input parameters changed in adjusted model
Input parameter
Initial crack size
POD-value
Geometry function Y
Crack growth exponent, m
Stress range
Comment
Changed parameter value in the exponential distribution from 0.11 to
0.36 mm according to measured values, see ref. /12/.
Changed parameter value in the exponential distribution from 1.2 / 1.4
to 1.95 mm according to measured values, see ref. /12/.
Selected for modification as initial crack size is altered. Parameter
value in lognormal distribution modified
Selected for modification to represent capacity. Fixed value modified.
Selected for modification to represent load. A normal distributed bias
factor multiplied with value calculated from fatigue lifetime estimate.
A procedure to adjust the selected basic variables to achieve the best possible correlation between
adjusted theoretical analysis and observations was initiated. The observations were given by the
reliability curve β‘ which represents the frequency of occurrence, i.e.
β‘ = c0 + c1∗β T
33
where
β‘ - the reliability value which represents the frequency of observations
c0 - the regression parameter which represents the systematic deviation
c1 - the regression parameter which represents the change of inclination of the
occurrence rate of fatigue cracks upon given fatigue potential estimated
β T - the initial predicted reliability against fatigue crack growth
Two approaches, which we will refer to as, step 1 and 2 have been applied.
Step 1:
A single representative joint is considered. The reliability curve observed β‘ is compared with the
adjusted reliability index β a calculated based on adjustment of the basic variable given in Table 5.6.
The requirement was to perform the adjustment on the basic variables selected which minimised the
dicrepancy e, where
e = Σall iβ‘(lnAi)- β a(lnAi),
i.e. minimum divergence between the curve of β‘ and β a is given as a function of the Weibull scale
parameter which represents the initial given fatigue life. The load parameter lnA was varied within the
range of 1.4 to 3 which represents fatigue life estimates of 5 years to infinity.
Step 2:
A subset of inspections from the database was chosen. In the present case, structures with first time
inspection of at least 15 years after installation were chosen based on relevancy considerations with
regard to a specific structure to be analysed. From the result of step 1 above, one step of the iterative
procedure as outlined in Section 5.2, was performed. There is no intention to combine the two
approaches. The presentation herein should be considered as a combination of results from two
different investigations.
Input parameter
Initial crack size
POD-value
Geometry function Y
Crack growth exponent, m
Logarithm of Stress range
Table 5.7
Revised input parameters
Initial model
Exponential: λ = 0.11
Exponential: λ = 1.2 (MPI)
Lognormal: µ=1.0 cov=0.1
Fixed value 3.1
Normal :µ=X σ=0.20
Adjusted model
Exponential: λ = 0.36
Exponential: λ = 1.95
Lognormal: µ=.9 σ=0.63
Fixed value 3.34
Normal: µ=.769 *X
σ = 0.09238+ 0.0565*X
( X : the result from the FLS calculations, ref.
Figure 8.2 which contains the relationship
between lnA=X and the fatigue life estmate.)
The selected values for the adjusted parameters as presented in Table 5.7, give a significant
improvement of theoretical predictions which represent the observed frequency β‘, see figure 5.2 and
5.3.
The adjustments are based on the deviation between theoretical predictions and observed frequency
for the event fatigue crack detection. A transformation to the event through thickness crack is based on
the functional relationship observed for the initial PIA analysis i.e. the PIA analysis given before
adjustments are given. This relationship is also used to transform the observed “reliability” of fatigue
crack detection to the event through thickness fatigue crack i.e. the calibrated through thickness
reliability curve. Figure 5.2 and 5.3 contain the reliability curves for the cases:
34
Name
NO modification through
thickness
Adjusted through thickness
Description
The original reliability curve calculated by PIA for a fatigue
crack to have grown through thickness.
The reliability curve calculated by PIA upon implementation
of the adjustment given in Table 5.7.
The reliability curve which represent the observed frequency
of occurrence
Calibrated through thickness
crack based on co/c1 for
fatigue crack detection
5
4
3
Reliability
2
1
0
NO modification through thickness crack
-1
Adjusted through thickness crack
Calibrated through thickness crack based
on c0/c1 for fatigue crack detection
-2
-3
1,4
1,6
1,8
2
2,2
2,4
2,6
2,8
3
Weibul scale, lnA
Figure 5.2
The modified reliability index based on the adjustment of the basic variables given in Table 5.7.
Reliability as function of change in Weibull scale parameter lnA.
35
Reliability
Observed vs. Adjusted and Initial Predicted Reliability
5
4
3
2
1
Initial Predicted Reliability
0
-3
-2
-1
0
1
-1
2
3
4
5
NO modification through thickness crack
Adjusted through thickness crack
-2
Calibrated through thickness crack based
on c0/c1 for fatigue crack detection
-3
Figure 5.3
The modified reliability index based on the adjustment of the basic variables given in Table 5.7. The
comparison is given in a β vs. β plot.
The exercise used for adjustment of the calculated reliability based on a limited number of basic
variable has important shortcomings:
−
All brace to chord intersections are equally adjusted although the comparison study clearly
shows systematic deviations between observations and predictions as function of location and
joint characteristics.
−
The adjustments are included with a limited evaluation based on physical interpretations.
−
To restrict the adjustment to only 5 basic variable is most likely a simplification, which gives
major deviations from an adjustment, based on the 66 initial defined adjustment factors.
The example of adjustment factors gives a conservative reliability estimate. The adjustment values in
table 5.7 may from a physical point of view, be explained and related to published research results.
The final adjusted PIA (calibrated PIA) which give reliability estimates representing the frequency of
occurrence, can be obtained by a combination of basic variable definitions and assumption which are
in accordance to published research results.
Generally, for the utilisation of adjustment results based on a limited number of adjustment factors,
which have not been given a physical interpretation and reference to published results, a conservative
approach is required. The philosophy applied for inspection planning is to specify a required amount
of inspection, which give sufficient information to document the adjusted theoretical predictions so
they are conservative.
36
6. Consequences of the Results
6.1 INTRODUCTION
The completed work has measured the deviation between theoretical predictions and in-service
observations. The aim has been a validation of the inspection planning procedures.
The deviations between theoretical predictions and observations are measured. A validation of the
inspection planning procedure is given through the measured performance of the theoretical
predictions. The identified shortcomings suggested a need for improvement of the inspection planning
procedure.
This chapter first discusses the observed major deviations between measured observations and
theoretical predictions for the components with a reliability index, β, level above 2 and less than -0.7,
i.e. probability of 2.3% and 75.8% for the event {through thickness crack} respectively. The observed
unconservative predictions for reliability values greater than 2 are discussed in relation to components
that require a high reliability level.
The observed high degree of overprediction for β < -0.7 may give unconservative reliability values if
Bayesian statistics or comparable methods are used to update the procedure for reliability calculation,
i.e. Bayesian updating of a basic variable by use of the given set of inspection results.
The three last subsections give comments regarding the use of the results for the purpose of design,
operation and life time extension.
6.2 RELIABILITY OF COMPONENTS ESTIMATED TO HAVE LIMITED POTENTIAL FOR FATIGUE CRACK
GROWTH
The comparison study documents the correlation between theoretical fatigue life predictions and
actual fatigue performance. It is also estimated upper bound value of 1 to 4% of joints not scheduled
for inspection by the target reliability inspection planning methods develop cracks, see Section 3. A
mean value of the percentage may be in the order of 1% and the number of fatigue cracks may be
assumed to be Poisson distributed (low probability and a high number of possible occurrences).
The occurrence rate of 1% corresponds to a reliability index of 2.3. This is the observed reliability
index related to the event fatigue crack detection. The interest is related to the reliability against
fatigue failure (for this study the event through thickness crack is defined as a fatigue failure, a
normally conservative approximation). The reliability index is calculated for the event:
−
−
−
fatigue crack detection, β DC
detection of crack deeper than 5 mm, β 5mm
detection of through thickness crack, β ttc
Table 6.1 gives a typical correspondence between the reliability values for the different comparison
events.
37
Table 6.1
Relationship between reliability indexes for different comparison events.
βDC
β5mm
βttc
2.3
4.3
4.8
1.21
2.37
2.88
The observation that approximately 1% of the low fatigue potential welds develops fatigue crack is
related to the event fatigue crack detection β DC. The probability of 1% corresponds to a reliability
index of 2.3. Based on the results in Table 6.1 the fatigue failure reliability will be 4.8, i.e. a through
thickness crack.
As a control of the relationship, the observed percentage of 5mm fatigue cracks is calculated for the
following criteria:
−
−
the fatigue crack classification criterion is 70% belief that the crack will be due to fatigue
the initial fatigue life is more than 800 years, i.e. the reliability level for 30 years service with
no inspection initially required level is above 3.7, see table 3.16.
The observed frequency for the 5 mm crack is 0.8%, which is related to an observed reliability index
of 2.38. The corresponding frequency for the event fatigue crack detection is 1.2%, which is related to
an observed reliability of 1.18. The theoretical predicted values for the correspondence between
reliability values for the different comparison criteria given in Table 6.1 give respectively 2.37 and
1.21, compared with the observations 2.38 and 1.18. The relationship between the different reliability
estimates for the different comparison event seems to correspond with the observations.
The observed development of fatigue cracks in 1% of joints corresponds to components with fatigue
life > 800 years. The observed frequency of 1% is mainly based on observations after 10 to 15 years
in-service. Most likely some joints not observed with crack growth will develop crack growth after 10
to 15 years in-service i.e. the observed frequency of 1% is a lower limit. The deduced reliability value
of 4.8 for through thickness crack will be an upper limit. A reliability level of the order 3.5 to 4.5 may
therefore be used as an upper limit in documented safety against fatigue to be achieved by FLS
analysis. Improved documentation of reliability level will require additional information to be
included. Examples of additional information are:
−
−
−
−
−
inspection performed during operation
high quality fatigue analysis performed for joints
measurements of load effect which are correlated to the long term stress range
additional information of initial weld quality
in-service inspection results given for joints with correlated fatigue potential
The requirement of less than 10-4 probability or reliability index of 3.72 for an accidental event to
occur, ref. /12/, may therefore not be ensured by the requirement of Miner’s sum of less than 0.1.
Additional information as in the example given above is recommended for consideration if the
component has a limited degree of redundancy. The term redundancy may also include
redundancy including presence of a number of fatigue failures. The observed 1% of joints
developing crack growth imply a traditional jacket of 300 brace to chord intersections to have
approximately 3 growing cracks in joints not identified to have a fatigue potential.
38
6.3 IMPLEMENTATION OF THE OBSERVED CONSERVATISM
Generally, the theory predicts 4 to 10 times as many fatigue cracks as observed, see Tables 3.1 and
3.2. Use of reliability methods could be used to obtain a higher degree of optimisation of design,
improved safety, more cost effective operation and life time extension.
The limitations of the theoretical predictions have to be taken into account. As discussed in Section
6.2, the present FLS analysis procedures have more or less an upper limit of reliability, which may be
obtained without additional information, see Section 6.2. At the same time the FLS analysis has a
lower limit of reliability. The theory fails to predict fatigue crack growth with a higher probability
than 30 %, see Figures 4.6 to 4.8.
An adjustment or modification by use of Bayesian statistics to update the general level of reliability or
a limited number of the basic variables in a probabilistic model for fatigue crack growth has to include
the lower bound value of theoretical predictions, i.e. the lower bound for the present industrial
standard of FLS analysis. A very high confidence level in the quality of the prediction, may give
unconservative updated reliability estimates.
The degree of nonconservation in the reliability estimate using Bayesian statistics or comparable
methods to update the procedure/method of prediction reduces as the number of in-service
observations collected increases. The data set has to contain more than a minimum number of
observations and contain observations on components with a scatter level of priori reliability values.
6.4 POTENTIAL EFFECT ON DESIGN
The fatigue life estimate is found to be highly uncertain. The study finds that the fatigue life estimate
is generally conservative. The fatigue limit state for structural components could be further optimised
(the fatigue limit state is one of several design conditions):
−
−
−
−
improved prediction of the fatigue potential may reduce steel weight
improved weld quality may reduce steel weight
inspection during fabrication to give initial reliability level
effect of weld improvements methods may be further utilised
The collected in-service observations are a unique opportunity to measure the fatigue crack prediction
tools quality and identify the cost effect from improvement of quality. The results presented in ref. /8/
show the fatigue cracks mainly start from major fabrication imperfections. Improved fabrication
quality may therefore have a very high impact on the fatigue reliability. The regulations may give the
opportunity to better utilise the effect of improved weld quality and fatigue improvement methods.
The results from this comparison could be reorganised and used for documentation of the effects
related to initial weld quality.
As discussed in Section 6.2, there is an upper limit on the reliability to be obtained by traditional
information from design and fabrication. The study shows the need for special attention to fatigue
exposed components that are not redundant. The possibility for in-service inspection and/or special
quality control during design, fabrication and installation are recommended for these components,
even if the fatigue life is estimated to be greater than 1000 years. The target failure probability of 10-4
(β = 3.72) may not be obtained generally if the assessment is limited to standard procedure for design
and fabrication.
39
The present regulations and guidelines may need to include additional information for components
where reliability levels above 3.72 (probability above 10-4) are required.
6.5 EFFECT ON INSPECTION PLANNING
Reliability analysis is used widely for the purpose of inspection planning related to fatigue crack
growth. The motivation to use this method has mainly been the ability to include information from
inspections performed previously on given joints. Figure 4.6 and the curve for second inspection
regression 4, are documented to give a very good correspondence with the observations. A significant
improved correlation may not be obtainable.
The reliability curve of second inspection upon repair, Figure 4.6 and regression 6 is mainly nonconservative. The repair may either be grinding or welding. The effect of a field weld giving less
fatigue capacity is most likely to be included and the fatigue capacity improvement of the order 10
upon grinding may have been too optimistic. Further investigations are suggested to better distinguish
between the effects of grind repair and repair welding. Initially, it is suggested that a reduction in the
improved fatigue capacity by grinding from a factor of 10 to a factor of 5 and the initial crack size of
field welds to be increased from 0.11 mm to 1 mm.
The data from the structures covered in this study show that the inspection planning procedure is
unconservative for the components with long fatigue lives, i.e. above 165 years (ref. Section 3 and
Figures 4.6 and 4.8. For non-redundant components, inspection is required. Previously, such
components have not been scheduled for inspection if the fatigue life estimate was higher than 800
years which represents a predicted reliability index level of 3.7.
As long as 1 - 4% of the joints not scheduled for inspections have developed detectable fatigue cracks,
the inspection planning should also include an engineering judgement approach. According to Section
3, approximately 40-50% of the fatigue cracks developing is detected on joints, which the theoretical
analyses would not have scheduled for inspection. A requirement for a minimum amount of inspection
is recommended regardless of the theoretical predictions.
As an example, the following recommendations could be used:
−
−
−
−
the number of components with fatigue crack growth is Poisson distributed
a required amount of inspection is specified to verify the components have a reliability above a
specific minimum value (minimum reliability of 2 will require 100 components to be inspected
by FMD)
FMD inspections are specified as a periodic activity
if a through thickness crack is detected the inspection programme has to be expanded and
detailed evaluation performed
6.6 EFFECT ON STRUCTURE ASSESSMENT FOR LIFE TIME EXTENSION
With increasing service life, the uncertainty related to fatigue strength is significantly reduced. Using a
calibrated probabilistic method for the prediction of fatigue crack growth, it should be possible to
predict the reliability for failure by fatigue with a high degree of confidence.
As given in Section 6.4, the lower bound value of the reliability index, estimated from the fatigue life,
should be used. As long as the quality of the probabilistic methods is measured/validated the full
potential of the inspection history may be used. The inspection history will most likely be the item
with highest importance for a structural reliability estimate, i.e. the highest impact on life time
extension.
40
6.7 IMPROVEMENT OF FLS ANALYSIS PROCEDURES
The shortcomings in the FLS procedures were measured. A procedure for systematic comparison of
the theory and reality was developed. The areas for improvement of the fatigue life assessment were
identified in a systematic manner.
41
7. Recommendations for Further Work
7.1 INDUSTRIAL CONSENSUS
The inspection philosophies adopted by operators of offshore structures vary widely. The collation and
utilisation of additional in-service observations will require industry consensus. An example of
concept is the PIA calibration procedure presented in ref. /1/. A strategy is required to achieve
agreement within the industry to use the PIA calibration procedure or identify the improvements
required is to make the procedure, tool and database externally available.
7.2 RECOMMENDED PRACTICE
The results obtained from a probabilistic assessment of the fatigue failure will depend on the values
used for the following key items in addition to the procedure used:
−
−
−
−
the target level to be given as function of the component importance
a maximum value of reliability to be used if additional information and reliability update are not
included
a minimum value of reliability to be used if additional information and reliability update are not
included
level of uncertainty related to load effect and fatigue capacity
The results achieved depend on a combination of procedure used and values given for the key items. A
recommended practice for probabilistic assessment related to the fatigue failure may therefore be
given as an example or reference procedure and values given for the key items. Deviations from the
procedure will require new values to be used for the key items. The new values for the key items
should be given from a comparison between the reference procedure and procedure used. The
comparison with the reference procedure should be performed in relation to one or several uncertainty
elements. An example of a set of uncertainty elements is given in ref. /3/. To establish the reference
procedure the following activities are recommended:
−
−
−
−
−
perform a set of FLS analyses based on an example structure to quantify the deviation between
the procedures used
review of the assumptions and procedure used for the comparison study performed, i.e.
−
fatigue crack classification
−
method for comparison (the regression analysis)
−
review of the result interpretation
improve the database and related analysis tools used in the PIA calibration project which make
them available for external use due to :
−
external quality assurance
−
industry acceptance of the result
−
possibility for other assessment procedure to be compared with the collected information
and reference procedure defined
collect more in-service observations to improve the results from future comparison studies
−
in-service inspection
−
extension of the calibration database and tools to also include measures of load effect
start the process to identify uncertainty elements which are to be adjusted to achieve better
correlation between theoretical predictions and observations
42
7.3 AVAILABILITY OF IN-SERVICE EXPERIENCE
The PIA calibration database and tools for comparison between theoretical predictions and in-service
observations may be compared with the reliability databases by function. As the reliability databases
the concept of PIA calibration is a systemisation of the in-service experience. The reliability databases
focusing the component performance and the PIA calibration database focus the performance of the
theoretical analysis to predict the fatigue crack growth.
To make this concept available for the operators, research organisations, engineering companies and
regulatory bodies, the experience from operation shall be made available.
The industrial development may benefit from one of the example results gained from operational
experience:
−
−
−
−
−
measured bias values of the FLS analysis results
measured values of the FLS analysis level of uncertainty
identification of the FLS analysis application areas
the adjustment required of the PIA predictions to represent the frequency of occurrence
identification of the theoretical predictions’ shortcomings
Other examples of results that can be achieved using the in-service observations collected are:
−
−
−
improved values of the initial crack depth and the POD values of the inspection methods used,
ref. /8/
crack growth rate as function of crack depth which represents observed crack growth, ref. /13/
(the crack growth rate in tubular joints is less than predicted, the preliminary results with
introduction of load shedding give only minor improvements)
Examination of the load effects experienced
43
8. References
/1/
Description of the procedure used in the PIA calibration projects, 580235-N-Q20001, Aker Offshore Partner, Bergen 1997
/2/
The PIA Calibration Database, 580235-N-Q20-002, Aker Offshore Partner, Bergen
1997
/3/
The PIA Calibration Mapping Procedure, 580235-N-Q20-003, Aker Offshore
Partner, Bergen 1997
/4/
The PIA User Manual, Aker Offshore Partner, Bergen 1997
/5/
The PIA Theory Manual, Aker Offshore Partner, Bergen 1997
/6/
PROBAN User Manual, Veritas SESAM system
/7/
PROBAN Theory Manual, Veritas SESAM system
/8/
Moan, T., Vårdal, O.T., Hellevig, N-C, and Skjoldli, K. “In-Service Observations of
Cracks in North Sea Jackets. A Study on Initial Crack Depth and POD Values.”
OMAE-97, Paper1335, Okohama Japan.
/9/
Vårdal,O.T., Moan, T. “Predicted versus Observed Fatigue Crack Growth.
Validation of Probabilistic Fracture Mechanics Analysis of Fatigue in North Sea
Jackets.” OMAE-97, Paper1334, Okohama Japan.
/10/
Experience gained through long term inspection planning programs developed for
Phillips Petroleum Company Norway, Elf Norway, Amoco Norway, Norsk Hydro
and Statoil in the period from 1990 to 1997 and review of these organisations
procedure manuals for inspection planning.
/11/
"GLIM4, The Statistical System for Generalised Linear Interactive Modelling",
delivered by NAG (The Numerical Algorithms Group)
/12/
Regulations relating to load bearing structures in the petroleum activities, NPD
1995
/13/
Comparison between predicted and measured cracks in tubular joints, student thesis
of Jahn O. Gullestad NTNU 1997
44
Appendix A
Summary of In-Service Observations
45
46
The headings read in Table A.1 :
First time:
First EC/MPI inspection performed
Follow-no find:
Re-Inspection of a joint where no cracks have been observed
Follow-repair:
Re-Inspection of a joint where cracks have been repaired
Follow-not repair: Re-Inspection of a joint where cracks have been observed but not repaired
Joints:
Number of joints inspected/having a reported crack
Total:
Total number of inspections/cracks
Member importance:
pri:
Primary structural components, (Legs bracing in vertical frames and rows)
sec
Secondary structural components, (Support frames)
ter
Tertiary structural components (Conductor ladders, riser supports etc.)
Elevation in structure: ( relative to mean water level )
toplevel:
Typically +35 feet
level-1:
Typically -35 feet
level-2:
Typically -90 feet
level-3:
Typically -125 feet
level-4:
Typically -180 feet
level-5:
Bottom Frame
Chord thickness
1/2"
less than 15 mm
3/4"
range 15 - 22 mm
1"
range 22 - 28 mm
11/4"
range 28 - 35 mm
11/2"
range 35 - 44 mm
2"
more than 44 mm
47
Table A.1
Inspections
Overview of inspection data.
First-time Follow-no find
Follow-repair
Follow not repaired
Joints
Total
pri
sec
ter
toplevel
level-1
level-2
level-3
level-4
level-5
1/2"
3/4"
1"
11/4"
11/2"
2"
1983
626
140
900
687
576
122
202
262
644
248
136
37
500
1184
525
94
2
242
142
102
33
30
72
97
46
33
3
173
269
210
107
58
220
62
50
4
11
28
158
36
16
3
35
127
167
53
12
38
54
96
5
9
30
50
77
5
0
44
56
1983
626
140
900
687
576
122
202
262
644
248
136
37
500
1184
2885
880
212
1400
945
824
164
252
392
949
407
190
43
752
1636
sum
2749
621
375
232
2749
3977
Cracks
Follow-repair
Follow not repaired
Joints
Total
pri
sec
ter
toplevel
level-1
level-2
level-3
level-4
level-5
1/2"
3/4"
1"
11/4"
11/2"
2"
First-time Follow-no find
239
118
65
163
111
77
14
33
24
163
58
21
4
54
122
60
30
0
40
20
20
1
2
7
29
10
3
0
20
28
37
54
25
74
12
18
4
2
6
74
7
7
0
8
20
140
36
11
29
41
78
5
2
32
36
67
6
0
41
37
299
148
65
203
131
97
15
35
31
192
68
24
4
74
150
476
238
101
306
184
193
24
39
69
302
142
37
4
123
207
sum
422
90
116
187
512
815
Fatigue Crack First-time Follow-no find
Follow-repair
Follow-not repair
Joints
Total
pri
sec
ter
toplevel
level-1
level-2
level-3
level-4
level-5
1/2"
3/4"
1"
11/4"
11/2"
2"
55
72
54
106
38
24
2
4
7
116
30
11
0
10
14
16
27
0
28
7
7
0
1
0
26
6
0
0
6
5
18
47
25
50
24
9
4
0
3
69
4
5
0
4
8
93
28
11
21
27
68
3
1
12
31
61
6
0
23
11
71
99
54
134
45
31
2
5
7
142
36
11
0
16
19
182
174
90
205
96
108
9
6
22
242
101
22
0
43
38
sum
181
43
90
132
224
446
48
Per Cent of First Time Inspections which are Classified as
Fabrication Defects
Per Cent of First Inspection Results Classified as Fabrication Crack,
structures installed between 1975 and 1978
0,3
0,35
0,25
0,3
0,25
0,2
FAT 90%
FAT 90%
0,2
FAT 70%
FAT 50%
0,15
FAT 30%
FAT 70%
0,15
FAT 50%
FAT 30%
0,1
0,1
0,05
0,05
22
19
18
17
16
15
14
13
12
11
9
10
8
7
6
5
4
3
2
Years in service
1
0
0
20
18
16
14
12
10
8
6
4
2
0
0
Years in service
Per Cent of Inspection Results Classified as Fabrication Cracks,
structures installed before 1975
Per Cent of First Time Inspection Results Classified as Fabrication
Cracks, structures installed after 1978
0,45
0,6
0,4
0,5
0,35
0,3
0,4
FAT-30%
0,25
FAT 90%
FAT-50%
FAT-70%
0,2
FAT 70%
0,3
FAT 50%
FAT-90%
0,15
FAT 30%
0,2
0,1
0,1
0,05
22
20
18
16
14
12
10
8
6
4
2
0
0
0
0
1
Years in service
2
3
4
5
6
7
8
9
Years in service
Figure A.1 Fraction of the first time inspections giving detection of fabrication cracks. The figure, top, left corresponds, to Figure 2.4 while the
other figures correspond to different sub sets with respect to time in service after installation.
49
Ratio of Fabrication and Fatigue Crack Detections, 90%
confidence applied for the fatigue crack classification
Ratio of Fabrication and Fatigue Crack Detections, 50%
confidence related to the fatigue crack classiifcation
0,25
0,25
0,2
0,2
0,15
0,15
FAT 90%
0,1
Fab-cra 90%
FAT 50%
0,1
Fab-cra 50%
0,05
0,05
0
0-2
3-5
6-8
9-11
12-14
15-17
0
18-20
0-2
Years in service
3-5
6-8
9-11
12-14
15-17
18-20
Yesr in service
Ratio of Fabrication and Fatigue Crack Detections, 30 %
confidence related to the fatigue crack classification
Ratio of Fabrication and Fatigue Crack Detections, 70 %
confidence applied ofr the fatigue crack classification
0,25
0,25
0,2
0,2
0,15
0,15
FAT 70%
Fab-cra 70%
0,1
FAT 30%
0,1
Fab-cra 30%
0,05
0,05
0
0-2
0
0-2
3-5
6-8
9-11
12-14
15-17
18-20
3-5
6-8
9-11
12-14
15-17
18-20
Years in service
Yesr in service
Figure A.2 Ratio of fabrication and fatigue cracks related to the number of inspections of intersections which previously have not been inspected
or for which no findings have been reported. Data collected for structures installed in the period 1975 to 1978.
50
Ratio of Fabrication and Fatigue Crack Detections, 90%
confidence applied for the fatigue crack classification
Ratio of Fabrication and Fatigue Crack Detections, 50%
confidence related to the fatigue crack classiifcation
0,3
0,3
0,25
0,25
0,2
0,2
FAT 90%
0,15
Fab-cra 90%
0,1
FAT 50%
0,15
Fab-cra 50%
0,1
0,05
0,05
0
0-2
3-5
6-8
911
1214
1517
1820
0
2123
0-2
3-5
6-8
Years in service
911
1214
1517
1820
2123
Yesr in service
Ratio of Fabrication and Fatigue Crack Detections, 30 %
confidence related to the fatigue crack classification
Ratio of Fabrication and Fatigue Crack Detections, 70 %
confidence applied ofr the fatigue crack classification
0,3
0,3
0,25
0,25
0,2
0,2
FAT 70%
0,15
Fab-cra 70%
0,15
FAT 30%
Fab-cra 30%
0,1
0,1
0,05
0,05
0
0-2
0
0-2
3-5
6-8
911
1214
1517
1820
2123
3-5
6-8
911
1214
1517
1820
2123
Years in service
Yesr in service
Figure A.3 The ratio of fabrication and fatigue cracks related to the number of inspections of intersections which previously have not been inspected or
for which no findings have been reported. The data is collected for structures installed before 1975.
51
Printed and published by the Health and Safety Executive
C0.50
3/02
ISBN 0-7176-2305-X
OTO 1999/059
£10.00
9 780717 623051