RR088 - Component-Based Calibration

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HSEHealth & Safe ty

Executive

Component-based calibration of North West Europeanannex environmental load factors for the ISO

fixe d stee l offshore structure s code 19902

Prep are d by BOMEL LtdOn behalf of a Joint Ind ustry Project in which the

Health and Safe ty Executive was a p articipant (2003)

RESEARCH REPORT 088



HSEHealth & Safe ty

Executive

Component-based calibration of North West Europeanannex environmental load factors for the ISO

fixe d stee l offshore structure s code 19902

BOMEL LimitedLe dger House

Forest Green RoadFifield

MaidenheadBerkshire

SL6 2NR

This report presents results of the classical component-based approach used in the Joint Industry

Project (JIP) to derive extreme environmental load factors for a North West European Annex to the ISOfixed steel offshore structures Code 19902.

The ISO 19902 Code introduces new provisions and changes in design practice; these changes,together with a new understanding of the NW Europe environment, meant that it was necessary toreview the levels of safety and economy of structures that may be achieved by the use of the newCode for the design of NW European fixed offshore steel structures. The main objective of this JIP wasto calibrate the load factors for the NW European environment, although other load and resistancefactors were assessed also.

The project was developed in collaboration with a broad industry grouping of consultants, oilcompanies and regulators from across Europe; BOMEL led the JIP load factor calibration phase. TheJIP involved calibration using both a system-based approach and a component-based approach. Theclassical component-based calibration is described in this report..

This report and the work it describes were funded in part by the Health and Safety Executive (HSE) asone of the JIP sponsors. Its contents, including any opinions and/or conclusions expressed, are thoseof the authors and the JIP Steering Committee alone and do not necessarily reflect HSE policy.

HSE BOOKS



© Crown copyright 2003

First published 2003

ISBN 0 7176 2215 0

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means (electronic, mechanical, photocopying, recording or otherwise) without the prior written permission of the copyright owner.

Applications for reproduction should be made in writing to:Licensing Division, Her Majesty's Stationery Office,St Clements House, 2-16 Colegate, Norwich NR3 1BQor by e-mail to [email protected]

ii



CONTENTS

Page No

EXECUTIVE SUMMARY ii v

1. INTRODUCTION 1 1.1 BACKGROUND 1 1.2 SCOPE OF WORK 1

2. METHODOLOGY FOR COMPONENT-BASED APPROACH TO CALIBRATION 3 2.1 SUMMARY 3 2.2 BACKGROUND OF CLASSICAL COMPONENT-BASED APPROACH 3 2.3 METHODOLOGY FOR CLASSICAL COMPONENT-BASED APPROACH 4

3. CALIBRATION POINT DATA AND WEIGHTING FACTORS 9 3.1 SUMMARY 9 3.2 CALIBRATION POINT DATA 9 3.3 WEIGHTING FACTOR DATA 12

4. PROBABILISTIC MODELLING 21 4.1 SUMMARY 21 4.2 FAILURE FUNCTION 21 4.3 PROBABILISTIC MODELLING 23

5. RELIABILITY ANALYSIS RESULTS FOR TYPICAL INDIVIDUAL COMPONENTS 29 5.1 SUMMARY 29 5.2 AXIAL TENSION 30 5.3 AXIAL COMPRESSION 32 5.4 BENDING 34 5.5 COMBINED TENSION & BENDING 37 5.6 COMBINED COMPRESSION & BENDING 39

5.7 COMBINED TENSION, BENDING & HYDROSTATIC PRESSURE 405.8 COMBINED COMPRESSION, BENDING & HYDROSTATIC PRESSURE 42

5.9 VARIATION OF ENVIRONMENTAL LOAD FACTOR 44 5.10 VARIATION OF COLUMN SLENDERNESS PARAMETER 45

5.11 VARIATION OF D/T RATIO 45

5.12 VARIATION OF BENDING AMPLIFICATION FACTOR, C M 45

5.13 VARIATION OF BENDING TO AXIAL STRESS RATIO 48

6. CALIBRATION POINT RESULTS 49 6.1 SUMMARY 49 6.2 BRACE MEMBERS 49 6.3 LEG MEMBERS 53

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7. HISTORICAL ASSESSMENT AND TARGET ASSESSMENT 57 7.1 HISTORICAL ASSESSMENT 57 7.2 TARGET ASSESSMENT 59

8. SENSITIVITY STUDIES 67 8.1 SUMMARY 67 8.2 WEIGHTING FACTORS 67 8.3 20-YEAR RELIABILITIES 69 8.4 TRUNCATION OF DESIGN LOAD UNCERTAINTY DISTRIBUTION 70 8.5 OPPOSING LOAD CONDITION 71

9. TUBULAR JOINTS 77 9.1 SUMMARY 77 9.2 CALIBRATION POINT DATA 77 9.3 WEIGHTING FACTOR DATA 79 9.4 PROBABILISTIC MODELLING 81 9.5 RELIABILITY ANALYSIS FOR TYPICAL JOINTS 81 9.6 CALIBRATION POINT RESULTS 95 9.7 TARGET ASSESSMENT 99

10. FOUNDATIONS 101 10.1 SUMMARY 101

10.2 CALIBRATION POINT DATA 101 10.3 PROBABILISTIC MODELLING 103 10.4 RELIABILITY ANALYSIS FOR TYPICAL INDIVIDUAL PILES 106 10.5 CALIBRATION POINT RESULTS 114 10.6 NORMALISED PILE CAPACITY 115 10.7 TARGET ASSESSMENT 11 7

11. EFFECT OF REDUCTION OF PERMANENT AND VARIABLE PARTIAL LOAD FACTORS 119 11.1 SUMMARY 11 9 11.2 MEMBERS 11 9

11.3 JOINTS 12 0 11.4 FOUNDATIONS 12 0 11.5 DISCUSSION 1 21

12. EFFECT OF INCREASE IN ENVIRONMENTAL DESIGN LOAD UNCERTAINTY 123 12.1 SUMMARY 12 3 12.2 ENVIRONMENTAL DESIGN LOAD UNCERTAINTY MODELLING 12 3 12.3 RESULTS 12 4 12.4 DISCUSSION 12 7

iv



13. CONCLUSIONS 129

14. GLOSSARY 131

15. REFERENCES 133

v



vi



EXECUTI VE SUMMA RY

This report presents results of the classical component-based approach for the Joint Industry Project (JIP) toderive extreme environmental load factors for a North West European Annex to the ISO fixed steel offshore

structures Code 19902.

The ISO 19902 Code introduces new provisions and changes in design practice; these changes, together with a new understanding of the NW Europe environment, mean that it is necessary to review the levels of safety and economy of structures that may be achieved by the use of the new Code for the design of NWEuropean fixed offshore steel structures. The main objective of this JIP is to calibrate the load factors for theNW European environment, although other load and resistance factors are assessed also.

The project has been developed in collaboration with a broad industry grouping of consultants, oil companiesand regulators from across Europe; BOMEL led the JIP load factor calibration phase. The JIP involvedcalibration using both a system-based approach [1] and a component-based approach. The classicalcomponent-based calibration is described in this report.

First-order reliability analyses have been undertaken using a database of tubular components withrepresentative geometries, bending-to-axial stress ratios, dead-to-live load ratios, environment-to-gravityload ratios, etc.; the results have been weighted to reflect their frequency of occurrence in North Sea fixedsteel structures. The reliability analysis has been undertaken using environmental load modelling derived tobe representative of NW European waters. Unless noted otherwise, an annual reference period has beenused; thus annual probabilities of failure have been evaluated.

Weighted average failure probabilities have also been evaluated for the components designed to be fullyutilised to 20 th (21 st) Edition RP2A-WSD [2], 1 st Edition RP2A-LRFD [3], together with earlier Editions of RP2A-WSD (as applied in typical North Sea practice), in order to provide a context for the reliabilitymodelling, and to assist in the assessment of target reliability(s).

Weighted average failure probabilities have been evaluated for the components designed to be fully utilisedto the ISO code formulations using an extreme storm environmental load factor of 1.35; the analyses havealso been repeated for a range of environmental load factors. (The partial resistance factors have beentaken from the Code.) All work in this report has been based on the Committee Draft of the ISO Code dated

June 2001 [4].

A range of sensitivity studies have also been undertaken, including analysis with increased environmentaldesign loading uncertainty (using a CoV of 25%).

vii



RESULTS SUM MA RY

A target has not been recommended in this report. However, the results show that if the target were to bebased on the weighted average probabilities inherent in 20 th (21 st) Edition API RP2A-WSD, an environmentalload factor of 1.25 with the new ISO provisions will on average achieve similar reliability levels.

In addition to the above reliability analyses, detailed reliability analyses have been undertaken for differentload effects (axial Compression, Compression & Bending, etc) for selected components. Results are alsopresented to show the trends with reliability for environment-to-gravity load ratio for a number of other effects, including:

• the influence of the operating and still water conditions

• different environmental load factors• 20-year reference period (as opposed to an annual reference period)

• member slenderness

• moment amplification factor, C m.

The only unexpected result was that analysis for the C m factor showed that reliability for tubular membersgoverned by axial compression and bending is sensitive to the value of this term; in some design casesselection of the most appropriate value of the C m factor is a matter of judgement. It is recommended thatthis is considered further by the ISO members panel.

Sensitivity studies have also been undertaken to investigate the effect of the weighting factors, andtruncation of the distribution for design load uncertainty. These sensitivity studies have confirmed therobustness of the calibration approach.

Analysis to investigate the Opposing Load Condition has been undertaken. This condition rarely governsmember design, but in cases where it does, designs to ISO with an environmental load factor of 1.25 or more would generally achieve a higher and more consistent level of reliability than those to RP2A-WSD.

Reliability analyses have been undertaken for tubular joints to assess the appropriateness of the resistancefactors. Reliabilities for all joint types and the single load effects analysed were shown to be reasonablyconsistent for designs to the ISO Code, suggesting that the published resistance factors are appropriate.However, no reliability analysis has been undertaken to assess the appropriateness of the load effectinteraction equation in the ISO Code, which has been changed from API RP2A. On the basis of the jointcalibration results, an environmental load factor of 1.25 would raise average reliability levels for joint designsto the ISO code above the API RP2A-WSD 20 th (21 st) Edition values.

Some illustrative reliability-based analyses were undertaken for the axial capacity of piled foundations. Theresults indicate that because of the very large uncertainties associated with the prediction of pile behaviour,there is little effect on reliability for piles in compression from reducing the extreme environmental load factor

from 1.35 to 1.25. For piles governed by tension, a 1.25 environmental load factor leads to a similar (but

viii



greater) level of safety than achieved by RP2A-WSD; a 1.35 factor leads to a significant increase in safetylevel (and hence required pile length) compared to RP2A-WSD.

Finally, a study to assess the implications of increased environmental design loading uncertainty wasundertaken; the CoV was increased from 16.5% to 25% to reflect concerns of some Participants. Theresults of this study lead to an order of magnitude increase in evaluated failure probability. These resultscannot be reconciled with the base case results, and this makes the selection of a target reliability verydifficult, particularly if cost-benefit considerations are used. (Cost-benefit considerations may be used todefine targets for different Exposure Levels and for reassessment). Consequently, a consensus could not beachieved on a suitable value of target reliability.

CONCLUSIONS

The results suggest that adoption of a 1.35 factor on quasi-static extreme environmental loading with other ISO 19902 partial factors and provisions would result in structures being designed which deliver reliabilitylevels for extreme weather at least consistent with traditional practice in all NW European regions.

For design use with NW European offshore structures, it is proposed by the Participants of the JIP to retainthe existing value of environmental load factor at 1.35. However, there should be an option to derivestructure-specific partial load factors using detailed analysis; this analysis should use site-specificenvironmental data and take into consideration the specific form of the structure.

No change is suggested in the present values in the ISO Code of the partial resistance factors for tubular members and joints, and the gravity load factors and load factors for the still water, operating and opposingloads condition.

ix



x



1 . INTRODUCTION

1.1 BACKGROUND

The Joint Industry Project (JIP) concerns the derivation of environmental load factors for a NorthWest European Annex to the ISO fixed steel offshore structures Code 19902. With the newprovisions and changes in design practice introduced into the ISO 19902 Code, together with anew understanding of the NW Europe environment, it is necessary to review the levels of safetyand economy of structures that may be achieved by the use of the new Code for the design of NWEuropean fixed offshore steel structures.

The project has been developed in collaboration with a broad industry grouping of consultants, oilcompanies and regulators from across Europe. This JIP phase is led by BOMEL.

The JIP is using calibration approaches based on both system and component methods. Byfollowing both approaches it is believed that concerns with each of the system and componentbased methods can be addressed and enough information generated to be able to make aninformed judgement on the value(s) of the extreme environmental load factor(s).

This report is concerned with the classical component-based method for safety factor calibration.The purpose of this report is to present results for the calibration analysis.

1.2 SCOPE OF WORK

The scope of work was as follows:

• Assemble database of components representing the practical range of application of theCode – these are termed calibration points, and assess weighting factors to reflect their frequency of occurrence in NW European waters.

• Assess the uncertainty of all of the variables influencing component failure and modelthem using probability distribution functions

• Perform reliability analysis to assess the probability of failure for each calibration point(component), and calculate the weighted average probability of failure.

• Repeat the reliability analysis for a range of environmental load factors.

• Repeat reliability analyses for a range of design Codes to assess historic changes ininherent reliability levels.

• Target assessment, e.g. based on generic Cost Benefit Analysis.

1



• Sensitivity analyses.

• Prepare report.

For brevity, throughout this report, the term “Code” is used to refer to the ISO and API designdocuments. A new 21 st Edition of RP2A-WSD has recently been published; the changes betweenthe 20 th and 21 st Editions do not affect the analysis work undertaken for this report.

2



2 . METHODOLOGY FOR COMPONENT-BASED

APPROACH TO CALIB RATI ON

2.1 SUMMARY

This section discusses the basis and the methodology of the component-based approach to thecalibration of the environmental load factor.

2.2 BACKGROUND OF CLASSICAL COMPONENT-BASED APPROACH

Probabilistic methods have been employed in the calibration of the factors of safety in Codes of Practice, in particular limit state Codes, for around 30 years.

Typically, where a limit state format Code has been developed to replace a traditional workingstress design Code, the objective of the calibration has been to derive safety factors for the limitstate Code, which achieve designs with similar reliabilities to those inherent in designs to theworking stress Code. Most often they have been employed at the component or structuralelement level.

Where a limit state Code is introduced as a direct replacement to an existing working stress Code

the choice of the target reliability is relatively straightforward, provided that the existing Code isconsidered to produce designs with acceptable reliability and economy. The target reliability isthen derived as follows.

1. The objective of the calibration is defined. This may involve evaluating targets for anumber of groups of different component types under different loading modes – theseare referred to as the calibration classes.

2. A set of structural components is selected to reflect the range of components coveredby the Code. The designs are then usually weighted to reflect their frequency of usage.

3. The components are designed to be fully utilised to the existing working stress design(WSD) Code.

4. The probability of failure of each design is evaluated using structural reliability methods.

5. The target reliability for each calibration class is then evaluated as the weighted averageof the failure probabilities. Alternative definitions are sometimes used, includingweighted average reliability indices, lower bound reliability index, or more complexfunctions.

3



This basic process was followed for the calibration of the safety factors for steel design in the UKlimit state bridge Code BS 5400 from the old allowable stress Code BS 153. The target failureprobability was determined as the weighted average failure probability for selected componenttypes designed to BS 153; some component types (notably stiffened compression flanges) werenot included in the target assessment because they ‘had not been shown to behave satisfactorilyin service’ [5]. The evaluated target of 0.63 ×10 -6 was then used to calibrate safety factors for allcomponent types in the new Code using a mathematical optimisation procedure.

The advantage of this type of calibration is that the target probability can readily be considered asnotional because the calibration is undertaken on a like-for-like basis. Indeed, when this type of calibration was originally undertaken, mean value reliability methods were considered adequate.

Unfortunately, it is not always possible or desirable to calibrate back to an existing Code or designpractice. In such situations, the target reliability must be selected using alternative methods.Judgement is often necessary in selecting the target, and it is strongly advisable that theevaluated failure probabilities are obtained using the best available data, knowledge andmethodology.

2.3 METHODOLOGY FOR CLASSICAL COMPONENT-BASEDAPPROACH

2.3.1

Definition of Structure ClassThe Class of Structure for the calibration has been defined as offshore, fixed, steel, space frame(jacket and tower) sub-structures in intermediate to deep waters. It is assumed that theenvironmental loading on the structures is dominated by drag loading; the load factors derived onthis basis are likely to be conservative for (the small number of) structures dominated by inertialoading. It is also assumed that the structures are not significantly affected by dynamic responseunder environmental loading, and no attempt has been made within this report to consider theaffect or influence of the additional partial factor on dynamic response.

Mono-towers, including caissons and tripods, have not been explicitly considered in the

calibration; because of their reduced levels of structural redundancy these require particular consideration.

The calibration reported in this document has been undertaken on a component basis. Theprincipal components employed in the calibration assessment of the environmental load factor aretubular brace members and legs – only primary structural diagonal and horizontal braces areconsidered.

Reliability analyses have also been undertaken for tubular joints to assess the consistency of thereliability achieved by the resistance factors in the ISO Code.

4



A brief investigation has also been undertaken to consider the effects of the load factors on thereliability of piled foundations.

2.3.2 Goal of the CodeTypically, some reliability, utility, cost benefit or other targets are set in some form prior to thecalibration of partial factors. As discussed above, it is not uncommon to use a weighted averagereliability derived from the old Code as a target for the new one.

In the present study, the activity of goal selection has been delayed. However, reliabilities basedon API RP2A-WSD 20 th (21 st) Edition and all previous Editions have been evaluated, along withvalues based on RP2A-LRFD. The aim is to present a historic basis of reliabilities evaluated usingthe probabilistic modelling applied in this project. The target values suggested by Efthymiou et al[6] for members that carry significant extreme environmental load have also been considered for illustrative purposes.

2.3.3 Code FormatThe format is the form of the equations used for the integrity checks in the ISO Code. They havealready been specified and follow “load and resistance factor design” or LRFD. The scope of thepresent study is restricted to the factor on extreme environmental load. The values for other factors are taken as given by the existing ISO draft.

2.3.4 Calibration Points and Importance Weighting

In order to carry out a component-based calibration, it is necessary to identify some calibrationpoints for the study. These have been chosen to reflect the most frequently found member types,ratios of dead load to live or environmental load. Greater weighting in the calibration exercise hasbeen given to the more frequently found member types. Moreover, since the present study isrestricted to the environmental load factor, emphasis has gone to the structural elements that aremost likely to fail under environmental load. This significantly reduces the number of member types to be considered. They have been selected on the basis of experience and the designrequirements of the element. In practice for new structures designed to the ISO Code, jointsshould be stronger than members and do not need to be considered in the calibration for theenvironmental load factor. However, some reliability analysis has been undertaken to assess theappropriateness of the joint strength resistance factors. Analyses have also been undertaken toconsider the effect of the load factor on the reliability of piled foundations.

2.3.5 Measure of FitUsually, when all of the safety factors in a Code are calibrated it is necessary to measure thedeparture of the Code from the goal that has been set. Academic books suggest that this may bemade in economic terms, and this may be attractive, particularly if the target(s) used account for cost/benefit analysis. At the moment, the mean square deviation of the reliability index from thetarget value has been used. Given the restricted nature of the project, in only defining the

environmental load factor, this is considered adequate. In all cases, care should be taken over

5



outliers, particularly on the low reliability side. Since the cost of failure is always subject itself tosome uncertainty, it is better to err to the conservative.

2.3.6 Element DesignThe present (and previous) Code(s) are used to design structural members that are considered tobe important calibration points.

2.3.7 Limit StatesFor the reliability analysis it is necessary to be able to predict failure of each calibration pointcomponent. Failure functions (or limit state functions) are defined for each limit state for eachmember. In this analysis they are based on the functions given in the draft ISO Code (withoutpartial factors). The uncertainty in the failure load or resistance predicted from the ISO Codeformulations is included by using a set of model uncertainties. Model uncertainties have beenderived from databases of large and full scale tests for this project by MSL [7].

2.3.8 Statistical Properties of Basic VariablesProbability distributions are assigned to each element of the set of basic variables { xi} on both theload and resistance side. Well-developed, robust methods of generating load statistics should beused with adequate input from oceanographers and probabilistic wave load experts. Theenvironmental load modelling has been derived for this project by Tromans & Vanderschuren [8].

2.3.9 Estimate Reliability of Members Designed to Old Codes

The first-order reliability method (FORM) has been used (checks were also undertaken usingsecond-order analysis methods). Reliability estimates have been evaluated for different member types designed using a number of earlier Editions of design Codes for a range of conditions (e.g. arange of ratios of live to dead load, and gravity to environmental load). The aim is to help inselecting a target reliability to calibrate the new Code to, and to obtain a feel for how reliability hasevolved over time. This will often show that old practices have given very different (thoughprobably high) levels of reliability and will put the present developments into context.

2.3.10 Estimate Partial Factors for New CodeFurther FORM studies have been undertaken for the calibration points designed to the ISO Code

with different trial partial safety factors. Through an iterative process it is possible to converge onpartial factors that provide a level of reliability that is reasonably uniform and close to the target.Since the present study is limited to producing the environmental load factor, it is possible to makethis step by plotting a graph.

2.3.11 Engineering Judgement and Sensitivi ty StudiesThe final step is a subjective review of the results. The FORM study indicates which basicvariables play the main role in determining reliability. It is wise to investigate the effects of crediblechanges in their distributions. It is desirable to make a quick review of consequences for structuralelements that were not treated as main calibration points, but are influenced by environmental

6



load. Undoubtedly, the Code will be used to design structures “which are covered by the standardonly to the extent that the provisions are applicable”.

A number of sensitivity studies have been undertaken, and are reported in Section 8.

7



8



3 . CALIB RATION POINT DATA AND WEIGHTING

FACTORS

3.1 SUMMARY

This section discusses the selection of the calibration point data and weighting factors to reflectthe occurrence of designs in practice.

A statistical survey was carried out for the AME calibration of the draft LRFD for North Seaapplication [9] to determine the relative frequency of occurrence of the various geometricconfigurations and load effects for tubular joints, braces and legs of North Sea jackets. The

weighting factors derived in Reference 9 were modified using engineering judgement to reflectcurrent practice.

3.2 CALIBRATION POINT DATA

3.2.1 GeometryRepresentative geometries for diagonal and horizontal tubulars have been selected and areshown in Table 3.1; Table 3.2 shows representative geometries for leg members. The geometrieshave been selected to reflect a range of slendernesses and D/T ratios.

Unbraced length given in the table below is face-to-face length. It has been assumed for thepurpose of this study that the node-to-node length (required for ISO determination of slendernessratio) is 5% greater than the face-to-face length.

G1 G2 G3 G4

1400 700 1400 1600

Thickness, T (mm) 50 25 45 40

9720 8000 28740 417500.7 0.7 0.7 0.7

λ 0.19 0.32 0.57 0.72

D/T 28 28 31.1 40

Cm 0.4 0.85 0.85 0.6

Yield Stress, F y (N/mm 2) 340 345 340 340

Young’s Modulus, E (N/mm 2) 207000 207000 207000 207000

Diameter, D (mm)

Unbraced length, L (mm)Effective Length Factor, K

Column slenderness parameter,

Table 3.1 Geometry of Tubular Brace Members

9



G1 G2(a) G2(b) G3

2300 3300 3300 2000

Thickness, T (mm) 50 50 60 60

Unbraced length, L (mm) 9750 33270 33270 36330

1.0 1.0 1.0 1.0

λ 0.17 0.40 0.39 0.72

D/T 46 66 55 33.33

Cm 0.85 0.85 0.85 0.85

Yield Stress, Fy

(N/mm2

) 340 340 340 340Young’s Modulus, E (N/mm 2) 207000 207000 207000 207000

Diameter, D (mm)

Effective Length Factor, K

Column slenderness parameter,

Table 3.2 Geometry of Leg Members

3.2.2 Load EffectsThe load effects studied were as follows:

− Axial Compression and Bending C+B

− Axial Tension and Bending T+B

− Axial Tension, Bending and Hydrostatic Pressure T+B+H

− Axial Compression, Bending and Hydrostatic Pressure C+B+H

3.2.3 Load CombinationsThe combinations of stress ratios considered for tubular braces and legs are listed in Table 3.3.The combinations of dead to live load ratio considered are listed in Table 3.4.

The effect of platform location is reflected in the frequencies of usage with the Central North Sea(CNS) jackets experiencing less extreme environmental loading than the platforms in the Northernsector of the North Sea (NNS). Higher weighting has been assigned to the higher W e/G ratios for elements located near the seabed to account for the larger environmental loading experienced bytubulars near the seabed. Conversely, the frequencies for lower W e/G ratios for tubulars located inthe splash zone are higher reflecting the increased relative contribution of gravity loading.

10



Combined Stress Ratios

Compression:Bending

Compression:Bending:(Hydrostatic*)

Range of Equally Weighted Stress Ratios for the Combined Load Effects Consideredfor Extreme Loading Condition

We:G D:L

0.3

1.0

3.5

11.5

Low - 0.25:0.75

Medium - 0.50:0.50

High - 0.75:0.25

Tension:Bending

Low - 0.33:0.67

Medium - 0.67:0.33

High - 0.9:0.1

Low - 0.33:0.67

Medium - 0.40:0.60

High - 0.50:0.50

Tension:Bending:(Hydrostatic*)

Low - 0.33:0.67

Medium - 0.50:0.50

High - 0.66:0.34*hydrostatic component input as proportion of axial+bending stress – proportion dependent on whether NNS/CNS and leg/brace – see

Low - 0.5:0.5

Medium - 0.7:0.3

High - 0.9:0.1

Low - 0.6:0.4

Medium - 0.7:0.3

High - 0.9:0.1

Low - 0.6:0.4

Medium - 0.8:0.2

High - 0.9:0.1

Low - 0.7:0.3

Medium - 0.8:0.2

High - 0.9:0.1

section 3.2.4

Table 3.3

Table 3.4 Range of Equally Weighted Gravity Load Ratios for Each Environmental-to-GravityLoad Ratio for the Extreme Loading Condition

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3.2.4 Hydrostatic PressureThe hydrostatic load component was input as a proportion of the axial+bending stress; theproportion being dependent on the member D/t ratio and whether the case was for NNS or CNS.

The proportions were identical for T+B+H and C+B+H cases and were calculated as follows;

D/t×hfactphydro = (3.1)

28

where p hydro is the proportion of the axial+bending stress and h fact varies with W e/G ratio as follows:

hfact

We/G ratio NNS CNS0.3 0.006 0.0061.0 0.015 0.0153.5 0.03 0.0211.5 0.06 0.04

Table 3.5 Factors used in calculation of proportion of hydrostatic pressure

Values of h fact were chosen to give realistic water depths for splash zone, mid-depth zone andseabed appropriate to NNS or CNS platforms. Using this approach the actual water depths varyslightly with design load for each of the codes.

3.3 WEIGHTING FACTOR DATA

The weighting factors used for the reliability analysis are presented in Figure 3.1 to Figure 3.7 inthe form of weighting trees.

As shown in Figure 3.1, fixed steel platforms are distributed throughout the North Sea with themajority being located in the Southern North Sea. Southern North Sea (SNS) platforms wereexcluded from the calibration for two reasons. Firstly, because most SNS platforms are notconsidered representative of modern design due to their age, and secondly because the majorityof components for recent SNS jacket structures have been designed for installation and fatigueloads. The frequencies of occurrence assigned to NNS and CNS structural components werenormalised to account for the exclusion of SNS platforms.

Most Central North Sea platforms are located in the 50-75m water depth range. Northern NorthSea platforms are approximately evenly distributed over the 100-175m depth range [9].

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NORTH SEA

MEMBERSFigure 3.2, 3.3

LEGSFigure 3.6

JOINTSFigure 9.1

NNS0.12 (0.29)*

MEMBERSFigure 3.4, 3.5

LEGSFigure 3.7

JOINTSFigure 9.1

CNS0.27 (0.71)*

SNS0.61

* Normalised values

Figure 3.1 Key to Weighting Trees for Fixed Steel Platforms in the North Sea

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NNSHORIZONTALS

0.7

S

0.30

G2

0.46

L

0.20

0.3

0.20

G3

0.28

G4

0.21

M

0.30

H

0.50

1.0

0.25

3.5

0.25

12

0.30

C+B

0.60

T+B

0.30

T+B+H

0.05

C+B+H

0.05

G1

0.05

M

0.52

G2

0.46

L

0.20

0.3

0.10

G3

0.19

G4

0.33

M

0.30

H

0.50

1.0

0.20

3.5

0.35

12

0.35

C+B

0.60

T+B

0.20

T+B+H

0.05

C+B+H

0.15

G1

0.02

B

0.18

G2

0.25

L

0.20

0.3

0.05

G3

0.31

G4

0.42

M

0.30

H

0.50

1.0

0.10

3.5

0.40

12

0.45

C+B

0.32

T+B

0.08

T+B+H

0.12

C+B+H

0.48

G1

0.02

L

0.33

M

0.33

H

0.33

L

0.33

M

0.33

H

0.33

L

0.33

M

0.33

H

0.33

ELEMENTTOPOLOGY

WATER DEPTHRANGE

DESIGNGROUP

G1: <0.25G2: 0.26 - 0.5G3: 0.51 - 0.75G4: >0.75

LOADEFFECTS

STRESS RATIOCOMBINATIONS

LOADCOMBINATIONS

We/G

DEAD TO LIVELOAD RATIOS

Figure 3.2 Tree Diagram for Horizontal Tubular Braces – Extreme Loading Condition – NNS

14



NNSHORIZONTALS

0.7

S

0.30

G2

0.46

L

0.20

0.3

0.20

G3

0.28

G4

0.21

M

0.30

H

0.50

1.0

0.25

3.5

0.25

12

0.30

C+B

0.60

T+B

0.30

T+B+H

0.05

C+B+H

0.05

G1

0.05

M

0.52

G2

0.46

L

0.20

0.3

0.10

G3

0.19

G4

0.33

M

0.30

H

0.50

1.0

0.20

3.5

0.35

12

0.35

C+B

0.60

T+B

0.20

T+B+H

0.05

C+B+H

0.15

G1

0.02

B

0.18

G2

0.25

L

0.20

0.3

0.05

G3

0.31

G4

0.42

M

0.30

H

0.50

1.0

0.10

3.5

0.40

12

0.45

C+B

0.32

T+B

0.08

T+B+H

0.12

C+B+H

0.48

G1

0.02

L

0.33

M

0.33

H

0.33

L

0.33

M

0.33

H

0.33

L

0.33

M

0.33

H

0.33

ELEMENTTOPOLOGY

WATER DEPTHRANGE

DESIGNGROUP

G1: <0.25G2: 0.26 - 0.5G3: 0.51 - 0.75G4: >0.75

LOADEFFECTS


LOADCOMBINATIONS

We/G


Figure 3.3 Tree Diagram for Diagonal Tubular Braces – Extreme Loading Condition – NNS

15



CNSHORIZONTALS

0.59

S

0.51

G2

0.50

L

0.20

0.3

0.20

G3

0.14

G4

0.11

M

0.30

H

0.50

1.0

0.30

3.5

0.30

12

0.20

C+B

0.67

T+B

0.33

T+B+H

0.00

C+B+H

0.00

G1

0.25

M

0.32

G2

0.55

L

0.20

0.3

0.15

G3

0.12

G4

0.13

M

0.30

H

0.50

1.0

0.25

3.5

0.35

12

0.25

C+B

0.60

T+B

0.20

T+B+H

0.05

C+B+H

0.15

G1

0.20

B

0.17

G2

0.33

L

0.20

0.3

0.10

G3

0.34

G4

0.22

M

0.30

H

0.50

1.0

0.15

3.5

0.45

12

0.30

C+B

0.64

T+B

0.16

T+B+H

0.05

C+B+H

0.15

G1

0.11

L

0.33

M

0.33

H

0.33

L

0.33

M

0.33

H

0.33

L

0.33

M

0.33

H

0.33

ELEMENTTOPOLOGY

WATER DEPTHRANGE

DESIGNGROUP

G1: <0.25G2: 0.26 - 0.5G3: 0.51 - 0.75G4: >0.75

LOADEFFECTS


LOADCOMBINATIONS

We/G


Figure 3.4 Tree Diagram for Horizontal Tubular Braces – Extreme Loading Condition – CNS

16



CNSDIAGONALS

0.41

S

0.33

G2

0.34

L

0.20

0.3

0.20

G3

0.15

G4

0.25

M

0.30

H

0.50

1.0

0.30

3.5

0.30

12

0.20

C+B

0.67

T+B

0.33

T+B+H

0.00

C+B+H

0.00

G1

0.26

M

0.39

G2

0.26

L

0.20

0.3

0.15

G3

0.24

G4

0.25

M

0.30

H

0.50

1.0

0.25

3.5

0.35

12

0.25

C+B

0.60

T+B

0.20

T+B+H

0.05

C+B+H

0.15

G1

0.25

B

0.28

G2

0.54

L

0.20

0.3

0.10

G3

0.14

G4

0.12

M

0.30

H

0.50

1.0

0.15

3.5

0.45

12

0.30

C+B

0.64

T+B

0.16

T+B+H

0.05

C+B+H

0.15

G1

0.20

L

0.33

M

0.33

H

0.33

L

0.33

M

0.33

H

0.33

L

0.33

M

0.33

H

0.33

ELEMENTTOPOLOGY

WATER DEPTHRANGE

DESIGNGROUP

G1: <0.25G2: 0.26 - 0.5G3: 0.51 - 0.75G4: >0.75

LOADEFFECTS


LOADCOMBINATIONS

We/G


Figure 3.5 Tree Diagram for Diagonal Tubular Braces – Extreme Loading Condition – CNS

17



ELEMENTTOPOLOGY

NNSLEGS0.29

M

0.70

G20.54 G1

0.36

C+B

local1.00

G3

0.10

G4

0.00G2a

D/T > 600.50

G2bD/T < 60

0.50

C+B

o/all0.95

T+B

0.00

T+B+H

0.00

C+B+H

0.05

S

0.12

G2b

0.50

L

0.20

0.3

0.20

G3

0.50

G4

0.00

M

0.30

H

0.50

1.0

0.30

3.5

0.30

12

0.20

L

0.33

M

0.33

H

0.33

C+B

o/all1.00

T+B

0.00

T+B+H

0.00

C+B+H

0.00

G1

0.00

L

0.20

0.3

0.20

M

0.30

H

0.50

1.0

0.25

3.5

0.35

12

0.25

L

0.33

M

0.33

H

0.33

B

0.18

G21.00 G1

0.00

C+B

local1.00

G3

0.00

G4

0.00G2aD/T > 60

0.40

G2bD/T < 60

0.60

C+B

o/all0.90

T+B

0.00

T+B+H

0.00

C+B+H

0.10

L

0.20

0.3

0.10

M

0.30

H

0.50

1.0

0.15

3.5

0.45

12

0.30

L

0.33

M

0.33

H

0.33

WATER DEPTHRANGE

DESIGNGROUP

G1: <0.25G2: 0.26 - 0.5G3: 0.51 - 0.75G4: >0.75

LOADEFFECTS


LOADCOMBINATIONS

We/G


Figure 3.6 Tree Diagram for Leg Members – Extreme Loading Condition – NNS

18



ELEMENTTOPOLOGY

CNSLEGS0.71

M

0.50

G20.84 G1

0.16

C+B

local1.00

G3

0.00

G4

0.00G2a

D/T > 600.50

G2bD/T < 60

0.50

C+B

o/all0.95

T+B

0.00

T+B+H

0.00

C+B+H

0.05

S

0.16

G2b

0.67

L

0.20

0.3

0.20

G3

0.00

G4

0.00

M

0.30

H

0.50

1.0

0.30

3.5

0.30

12

0.20

L

0.33

M

0.33

H

0.33

C+B

o/all1.00

T+B

0.00

T+B+H

0.00

C+B+H

0.00

G1

0.33

L

0.20

0.3

0.20

M

0.30

H

0.50

1.0

0.25

3.5

0.35

12

0.25

L

0.33

M

0.33

H

0.33

B

0.34

G20.85 G1

0.15

C+B

local1.00

G3

0.00

G4

0.00G2a

D/T > 600.40

G2bD/T < 60

0.60

C+B

o/all0.90

T+B

0.00

T+B+H

0.00

C+B+H

0.10

L

0.20

0.3

0.10

M

0.30

H

0.50

1.0

0.15

3.5

0.45

12

0.30

L

0.33

M

0.33

H

0.33

WATER DEPTHRANGE

DESIGNGROUP

G1: <0.25G2: 0.26 - 0.5G3: 0.51 - 0.75G4: >0.75

LOADEFFECTS


LOADCOMBINATIONS

We/G


Figure 3.7 Tree Diagram for Leg Members – Extreme Loading Condition – CNS

19



20



4 . PROBABIL ISTIC MODELLIN G

4.1 SUMMARY

This section outlines the definition of the failure function used in the reliability analysis, anddescribes the probabilistic modelling of the basic variables.

4.2 FAILURE FUNCTION

In structural reliability analysis, a failure function is used to define the failure event. At its simplest,the failure function is:

Z = Resistance − Load (4.1)

In the reliability analysis for safety factor calibration in this project:

• The loadingterm is based on the load level on a component to cause a utilisation ratioof unity to a particular design code, i.e. it is based on the strength formulations for theparticular code and it includes the safety factors, or load and resistance partial safetyfactors, for the code.

• The resistance term should be based on the “best” model available for predicting thestrength of a component. For the reliability analysis in this project, the ISO formulations(without safety factors) have been used.

The loadingterm can be considered to represent the factored design load to a particular designcode, and thus Eqn (4.1) gives the safety margin between the ultimate strength of the componentand the factored design load. By using the same model to define the ultimate strength of thecomponents, failure probabilities can be directly compared for different design codes.

In reality Eqn (4.1) is more complex, since both the resistance and loading terms include a number of uncertainties. The uncertainties are defined for the basic variables influencing the failure event.The failure function given by Eqn (4.1) can be expressed in notational form as:

yZ = X,F,tR m etc, ) − (dD +lL+wW / X ) Rdes (4.2)w

where R(t, F y, Xm, etc) is the uncertain resistance of the component evaluated using the ISOformulations without safety factors, and is a function of the uncertain geometric andmaterial parameters, and the model uncertainty associated with the particular ISOformulation

21



Rdes is the design resistance (or maximum load to give a utilisation of unity) for thenominal component to the appropriate Code, and is a function of the load andresistance partial factors (or safety factors in WSD), the nominal geometric and materialparameters and the proportions of unfactored gravity and environmental load (d, l, andw)

d, l and w are the proportions of unfactored dead, live and environmental load in thecomponent (Note: d+l+w = 1.0)

D, L and W are the random variables for the uncertainty in dead, live and environmentalloading

and X w is the model uncertainty in the evaluation of the environmental design loading

Egn (4.2) may be used for single load effects (axial tension, bending, etc.). For interaction effects,the failure function in the reliability analysis can also be considered as follows. The uncertain axialforce in a component may be expressed as:

(dD +lL+wW / X )R ( p.Area )X

F = w desaxial (4.3)

m

the uncertain bending moment may be expressed as:

w desM = (dD +lL+wW / X )R ( p.ulusmodSection bending ) (4.4)Xm

R

etc. where p axial and p bending are deterministic pre-defined proportions of axial and bending stress.Thus, the deterministic axial force to give full utilisation to the design Code, WSD say, is

des . ( p.Area ) .axial

The safety margin in the reliability analysis is evaluated by deriving the uncertain stresses, f a. f b,etc, from the forces and moments, F and M, etc, and substituting into the particular ISO strength

formulations (without safety factors). In the evaluation of the safety margin, random variables for diameter and thickness are used to evaluate the stresses from the above forces, and for yieldstress, effective length, etc.

An assumption of this approach is that the ratio of axial to bending stress remains constant. Thisis an artifice of calibration analysis methodology, which is considered acceptable because of theaveraging process undertaken over the component database.

22



4.3 PROBABILISTIC MODELLING

Probability distributions have been assigned to both loading and resistance terms. All basic

variables have been assumed to be independently distributed, i.e. uncorrelated.

The modelling of the uncertainty in gravity and environmental loading is the same as that adoptedin the component-based calibration approach [1].

Xm Resistance model uncertainty LN [see Table 4.1]The resistance uncertainty parameters, i.e. mean bias and coefficient of variation (CoV), for thevarious strength formulations are as given in the ISO code and are presented in Table 4.1.Lognormal distributions have been assumed for all of the resistance model uncertainties. For theinteraction equations, the basic variable for model uncertainty has been applied to the load termsin a manner consistent with its derivation.

Design Equation Bias St Dev

AXIAL TENSION 1.000 0.0000

column buckling 1.057 0.0433AXIAL COMPRESSION

local buckling 1.065 0.0724

BENDING 1.109 0.0943HYDROSTATIC PRESSURE 1.142 0.1416TENSION AND BENDING 1.109 0.0943

column buckling 1.029 0.0844COMPRESSION AND BENDING


TENSION, BENDING AND HYDROSTATIC 1.075 0.1054

column buckling 1.197 0.1089COMPRESSION, BENDING AND HYDROSTATIC


Table 4.1 Resistance Modelling Uncertainties

W Annual environmental loading Tromans[A=0.327, B=0.146]The probability distribution for environmental loading is based on recommendations by Tromans &Vanderschuren [8]. The annual probability of exceedence of extreme load, normalised on its 100year value, is

L* −A Q(L* ) = exp −

(4.5)

B

23



where L * = L/L100 , A = 0.327 and B = 0.146.

The cumulative probability distribution is given by:

( L*

L* −A LF * ) = 1 −Q( ) = 1−exp −

B (4.6)

This is an exponential distribution, which is only valid for L * ≥A. The mean of the distribution isA + B = 0.473, and standard deviation is B = 0.146; the coefficient of variation (CoV) is thus 0.31.

A distribution based on annual exceedence has been used, and thus annual probabilities of failurehave been evaluated.

In some cases reliability analyses have been undertaken for a 20-year reference period; thus 20year probabilities of failure have been evaluated. 20-years was assumed to be representative of platform design lives in the API TAC-22 work [10], and the AME calibration of the draft LRFD for North Sea application [9].

The distribution for 20-year maxima was defined using Order statistics as:

20** (FL20 (L ) = { LF ) } (4.7)1

This distribution has a mean of 0.852, and standard deviation of 0.184; the CoV is thus 0.216.

These distributions are for structures dominated by drag loading. When used in reliability analysisfor a component, it is assumed that the environmental loading effects on the component areproportional to the global environmental load (base shear or base overturning moment) on thestructure. Thus dynamic effects, vortex shedding considerations, and member wave slam andslap are ignored.

Xw Design load uncertainty Truncated N[1.09, 0.18, truncated at ±1.5σ]The environmental design load arising from the ISO Code and standard practices is estimated to

be subject to a 9% conservative bias and a CoV of 16.5% relative to the ‘true’ 100 year value. Theuncertainty is modelled by a normal distribution truncated at ±1.5 standard deviations, assuggested by Tromans [8]. The truncation is introduced because it is considered that any valuesbeyond the truncation limit will be filtered out during the course of the design process.

Uncertainty and bias in the environmental design load arise from two main sources:• the application of the wave force recipe• the environmental design criteria themselves.

The interpretation of questionnaires undertaken by Tromans & Vanderschuren of oceanographers[8] is that there is a CoV of 15 % on design wave load arising from uncertainty in extrapolation of metocean data, and a conservative bias of 9 % from the wave force recipe. The uncertainty in the

24



L

load arising from the recipe is a matter of application details; study by Digre et al [11] suggeststhat it can be represented by a CoV of 7 %.

D Dead load N[1.0, 0.06]In the preliminary stages of a design process conservative contingency factors are often applied toweight estimates to reflect the uncertainty in topsides equipment weight and layout, etc. As thedesign process proceeds, the contingency factors are progressively reduced.

The uncertainty in the dead load component in members participating in the failure mode isproportional to dead loading on the structure. Uncertainty in dead loading includes rollingtolerances, fabrication aids, paint and fire protection, approximations in weight take-off, marinegrowth, etc.; also included within the definition of dead load is buoyancy. Based on calibrationwork undertaken for the North Sea adaptation of the Draft LRFD Code in 1990 [9] the uncertaintyin dead loading has been modelled by a normal distribution with a bias of 1.0 and a CoV of 0.06.

This modelling was assumed to cover all permanent load on the structure; for the ISO Code, it wasassumed to encompass both categories of permanent load (action) (i.e. G 1 and G 2).

Live load N[1.0, 0.10]Uncertainty in live loading arises from variation in fluid volumes and densities, drill pipe volumes,drill rig position, load distribution, etc. Based on calibration work undertaken for the North Seaadaptation of the Draft LRFD Code in 1990 [9] the uncertainty in live loading has been modelledby a normal distribution with a bias of 1.0 and a CoV of 0.10.

For the ISO Code, live load is categorised as variable load (action) (i.e. Q 1). Short duration loads(actions) (i.e. Q 2 in ISO) only affect the operating and still water design conditions; the influence of this type of loading on primary jacket member design is usually small; it has been neglected inanalysis for the operating condition.

H Hydros tatic load N[1.0, 0.06]The uncertainty in hydrostatic loading arises from salinity, platform settlement, tidal variation,storm surge etc. Based on calibration work undertaken for the North Sea adaptation of the Draft

LRFD Code in 1990 [9], a normal distribution with a bias of 1.0 and CoV of 0.06 was adopted; thisis conservative. Hydrostatic pressure was assumed to be independent of wave height (althoughextreme hydrostatic pressure is influence by crest height, this is a secondary effect for thepurposes of this analysis).

XD Diameter N[1.0, 0.0025]Based on calibration work undertaken for the North Sea adaptation of the Draft LRFD Code in1990 [9], member diameter was assumed to have a bias of 1.0 and CoV of 0.0025.

25



XT Thickness N[1.0, 0.004+0.25/T]Based on calibration work undertaken for the North Sea adaptation of the Draft LRFD Code in1990 [9], member thickness was found to have a bias of 1.0 and a standard deviation of 0.004+0.25/T (in mm).

XL Length N[1.0, 0.0025]Based on calibration work undertaken for the North Sea adaptation of the Draft LRFD Code in1990 [9], unbraced length was assumed to have a bias of 1.0 and CoV of 0.0025.

XF Yield stress LN[1.1266, 0.0572]As for the North Sea adaptation of the Draft LRFD Code in 1990 [9], the distribution of yield stresswas modelled with a lognormal distribution. The nominal design value was taken as the 1%fractile, and a standard deviation was assumed to be independent of the nominal value and avalue of 20 N/mm 2 was used. The parameters given above are for steel with a nominal designstress of 350 N/mm 2, and correspond to a CoV of 5%.

XE Young’s Modulus N[1.0, 0.05]Based on calibration work undertaken for the North Sea adaptation of the Draft LRFD Code in1990 [9], no bias was found for Young’s Modulus CoV was taken as 0.05 (this is a typical valuewidely used for structural reliability analysis). A normal distribution was found to adequately fitavailable data.

XK Effective length factor N[see Table 4.2]Effective length factors for tubular columns have been examined in some detail by Hu and Lai [12]and Earl and Teer [13]. The first of these considered most types of braces and piled legs while thesecond examined braces only. The analyses in both references give similar results wherecomparisons are possible.

For tubular bracing members (diagonals and horizontals) random modelling parameters wereevaluated by combining these results. Since no results were available for un-piled legs themodelling parameters used were based on judgement. This basic variable represents theuncertainty in effective length factor, and is a multiplier on the ISO K-factor (i.e. 0.7 for braces and

1.0 for legs). A normal distribution function was assumed.

26



The assigned probability distributions are summarised in Table 4.2.

Distribution Mean Bias StandardDeviation

Other parameter

Source of data

Resistance model X m Lognormal ISO 19902uncertainty

Load modeluncertainty

Xw Truncatednormal

0.18 ±1.5

Environmental load W Annual A = 0.327 B = 0.146

Dead Load D Normal 1.0 0.06

Live Load L Normal 1.0 0.10

Hydrostatic load H Normal 1.0 0.06

Diameter X D Normal 1.0 0.0025

Thickness X T Normal 1.0 0.004+0.25/T

Length X L Normal 1.0 0.0025

Yield stress X F Lognormal 1.1266 0.0572

Young’s Modulus X E Normal 1.0 0.05

Effective lengthfactor (braces)

XK Normal 0.875 0.097

Effective length X K Normal 1.1 0.0935factor (legs)

Basic Variables

See Table 4.1

1.09 Reference 8

Reference 8

Reference 9

Reference 9

Reference 9

Reference 9

Reference 9

Reference 9

Reference 9

Reference 9

Reference 9

Reference 9

Table 4.2 Summary of Probabilistic Modelling

27



28



5 . RELIA BIL ITY ANA LYSIS RESULT S FOR TYPICAL

INDIV IDUAL COMPONENTS

5.1 SUMMARY

In order to investigate aspects of component reliability for the different load effects and designformulations for tubular members, first-order reliability analyses were undertaken for singlecomponents using a spreadsheet macro. Ranges of parameters were evaluated, whilst all other input parameters were kept constant. Unless noted otherwise, all analyses for the extreme stormcondition to the ISO Code have been undertaken with the published partial factors, i.e. values of 1.1 on the gravity loads and 1.35 on extreme environmental load. The factored load for theextreme storm condition, F d, in the notation used in this report, is given by:

= D1.1 + L1.1 γ + W (5.1)Fd w

where γ w is the extreme environmental load factor for the region. (The quasi-static dynamicload factor and dynamic response have been ignored).

Using ISO practice, the minimum design strength of a member (for a member dominated by axialcompression for instance) is given by:

RISO ≤ Fd (= D1.1 + L1.1 γ + W) (5.2)wγ R

where γ R = resistance factor for the component and load type. γ R = 1.05 for tubular membersunder axial tension, 1.18 for axial compression, 1.05 for bending and 1.25 for hoopbuckling

For comparison, results are also evaluated for designs based on RP2A-WSD 20 th (21 st) Editionand RP2A-LRFD (with API recommended load and resistance factors).

This type of analysis, using a single typical member, was undertaken to investigate the effects of axial-to-bending stress ratio, column slenderness ratio, D/t ratio, C m (bending amplification factor),etc.

All evaluated reliabilities are annual unless noted otherwise. All results are for the extreme stormcondition unless noted otherwise. For most cases, the curvature of the failure surface wasinvestigated at the β-point using second-order reliability analysis, but this had very little effect onthe failure probability. Thus, first-order reliability was considered adequate for the presentpurposes.

29



The typical member used as the base case for this study was as follows:

Parameter Value

Geometry )

Dead:live load ratio 1:1

Hydrostatic load proportion (where 0.066used)*

γ W 1.35

Brace G3 (see Table 3.1

Environmental load factor,*hydrostatic component input as proportion of axial+bending stress

Table 5.1 Base Case for Study of Effect of Different Parameters

5.2 AXIAL TENSION

Member designs governed by axial tension alone rarely, if ever, occur in offshore structures.However, it is instructive to consider how the reliability varies between Codes and for differentenvironmental-to-gravity load ratios because the failure function, or strength formulation, is simple.The basic form of the formulation, without safety factors, is identical between API RP2A and ISO,and so the differences in reliability are purely due to the different effects of the partial safetyfactors.

The results for a typical member geometry are shown in Figure 5.1; partial factors are based onthe published values.

Since the formulation for ISO and RP2A-LRFD is identical, and since (with an environmental factor of 1.35) the load and resistance factors are the same, there is no difference between thereliabilities achieved for designs to the two Codes. However, it can be seen that at highenvironment-to-gravity load ratios the reliability for both Codes is higher than that achieved byRP2A-WSD designs.

The curves for the partial factor Codes are less steep than the curve for WSD. However, evenmore consistency in reliability may be achieved by the ISO Code if the gravity load factor for theextreme condition were to be reduced; this is illustrated in Section 11 along with some of the other consequences.

30



Reliability Index versus W e /G behaviour for member axialtension

0.0

1.0

2.0

3.0

4.0

5.0

6.0

β ISO

R e

l i a b i l i t y I n d e x ,

API LRFD

API WSD

0.1 1 10 100

Extreme Environment/Gravity Load Ratio, W e/G

Figure 5.1 Axial Tension - Effect of Variation in Environment-to-Gravity Load Ratio

Typical results from the first-order reliability analysis for the ISO Code for an environment-to-gravity load ratio of 1.0 are shown in Table 5.2. The reliability index for this case is 3.900.

The results show that the reliability is most sensitive to the environmental load and load modeluncertainty. The results are not very sensitive to the geometry parameters.

β(x* values)

Sensitivi ty coefficient(α

Model uncertainty X m 1.000 0.000

Load model uncertainty X w 0.906 0.334

Yield stress X F 1.080 0.206

Thickness X T 0.999 0.037

Outer Diameter X D 0.999

Environmental load W 1.590

return period storm

Dead Load D 1.010

Live Load L 1.029

Basic Variables -point values-factors)

0.011

-0.915equivalent to 6,000-year

-0.044

-0.073

Table 5.2 Reliability Analysis Basic Variable β-point Values and Sensitivities – Axial Tension

31



5.3 AXIAL COMPRESSION

The results for a typical member geometry are shown in Figure 5.2; partial factors are based on

the published values. The strength formulations for RP2A-LRFD and ISO are similar, and againreliabilities achieved by the two Codes (with γ w = 1.35) are similar. However, reliabilities for RP2AWSD designs are again lower at high environment-to-gravity load ratios.

Reliability index versus W e /G behaviour for member axialcompression

0.0

1.0

2.0

3.0

4.0

5.0

6.0

R e

l i a b i l i t y I n d e x , β

ISO

API LRFD

API WSD

0.1 1 10 100

Environme nt/Gravity Load Ratio, W e /G

Figure 5.2 Axial Compression - Effect of Variation in Environment-to-Gravity Load Ratio


The results show that the reliability is most sensitive to the environmental load and load modeluncertainty. The very high equivalent return period for the environmental load shows the veryextreme nature of an event likely to cause failure of such a compression member. (Note: any step

change in environmental loading due to wave-in-deck loading is not considered here).

32



β(x* values)


Model uncertainty(column buckling)

Load model uncertainty

Effective length factor (multiplier on K)

Young’s Modulus

Length

Yield stress

Outer Diameter

Environmental load

Dead LoadLive Load

Xm 1.023 0.163

Xw 0.908 0.354

XK 0.909

XE 0.996 0.018

XL 1.000

XF 1.078 0.183

XT 0.998 0.037

XD 0.999 0.012

W 1.984

return period storm

D 1.010L 1.029


Thickness

-0.076

-0.002


-0.037-0.062

Table 5.3 Reliability Analysis Basic Variable β-point Values and Sensitivities – Axial Compression

33



5.4 BENDING

The results for a typical member geometry are shown in Figure 5.3; partial factors are based onthe published values.

Reliability index versus W e /G behaviour for memberbending

R e


β

ISO

0.0

1.0

2.0

3.0

4.0

5.0

6.0

API LRFD

API WSD

0.1 1 10 100

Environment/Gravity Load Ratio, W e /G

Figure 5.3 Bending - Effect of Variation in Environment-to-Gravity Load Ratio


β(x* values)

Sensitivity coefficient(α



Young’s Modulus X E 0.994 0.028

XF 1.087 0.167

Thickness X T 0.998 0.040

Outer Diameter X D 0.999 0.019


return period storm

Dead Load D 1.010

Live Load L 1.029


Yield stress


-0.042

-0.071Table 5.4 Reliability Analysis Basic Variable β-point Values and Sensitivities – Bending

34



The results show that the reliability is again most sensitive to the environmental load and modeluncertainty.

5.4.1 Effect of Operating Condit ionThe results at low environment-to-gravity load ratios are for component designs that are very likelyin practice to be governed by the operating or still water conditions. The operating designcondition is chosen by the Operator and in the North Sea is often based on storms with a returnperiod of between 1-month and 1-year; in other regions of the world 1- to 5-year return periodstorms are used. Typically, the global base shear is around half of that for the 100-year load; for the purposes of this assessment, member environmental load is considered proportional to baseshear.

For the Operating Condition, the factored load to the ISO Code, in the notation used in this report,is given by:

Fd = D3.1 + L5.1 + 9.0 γ wWo (5.3)

where W o is the operating load (zero for the Still Water condition)and γ w is the extreme environmental load factor for the region, taken as 1.35 in this

subsection.

Strictly, the live load component should include short duration loads imposed on the structure fromoperations (defined as Q 2 loads in ISO); this has been neglected here.

Typical results for a component governed by bending are shown in Figure 5.4. The reliabilityachieved for RP2A-WSD is significantly higher than ISO and RP2A-LRFD; this is largely becauseof the one-third increase in allowable stress in the WSD Code. For ISO and LRFD, the componentdesign in the figure is governed by the operating condition for extreme environmental–to-gravityload ratios of around 0.4 and less.

35



Reliability Index versus W e /G behaviour for member bending

R e


β

8.0

7.0

6.0

5.0

4.0

3.0

2.0

1.00.0

ISO

ISO

0 0.5 1 1.5 2Extreme

Extreme Environment/Gravity Load Ratio, W e /G Operating

API LRFD

API WSD

API LRFD

API WSD

Figure 5.4 Comparison of Reliabilities for Extreme and Operating Conditions at LowEnvironment-to-Gravity Load Ratios

The effect of different operating to extreme environmental load ratios is illustrated in Figure 5.5 for the ISO Code, where reliabilities for ratios from 0.7 to the still water condition are shown. Even thestill water condition eliminates the sharp reduction in reliability that occurs for the extremecondition at W e/G ratios less than 0.4 for this case.

36



Reliability Index versus W e

0.01.0

2.0

3.0

4.0

5.0

6.0

0 0.5 1 1.5 2

e /G

βCondition

Wo=0.7We

Wo=0.5We

Wo=0.3We

Still Water

/G behaviour for memberbending

Extreme Environment/Gravity Load Ratio, W

R e


Extreme

Figure 5.5 Comparison of Reliabilities for Extreme, Operating and Still Water Conditions at LowEnvironment-to-Gravity Load Ratios

5.5 COMBINED TENSION & BENDING

The format of the interaction equation in ISO and RP2A-WSD is based on a linear-form of equation, whereas in RP2A-LRFD it is based on a cosine-form. The difference is significant atintermediate ratios of tension-to-bending stress.

The results for a typical member geometry are shown in Figure 5.6; partial factors are based onthe published values. The reliabilities achieved by RP2A-LRFD are less than those for ISO at allvalues of environment-to-gravity load ratio. Coincidentally in this case, the reliabilities achieved byRP2A-WSD and LRFD are similar at high W e/G ratios. The ratio of tension to bending stress usedwas 0.67:0.33.

37



Reliability index versus W e/G behaviour for member combinedtension and bending

R e


β

ISO

0.0

1.0

2.0

3.0

4.0

5.0

6.0

API LRFD

API WSD

0.1 1 10 100

Environment/Gravity Load Ratio, W e/G

Figure 5.6 Combined Tension and Bending - Effect of Variation in Environment-to-Gravity LoadRatio

Typical results from the first-order reliability analysis for the ISO Code for an environment-to-gravity load ratio of 1.0 are shown in Table 5.5. The reliability index for this case is 4.056. Theresults show that the reliability is most sensitive to the environmental load and model uncertainty.

The curvature of the failure surface was investigated at the β-point using second-order reliabilityanalysis, but this had very little effect on the failure probability.

β(x* values)





Yield stress X F 1.083 0.188Thickness X T 0.999 0.037



return period storm

Dead Load D 1.010

Live Load L 1.029


0.010


-0.042

-0.071

Table 5.5 Reliability Analysis Basic Variable β-point Values and Sensitivities – Combined Tensionand Bending

38



5.6 COMBINED COMPRESSION & BENDING

The formulations for Compression & Bending are probably the most important formulations for

member design. The results for a typical member geometry are shown in Figure 5.7; partialfactors are based on the published values. The ratio of compression to bending stress used was0.25:0.75.

Reliability index versus W e /G behaviour for membercombined compression and bending

0.0

1.0

2.0

3.0

4.0

5.0

6.0

R e


β

ISO

API LRFD

API WSD

0.1 1 10 100


Figure 5.7 Combined Compression and Bending - Effect of Variation in Environment-to-GravityLoad Ratio


The results show that the reliability is most sensitive to the environmental load, model uncertaintyand load model uncertainty.

39



Sensitivi ty coefficient(x* values)

β(α

Model uncertainty X m 0.925 0.316(column buckling)

Xw 0.909 0.318

Effective length factor X K 0.904(multiplier on K)


Length X L 1.000

Yield stress X F 1.089 0.161Thickness X T 0.998 0.040



return period storm

Dead Load D 1.010

Live Load L 1.029



-0.075

-0.002

0.011


-0.043

-0.072

Table 5.6 Reliability Analysis Basic Variable β-point Values and Sensitivities – CombinedCompression and Bending

5.7 COMBINED TENSION, BENDING & HYDROSTATIC PRESSURE

The results for a typical member geometry are shown in Figure 5.8; partial factors are based onthe published values. The ratio of tension to bending stress used was 0.66:0.34.


The results show that the reliability is most sensitive to the environmental load and modeluncertainty.

40



Reliability index versus W e/G behaviour for member combinedtension, bending & hydrostatic pressure

β

6.0

5.0

4.0

3.0

2.0

1.0

0.0

ISO

R e


API LRFD

API WSD

0.1 1 10 100


Figure 5.8 Combined Tension, Bending and Hydrostatic Pressure - Effect of Variation inEnvironment-to-Gravity Load Ratio

β(x* values)


Model uncertainty


Hydrostatic loaduncertainty

Young’s Modulus

Yield stress

Thickness

Outer Diameter

Environmental load

Dead Load

Live Load

Xm 0.929 0.374

Xw 0.915

H 1.000

XE 0.997 0.014

XF 1.086 0.180

XT 0.999 0.040

XD 0.999 0.009

W 1.438

return period storm

D 1.010

L 1.029


0.311

-0.001


-0.044

-0.074

Table 5.7 Reliability Analysis Basic Variable β-point Values and Sensitivities – CombinedTension, Bending and Hydrostatic Pressure

41



5.8 COMBINED COMPRESSION, BENDING & HYDROSTATICPRESSURE

The results for a typical member geometry are shown in Figure 5.9; partial factors are based onthe published values. The ratio of compression to bending stress used was 0.33:0.67.

Reliability index versus W e /G behaviour for membercombined compression, bending & hydrostatic pressure

0.0

1.0

2.0

3.0

4.0

5.0

6.0

R e


β

ISO

API LRFD

API WSD

0.1 1 10 100

Env ironment/Grav ity Load Ratio, W e /G

Figure 5.9 Combined Compression, Bending and Hydrostatic Pressure - Effect of Variation inEnvironment-to-Gravity Load Ratio


The results show that the reliability is most sensitive to the environmental load and modeluncertainty.

42



β(x* values)


Model uncertainty (localbuckling)


Hydrostatic loaduncertainty

Young’s Modulus

Yield stress

ThicknessOuter Diameter

Environmental load

Dead Load

Live Load

Xm

Xw 0.913

H 1.003

XE 0.996

XF 1.085

XT 0.998XD 0.999

W 1.473

return period storm

D 1.010

L 1.028

0.497

0.291

0.020

0.170

0.0400.007


0.899

equivalent to 2,500-year

-0.011

-0.795

-0.041

-0.068

Table 5.8 Reliability analysis basic variable β-point values and sensitivities – combinedcompression, bending and hydrostatic pressure

43



5.9 VARIATION OF ENVIRONMENTAL LOAD FACTOR

For illustration, the effect of different environmental load factors was investigated for a typicalmember in combined compression and bending for design to the ISO code. The results areshown in Figure 5.10. The results show that there is not a great deal of variation in reliability indexfor environmental load factors in the range 1.2 to 1.4. The ratio of compression to bending stressused was 0.25:0.75.

Effect of environmental load factor on reliability indexversus W e /G behaviour

0.0

1.0

2.0

3.0

4.0

5.0

6.0

R e


β

1.2

1.25

1.3

1.35

1.4

γ W

0.1 1 10 100


Figure 5.10 Combined Compression and Bending - Effect of Variation in Environment-to-GravityLoad Ratio for Different Environmental Load Factors

44



5.10 VARIATION OF COLUMN SLENDERNESS PARAMETER

The effect of different column slenderness parameters was investigated for a typical member incombined compression and bending for design to the ISO code. The results are shown in Figure5.11. The results show that there is only a small variation in reliability index over a wide range of column slenderness parameter values of 0.2 to 1.13.

The ratio of compression to bending stress used was 0.25:0.75.

Effect of W e /G ratio on reliability index versus columnslenderness parameter

0.0

1.0

2.0

3.0

4.0

5.0

6.0

β

1

2

5

25

We /G ratio

R e


0.0 0.2 0.4 0.6 0.8 1.0 1.2

Column Slenderness Parameter, λ

Figure 5.11 Combined Compression and Bending - Effect of Variation in Column SlendernessParameter for Different Environment-to-Gravity Load Ratios

5.11 VARIATION OF D/T RATIO

Investigation showed that reliability results were not sensitive to variation of D/T ratio.

5.12 VARIATION OF BENDING AMPLIFICATION FACTOR, C m

For tubular members subject to combined axial compression & bending the design must satisfytwo equations in the Codes. One is a local check for 'plasticity' or yielding (it should be applied atsections along the length of the member); the other is a stability check for the member whichaccounts for the moment amplification due to the action of the axial force on the out-of-straightmember. The form of the stability checking equation is:

45



0.1Ff

'F/f 1C

Ff

b

b

Ea

m

a

a ≤−+ (5.3)

where f a, f b, Fa and F b are the acting and allowable axial and bending stresses respectively,F'e is related to the Euler buckling stress for the member Cm is the moment amplification factor.

A similar stability check is also used for members subject to combined compression, bending andhydrostatic pressure.

The results of reliability analyses for a typical member geometry (brace G4 – see Table 3.1) areshown in Figure 5.12 for C m values of 0.4 and 0.85. The ratio of compression to bending stressused was 0.33:0.67.

For this component the governing API RP2A -WSD 20 th (21 st) Edition design equation for compression, bending and hydrostatic pressure is independent of C m. For the API RP2A-LRFDdesign equation there is a large variation in reliability index with C m value. For the ISO designequation the variation is not as great.


0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100


R e l i a b i l i t y

I n d e x , β

ISO -Cm=0.85

API LRFD- Cm=0.85

API WSD -Cm=0.85

ISO -Cm=0.4

API LRFD- Cm=0.4

API WSD -Cm=0.4

Figure 5.12 Combined Compression, Bending and Hydrostatic Pressure - Effect of Variation inEnvironment-to-Gravity Load Ratio for Different C m Values

This variation in reliability with C m value was found to have a significant effect on the reliabilityanalysis results. In the Codes, the C m factor is evaluated from one of three cases specified in a

table (see Table 5.9 below) which is similar in all three Codes (WSD, LRFD and ISO). However,for main diagonals and horizontals there is a choice, depending on whether or not the member

46



has transverse load; in practice most members have some transverse load from self weight,and/or local wind or wave action. Thus, in some cases the most appropriate value is a matter of

judgement.

Structural element Cm (see definition below)

Superstructure LegsBracedPortal (un-braced)

(a)(a)

Jacket Legs & PilingGrouted Composite SectionUngrouted Jacket LegsUngrouted Piling Between Shim Points

(c)(c)(b)

Jacket BracesPrimary Diagonals & HorizontalsK-bracesLonger segment length of X-braces

(b) or (c)(c)(c)

Secondary Horizontals (c)

Table 5.9 Moment reduction factors (C m) for ISO member strength checking

Cm values for the three cases defined in the table above are as follows:

a) 0.85

b) for members with no transverse loading,

Cm = 0.6 - 0.4M 1/M2

where M 1/M2 is the ratio of smaller to larger moments at the ends of that portion of themember unbraced in the plane of bending under consideration. M 1/M2 is positive when themember is bent in reverse curvature, negative when bent in single curvature.

c) for members with transverse loading,

Cm = 1.0 - 0.4f c/Fe, or 0.85, whichever is less,

and F e = F ey or F ez as appropriate

The above definition for C m occurs in RP2A-WSD, RP2A-LRFD and ISO. However, because inthe LRFD and ISO Codes C m is evaluated using factored member forces and stresses, the valuesof Cm evaluated for a particular component may vary (if the load factors are different) and mayvary from WSD.

47



5.13 VARIATION OF BENDING TO AXIAL STRESS RATIO

The variation of reliability index with bending to axial stress ratio for a typical member geometry

subject to combined axial compression and bending and designed to the ISO code is shown inFigure 5.13. The results show that the bending to axial stress ratio does not have a significanteffect on the reliability index.

Effect of W e /G ratio on reliability index versus bending tocompressive stress ratio

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0

Ratio bending to compressive stress

R e l i a b

i l i t y I n d e x ,

β

0.3

0.5

1

2

5

10

We /Gratio

Figure 5.13 Combined Compression and Bending - Effect of Variation in Bending to CompressiveStress Ratio for Different Environment-to-Gravity Load Ratios

48



6 . CALIB RATION POINT RESULTS

6.1 SUMMARY

In this section reliability analysis results are presented for all of the calibration points in thedatabase.

The calibration exercise was carried out using a comprehensive suite of software developed andassembled for reliability based code calibration. The software performs a first order secondmoment reliability analysis. Independent checks were carried out using a purpose-written firstorder reliability analysis spreadsheet.

6.2 BRACE MEMBERS

Graphs of results for all calibration points for brace members (Northern North Sea) are presentedbelow in Figures 6.1 to 6.5 for ISO with γ W=1.35, and Figure 6.6 for API RP2A - WSD. The graphsshow that the widest range of reliability values is obtained for compression and bending cases.

The general trend in reliability with W e/G ratio is less marked for ISO (see Figure 6.1 to Figure 6.5)than for RP2A-WSD (see Figure 6.6), and for many load effects the reliabilities for ISO arereasonably consistent over a wide range of W e/G ratios.

Table 6.1 shows the average probabilities of failure and equivalent reliabilities for each load effectfor API RP2A – WSD and ISO. It can be seen that equivalent reliabilities for all load effectscombined are close to the values for compression and bending alone.

API - WSD ISO ( γ w = 1.35)

Load EffectPf

Equivalent β Pf

Equivalent β

Compression & Bending 1.063E-04 3.704 3.569E-05 3.972

Tension & Bending 1.386E-04 3.636 5.804E-05 3.854

Tension, Bending & Hydrostatic 5.868E-05 3.852 9.970E-05 3.720

Compression, Bending & Hydrostatic 7.289E-05 3.798 2.153E-05 4.090

All 1.074E-04 3.701 4.131E-05 3.937

Table 6.1 Weighted Average P f and Equivalent β for each Load Effect – Brace Members

49



Reliability index of calibration points vs W e /G for bracemembers in extreme loading condition (ISO NNS

γ w =1.35)

0

1

2

3

4

5

6

0.1 1 10 100We/G ratio

R e l i a b


β

Tension &Bending

Tension &Bending &HydroCompression& Bending &HydroCompression& Bending

Figure 6.1 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – Brace Members – ISO

Reliability index of calibration points vs W e /G formembers in extreme loading condition (ISO NNS

γ w =1.35)

0

1

2

3

4

5

6

0.1 1 10 100We/G ratio

R e l i a b i l i t y I n

d e x , β

Compression &Bending

Figure 6.2 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – Brace Members – ISO – Combined Compression and Bending

50



Reliability index of calibration points vs W e/G formembers in extreme loading condition (ISO NNS

γ w=1.35)

0

1

2

3

4

5

6

0.1 1 10 100

We/G ratio

R e l i a b

i l i t y I n d e x , β

Tension &Bending

Figure 6.3 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – Brace Members – ISO – Combined Tension and Bending

Reliability index of calibration points vs W e/G formembers in extreme loading condition (ISO NNS

γ w=1.35)

0123

456

0.1 1 10 100We /G ratio

R e l i a b

i l i t y

I n d e x , β

Tension &Bending &Hydro

Figure 6.4 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – Brace Members – ISO – Combined Tension, Bending and Hydrostatic

51



Reliability index of calibration points vs W e /G formembers in extreme loading condition (ISO NNS

γ w =1.35)

0

1

2

3

4

5

6

0.1 1 10 100We /G ratio


I n d e x , β

Compression& Bending &Hydro

Figure 6.5 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – Brace Members – ISO – Combined Compression, Bending and Hydrostatic

Reliability index of calibration points vs W e/G for members inextreme loading condition (API-WSD 17-20 NNS)

0

1

2

3

4

5

6

0.1 1 10 100

We/G ratio

R e l i a b i l

i t y I n d e x ,

β

Tension &Bending



Compression& Bending

Figure 6.6 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – Brace Members – API WSD 17-20 th (21 st) Edition

52



6.3 LEG MEMBERS

Graphs of results for all calibration points for leg members (Northern North Sea) are presented

below in Figures 6.7 to 6.9 for ISO, and Figure 6.10 for API RP2A - WSD. The graphs show thatagain the widest range of reliability values is obtained for compression and bending cases.

The general trend with W e/G ratio is less marked for ISO (see Figure 6.7 to Figure 6.9) than for RP2A-WSD (see Figure 6.10), and for many load effects the reliabilities for ISO are reasonablyconsistent over a wide range of W e/G ratios.

Table 6.2 shows the average probabilities of failure and equivalent reliabilities for each load effectfor API RP2A – WSD and ISO. It can be seen that equivalent reliabilities for both load effectscombined are close to the values for compression and bending alone.

API - WSD ISO ( γ w = 1.35)

Load EffectPf

Equivalent β Pf

Equivalent β

Compression & Bending 2.403E-04 3.492 5.829E-05 3.844

Compression, Bending & Hydrostatic 7.756E-05 3.783 1.417E-05 4.186

All 2.362E-04 3.496 5.927E-05 3.849

Table 6.2 Weighted Average P f and Equivalent β for each Load Effect – Leg Members

53



Reliability index of calibration points vs W e /G for legs inextreme loading condition (ISO NNS&CNS γ w=1.35)

01

2

3

4

5

6

0.1 1 10 100

We /G ratio

R e l i a b

i l i t y I n d e x , β Compression

& Bending &Hydro


Figure 6.7 Reliability index of calibration points against extreme environmental/gravity load ratios – leg members – ISO

Reliability index of calibration points vs W e/G for legs inextreme loading condition (ISO NNS&CNS γ w=1.35)

0

1

23

4

5

6

0.1 1 10 100

We/G ratio

R e l i a b

i l i t y

I n d e x , β

Compression &

Bending

Figure 6.8 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – Leg Members – ISO – Combined Compression and Bending

54



Reliability index of calibration points vs W e/G for legs inextreme loading condition (ISO NNS&CNS γ w=1.35)

0

1

2

3

4

5

6

0.1 1 10 100We/G ratio

R e l i a b

i l i t y I n d e x , β


Figure 6.9 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – Leg Members – ISO – Combined Compression, Bending and Hydrostatic

Reliability index of calibration points vs W e/G for legs inextreme loading condition (API - WSD 17-20 NNS&CNS)

0

1

2

3

4

5

6

0.1 1 10 100

We/G ratio

R e l i a b i

l i t y I n d e x ,

b Compression& Bending &Hydro


Figure 6.10 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – Leg Members – API-WSD 17-20 th (21 st) Edition

55



56



7. HI STORICAL ASSESSMENT AN D TARGET

ASSESSMENT

7.1 HISTORICAL ASSESSMENT

In order to assess the reliability levels and as an aid to judge an acceptable level of reliability, theanalysis has been undertaken to reflect the historic changes in design practice. In the historicassessment both the changes in design resistance based on the publication date of the variousCodes, and the changes in design loading as applied in the North Sea have been considered.The changes in design loading are more difficult to assess and have been based on aquestionnaire by Tromans [8] (see Figure 7.1).

0.0

1.0

2.0

3.0

4.0

5.0

'70 '74 '78 '82 '86 '90 '94 '98

Year

Design storm load North Sea

Gulf of Mexico

True 100 year load

Figure 7.1 History of Changes in Design Loading

Weighting factors, as discussed in Section 3, were applied to each of the calibration points using apurpose written spreadsheet. Weighting factors were applied to the probability for each calibrationpoint. The average equivalent reliability was then calculated from the sum of weightedprobabilities. This weighting exercise was repeated for each set of probability results, which wererun for each change in design resistance or design loading. The resulting variation of averagereliability with time is shown in Figure 7.2 and Figure 7.3 for brace and leg members respectively.

The average reliability to the ISO code for an environmental load factor of 1.35 is shown for comparison. For both braces and legs this is higher than the API RP2A – WSD or RP2A – LRFD

57



average reliabilities for current design loading showing there is scope for reducing theenvironmental load factor to less than 1.35. Selection of an environmental load factor is discussedfurther in Section 7.2.

Variation of Reliability with time - North Sea Brace Members

0

1

2

3

4

5

1970 1980 1990 2000

Year


ISO 1.35

API - LRFD

API - WSD

Figure 7.2 Historical Variation of Reliability – Brace Members

Variation of Reliability with time - North Sea Legs

0

1

2

3

4

5

1970 1975 1980 1985 1990 1995 2000

Year


ISO 1.35

API - LRFD

API - WSD

Figure 7.3 Historical Variation of Reliability – Leg Members

58



7.2 TARGET ASSESSMENT

7.2.1 Selection of Environmental Load Factor The effect on reliability of varying the environmental load factor for brace and leg members isshown in the Figures below. By comparison with the target reliabilities calculated to API RP2A –WSD and LRFD from Figure 7.2 and Figure 7.3 and the target recommended by Efthymiou [6], arange of environmental load factors may be suggested for further discussion. It should be notedthat Efthymiou's target was derived for system reliability; it is conservative to use this value for component reliability.

The weighted probabilities and equivalent reliabilities represented in Figure 7.4 to Figure 7.6 aregiven in Table 7.1.

Comparison of Figure 7.4 and Figure 7.5 shows that the overall weighted reliability based on allfour types of load effects is not too different from compression and bending alone.

Variation of weighted reliability with environmentalload factor - ISO brace members

4.014

3.701

0

1

2

3

4

5

1.1 1.2 1.3 1.4 1.5

Environmental load factor

W e i g h

t e d r e l i a b i l i t y , β

braccemembers(NNS&CNS)

TargetReliability(Efthmyiou)

TargetReliability(API - LRFD)

TargetReliability(API - WSD)

Figure 7.4 Variation of Weighted Reliability With Environmental Load Factor – ISO BraceMembers

59



Variation of weighted reliability with environmentalload factor - ISO brace members (compression &

bending )

4.0143.704

0

1

2

3

4

5

1.1 1.2 1.3 1.4 1.5


W

e i g h t e d r e l i a b

i l i t y , β

braccemembers(NNS&CNS)




Figure 7.5 Variation of Weighted Reliability With Environmental Load Factor – ISO BraceMembers – Combined Compression and Bending Only

Variation of weighted reliability with environmentalload factor - ISO leg members

4.0143.781

3.496

0

1

2

3

4

5

1.1 1.2 1.3 1.4 1.5


W e i g

h t e d r e

l i a b i l i t y , β

legmembers(NNS &CNS)TargetReliability(Efthmyiou)



Figure 7.6 Variation of Weighted Reliability With Environmental Load Factor – ISO Leg Members

60



brace membersbrace members(compression &bending only)

leg members

Code

Pf Equivalent

β Pf

Equivalentβ

Pf Equivalent

β

API–WSD 20th 1.074E-04 3.701 1.063E-04 3.704 2.362E-04 3.496

γ w-1.2 1.243E-04 3.664 1.093E-04 3.697 1.753E-04 3.575

γ w-1.25 8.588E-05 3.757 7.509E-05 3.791 1.218E-04 3.669

γ w-1.3 5.949E-05 3.848 5.171E-05 3.882 8.488E-05 3.760

γ w-1.35 4.131E-05 3.937 3.569E-05 3.972 5.927E-05 3.849

γ w-1.4 2.874E-05 4.023 2.468E-05 4.059 4.149E-05 3.936

ISO

γ w-1.45 2.004E-05 4.107 1.711E-05 4.143 2.912E-05 4.020

Table 7.1 Weighted Average P f and Equivalent β for Different Environmental Load Factors

On the basis of the results above, an environmental load factor of 1.25 would give reliability levelsfor the ISO code slightly above the API RP2A - WSD 20 th (21 st) Edition values for both braces andlegs. The effect of selecting an environmental load factor of 1.25 is investigated in the followingsections.

7.2.2 Typical Member The effect of reducing the environmental load factor from 1.35 to 1.25 is shown in the graphsbelow (Figure 7.7 to Figure 7.10) for a typical member, as investigated in Section 5. The reliabilityvalues are compared with the API RP2A - WSD 20 th (21 st) Edition values. In all cases exceptcombined tension, bending and hydrostatic pressure, the ISO code reliability with environmentalload factor of 1.25 is close to the API-WSD 17-20 th (21 st) Edition values for W e/G values greater than 2.0.

61



Reliability index versus W e/G behaviour for membercombined tension and bending

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100


R e l i a b

i l i t y I n d e x , β ISO -

1.35

ISO -1.25

APIWSD

Figure 7.7 ISO Code Reliability - Effect of Reducing Environmental Load Factor From 1.35 to1.25 for Typical Member for Combined Tension and Bending


0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100


R e l i a

b i l i t y I n d e x ,

β

ISO -1.35ISO -1.25API WSD

Figure 7.8 ISO Code Reliability - Effect of Reducing Environmental Load Factor From 1.35 to1.25 for Typical Member for Combined Compression and Bending

62



Reliability index versus W e /G behaviour for membercombined tension, bending & hydrostatic pressure

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100



I n d e x ,

β ISO -1.35ISO -1.25APIWSD

Figure 7.9 ISO Code Reliability - Effect of Reducing Environmental Load Factor From 1.35 to1.25 for Typical Member for Combined Tension, Bending and Hydrostatic Pressure


0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100



I n d e x ,

β ISO -1.35ISO -1.25APIWSD

Figure 7.10 ISO Code Reliability - Effect of Reducing Environmental Load Factor From 1.35 to1.25 for Typical Member for Combined Compression, Bending and Hydrostatic Pressure

63



7.2.3 Calibration PointsThe effect of reducing the environmental load factor from 1.35 to 1.25 for the individual calibrationpoints is shown in the graphs below for braces and legs. The results in Table 7.1 show that on anaverage basis the reliability achieved for ISO designs with a load factor of 1.25 exceeds thereliability inherent in RP2A-WSD, it can be seen that the reliabilities evaluated for a significantnumber of individual calibration points falls below the API RP2A-WSD 20 th (21 st) Edition 'target'reliability. Many of these points receive low weighting factors in the calibration, indicating that theydo not occur all that frequently in practice.

It is worth noting that, from comparison with Figure 6.6 and Figure 6.10, the calibration point withthe lowest reliability evaluated for the ISO Code with γ W=1.25 exceeds the minimum reliabilityevaluated for all of the corresponding designs to RP2A-WSD. Whilst the calibration point

database has been selected to be representative of the range of North Sea components anddesigns, it is not exhaustive. Thus, some of these outlying points may need to be investigated inmore detail once the value of the load factor is chosen.

64




γ w =1.25)

0

1

2

3

4

5

6

0.1 1 10 100We/G ratio

R e l i a

b i l i t y I n d e x ,

β

Tension &Bending




Target(Efthmyiou)

Target API -LRFD

Target API -WSD

Figure 7.11 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – Brace Members – ISO γ W=1.25


γ w =1.35)

0

1

2

3

4

5

6

0.1 1 10 100We/G ratio

R e l i a b i

l i t y I n d e x ,

β

Tension &Bending




Target(Efthmyiou)

Target API -LRFD

Target API -WSD

Figure 7.12 Reliability Index of Calibration Points Against Extreme Environmental/gravity Load

Ratios – Brace Members – ISO γ W=1.35

65



Reliability index of calibration points vs W e /G for legs inextreme loading condition (ISO NNS&CNS γ w =1.25)

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

0.1 1 10 100We/G ratio

R e l i a b


β



Target(Efthmyiou)

Target AP I -LRFD

Target AP I -WSD

Figure 7.13 Reliability Index of Calibration Points Against Extreme environmental/Gravity LoadRatios – Leg Members – ISO γ W=1.25

Reliability index of calibration points vs W e /G for legs inextreme loading condition (ISO NNS&CNS γ w=1.35)

0

1

2

3

4

5

6

0.1 1 10 100We/G ratio

R e l i a

b i l i t y I n d e x , β



Target(Efthmyiou)

Target API -LRFD

Target API -WSD

Figure 7.14 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – Leg Members – ISO γ W=1.35

66



8 . SENSITI VIT Y STUDIES

8.1 SUMMARY

A number of sensitivity studies have been carried out, the results of which are presented in thissection. The aim of the studies is to establish the robustness of the calibration process.

8.2 WEIGHTING FACTORS

The weighting factors assigned to the calibration points are somewhat subjective. The sensitivityto the chosen weighting factors was investigated by comparing average weighted reliabilities withaverage unweighted (or equally weighted) reliabilities. The results are shown in the tables below.The results show a change of less than 2% for equivalent reliability between weighted andunweighted values. However, the unweighted results would suggest that a load factor of closer to1.30 may be more appropriate for brace members if the target were to be based solely onunweighted RP2A-WSD designs. This is because the tension & bending and tension, bending &hydrostatic results have a far greater influence in the unweighted calibration analysis. Theunweighted case is not very representative or realistic, but nevertheless the study shows that theweighting factors do not have a very significant influence on the value of the partial factor.

Weighted Unweighted(or equally weighted)

Code

Pf Equivalent

β Pf

Equivalentβ

API–WSD 20th 1.074E-04 3.701 7.670E-05 3.786

γ w-1.2 1.243E-04 3.664 1.362E-04 3.640

γ w-1.25 8.588E-05 3.757 9.543E-05 3.731

γ w-1.3 5.949E-05 3.848 6.705E-05 3.819γ w-1.35 4.131E-05 3.937 4.722E-05 3.904

γ w-1.4 2.874E-05 4.023 3.334E-05 3.988

ISO

γ w-1.45 2.004E-05 4.107 2.360E-05 4.069

Table 8.1 Comparison of Weighted and Unweighted Average P f and Equivalent β for DifferentEnvironmental Load Factors for Brace Members

67



WeightedUnweighted

(or equally weighted)Code

Pf Equivalentβ

Pf Equivalentβ

API–WSD 20th 1.063E-04 3.704 7.592E-05 3.788

γ w-1.2 1.093E-04 3.697 8.771E-05 3.752

γ w-1.25 7.509E-05 3.791 6.031E-05 3.845

γ w-1.3 5.171E-05 3.882 4.159E-05 3.935

γ w-1.35 3.569E-05 3.972 2.874E-05 4.023

γ w-1.4 2.468E-05 4.059 1.991E-05 4.109

ISO

γ w-1.45 1.711E-05 4.143 1.382E-05 4.192

Table 8.2 Comparison of Weighted and Unweighted Average P f and Equivalent β for DifferentEnvironmental Load Factors for Brace Members (Compression and Bending Only)

WeightedUnweighted

(or equally weighted)Code

Pf Equivalent

β Pf

Equivalentβ

API–WSD 20th 2.362E-04 3.496 2.777E-04 3.453

γ w-1.2 1.753E-04 3.575 1.529E-04 3.610

γ w-1.25 1.218E-04 3.669 1.072E-04 3.702

γ w-1.3 8.488E-05 3.760 7.527E-05 3.790

γ w-1.35 5.927E-05 3.849 5.301E-05 3.876

γ w-1.4 4.149E-05 3.936 3.743E-05 3.960

ISO

γ w-1.45 2.912E-05 4.020 2.650E-05 4.042

Table 8.3 Comparison of Weighted and Unweighted Average P f and Equivalent β for DifferentEnvironmental Load Factors for Leg Members

68



8.3 20-YEAR RELIABILITIES

In the TAC-22 [10] and AME [9] work to calibrate the Draft LRFD, a 20-year reference period wasused for the distribution of environmental load, see Eqn (4.7). 20-year reliability results for atypical member for combined compression and bending (with γ W=1.35 where required) arepresented in Figure 8.1. Also shown is a curve for the corresponding reliability results for a 1-year reference period for ISO. Clearly, the reliability levels are less for a 20-year exposure period. Thehigher mean of the environmental load variable for a 20-year reference period means that thisvariable has a more significant influence on the 20-year reliabilities than annual reliabilities,particularly at high W e/G ratios; this is more marked in terms of probability than reliability index.

Since the CoV for the 20-year distribution is less than the annual distribution, and since theenvironmental load factor reflects the uncertainty in the variable, it is likely that the value of thepartial factor evaluated on a like-for-like basis using a 20-year distribution would be marginally lessthan if evaluated by using a 1-year distribution. Unless the target is based solely on the inherentreliability evaluated for RP2A-WSD, it is more difficult to define an appropriate target for a 20-year reference period.


0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100


R e l i a b


β ISO - 1year

ISO - 20yearAPI WSD- 20 year

API LRFD- 20 year

Figure 8.1 20-year Reliabilities for Combined Compression and Bending

The calibration exercise was repeated for brace members using a 20-year reference period for thedistribution of environmental load. The analysis was undertaken assuming that the uncertainty inall of the other variables is unchanged over a 20-year period, i.e. the modelling was based onTable 4.2. The reliability was undertaken for failure modes arising from the extreme storm hazard

only. No allowance was included for contributions to the overall failure probability from fatigue,

69



accidental loading, etc; tt should be noted that over the lifetime of a structure these effects couldbecome important.

The results are presented in Figure 8.2 together with the API RP2A - LRFD and – WSD 20 th (21 st)Edition target reliabilities. It can be seen that, as with the 1-year reference period, anenvironmental load factor of 1.25 would give reliability levels for the ISO code slightly above theAPI RP2A - WSD 20 th (21 st) Edition values. Hence, the calibration method is not sensitive to thechosen reference period for the distribution of environmental load.


2.880

0

1

2

3

4

5

1.1 1.2 1.3 1.4 1.5


W e i g

h t e d r e l i a b

i l i t y , β

Bracemembers(NNS&CNS)


TargetReliability

(API - WSD)

Figure 8.2 Variation of Weighted Reliability with Environmental Load Factor for 20-year Reference Period – ISO Brace Members

8.4 TRUNCATION OF DESIGN LOAD UNCERTAINTY DISTRIBUTION

In the calibration analysis, the design load uncertainty was represented by a normal distributiontruncated at ±1.5 standard deviations, as suggested by Tromans [8]. The sensitivity to the effectof this truncation was investigated by repeating the calibration exercise for brace members with anormal distribution with no truncation assumed for the design load uncertainty. The results arepresented in Figure 8.3 together with the API RP2A - LRFD and – WSD 20 th (21 st) Edition targetreliabilities. It can be seen that, as with the truncated distribution, an environmental load factor of 1.25 would give reliability levels for the ISO code slightly above the API RP2A - WSD 20 th (21 st)Edition values. Hence the calibration method is not sensitive to the chosen truncation for the

distribution of design load uncertainty.

70




3.549

0

1

2

3

4

5

1.1 1.2 1.3 1.4 1.5


W e i g

h t e d r e l i a b

i l i t y , β

Bracemembers(NNS&CNS)



Figure 8.3 Variation of Weighted Reliability With Environmental Load Factor for design loaduncertainty with no truncation – ISO Brace Members

8.5 OPPOSING LOAD CONDITION

The ISO Code (and RP2A-LRFD) includes a design check for components where the internalforces due to gravity loads oppose the internal forces due to environmental loads caused by wind,wave and current. The partial load factors applied to the gravity loads are reduced for thiscondition. The ISO factored design load for this condition, in the notation used in this report, isgiven by:

WL8.0D9.0F Wd γ ++= (8.1)

This load condition is often considered to be one of the benefits of the LRFD approach. The CoVof the uncertainty in the overall loading for the non-opposing loads case (i.e. the usual additiveload case) and the opposing loads case may be approximated by:

WLD

2W

22L

22D

2

wld

wld

µ+µ+µσ+σ+σ

WLD

2W

22L

22D

2

wld

wld

µ−µ+µσ+σ+σ

(8.2)

Clearly, uncertainty in the loading, i.e. CoV, is much greater for the opposing loads case, and is amaximum (infinite) for this case when the mean gravity and environmental loads are equal.

71



The most famous illustration of the importance of this case is the Ferrybridge cooling towers,which failed because tension reinforcement to resist uplift had not been used in areas of thetowers where the gravity loading was slightly larger than the effects of the design wind loading.The towers failed because of an underestimate in the wind loading.

For the ISO and API Codes, graphs of variation of reliability with W e/G ratio for a typical tubular member for the opposing load condition are presented in Figure 8.4 to Figure 8.10 for the variousload effects. The results are shown for γ W=1.35 and γ W=1.25 for ISO. In each case the reliabilityto ISO or API RP2A-LRFD is fairly constant with W e/G ratio. The reliabilities to API RP2A-WSDare less than to ISO and API RP2A-LRFD, except for the single case of tension, bending andhydrostatic pressure for γ W=1.25 for ISO, where the reliability is marginally less than to API RP2A-WSD. Thus, the reliability of designs to ISO and LRFD Codes is improved for members governed

by this condition.

The large variation in reliability with W e/G ratio that occurs for designs to WSD is due to the WSDformat which effectively applies the same safety factor to both gravity and environmental load.ISO and RP2A-LRFD achieve a consistent reliability across a wide range of W e/G ratios.

The reliability levels achieved for the ISO Code for the opposing load condition are similar to thereliability levels achieved for the non-opposing load condition discussed in Section 5. For examplecompare Figure 8.5 for the opposing load condition for a typical member under axial compressionwith Figure 5.2; a reliability index of around 4.0 is shown in both figures.

Reliability Index versus W e /G behaviour for member axialtension

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100

Extreme Environment/Gravity Load Ratio, W e /G

R e l i a b


β ISO -1.35

ISO -1.25

APILRFD

APIWSD

Figure 8.4 Axial Tension - Effect of Variation in Environment-to-Gravity Load Ratio – OpposingLoad Condition

72



Reliability index versus W e /G behaviour for member axialcompression

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100


R e l i a b


β ISO -1.35

ISO -1.25

APILRFD

APIWSD

Figure 8.5 Axial Compression - Effect of Variation in Environment-to-Gravity Load Ratio –Opposing Load Condition

Reliability index versus W e /G behaviour for memberbending

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100


R e l i a b i l i t y I n d e x ,

β ISO -1.35

ISO -1.25

APILRFD

APIWSD

Figure 8.6 Bending - Effect of Variation in Environment-to-Gravity Load Ratio – Opposing LoadCondition

73




0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100Environment/Gravity Load Ratio, W e/G


I n d e x , β

ISO -1.35

ISO -1.25

APILRFD

APIWSD

Figure 8.7 Tension and Bending - Effect of Variation in Environment-to-Gravity Load Ratio –Opposing Load Condition


0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100


R e l i a b


β ISO -1.35

ISO -1.25

APILRFD

APIWSD

Figure 8.8 Compression and Bending - Effect of Variation in Environment-to-Gravity Load Ratio –Opposing Load Condition

74




0.0

1.0

2.0

3.0

4.0

5.0

6.0



I n d e x , β

ISO -1.35

ISO -1.25

APILRFD

APIWSD

Figure 8.9 Compression, Bending and Hydrostatic Pressure - Effect of Variation in Environment-to-Gravity Load Ratio – Opposing Load Condition

Reliability index versus W e /G behaviour for membercombined tension, bending & hydrostatic pressure

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100


R

e l i a b i l i t y I n d e x , β

ISO -1.35

ISO -1.25

APILRFD

APIWSD

Figure 8.10 Tension, Bending and Hydrostatic Pressure - Effect of Variation in Environment-to-Gravity Load Ratio – Opposing Load Condition

75



76



9 . T U B U L A R J O I N T S

9.1 SUMMARY

Reliability analysis for tubular joints has been undertaken to assess the effect of differentenvironmental partial load factors, and to consider the appropriateness of the partial resistancefactors.

In this Section reliability analyses have only been undertaken for individual load effects (e.g. axialtension, in-plane bending, etc.). This is because model uncertainty data are not available toassess the uncertainty associated with the interaction of load effects for tubular joints. There aresignificant differences in the form of the interaction equations between RP2A-WSD, RP2A-LRFDand ISO 19902, which will be reflected in differences in reliability levels between the variousCodes. It is recognised that this aspect has not been addressed in the studies undertaken here.


9.2.1 GeometryRepresentative geometries for joints have been selected and are shown in Table 9.1 to Table 9.3.

G1 G2 G3 G4

Chord Diameter, D (mm) 3500 800 1000 1500

Chord Thickness, T (mm) 75 30 25 40

Brace Diameter, d (mm) 1400 500 700 1400

Brace Thickness, t (mm) 30 12 25 38

β=d/D 0.400 0.630 0.700 0.930

γ =D/2T 23.330 13.330 20.000 18.750

Gap, g (mm) 50 50 50 50

Brace/Chord Angle, θ (deg) 33.79 48.72 63.82 41.76

Table 9.1 Geometry of K Joints

77



9.2.3 Load CombinationsThe combinations of dead to live load ratio considered are the same as for members as listed inTable 3.4.

9.3 WEIGHTING FACTOR DATA

The weighting factors used for the reliability analysis are presented in Figure 9.1 in the form of aweighting tree.

79



CNS

0.71

K

0.26

G2

0.31

0.3

0.15

G3

0.29

G4

0.02

1.0

0.25

3.5

0.35

1.2

0.25

AT

0.20

AC

0.31

IPB

0.22

OPB

0.27

G1

0.38

JOINTTYPE

LOADCOMBINATIONS

We/G

LOADEFFECTS

A

0.33

B

0.33

C

0.33

Y

0.56

G2

0.35

0.3

0.15

G3

0.21

G4

0.15

1.0

0.25

3.5

0.35

1.2

0.25

AT

0.15

AC

0.22

IPB

0.41

OPB

0.22

G1

0.29

A

0.33

B

0.33

C

0.33

X

0.18

G2

0.22

0.3

0.15

G3

0.34

G4

0.29

1.0

0.25

3.5

0.35

1.2

0.25

AT

0.22

AC

0.50

IPB

0.18

OPB

0.10

G1

0.15

A

0.33

B

0.33

C

0.33

NNS

0.29

K

0.3

G2

0.42

0.3

0.10

G3

0.18

G4

0.08

1.0

0.20

3.5

0.35

1.2

0.35

AT

0.33

AC

0.47

IPB

0.08

OPB

0.12

G1

0.32

A

0.33

B

0.33

C

0.33

Y

0.52

G2

0.42

0.3

0.10

G3

0.18

G4

0.27

1.0

0.20

3.5

0.35

1.2

0.35

AT

0.05

AC

0.45

IPB

0.22

OPB

0.28

G1

0.13

A

0.33

B

0.33

C

0.33

X

0.18

G2

0.24

0.3

0.10

G3

0.22

G4

0.49

1.0

0.20

3.5

0.35

1.2

0.35

AT

0.16

AC

0.39

IPB

0.24

OPB

0.21

G1

0.05

A

0.33

B

0.33

C

0.33

JOINTS

GEOGRAPHICLOCATION

DESIGNGROUPB

G1 0.20-0.45G2 0.46-0.65G3 0.66-0.85G4 >0.85


Figure 9.1 Tree Diagram for Tubular Joints – Extreme Loading Condition

80




Probability distributions have been assigned to both loading and resistance terms. All basicvariables have been assumed to be independently distributed, i.e. uncorrelated.

Xm Resistance model uncertainty LN [see Table 9.4]The resistance uncertainty parameters, i.e. mean bias and coefficient of variation (CoV), for thevarious strength formulations are as given in the ISO code and are presented in Table 9.4.Lognormal distributions have been assumed for all of the resistance model uncertainties.

K (gapped) Joint Y&T Joint X Joint

MeanStandardDeviation Mean

StandardDeviation Mean

StandardDeviation

Axial Tension 1.229 0.1745 1.708 0.4082 1.447 0.2720

Axial Compression 1.229 0.1745 1.265 0.1657 1.169 0.1075

In-Plane Bending 1.243 0.1305 1.213 0.1286 1.235 0.0926

Out-of-Plane Bending 1.217 0.1874 1.268 0.1496 1.139 0.0683

Table 9.4 Resistance Modelling Uncertainties

Annual environmental load, design load uncertainty, dead load, live load, chord diameter, bracediameter, chord thickness, brace thickness and yield stress distributions were all the same as for members, as described in Section 4.3.

9.5 RELIABILITY ANALYSIS FOR TYPICAL JOINTS

9.5.1 SummaryIn order to investigate the effect of different values of partial factors on the different load effects

and design formulations for tubular joints, first-order reliability analyses were undertaken for singlecomponents using a spreadsheet macro. Ranges of parameters were evaluated, whilst all other input parameters were kept constant. The partial resistance factor for tubular joints is 1.05 in ISO.

For comparison, results were also evaluated for designs based on RP2A-WSD 20 th (21 st) Editionand RP2A-LRFD (with API recommended load and resistance factors).

This type of analysis, using a single typical joint geometry, was undertaken to investigate theeffects of joint beta ratio, joint gamma ratio, Q f factor, etc. For these cases, an environment-to-gravity load ratio of 1.0 was assumed.

All evaluated reliabilities are annual. All results are for the extreme storm condition.

81



The typical joint used as the base case for this study was as follows:

Parameter Value

Geometry G3 (see Table 9.1 to Table 9.3)

Dead:live load ratio 1:1

Qf factor 1.0

Environmental load factor, γ W 1.35

Table 9.5 Joint Base Case for Study of Effect of Different Parameters

Geometry 3 was chosen as all parameters were the same for each joint type.

9.5.2 Axial TensionThe results for a typical joint are shown in Figure 9.2 to Figure 9.4; partial factors are based on thepublished values. It can be seen that, whilst the reliability to the ISO code remains fairly constantat around 4.0 for all joint types, the API RP2A - LRFD and WSD values are lower than ISO for theK-joint, higher than ISO for the Y-joint and about the same for the X-joint.

Reliability Index versus We/G behaviour for K-joint axial tension

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100

Extreme Environment/Gravity Load Ratio, We/G

R e

l i a b i l i t y I n d e x

, β

ISO

API LRFD

API WSD

Figure 9.2 K-Joint Axial Tension - Effect of Variation in Environment-to-Gravity Load Ratio

82



Reliability Index versus We/G behaviour for Y-joint axial tension

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100


R e


, β

ISO

API LRFD

API WSD

Figure 9.3 Y-Joint Axial Tension - Effect of Variation in Environment-to-Gravity Load Ratio

Reliability Index versus We/G behaviour for X-joint axial tension

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100


R e


, β

ISO

API LRFD

API WSD

Figure 9.4 X-Joint Axial Tension - Effect of Variation in Environment-to-Gravity Load Ratio

83



Reliabili ty Index versus We/G behaviour for X-joint axialcompression

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100

Extreme Environment/Gravity Lo ad Ratio, We/G

R e


, β

ISO

API LRFD

API WSD

Figure 9.6 X-Joint Axial Compression - Effect of Variation in Environment-to-Gravity Load Ratio

9.5.4 In-Plane Bending

The results for a typical joint are shown in Figure 9.7 to Figure 9.9; partial factors are based on thepublished values. For all codes and all joint types the reliabilities are above or only marginallybelow 4.0.

Reliabilit y Index versus We/G behaviour fo r K-joint in-plane bending

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100


R e


, β

ISO

API LRFD

API WSD

Figure 9.7 K-Joint In-Plane Bending - Effect of Variation in Environment-to-Gravity Load Ratio

85



Reliabili ty Index versus We/G behaviour fo r Y-joint i n-plane bending

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100


R e


, β

ISO

API LRFD

API WSD

Figure 9.8 Y-Joint In-Plane Bending - Effect of Variation in Environment-to-Gravity Load Ratio

Reliabili ty Index versus We/G behaviour fo r X-joint in-plane bending

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100


R e


, β

ISO

API LRFD

API WSD

Figure 9.9 X-Joint In-Plane Bending - Effect of Variation in Environment-to-Gravity Load Ratio

86



9.5.5 Out-of-Plane BendingThe results for a typical joint are shown in Figure 9.10 to Figure 9.12; partial factors are based onthe published values. Reliabilities for the ISO code are around 4.0 (slightly lower for the K-joint)with the API RP2A – LRFD and WSD values fairly close to the ISO values.

Reliabilit y i ndex versus We/G behaviour for K-joint out-of-planebending

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100Environment/Gravity Load Ratio, We/G

R e l i a b

i l i t y I n d e x , β ISO

APILRFD

APIWSD

Figure 9.10 K-Joint Out-of-Plane Bending - Effect of Variation in Environment-to-Gravity LoadRatio

87



Reliabili ty i ndex versus We/G behaviour f or Y-joint out-of-planebending

0.0

1.0

2.0

3.0

4.0

5.0

6.0


R e


, β ISO

APILRFD

APIWSD

Figure 9.11 Y-Joint Out-of-Plane Bending - Effect of Variation in Environment-to-Gravity LoadRatio

Reliabilit y in dex versus We/G behaviour for joi nt out-of-planebending

0.0

1.0

2.0

3.0

4.0

5.0

6.0


R e

l i a

b i l i t y I n d e x

, β ISO

APILRFD

API

WSD

Figure 9.12 X-Joint Out-of-Plane Bending - Effect of Variation in Environment-to-Gravity Load

Ratio

88



Effect of jointβ ratio on Reliability Index - K-joint Balanced Axial

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Joint β ratio

R e


, β

ISO

API LRFD

API WSD

Figure 9.14 Effect of Variation of Joint Beta Ratio on Reliability Index for K-joint subject to AxialTension

Effect of jointβ ratio on Reliability Index - Y-joint Axial Tension

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Joint β ratio

R e


, β

ISO

API LRFD

API WSD

Figure 9.15 Effect of Variation of Joint Beta Ratio on Reliability Index for Y-joint subject to AxialTension

90



Effect of jointγ ratio on Reliability Index

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 10 20 30 40 50 60

Joint γ ratio

R e


, β

K-joint AxialTension

ISO

API LRFD

API WSD

Figure 9.17 Effect of Variation of Joint Gamma Ratio on Reliability Index for K-joint subject toAxial Tension

Effect of joi ntγ ratio on Reliability Index

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 10 20 30 40 50 60

Joint γ ratio

R e


, β

X-joint Out-of-PlaneBendingISO

API LRFD

API WSD

Figure 9.18 Effect of Variation of Joint Gamma Ratio on Reliability Index for X-joint subject toOut-of-Plane Bending

92



9.5.9 Variation of Qf Factor Variation of Q f factor was investigated by varying the unfactored chord stress while keeping allother parameters constant. Typical results are shown in Figure 9.19 to Figure 9.21. The graphsshow that while reliability index remains fairly constant at around 4.0 with variation in chord stress(or Q f factor) for the ISO code, there is a large variation for API RP2A LRFD and WSD due to thedifferences in the formulation and definition of the Q f factor. The results show that when the chordutilisation is high, i.e. when the Q f factor becomes more significant in joint design, the reliabilityevaluated for joints designed to ISO is significantly greater than for designs to RP2A.

It should be noted that no additional model uncertainty has been included for the Q f term. Theresistance model uncertainty in Table 9.4 for the various load effects has been derived using theresults of large and full scale tests conducted, in the main, on joints without chord load, i.e. with

Qf = 1.0.

Some test data are available for chord effects, and statistics for selected load effects and jointtypes are given in Table A.14.3-4, ISO 19902. These data suggest that bias and CoV for modeluncertainty do not change significantly, e.g. for T, Y joints under compression the bias and CoV for

joints including chord load effects is 1.338 and 0.151 compared with 1.265 and 0.131 without, andfor gapped K-joints under balanced axial load the bias and CoV for joints including chord loadeffects is 1.295 and 0.136 compared with 1.229 and 0.142 without. These differences in modeluncertainty parameters will not materially affect the evaluated reliabilities.

Effect of We/G ratio on reliability index versus chord stress

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 50 100 150 200

Unfactored chord stress (N/mm2)

R e


, β

K-joint In-PlaneBendingISO

API LRFD

API WSD

Figure 9.19 Effect of Variation of Q f Factor on Reliability Index for K-joint subject to In-PlaneBending

93




0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 50 100 150 200


R e


, β

Y-joint Out-of-PlaneBendingISO

API LRFD

API WSD

Figure 9.20 Effect of Variation of Q f Factor on Reliability Index for Y-joint subject to Out-of-PlaneBending


0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 50 100 150 200


R e l i a b i l i t y I n d e x

, β

X-joint AxialCompression

ISO

API LRFD

API WSD

Figure 9.21 Effect of Variation of Q f Factor on Reliability Index for X-joint subject to AxialCompression

94



9.6 CALIBRATION POINT RESULTS

In this section reliability analysis results are presented for all of the calibration points in the

database. The calibration exercise was carried out using a purpose-written first order reliabilityanalysis spreadsheet.

Graphs of results for all calibration points for joints are presented below in Figure 9.22 to Figure9.26 for ISO with γ W=1.35, and Figure 9.27 for API RP2A - WSD.

The general trend in reliability with W e/G ratio is less marked for ISO than for RP2A-WSD, and for many load effects the reliabilities for ISO are reasonably consistent at around 4.0 (for γ w=1.35)over a wide range of W e/G ratios. This is confirmed by the average reliability indices for each loadeffect and each joint type given in Table 9.6 which are all around 4.0. This suggests that a partialresistance factor of 1.05 for all load effect types for tubular joints is appropriate.

Reliability index of calibration points vs We/G for joint s in extreme

loadin g con dition (ISO γ w=1.35)

0

1

2

3

4

5

6

0.1 1 10 100We/G ratio

R e


, β

Axial Tension

AxialCompression

In-plane bending

Out-of-planebending

Figure 9.22 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – All Joints – ISO

95



Reliability i ndex of calibration points vs We/G for joints subject to

axial tension in extreme loading c onditio n (ISO γ w=1.35)

0

1

2

3

4

5

6

0.1 1 10 100We/G ratio

R e


, β

K-joints

Y-joints

X-joints

Figure 9.23 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – All Joints Axial Tension – ISO

Reliability i ndex of calibration points vs We/G for joints subject to

axial compression in extreme loading condition (ISO γ w=1.35)

0

1

2

3

4

5

6

0.1 1 10 100We/G ratio

R e


, β K-joints

Y-joints

X-joints

Figure 9.24 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – All Joints Axial Compression – ISO

96



Reliabilit y index of calibration points vs We/G for joints subject to

in-plane bending in extreme loading condition (ISO γ w=1.35)

0

1

2

3

4

5

6

0.1 1 10 100We/G ratio

R e


, β K-joints

Y-joints

X-joints

Figure 9.25 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – All Joints In-Plane Bending – ISO

Reliability index of calibration points vs We/G for joints subject toout -of-plane bending in extreme loading cond ition (ISO γ w=1.35)

0

1

2

3

4

5

6

0.1 1 10 100

We/G rati o

R e l i a


, β K-joints

Y-joints

X-joints

Figure 9.26 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – All Joints Out-of-Plane Bending – ISO

97



Reliability index of calibration points vs We/G for joint s in extremeload ing condi tion (API WSD 17-20)

0

1

2

3

4

5

6

0.1 1 10 100We/G ratio

R e


, β

AxialCompression

In-plane bending

Out-of-planebending

Axial Tension

Figure 9.27 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – All Joints – API WSD 17-20 th (21 st) Edition

K-Joint Y-Joint X-Joint

Load EffectPf β Pf β Pf β

Axial Tension 4.623E-05 3.910 1.847E-05 4.126 2.36299E-05 4.069

Axial Compression 4.623E-05 3.910 2.635E-05 4.043 3.51588E-05 3.975

In-Plane Bending 1.973E-05 4.111 2.707E-05 4.037 1.39708E-05 4.190

Out-of-Plane Bending 7.576E-05 3.789 1.965E-05 4.112 3.2749E-05 3.992

All 4.825E-05 3.899 2.413E-05 4.064 2.83447E-05 4.026

Table 9.6 Weighted Average P f and Equivalent β for each Load Effect and Joint Type (ISOγ w=1.35)

98




The effect on reliability of varying the environmental load factor for joints is shown in Figure 9.28below. By comparison with the target reliabilities calculated to API RP2A – WSD and LRFD andthe target recommended by Efthymiou [6] (for a structural system), a range of environmental loadfactors may be suggested for further discussion. The weighted probabilities and equivalentreliabilities represented in Figure 9.28 are given in Table 9.7. On the basis of the results, anenvironmental load factor of 1.25 would give reliability levels for the ISO code above the API RP2A- WSD 20 th (21 st) Edition values.

Variation of weighted reliability with environmental load factor -ISO joints

4.014

3.415

0

1

2

3

4

5

1.1 1.2 1.3 1.4 1.5


W e i g

h t e d R e l i a b

i l i t y , β

Joints


TargetReliability (API

- LRFD)TargetReliability (API- WSD)

Figure 9.28 Variation of Weighted Reliability With Environmental Load Factor – ISO Joints

99



JointsCode Pf Equivalentβ

API–WSD 20 th 3.191E-04 3.415

γ w-1.2 9.099E-05 3.743

γ w-1.25 6.355E-05 3.832

γ w-1.3 4.459E-05 3.918

γ w-1.35 3.143E-05 4.002

ISO

γ w-1.4 2.226E-05 4.083

Table 9.7 Weighted Average P f and Equivalent β for Different Environmental Load Factors

10 0



10. FOUNDATIONS

10.1 SUMMARY

Reliability analysis for pile axial capacity has been undertaken to assess the effect of differentenvironmental partial load factors. The aim of the work here is to briefly investigate the effect of the partial load factors on foundation reliability; it is not to undertake a rigorous analysis to assessfailure probabilities for piled foundations.

Pile axial capacity predictions for use in the reliability analysis have been undertaken using thestandard pile strength formulations for sand and clay soils in the main body of the ISO Code (thealternative methods suggested in the Commentary have not been used). Model uncertainties for shaft friction (and end bearing) in sand and clay soils have been assessed on the basis of largescale tests, but it is worth noting that the uncertainties associated with the ISO pile strengthformulations are large. Better strength models are available (which fit the available test data moreclosely), but these have not been used here as they need specialist geotechnical input. It is alsoworth noting that, because the number of suitable test results is small and because the variabilityin results is so large, the statistical modelling of model uncertainty is very dependent on theselection and screening of the database. (The model uncertainty was based on 48 test results for piles in sand and 43 test for piles in clay).

In reality, the ultimate axial strength of piles is also influenced by a number of factors which are notreflected in static pile load tests. An attempt was made to allow for the following factors in theanalysis: load rate, cyclic loading, set-up or strength gain with time in cohesive soils, anduncertainty in pile loading due to soil/structure interaction.

No structural reanalysis has been undertaken here, thus no explicit effect from the loadredistribution between piles as a result of non-linear soil/pile interaction has been evaluated.


A range of calibration points was chosen so that trends in reliability could be evaluated. However,weighted average reliabilities were not calculated as they would not give meaningful results due tothe large range in reliabilities and the select (small) database analysed.

10.2.1 Soil TypeFour idealised soil profiles were selected as representative of North Sea soil conditions. Theseare:

• Normally consolidated (NC) clay – c ranging from 5 kPa at the seabed to 175 kPa at a

depth of 100m

10 1



• Firm overconsolidated (OC) clay – c of 150kPa assumed constant with depth

• Hard overconsolidated (OC) clay – c of 300kPa assumed constant with depth

• Dense sand – δ of 35º, N q of 50, assumed constant with depth

For the purposes of this analysis a submerged soil density of 8 kN/m 3 was assumed. For theassessment of capacity for sand soils, the K value was assumed to be 0.8 for compression and0.7 for tension loading. It was assumed to be the same for both API and ISO foundation designs.

10.2.2 GeometryFor each soil type, three pile diameters were chosen in the range 48” (1.219m) to 108” (2.743m).Typically larger pile diameters are used with weaker soil conditions and this was reflected in the

pile diameters chosen for the calibration data.

Pile penetrations were selected to give a range of aspect ratios, whilst encompassing the range of actual pile penetrations in the central and northern North Sea regions. Pile penetrations variedfrom 30m to 90m.

10.2.3 Load EffectsThe load effects considered were:

• Maximum compressive load for the extreme storm condition (pile plunging)

• Maximum tensile load for the extreme storm condition, i.e. an opposing load conditionwhere gravity loads oppose environmental loads (pile pull-out).

10.2.4 Load CombinationsThe combinations of gravity to environmental load and dead to live load ratio considered for bothcompression and tension load cases are listed in Table 10.1.

10 2



We:G (compression) We:G (tension) D:L

5.0

4.00.5 -1.7

3.0

3.5

4.50.7 -2.0

4.0

4.0

3.01.0 -2.25

3.5

3.0

5.01.7 -3.0

4.5

4.5

3.53.0 -4.0

5.0

Table 10.1 Range of Gravity Load Ratios for Each Environmental-to-Gravity Load Ratio for theExtreme Loading Condition


It must be recognised that because of the uncertainties and unknowns involved, reliabilitiesevaluated for axial pile failure are not comparable with those evaluated for tubular member failure,

or even tubular joint failure.

There are a number of uncertainties affecting pile resistance, including:

• Model uncertainty

• Soil parameter uncertainty

• Load rate

•Effects of repeated load, cyclic load

10 3



• Group effects

• Effects of scour or slotting

• Method of pile installation

• Time delay between pile installation and load application

• Pile geometry

Soil parameter uncertainty has been assumed to be included in the analysis of load test results,since the process of estimating and assigning soil conditions is part of the capacity predictionmodel. However, the influence of load rate, cyclic loading, group effects, time delay, scour, etc.,

are additional effects which are not accounted for by static load tests. Scour or pile slotting do notusually have a significant affect on axial capacity, and have been neglected. The influence of group effects and pile geometry has not been considered.

Probability distributions have been assigned to both loading and resistance terms, and the failurefunction in the reliability analysis was simply defined as the difference between ultimate capacityand acting axial load. Because of the different behaviour of sand and clay soils, separate load andresistance models were derived for each.

All basic variables have been assumed to be independently distributed, i.e. uncorrelated.

10.3.1 Probabili stic Modelling for ClaysThe axial capacity of a piled foundation in clay soils depends on the shaft friction, the end bearing,the set-up or effect of time since the pile was driven or last disturbed, and the cyclic nature of theloading. The capacity prediction equation which has been assumed for piles in clay soil under compression is as follows:

Capacity = (Friction X friction Xdelay + Bearing X bearing ) Xcyclic (10.1)

For piles in tension, end bearing is zero. The parameters for the various uncertainties in clay soil

are listed in Table 10.2 below. All variables are considered lognormally distributed.

10 4



Basic Variables Distribution Mean Bias StandardDeviation

Source of data

FrictionNC clayOC clay

Xfriction Lognormal0.730.97

0.190.25

Reference 14Reference 14

Bearing X bearing Lognormal 0.91 0.43 Reference 14

Delay X delay Lognormal 1.0 0.07 Reference 15

Cyclic X cyclic Lognormal 0.86 0.02 Reference 15

Table 10.2 Basic Variable Modelling for Clay Soils

10.3.2 Probabili stic Modelling for SandsThe capacity prediction equation which has been assumed for piles under compression in sandsoils is as follows:

Capacity = (Friction X friction Xrate + Bearing X bearing ) (10.2)

For piles in tension, end bearing was neglected. The parameters for the various uncertainties for sands are listed in Table 10.3 below. All variables are considered lognormally distributed.

Basic Variables Distribution Mean Bias StandardDeviation

Source of data

Friction X friction Lognormal 1.84 1.52 Reference 14

Bearing X bearing Lognormal 2.19 1.86 Reference 14

Rate X rate Lognormal 0.95 0.03 Reference 15

Table 10.3 Basic Variable Modelling for Sand Soils

Table 10.3 shows that the CoV for skin friction and end bearing using the API/ISO soils models isover 0.80.

10.3.3 Probabili stic Modelling of Pile LoadingAnnual environmental load, design load uncertainty, dead load, and live load distributions weremodelled the same as for tubular members, i.e. as described in Section 4.3.

An additional uncertainty due to soil/structure interaction was introduced. It has been modelledwith a bias of 1.0 and a CoV of 0.02; it has been assumed to be lognormally distributed.

10 5



10.3.3.1 Loading Uncertainty for Clay SoilsThe load modelling equation that has been assumed for clay soils, including the load rate effect, isas follows:

interactRate

w XX

1X/wWlLDdLoad

++= (10.3)

The load rate effect is assumed lognormally distributed with a mean bias of 1.53 and standarddeviation of 0.12.

10.3.3.2 Loading Uncertainty for SandsThe load modelling equation that has been assumed for sand soils is as follows:

Load = (dD + lL + wW/X w) Xinteract (10.4)

10.4 RELIABILITY ANALYSIS FOR TYPICAL INDIVIDUAL PILES

10.4.1 SummaryIn order to investigate the effect of different values of partial factors on the different load effectsand design formulations for pile capacity, first-order reliability analyses were undertaken for singlecomponents using a spreadsheet macro. The variation of reliability with W e/G ratio was evaluated.For comparison, results were also evaluated for designs based on API RP2A-WSD 20 th (21 st)Edition and RP2A-LRFD (with API recommended load and resistance factors).

All evaluated reliabilities are annual. All results are for the extreme storm condition.

10.4.2 Axial CompressionThe results for a typical pile are shown in Figure 10.1 to Figure 10.4; partial load and resistancefactors are based on the published values (the partial resistance factor for the extreme condition is1.25). Reliabilities for axial pile capacity calculated to ISO are similar to, or slightly higher than,API RP2A-WSD 20 th (21 st) Edition values for all soil types.

The evaluated reliabilities are all very low, but it is the relative values and trends that areimportant, not the absolute values.

Typical results from the first-order reliability analysis for the ISO Code for an environment-to-gravity load ratio of 1.0 are shown in Table 10.4. The results show that the reliability is mostsensitive to the environmental load and shaft friction for clays and shaft friction and end bearingfor sands.

10 6



Reliabil ity Ind ex versus We/G behaviour f or pi le in axialcompression

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10


R e


, β

ISO

API LRFD

API WSD

Figure 10.1 Pile in Normally Consolidated Clay in Axial Compression - Effect of Variation inEnvironment-to-Gravity Load Ratio

Reliabil ity Ind ex versus We/G behaviour f or p ile in axialcompression

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10


R

e l i a b i l i t y I n d e x

, β

ISO

API LRFD

API WSD

Figure 10.2 Pile in Firm Overconsolidated Clay in Axial Compression - Effect of Variation inEnvironment-to-Gravity Load Ratio

10 7



Reliabil ity Ind ex versus We/G behaviour f or p ile in axialcompression

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10


R e


, β

ISO

API LRFD

API WSD

Figure 10.3 Pile in Hard Overconsolidated Clay in Axial Compression - Effect of Variation inEnvironment-to-Gravity Load Ratio

Reliabil ity Index versus We/G behaviour for p ile in axialcompression

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10


R e


, β

ISO

API LRFD

API WSD

Figure 10.4 Pile in Sand in Axial Compression - Effect of Variation in Environment-to-GravityLoad Ratio

10 8



Basic Variables NC clay Firm OC clay Hard OC clay Sand

Shaft friction 0.839 0.824 0.801 0.471

End bearing 0.277 0.211 0.271 0.853Load rate 0.073 0.081 0.083 0.020

Cyclic loading 0.091 0.087 0.087 -

Time delay 0.231 0.229 0.222 -

Soil/structureinteraction

-0.078 -0.075 -0.076 -0.036


0.135 0.153 0.157 0.083

Environmental load -0.323 -0.402 -0.413 -0.194Dead Load -0.138 -0.124 -0.125 -0.058

Live Load -0.066 -0.059 -0.059 -0.027

Table 10.4 Reliability Analysis Basic Variable Sensitivity Coefficients ( α-factors) –Axial Compression

10.4.3 Axial TensionFor piles in axial tension, the opposing loads condition governs for the ISO and LRFD Codes. The

results for a typical pile are shown in Figure 10.5 to Figure 10.8; partial factors are based on thepublished values. Reliabilities for axial pile capacity calculated to ISO are higher than API RP2A-WSD 20 th (21 st) Edition values for all soil types, i.e. design to ISO is more reliable. This meansthat designs to ISO for piles governed by axial tension will generally lead to a requirement for longer pile lengths than designs to RP2A-WSD; this is most significant for piles in sand soils.

Typical results from the first-order reliability analysis for the ISO Code for an environment-to-gravity load ratio of 2.25 are shown in Table 10.5. The results show that the reliability is mostsensitive to the environmental load, load model uncertainty and shaft friction for clays and sand.

10 9



Reliability Index versus We/G behaviour for pil es in axial tension

0.0

1.0

2.0

3.0

4.0

5.0

6.0

1 10


R e


, β

ISO

API LRFD

API WSD

Figure 10.5 Piles in Normally Consolidated Clay in Axial Tension -Effect of Variation in Environment-to-Gravity Load Ratio


0.0

1.0

2.0

3.0

4.0

5.0

6.0

1 10


R e


, β

ISO

API LRFD

API WSD

Figure 10.6 Piles in Firm Overconsolidated Clay in Axial Tension -Effect of Variation in Environment-to-Gravity Load Ratio

11 0




0.0

1.0

2.0

3.0

4.0

5.0

6.0

1 10


R e


, β

ISO

API LRFD

API WSD

Figure 10.7 Piles in Hard Overconsolidated Clay in Axial Tension -Effect of Variation in Environment-to-Gravity Load Ratio

Reliabili ty Index versus We/G behaviour fo r piles in axial tension

0.0

1.0

2.0

3.0

4.0

5.0

6.0

1 10


R e


, β

ISO

API LRFD

API WSD

Figure 10.8 Piles in Sand in Axial Tension -Effect of Variation in Environment-to-Gravity Load Ratio

11 1



Basic Variables NC clay Firm OC clay Hard OC clay Sand

Shaft friction 0.319 0.353 0.353 0.635

Load rate 0.180 0.183 0.183 0.029Cyclic loading 0.029 0.033 0.033 -

Time delay 0.088 0.098 0.098 -

Soil/structureinteraction

-0.025 -0.028 -0.028 -0.018


0.319 0.311 0.311 0.265

Environmental load -0.867 -0.855 -0.855 -0.723

Dead Load 0.049 0.044 0.044 0.042Live Load 0.023 0.021 0.021 0.020

Table 10.5 Reliability Analysis Basic Variable Sensitivity coefficients ( α-factors) –Axial Tension – ISO

10.4.4 Variation of Environmental Load Factor For illustration, the effect of different environmental load factors was investigated for a typical pilein clay and sand in axial compression for design to the ISO code. The results are shown in Figure10.9 and Figure 10.10. The results show that there is very little variation in reliability index for environmental load factors in the range 1.2 to 1.4. A similar variation is obtained for the case of piles in tension.

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Effect of environmental load factor on reliability index versus We/Gbehaviour

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10

Environment/Gravity Load Ratio, We/G

R e


, β

1.21.251.31.351.4

γ W

Figure 10.9 Piles in Firm Overconsolidated Clay in Axial Compression -Effect of Variation in Environment-to-Gravity Load Ratio for Different Environmental Load Factors

Effect of environmental load factor on reliability index versus We/Gbehaviour

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10


R e l i a b

i l i t y

I n d e x , β

1.21.25

1.31.351.4

γ W

Figure 10.10 Piles in sand in Axial Compression -

Effect of Variation in Environment-to-Gravity Load Ratio for Different Environmental Load Factors

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10.5 CALIBRATION POINT RESULTS

In this section reliability analysis results are presented for all of the calibration points in the

database. The analysis was carried out using a purpose-written first order reliability analysisspreadsheet.

Graphs of results for all calibration points for piles are presented below in Figure 10.11 and Figure10.12 for ISO with γ W=1.35. The graphs show there is little spread in reliability for the differentcalibration points for each soil type and W e/G ratio. However, the difference in reliability betweensoil types and between different environment-to-gravity load ratios is large, and is significantlylarger than the variation in reliability that may be introduced by varying the load factor, see Figures10.9 and 10.10.

Reliability index of calibration points vs We/G for piles subject to

axial compression in extreme loading condition (ISO γ w=1.35)

0

1

2

3

4

5

6

0.1 1 10We/G ratio

R e


, β

NC Clay

Firm OCClay

Hard OCClay

Sand

Figure 10.11 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – All Piles – Axial Compression - ISO

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Reliability index of calibration points vs We/G for piles subject to

axial tension in extreme loading condition (ISO γ w=1.35)

0

1

2

3

4

5

6

0.1 1 10We/G ratio

R e


, β

NC Clay

Firm OCClay

Hard OCClay

Sand

Figure 10.12 Reliability Index of Calibration Points Against Extreme Environmental/Gravity LoadRatios – All Piles – Axial Tension – ISO

10.6 NORMALISED PILE CAPACITY

A crude calibration analysis may be carried out by examining the variation in normalised pilecapacity with environmental to gravity load ratio for different extreme environmental load factors.(Normalised load is maximum design load divided by G+W e). The normalised pile capacity isplotted in Figure 10.13 for API RP2A-WSD and Figure 10.14 for ISO for extreme, operating andstill water conditions for axial compression; the tension (or opposing loads) case is also shown for the ISO Code in Figure 10.14.

For WSD, Figure 10.13 shows that the normalised pile capacity varies from 2.0 when there is noenvironmental loading to 1.5 for piles governed by the extreme condition.

Figure 10.14 shows that for W e/G ratios less than about 1.0, the operating condition governs. For We/G ratios greater than about 1.0, i.e. the extreme condition, the normalised pile capacity to ISOwith γ w = 1.35 is greater than the equivalent API RP2A-WSD normalised capacity. This impliesthat designs to ISO would be slightly more conservative, i.e. longer pile lengths, than to RP2A-WSD. If an extreme load factor of 1.25 is used with ISO the normalised capacity is slightly greater than RP2A-WSD for W e/G ratios greater than 1.5. . For W e/G ratios between 1 and 1.5 thenormalised pile capacity to ISO is marginally less than 1.5 for γ w of 1.25; the magnitude of thereduction is not considered significant.

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For piles under tension there is a significant difference in normalised capacity between γ w = 1.35and 1.25 for the ISO Code. Figure 10.14 illustrates that for γ w = 1.35 the normalised capacity ismuch higher than the equivalent RP2A-WSD normalised capacity. This means that in practice,piles governed by tension would be designed for much more onerous criteria to ISO than thosedesigned to RP2A-WSD, resulting in longer pile lengths. With γ w = 1.25, the normalised capacityis still greater than RP2A-WSD, but the difference is much less. Thus even with γ w = 1.25, pilesgoverned by tension are expected to be longer when designed to ISO than those designed toRP2A-WSD. Tensile capacity is much more of a concern for piles founded in sand soils. Piles inclay soils generally tend to be governed by compressive capacity; this is because the end bearingcapacity for piles in sand soils usually contributes much more to compressive pile capacity than itdoes for piles in clay soils.

Variation of Normalised Pile Capacity with Environmental to GravityLoad Ratio - WSD

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5


N o r m a

l i s e

d P i l e

C a p a c

i t y Extremecondition

Still water

Operating(Wo=We/4)

Operating(Wo=We/2)

Figure 10.13 Variation of Normalised Pile Capacity with Environmental to Gravity Load Ratio –API RP2A-WSD

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Variation of Normalised Pile Capacity with Environmental to GravityLoad Ratio - ISO

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5


N o r m a

l i s e

d P i l e C a p a c

i t y

Still water

Operating(Wo=We/4)

Operating(Wo=We/2)

Extremecondition1.35Extremecondition1.25

ExtremeTension1.35ExtremeTension1.25

Figure 10.14 Variation of Normalised Pile Capacity with Environmental to Gravity Load Ratio -ISO


The high uncertainties in pile axial capacity mean that a calibration analysis using weightedaverage reliabilities and a target assessment would not give meaningful results.

Analysis of typical piles for axial compression shows that an extreme environmental load factor of 1.35 would give reliabilities similar to or higher than API RP2A-WSD. For axial tension, reliabilitiesto ISO are greater than API RP2A-WSD for all W e/G ratios.

The variation of reliability for pile axial capacity with extreme environmental load factor of 1.2 to

1.4 is small.

A crude calibration analysis based on normalised pile capacity for axial compression shows thatan extreme environmental load factor of 1.35 would give capacities higher than API RP2A-WSD.An extreme environmental load factor of 1.25 would give capacities higher than API RP2A-WSDfor most W e/G ratios and only marginally lower for ratios less than 1.5.

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11 8



11 . EFFECT OF REDUCTI ON OF PERMA NENT AN D

VA RIABL E PARTIAL LOAD FACTORS

11.1 SUMMARY

The effect of reducing the partial factor on permanent and variable loads from 1.1 to 1.0 has beenexamined in an attempt to produce a more uniform reliability level, particularly at lower W e/Gratios.

11.2 MEMBERS

The effect of reducing the partial factor on permanent and variable loads from 1.1 to 1.0 for atypical member is shown in Figure 11.1 for combined tension and bending. The graph of ‘ISO -1.35’ ( γ W=1.35) has a partial factor on permanent and variable loads of 1.1. For the graph ‘ISO –1.35, gammaD = 1’ the partial factor on permanent and variable loads is 1.0 ( γ W=1.35). The effectof reducing the partial factor on permanent and variable loads is to reduce the reliability for W e/Gratios less than about 3.0. For W e/G ratios greater than 3.0, there is no significant change inreliability. For W e/G ratios less than 0.5 there is a significant reduction in reliability but theoperating condition will govern design for these W e/G ratios, as shown by the graph ‘ISO –operating’. For W e/G ratios in the range 0.5 to 3.0 there is a slight reduction in reliability giving amuch more uniform variation in reliability with W e/G ratio.


0.0

1.0

2.0

3.0

4.0

5.0

6.0



I n d e x , β

ISO -1.35

ISO -oper-ating

APIWSD

ISO-1.35gammaD=1

Figure 11.1 Combined Tension and Bending - Effect of reduction of partial factor on permanentand variable loads from 1.1 to 1.0

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11.3 JOINTS

The effect of reducing the partial factor on permanent and variable loads from 1.1 to 1.0 for a

typical K-joint is shown in Figure 3.1 for axial tension. The graph of ‘ISO - 1.35’ ( γ W=1.35) has apartial factor on permanent and variable loads of 1.1. For the graph ‘ISO – 1.35, gammaD = 1’ thepartial factor on permanent and variable loads is 1.0 ( γ W=1.35). The effect of reducing the partialfactor on permanent and variable loads is to reduce the reliability for W e/G ratios less than about5.0. For W e/G ratios greater than 5.0, there is no significant change in reliability. For W e/G ratiosless than 0.5 there is a significant reduction in reliability but in most cases the operating conditionwill govern design for these W e/G ratios, as shown by the graph ‘ISO – operating’. For W e/G ratiosin the range 0.5 to 5.0 there is a slight reduction in reliability giving a much more uniform variationin reliability with W e/G ratio.

Reliability Index versus We/G behaviour for jo int axial tensio n

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10 100


R e l i a


, β

ISO - 1.35

ISO -operating

API WSD

ISO -1.35,gammaD=1

Figure 11.2 K-Joint Axial Tension - Effect of reduction of partial factor on permanent and variableloads from 1.1 to 1.0

11.4 FOUNDATIONS

The effect of reducing the partial factor on permanent and variable loads from 1.1 to 1.0 for atypical pile in firm overconsolidated clay is shown in Figure 11.3 for axial compression. The graphof ‘ISO - 1.35’ ( γ W=1.35) has a partial factor on permanent and variable loads of 1.1. For thegraph ‘ISO – gammaD = 1’ the partial factor on permanent and variable loads is 1.0 ( γ W=1.35).The effect of reducing the partial factor on permanent and variable loads is to reduce the reliabilityfor all W e/G ratios.

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Reliability index versus We/G behaviour for pil e compression

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0.1 1 10


R e


, β

ISO - 1.35

ISO -gammaD=1

API WSD

Figure 11.3 Pile in Firm Overconsolidated clay - Effect of reduction of partial factor on permanentand variable loads from 1.1 to 1.0

11.5 DISCUSSION

This study shows that in most cases, reducing the partial factor on permanent and variable loadsfrom 1.1 to 1.0 would produce a more uniform variation in reliability with W e/G ratio. However there may be certain cases where reliability would be significantly reduced for low W e/G ratios if the operating condition does not govern; some tubular joints in particular exhibit a fall in reliabilitylevels at low environment-to-gravity load ratios, see Section 9. Generally, the operating conditionwill govern design at low W e/G ratios, but there may be cases, for example in the splash zone,where it does not. Therefore, any reduction in partial factor on permanent and variable loadsshould be applied with caution.

It is considered that the overall benefits in achieving more uniform reliabilities across a wide rangeof We/G ratios by reducing the gravity factor will be small, whereas for some components or loadeffect types, particularly for low W e/G ratios, it is possible that reliability may be significantlyreduced.

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12 . EFFECT OF IN CREASE IN ENVI RONMENT AL DESIGN

LOAD UNCERTAINT Y

12.1 SUMMARY

Some of the Participants were concerned about the level of uncertainty associated with thedefinition of the environmental design loading. A study was undertaken to investigate the effect of increasing the CoV of the environmental design load uncertainty from 16.5%, which was used inall of the other analyses in this report and in the system-based calibration study [1], to 25%.

12.2 ENVIRONMENTAL DESIGN LOAD UNCERTAINTY MODELLING

Xw Design Load Uncertainty N[1.0, 0.25]In the previous analyses (except the sensitivity study reported in Section 8.4), the design loadarising from the ISO Code and standard practices was estimated to be subject to a 9%conservative bias and a CoV of 16.5% relative to the ‘true’ 100 year value; and the uncertaintywas modelled by a normal distribution truncated at ±1.5 standard deviations.

Uncertainty and bias in the design load arise from two main sources:• the application of the wave force recipe

• the environmental design criteria.

The accuracy of the environmental load recipe has been investigated in various research studiesincluding: Heideman & Weaver [16], Atkins in the Tern project [17], etc. For this JIP, Kvitrud [18]has summarised the results of a number of full scale load measurement comparisons for differentNorth Sea structures, including: Ekofisk 2/4-A and 2/4-W, Valhall QP, Draupner, Gorm, Magnusand Tern. A direct comparison of the results for the various studies is difficult because the studieswere undertaken by a number of engineers/analysts/companies, at different times using different(sometimes un-stated) assumptions, and are reported in a variety of papers/reports. It is not evenalways clear from the published information whether the comparisons are on a wave-by-wave or astorm-by-storm basis. Kvitrud shows that there is considerable scatter in the bias and CoVstatistics for the various studies, but suggests that ‘the COV is high for a given sea state or wave,an average will be 25-30%’.

It has also been suggested by ExxonMobil [19] that there is generally a lack of familiarity andexperience from operators and contractors in using the ‘new’ environmental load recipe within theISO code, and this could lead to potential differences in interpretation and application. ExxonMobiltraditionally model uncertainty in the environmental design loading with a CoV of 20-30% in

reliability analysis.

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In this study, a CoV of 25% has been considered. This has been assumed to be unbiased, and anun-truncated normal distribution has been used. This modelling was chosen rather arbitrarily, andis intended solely for the purposes of this study.

Whilst improved QA, better education or information could in principle reduce some of theuncertainty in the definition of the design load, there is an additional source of uncertainty thatcould be considered to affect the definition of the 100-year design load. This additional uncertaintyarises from the dataset itself that is used to derive the 100-year parameters. For any particular site, the definition of the 100-year design parameters changes from year-to-year as a result of alonger dataset, and changes to the hindcast model, e.g. NESS, NEXT, NEXTRA, etc. Whilst anallowance for the uncertainty in statistical analysis or data-fitting has been included (e.g.distribution type, fitting method, etc), this additional uncertainty in the dataset itself has not been

included. By its very nature, this uncertainty is very difficult if not impossible to quantify.

12.3 RESULTS

The reliability analyses for brace members and legs presented and discussed in Section 6 werere-run with the above environmental design load uncertainty, and the results were weighted andcombined as discussed in Section 7. The results are shown in Figures 12.1 to 12.3, and aresummarised numerically in Table 12.1. The results can be compared with the previous results for design load CoV of 16.5% presented in Figures 7.4 to 7.6 and Table 7.1.

Due to the very large environmental design load uncertainty, this variable has a significantinfluence on the reliability for many of the calibration points. The first-order reliability analysisprocedure failed to converge for some of the calibration points, and converged to clearlyerroneous results for a small number of other calibration points. Ordinarily, the reliability analysiswould be investigated in greater depth and re-run for these calibration points. Given the nature of this study, this was not done fully for the results presented in this Section. The affected calibrationpoints all had very low weighting factors and were simply eliminated from the cumulated totals.

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4.014

2.844

0

1

2

3

4

5

1 1.1 1.2 1.3 1.4 1.5


W e i g

h t e d r e l i a b

i l i t y , β

bracemembers(NNS&CNS)




Figure 12.1 Variation of Weighted Reliability with Increased Design Load Uncertainty – ISO Brace Members

Variation of weighted reliability with environmentalload factor - ISO brace members (compression &

bending )

4.014

2.840

0

1

2

3

4

5

1 1.1 1.2 1.3 1.4 1.5


W e i g h t e d r e l i a b

i l i t y , β

bracemembers(NNS&CNS)




Figure 12.2 Variation of Weighted Reliability with Increased Design Load Uncertainty – ISO Brace Members – Combined Compression and Bending Only

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Variation of weighted reliability with environmentalload factor - ISO leg members

4.014

2.8712.711

0

1

2

3

4

5

1.1 1.2 1.3 1.4 1.5


W

e i g h t e d r e l i a b

i l i t y , β

legmembers(NNS &CNS)TargetReliability(Efthmyiou)



Figure 12.3 Variation of Weighted Reliability with Increased Design Load Uncertainty – ISO Leg Members

brace membersbrace members(compression &bending only)

leg membersCode

Pf Equivalent

β Pf

Equivalentβ

Pf Equivalent

β

API–WSD 20th 2.233E-03 2.844 2.256E-03 2.840 3.360E-03 2.711

γ w-1.1 3.403E-03 2.707 3.276E-03 2.719 4.178E-03 2.638

γ w-1.2 2.405E-03 2.820 2.309E-03 2.833 2.922E-03 2.757

γ w-1.25 2.035E-03 2.873 1.965E-03 2.884 2.500E-03 2.807

γ w-1.3 1.740E-03 2.922 1.687E-03 2.932 2.116E-03 2.861

ISO

γ w-1.35 1.504E-03 2.967 1.460E-03 2.976 1.824E-03 2.907

Table 12.1 Weighted Average P f and Equivalent β with Increased Design Load Uncertainty for Different Environmental Load Factors

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12.4 DISCUSSION

Solely on the basis of the results in Table 12.1, an environmental load factor of 1.25 would give

reliability levels for the ISO code slightly above the values evaluated on the same basis for APIRP2A - WSD 20 th (21 st) Edition for both braces and legs.

However, a target failure probability of around 0.002 per year is considered to be a very highfailure rate that is not compatible with actuarial rates of component failure experienced in practice.

Comparison of the results in Table 12.1 with those in Table 7.1 shows an order of magnitudedifference in annual failure probability. This difference arises as a result of changes in theuncertainty modelling for the environmental design load. Given the nature of this uncertainty, it isvery difficult to quantify it, and the uncertainty modelling for this variable must be based largely on

judgement. This means that differences in evaluated reliability levels between models based on16.5% CoV and models based on 25% CoV cannot easily be reconciled.

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14. GLOSSARY

Basic variable A set of variables entering the failure function equation todefine failure. They may include basic engineeringparameters, such as wall thickness, yield stress, etc., aswell as model uncertainty in the failure function itself.

Beta-point, β-point, (design-point) The point on the failure surface that is closest to theorigin in U-space. It is also the point with maximumprobability density, and values of the basic variables atthis point represent the most probable values to causefailure.

CoV (Coefficient of Variation) The ratio of standard deviation to mean value of avariable.

Expected value, E[ ] The mean value of a variable. It is defined as the firstmoment of the distribution function of a variable, and isevaluated from the distribution function f X(x):

[ ] ( )dxxfxXE X∫ ∞∞−=

Failure function, Z The failure function in a reliability analysis is amathematical function used to predict the failure event for a component, part of a structure, or a structural system.The failure function is expressed in terms of the basicvariables, and is defined such that Z ≤ 0 corresponds tofailure.

Limit State design A design method in which requirements are defined for structural performance or operation. Such requirements

may include Ultimate (ULS) and Serviceability (SLS) LimitStates. Limit States can be defined as a specified set of states that separate a desired state from an undesirablestate which fails to meet the design requirements.

Model uncertainty The inherent uncertainty associated with themathematical models used to predict resistance (andloading).

Probability of failure, P f The probability of failure of an event is the probability that

the limit state criterion or failure function defining theevent will be exceeded in a specified reference period.

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Probability density function, pdf The probability that a random variable X shall appear inthe interval [x, x+dx] is f X(x) dx, where f X(x) is theprobability density.

Reference period Reliabilities and probabilities of failure should be defined

in terms of a reference period, which may typically be oneyear or the design life. Unless noted otherwise, a oneyear reference period has been used in this report.

Reliability The probability that a component will fulfil its designpurposes. Defined as 1 – P f .

Reliability analysis There are a number of techniques to evaluate failureprobability, or reliability. These include: numericalintegration, iterative procedures to evaluate first- or second-order estimates of P f , Monte Carlo simulation anda number of variance reduction techniques.

Reliability Index, β A useful measure to compare P f s. It is defined using thestandard normal distribution function ( )Φ ,

( )f1 P1 −Φ=β −

Sensitivity coefficient, α-factors The sensitivity coefficients reflect how sensitive thereliability is to the basic variables. The term importancefactors is sometimes used; importance factors aredefined as the square of the α-factors

Standard deviation, Sd[ ] The standard deviation is defined as the square root of the Variance of a variable.

Standard normal space, U-space A space of independent normally distributed randomvariables with zero mean and unit standard deviation.Basic variable space is transformed into standard normalspace in some reliability analysis procedures.

Target A target probability is used to judge reliabilities. It may bedefined by using data from designs known to performsatisfactorily, by expert judgement, by value analysis, or taken from norms in standards.

Variance, Var[ ] The variance of a variable is defined as the secondcentral moment of the distribution function of a variable,and is evaluated from the distribution function f X(x):

[ ] ( ) ( )dxxfxXVar X2

X∫ ∞∞− µ−=

where µX is the mean or expected value.

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15. REFERENCES

1 BOMEL Ltd. 'System-Based Calibration of North West European Annex Environmental LoadFactor to ISO Fixed Steel Offshore Structures Code 19902', Report No. C925\04\016R Rev A,February 2002.

2 API RP2A – ‘ Recommended Practice for Planning, Designing and Constructing Fixed OffshorePlatforms’, American Petroleum Institute, Washington DC, 20th Edition, August 1993.

3 API RP2A – LRFD ‘Recommended Practice for Planning, Designing and Constructing FixedOffshore Platforms’, American Petroleum Institute, Washington DC, 1st Edition, August 1 1993.

4 International Organization for Standardization. ISO 19902 – Petroleum and Natural GasIndustries – Fixed Steel Offshore Industries. Committee Draft 19 June 2001.

5 Thoft-Christensen P & Baker M J. ‘Structural reliability theory and its applications’. Springer-Verlag, Berlin, 1982.

6 Efthymiou M, van de Graaf, J W, Tromans, P S & Hines I M. ‘Reliability based criteria for fixedsteel offshore platforms’, Proc OMAE Conference, Florence, 1996.

7 MSL Ltd. ‘Load factor calibration for ISO 13819, Regional Annex – Component resistance s’.

Offshore Technology Report 2000/072, 2001.

8 Tromans P S & Vanderschuren L. ‘Extreme environmental load statistics in UK waters’. Reportfor this JIP.

9 Advanced Mechanics & Engineering Ltd. ‘API RP2A-LRFD - Its consequences for and adaptationto North Sea Offshore Design Practice’, May 1991.

10 Moses F. Final Reports for API PRAC 79-22 (1980), 80-22 (1981), 81-22 (1982), 82-22 (1983), 83-22 (1985), 85 –22 (1986), 87-22 (1987), prepared for American Petroleum Institute, Dallas.

11 Digre, K.A., Puskar, P.J., Aggarwal, R.K., Irick, J.T., Krieger, W.F., and Petrauskas, C.‘Modifications to and applications of the guidelines for assessment of existing platforms containedin section 17 of API RP 2A’, OTC 7779, 27th Offshore Technology Conference, Houston, 1995.

12 Hu K K & Lai D C . ‘Effective length factor for restrained beam-column’, Journal of StructuralEngineering, ASCE, Vol 112, No. 2, February 1986, 241-256.

13 Earl C P & Teer M J. ‘A rational and economical approach to the calculation of K-factors’, OffshoreTechnology Conference, Paper OTC 6162, 1989.

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14 Smith A K C, Turner R C & Mackenzie B. ‘The implications of the load and resistance factor designmethod for North Sea pile design’, Offshore Site Investigation and Foundation Behaviour ‘New

Frontiers’International Conference, London, 1998.

15 Fugro Ltd. ‘Joint Industry Study into the implications of the load and resistance factor designapproach for North Sea Structures’, Report No. 45035-4 Issue 01, August 1996.

16 Heideman, J.C. and Weaver, T.O. ‘Static wave force procedure for platform design‘, ASCE CivilEngineering in the Oceans V, 1992.

17 Atkins Oil & Gas Engineering. ‘Tern structural loading study‘, JIP Final Report, ReportG3356/RPT/010, London, 1994.

18 Kvitrud A. ‘Bias and CoV from environmental loading on jacket structures‘. Draft report for this JIPdated 22 April 2001

19 ExxonMobil. ‘BOMEL ISO Extreme Environmental Load Factor Calibration JIP Comments’. May2002.

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