GRI-04/0229

Guidelines for Reliability Based Design and

Assessment of Onshore Natural Gas Pipelines

Final Report

Prepared by:

Maher Nessim, PhD, PEng Wenxing Zhou, PhD, PEng

C-FER Technologies 200 Karl Clark Road

Edmonton, AB T6N 1H2 Canada

Prepared for:

GAS RESEARCH INSTITUTE GRI Contract No. 8565

GRI Project Manager

Charles E. French

July 2005

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LEGAL NOTICE

This Report was prepared by C-FER Technologies (1999) Inc., as an account of work sponsored by Gas Research Institute ("GRI"). Neither GRI, members of GRI, nor any person acting on behalf of any of these parties:

a. MAKES ANY WARRANTY OR REPRESENTATION, EXPRESS OR IMPLIED, WITH RESPECT TO THE ACCURACY, COMPLETENESS, OR USEFULNESS OF THE INFORMATION CONTAINED IN THIS REPORT, OR THAT THE USE OF ANY INFORMATION, APPARATUS, METHOD, OR PROCESS DISCLOSED IN THIS REPORT MAY NOT INFRINGE PRIVATELY OWNED RIGHTS, OR

b. ASSUMES ANY LIABILITY, INCLUDING WITHOUT LIMITATION, SPECIAL OR CONSEQUENTIAL DAMAGES, WITH RESPECT TO THE USE OF, OR FOR ANY AND ALL DAMAGES RESULTING FROM THE USE OF, ANY INFORMATION, APPARATUS, METHOD OR PROCESS DISCLOSED IN THIS REPORT.

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ACKNOWLEDGMENTS

This report is based on a project funded by the Gas Research Institute and carried out under supervision of the Design, Construction and Operations Committee of the Pipeline Research Council International (PRCI). The work was an extension of a previous project on the same topic that was carried out by C-FER Technologies and funded by TransCanada PipeLines and BP Exploration Operating Company. Members of the PRCI ad hoc group for this project are gratefully acknowledged for their guidance throughout the project. Special thanks are due to Joe Zhou, Brian Rothwell, Martin McLamb, Louis Fenyvesi, Rick Gailing, Keith Leewis, and Alan Glover for their ongoing advice and contributions to key decisions throughout the work.

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE

July 2005 3. REPORT TYPE AND DATES COVERED

Final Report 4. TITLE AND SUBTITLE

Guidelines for Reliability Based Design and Assessment of Onshore Natural Gas Pipelines

5. FUNDING NUMBERS

GRI Contract No. 8565

6. AUTHOR(S)

Maher Nessim, PhD, PEng and Wenxing Zhou, PhD, PEng

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

C-FER Technologies (1999) Inc. 200 Karl Clark Road Edmonton, Alberta T6N 1H2 Canada

8. PERFORMING ORGANIZATION

REPORT NUMBER

L080-1

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

GRI 1700 S. Mt. Prospect Rd. Des Plaines, IL 60018

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

GRI-04/0229

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

A set of guidelines for the application of Reliability Based Design and Assessment (RBDA) of onshore natural gas pipelines has been developed. These guidelines contain a general overview of RBDA methods and a discussion of the key issues associated with applying them to pipelines. Requirements for the application of RBDA are also given, specifying the design conditions that must be considered and the reliability targets that are to be met. In addition, the guidelines provide the technical information required to apply RBDA including methodologies to identify relevant limit states, construct limit states functions, develop probabilistic models for uncertain input parameters and estimate the lifetime reliability. Two example applications are given: one for the design of a new pipeline segment, and the other for a class upgrade assessment of an existing segment.

14. SUBJECT TERMS

15. NUMBER OF PAGES

235 16. PRICE CODE 17. SECURITY CLASSIFICATION OF REPORT

Unclassified

18. SECURITY CLASSIFICATION OF THIS PAGE

Unclassified

19. SECURITY CLASSIFICATION OF ABSTRACT

Unclassified

20. LIMITATION OF ABSTRACT

NSN 7540-01-280-5500 Standard Form 298 (Rev.2-89) Prescribed by ANSI Std 239-1B 298-102

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TABLE OF CONTENTS

Project Team and Revision History i Legal Notice ii Acknowledgements iii Report Documentation Page iv List of Figures and Tables ix Research Summary xiii Executive Summary xv

1. INTRODUCTION..................................................................................................................1

1.1 Purpose 1 1.2 Scope and Focus 1 1.3 Organization 1

2. DEFINITIONS.......................................................................................................................3

3. OVERVIEW OF RELIABILITY BASED DESIGN AND ASSESSMENT..............................7

3.1 Introduction 7 3.2 Historical Perspective 7 3.3 Sources of Uncertainty 8 3.4 Limit States 9 3.5 Reliability and Probability of Failure 10

3.5.1 Basic Concepts 10 3.5.2 Limit State Function 11 3.5.3 Calculation Methodology 13

3.6 Reliability Based Design and Assessment 14 3.7 Benefits 14

4. RBDA METHODOLOGY FOR PIPELINES .......................................................................16

4.1 Introduction 16 4.2 Key Issues for Pipeline Reliability 16

4.2.1 Time Variability 16 4.2.2 Impact of Maintenance 19

4.3 Implementation Methodology 19 4.4 Applicability 21

5. DESIGN AND ASSESSMENT REQUIREMENTS .............................................................22

5.1 General Requirements 22 5.2 Limit States 23

5.2.1 Categories of Limit States 23

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5.2.2 Loads and Limit States 23 5.3 Reliability Targets 25

5.3.1 Introduction 25 5.3.2 Ultimate Limit States 26

5.3.2.1 Approach 26 5.3.2.2 Format 26 5.3.2.3 Safety Criteria 27 5.3.2.4 Reliability Targets 28 5.3.2.5 Meeting the Targets 32

5.3.3 Leakage Limit States 35 5.3.4 Serviceability Limit States 36

6. IDENTIFICATION OF RELEVANT LIMIT STATES...........................................................37

6.1 Introduction 37 6.2 Deterministic Screening 38 6.3 Probabilistic Screening 39

6.3.1 Introduction 39 6.3.2 Continuously Applied Loads 40 6.3.3 Discrete Loads 42

7. DEVELOPING A LIMIT STATE FUNCTION .....................................................................44

7.1 Introduction 44 7.2 Generalized Definition of a Limit State Function 44 7.3 Overview of Development Procedure 45 7.4 Defining the Limiting Condition 45 7.5 Developing the Limit State Model 46

7.5.1 Introduction 46 7.5.2 Example 1 Using a Simple Analytical Model 47 7.5.3 Example 2 Using a Numerical Finite Element Model 49 7.5.4 Sources of Relevant Information 52

7.6 Model Uncertainty 54 7.6.1 Introduction 54 7.6.2 Characterizing Model Error 54

7.6.2.1 General 54 7.6.2.2 Proportional Error 55 7.6.2.3 Independent Error 55 7.6.2.4 Model Selection 57

7.6.3 Example 58

8. PROBABILISTIC CHARACTERIZATION OF INPUT VARIABLES..................................63

8.1 Introduction 63 8.2 Frequency of Random Events 64

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8.2.1 Introduction 64 8.2.2 The Poisson Process 64 8.2.3 Estimation of the Rate of Occurrence 64 8.2.4 Example 65

8.3 Probability Distributions of Time-independent Variables 65 8.3.1 Introduction 65 8.3.2 Data Analysis 66 8.3.3 Distribution Selection Based on Data 69

8.3.3.1 Introduction 69 8.3.3.2 Selection of Candidate Distribution Types 70 8.3.3.3 Distribution Parameter Estimation 71 8.3.3.4 Best Fit Distribution Selection 72

8.3.4 Other Distribution Selection Methods 75 8.4 Time-dependent Variables 77

8.4.1 Introduction 77 8.4.2 Discrete Random Process 78

8.4.2.1 Process Characterization 78 8.4.2.2 Maximum Load Distribution 79 8.4.2.3 Asymptotic Extremal Distributions 80 8.4.2.4 Estimation of Return Periods 83

8.4.3 Continuous Random Processes 83 8.5 Effect of Sample Size 85

8.5.1 Introduction 85 8.5.2 Example 1 Occurrence Rate of a Poisson Process 85 8.5.3 Example 2 Mean of a Distribution with Known Standard Deviation 88 8.5.4 General Procedure 90 8.5.5 Comments 91

9. RELIABILITY ESTIMATION ..............................................................................................92

9.1 Introduction 92 9.2 Single Time-independent Limit State 92

9.2.1 Introduction 92 9.2.2 General Methodology 93

9.2.2.1 Failure Rate 93 9.2.2.2 Conditional Failure Probability 94 9.2.2.3 Example 96

9.2.3 Special Methodology for Seismic Limit States 97 9.2.3.1 Failure Rate 97 9.2.3.2 Conditional Failure Probability 97

9.3 Single Time-dependent Limit State 99 9.3.1 Introduction 99 9.3.2 Failure Rate 100 9.3.3 Conditional Failure Probability 101 9.3.4 Impact of Rehabilitation 102

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9.3.4.1 Approach 102 9.3.4.2 Detection Capability 104 9.3.4.3 Sizing Accuracy 105 9.3.4.4 Defect Excavation and Repair 106 9.3.4.5 Failure Rate Calculation 107

9.3.5 Example 108 9.4 Multiple Limit States 111

9.4.1 Introduction 111 9.4.2 Example 1: Yielding and Burst of Defect-free Pipe 112 9.4.3 Example 2: Equipment Impact 113 9.4.4 Example 3: Corrosion 114

9.5 Reliability Calculation Tools 116

10. EXAMPLE APPLICATIONS ............................................................................................117

10.1 Example 1 New Pipeline Design 117 10.1.1 Introduction 117 10.1.2 Pipeline Information 117 10.1.3 Applicable Limit States 117 10.1.4 Reliability Targets 120 10.1.5 Limit State Functions 121 10.1.6 Probabilistic Characterizations of Input Parameters 121 10.1.7 Reliability Calculation 121 10.1.8 Design Process 124 10.1.9 Results 125 10.1.10 Sensitivity to Pressure 129

10.2 Example 2 Class Upgrade Deferral 130 10.2.1 Introduction 130 10.2.2 Limit States 131 10.2.3 Reliability Targets 131 10.2.4 Reliability Analysis 132 10.2.5 Results for Enhanced Maintenance 132 10.2.6 Comparison to Conventional Class Upgrade Approaches 134

11. CONCLUDING REMARKS..............................................................................................137

12. REFERENCES.................................................................................................................138

APPENDICES Appendix A Limit State Functions for Key Failure Causes Appendix B Probabilistic Models for Basic Variables Appendix C Methodology to Characterize Combined Proportional and Independent

Model Error Appendix D Basic Probability Concepts Appendix E Failure Probability Calculation for Seismic Loading

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LIST OF FIGURES AND TABLES

Figures

Figure 3.1 Illustration of Load Effect and Resistance Distributions

Figure 3.2 Illustration of the Limit State Surface

Figure 3.3 Illustration of Reliability Estimation for Internal Pressure

Figure 4.1 Types of Loading Processes Applicable to Onshore Pipeline

Figure 4.2 Types of Resistance Processes

Figure 4.3 Steps Involved in Implementing Reliability Based Design and Assessment

Figure 5.1 Reliability Targets from All Three Criteria Considered

Figure 5.2 Reliability Targets by Class

Figure 5.3 Relative Expected Number of Fatalities for Large Leaks and Ruptures

Figure 7.1 Procedure for Developing a Limit State Function

Figure 7.2 Illustration of an Excavator Impacting a Pipeline

Figure 7.3 Puncture Model Results Versus Test Data

Figure 7.4 Excavator Mass Versus Digging Force

Figure 7.5 Illustration of Frost Heave Loading Scenario

Figure 7.6 Applied Curvature from Finite Element Versus Regression Model

Figure 7.7 Illustration of Proportional Model Error

Figure 7.8 Illustration of Independent Model Error

Figure 7.9 Actual Burst Pressure Versus Model Results

Figure 7.10 Proportional and Independent Error Plots for the Corrosion Data in Figure 7.9c

Figure 7.11 Plot of Final Model with an Error Band of One Standard Deviation on Each Side

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Figure 8.1 Histogram Plot for the Yield Strength Data in Table 8.1

Figure 8.2 Cumulative Probability Plot for the Yield Strength Data in Table 8.1

Figure 8.3 Steps Involved in Fitting a Distribution to Statistical Data

Figure 8.4 Illustration of Goodness-of-Fit Test Statistics a) Chi-square Test b) K-S Test

Figure 8.5 Probability Paper Plots for the Yield Strength Data

Figure 8.6 Illustration of Time-dependent Random Variables (or Random Processes)

Figure 8.7 Distributions of Extremes for a Normal Parent Distribution

Figure 8.8 Extremal Load Distributions for Fixed and n (expected value of n = 10)

Figure 8.9 Exact and Gumbel Approximation of the Maximum Annual Impact Load

Figure 8.10 Illustration of Methods to Discretize a Continuous Random Process

Figure 8.11 Probability Distribution of Impact Rate for Different Sample Sizes

Figure 8.12 The 90% Probability Interval as a Function of Observation Period

Figure 8.13 Probability Distributions of the Mean Toughness for Various Sample Sizes

Figure 8.14 Toughness Probability Distributions for Various Sample Sizes

Figure 8.15 Cumulative Toughness Distributions for Various Sample Sizes

Figure 9.1 Probability Density Function of the Safety Margin Showing the Probability of Failure

Figure 9.2 Idealization of a Time-dependent Load as a Time-independent for Reliability Calculations

Figure 9.3 Illustration of the Rehabilitation Process

Figure 9.4 Probability of Detection as a Function of Defect Depth

Figure 9.5 Illustration of Measurement Error Band and Corresponding Probability

Figure 9.6 Failure Rate by Burst as a Function of Time

Figure 9.7 Impact of Rehabilitation on the Average Defect Depth Distribution

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Figure 9.8 Impact of Rehabilitation on the Failure Rate for Burst

Figure 9.9 Impact of a Specific Rehabilitation Plan on the Future Failure Rate for Burst

Figure 9.10 Limit States for Yielding and Burst Under Internal Pressure

Figure 9.11 Limit States for Different Failure Modes Associated with Equipment Impact

Figure 9.12 Limit States for Different Failure Modes Associated with Corrosion

Figure 10.1 Variation of the Population Density along the Right-of-Way

Figure 10.2 Calculated Versus Target Reliability for Section A

Figure 10.3 Calculated versus Target Reliability for Section B

Figure 10.4 Calculated Versus Target Reliability for Section C

Figure 10.5 Reliability Compared to Target for Status Quo and Enhanced Maintenance

Figure 10.6 Reliability Comparisons of Replacement, Pressure Reduction and Enhanced Maintenance

Tables

Table 4.1 Classification of Limit States with Respect to Time Dependence

Table 5.1 Load Cases and Limit States Relevant to Onshore Pipelines

Table 5.2 Tolerable Societal Risk Levels Calibrated to ASME B31.8

Table 5.3 Population Density by Class Based on Structure Data for Actual Pipelines (Nessim and Zhou 2005)

Table 6.1 Probability Estimates for Soil Displacement

Table 7.1 Actual and Calculated Burst Pressure for Corroded Pipe Specimens

Table 8.1 Yield Strength Data for X60 Steel

Table 8.2 Range and General Shape of Some Commonly Used Probability Distributions

Table 8.3 Results of Goodness-of-Fit Tests for Yield Strength Data

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Table 8.4 Gumbel Distribution Parameters for a Number of Parent Distribution Types (Maes 1985)

Table 9.1 Deterministic Pipeline Parameters for Example

Table 9.2 Probability Distributions of Basic Random Variables for Example

Table 9.3 Basic Variable Distributions Used in the Example

Table 10.1 Preliminary Applicable Limit States for Segment 1

Table 10.2 Final List of Applicable Limit States

Table 10.3 Pipeline Segments and Reliability Targets

Table 10.4 Probability Distributions for Uncertain Limit State Input Parameters

Table 10.5 Parameters used in Calculating Equipment Impact Frequency

Table 10.6 Metal Loss Inspection Tool Accuracy Specifications

Table 10.7 Wall Thickness and Equivalent Design Factors

Table 10.8 Calculated Reliability for SLS Under Hydrostatic Test Pressure

Table 10.9 Wall Thickness and Equivalent Design Factors

Table 10.10 Inspection Interval and Defect Repair Criteria

Table 10.11 Limit States Analyzed in Example 2

Table 10.12 Target Reliability Levels

Table 10.13 Probability Distributions for Uncertain Limit State Input Parameters

Table 10.14 Basic and Enhanced Failure Prevention Measures for Equipment Impact

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RESEARCH SUMMARY

TITLE: Guidelines for Reliability Based Design and Assessment of Onshore Natural Gas Transmission Pipelines

CONTRACTOR: C-FER Technologies

PRINCIPAL INVESTIGATORS:

Maher A. Nessim, PhD, PEng Wenxing Zhou, PhD

REPORT PERIOD: January 2003 July 2005

OBJECTIVES: The objective of this project was to develop a set of guidelines for the application of Reliability Based Design and Assessment (RBDA) to onshore natural gas pipelines.

TECHNICAL PERSPECTIVE:

The guidelines provided a set of reliability targets and a methodology to demonstrate that the targets are met. They are intended to facilitate the application of RBDA in practical situations and ensure that the resulting pipelines are safe and serviceable.

TECHNICAL APPROACH:

The design and assessment requirements developed for this project were based on risk analysis principles. They have been developed to ensure that the average safety of pipelines designed and operated using the RBDA approach equals or exceeds the average safety associated with new pipelines that conform to current codes and best practice. The steps involved in the reliability methodology include identification of the relevant limit states, development of limit state models, characterizing the uncertainties associated with the limit state parameters, calculating reliability, and comparing the calculated reliability to specified minimum targets.

RESULTS: The guidelines consist of a main document describing the methodology and containing two example applications, as well as a number of appendices containing supporting information on limit state functions, statistical parameter definitions, and failure probability calculation for seismic limit states.

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PROJECT IMPLICATIONS:

RBDA is a tool to support engineering decision-making based on rigorous analysis. Its benefits include consistent safety levels, best use of resources and an ability to deal with non-standard problems. The guidelines in this document will help make these benefits accessible for onshore natural gas pipelines. To facilitate use by pipeline engineers, these guidelines provide explicit procedures and examples for the steps involved in applying RBDA techniques. The reliability targets used in this document were developed as minimum requirements to ensure that adequate human safety is maintained throughout the life of a pipeline. Economic considerations were not taken into account because they vary widely for different pipelines. In some situations, lifetime costs could be minimized by exceeding the targets used in this document. As with any tool, RBDA methodology should be applied with good engineering judgment.

PROJECT MANAGER:

Charles E. French, P.E. Program Manager Compression and Measurement Gas Operations

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EXECUTIVE SUMMARY

General

This document contains a set of guidelines for the application of Reliability Based Design and Assessment (RBDA) to onshore natural gas transmission pipelines. The guidelines describe the reliability analysis framework and give detailed guidance on how to develop the deterministic and probabilistic models required to apply it to specific pipelines. They also contain state-of-the-art models for some key design conditions and failure causes including yielding and burst, equipment impact, and corrosion, making analysis of these failure causes possible without any further development. To facilitate use by pipeline practitioners, the guidelines provide explicit procedures and illustrative examples for the various steps involved in applying reliability-based design and assessment methods.

The guidelines are applicable to decisions that influence the structural integrity of a pipeline. These include design decisions for new pipelines, fitness-for-service evaluation for existing lines, assessment of changes in operational parameters (e.g. location class changes, fluid changes, damage) and evaluation of maintenance alternatives.

Overview of Probabilistic Limit States Design

A limit state is formally defined as a state beyond which the structure no longer satisfies a particular design requirement. Depending on the design requirement that is violated, pipeline limit states can be grouped into: 1) ultimate limit states, such as large leaks and ruptures, which are concerned with loss of containment events that could lead to significant safety consequences; 2) leakage limit states, which are defined as small leaks that do not lead to significant safety consequences; and 3) serviceability limit states, such as ovalization and denting, which affect functionality without jeopardizing pressure containment.

The essence of the limit states concept is to identify the true failure modes of the pipeline and to make decisions that ensure appropriate conservatism, considering the severity of the failure consequences. Instead of designing a pipeline primarily against hoop yield as required by current elastic limit design codes, the limit states approach suggests that the pipeline should be designed for the above-mentioned limit state categories. Since the consequences of serviceability limit states are much less serious than those of ultimate limit states, more conservatism is required for the latter. This ensures proper consideration of the true failure mechanisms, such as corrosion and equipment impact, resulting in more consistent safety levels than the stress limit design approach.

Acknowledging the uncertainties associated with structural performance, RBDA uses reliability as a measure of structural safety. Reliability with respect to a particular limit state category is defined as the probability that a given length of the pipeline will not reach any limit states within

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that category for a specified period of time. As such it is equal to the probability of reaching a limit state (i.e. probability of failure per km-year) subtracted from one.

The probability of failure for a given limit state is calculated as the probability that the load effect will exceed the corresponding resistance (i.e. combined probability of overload and under-resistance). The load effect and resistance distributions are usually estimated from other (more basic) variables using analytical models. Examples are the estimation of earthquake load effects from peak ground accelerations or the calculation of pipeline pressure resistance from yield strength, diameter and wall thickness. Ultimately, a limit state function is formulated, which defines combinations of the basic parameters that lead to failure. Standard methods are available to calculate the failure probability from the limit state function and the probability distributions of the basic parameters.

RBDA is a design and assessment method, in which the pipeline is designed and operated to meet a pre-defined set of target reliability levels. The targets must be met along the entire pipeline throughout its operational life. Failure consequences are accounted for by requiring more stringent target reliability levels for limit states with more severe consequences.

Benefits of the Reliability Based Approach

Design for the true structural behaviour. By identifying the true modes of pipeline failure and making decisions that mitigate the actual consequences of these failures, unrealistic design criteria and excessive conservatism are avoided.

Consistent safety levels. By requiring lower failure rates (or higher reliability levels) for pipelines with more severe failure consequences, a consistent safety level can be achieved. This is an improvement over the use of fixed safety factors, which result in unknown and highly variable risk levels for different pipelines.

Cost savings. Conservatism is placed where it is most needed (e.g. higher reliability for ultimate limit states than for serviceability limit states), leading to minimum cost solutions for a given level of overall safety.

Adaptability to new problems. Reliability levels are calculated from basic principles, making the approach well suited to new problems (e.g. stress corrosion cracking), unconventional environmental conditions (e.g. northern pipelines) and the application of new technology (e.g. the use of high strength steels).

Integration of design and operational practices. Since reliability is a function of both design and operational parameters, reliability gains due to in-service maintenance activities can be incorporated at the design stage, resulting in potential reductions in capital expenditures. This could have significant economic benefits in view of the recent and on-going improvements in inspection and maintenance technologies and practices.

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Summary of the Guidelines

Applying reliability-based methods to onshore pipelines requires two key departures from current design and assessment practice:

Design and assessment checks. Since the reliability-based limit states approach requires consideration of the actual failure causes, dominant failure mechanisms such as corrosion, mechanical damage and, for some pipelines, ground movement must be considered more explicitly in the design and assessment process.

Life cycle reliability. Since reliability varies with time for some of the major failure mechanisms such as corrosion, design should be based on lifetime reliability, taking the impact of maintenance into consideration.

The steps involved in implementing reliability-based design and assessment for a specific segment of a given pipeline are summarized in the figure shown below, along with the main inputs required for each step. The process is an iterative one in which various alternatives are identified, analyzed and evaluated against the appropriate safety and economic criteria, until the most economic alternative that satisfies the safety requirements is identified. The figure assumes that the pipeline route and main operating parameters (e.g. throughput, diameter and pressure) are defined.

The details of each step shown in the figure are addressed in a separate section of the guidelines, with example applications given in the final section. A brief description of these steps is given in the following.

1. Identify relevant limit states. The relevant limit states are identified based on the fluid being transported, internal pressure and external loads. Chapter 5 provides a list of possible limit states and Chapter 6 describes a procedure that can be followed to determine their applicability to a given pipeline. The procedure involves sequential application of a number of simple, conservative checks (both deterministic and probabilistic) to the limit state under consideration. Passing any one of these checks implies meeting the target reliability requirements, thus eliminating the need for a detailed reliability calculation.

2. Develop limit state functions. Guidelines for developing limit state functions are given in Chapter 7, along with some information on availability of the required deterministic pipe behaviour models. A simple procedure is given for limit state functions utilizing semi-empirical models, which are available for most pipeline limit states including yielding, burst, corrosion and equipment impact. A second procedure is provided for limit states involving more complex structural analyses, such as frost heave and thaw settlement. Appendix A gives limit state functions for some of the key limit states associated with onshore pipelines.

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Select DesignParameters and

Maintenance Plan

Identify RelevantLimit States

Calculate Reliability

ReliabilityTarget met ?

Economic Criteria met ?

Acceptable Design

No

Yes

No

Yes

Route Data and Loading Conditions

Operational Parameters and

Regulations

Target ReliabilityLevels

Probability Calculation Method

Develop Limit StateFunctions

Develop ProbabilisticModels of Basic

VariablesStatistical Data

Deterministic Behaviour Models

Steps Involved in Implementing Reliability Based Design and Assessment

3. Develop probabilistic models for basic variables. The uncertain parameters (referred to as basic random variables) used in each limit state function must be characterized by appropriate probabilistic models. Definition of these models is usually based on statistical data, theoretical considerations and judgment. Chapter 8 provides guidelines for the selection of appropriate probabilistic models. A procedure is given for selecting probability distributions to model time-independent parameters, such as yield strength and wall thickness. Also described is the development of stochastic process models for parameters that vary randomly with time, such as wind speed and equipment impact loads. The use of stochastic process models to estimate the extreme parameter values required for reliability calculation (e.g. maximum load and minimum resistance) is also covered. Procedures to deal with the additional uncertainties associated with small data sets are included. Appendix B

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gives a review of publicly available data and models for the basic random variables used in key pipeline limit states.

4. Select design parameters and maintenance plan. An initial set of design and maintenance parameters (including, for example, inspection frequencies, repair criteria, equipment impact prevention measures) should be proposed, taking into account any regulatory or policy constraints. In addition to defining the steel grade and wall thickness, it is necessary to define the set of supplementary measures that will be used to ensure reliable operation of the pipeline throughout its design life. These measures include quality assurance plans such as material testing and weld inspection procedures; corrosion mitigation strategies such as coating type and cathodic protection system characteristics; damage prevention activities such as burial depth, right-of-way patrols and first call system; and in-line inspection plans including tools to be used, inspection frequency and repair criteria. This information is required to evaluate life cycle reliability as discussed earlier. For existing pipelines, some of these parameters will be already defined and can be treated as constraints.

5. Calculate reliability. A reliability calculation methodology suitable for the main limit state functions affecting onshore pipelines is described in Chapter 9. The methodology addresses both time-independent and time-dependent limit states. A time-independent limit state is based on load and resistance processes that do not change systematically with time, and therefore the corresponding failure rate does not change with time. Examples include yielding and rupture of new pipe, and failure due to accidental equipment impacts. Time-dependent limit states involve systematic changes in the failure rate due to changes in the underlying load or resistance processes. Examples include gradual deterioration mechanisms such as corrosion or fatigue crack growth and slow developing loads such as deformations induced by frost heave. In addition, methodologies are described for simultaneous consideration of multiple limit states, which is required in cases involving multiple failure mechanisms (e.g. puncture of gouged dent failure due to equipment impact) and/or multiple failure modes (e.g. leaks and ruptures).

6. Compare to target reliability. The calculated reliability levels for various limit states are compared to the target values. The target values must be pre-defined based on an overall safety philosophy, which takes into account the severity of the consequences associated with each class of limit states. Chapter 5 summarizes the target reliability levels selected for natural gas pipelines. These targets define minimum requirements to ensure adequate safety levels throughout the life of a pipeline. Economic considerations were not taken into account because they vary widely for different pipelines. According to the limit state categories defined earlier, only ultimate limit states have significant safety-related consequences. The reliability targets for ULS were therefore developed using a risk-based approach that ensures consistent and adequate safety levels for all pipelines. Reliability targets for leakage (i.e. small leaks) and serviceability limit states were defined on the basis of historical information and published precedent. Details of the methodology used in developing the reliability targets are described in a separate document (Nessim and Zhou 2005).

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7. Assess economic implications. This step involves a check to ensure that the safety criteria are met at a reasonable cost and without undue conservatism. It may involve comparing various design alternatives that meet the target reliability levels for the purpose of selecting the minimum cost alternative. An example would be comparing a thick walled design coupled with a standard maintenance plan to a thinner walled pipeline combined with an enhanced maintenance plan. This analysis involves calculating the life cycle costs associated with each design/maintenance alternative. Although this is a key step in developing an optimal design, it is highly project-specific and is therefore not addressed in detail in this document.

Example applications involving the design of a new pipeline and the assessment of an existing pipeline are given in Chapter 10. The examples demonstrate use of the approach and provide some comments on how the results compare to conventional approaches.

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1. INTRODUCTION

1.1 Purpose

These guidelines have been prepared in partial fulfillment of the requirements of a project carried out by C-FER Technologies for the Gas Research Institute (GRI) under the supervision of the Design, Construction, and Operations Committee of PRCI. The objectives of the project were to develop a set of guidelines for applying Reliability Based Design and Assessment (RBDA) methods to onshore natural pipelines.

The document is intended as a tool to guide pipeline engineers through the process of applying RBDA to the planning, design and operation of natural gas pipelines. It can also be used as a guide for carrying out the analysis required to develop deterministic reliability-based design and assessment checks such as those based on Load and Resistance Factor Design (LRFD) methods.

1.2 Scope and Focus

These guidelines describe the reliability analysis framework and give detailed guidance on how to apply it to the design and assessment of natural gas transmission pipelines. They list the key failure modes that threaten pipelines and specify a set of reliability targets that must be met to ensure adequate safety and serviceability. They also describe the procedure used to calculate reliability for a particular pipeline and evaluate the results in relation to the targets. This procedure involves the use of deterministic structural behaviour models and statistical data on the input parameters to these models. The guidelines contain a state-of-the-art compilation of available models and data for some key conditions including yielding and burst, equipment impact, corrosion, seismic loading. Limit states for upheaval buckling and ground deformations are outlined in separate reports that are being prepared in conjunction with this project (Xie et.al. 2004 and Zhou 2005). They also contain a detailed description of how the required information can be developed for new and unique design conditions.

The guidelines focus on application and implementation rather than theoretical background. Specific procedures and illustrative examples are provided for different steps to ensure that the process can be followed without ambiguity. Reference is made to other documents that contain the required theoretical background.

Finally, the term Reliability Based Design and Assessment (and the acronym RBDA) is used throughout the document to indicate that the methodology is applicable to decision making in a general sense, including design decisions for new pipelines, fitness-for-service evaluation for existing lines, assessment of changes in operational parameters (e.g. location class or pressure changes), and evaluation of inspection and maintenance alternatives.

1.3 Organization

Chapter 2 contains definitions of the technical terms used in the document first appearance of each term defined in Chapter 2 is italicized. Chapter 3 contains a general overview of Reliability

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Based Design and Assessment (RBDA), including some background information, essential definitions, basic calculations and benefits. Chapter 4 describes implementation of the methodology for pipelines, discussing some of the key issues that are specific to pipeline reliability estimation.

Requirements for the application of RBDA to onshore natural gas transmission pipelines are given in Chapter 5. These requirements specify the design conditions (limit states) that must be considered and the reliability targets that need to be satisfied. Chapters 6 through 9 provide the technical information required to apply RBDA including methodologies to identify relevant limit states, construct limit states functions, develop probabilistic models for uncertain input parameters and estimate the lifetime reliability.

Chapter 10 gives two example applications, one for the design of a new pipeline segment and the other for a class upgrade assessment of an existing segment.

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2. DEFINITIONS

Accidental Load: Load resulting from an accidental event such as equipment impact due to excavation activity. Accidental events are typically discrete rare.

Allowable Stress Design: Design method in which the elastic stresses in the pipeline are limited to a specified fraction of the minimum resistance.

Assessment Area: Area within which the occupants of buildings and facilities are counted for the purpose of calculating the population density.

Basic Variable: Random variable (x) used in a limit state function. The basic variables can include loads, pipe geometry, pipe mechanical properties, and defect properties.

Characteristic Value: The parameter value used in a deterministic (e.g. LRFD) design check. It is typically defined as the value corresponding to a specified probability level (on the upper tail for load parameters and lower tail for resistance parameters).

Continuous Load: A load resulting from a continuous random process.

Continuous Random Process: A random process, whose parameter changes continuously with time (e.g. wind load). Although the parameter may assume an instantaneous value of zero, its value is generally non-zero.

Design Factor: Design load effect divided by design resistance. It is the inverse of the factor of safety.

Discrete Load: A load resulting from a discrete random process (e.g. seismic or equipment impact loads).

Discrete Random Process: A random process, whose parameter assumes non-zero values only at discrete points in time.

Distributed Limit State: A limit state that is equally likely to occur anywhere along the pipeline segment. This includes continuously applicable limit states, such as yielding of defect free pipe under internal pressure, and limit states with unknown locations, such as equipment impact.

Environmental Loads: Loads caused by environmental processes, which are generally variable with respect to time. They include loads due to thermal variations, ground movement, earthquakes and wind.

Evaluation Length. Maximum pipeline length over which the reliability targets must be met.

Extreme Distribution: The probability distribution of the maximum or minimum value occurring in a number of realizations of a random variable.

FORM: First Order Reliability Method

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Factor of Safety: Design resistance divided by design load effect. It is the inverse of the design factor.

Failure: A condition in which the pipeline violates one of its limit states.

Fatigue Limit States: Limit state resulting from fatigue under cyclic loading.

Independent Model Error: A random model error component whose magnitude is independent of the model output.

Individual Risk: Annual probability of fatality due to a pipeline incident for an individual situated at a particular location.

Intermittent Random Process: A continuous random process that is interrupted by periods during which the process parameter is zero.

Leakage Limit State: A limit state characterized by a small leak (less than 10 mm in diameter), leading to limited loss of containment that does not normally result in a safety hazard.

Limit State: A state beyond which the pipeline no longer satisfies a design requirement.

Limit State Function: Function of the basic variables that assumes negative values when the limit state is exceeded (i.e. the pipeline fails) and positive values when the limit state is not exceeded (i.e. the pipeline is safe).

Limit State Surface: A surface in the basic variable space that is defined by setting the value of the limit state function to zero. It defines the boundary between random variable combinations leading to failure and random variable combinations leading to safe performance.

Load and Resistance Factor Design (LRFD): Design method in which reliability-calibrated load and resistance factors are used. The design procedure is deterministic, but the design method is considered probabilistic, as the load and resistance factors are calibrated to meet specified reliability targets.

Load Effect: Effect of a single load or combination of loads on the pipeline. The load effect can be defined in terms of such parameters as force, stress, strain, deformation, or displacement.

Location-specific limit state. A limit state that occurs at a known location, such as failure of a known corrosion defect or at a known moving slope. The probability of failure for a location-specific limit state is defined on a per location basis.

Margin of Safety: Load effect subtracted from resistance.

Model Bias: The average value of model error.

Model Scatter: The random scatter associated with model error.

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Operational Loads: Loads associated with normal activities during construction or operation. They are generally variable with respect to time and include internal pressure, weight of contained fluids, thermal forces due to construction-operation temperature differential and variable surcharge (e.g. crossing traffic).

Parent Distribution: The probability distribution of a single realization of a random variable. The term parent is used in the context of external analysis to distinguish the probability distribution of the random variable from the probability distributions of its extreme values (maxima or minima).

Partial Safety Factors: Factors by which the characteristic value of a design variable is multiplied to give the design value. Partial safety factors can be divided into load factors and resistance factors.

Permanent Loads: Constantly applied loads whose value does not change with time. They include pipe weight, weight of permanent equipment and coatings, and permanent overburden.

Probabilistic Design: Design method that uses reliability as a measure of structural safety.

Probability of Failure: The probability that a component or a system will fail during a specified time interval (usually taken as one year). It is equal to the reliability subtracted from one.

Proportional Model Error: A random model error component whose magnitude is proportional to the model output.

Reliability: The probability that a component or system will perform its required function without failure during a specified time interval (usually taken as one year). It is equal to the probability of failure subtracted from one.

Reliability Based Design and Assessment: Design and assessment method in which the pipeline is designed and operated to meet specified target reliability levels.

Resistance: The maximum load effect that can be borne by a pipeline without leading to a limit state being exceeded (i.e. without leading to failure).

Return Period: Average time period between occurrences of an uncertain event such as exceedance of a particular value of a given random variable.

Risk: Probability of failure multiplied by a measure of the adverse failure consequences.

Risk Based Design and Assessment: Design and assessment method in which the pipeline is designed to meet specified tolerable risk levels.

SORM: Second Order Reliability Method

Safety Class: A classification of the criticality of the pipeline system or part thereof.

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Serviceability Limit State: A limit state that limits ability of the structure to meet its functional requirements, without jeopardizing the primary structural function or leading to safety or environmental risks. For natural gas pipelines, it is defined as a limit state that violates a design or service requirement without leading to loss of containment.

Societal Risk: A measure of the overall expected number of fatalities occurring due to pipeline failures. It can be defined as the expected number of fatalities, in which case it reflects a constant level of risk for incidents. Alternatively, it can be defined as the expected value of the number of fatalities raised to a power greater than one, in which case it reflects societal aversion to incidents causing a large number of fatalities.

Target Reliability Levels: Minimum reliability levels that are considered acceptable for a specific limit state or class of limit states.

Time-Dependent Reliability: Reliability with respect to a limit state for which the annual probability of failure changes as a function of time.

Time-Independent Reliability: Reliability with respect to a limit state for which the annual probability of failure does not change as a function of time.

Ultimate Limit State: A limit state relating to loss of the primary structural function and is likely to have adverse safety and environmental consequences. For natural gas pipelines, it is defined as a limit state that leads to loss of containment and results in a safety hazard.

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3. OVERVIEW OF RELIABILITY BASED DESIGN AND ASSESSMENT

3.1 Introduction

The basic objectives of structural design and operation are to ensure that: 1) a structure can sustain all anticipated loads and deformations during its design life with an adequate margin of safety against failure; and 2) the performance of the structure does not conflict with its functional and operational requirements. For many types of structures, including pressure vessels and pipelines, these objectives were historically achieved by using the allowable stress design approach, in which the elastic stresses in the structure are limited to some fraction of the anticipated minimum material strength. Safety against failure in this approach is based on a factor of safety, defined as the material strength divided by the operating stress (or a design factor, defined as the inverse of the factor of safety). Minimum factors of safety were established by code writing bodies on the basis of past experience and professional judgment.

Codes generally started by using conservative safety factors, but as more experience was gained and material quality improved, less conservative factors were adopted. In the case of the ASME Boiler and Pressure Vessel Code (BPVC) for instance, the minimum factor of safety on the tensile strength of steel was originally given a value of 5.0 in 1931, modified to 4.0 in 1950 and finally set to its current value of 3.0 (Farr 1982). This is a reflection of the fact that safety factors are meant to compensate for the uncertainties associated with structural systems and, therefore, these factors can be made less conservative as uncertainty decreases.

The essence of the Reliability Based Design and Assessment (RBDA) approach is to quantify design uncertainties and use them to calculate a probabilistic safety measure that forms the basis for evaluating specific designs. This measure, which is referred to as the reliability, is defined as the probability that failure will not occur during a specified period of time. This section contains an overview of RBDA methods as they apply to pipelines.

3.2 Historical Perspective

The classical theory of structural reliability, which is the basis for all probabilistic design methods, was developed after the Second World War as a tool to model the uncertainties associated with the performance of structures (Pugsley 1951 and Freudenthal et al. 1966). Key publications, such as Freudenthal (1947), Pugsley (1966) and Ferry-Borges and Castenheta (1971) describe the foundations of the theory.

Initially, there was little application of the theory in practical design situations because deterministic design methods had been well established and probabilistic design was viewed as complex and computationally demanding. This began to change, however, when it was shown that reliability could be related to a set of deterministic safety factors applied to the load effect and resistance (Lind 1973). This development made it possible to define deterministic design checks that are calibrated to meet certain reliability targets, which meant that the benefits of the approach could be realized through practical design methods based on the Load and Resistance Factor Design (LRFD) approach.

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In the last three decades, probabilistic design methods have been used as a basis for many structural design codes. Building codes pioneered this effort on the basis of a number of key research studies (CIRIA 1977, Ellingwood et al. 1980, MacGregor 1976, Kennedy and Gad Aly 1980, and Ravindra and Galambos 1978). Major codes that adopted this methodology in the early 1970s include ACI (1971), CSA (1973) and CEB (1975). LRFD codes are now used almost exclusively in North America for designing steel and reinforced concrete buildings (AISC 1986, CSA S16.1 1994, ACI 318 1983, and CSA A23.3 1994).

Significant advances in reliability theory, software tools and computer hardware over the last two decades made reliability calculations much more efficient. Most significant in the 1970s and 1980s was the development of first and second order reliability concepts (Hasofer and Lind 1974, Rackwitz and Fiessler 1978, and Madsen et al. 1986), which have resulted in several order-of-magnitude reductions in computational requirements. Although these methods made it much more practical to apply the theory with the computers of that era, they are based on specific assumptions (see Section 9.2.2.2) and do not necessarily work for all cases. Recent increases in the processing speed of computers have provided a solution to this problem by allowing a return to simulation methods for problems that cannot be solved using first and second order reliability methods. Due to these advances, the calculations required to implement probabilistic design have become much more efficient, and this resulted in the quick evolution of probabilistic design methods for many types of structures. Examples are offshore structures (e.g. API RP 2A-LRFD 1993, DNV 1989, FIP 1985 and CSA 1992), bridges (CSA S6 1988), and nuclear containment structures (Nessim and Hong 1993, and Hwang et al. 1986).

Although reliability-based methods have not yet been widely adopted in the pipeline industry, interest in these approaches has been growing in recent years, as their potential to achieve consistent safety at a lower cost is better recognized. This is evidenced by the adoption of these methods as a basis for the DNV Rules for Submarine Pipeline Systems (DNV 1996), and the ongoing development of a new ISO standard on Reliability Based Limit State Methods for pipelines (ISO DIS 16708 2004). Probabilistic methods are also mentioned as a possible design philosophy in the Canadian Standards Associations pipeline design standard Z662 (CSA 2003) and the draft International Standards Organizations pipeline design code (ISO DIS 13623 2004). In addition to these design applications, reliability-based methods have been used in the industry as a basis for increasing the pressure in operating lines (Francis et al. 1998) and making inspection and maintenance decisions (Nessim and Pandey 1997, and Nessim and Stephens 1998).

3.3 Sources of Uncertainty

Different classification schemes for the sources of uncertainty have been proposed in the literature (e.g. Ditlevsen 1981b, Der Kiureghian 1989, Melchers 1999 and ISO 2001). The classification proposed in this document is based on the premise that all uncertainties arise from lack of precise knowledge of the value of a quantity that is required to forecast the behaviour of a given pipeline. Uncertainties are classified with respect to the source of lack of knowledge into the following categories:

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a) Random variations - defined as uncertainty regarding the future value of a parameter that changes randomly with time. Examples are internal pressure, environmental loads (such as wind loads) and the forces resulting from equipment impact. This uncertainty stems from the fact that pipelines are designed and operated to perform adequately under future conditions. Some of the parameters defining these conditions cannot be determined with certainty at the time of making the required design or operational decisions, even if perfect models and data were available.

b) Measurement uncertainty - defined as uncertainty regarding the value of a fixed parameter due to limitations on the ability to measure its value. Examples are material properties, defect sizes and defect growth rates. Although it is possible, in principle, to measure these parameters with great precision, it is usually not practical to do so. For example, the yield strength at a particular location of a pipeline can only be determined from a destructive coupon test. Similarly, in-line inspection tools, which are the most practical means of measuring defect sizes, have some accuracy limitations.

c) Model uncertainty - defined as uncertainty regarding the value of a calculated physical parameter due to the assumptions and idealizations associated with the model used in the calculation. An example is uncertainty about the remaining strength of corroded pipe as calculated from ASME Standard B31G (ASME 1991). This uncertainty can be reduced by developing better (physical) models.

d) Statistical uncertainty - defined as uncertainty regarding a hypothesized probabilistic model (or distribution) used to characterize an uncertain parameter. For example, the probability distribution of the fracture toughness is required to determine the probability of crack failure. The type and parameters of the fracture toughness distribution may themselves be uncertain if they are estimated from a limited amount of data. This uncertainty can be reduced by obtaining more data. It may be interpreted as a subset of model uncertainty (see item c above) relating to a probabilistic rather than a physical model. To simplify the terminology, model uncertainty will be used to refer to uncertainties arising from physical models and statistical uncertainty to denote uncertainty arising from probabilistic models.

3.4 Limit States

A limit state is defined as a state beyond which the structure no longer satisfies a particular design requirement. It can be regarded as a failure mode, where failure is understood in the broad sense of failing to meet a design requirement. To maintain consistent risk for all failures, limit states are typically classified into categories with similar failure consequences and higher reliability targets assigned to limit states with more severe failure consequences.

There are two basic limit state categories that are used in all structural codes:

1. Ultimate limit states (ULS) are concerned with loss of the primary structural function. They usually refer to loss of strength or stability and are likely to have adverse safety and environmental consequences. Examples of ultimate limit states for pipelines are burst and rupture.

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2. Serviceability limit states (SLS) are concerned with the ability of the system to meet its functional requirements. They often refer to excessive deformations that affect functionality without jeopardizing the structural integrity or leading to safety or environmental risks. Examples of serviceability limit states for pipelines include ovalization and denting.

Some references define other limit state categories that overlap the ULS category. For example, DNV (2000) and ISO (2004) define Fatigue Limit States (FLS) and Accidental Limit States (ALS) as separate categories. In these codes, fatigue limit states relate to failure resulting from cyclic loading (e.g. weld cracks), and accidental limit states address severe, rare accidental loading conditions such as fires or dropped objects. The above codes assign the same reliability targets to ULS, FLS and ALS.

The essence of the limit states concept is to identify the true failure modes of the pipeline and to make design decisions that ensure appropriate conservatism, considering the severity of the failure consequences. For example, the commonly used approach of designing a pipeline primarily against hoop yield (elastic limit design) could be challenged on the basis that a small amount of yielding does not necessarily have adverse effects on the pipeline. The real concern is the possibility of burst leading to loss of containment. Given that the ratio of burst pressure to yield pressure varies significantly with the post-yield stiffness of the steel, designing against yield will result in variable safety against burst. In this example, a limit states approach would lead one to consider burst as an ultimate limit state and ensure that the design is appropriately conservative considering the corresponding consequences.

3.5 Reliability and Probability of Failure

3.5.1 Basic Concepts

Reliability, R, is defined as the probability that the pipeline will meet all of its design requirements for a specified period of time. Selecting the time period to be used as a basis for the definition of reliability is a question of units that does not have a significant impact on the results. The time period is usually taken as one year. Reliability is related to the probability of failure, pf, during the same time period by:

fpR = 1 [3.1]

If the probability of failure due to corrosion is 10-4 per km-year, for example, then the reliability with respect to corrosion is 1-10-4 or 0.9999 per km-year. This simple one-to-one relationship between R and pf means that knowledge of one implies knowledge of the other. In practice, pf is calculated from the probability distributions of the load and resistance and R is calculated from pf using Equation [3.1]. Since reliability is typically very close to 1.0, it is difficult to read its value in a simple fractional form (e.g. 0.9999 or 0.99999). It has therefore been customary to calculate and use the probability of failure as an indication of reliability (e.g. if the probability of failure is 10-5 per km-year, then reliability is expressed as 1-10-5 rather than 0.99999 per km-year).

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Figure 3.1 shows two probability distributions representing the load effect and resistance corresponding to a specific limit state for a given structural member. It shows that the resistance is generally higher than the load effect but that the two distributions have a small overlap. This overlap represents situations in which the load effect exceeds the resistance, leading to the limit state being exceeded (i.e. failure).

Load or ResistanceMean

ResistanceMean Load

Probability Distribution of theResistance (r)Probability Distribution of the

Load (l)

Figure 3.1 Illustration of Load Effect and Resistance Distributions

The probability of failure depends on the degree of overlap between the two distributions, which is a function of:

Separation between the two distributions as determined, for example, by the ratio between the mean resistance and the mean load effect. Higher values of this ratio imply that the two distributions will be further apart, leading to smaller overlap area and lower probabilities of failure.

Uncertainty associated with the distributions as measured by its standard deviation or Coefficient of Variation (COV). For a given ratio between the mean load and mean resistance, a higher COV results in a distribution that is more spread out, resulting in a larger overlap area and a higher probability of failure.

The basic idea of RBDA is to make decisions that maintain a minimum required level of reliability (referred to as a reliability target) or, synonymously, a maximum permissible failure rate. Reliability targets are usually selected to maintain uniform risk, where risk is defined as the failure probability multiplied by the failure consequences. To achieve this, higher reliability targets (i.e. lower permissible failure probability levels) are usually specified for limit states with more severe consequences.

3.5.2 Limit State Function

The probability of failure, pf, can be expressed mathematically as:

)0()( === lrmplrpp f [3.2]

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where r is the resistance, l is the load effect and m is the margin of safety defined as the difference between the resistance and the load effect. The load effect and resistance distributions are usually estimated from other (more basic) variables using analytical models. Examples are the estimation of earthquake load effects from peak ground accelerations or the calculation of pipeline pressure resistance from yield strength, diameter and wall thickness. Given this, the margin of safety, m, can be expressed as a function of a set of n basic variables (denoted by vector x = x1, x2,.,xn) that determine the load effect and resistance. This function is denoted g(x), and is called the limit state function. Equation [3.2] becomes:

([ gmpp f == x ]0) [3.3]

A simple example can be constructed for burst of a pipeline under internal pressure. In this case, the load is calculated as the product of the internal pressure, P, and diameter, D (i.e. l = P D). The resistance equals twice the product of the wall thickness, t, and the flow stress, f, multiplied by a factor, a, representing model uncertainty (i.e. r = 2 a t f). Using this information in Equation [3.1], leads to the following limit state function:

g = 2 a t f P D [3.4] Since g equals the safety margin as indicated in Equation [3.3], g(x) 0 indicates a negative safety margin, which implies failure, while g(x) > 0 indicates a positive safety margin, which implies that failure will not occur (safe). This means that the g(x) = 0 separates combinations of x that lead to failure from those that lead to a safe pipeline. This is illustrated in Figure 3.2 for a special case with two basic random variables. Because g(x) = 0 defines the boundary between the failure region and the safe region (see Figure 3.2), it represents the failure condition and is usually referred to as the limit state surface.

X 2

X1

Limit State Surfaceg (X1 ,X2 ) = 0

g (X1, Y2) > 0Safe region

g (X1, X2) < 0

Failure region

Figure 3.2 Illustration of the Limit State Surface

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3.5.3 Calculation Methodology

Estimation of the probability of failure involves solving Equation [3.3] for a given function g and a given set of probability distributions of the basic variables x. This is illustrated in Figure 3.3 for the limit state function in Equation [3.3]. Assuming that the uncertainties associated with D are relatively small, the probability of failure can be calculated from Equation [3.4] and the probability distributions of t, P, f and a as illustrated in the figure. Several approaches are available to carry out this calculation, including First and Second Order Reliability Methods (Madsen et al. 1986, Thoft-Christensen and Baker 1982, and Gollwitzer et al. 1988) and various simulation techniques including Monte Carlo (Rubinstein 1981), importance sampling (Engelund and Rackwitz 1992) and Latin Hypercube (LEcuyer 1994, and Avramidis and Wilson 1996). A discussion of the basic approach and advantages/limitations of each of these methods is given in Section 9.2.2.2. The important point for the purpose of this section is to recognize that, with the variety of available methods and the power of recent computers, estimating the probability of failure does not present a practical obstacle to the application of RBDA, provided that the limit state function and input variable distributions are available.

Maximum Pressure

Prob

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Reliability Estimates

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Operating pressureprofile

Yield strength data

Failure modeluncertainties

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x xx

xx

x xx

Random pressure fluctuations

Operating pressureprofile

Yield strength data

Failure modeluncertainties

Wall Thickness

Freq

uenc

y

Wall thickness data and

tolerances

Figure 3.3 Illustration of Reliability Estimation for Internal Pressure

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3.6 Reliability Based Design and Assessment

The essence of RBDA is to use reliability (as defined in Section 3.5) as a measure of the safety of a given structure or facility. This is a rational measure of the degree of success in achieving the main goal of structural design and operation, namely to ensure safety by minimizing any chanceof failure. Because reliability is a direct indication of the ultimate safety objective, it provides a meaningful and consistent measure of the effectiveness of various design and operational options in achieving the objective. In addition, it allows all structures of a given type to be evaluated and compared on an equal basis.

The implementation of RBDA involves designing and operating the structure or facility to meet specified target reliability levels for all applicable limit states. Different target reliability levels are usually defined for different limit state categories, with higher targets being required for limit states with more severe consequences. For example, higher reliability targets are usually specified for ultimate limit states than for serviceability limit states. This helps achieve overall risk consistency by ensuring that failures with more severe consequences are less likely to occur.

3.7 Benefits

The benefits of RBDA include the following:

1. Design for the true structural behaviour. Reliability-based limit states methods identify the true modes of pipeline failure and result in solutions that mitigate the actual consequences of these failures. This avoids unrealistic criteria that lead to undue conservatism. For example, it may be unrealistic to design pipelines to remain elastic in areas subject to large ground movements (e.g. areas subject to frost heave and thaw settlement). A reliability-based approach allows the designer to recognize that a certain amount of plastic deformations could be acceptable as long as it does not lead to loss of containment or impaired operations.

2. Consistent safety levels. The objective of industry is to achieve adequate safety levels. Recognizing the uncertainties associated with pipeline design and operation, adequate safety can most readily be achieved by limiting the probability of a failure to a tolerable level. It is also reasonable to maintain consistent risk levels (and consequently consistent safety levels) by requiring lower failure probabilities (or higher reliability levels) for pipelines with more severe failure consequences. This approach is more consistent than the approach used in current codes, which use fixed safety factors that result in unknown and highly variable reliability levels for pipelines with similar consequences.

3. Optimal use of resources. Although higher safety levels are always desirable, the resources available to improve safety are finite. The best design approach is one that achieves the highest possible overall level of safety for a given cost. The reliability-based approach achieves this by ensuring that resources are not wasted on unnecessary conservatism.

4. Adaptability to new problems. The safety measures used in the reliability-based approach (i.e. risk or reliability) can be calculated from basic principles. Because of this, they are less

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dependent than traditional design methods on a successful track record of application. Reliability-based methods are therefore suitable for unique projects involving newly recognized problems (e.g. stress corrosion cracking), unconventional environmental conditions (e.g. frost heave and thaw settlement) and the application of new technology (e.g. the use of high strength steels).

5. Integration of design and operational decisions. Reliability-based methods are capable of evaluating the lifetime reliability of a pipeline considering the impact of operational practices and integrity maintenance activities. This allows design and operational decisions to be considered simultaneously, leading to cheaper overall solutions. For example, the reliability gains due to in-service maintenance activities to be incorporated at the design stage, resulting in potential reductions in capital expenditures. This could have significant economic benefits in view of the recent and on-going improvements in inspection and maintenance technologies and practices.

6. Unified safety measure. The reliability targets used in RBDA provide an objective and direct measure of safety that is consistent with risk assessment principles. Industry-accepted reliability targets combined with a standardized approach to reliability estimation provide the necessary tools for both industry and regulators to measure and evaluate safety performance in the context of design, operations and risk assessment.

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4. RBDA METHODOLOGY FOR PIPELINES

4.1 Introduction

There are a number of key issues that arise in applying of RBDA to pipeline systems. These issues include reliability variation as a function of time (due to deterioration mechanisms such as corrosion and SCC) and periodic reliability improvements due to maintenance and rehabilitation. The purpose of this chapter is to describe these issues and present an overall methodology that takes them into account in applying RBDA to pipelines.

Pipeline-specific issues that need to be considered in estimating and evaluating are described in Section 4.2. This description focuses on introducing the issues and explaining them to the extent required to follow the overall RBDA methodology described in Section 4.3. A more detailed description of how these issues are taken into consideration in estimating reliability is given later in Chapter 9.

A step-by-step process for applying the RBDA methodology to pipelines is described in Section 4.3. An overview of each step in the process is provided, describing its purpose, outlining the basic information required for its execution, and showing how it fits in with other steps. The major analytical steps in this process are addressed in detail in separate subsequent chapters of these guidelines.

Section 4.4 provides a discussion of the applicability of RBDA to decision-making in the context of pipeline design and operations.

4.2 Key Issues for Pipeline Reliability

4.2.1 Time Variability

Reliability varies with time for some of the major pipeline failure mechanisms such as corrosion and ground movements. In the case of corrosion, for example, defects grow continuously with time and this causes resistance to internal pressure to drop. This means that, without intervention, the resistance distribution in Figure 3.1 will continue to move closer to the load distribution, resulting in an ongoing increase in failure probability. Because of this, reliability must be estimated as a function of time, and this requires information on the rate of change of the parameters governing deterioration (e.g. corrosion growth or ground movement rates).

In general, pipeline limit states can be classified as either time-dependent if the reliability changes with time or time-independent if the reliability does not change with time. This classification depends on the time characteristics of the load and resistance processes involved. Figure 4.1 shows the types of load processes relevant to onshore pipelines. They are:

a) Time-independent. The load is fixed with respect to time, although its value may be uncertain (i.e. a random variable). This category includes permanent loads such as dead load, which does not change with time but could be uncertain because of variability in wall thickness.

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Time

Load

Time

Load

Time

Load

Time

Load

a) Time-independent

c) Time-dependent stationary - discrete

b) Time-dependent stationary - continuous

d) Time-dependent increasing

Time

Load

Time

Load

Time

Load

Time

Load

Time

Load

Time

Load

Time

Load

Time

Load

a) Time-independent

c) Time-dependent stationary - discrete

b) Time-dependent stationary - continuous

d) Time-dependent increasing

Figure 4.1 Types of Loading Processes Applicable to Onshore Pipeline

b) Time-dependent stationary continuous. The load is continuously applied to the pipeline, but its value changes randomly as a function of time. Stationary means that, although the load value changes randomly as a function of time, the statistical properties of the load process do not change due to a shift of the time scale. The figure shows that the load could be changing either continuously or at specific points in time. Intermittent processes are also included in this category as they can be treated as continuous processes applied for a certain proportion of time. Examples of loading processes in this category include wind and internal pressure loads (continuous and continuously changing), operational loads (continuous and changing at specific points in time) and snow and ice loads (intermittent).

c) Time-dependent stationary - discrete. The load occurs at specific (discrete) points in time and has a very short duration when it occurs. Its value changes randomly between different occurrences, but its statistical properties do not change due to a shift of the time scale (stationary). Examples are equipment impact, earthquakes and severe storms.

d) Time-dependent increasing. The load is applied continuously and has an increasing value as a function of time. The increase is not subject to random fluctuations, although the parameters governing the change may be uncertain. An example is ground movement due to frost heave, which will increase continuously with time. The change is governed by uncertain parameters such as the soil properties and moisture content but is not subject to significant random time fluctuations.

Resistance processes fall into one of two major categories (Figure 4.2):

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Time

Resistance

Time

Resistance

a) Time-independent b) Time-dependent decreasing

Time

Resistance

Time

Resistance

Time

Resistance

Time

Resistance

a) Time-independent b) Time-dependent decreasing

Figure 4.2 Types of Resistance Processes

Time-independent. The resistance is fixed with respect to time, although its value may be uncertain (i.e. a random variable). Examples are the yield and burst resistance for defect-free pipe and pipe resistance to equipment impact loads.

Time-dependent decreasing. Resistance decreases with time without being subject to random fluctuations. Examples include resistance at growing defects or deterioration mechanisms such as corrosion, SCC or weld cracks. The parameters governing the change (such as defect growth rates) may be uncertain.

Table 4.1 shows the type of limit state arising from each combination of load and resistance processes described earlier. Combinations that are unlikely to apply to onshore natural gas pipelines are denoted as N/A. The table shows that a time-dependent stationary load or resistance results in a time-independent limit state. This is the case because reliability with respect to a given limit state is a function of the statistical properties of the load or resistance process, which do not change with time in the case of a stationary process. Only systematically increasing or decreasing load or resistance processes lead to time-dependent limit states.

Loading Process

Resistance Process Time-independent

Time-dependent Stationary - continuous

Time-dependent Stationary -

discrete

Time-dependent increasing

Time-independent Time-independent Time-independent Time-independent Time-dependentTime-dependent

decreasing N/A Time-dependent N/A N/A

Table 4.1 Classification of Limit States with Respect to Time Dependence

The classification given here is not entirely comprehensive or strictly representative of all possible limit states. It is, however, adequate to represent the great majority of onshore gas pipeline problems and is therefore used as a basis for the models included in these guidelines. Special cases in which these idealizations are not deemed appropriate must be addressed from first principles.

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4.2.2 Impact of Maintenance

As mentioned in Section 4.2.1, reliability with respect to time-dependent limit states such as corrosion will decrease with time as defects grow. A maintenance event such as an inline inspection followed by appropriate repairs will eliminate the most critical defects resulting in an immediate increase in reliability. Maintenance can also influence reliability for time-independent limit states. For example, the probability of failures due to equipment impact can be reduced by improving damage prevention measures, such as public awareness programs, one-call systems and pipe location and excavation procedures.

The foregoing indicates that a correct forecast of reliability as a function of time must take account of all maintenance and prevention activities affecting the limit states being considered. This implies that maintenance activities must be planned at the evaluation stage and incorporated in the reliability calculations.

4.3 Implementation Methodology

The steps involved in implementing RBDA for a specific pipeline segment are shown in Figure 4.3, along with the main inputs required for each step. The process is applicable to design decisions involving the selection of wall thickness and material properties, as well as operational decisions involving replacements, inspections, rehabilitation, pressure testing and damage prevention planning.

The following is a discussion of steps involved in Figure 4.3 with reference to other sections of the guidelines where these steps are described in more detail.

1. Identification of relevant limit states. The limit states relevant to a given pipeline are identified based on the loading conditions associated with the proposed route and operational conditions. Section 5.2.2 provides a list of possible limit states and Chapter 6 describes a procedure that can be followed to determine their applicability in a given situation.

2. Development of limit state functions. For each limit state, a limit state function is required (see Section 3.5.2). Limit state functions are deterministic models that can be developed based on the structural behaviour of the pipe. Guidelines for developing limit state functions and comments on the availability of relevant structural models are described in Chapter 7. Appendix A gives limit state functions for some of the key limit states associated with onshore pipelines.

3. Development of probabilistic models for basic variables. The uncertain parameters (referred to as basic random variables) used in each limit state function must be characterized by appropriate probabilistic models. Definition of these models may be based on statistical data, theoretical models or engineering judgment. Chapter 8 provides guidelines for the selection of appropriate probabilistic models, and Appendix B gives a review of publicly available data and models for the basic random variables used in key pipeline limit states.

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Select DesignParameters and

Maintenance Plan

Identify RelevantLimit States

Calculate Reliability

ReliabilityTarget met ?

Economic Criteria met ?

Acceptable Design

No

Yes

No

Yes

Route Data and Loading Conditions

Operational Parameters and

Regulations

Target ReliabilityLevels

Probability Calculation Method

Develop Limit StateFunctions

Develop ProbabilisticModels of Basic

VariablesStatistical Data

Deterministic Behaviour Models

Figure 4.3 Steps Involved in Implementing Reliability Based Design and Assessment

4. Selection of design parameters and maintenance plans. All the parameters required to evaluate lifetime reliability are required for this step. These include material properties; design parameters; corrosion mitigation strategies such as coating type and cathodic protection system characteristics; damage prevention activities such as burial depth, right-of-way patrols and first call system; and in-line inspection plans including tools to be used, inspection frequency and repair criteria. Depending on the application, some of these parameters will be treated as decision variables, while others will be treated as constraints. For a design application, there is a high degree of flexibility, and most of required parameters can be treated as decision variables. For existing pipelines, the pipeline physical attributes are fixed, and decisions are typically limited to operational aspects such as defining a safe operating pressure or a suitable inspection interval. The purpose of this step is to obtain the values of the parameter that will be treated as constraints and select a set of viable initial

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values for the parameters that will be treated as decision variables. Selection of a reasonable set of initial values must take any regulatory or policy constraints into consideration.

5. Reliability calculation. For a given limit state, standard probabilistic analysis techniques can be used to calculate the reliability from the probabilistic models of the basic random variables and the deterministic limit state surface. A reliability calculation methodology suitable for the main limit states affecting pipelines is described in Chapter 9.

6. Reliability evaluation. The calculated reliability levels for various limit states are compared to the target values. The target values must be pre-defined based on an overall safety philosophy, which takes into account the severity of the consequences associated with each class of limit states. Section 5.3 states the target reliability levels developed for natural gas pipelines. The approach used in developing these targets is described in detail by Nessim and Zhou (2005). If the reliability targets are not met, then steps four, five and six must be repeated with a new set of decision variables.

7. Economic assessment. This step determines that the safety criteria are met at a reasonable cost