NUREG/CR-6920

SAND2006-3 772P

Risk-Informed Assessment of

Degraded Containment Vessels

Sandia National Laboratories

U.S. Nuclear Regulatory Commission

Office of Nuclear Regulatory Research

Washington, DC 20555-0001
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NUREG/CR-6920

SAND2006-3772P

Risk-Informed Assessment of

Degraded Containment Vessels

Manuscript Completed: June 2006

Date Published: November 2006

Prepared by

B.W. Spencer, J.P. Petti, D.M. Kunsman

Sandia National Laboratories

Operated by Sandia Corporation for the

U.S. Department of Energy

P.O. Box 5800

Albuquerque, NM 87 185-0744

H.L. Graves, 1111, NRC Project Manager

Prepared for

Division of Fuel, Engineering and Radiological Research

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Job Code Y6164

Abstract

Various forms of degradation have been observed in the containment vessels of a number of operating

nuclear power plants in the United States. Examples of degradation include corrosion of the steel shell or

liner, corrosion of reinforcing bars and prestressing tendons, loss of prestressing, and corrosion of

bellows. The containment serves as the ultimate barrier against the release Of radioactive material into the

environment. Because of this role, compromising the containment could increase the risk of a large

release in the unlikely event of an accident.

It is possible to assess the effect that degradation has on the pressure retaining capacity of the containment

vessel by performing structural analysis using a model that takes into account the effects of the

degradation. While such an analysis provides useful information about the effects of the degradation on

the structural capacity of the containment, it does not necessarily provide a perspective on the effect that

the degradation could have on the risk associated with operating a nuclear power plant. To understand the

risk, one must take into account both the structural capacity of the containment and the probabilities of

occurrence of a variety of loading scenarios.

In this study, structural analysis results are integrated with risk models to gain a risk-informed perspective

on the issue of containment degradation. Risk models require a probabilistic description of the capacity

of the containment to resist a number of different failure mod 'es. Latin hypercube sampling is used to

develop sets of inputs for detailed finite element models of the containment in both its original and

degraded condition. Probabilistic descriptions of the containment capacity are obtained from the results

of the structural analysis models, and used as input for the risk model. By using this approach, both the

risk and the change in risk associated with the degradation can be measured.

The approach described above has been applied to case studies of containment degradation at four

"typical" U.S. nuclear power plants. These include a Pressurized Water Reactor (PWR) with a large, dry

reinforced concrete containment, a Boiling Water Reactor (BWR) with a Mark I steel containment, a

PWR with a steel ice condenser containment, and a PWR with a large, dry prestressed concrete

containment. In this study, each of these containments is subjected to a number of hypothetical

degradation scenarios. While this degradation is typical of that which has been observed in actual plants,

it is not implied that such degradation was actually observed in the plants studied here.

The risk analysis results reflect the effects of degradation and are evaluated with respect to the guidelines

given in the U.S. Nuclear Regulatory Commission (NRC) Regulatory Guide 1. 174. Recommendations

are made on the appropriateness and limitations of this approach. Integrating structural analysis with risk

analysis can give plant operators and regulators improved information to make the best decisions on how

to deal with containment degradation.

iii

FOREWORD

Through the years, the containment vessels of operating nuclear power plants in the United States

have exhibited various forms of degradation, including corrosion of the steel shell or liner, reinforcing bars,

and prestressing tendons; loss of prestressing; and corrosion of bellows. Because the containment serves

as the ultimate barrier against the release of radioactive material into the environment, compromising

the containment could increase the risk of a large release in the unlikcely event of an accident.

It is possible to assess the effect of degradation on the pressure-retaining capacity of the containment vessel

by performing a structural analysis using a model that considers the effects of degradation. While such

an analysis provides useful information about the effects of degradation on the structural capacity

of the containment, it does not necessarily provide a perspective on the potential effect of degradation

on the risk associated with operating a nuclear power plant. To understand that risk, one must consider

both the structural capacity of the containment and the probabilities of occurrence of a variety of loading'

scenarios.

This study integrates structural analysis results with risk models to gain a risk-informed perspective

on the issue of containment degradation. Risk models require a probabilistic description of the capacity

of the containment to resist a variety of failure modes. Latin hypercube sampling is used to develop

sets of inputs for detailed finite element models of the containment in both its original and degraded conditions.

Probabilistic descriptions of the containment capacity are obtained from the results of the structural

analysis models, and used as input for the risk model. Using this approach, one can measure both the risk

and the change in risk associated with the degradation. Moreover, integrating structural and risk analyses

can give plant operators and regulators improved information to make the best decisions on how to deal with

containment degradation.

This study applied the approach described above to case studies of containment degradation at four "typical"

U.S. nuclear power plants, including a pressurized-water reactor (PWYR) with a large, dry reinforced

concrete containment; a boiling-water reactor (BWR) with a Mark I steel containment; a PWsR with a steel

ice condenser containment; and a PWVR with a large, dry prestressed concrete containment. In this study,

each of these containments was subjected to a number of hypothetical degradation scenarios. While this

degradation is typical of that. observed in actual plants, the reader should not infer that such degradation

was actually observed in the plants studied here.

The risk analysis results of the effects of degradation were evaluated with respect to the guidelines

in U.S. Nuclear Regulatory Commission (NRC) Regulatory Guide 1. 174, "An Approach for Using

Probabilistic Risk Assessment in Risk-informed Decisions on Plant-Specific Changes to the Licensing Basis,"

Rev. 1, dated November 2002. Recommendations are made on the appropriateness and limitations of this

approach. With magnitudes depending on the depth and location, liner/shell corrosion significantly reduces

the capacity of a given containment. Nonetheless, only the case involving 50% corrosion at the basemnat

of the steel PWR ice condenser containment shows low probabilities of leakage near the design pressure.

Other degradation cases throughout these containment studies show shifts in the fragility curves, but not

aipproaching the design pressure even at low proba'bj*ies 2 ,,

Brian U. SheroS, birector

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

v

Table of Contents

A bstract ................... ....................................................... ...... 1i

Foreword..............................................................................................................V

Table of Contents.................................................................................................. vii

Figures............................................................................................................... ix

Tables ............................................................................................................... xi

Executive Summary .............................................................................................. xiii

Acknowledgements.................................................................................................XV

Acronyms......................................................................................................... xvii

I1. Introduction....................................................................................................I

2. Approach for Risk-Informed Assessment of Containment Degradation ................................. 2

2.1 Guidelines for Probabilistic Risk Assessment of Plant Modifications ............................. 2

2.2 Application of Risk Assessment Guidelines to Degraded Containments........................... 4

2.3 Containment Performance Characterization....;..................................................... 4

2.4 Containment Modeling................................................................................. 6

2.4.1 Steel Containments.................................................................................. 7

2.4.1.1 Leak Criterion ................................................................................. 7

2.4.1.2 Rupture and Catastrophic Rupture Criteria ................................................. 9

2.4.2 Reinforced and Prestressed Concrete Containments ............................................ 14

2.4.2.1 Leak Criterion................................................................................ 14

2.4.2.2 Rupture Criterion ............................................................................ 16

2.4.2.3 Catastrophic Rupture Criterion ............................................................. 17

2.5 Procedure for Risk-Informed Containment Analysis............................................... 18

2.5.1 Computation of Overall and Conditional Probabilities from Analysis Results ............... 19

2.5.2 Risk Assessment of Plant with Degraded Containment ........................................ 22

2.5.3 Approach ........................................................................................... 22

2.5.4 Un-Damaged Case Analysis ........................ ............................................. 24

2.5.5 Corroded Case Analysis........................................................................... 24

2.5.6 Risk Analysis Summary........................................................................... 24

3. Risk Analysis of PWVR Plant with Reinforced Concrete Containment.................................. 26

3.1 Structural Model of Reinforced Concrete Containment ........................................... 27

3.1.1 Axisymmetric Global Model...................................................................... 28

3.1.2 Local Detail and Corrosion Modeling............................................................ 29

3.1.3 Structural Analysis with Best Estimate Properties .............................................. 31

vii
3.2 Fragility Analysis of Degraded Containment ...................................................... 34

3.3 Risk Analysis Results................................................................................. 42

4. Risk Analysis of BWIR Plant with Mark I Steel Containment .......................................... 46

4.1 Structural Model of Steel Mark I Containment .................................................... 46

4. 1.1 Global Baseline Containment Model............................................................ 47

4.1.2 Containment Penetration Models ................................................................ 49

4.1.2.1 Global Model with Large Penetrations .................................................... 49

4.1.2.2 Detailed Models of Smaller Penetrations ................................................. 51

4.1.3 Analysis of Drywell Head Gasket ............................................................... 55

4.1.4 Corroded Region Models......................................................................... 55

4.1.4.1 Corroded Shell Models...................................................................... 56

4.1.4.2 Corroded Bellows Model .................................................................. 58

4.1.5 Structural Analysis with Best Estimate Properties.............................................. 61

4.2 Fragility Analysis of Degraded Steel Mark!I Containment ....................................... 64

4.3 Risk Analysis Results................................................................................. 76

5. Risk Analysis of PWYR Ice Condenser Containment..................................................... 81

5. 1 Structural Model oJPWR Ice Condenser Containment............................................ 81

5.1.1 Global Baseline Containment Model............................................................ 82

5.1.2 Containment Local Models....................................................................... 84

5.1.2.1 Basemat Region ............................................................................. 84

5.1.2.2 Ice Basket Region........................................................................... 85

5.1.2.3 Upper Floor Region......................................................................... 86

5.1.2.4 Upper Containment Region ................................................................ 87

5.1.3 Corroded Regions .......................................................................... *.......88

5.1.3.1 Corroded Basemat Region.................................................................. 89

5.1.3.2 Corroded Ice Basket Region ............................................................... 90

5.1.3.3 Corroded Upper Floor Region ............................................................. 91

5.1.4 Analysis of the Bellows .......................................................................... 92

5.1.5 Structural Analysis with Best Estimate Properties.............................................. 93

5.2 Fragility Analysis ofDegraded PWR Ice Condenser Containment .............................. 95

5.3 Computational Issues Discovered with the NUREG-1 150 Ice Condenser PRA Model ......104

5.4 Risk Analysis Results ............................................................................... 105

6. Risk Analysis of PWR Plant with Prestressed Concrete Containment................................ 109

6.1 Structural Model ofPresfressed Concrete Containment......................................... 110

6.1.1 3-D Global Models ............................................................................ 111.II

6.1.2 Local Models with Liner Corrosion............................................................ 113

6.1.3 Degraded Tendon Analyses..................................................................... 115

6.1.4 Structural Analysis with Best Estimate Properties ............................................ 115

6.2 Fragility Analysis of Degraded Prestressed Concrete Containment............................ 119

6.3 Risk Analysis Results ............................................................................... 130

7. Use of Regulatory Guide 1. 174 and PRA Models in Assessing Containment Degradation......... 134

Viii
7.1 Use of Regulatory Guide 1. 174 Methodology Assessment....................................... 134

7.2 Limitations of PRA Models for Assessing the Effects of Containment Degradation ........... 136

8. Summary and Conclusions................................................................................ 138

8.1 Program Overview ................................................................................. 138

8.2 Effects of Degradation on the Fragility, LERF, and other Risk Metrics........................ 138

9. References ................................................................................................. 141

Figures

Figure 2. 1: Acceptance Guidelines for Core Damage Frequency.............................................. 3

Figure 2.2: Acceptance Guidelines for Large Early Release Frequency...................................... 3

Figure 2.3: Hypothesized Effect of Degradation on Containment Performance ............................. 6

Figure 2.4: Finite Element Mesh of Plate with 5.08 m (200 in) Crack....................................... 10

Figure 2.5: Hole Area vs. Applied Stress for Various Crack Lengths ....................................... 10

Figure 2.6: JR Curve for A516 Gr. 70 Steel with Cutoff Used in Current Work........................... 12

Figure 2.7: Methodology for Computing Critical Crack Length (Lam and Sindelar, 2000) ............... 13

Figure 2.8: Stability Limit for Applied Far-Field Stress vs. Crack Length for A516 Gr. 70 Steel......... 14

Figure 2.9: Strain Magnification Factors for Typical Discontinuities in RC Containments (Tang et al.,

1995) ........................................................................................................ 15

Figure 2. 10: Strain Magnification Factors for Typical Discontinuities in Prestressed Containments (Tang

et al., 1995).................................................................................................. 16

Figure 3. 1: Postulated Corrosion in Liner of RC Containment............................................... 26

Figure 3.2: Axisymmetric Finite Element Model of RC Containment....................................... 29

Figure 3.3: Finite Element Mesh of Corrosion at Midheight ................................................. 30

Figure 3.4: Finite Element Mesh of Corrosion in Wall Near Basemnat ............................. .......... 31

Figure 3.5: Failure Potential at Corrosion and Discontinuity Locations ..................................... 32

Figure 3.6: Fragility Curves for Leak at Discontinuity Locations............................................ 37

Figure 3.7: Fragility Curves for Leak at Corroded Locations................................................. 37

Figure 3.8: Fragility Curves for Rupture and Catastrophic Rupture ......................................... 38

Figure 3.9: Comparison of the Undamaged Containment Fragilities from the Current Study and NUREG1150 ......................................................................................................... 38

Figure 3.10: Cumulative Probability of Failure Curves for Original and Degraded RC Containment.....39

Figure 3.11: Conditional Probability of Failure for Original Containment (No Corrosion)................ 40

Figure 3.12: Conditional Probability of Failure for 50% Corrosion at Basemnat ............................ 40

Figure 3.13: Conditional Probability of Failure for 65% Corrosion at Basemat ........................... 41

Figure 3.14: Conditional Probability of Failure for 50% Corrosion at Midheight.......................... 41

Figure 3.15: Conditional Probability of Failure for 65% Corrosion at Midheight.......................... 42

Figure 4. 1: Postulated Corrosion in Liner of Steel Mark I Containment .................................... 46

Figure 4.2: Finite Element Mesh of Drywell, Vent Line, and Wetwell ...................................... 48

Figure 4.3: Detailed View of Mesh in Vent Line Region..................................................... 48

Figure 4.4: Approximate Locations of Local Details Analyzed in Steel Mark I Containment ............. 49

Figure 4.5: Finite Element Mesh of Containment with Large Penetrations.................................. 50

Figure 4.6: Mesh Detail of Equipment Hatch Area ........................................................... 51

Figure 4.7: Mesh Detail of Wetwell Access Hatch Area...................................................... 51

Figure 4.8: Steam Line Penetration Submodel ................................................................ 52

Figure 4.9: Floor Drain Penetration Submodel ................................................................ 53

ix
Figure 4. 10: Containment Spray Line Penetration Submodel................................................ 53

Figure 4.11: Wetwell Instrumentation Line Penetration Submodel .......................................... 54

Figure 4.12: Wetwell HPCI Test Line Penetration Submodel................................................ 54

Figure 4.13: Mesh Detail of Drywell Knuckle Corrosion Area .............................................. 56

Figure 4.14: Mesh Detail of Corroded Area at Sand Pocket ................................................... 57

Figure 4.15: Mesh Detail of Corroded Area at Wetwell Waterline .......................................... 58

Figure 4.16: Mesh Detail of Corroded Bellows Area ......................................................... 60

Figure 4.17: Leakage Potential for All Penetration Details and 25% Corrosion Locations................ 61

Figure 4.18: Leakage Potential for All Penetration Details and 50% Corrosion Locations (Including I Ply

Bellows Corrosion) ........................................................................................ 62

Figure 4.19: Raw and Fitted Fragility Curves for the Drywell Head Region................................ 67

Figure 4.20: Raw and Fitted Fragility Curves for Individual Locations in the Drywell Region (Note: No

Observed Failures at Floor Drain Penetration) ........................................................... 67

Figure 4.2 1: Raw and Fitted Fragility Curves for Individual Locations in the Wetwell Region (Note: No

Observed Failures at Wetwell Access Hatch)............................................................ 68

Figure 4.22: Raw and Fitted Fragility Curves for Corrosion Location (25% and 50% depths) in the

Drywell Knuckle Region................................................................................... 69

Figure 4.23: Raw and Fitted Fragility Curves for Corrosion Location (25% and 50% depths) in the

Drywell Sand Pocket Region.............................................................................. 69

Figure 4.24: Raw and Fitted Fragility Curves for Corrosion Locations at Wetwell Waterline (25% and

50% depths) and Vent Line Bellows (1 Ply Corroded).................................................. 70

Figure 4.25: Overall Fragilities for Original Condition and All Corroded States Investigated ............ 71

Figure 4.26: Conditional Probabilities of Failure Modes for Original Containment........................ 72

Figure 4.27: Conditional Probabilities of Failure Modes for Containment with 25% Corrosion at Drywell

Knuckle...................................................................................................... 72

Figure 4.28: Conditional Probabilities of Failure Modes for Containment with 50% Corrosion at Dryiwell

Knuckle...................................................................................................... 73

Figure 4.29: Conditional Probabilities of Failure Modes for Containment with 25% Corrosion at Drywell

Sand Pocket................................................................................................. 73

Figure 4.30: Conditional Probabilities of Failure Modes for Containment with 50% Corrosion at Drywell

Sand Pocket................................................................................................. 74

Figure 4.3 1: Conditional Probabilities of Failure Modes for Containment with 25% Corrosion at Wetwell

Water Line................................................................................................... 74

Figure 4.32: Conditional Probabilities of Failure Modes for Containment with 50% Corrosion at Wetwell

Water Line................................................................................................... 75

Figure 4.33: Conditional Probabilities of Failure Modes for Containment with Corrosion in One of Vent

Line Bellows Plies.......................................................................................... 75

Figure 5. 1: Postulated Corrosion in PWvR Ice Condenser Steel Shell ........................................ 81

Figure 5.2: Finite Element Mesh of PWR and Detailed View of the Basemat Region..................... 83

Figure 5.3: Illustration of the Variation in Shell Plate Thickness (cm) for the PWR ....................... 83

Figure 5.4: Regions of Stress and Strain Concentration for the PWR ....................................... 84

Figure 5.5: Detailed View of the Basemat Region (Intersection of Steel Shell and Concrete Basemat) ... 85

Figure 5.6: Detailed View of the Ice Basket Region Submodel.............................................. 86

Figure 5.7: Detailed View of the Upper Floor Region Submodel............................................ 87

Figure 5.8: Detailed View of the Upper Containment Region Submodel ................................... 88

Figure 5.9: Locations of Corrosion Postulated for the PWR ................................................. 89

Figure 5. 10: Detailed View of the Corroded Basemnat Region ............................................... 90

Figure 5.11: Detailed View of the Corroded Ice Basket Region Submodel ................................. 91

Figure 5.12: Detailed View of the Corroded Upper Floor Region Submodel............................... 92

Figure 5.13: Approximate Bellows Location Relative to Upper Containment Submodel.................. 92

Figure 5.14: PWR Leakage Potential for All Locations and Corrosion Levels ............................. 94

x
Figure 5.15: Fragility Curves for Locations Contributing to the Bypass Mode: (top) Basemat Location,

(bottom) Upper Floor and Ice Basket Locations ......................................................... 97

Figure 5.16: Fragility Curves for Locations Contributing to the No Bypass Mode ......................... 98

Figure 5.17: Cumulative Probability of Failure for Each Containment Condition.......................... 99

Figure 5.18: Conditional Probabilities for the Original Condition (No Corrosion)........................ 100

Figure 5.19: Conditional Probabilities for 50% Corrosion at the Basemat................................. 101

Figure 5.20: Conditional Probabilities for 25% Corrosion at the Basemat................................. 101

Figure 5.2 1: Conditional Probabilities for 65% Corrosion at the Upper Floor............................. 102

Figure 5.22: Conditional Probabilities for 50% Corrosion at the Upper Floor............................. 102

Figure 5.23: Conditional Probabilities for 50% Corrosion at the Ice Basket............................... 103

Figure 5.24: Conditional Probabilities for 25% Corrosion at the Ice Basket............................... 103

Figure 5.25: Conditional Probabilities for Bellows Corrosion.............................................. 104

Figure 6. 1: Postulated Degradation in Prestressed Concrete Containment................................. 110

Figure 6.2: 3-D Wedge Finite Element Model of Prestressed Containment ......................... ;.......112

Figure 6.3: Submodel Finite Element Mesh.................................................................. 114

Figure 6.4: Corroded Region in Submodel Finite Element Mesh........................................... 114

Figure 6.5: Failure Potential at Liner Corrosion and Discontinuity Locations............................. 116

Figure 6.6: Failure Potential at Discontinuity Locations for 50% Area Degradation in the Midheight

Tendons .................................................................................................... 118

Figure 6.7: Failure Potential at Discontinuity Locations for 50% Loss of Prestressing of the Midheight

Tendons .................................................................................................... 119

Figure 6.8: Fragility Curves for Leak at Discontinuity Locations .......................................... 123

Figure 6.9: Fragility Curves for Leak at Corroded Locations ............................................... 123

Figure 6. 10: Fragility Curves for Rupture and Catastrophic Rupture....................................... 124

Figure 6.11: Fragility Curves for 50% Area Reduction in Midheight Tendons ........................... 124

Figure 6.12: Fragility Curves for 50% Prestressing Loss for the Midheight Tendons .................... 125

Figure 6.13: Cumulative Probability of Failure Curves for Original and Degraded Prestressed

Contaimnment............................................................................................... 126

Figure 6.14: Conditional Probability of Failure for Original Containment (No Corrosion)............... 127

Figure 6.15: Conditional Probability of Failure for 50% Corrosion at Basemnat........................... 127

Figure 6.16: Conditional Probability of Failure for 65% Corrosion at Basemnat........................... 128

Figure 6.17: Conditional Probability of Failure for 50% Corrosion at Midheight......................... 128

Figure 6.18: Conditional Probability of Failure for 65% Corrosion at Midheight......................... 129

Figure 6.19: Conditional Probability of Failure for 50% Area Reduction of the Midheight Tendons .... 129

Figure 6.20: Conditional Probability of Failure for 50% Loss of Prestressing for the Midheight Tendons

......................................................................................................... 130

Tables

Table 3. 1: Summary of Locations and Failure Pressures...................................................... 33

Table 3.2: Random Input Parameters........................................................................... 36

Table 3.3: Core Damage Frequency (yf')...................................................................... 42

Table 3.4 Large Early Release Frequency (yr-1)............................................................... 42

Table 3.5: Probability of Large Early Containment Failure Conditional on Core Damage................. 43

Table 3.6: Change in the Large Early Release Frequency (yf 1) due to Degradation ....................... 43

Table 3.7: Small Early Release Frequency (yr') .............................................................. 44

Table 3.8: Probability of Small Early Containment Failure Conditional on Core Damage................. 44

Table 3.9: Change in the Small Early Release Frequency (yf') due to Degradation ....................... 44

Table 3.10: Total Early Release Frequency (yf-1) ............................................................. 45

xi
Table 3.11: Probability of Total Early Containment Failure Conditional on Core Damage................ 45

Table 3.12: Change in the Total Early Release Frequency (yr.') due to Degradation ...................... 45

Table 4. 1: Summary of Locations and Failure Pressures ..................................................... 63

Table 4.2: Risk Model Failure Mode Abbreviations.......................................................... 64

Table 4.3: Random Input Parameters........................................................................... 65

Table 4.4: Core Damage Frequency (yr')..................................................................... 76

Table 4.5: Mean Probabilities of Early Containment Failure Conditional on Core Damage............... 76

Table 4.6: Large Early Release Frequency (yf1) .............................................................. 78

Table 4.7: Probability of Large Early Containment Failure Conditional on Core Damage................. 78

Table 4.8: Change in the Large Early Release Frequency (yf 1) due to Degradation ....................... 78

Table 4.9: Small Early Release Frequency (yf1) .............................................................. 79

Table 4. 10: Probability of Small Early Containment Failure Conditional on Core Damage ............... 79

Table 4.11: Change in the Small Early Release Frequency (yr'1) due to Degradation...................... 79

Table 4.12: Total Early Release Frequency (yf ') ............................................................. 79

Table 4.13: Probability of Total Early Containment Failure Conditional on Core Damage................ 80

Table 4.14: Change in the Total Early Release Frequency (yr'1) due to Degradation ...................... 80

Table 5. 1: Summary of Locations and Failure Pressures ..................................................... 95

Table 5.2: Random Input Parameters........................................................................... 96

Table 5.3: Core Damage Frequency (yf 1).................................................................... 105

Table 5.4: Large Early Release Frequency (yf'1)............................................................. 105

Table 5.5: Probability of Large Early Containment Failure Conditional on Core Damage ............... 105

Table 5.6: Change in the Large Early Release Frequency (yt') due to Degradation...................... 106

Table 5.7: Small Early Release Frequency (yt-')............................................................. 106

Table 5.8: Probability of Small Early Containment Failure Conditional on Core Damage ............... 107

Table 5.9: Change in the Small Early Release Frequency (yr71) due to Degradation...................... 107

Table 5.10: Total Early Release Frequency (yf')............................................................ 107

Table 5.11: Probability of Total Early Containment Failure Conditional on Core Damage............... 107

Table 5.12: Change in the Total Early Release Frequency (yf 1) due to Degradation..................... 108

Table 6. 1: Summary of Locations and Failure Pressures without Tendon Degradation................... 117

Table 6.2: Summary of Locations and Failure Pressures with 50% Area Reduction of the Midheight

Tendons .................................................................................................... 118

Table 6.3: Summary of Locations and Failure Pressures with 50% Prestressing Reduction of the

Midheight Tendons ....................................................................................... 119

Table 6.4: Random Input Parameters .......................................................................... 122

Table 6.5: Core Damage Frequency (yf 1).................................................................... 130

Table 6.6: Large Early Release Frequency (yf 1)............................................................. 131

Table 6.7: Probability of Large Early Containment Failure Conditional on Core Damage ............... 131

Table 6.8: Change in the Large Early Release Frequency (yf 1) due to Degradation...................... 131

Table 6.9: Small Early Release Frequency (yr41)............................................................. 132

Table 6. 10: Probability of Small Early Containment Failure Conditional on Core Damage.............. 132

Table 6.11: Change in the Small Early Release Frequency (yf'1) due to Degradation .................... 132

Table 6.12: Total Early Release Frequency (yf') ............................................................ 133

Table 6.13: Probability of Total Early Containment Failure Conditional on Core Damage............... 133

Table 6.14: Change in the Total Early Release Frequency (yr'1) due to Degradation ..................... 133

xii
Executive Summary

Various forms of degradation have been observed in the containment vessels of a number of operating

nuclear power plants in the United States. Examples of degradation include corrosion of the steel shell or

liner, corrosion of reinforcing bars and prestressing tendons, loss of prestressing, and corrosion of

bellows. The containment serves as the ultimate barrier against the release of radioactive material into the

environment. Because of this role, compromising the containment could increase the risk of a large

release in the unlikely event of an accident.

It is possible to assess the effect that degradation has on the pressure retaining capacity of the containment

vessel by performing structural analysis using a model that takes into account the effects of the

degradation. While such an analysis provides useful information about the effects of the degradation on

the structural capacity of the containment, it does not necessarily provide a perspective on the effect that

the degradation could have on the risk associated with operating a nuclear power plant. To understand the

risk, one must take into account both the structural capacity of the containment and the probabilities of

occurrence of a variety of loading scenarios.

Structural analysis results are integrated with risk models in this study to gain a risk-informed perspective

on the issue of containment degradation. Risk models require a probabilistic description of the capacity

of the containment to resist a number of different failure modes. Probabilistic effects are introduced into

the analyses using Latin hypercube sampling to develop sets of inputs for detailed finite element models

of the containment in both its original and degraded condition. The results of the structural analysis

models are used to obtain the probabilistic descriptions of the containment capacity and used as input for

the risk model. By using this approach, both the risk and the change in risk associated with the

degradation can be measured.

The approach described above has been applied to case studies of containment degradation at four

"typical" U.S. nuclear power plants. These include a Pressurized Water Reactor (PWR) with a large, dry

reinforced concrete containment, a Boiling Water Reactor (BWYR) with a Mark I steel containment, a

PWR with a steel ice condenser containmient, and a PWR with a large, dry prestressed concrete

containment. In this study, each of these containments is subjected to a number of hypothetical

degradation scenarios. While this degradation is typical of that which has been observed in actual plants,

it is not implied that such degradation was actually observed in the plants studied here.

The results of the risk analysis of the effects of degradation are evaluated with respect to the guidelines

given in the U.S. Nuclear Regulatory Commission (NRC) Regulatory Guide 1. 174. Recommendations

are made on the appropriateness and limitations of this approach. Integrating structural analysis with risk

analysis can give plant operators and regulators improved information to make the best decisions on how

to deal with containment degradation.

The results of the fragility and PRA models for each plant with various forms of degradation can be

summarized easily due to the observed consistent trends. With magnitudes depending on the depth and

location, liner/shell corrosion significantly reduces the capacity of a given containment. Only the 50%

corrosion at the basemat case for the steel PWR ice condenser containment shows that leaks are possible

near the design pressure. Other degradation cases throughout the containments studies here show shifts in

the fragility curves, but not approaching the design pressure even at low probabilities.

PRA models suggest that liner/shell degradation causes a small increase in Large Early Release

Frequency (LERF) in cases where catastrophic rupture dominates the failure mode. In such cases,

xiii
containment failure proceeds directly from leak to catastrophic rupture with little or no gap between the

failure modes. This is observed in the steel shell containments where sufficient energy exists within the

pressurized containment to propagate a crack after the initiation of a leak. Of the catastrophic rupture

dominated cases examined here with corrosion in the steel shell of a steel containment, all remain within

Region III of Figure 2.2.

Concrete containments also show increases in LERF with degradation when the overall capacity is

affected by the degradation. The two cases of tendon degradation of the prestressed concrete containment

show increases in LERF. The largest increase occurs when 50% of the area is reduced for the midheight

hoop tendons. The degradation of the tendons leads to a significant probability of catastrophic rupture at

low pressures. Here, LERF increases enough to enter Region 11 of Figure 2.2. Based on Regulatory

Guide 1. 174, the increase in risk is still considered small and may still be permitted.

Other cases actually show LERF remaining constant or even experiencing a reduction with degradation.

*These cases were encountered when leak was the dominant failure mode at low pressures. Specifically,

these cases occurred in the basemat and bellows corrosion cases for the steel PWrR ice condenser and the

two concrete containments with liner corrosion. The large bending field at the base of the ice condenser

containment causes leaks at low pressures prior to catastrophic rupture. The concrete containment liners

tear at relatively low pressures compared to the overall capacity of the concrete vessel.

Since LERF was found to decrease in some cases where leaks dominates and would cause a release, the

Small Early Release Frequency (SERF) was included in the PRA results for each containment. When

leak dominates the failure, SERF increases and leads to the observed decrease in LERF. In these cases,

the leak site acts as a "vent" at low pressures, slowly releasing material with the possibility of preventing

or delaying a catastrophic rupture.

Since SERF decreases for the cases where catastrophic rupture dominates, the Total Early Release

Frequency (TERF = LERF + SERF) was computed for each containment at each degradation case. TERF

was included to illustrate that the total frequency increases or remains constant when introducing

degradation regardless of the dominant failure mode.

If limits were placed on the increase in SERF or TERF that where analogous to those for LERF in Figure

2.2, Region 11 would be reached for several additional degradation cases in this study. In addition, the

PRA models used here do not directly compute LERF or SERF. The binning process is performed during

the post-processing of the PRA results. It is at this point where the results from the event tree analysis are

placed into LERF, SERF, and other "bins" depending on the. failure mode (e.g. leak, rupture, etc). This

study places leak failures into the SERF bin, and ruptures and catastrophic ruptures into the LERF bin.

This was done assuming that a leak would not depressurize the containment in less than two hours

(N1JREG- 1150 definition).

This study has examined several representative examples of containment degradation. The specific

results presented here should not be applied to any existing plant since actual degradation may be

considerable more severe or widespread than examined here. The purpose of this study was to

demonstrate a methodology of applying a risk-informned assessment to structural degradation. This

methodology could be applied to specific degradation found in an existing plant. Although, many of the

assumptions and techniques adopted in this study are still the subject of open research. In addition, the

definitions for leak, rupture, and catastrophic rupture and associated failure criteria were used here to

remain consistent with the existing NIJREG-1 150 PRA models. In reality, containments leak as a

continuous function of pressure. These items should be considered when examining the findings

illustrated in this report.

xiv
Acknowledgements

The project team acknowledges the continuous guidance, support, and encouragement from Herman L.

Graves III, Engineering Research Applications Branch, Division of Fuel, Engineering and Radiological

Research, Office of Nuclear Regulatory Research.

Special thanks are extended to everyone involved for their support and contribution to this project. The

project team would also like to thank Sandia colleagues Jason V. Zuffranieri, Michael F. Hessheimer,

Eric W. Klamerus, Jeffrey A. Smith, Jeffrey L. Cherry, Matthew C. Turgeon, David G. Robinson,

Gregory D. Wyss, Sharon L. Daniel, and Mark T. Leonard for valuable discussions and help in all phases

of this project.

Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for

the United States Department of Energy's National Nuclear Security Administration under Contract DEACO4-94AL85000.

xv

Acronyms

APB accident progression bin

APET accident progression event tree

BWR boiling water reactor

CDF core damage frequency

CDWR catastrophic drywell rupture

COV coefficient of variation

CWWR catastrophic wetwell rupture

DW'HL drywell head leak

DWHR drywell head rupture

DWL drywell leak

DWR drywell rupture

EPFM elastic-plastic fracture mechanics

IPE individual plant evaluation

LEFM linear-elastic fracture mechanics

LERE large early release frequency

LHS Latin hypercube simulation

LOCA loss of coolant accident

PCCV prestressed concrete containment vessel

PRA probabilistic risk assessment

PWR pressurized water reactor

RC reinforce concrete

SERF small early release frequency

TERF total early release frequency

WWLaW wetwell leak above waterline

WWLbW wetwell leak below waterline

WWRaW wetwell rupture above waterline

WWRbW wetwell rupture below waterline

xvii

1. Introduction

Containment structures in nuclear power plants fill the critical role of providing the final barrier

against the release of radioactive materials in the event of a severe accident. The ability of the

containment structure to resist internal pressures without leaking can have a significant effect on

the risk that operation of a plant could result in a release of radionuclides to the surrounding

environment.

In the United States, degradation of the containment vessel has been observed at a large number

of nuclear power plants. Corrosion has been observed in a number of steel containments, as well

as in the steel liners of reinforced concrete containments. Loss of prestressing in the tendons of

prestressed concrete containment vessels has also been observed. Degradation of bellows, which

are another critical part of the pressure boundary, is also of concern.

Any of these modes of degradation can have an adverse effect on the ability of a containment

vessel to perform its intended function. Previous studies have investigated the ability of

containments to resist leakage under overpressurization. Cherry and Smith (2001) investigated

how corrosion of the steel shell or liner affects the capacities of steel, reinforced concrete, and

prestressed concrete containments under internal pressurization. The effect of the loss of

prestressing force on the pressure capacity of prestressed concrete containment vessels was

investigated by Smith (200 1). Ellingwood and Cherry (1999) developed fragility curves for a

steel containment with corrosion damage under overpressurization.

Although the aforementioned studies provide valuable information on the pressure capacity of a

degraded containment, they provide little insight into the effect that the degradation has on the

risk of a radiation release. In the studies mentioned above, the pressure capacities of

containments were generally found to be well in excess of their design pressures, even with

significant degradation. However, under severe accident conditions, pressures far above the

design pressure can potentially be encountered.

The goal of this study is to take the previous studies on degraded containments one step further

and determine the significance of containment degradation on the risk of a radiation release. This

can give valuable insight into the performance of the containment under beyond-design-basis

loading events. A better understanding of the significance of the various factors that contribute to

the risk can lead to improved decisions on how to allocate resources to best ensure the safety of a

nuclear power plant.

I
2. Approach for Risk-Informed Assessment of Containment

Degradation

2.1 Guidelines for Probabilistic Risk Assessment of Plant

Modifications

The judicious application of probabilistic risk assessment (PRA) techniques to engineering

problems can lead to improved safety and better allocation of limited resources. The United

States Nuclear Regulatory Commission (NRC) recognizes the value of these techniques for

nuclear applications, and has released a policy statement (USNRC, 1995) encouraging greater use

of PRA in all areas of regulatory decision-making. As part of its effort to increase the use of PRA

in the regulatory process, the NRC developed guidelines for using PRA to make risk-informed

decisions regarding changes to a nuclear power plant's licensing basis. These are outlined in

Regulatory Guide 1. 174 (USNRC, 200 1).

In Regulatory Guide 1. 174, five principles to guide a risk-informed licensing basis chknge are

outlined:

* "The proposed change meets the current regulations unless it is explicitly related to a

requested exemption or rule change, i.e., a "specific exemption" under 10 CFR 50.12 or a

"petition for rulemaking" under 10 CFR 2.802."

" "The proposed change is consistent with the defense-in-depth philosophy."

" " The proposed change maintains sufficient safety margins."

' When proposed changes result in an increase in core damage frequency (CDF) or risk,

the increases should be small and consistent with the intent of the Commission's Safety

Goal Policy Statement. " (USNRC, 1986)

*"The impact of the proposed change should be monitored using performance

measurement strategies."

As mentioned in the fourth principle above, if a change results in an increase in risk, the increase

in risk must be small and fall within certain acceptance guidelines. In Regulatory Guide 1. 174,

core damage frequency and large early release frequency (LERF) have been designated as criteria

for determining the acceptance of a proposed change. If a proposed change in the licensing basis

results in an increase in either the CDF or LERF, the change is only deemed acceptable if the

baseline values of CDF and LERF, as well as the change in those values due to the proposed

change, fall within certain bounds. The changes in CDF and LERF due to the licensing basis

change are denoted as ACDF and ALERF, respectively.

The acceptance criteria for a proposed licensing basis change are shown graphically in terms of

CDF and LERF in Figure 2.1 and Figure 2.2, respectively. In both cases, the change in the risk

metric is plotted versus the baseline metric. This space is divided into three regions. In the area

denoted as Region 1, the risk of the proposed change is deemed too high to be acceptable, and the

change is not permitted. In Region 11, the risk increase is considered small, and the change is

permitted. In Region 1I1, the risk increase is considered very small, and the change is permitted.

In this case, however, the risk increase is deemed small enough that there is no longer a need to

compute the value of the baseline risk metric. A proposed change must meet the acceptance

guidelines for both CDF and LERF to be deemed acceptable. If a change is deemed acceptable,

the cumulative impact of other plant changes on the risk over time must be monitored.

2
i0ý

rUz

10- 

01 

5 

D

Figure 2. 1: Acceptance Guidelines for Core Damage Frequency

4

1 O-1

iO-1

10-610-

LERF

Figure 2.2: Acceptance Guidelines for Large Early Release Frequency

When proposing risk-informed changes to a plant's licensing basis, licensees are expected to

clearly define the proposed change, and perform an appropriate engineering analysis of the

change to ensure that it meets the aforementioned principles. They also must define an

implementation and monitoring strategy before submitting the proposed change.

The approach defined in Regulatory Guide 1. 174 for risk-informed decision-making is not

intended to relieve the duty of licensees to do things that they view as undesirable simply because

I
those things can be demonstrated to have a minimal impact on the risk. If a proposal results in a

risk increase, there must be clearly demonstrated benefits that outweigh the risk.

2.2 Application of Risk Assessment Guidelines to Degraded

Containments

Degradation of various types has been observed in the containments of many U.S. commercial

nuclear power plants during routine inspections. Any degradation of a containment vessel could

potentially decrease the capacity of the containment to resist intemnal pressure without leaking.

This could lead to a release of radiation to the outside of the containment earlier than would have

been the case had the containment been in its original, un-degraded state.

It is useful to study the problem of containment degradation with a risk-informed perspective to

determine its relative significance. In this study, the guidelines of Regulatory Guide 1. 174 are

applied to assess the risk associated with various types of postulated degradation of containment

vessels and bellows. The degradation is considered to be a temporary change in the plant's

licensing basis, and recommendations for action are made based on the outcome of the PRA and

Regulatory Guide 1.174.

While actual plants are being used as examples in this study, it should be emphasized that the

analyses in this report are not intended to represent the actual condition of the plants. The

information concemning the plant systems and structures used in the analyses is not current, and

current operating conditions likely differ considerably from those assumed in the analyses. Most

important, degradation is assumed only to demonstrate an analytical methodology, and does not

represent actual degradation that has been observed at any of the plants. Any similarity between

the degradation assumed in this study and that observed in the plants used for these

demonstrations is purely coincidental.

2.3 Containment Performance Characterization

A number of different criteria can be used to characterize the performance of a structure. In

design codes, structures are typically required to satisfy a number of different criteria to be

deemed acceptable. The most obvious of these is that the structure must have adequate strength

to resist the loads that it is designed for, with appropriate safety factors. For acceptable

performance, the structure also must meet deflection criteria under those loads. Design codes

also impose a number of other requirements that ensure that if a structural failure occurs, it will

fail in a manner that will present the least possible danger to the public.

When studying the pressure capacity of containment vessels, it is important to have an

understanding of how these structures behave under pressure loading, and of how the

performance under this load can be measured. One of the most difficult and important tasks

when performing a structural analysis of a containment structure is to determine how

performance is to be measured and how the structural analysis results can be interpreted in terms

of the chosen performance criterion. By their nature, the behavior and performance

characteristics of containment vessels are somewhat different than that of typical civil structures.

Arguably, the most important performance metric of a containment vessel undergoing

pressurization is its leak rate at a given pressure. For every type of containment vessel, there

exists a limiting pressure beyond which the structure can no longer be pressurized. This

structural capacity limit pressure is also an important performance characteristic, although it can,

be of secondary importance simply because it is often far in excess of the pressure at which the

4
containment first begins to leak, especially for reinforced and prestressed concrete containment

vessels. As with all structures, deflections can also be an important characteristic of containment

performance. Deflections are important in containments because they may adversely affect the

performance of components attached to the containment walls.

Over the past 20 years, Sandia National Laboratories has conducted overpressurization tests of a

number of scale models of different types of containment vessels for the NRC and Japan's

Nuclear Power Engineering Corporation (NUPEC). These have included tests on models of

different types of steel containmients, a reinforced concrete containment, and most recently, a

prestressed concrete containment. These tests have provided valuable insights into the behavior

of these different types of containment vessels under internal pressurization loads, and efforts

have been made to incorporate the insights of those tests in the present work.

In the NUREG- 1150 risk analyses, containment performance was characterized by three

categories of failures: "Leak", "Rupture", and "Catastrophic Rupture". While the leak rate is in

reality a continuous function of the internal pressure, these categories are used for computational

convenience in the binning process used in these risk analyses. A leak is defined as "... an

opening that would arrest a gradual containment pressure buildup but would not result in

containment depressurization within 2 h." "... A rupture is an opening that would result in rapid

(<2 h) containment depressurization." A catastrophic rupture "... would eliminate major portions

of the containment structures". Based on these definitions, specific sizes of holes corresponding

to the threshold leak rates for leak and rupture were given.

Figure 2.3 shows a hypothetical plot of the leak rate vs. pressure for a containment vessel. The

solid line shows the leak rate for a containment in its original condition, and is based roughly on

observations from the 1:4 scale prestressed concrete containment vessel (PCCV) model test

conducted at Sandia (Hessheimer et. al., 2003). At the design pressure, the leak rate is equal to

the design leak rate, and the leak rate steadily increases as the pressure is increased. Horizontal

lines are shown to approximately show the leak rates corresponding to the "leak" and "rupture"

criteria used in the NUREG-1 150 analyses, and solid vertical lines show corresponding pressures

for the containment in its original state. At a certain pressure, denoted by the solid vertical line

with the label "Original Catastrophic Rupture", the structural capacity of the containment is

reached. This is the limit state of the containiment, and it should be emphasized that this is not

related to a leak rate, unlike the "leak" and "rupture" pressures. The pressure shown here is what

was observed in the "structural failure mode test" phase of the 1:4 scale PCCV model test.

In addition to the performance of the containment in its original state, Figure 2.3 also illustrates

with dashed lines how degradation of the containment might affect its performance. Depending

on the type of degradation, any or all of the three performance criteria used in the risk model may

be altered. The performance of the degraded containment in this plot is purely hypothetical, and

is simply used for illustrative purposes.

In the NUREG-l 1150 risk models, as well as in the current work, the pressures corresponding to

the three failure modes mentioned above sumnmarize containment performance. Random

sampling is used to generate probability distributions of these failure pressures, as described in

the previous section.

5
- Original I -- Degraded/

100

as/ V-Ir

/L 2 

/2

Rutueak Leak Rate ~

0.1'- [0.ý

0 1' 22

Prssr (P

inegatL tet.I eak eeeacdn Rate cnrohntecnaineti'ubetdt

desgn Designmen 

Fiue232yoteie.fetofDgaaino Containment Performanc

radtesmise quthe complex Whn aikdet containment i desgnedtooeo aloabestesst the pecribeda bysk the

deig deveso assrcurelmdl thatthlekg will bcuaeles thanic the presuriedesigntleakcrathe durings

inegfrmated leakt raequtests bn sheveres accdntlysceaisosere when the containment sujete is ito

pressur"esk"igifcatlyuiger, ancthanstroheeign rpresure, translatin mdsmetructura repnste mretricus

scuchasl stran adidislaeent iefomncto leakt raiterstca becquite difficultmandepndets one thefie

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Tousdetemin thels lchangeointrisk duetis tor contaonment degradaetiooe diesosof motcitcltaesksi thes 

toer drevgelonsetrall mordels thagntuwillmaccuratelhpedc the pvressudiensos atwhc the vonariousnt

phesrfotrmanc lmoeits requredaby thken risk alyis mode are mebafntwen telcntiment isel in its

cnarenten "laktrupture" and "capta dstrphicmepture fntaiure modes mrentioed isbondtearevou

scdtion. for oefned ofinthe plantst stdidhees af BWRa withail Markgon steels whr contanentenreareon

noAolylntem of the failureelsizemobutsalso in termsstofytheelocationgo the fBailure.K202

codiinea-upse fornreinedr finite element modelyss ofroral. deaisonlreionsewhr costrtties concentfrain

6
steel and concrete are used in an effort to model structural response into the nonlinear regime as

realistically as possible using current commercially available technology.

Because steel and concrete containments exhibit fundamentally different behavior, the

approaches used to model them differ somewhat. The basic principles used in this study for

determining when the performance limits have been reached for steel and concrete (reinforced

and prestressed) containments are outlined below. These basic guidelines are sometimes

modified for analyses of specific containments. Such modifications will be outlined in the

descriptions of the containment analyses for those plants in later chapters.

2.4.1 Steel Containments

2.4.1.1 Leak Criterion

For the steel containments considered in this study, it is assumed that the "leak" criterion is met

when a tear initiates in the steel shell. At intemnal pressures below the level at which a tear first

initiates, there is a small amount of leakage, but it is assumed to be below the level of the "leak"

threshold as defined in the risk analysis.

Determining where the first tear is likely to occur is a difficult because of the large number of

local details that can potentially have a stress 'rising effect. The approach taken here is to analyze

submodels of a representative group of local details distributed throughout the containment.

Engineering judgment is used to select details that appear to have the highest potential for early

failure. It is of course possible that a detail more critical than those selected for analysis could

exist in the containment. Because of the large number of details present in a containment, one

has to accept the fact that resources are limited and that not every detail can be analyzed. The

level of detail used in this study is believed to offer a reasonable balance between computational

effort and desired accuracy given the available resources.

After the local models are run, their results are post-processed to determine the point at which

tearing occurs. Tearing is assumed to occur when the effective plastic strain, epeff , reaches a

limiting value. The baseline limiting value of ep~eff is the plastic strain found from a uniaxial

tension test, denoted as 'rf,uniaxiai.* Various conditions may be present that can cause a tear to

initiate when Ep~eff is less than 8 fn~a*An approach similar to that of Cherry and Smith (2001)

is used to account for these conditions. The effective plastic strains from the analysis are

multiplied by factors to account for the multiaxial stress state, the effect of corrosion on the

failure strain, and the model sophistication, or gauge length:

ýp =fn f7cfc- ufgfFEM -u -p, eff (2.1)

In this equation,

f.I accounts for the effects of multiaxial stress state,

* accounts for the presence of corrosion,

* fl-. accounts for the uncertainty in f~,

f g is a gauge length factor,

f FEM-u, denotes a finite element modeling uncertainty factor,

* P denotes the factored plastic strain, and

* 8 fnioialdenotes the uniaxial tensile strength.

7
The factored plastic strain, .6p accounts for all of these effects. Failure occurs when -is greater

than 8

cf,uniaxita1'

Whereas Cherry and Smith multiplied funailby factors to reduce the failure strain due to these

effects, the approach taken here is to multiply ep~eff by equivalent factors to increase the plastic

strain. This difference has no effect on the results. This slightly different approach was chosen

for compatibility with strain magnification factors used to represent details in concrete

containments, which are described in the next section.

The multiaxial stress state factor used in this study, denoted as f. is that developed by Hancock

and Mackenzie (1976):

1.0 (2.2)

fm=1.648 e -a 1 +'2 +3v cm

V/here oi are the principal stresses and Urvm is the von Mises stress.

Cherry and Smith found from experiments that if a steel plate is thinned by corrosion, the

corrosion can be reasonably represented in an analytical model by appropriately reducing the

thickness of the plate. However, in the. experiments, the failure strain in the corroded areas was

about 50% of the failure strain of steel without corrosion. This is due to the fact that the corroded

surface is uneven, and pits in the surface serve as local strain risers. Based on these observations,

corrosion in the steel shell or liner is modeled by thinning an appropriate area and applying a

corrosion factor, f, of 2.0 to account for the effects of pitting. In order to further account for the

uncertainty in the effect of corrosion on failure, f,- is introduced as a random parameter which

is varied with the LHS method. The value of f,-, follows a lognormal distribution with 1.0 as

the median and 0.2 as the ,8 factor. In all other areas of the model, f. and f,-, are set equal to

1.0.

The final adjustment factor is the analysis sophistication, or gauge length factor, denoted as fg9

The purpose of this factor is to account for the fact that strains tend to localize in areas of minor

*imperfections in the material. These localized strains can be much higher than the strains in the

rest of the material a short distance from the localization area. Tang et al. (1995) used a gauge

length factor of 4.0 in the derivation of strain magnification factors used to represent typical

details in reinforced and prestressed concrete containments. As described in the next section,

these magnification factors are used in the current work to simplify the analysis of the concrete

containments studied here. Since gauge factor of 4.0 may be overly conservative for steel

containments, a constant gauge length factor of 2.0 is used in this study for all detailed models of

steel shells. In addition, fFEM-, is included to reflect the uncertainty in the local strains

produced by the finite element model. The value of IFEM-u, follows a lognormal distribution

with 1.0 as the median and 0.30 and 0.35 as the 86 factors for 3D models and shell models,

respectively.

8
Apost-processing program was developed to automatically cycle through the integration points

of all elements in a model and compute the value of Zý, based on the local stress and strain states.

When Z exceeds -fluniaxial I tearing occurs and thus, the "leak" performance limit has been

reached.

2.4.1.2 Rupture and Catastrophic Rupture Criteria

While the criteria for initiation of tearing are fairly well accepted, determining when a tear

reaches sufficient size to be considered a "rupture" or a "catastrophic rupture" is a more difficult

problem. Once a tear has initiated, it will continue to grow if the stress state at the tip of the crack

is sufficiently high. Otherwise, it will remain stationary. Determining whether the crack will

grow or arrest itself is considerably complicated by the fact that crack growth is a function not

only of the stress state at the crack tip, but also of the crack length.

In the current work, it is assumed that all cracks form in the regions of elevated stress that occur

in discontinuity or corrosion regions. It is also assumed that if the stress is high enough to cause

crack initiation in that region, it is also high enough to force the crack to propagate across the fall

length of the region of elevated stress. This leng th is conservatively taken to be equal to the

dimension of the discontinuity feature.

As mentioned already, in the NUREG-1 150 risk analyses, a "rupture" is defined as a hole large

enough to depressurize the containment in less than about 2 hours. In that work, early analyses

estimated the hole area correspond 'ing to that depressurization rate to be about 0. 167 M2 (1.8 ft2

).

In later analyses, the hole area was estimated to be from 0.028 M2 (0.3 ft2

) to 0.046 M2 (0. 5 ft 2).

In developing a rupture criterion, it is important to have a basic understanding of the length of

crack that will result in a leak area equal to the "rupture" hole area mentioned above. If a crack

the length of a sufficiently large stress rising feature were to be under elevated tensile stress, but

not sufficiently high to result in unstable crack growth, the resulting leak area could potentially be

large enough for that crack to cross the "rupture" threshold, even though the crack does not

experience unstable growth.

To address this issue, quarter symmetry finite element models were developed of plates

containing stationary cracks of lengths varying from 1.02 mn (40 in) to 5.08 mn (200 in). Figure

2.4(a) shows a view of the un-deformed mesh of a plate with a 5.08 mn (200 in) crack. The crack

is actually 2.54 m (100 in) long, but by symmetry, it is equivalent to a crack twice its length. The

overall length and width of the quarter symmetry panel are 25.4 mn (1000 in). The panel is

modeled using plane stress 2D elements with a thickness of 19.1 mm (0.75 in) and the material

properties for A5 16 Gr. 70 steel, which is typical of that used in steel containments. The panel

thickness actually has no effect on the computed opening area because of the 2D plane stress

assumption.

The panels with shorter cracks use very similar meshes. The only difference is that the crack is

shorter and the refined area around the crack is proportional to the crack length. Tensile stresses

were applied in the far field in the direction perpendicular to the crack, and the analysis results

were post-processed to compute the crack opening area at a given far-field stress for each of the

crack lengths. Figure 2.4(b) shows a zoomed-in view of the deformed mesh at the point when the

applied far-field stress is equal to the yield strength of the material.

9
H+H

9

FEE]

H-EH

I

(a) Full view of original mesh (b) Zoomed-in view of deformed mesh at yield

(3x deformation magnification)

Figure 2.4: Finite Element Mesh of Plate with 5.08 mn (200 in) Crack

Figure 2.5 shows a series of plots of the computed hole area vs. the applied far field tensile stress

(given as the ratio of the applied stress, ~applied to the yield strength, cy) From these plots, it

can be seen that the crack has to be quite long, and subjected to fairly significant stress to create a

hole large enough to satisfy the "rupture" criterion. As mentioned previously, the hole size

required to meet this criterion is not clearly defined, but even using the lowest estimate of 0.02 8

mn2 (0.3 ft'), a 3.05 mn (120 in) crack would be large enough to be considered a "rupture" only

when the far-field stresses reach the yield stress. As will be demonstrated later, a crack of that

size would go unstable at a stress level well below the yield stress. Therefore, in this study, a

crack is considered to be a "rupture" only at the point when the applied far field stress is high

enough to cause unstable growth.

0.3 I I I I I I I I I

0.25 1-

Crack Length=1 .02 mn (40 in)

Crack Length=2.03 mn (80 in)

Crack Length=3.05 mn (120 in)

Crack Length=4.06 mn (160 in)

Crack Length=5.08 mn (200 in) 0.2 Hc4-

E

(D

0

X:

0.15 1-

7 /*

3

2.5

2

1.5

01

0.5

0.1 -

0.05

. . . . . . . ..... . . ....... nI -- h&u I . -- I . -7 1 n 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Gapplied / y

Figure 2.5: Hole Area vs. Applied Stress for Various Crack Lengths

As mentioned previously, cracks are conservatively assumed to propagate along the full length of

the stress rising feature at which they formed. Principles of fracture mechanics are used to

10
determine the applied internal pressure at which the crack experiences unstable growth, and

hence, makes the transition from "leak" to "rupture".

Because of the ductile nature of the steel used in containment vessels, the yielding zone ahead of

a propagating crack is significant. Thus, it is more appropriate to. use elastic-plastic fracture

mechanics (EPFM) than linear elastic fracture mechanics (LEFM). The text of Anderson (1995)

gives a good overview- of this topic. In materials with high toughness, the traditional stress

intensity factors used in LEFM fail to properly characterize the onset of unstable crack growth.

The J integral has been found to be a useful indicator of stress intensity that can be used to predict

unstable crack growth when significant yielding exists ahead of the crack tip. J is a measure of

the energy release rate, and is computed by taking a line integral around an arbitrary contour

around a crack tip. The value obtained by computing the J integral is independent of the contour

line chosen for integration.

To apply EPFM to an engineering problem, it is necessary to obtain a family of plots of the J

integral vs. the crack length. This can be done by performing a number of detailed finite

elements analyses of specimens having cracks of various lengths. There are also a number of

analytical equations in the literature. For the present work, it is reasonable to model the crack as

a crack in an infinite plate. Shih and Hutchinson (1976) developed simple equations for J for a

number of different geometries of cracks, including a crack in an infinitely wide plate for an

arbitrary material whose stress-strain relationship can be described by the following RambergOsgood power law:

n (2.3)

In this equation, a and n are dimensionless parameters fitted to describe a particular material,

and a, and co are reference values of the stress and strain (typically chosen as the yield stress

and strain). For the A516 Gr. 70 steel investigated in this study, values of a and n were fit to

the stress-strain curves at a given temperature.

The equation given by Shih and Hutchinson for the plastic component of the J integral for a crack

in an infinite sheet is given below:

.'1 = ao0 60 a [3.85V-n(1 - I /n) + ;r / njo /070 )n+1 (2.4)

where a is half of the crack length, and a' is the far-field applied stress.

The elastic component is given by the common equation:

JI/=(al) 2 r aeff /IE (2.5)

where E is the elastic modulus and

aeff =a + a I±( n -1(,-~ (2.6)

for a << W (W denotes half of the specimen or structure width).

The total J integral is simply:

I1I
J=j el +j P1 * (2.7)

In addition to the driving J caused by the load, it is also necessary to characterize the resistance of

the material, denoted here as JR . By performing a series of laboratory tests, it is possible to

generate a plot of JR vs. the crack length for a material. Figure 2.6 shows such a plot for A516

Gr. 70 steel based on data for quasi-static tests given by Papaspyropoulos et at. (1986). The

specimen tested is relatively large, a l0T (25.4 cm (10 in) remaining ligament and initial crack

length) compact tension specimen (C(T)) with a 2.54 cm thickness (1 in). This test was

performed at 288 0C (550 OF). The 2.54 cm thickness is similar to the containment thicknesses

examined here. While, the inplane dimension of 25.4 cm remains significantly smaller than the

inplane dimensions. The resistance curve will obviously be affected by temperature, constraint

conditions, local features, biaxial loading, etc.

6000

5000

3000

0 20 40 60 80 100 120

crack extension, mm

Figure 2.6: JR Curve for A516 Gr. 70 Steel with Cutoff Used in Current Work

Unstable crack propagation occurs when the]J curve is tangent to the JR curve. The tearing

modulus, proportional to the slope of the J curve, is useful in determining when this occurs. The

tearing modulus is defined by:

T _ (J (2.8)

where E is the elastic modulus of the material. The applied tearing modulus, associated with the

to the applied]J, is denoted here as T, while the modulus of tearing resistance is denoted as TR, to

correspond with JR Unstable crack growth occurs when J Ž! JR and T > TR. The procedure for

determining the length at which a crack will grow unstably is shown graphically in Figure 2.7, as

described in Sindelar et al. (2000) and Lam and Sindelar (2000). Instability will occur at the

point when the plot of J vs. T intersects the plot of JR vs. TR. The critical crack length under a

given far field stress is found from the J vs. crack length curve using the value of]J at the

instability point found from the intersection of the two curves.

12
i

In stability

Crack Length

Crack Length T, T,

Figure 2.7: Methodology for Computing Critical Crack Length (Lam and Sindelar, 2000).

Permission to use this copyrighted material is granted by the American Society of

Mechanical Engineers.

One challenge encountered in applying this method is that the JR curve is only available for

relatively short crack lengths due to the size of the laboratory specimens. This curve would have

to be extrapolated significantly to obtain values Of JR for crack lengths of interest in the present

application. The approach taken here is that used by Lam and Sindelar (2000). A cutoff value of

JR is selected at the upper bounds of the experimentally observed values. The slope of the JR

curve remains nearly linear below 5000 N/mm and then decreases with further crack extension.

For the current work, a slightly lower cutoff value of 4375 N/mm is used, as illustrated

graphically in Figure 2.6. As mentioned previously, the resistance curve and applied J (Equation

2.7) will be strongly affected by the conditions specific to a given containment. The method

presented above is used as a simple estimate for catastrophic rupture. For cracks assumed to have

lengths within the range of the experiment (<25.4 cm), the Lam and Sindelar method is

employed. For longer cracks, instability is conser-vatively assumed to occur when J (applied)

exceeds JR~cuifoff The applied J is calculated with interpolated values of a , n, co and co at a

given temperature (the elastic modulus, E, is assumed to remain constant with temperature). A

value for the crack length, a, is also assumed for specific locations of concern within the

discussion for each analyzed containment.

The stress raising features, and hence, the assumed crack lengths are all larger than the crack

lengths tested experimentally. Therefore, this study always computes unstable fracture based on

JR,culoff * Figure 2.8 shows an example plot of the far field tensile stress at the stability limit vs.

crack length (2a) for A5 16 Gr. 70 steel. The material properties, and therefore the curve in

Figure 2.8, vary with temperature. This example uses constant values of a = 5. 1, n = 5.2,

U0= 402.3 MPa, and E = 200 GPa. Once a tear, and hence, a "leak" is found to occur using

the procedures outlined in the previous section, this curve is used to check for unstable crack

growth.

13
Crack length (in)

0 50 100 150

1.2

1

0.8

()

:ý-L0.6

C0.4

0.2 Stable

0 1 I I I I

0 1 2 3 4 5

Crack Length (in)

Figure 2.8: Stability Limit for Applied Far-Field Stress vs. Crack Length for A516

Gr. 70 Steel

In most cases, it is assumed that if unstable crack growth occurs in a steel containment, the crack

quickly grows large enough that it can be considered a "catastrophic rupture", completely

skipping the "rupture" mode. The exception to this is that when the containment would come in

contact with a shield building, the presence of that building is assumed to prevent the crack from

causing a failure that could be considered "catastrophic rupture". This is consistent with the

observations made in the 1:6 scale test of a steel containment vessel model conducted at Sandia

(Luk et al., 2000).

2.4.2 Reinforced and Prestressed Concrete Containments

2.4.2.1 Leak Criterion

In reinforced and prestressed concrete containments, it is assumed that the "leak" criterion is met

when tearing occurs in the steel liner, just as was assumed for steel containment shells. The same

tearing criterion used for the steel containments is applied to these liners. The modeling process

is complicated somewhat by the presence of studs and anchors, but the theory is the same.

One could construct detailed models of typical discontinuities in concrete containiments to check

for tearing at stress risers just as is done for steel containments in this study. This step was not

necessary, however, because the results of analytical models and experiments on such details

have been applied in a study reported by Tang et al. (1995). In this study, which is reported 'in

more detail in Castro et al. (1993), strain magnification factors were developed to approximate

the effects of discontinuities typical of those found in the liners of reinforced and prestressed

concrete containments.

14
Four locations have been identified as being critical for tearing: at large steam penetrations, at

the junction of the wall and the basemnat, at personnel or equipment hatches, and at the springline.

Detailed finite element models, and in some cases, experimental models, were developed to find

the level of strain concentration at those locations. From these models, a set of strain

magnification factors were developed to compute the plastic strain in a discontinuity region from

the global strain, which is found from an axisymmetric model of the whole containment. For the

steam penetration and hatch locations, the global strain quantity is the hoop strain, whereas for

the wall-basemat junction and spring line, the meridional strain in the wall is used as the global

strain quantity. For the reinforced and prestressed containments, Figure 2.9 and Figure 2. 10 show

plots of these four magnification factors as functions of the normalized global strain. The

normalized global strain is simply the appropriate global strain quantity divided by the yield

strain of the liner material.

ht,

--- Steam Penetration

Wall-Basemat Junction - .. Hatch

Springline

50

0

0

40 F-

....................- ...- .

30 I20 k10

(1

*-0. 1

Normalized Global Strain 10

Figure 2.9: Strain Magnification Factors for Typical Discontinuities in RC

Containments (Tang et al., 1995). Permission to use this copyrighted material

is granted by Elsevier.

15
40

30

LL

C 2 0

20

10 - Steam Penetration

- / - -Wall-Basemat Junction

- Hatch

- -Springline

0.1 1 10 100

Normalized Global Strain

Figure 2. 10: Strain Magnification Factors for Typical Discontinuities in Prestressed

Containments (Tang et al., 1995). Permission to use this copyrighted material is granted

by Elsevier.

These strain magnification factors account for the effects of multiaxial stress states, and also

include a "gauge length" factor of 4.0 to account for the fact that when strains begin to localize,

the actual strains at the tear location are much higher than those observed in strain gauges in

experiments or in finite element models. This is analogous to the "analysis sophistication" factor

used by Cherry and Smith (2000), although the factor is considerably higher.

To use the strain magnification factors to check for failure, one first computes the global strain,

eat the specific discontinuity location within an axisymmetric model. This is normalized, and

the magnification factor, M, is found from the appropriate curve in Figure 2.9. The localized

plastic strain, Zý,i then simply computed as:

Zp= M JFEM-u _g (2.9)

where fFEm_, denotes a finite element modeling uncertainty factor. If T, is greater than the

uniaxial plastic failure strain of the liner material, efa,i' a tear has initiated and a leak has formed.

Equation 2.9 assumes no corrosion exists at these locations. Corrosion is introduced in analyses

of detailed liner submodels which adopt the same leakage criterion (Equation 2. 1) as for the steel

containments.

2.4.2.2 Rupture Criterion

As mentioned previously, the hole size in the steel liner required to meet the rupture criterion is

not clearly defined, often estimated between 0.028 m2 (0.3 ft') and 0.093 M2 (1.0 ft2). Here we

define rupture using the more conservative value of 0.028 M2 (0.3 ft 2). Since the analyses

performed here do not explicitly model the actual crack (leak) initiation and growth, an

16
approximate method must be employed to estimate the hole size. The method developed by

Dameron et al. (1995) is used here for that purpose. Given a location and orientation (meridional

or hoop) of an assumed crack within a model, a crack width is calculated by

W=6g S (2.10)

where egdenotes the global strain and s equals the span or spacing between anchorages or stud

layers perpendicular to the liner crack. The area of the opening can be estimated by multiplying

the crack width by an assumed crack length, a.

A = w a (2.11)

The length of the crack can be estimated as the region of uniform peak strains or stresses, the size

of local features, or the spacing of anchorages of studs in the direction of the crack. Equation

2.11 leads to a conservative estimate of the opening area since the opening is assumed square.

Alternate estimates of the crack area can be constructed, but Equation 2. 11 is assumed sufficient

due to the large number of approximations employed here.

Since Equation 2. 11 estimates the area for only one crack, the total open area at a given load step

(or pressure) is computed by

A total = frupt1a(Al 91fn, + A2 1 2n 2 +... (2.12)

where the subscripts 1 and 2 are associated with different locations within the model where

cracks are assumed to have a possibility of initiating.

* Ai denotes the crack area for one crack at location i,

* Si equals I if the leakage criterion has been obtained at location i and equals 0 if no leak

has initiated,

* n, denotes the number of cracks assumed to exist and initiate at location i, and

* __- accounts for the uncertainty in the total area.

The variable, -5iI enforces the requirement that a leak must initiate prior to a specific location

contributing to the total open area. The crack number variable, ni . enables the inclusion of the

effects of multiple cracks initiating near the same location. Based on Equation 2.12, rupture

occurs at a given pressure when the total area, Atotal , equals 0.028 M2 (0.3 ft2

). If at a given

pressure the rupture criterion is not reached, the pressure at the next load step is examined. Due

to the increase in global strain, the area will increase in size for locations which previously

contributed to the total rupture area. The leak criterion may also be obtained at additional

locations, which would then also contribute to the total area.

2.4.2.3 Catastrophic Rupture Criterion

A simple method is used to estimate the onset of catastrophic rupture. By assuming a cylinder

with contributions only from the rebar, liner, and tendons for the prestressed containment, the

pressure to cause catastrophic rupture is computed with

Pcat-rapt = fcat-u (0. 9)r Crebar-ult Arebar + aIiner-ull tliner +- atendon-ult A tendon"1(.3

y R S tebar R R stendon )

where

* Crebar-uh ) 0 71iner-uit , and Cle,,don-ult denote the ultimate strength for the rebar, liner, and

tendons,

" Arebar and Atenda,, are the area of the rebars and tendons

17
* Srebar and s tendon denote the spacing of the rebars and tendons,

* t~iner is the thickness of the liner,

*R equals the radius of the containment, and

. Co-u accounts for the uncertainty in the catastrophic rupture pressure.

in addition, Equation 2.13 includes a reduction factor of 0.9. This factor reflects overestimation

of the simple method observed in the analysis and testing of a 1:4-scale prestressed containment.

The 1:4-scale prestressed containment tested at Sandia National Laboratories (Flessheimer et al.,

2003) failed at 1.42 MWa, while the simple ultimate strength estimated failure at 1.54 MPa

(Dameron et al., 2000). The ratio of 1.42 MPa to 1.54 MPa is reduced slightly to 0.9.

2.5 Procedure for Risk-Informed Containment Analysis

Ini this study, risk models that have been developed for previous analyses are being adapted to

study the effect of containment degradation on the risk. During an accident scenario, there are

many potential modes in which the integrity of the containment vessel can be breached. The

containment may be subject to excessive pressures and temperatures, direct contact with core

material, and debris generated from internal explosions. The containment system may also fail to

perform its function in a bypass mode due to a hatch being left open during an accident. This

listing is not inclusive of all of the potential modes in which a containment can fail to perform its

primary function. For the purposes of this study, it is assumed that the degradation only affects

the capacity of the containment under over-pressurization. The probabilities associated with all

of the other containment failure modes investigated in the previous studies are assumed to remain

the same.

The structural fragility serves as the interface between the structural analysis model and the risk

model of the systems. Traditionally, a structural analysis results in a deterministic estimate of a

structure's capacity under a given loading. In a risk-informed analysis, a probabilistic

distribution of the structural capacity is required in place of the traditional deterministic estimate

of that capacity. A fragility curve is a cumulative probability distribution of a structure's capacity

to resist a given load.

Contributors to the uncertainty of the structural capacity can be grouped into two main categories:

inherent randomness in the components that make up the system, and uncertainty in the analyst's

ability to characterize the behavior of the system. These are often referred to as aleatory

uncertainty and epistemic uncertainty, respectively (Ellmngwood and Cherry, 1999).

There are several ways that an analyst can approximate the probability distribution function for

the strength of a structure. A basic method is to estimate the mean capacity of the structure using

traditional analysis methods, and then make assumptions about the overall aleatory and epistemic

uncertainty inherent in the system. An appropriate probability distribution function (typically

log-normal for structures) is chosen and used in conjunction with the analytical mean strength and

assumed uncertainty to describe the uncertainty in the system. While fairly simplistic, this is a

reasonable method, and has been used to describe the containment fragility in many of the risk

assessments of nuclear power plants submitted as part of the Individual Plant Evaluation (IPE)

program.

A more rigorous method to determine the structural fragility is to consider the probability

distributions of the individual components that make up the structure. Structural analysis models

are typically far too complex to incorporate the probability distributions of the components in a

18
closed form manner. Instead a large number of samples of the individual random variables that

describe the components of the system can be generated. The structural analysis is performed for

each set of samples, and a fragility curve can be developed from the distribution of the outcomes

of all of the structural analyses. This method is known as Monte Carlo simulation.

For complicated structural systems, the time required to analyze the system with a single set of

parameters can be significant. Classical Monte Carlo simulation requires a large number of

samples to give reasonable results. The Latin Hypercube Simulation (LHS) technique (McKay et

al, 1979) reduces the number of samples required to a much more reasonable number by dividing

the sample space of each variable into a limited number of equiprobable strata. Instead of

generating a purely random variable for each sample, in this technique, the stratum for each

variable is randomly selected, and a value for that variable that falls within the selected stratum is

used for the analysis.

The LHS technique is used in this study to generate the structural fragility curves because it offers

the ability to explicitly account for the probabilities of the individual components in a structural

system with a reasonable amount of computational effort. The DAKOTA (Eldred et al, 2001)

uncertainty analysis software was used to generate the LHS samples for the structural analyses in

this study.

The risk analyses of the plants are essentially sensitivity studies of the effect of structural

degradation on the overall risk. With the exception of the fragilities for containment

overpressurization, the risk models are the same as those used for the NUREG-1 150 study

(USNRC, 1990). To ensure that the fragilities of the containments in their original and degraded

states are consistent with each other, new fragilities of the containments in their original state

have been developed and replace the containment fragilities used in the NIJREG-1 150 analyses.

2.5.1 Computation of Overall and Conditional Probabilities from Analysis

Results

The NUREG-1 150 risk analysis models require two inputs to describe the performance of the

containment vessel. The first of these is an overall fragility curve, which describes the

cumulative probability of failure as a function of the internal pressure. In addition to this,

probabilities of failure in the various possible modes given that failure has occurred must be

provided. These are also functions of the failure pressure. The determination of which modes are

needed from the containment analysis is based on the effects that various modes of failure may

have on the outcome of an accident progression. In the simplest plant risk models, the number of

failure modes can be quite small. In some cases, the risk model only requires that the conditional

probabilities of leak, rupture, and catastrophic rupture be provided. In the more complex models,

the conditional probabilities must be specialized to provide probabilities of leak, rupture, and

catastrophic rupture at a number of different locations. The procedure used to develop overall

and conditional probability distributions for the failure modes needed by the risk model will be

described in this section.

The LHS procedure mentioned above is used to generate 30 sets of random parameters to be used

as input into the analytical models of the containment. For each containment, a number of

different locations where failure could potentially occur are modeled. The results of these models

of local details are compared against failure criteria to determine the pressure at which failure

would occur at a given detail. Ideally, for each of the sample sets, the analysis procedure would

19
produce a failure pressure for each detail. However, in some cases, the local details under

consideration are not very likely to fail at low pressure, and as a result, the failure criterion is not

met before the analysis is completed. At high pressures, the containment models typically

experience very large deformations in some areas, making it very difficult to advance the solution

to higher pressures. Because of this, it is often simply not practical to advance the solution to

reach a pressure at which every monitored detail would fail.

A fragility curve describing the cumulative probability of failure vs. pressure for a given failure

location can be produced by sorting the analytical failure pressures in ascending order. If there

are n LHS sample sets, the lowest failure pressure is assigned a cumulative probability of 1/(n+2),

the next highest is assigned a probability of lI(n+2)+ 1/n, and so forth. Due to the large amount of

time required to run one set of analyses, it is impractical to run a large number of samples. The

lowest probability for which a failure pressure is available is 11(n+2). Lognormal distributions

are fitted to the results to provide extrapolated information in the tail regions that would

otherwise be unavailable.

If failure pressures are obtained at a location for all of the sample sets, the parameters of the

lognormal distribution to fit the data are found in the standard manner based on the mean and

variance of the data. If failure does not occur at a given location because of an early termination

of the analysis, which might occur for the reason described above, an altemnative procedure is

used. First, an attempt is made to obtain more failure pressure data points by linearly

extrapolating the results from the last two time steps of the analysis. If a location is already

relatively close to the point of failure at the end of the analysis, this can be reasonably accurate.

Extrapolated pressures are only used if they are less than 15% higher than the pressure in the last

analysis step. Due to the nonlinear nature of the structural behavior, it is not reasonable to

extrapolate beyond that amount.

If the set of results is still incomplete after extrapolation, the available data is sorted and a

probability is assigned to each available failure pressure starting with the lowest pressure as

described previously. It is assumed that all cases that did not fail have failure pressures above the

highest actual recorded pressure. A nonlinear least squares procedure is used to fit a lognormal

cumulative distribution function to the available data.

After the parameters of fitted distributions are estimated from the raw data for all of the failure

locations, the process of developing an overall fragility curve from these is fairly straightforward.

Using de Morgan's rule (Ang and Tang, 1975), the probability of occurrence of any one of a

number of statistically independent events E, can be computed as:

P(El ~uE2 E, I 1-(1- P(El ))(1- P(E 2)) (1 -P(E,)) (2.1)

Failure in containments typically occurs at stress concentrations around penetrations, and the

various penetrations in a containment can reasonably be assumed to be statistically independent.

The penetrations modeled are just a sample of what may be a large number of very similar

penetrations. For an arbitrary number of penetrations similar to the ones being modeled, at a

given pressure, the overall probability of failure P(F) can be computed from the cumulative

failure probabilities of the locations investigated by

P(F) = 1- (1 -P(F 1 )) m (1 -P(E2 )) "2... (1-P(E,,))m " (2.2)

where P(F7i) is the cumulative probability of failure at location i at a given pressure, and m, is the

number of penetrations having similar characteristics and loading as that at location i. Because

the overall fragility is the cumulative distribution of the probability of a failure of any size, and a

larger size of failure at a location can only occur after the smallest size of failure at that location

20
can occur, the distribution function for the smallest failure mode at every location is used in this

calculation.

Computing the conditional probabilities of failure for the modes used in the risk analysis is less

straightforward. Because the various locations where failure could occur are statistically

independent, there is a potential that failure could occur at more than one location simultaneously.

In the event trees used in the risk model, it is assumed that failure cannot occur in more than one

mode simultaneously. The failure modes needed by the risk model are defined in terms of failure

sizes and locations. The locations generally cover a large area of a containment, and failure may

occur at any number of locations within the location grouping defined by the risk model.

The first step is to compute the conditional probabilities of failure of the three sizes (leak, rupture,

and catastrophic rupture) at each of the location groupings and at each pressure increment for

which output will be given. This is done using Equation 2.2 for the leak, rupture, and

catastrophic rupture distribution functions for every considered detail located within the grouping.

This provides distributions for the pressures at which a leak, rupture, or catastrophic rupture will

occur at each grouping.

A leak is a breach that is smaller than the rupture size. A rupture is bigger than the rupture size,

but smaller than the catastrophic rupture size. The conditional probability of leak is obtained by

subtracting the rupture probability from the leak probability and dividing by the leak probability.

Likewise, the rupture conditional probability is obtained by subtracting the catastrophic rupture

probability from the rupture probability and dividing by the leak probability. The catastrophic

rupture conditional probability is computed by dividing the catastrophic rupture probability by the

leak probability.

Once the overall probability distributions for each of the location groupings and the conditional

probabilities for the various sizes of failure in each of those groupings are formed, a Monte Carlo

sampling method is used to determin~e conditional probabilities of failure for all of the groupings

and sizes of failure within those groupings. A large number of sets of random numbers are

generated. For each grouping, two random numbers are generated: one conforms to the overall

failure probability distribution for that location, and the second is a uniformly distributed random

number in the range from 0 to 1. The second number is used in conjunction with the conditional

distributions of failure size at that location to determine the failure size at a given pressure.

For each set of randomly generated samples, an algorithm is used to determine at every output

pressure interval whether the containment fails, and the grouping and size of failure if failure does

occur. The algorithm starts at a low pressure and incrementally increases the pressure. Once the

pressure is higher than at least one of the randomly sampled overall failure pressures for the

various groupings, the containment is assumed to have failed at the grouping with the lowest

sampled pressure. That location grouping is assumed to be controlling unless another grouping

has a failure of a larger size than the failure at that grouping. In this manner, a dominant failure

location and size is determined for every pressure interval for each of the samples. The sum of

the number of failures at each pressure interval is taken over every sample and divided by the

total number of samples to determine the conditional probability of failure of each of the modes.

The'assumption that the first location to experience a failure of a given size overrides all others of

that size allows for conditional probabilities that conform to the requirement that failure can only

occur in one mode at a time.

21
2.5.2 Risk Assessment of Plant with Degraded Containment

For the examination of potential risk increases caused by containment corrosion, the risk

assessment models developed for actual steel and concrete containments in the NUREG- 1150

(USNRC, 1990) study are used. The models are documented in both NUREG-1 150 and in detail

in NUREG/CR-455 1. It is very important to emphasize that the analysis performed here,

although based on an actual plants, is intended to be generic and not representative of actual

conditions at that plants. The models used date from the late 1980s, and the plants have changed

since then. Also, as mentioned previously, the corrosion assumed to exist in the containment is

purely hypothetical, and does not represent corrosion actually observed in any particular

containment. The analyses presented here are a "proof of concept." That is, it is an example of

how such an analysis could be done and, if corrosion existed, how the risk of a plant that had

containment corrosion might be affected.

For the NUREG- 115 0 study, the containments at the plants under investigation had no corrosion,

and experts from the government, academia, and industry estimated their failure pressure.

Several different failure types were believed possible, from bypasses to small leaks to larger

containmnent ruptures. As discussed previously, a rupture is differentiated from a leak by the fact

that it is large enough to depressurize the containment atmosphere after failure. Anything

smaller is simply referred to as a leak.

The risk measures used for this analysis are the frequency of large early releases of radioactive

material and the probability of a large early containment failure, given core damage.

2.5.3 Approach

As noted, the NUREG-1 150 risk analysis models are used as a starting point. A brief discussion

of the treatment of the uncertainties in those models is warranted. The risk analysis done for this

plant in NUREG-1 150 addressed uncertainties throughout the risk calculations. It used a

stratified Latin Hypercube sampling (LHS) routine for efficient representation of the

uncertainties. These uncertainties existed in all the individual portions of the risk analysis-the

Level I core damage frequency estimation, the Level II accident progression and source term

evolution calculations, and the Level Ill public consequence determination.

A total of around 100 parameters (the actual number varies by the plant) were included as having

uncertain values in the analysis, and their distributions were sampled in a sample size of 200

using LHS. These parameters represent more than the containment failure pressure. They

include component failure data, in-vessel 'phenomena, and containment loading physics. For each

sample member, each parameter value is a discrete number, and for each set of such discrete

numbers (with the thousands, or tens of thousands, of other discrete numbers in the models, those

that were not varied for the uncertainty analysis), the entire risk analysis was run, including all

core damage sequences, all possible paths through the accident progression event tree (there are

millions), and, if the particular analysis required it, all source term releases and health

consequences (the latter two are not needed for this application). Hence, each of the two hundred

runs can be viewed as a separate, complete, defensible answer of the risk of the plant, including

LERF.

The approach in this study is to perform calculations with the PRA model developed in the

NUREG- 1150 study but to substitute the containment fragilities developed in the current study

for those used in the original study. These calculations are carried through the Level 2 portion of

the overall risk assessment. As discussed in detail in following sections, a model of an undegraded containment is developed for this study, and that model is then modified to reflect

22
various possible corrosion conditions. The results of each of these containment models are

analyzed using the Level 2 NIJREG-1 150 PRA models. Furthermore, as the fragility analysis

described above is performed using two different uncertainty parameters, representing the "best

estimate" and the "lower bound" cases.

Since the un-degraded models developed here might produce results not exactly equivalent to

those of the NUREG-1 150 experts, a new fragility model for the containment in its original

condition is needed so that the model can be modified directly to represent possible corrosion. If

the risk analysis results from the NUREG-1 150 were to be used for the un-degraded case and

compared to a model incorporating corrosion, it would not be clear whether the differences were

due to the effects of corrosion, or due to differences in structural models.

Because CDF, LER.F and containment failure probability conditional on core damage are the risk

metrics desired in this study, there is no need to carry forward the calculations past the Level 2

risk assessment into radioactive dose estimates. Furthermore, the issue of containment corrosion

and its effect on containment failure pressure does not impact the evolution of core damage

accident sequences at these plants. Thus, the analysis of the core damage sequences and their

frequencies was not changed in this study.

The ARRAMIS suite of computer codes was used to address the problem in the current study.

This is simply a driver code that allows one to work with a suite of PRA codes interactively on

personal computers. Except for changes noted below, the accident progression event tree

(APET), post-event processing, and Latin hypercube sampling were all the same for this analysis

as they were for NUREG- 1150. While the codes and models were readily accessible, getting

them to run properly took some effort as computer operating systems have significantly changed

since the last time the codes and models were exercised.

For example, a thorough summary of the risk analysis process can be found in Breeding et. al.

(1990) for the Surry containment. As a very brief introduction to the PRA process, specifically

concerning an APET, p. S.2 and S.4 of that document are quoted:

The accident progression analysis uses large, complex event trees to determine the

possible ways in which an accident might evolve from each PDS [plant damage stategroups of core damage sequences]. The definition of each PDS provides enough

information to define the initial conditions for the accident progression event tree (APET)

analysis. Past observations, experimental data, mechanistic code calculations, and expert

judgment were used in the development of the model for accident progression that is

embodied in the AiPET and in the selection of the branch probabilities and parameter

values used in the APET. Due to the large number of questions in the Surry APET and

the fact that many of these questions have more than two outcomes, there are far too

many paths through the APET to permit their individual consideration in subsequent

source term and consequence analysis. Therefore, the paths through the trees are grouped

into accident progression bins (APBs), where each bin is a group of paths through the

event tree that define a similar set of conditions for source term analysis.

For this application, the APET APB output was re-grouped into different bins. The primary

interest in the current study is large early containment failures. Hence, the output was re-binned

so that all APBs with the characteristic of large early containment failures would be grouped

together.

23
For both the best estimate and lower bound sets of fragility curves, the entire analysis was run for

the original (no corrosion) model and various corrosion cases. For all of these cases, the datum

representing the containment failure pressure was replaced with a failure pressure derived from

the new fragility model for each of the 200 sample members. These new failure pressures were

computed so that they would have the same failure probability as the original sample member.

That is, if the nth sample member of the 200 sample members drawn for the NIJREG-1 150

analysis called for the 63d percentlfaur pressure, the 63d percentile from the new curve was

used in the nth sample member. In this way, a new sample did not have to be drawn, which

would have necessitated re-running the entire analysis. Instead, most of the old computations

could be used without introducing spurious correlations.

2.5.4 Un-Damaged Case Analysis

For all of the analyses, the event tree question needing changing is, "What is the containment

failure pressure?" As stated above, this was changed for each analysis by taking the appropriate

percentile response from the fragility curve of the case being examined. The results then needed

to be re-binned to automate the computation of the risk measures.

Except for the change to the fragility curve, everything in the original case analysis was the same

as that for the NUREG- 1150 analysis. The only reason that a new fragility curve was computed

was so that, when it was perturbed to represent different corrosion possibilities, comparisons

between it and the perturbations would be straightforward and not potentially confused with

differences in models.

2.5.5 Corroded Case Analysis

Each corroded case was analyzed separately to determine their effects on the risk. From the

containment fragility curves generated for these situations, failure pressures were identified for

each of the percentiles needed for the sample members. For each corrosion case, these pressures

were substituted for the original pressures in the LHS input files. Then, the entire ARRAMIS

analysis was re-run to ascertain the risk from the revised input.

As mentioned above, the uncertainty in the fragility curves was treated in two different ways, the

best estimate and the lower bound. Therefore, the analysis of "original case and several sensitivity

cases" was each actually run twice, once for each uncertainty output set of fragility curves.

Because the issue of corrosion, and more broadly, the issue of containment failure pressure, does

not affect the core damage frequency for the plants examined here, there was no need to re-visit,

revise, and then re-run the Level 1 PRA results. For applications to other types ofplants, this

likely will not be the situation. Hence, for other applications, more plant analysis and analysis

changes will be necessary to examine the corrosion issue.

2.5.6 Risk Analysis Summary

In this study, the process of performing an integrated risk-informed analysis will be demonstrated

for several contairnment types. The effect of different hypothetical areas of corrosion on the risk

of operating the plant will be investigated. Corrosion is introduced into the model by thinning an

area of the steel shell or liner plate. In addition to thinning the plate, corrosion is assumed to have

reduced the strain at which tearing would occur.

Latin hypercube sampling is used to generate a series of 30 sets of input parameters for the

structural analysis models for each containment. The analyses are run for each of these 30 cases,

and the failure pressures obtained from these analyses were sorted to obtain fragility curves.

24
Fragility curves are generated for the containment in its un-degraded state, and for each case of

corrosion. These fragility curves were used as input to a risk model of the plant, and estimates of

the core damage frequency and large early release frequency are found.

25
3. Risk Analysis of PWR Plant with Reinforced Concrete

Containment

A typical pressurized water reactor (PWR) nuclear power plant was chosen as the subject for a

risk-informed investigation of liner corrosion in a reinforced concrete (RC) containment vessel.

The effects of corrosion in the liner wall was investigated near the wall-basemat juncture and at

the mid-height of the containment. Figure 3.1 shows these two corrosion locations on a

schematic diagram of the containment building, along with potential paths for leakage from the

interior to the exterior.

Liner Corrosion at Mid-Height

Figure 3. 1: Postulated Corrosion in Liner of RC Containmnent

These locations were chosen both because they are regions of potentially high liner strains and

because water could potentially accumulate at those points, accelerating corrosion. There is a 61

cm (2 ft) thick non-structural concrete slab cast on top of the containment liner at the basemat.

Water could potentially leak through the seal between the side of that slab and the wall liner,

causing corrosion. At the containment mid-height, moisture could also accumulate on the liner

where a floor abuts the wall. It should be re-emphasized that although the dimensions and other

26
properties of the containment vessel were taken from the drawings of an actual plant, the

corrosion assumed for this study is not representative of actual corrosion observed at that plant.

3.1 Structural Model of Reinforced Concrete Containment

Experimental evidence from a pressurization test of a 1:6 scale RC containment vessel with a

steel liner (Florschel, 1988) indicates that this type of containment tends to fail by leakage due to

tearing in the liner at geometric disc ontinuities. In the 1:6 scale test, the containment exhibited

essentially elastic behavior and very little leakage up to an internal pressure of around 827 KPa

(120 psi). At that point, the containment began to experience global yielding of the reinforcing,

especially in the hoop direction in the mid-height region. As the pressure was increased to a final

level of 1.0 MPa (145 psi), the strains in the reinforcement, especially. in the hoop direction at the

mid-height, increased dramatically as the reinforcing steel began to yield. The final hoop strains

at the mid-height were between 1% and 2.5%

The leakage rate remained very low through most of the test as the internal pressure increased,

but began to increase rapidly at about 965 KPa (140 psi). The test had to be terminated at 1.0

MPa (145 psi) because the leak rate was too high to allow further pressurization. After the test,

several tears were found near discontinuities in the liner thickness around penetrations. The

concrete in the regions of those tears was essentially intact, but was fractured enough to allow the

gas to penetrate it.

Based on this experimental evidence, in this study it is assumed that a linear tear results in failure

of the containment. Because the liner serves primarily as a pressure-resisting boundary, and acts

relatively independently of the RC shell, which provides the structural strength, the liner can have

a significant tear without leading to a large rupture of the containment. This agrees with the

general consensus of the panel of experts who performed the structural analyses of an RC

containment for the NUREG-1 150 study.

The procedure used in this study to analyze the RC containment is very similar to that used by

Chenry'and Smith (2000). In that study, an axisymmetric model of the containment structure was

developed to find the global strains. This model included the effects of the liner, the concrete,

and the reinforcing steel. The global strains were then used as boundary conditions for refined 2-

D models of local areas that had experienced corrosion damage. An area of the liner with a

reduced thickness modeled corrosion damage. A strain criterion was used to determine the point

when tearing occurred. Factors were introduced in the failure criterion to account for the multiaxial stress state, the level of model refinement, and the level of refinement in the analytical

model.

The approach of this study closely follows the work done by Cherry and Smith, with a few

notable exceptions:* The global axisymmetric model of the containment has essentially remained

unchanged. Local 2-D models are also used to model the corroded regions in the liner. However,

the finite element meshes of the corroded areas have been modified to more realistically model

the shape of a corroded region. In the meshes used by Cherry and Smith, the corroded regions

were rectangular in shape, which resulted in stress concentrations at the corners of those regions.

The edges of the corroded regions have been rounded, and the transition between the corroded

and non-corroded areas has been made more gradual.

The work of Cherry and Smith was primarily focused on finiding the failure pressure of degraded

containments. For the purposes of this study, it is important to not only characterize the strength

of degraded containments, but to find the difference between the containment in its original and

27
degraded conditions for the purposes of computing the change in risk. For this reason, an effort

has been made to model the un-degraded containment in more detail. In addition, we include

distinctions between leak, rupture, and catastrophic rupture, where Cherry and Smith only

considered leak in their failure estimates.

3.1.1 Axisymmetric Global Model

As mentioned previously, the global behavior of the containment is modeled with essentially the

same axisymmetric finite element model used by Chenry and Smith. The axisyrnmetric finite

element mesh of the containment is shown in Figure 3.2(a).

The concrete is modeled using the ANACAP-U (ANATECH, 1997) constitutive model, which is

linked with the ABAQUS program. Nonlinear behavior of the concrete is modeled with a stress-,

strain law evaluated at element integration points, so the effects of cracking and crushing are

"smeared out" over an element. When a tensile strain criterion, which takes multi-axial stress

states into account, is met at an integration point, a fixed smeared crack is initiated and softening

occurs. A hardening-softening model accounts for the nonlinear behavior of concrete in

compression.

Reinforcing bars are modeled by embedding them within the concrete elements with the

ABAQUS *REBAR command. A uniaxial model accounts for hardening in the reinforcing steel.

The liner is modeled with axisymmetric shell elements directly attached to the concrete elements

on the inside face of the containment. Nonlinear behavior of the steel in the shell is modeled

using a steel plasticity model. Nonlinear spring elements are used to approximate the contact

conditions between the containment and the soil below. The spring elements have a high elastic

stiffness in compression, and have no strength in tension.

The containment model is subjected to a monotonically increasing internal pressure loading. An

increasing temperature is applied to the containment in conjunction with the pressure loading.

Initially, the internal surface of the containment has a temperature of 2 10 Celsius (700 Fahrenheit).

This increases to a maximum of 1760 Celsius (3490 Fahrenheit) at a pressure of 1.38 MIPa (200

psi). Though possible during a severe accident, pressure and temperature spikes were not

included in these structural analyses. These spikes will affect the potential failures in the

containment, but they are assumed to be minimal (see International Standard Problem No. 48).

Because the analysis is performed using load control, it reaches a point where small increases in

the pressure result in very large deformations. At this point, the analysis cannot continue because

obtaining a converged solution becomes too difficult. This point is generally in the range of 1. 1

MPa (160 psi) for this model, but varies depending on the input parameters.

Figure 3.2(b) shows the deformed shape of the axisymmetric model for a typical case near the

end of the analysis. Deformations have been magnified by a factor of 10 in this figure. It is

evident from the figure that hoop strains are very large near the mid-height of the containment.

There are also large bending deformations in the basemat. From this analysis, it appears that

shearing in the wall near the junction with the basemat is not critical. However, smeared crack

models of concrete have a well-documented tendency to over-predict the capacity of structures

subjected to shear loading (Rots and Blaauwendraad, 1989). This over-prediction of shear

capacity isn't likely to be as severe in a shell as it would be in a typical structural member

because in this case, the strength in the hoop direction provides considerable resistance to

shearing at the base. Nevertheless, these results should still be treated with some caution, and

further research in this area would be helpful.

28
(a) Original Mesh (b) Deformed at 1.05 MPa (152 psi)

(magnified 1 Ox)

Figure 3.2: Axisymnimetric Finite Element Model of RC Containment

3.1.2 Local Detail and Corrosion Modeling

In the analysis of this containment, the strain magnification factors described in Section 2.4.2.1

are used to approximate strain concentrations in the liner at discontinuities, while detailed 2-D

finite element models are used to model regions of hypothetical corrosion. To determine the

relative significance of corrosion in different locations, two cases of liner corrosion are assumed:

at the mid-height of the containment, and in the wall just above the junction with the basemat.

In both cases, corrosion is assumed to0 have penetrated at two levels, 50% and 65%, of the liner

thickness. In the case of the mid-height model, corrosion was assumed to have occurred over a

region 8 cm (3 in) wide and 13 cm (5 in) high. The finite element mesh of this region is shown in

Figure 3.3. The mesh covers a 91 cm (36 in) wide square area. At the boundaries of the mesh,

the average length of an element edge is 25 mmn (1 in), while in the corroded area, the mesh is

refined considerably and the average element length is approximately 8 mmn (0.3 in).

A larger area of corrosion, also at 50% and 65% tbrough the wall thickness, is assumed near the

wall-basemat junction. Figure 3.4 shows the finite element mesh of that region. The corroded

region is 25 cm (10 in) wide and 18 cm (7 in) high. The corrosion is positioned so that the top of

the corroded coincides with the top of the non-structural floor. The shape of the area is intended

to represent what may occur if water leaks below the seal at the floor level. The same level of

mesh refinement used in the mid-height model is used in this model.

29
In both of these cases, a single layer of elements surrounding the fully corroded region is used to

make a more gradual transition from the un-damaged area to the corrosion zone. In that layer of

elements, the corrosion is assumed to penetrate 25% and 32.5% of the wall thickness for the 50%

and 65% corrosion cases, respectively. In these models, the steel is modeled using a plasticity

model. Nonlinear spring elements are used to approximate the behavior of the shear studs that

attach the liner to the concrete Wall. The stud locations are illustrated in the finite element

meshes, and are typical of details that would be seen in an actual RC containment. Many

variations of the size of the corroded area and its location relative to the studs were studied. The

ones chosen for these analyses are those that yielded the highest plastic strains. However, it was

found that the size of the corroded area and its location relative to the studs hýad a fairly minor

impact on the maximum strains.

The results from the local models are post-processed to determine the point at which tearing

(leak), rupture, and catastrophic rupture occurs. For a leak, the effective plastic strains are

multiplied by factors to account for the effects of the multiaxial stress state, corrosion, gauge

length, and modeling uncertainty, as described in Section 2.4. 1.1.

-Studs

R.-~ --

771 - - _c Crded Zone_-

~--- Tsition Zone_-

Figure 3.3: Finite Element Mesh of Corrosion at Midheight

30
--- ---------- ---------------.-------

- ~. -- ,CorrmdeZone--

- -- -- .- ~ ~ A Tns~iah onzone

Figure 3.4: Finite Element Mesh of Cýorrosion in Wall Near Basemat

3.1.3 Structural Analysis with Best Estimate Properties

The primary focus of the structural analysis in this study is to develop fragility curves to interface

with the risk model. However, it is instructive to study the results of a baseline analysis that uses

the median values of the input parameters that are randomly generated for the LHS analyses.

Six potential liner failure modes are considered: failure at the four locations of geometric

discontinuities for which magnification factors are used (see Section 2.4.2. 1), failure at a

corroded region at the wall midheight, and failure at a corroded region on the wall near the

basemat. To investigate the potential for failure (leak) at all of these locations, the global

axisymmetric model is analyzed, and results are extracted for use as displacement boundary

conditions for the two local corrosion models. The two local corrosion models are run with 50%

and 65% corrosion and post-processed to find the most critical value of ýpat every loading step

using the steel leak criterion (see Section 2.4. 1. 1). A separate post-processing tool is applied to

the results of the axisymmetric model to apply appropriate magnification factors to find -for the

four selected discontinuity locations at every loading increment. The uniaxial plastic failure

stai , fiI' was assumed to be 25% for these analyses. The gauge length factor was assumdt

be 4.0 for the local corrosion models in this baseline analysis.

Figure 3.5 shows the plot of the ratio of -pfor the 6 failure modes to .

6fail (0.25) as a function of

intemnal pressure for the baseline analysis. A horizontal line has been drawn at 1.0 to show the

failure criterion. It is evident that the failure condition is met first at the corroded area at the

midheight, and that the corroded area near the basemat appears to be the least critical location.

Of the geometric discontinuities, the steam penetration is the most critical. From this analysis, it

appears that a containment without any degradation would fail at 0.896 MIPa (129.9 psi) at the

steam penetration. If the postulated corrosion were present at the mid-height, it would fail at that

location at an internal pressure of 0.829 MIPa (120.3 psi) and 0. 812 MIPa (117.8 psi) for 50% and

65% corrosion, respectively. Leak near the corroded basemat does not occur until 0.947 MIPa

31
(137.4 psi) and 0.939 MPa (136.2 psi) for 50% and 65% corrosion, respectively. Leakage occurs

at the steam penetration prior to leak in the corroded basemat location. Table 3.1 summarizes the

leak pressures for each location.

Although Cherry and Smith (2001) assumed somewhat different corrosion patterns, it is useful to

compare their failure pressures with those obtained in this study. For their best estimate model of

the containment, they found that the un-damaged containment failed at 1.03 MPa (150 psi). With

corrosion 50% through the wall, they found that the containment failed at 0.880 MPa (127 psi)

when the corrosion was at the mid-height and 0.970 MPa (141 psi) with corrosion at the basemat.

The failure pressures for the un-damaged model and mid-height corrosion obtained in the current

study are somewhat lower than those found by Cherry and Smith. This is due to the fact that a

higher gauge length factor was used in this study. Cherry and Smith assumed corrosion to be

uniform around the entire circumference of the containment vessel at the basemat. In this study,

the corrosion at the basemat was only assumed to occur in a local area. This is a possible reason

for the higher capacity of the corroded area found in the current study.

- Leak Steam Penetration

2.0 -Leak Wall-Basemat Junction

__Leak HatchI

Leak Springline

-- Leak Base 50% Corrosion

-- Leak Base 65% Corrosion

15 _- Leak Midheight 50% Corrosion j

- Leak Midheight 65% Corrosion I i

Rupture No Corrosion

Rupture Bae5%Corso o Rupture Base 650% Corrosion

0 1.0 -- Rupture Midheight 50% Corrosion

- Rupture Midheight 65% Corrosion

cc 05D esign Pressure

I Catastrophic Rupture

0.0

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Pressure (MPa gauge)

Figure 3.5: Failure Potential at Corrosion and Discontinuity Locations

Figure 3.5 and Table 3.1 also include failure curves and pressures for five rupture cases: the

original containment with no corrosion, 50% corrosion at the basemat, 65% corrosion at the

basemat, 50% corrosion at the midheight, and 65% corrosion at the midheight. The procedure in

Section 2.4.2.2 is used to compute the ratio of the total rupture area, Aotai ý to the rupture area

limit of 0.028 m2 (0.3 ft2), as a function of pressure. The four features, steam penetration, wallbasemnat junction, hatch, and springline, are each assumed to contain four cracks ( ni) each after

the leak criterion has been reached. The choice of four cracks at each location is based on the

upper limit of the number of tears observed in the 1:6 scale reinforced concrete containment

testing at Sandia National Laboratories (Horschel, 1992). The number of cracks at each location

could have been introduced as a random variable, but due to the severely approximate nature of

the rupture estimate employed here, a random variable with a large uncertainty is imposed on the

32
total rupture area. One crack is assumed at the basemat and midheight locations for cases

considering corrosion.

For the two basemat corroded case, leak does initiate prior to the overall rupture failure. This has

only a negligible effect on the total rupture area, since only one crack is assumed to initiate at the

corroded location. Therefore, the rupture curves for the original case with no corrosion and the

two basemat corrosion cases share the same curve. A small increase in the rupture area is caused

by corrosion at the midheight. Since the global strains do not differ between the 50% and 65%

corrosion cases, the rupture curves are the nearly identical. Obviously, assuming more than one

corroded location for each case will increase the rupture area and lower the rupture pressure.

This is especially true or corrosion at. the midheight, where leak initiates at the corroded location

well before initiation at the steam penetration. The effect of multiple basemat corroded locations

will be minimal since leak at the corroded basemat initiates just prior to the current rupture

thresholds. Variation in the total area assumed to cause rupture (0.028 mn

2 or 0.3 ft 2) will also

affect the rupture pressure. As mentioned previously, a large uncertainty is imposed on the total

rupture area to account for the approximate nature of the rupture criterion. Finally, Figure 3.5

and Table 3.1 include the simple estimate for catastrophic rupture described in Section 2.4.2.3.

Table 3. 1: Summary of Locations and Failure Pressures

Location Failure Pressure

MPa (psig)

Leak Steam Penetration 0.896

(129.9)

Leak Wall-Basemat Junction 0.988

(143.3)

Leak Hatch 0.935

(135.6)

Leak Springline 0.992

_____________________________(143.9)

Leak Base 50% Corrosion 0.947

(137.4)

Leak Base 65% Corrosion 0.939

(136.2)

Leak Midheight 50%l Corrosion 0.829

(120.3)

Leak Midheight 65% Corrosion 0.8 12

(117.8)

Rupture No Corrosion 0.983

(142.6)

Rupture Base 50% Corrosion 0.983

(142.6)

Rupture Base 65% Corrosion 0.983

(142.6)

Rupture Midheight 50% Corrosion 0.976

(141.6)

Rupture Midheight 65% Corrosion 0.976

(141.6)

Catastrophic Rupture 1.195

(173.3)

33
3.2 Fragility Analysis of Degraded Containment

The principal goal of the current study is to integrate structural analyses of degraded

containments with risk analysis models to understand the significance of the degradation from a

risk-informed perspective. Fragility curves of containments under pressurization with and

without degradation serve as the interface between the structural and risk analyses. As explained

in Section 2.5, Latin Flypercube Sampling is used in this study to generate sets of random

variables to be used as input to the structural finite element analyses. In the current work, 19

input parameters were selected as random variables, and 30 samples of those parameters were

taken for analysis.

Of the 19 input parameters, 14 describe the inherent randomness, or aleatory uncertainty, in the

basic properties of concrete, reinforcing bars, and liner steel. The remaining 5 parameters

describe epistemic uncertainty, or uncertainty in the ability to characterize the failure pressure.

Several of the random input parameters are correlated with others. For concrete-, the tensile

strength, f', and modulus of elasticity, E,,, are correlated with the cylinder compressive

strength, f',. Likewise, there is correlation between the yield strength and ultimate strength of

steel.

Whenever possible, statistical test data was used as the basis for the probability distributions in

this study. When such data was unavailable, engineering judgment was used to provide

reasonable estimates of uncertainty. A thorough statistical analysis of concrete strength was

performed by Mirza et. al. (1979). Based on recommendations from that analysis, the elastic

modulus of concrete is computed as:

E = c, 60400 rP (3.3)

where c, is a random variable with a median of 1.0 and a coefficient of variation of 0.077.

Likewise, f', is computed as:

ff = C28. (3.4)

where c2 has a median of 1.0 and a coefficient of variation of 0. 196. Units of psi are used in

both of these equations. Under average control conditions, Mirza et al. suggest that a coefficient

of variation (COy) of 0.15 can be assumed for f'c

The RC containmnent investigated in this study has reinforcing bars of both Grade 40 and Grade

50 steel. Unfortunately, less information was available on the correlation between yield strength

and ultimate strength, and between the elastic modulus and strength for steel. The elastic

modulus, E, is assumed to be independent of the yield strength, I,,and the ultimate strength,

f.Correlation 1 is induced between I,, and f, in a manner similar to that for concrete:

where s is a random variable with a median of 1.0. The variable r is the ratio of the yield stress

to the ultimate stress, and differs depending on the type of steel. For Grade 40 reinforcement, a

value of 0.6 was assumed for r. For Grade 50 reinforcing, this value was set at 0.62, and for the

liner steel, a value of 0.535 was used.

Five separate variables are used to describe the epistemic uncertainty. Variable describes the

uncertainty inherent in predicting the global strains, the local strains from the 2-1) submodels with

34
corrosion, the strain magnification in the presence of corrosion, the calculation of the rupture

area, and the simple estimate for catastrophic rupture.

Each of these variables has a median value of 1.0. A COV of 0.3 was assumed for the global

strain prediction variable, JFEM-u, . This agrees well with the scatter in the analytical predictions

submitted by several analysts for the behavior of the 1:6 scale RC containment test conducted at

Sandia National Laboratories (Clauss, 1987). The magnification factors for the liner

discontinuities are simply multiplied by this uncertainty factor in Equation 2.9.

The COV of the local model uncertainty factor, fFEM-U' was set to 0.35 because it was felt that

there is more uncertainty in the local models than in the global models. For the local detailed

models, Equation 2.1 is used to compute the magnified strains. Since the local models contain

corrosion, the corrosion factor, f, equals 2 and is multiplied by an uncertainty factor, f,-, with

a COV of 0.20.

The final two epistemic factors account for the uncertainty in the rupture area, f.,- and

catastrophic rupture pressure, fC 0 A.'I Since the calculation of the rupture area in Equation 2.12

contains several approximations, a large COV is employed, equal to 0.40. The simple method

used here to compute the catastrophic rupture pressure (Equation 2.13) should provide a

reasonable estimate, enabling the use of a low COV of 0. 10. This uncertainty is in addition to the

variation in the ultimate strengths random variables used in Equation 2.13.

Table 3.2 shows all of the random input parameters. This table shows the median values of the

parameters, a measure of the variation assumed for the parameter, and the type of distribution.

For variables with normal distributions, the CCV is used as the measure of variation, while 8i is

used for variables represented with a lognormal distribution.

A total of 30 sets of these input parameters were generated based on analyses using the specified

distribution functions. Once the analyses were run, the 30 leak pressures were used to develop

fragility curves for each of the four locations of linear discontinuity. Figure 3.6 shows the

fragility curves based on the sorted analyses values and associated lognormal curve fits. The

fragility curves represent the leak pressure for the four discontinuity locations. Figure 3.7 shows

the fragility curves for leak at the two corroded locations, basemat and midheight, at the two

levels of corrosion, 50% and 65%. These plots indicate that increasing the level of corrosion

from 50% to 65% of the liner thickness has only a minimal effect. Due to the shape of the

distributions, the lognormal curve fits for each of the corroded cases requires one curve fit for

high probabilities and one curve fit for low probabilities.

35
Table 3.2: Random Input Parameters

Property Median COy!6 Distribution

Concrete_______

Compressive Strength (f )27.3 MPa T0.15 Lognormal

_________________________________(3.956 ksi) _____ ______

Elastic Modulus factor (c,) 1.0 0.077 Normal

Tensile Strength factor (c 2 ) 1.0 0.196 Normal

Grade 40 Reinforcing Steel___________ ______

Ultimate Strength (f)508.3 MIPa -- 0.09 Lognormal

________________________________(73.72 ksi) _____ ______

Yield Strength Factor (s1 ) 1.0 0.07 Normal

Elastic Modulus (E,) 200 Gpa 0.06 Normal

______________________________ -(29000 ksi) _____ ______

Grade 50 Reinforcing Steel___________ ______

Ultimate Strength f)590.5 MIPa 0.09 Lognormal

(85.65 ksi) ___________

Yield Strength Factor (s,) 1.0 0.07 Normal

Elastic Modulus (E,) 200 Gpa 0.06 Normal

________________________________(29000 ksi) ___________

Liner Steel

Ultimate Strength f)577.1 MPa 0.09 Lognormal

________________________________(83.70 ksi) ______

Yield Strength Factor (s1) 1.0 0.07 Normal

Elastic Modulus (E,) 200 GPa 0.06 Normal

(29000 ksi)

Uniaxial Failure Strain (fjau) 0.25 0.12 Normal

Corrosion Depth Uncertainty 1.0 0.10 Normal

Epistemic Uncertainty

Axisymmetric Model Strain Factor 1.0 0.30 Lognormal

Uncertainty (JFEM, )

Submodel Model Strain Factor Uncertainty 1.0 0.35 Lognormal

( fFEM -,,)

Corrosion Factor Uncertainty ( f,, 1.0 0.20 Lognormal

Leak Area for Rupture Uncertainty 1.0 0.40 Lognormal

Catastrophic Rupture Uncertainty 1.0 0.10 Lognormal

36
1.0

0.8

LL' 0.6

S0.4

0.2

0.0-

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Pressure (MPa gauge)

1.4 1.6 1.8 2.0

Figure 3.6: Fragility Curves for Leak at Discontinuity Locations

1.0

0.8

u0.6

.0

0.2

0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Pressure (MPa gauge)

1.4 1.6 1.8 2.0

Figure 3.7: Fragility Curves for Leak at Corroded Locations

As discussed previously, the rupture threshold is assumed to be reached when the total crack

opening caused by initiated leaks, exceeds 0.028 M2 (0.3 fl2) . Figure 3.8 shows the rupture

fragility curves for the five cases examined in this study. Since no significant change in pressure

occurs for the corroded basemat cases, the curves for these cases remain identical. The crack

opening near the midheight corroded locations are large enough to cause a slight decrease in

rupture pressure. Since the global strains are employed to estimate the rupture pressure, the 50%

and 65% corroded cases are the same. Figure 3.8 also illustrates the fragility curve for

catastrophic rupture. Since the criteria for catastrophic rupture is not affected my the corrosion in

the liner, the catastrophic rupture fragility remains the same for all five cases.

37
1.0

0.8 F

" Rupture - No Corrosion

" Rupture - Base 50% Corn

* Rupture - Base 65% Corn

* Rupture - Midheight 50%

* Rupture - Midheight 65%

* Catastrophic Rupture

2

.2 0.6 ICO 0.4 .0

0.2

0.0

~sion

)siofl4

Corrosion

Croio

Design Pressure

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Pressure (MPa gauge)

1.4 1.6 1.8 2.0

Figure 3.8: Fragility Curves for Rupture and Catastrophic Rupture

The leak fragilites for the four discontinuity locations were used to develop a cumulative

probability of failure curve for the original, non-corroded, containment. The fragility curve for

the same containment, compiled from several experts' analyses for the NUREG-1 150 study, is

also shown in Figure 3.9 for comparison. The correspondence between these two curves is fairly

close. The median values of the two curves are fairly close, but the variance from the current

work is somewhat lower.

1.0

.2 0.8

.0

2

~,0.4

E 0.2

0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Pressure (MPa gauge)

1.4 1.6 1.8 2.0

Figure 3.9: Comparison of the Undamaged Containment Fragilities from the Current

Study and NUREG-l 150

38
Figure 3. 10 shows the cumulative probability of failure (leak) curves obtained in the current study

for the containment with corrosion degradation at the midheight and at the base, along with the

fragility of the containment in its original condition. As would be expected from the baseline

analysis, the drop in capacity due to corrosion at the mid-height is much greater than that due to

corrosion at the basemat.

1.0

F2S0.8

Design Pressure

P0.6

Original - No Corrosion

2 - Base 50% Corrosion CL

W 0.4-Base 65% Corrosion

15_ -Midheight 50% Corrosion

E~- Midheight 65% Corrosion

0.2 _ _ _ _ _ _

0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Pressure (MPa gauge)

1.4 1.6 1.8 2.0

Figure 3.10: Cumulative Probability of Failure Curves for Original and Degraded RC

Containment

The conditional probability of failure curves were computed for each of the five cases and shown

in Figure 3.11 Figure 3.15. Since the rupture and catastrophic curves are relatively constant

throughout the five cases, the conditional probability distributions are extremely similar. At low

pressures (P < 0.65 MIPa), the probability of leak is equal to 1 with the rupture and catastrophic

rupture probabilities at 0. Increases in pressure cause the rupture and eventually the catastrophic

rupture conditional probabilities to increase. The leak probability decreases quickly as the

rupture probabilities increase. The rupture curve peaks at approximately 1. 1 M~a. At this point,

both the leak and rupture curves decrease gradually to probabilities of 0 and the catastrophic

curve increase to a probability of 1 at approximately 1.7 MPa.

39
1.0

S0.8

P0.6

2

0~

5 0.4

0

0.0 L..

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Figure 3.11: Conditional Probability of Failure for Original Containment (No Corrosion)

1.0

0.8

A! 0.6

0-0.4

S0.2

0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Pressure (MPa gauge)

Figure 3.12: Conditional Probability of Failure for 50% Corrosion at Basemat

2.0

40
1.0

20.8 -Rupture

-Catastrophic Rupture

P0.6

2

0. Design Pressure 0

6 0.2

0.0 L.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Pressure (MPa gauge)

Figure 3.13: Conditional Probability of Failure for 65% Corrosion at Basemnat

1.0J

-Leak

~ 0.8Rupture - Catastrophic Ruptjure

P06

0.6

2

CL0.4 Design Pressure

0

S0.2

0.0 ---

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Pressure (MPa gauge)

Figure 3.14: Conditional Probability of Failure for 50% Corrosion at Midheight

2.0

2.0

41
1.0

20.8 Rupture

W- Catastrophic Rupture 0L

p0.6

2

0~

0.2

0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Figure 3.15: Conditional Probability of Failure for 65% Corrosion at Midheight

3.3 Risk Analysis Results

Table 3.3 shows the CDF values from NUREG 1150. Because the containment response does not

affect the CDF for this plant, the results are the same for all of the cases studied.

Table 3.3: Core Damage Frequency (y(-1)

K as-e IMean 15% 150% 1195%

IAll I4.1E-5 I6.8E-6 I2.3E-5 I1.3E-4.

Table 3.4 shows the LERF results, and Table 3.5 shows the probability of large early containment

failure conditional on core damage. LERF is the product of the CDF and the probability of large

early containment failure conditional on core damage.

Table 3.4: Large Early Release Frequency (yr')

Case Mean 5% 50% 95%

Un-damaged (Reference) 1.1OE-7 0 3.61E-10 1.54E-6

Un-damaged (Current Study) l.OIE-7 0 3.16E-10 1. 12E-6

50% Corrosion near basemat L.OIE-7 0 3.16E- 10 1. 12E-6

50% Corrosion at midheight 1.OlE-7 ,0 3.16E- 10 1. 12E-6

65% Corrosion near basemnat L.01E-7 0+O 3.16E- 10 1. 12E-6

65% Corrosion at midheight LI OE-7 0 3.16E-10 1. 12E-6

42
Table 3.5: Probability of Large Early Containment Failure Conditional on Core Damage

Case Mean 5% 50% 95%

Un-damaged (Reference) 0.0027 0 1.57E-5 0.019

Un-damaged (Current Study) 0.0025 0 1.38E-5 0.0086

50% Corrosion near basemnat 0.0025 0 1 .38E-5 0.0086

50% Corrosion at midheight 0.0025 0 1.38E-5 0.06

65% Corrosion near basemat 0.0025 0 1 .38E-5 0.0086

65% Corrosion at midheight 0.0025 0 1.38E-5 0.0086

Table 3.6: Change in the Large Early Release Frequency (yr-) due to Degradation

Case Mean 5% 50% 95%___

50% Corrosion near basemat 0 0 0 0_____

50% Corrosion at midheight 0 0 0 0_____

65% Corrosion near basemat 0 0 00

65% Corrosion at midheight 0 0 0 0____

The key risk criteria for acceptance of a proposed plant change in Regulatory Guide 1. 174

(USNRC, 200 1) are the baseline values of CDF and LERF, and the changes in those values due to

the proposed modification, denoted as ACDF and ALERF. The acceptance criteria must be met

for both the pairs of ACDF and CDF and of ALERF and LERF. Because CDF is unaffected by

the containment properties in this particular plant, ACDF is 0, so the effects of the change clearly

fall within Region III for the CDF acceptance criteria, which can be seen in Figure 2.1 . In Region

III, it is not actually necessary to compute the baseline CDF, although for these analyses, the

mean CDF -was computed, and has a value of 4.l1E-5, which is clearly acceptable.

For both the lower bound and best estimate fragility curves, there is no change in LERF relative

to the un-damaged containment in the case where corrosion exists near the basemat or the

midheight. Because LERF is unaffected by the increases in leak introduced by the liner corrosion

in this particular plant, ALEFF is 0 (Table 3.6), so the effects of the change clearly fall within

Region III for the LERF acceptance criteria, which can be seen in Figure 2.2. Therefore, the

corrosion cases investigated in this study would be permissible modifications from a risk

standpoint by Regulatory Guide 1. 174, there are other criteria for acceptance that also must be

met. A change proposed under that risk-informned methodology must also satisfy other design

goals. It must still maintain defense in depth and acceptable safety margins.

The results presented above can potentially be somewhat misleading. One would intuitively

expect that at least a small increase in the risk measure would be observed in the cases with

containment degradation. This lack of increase in the risk measures presented in

Table 3.4 and Table 3.5 can be traced to the definition of LER.F used in the process of binning the

risk analysis results. LERF-is, by definition, the frequency of large, early containment failures

resulting fr~om accidents stemming from a certain set of initiating events. The question of

whether the failure is large is determined by the mode of failure, which is computed based on the

combination of the overall fragility curve and the conditional probabilities of leak, rupture, and

catastrophic rupture. Failure occurrences are grouped into LERF only if the containmnent fails in

a rupture or catastrophic rupture mode.

43
Because the types of degradation considered here only affect the containment liner, and not the

main load-bearing structural system, they only contribute to leakage failures. The increase in

probability of rupture failure due to such corrosion is very minor. To gain a more complete

perspective on the risk associated with these types of degradation, it is instructive to introduce an

additional risk metric: the small early release frequency (SERF). This is the frequency of small,

early containment failures that stem from the same set of initiating events used in computing

LERF. The values computed for SERF for the various degradation cases are shown in Table 3.7

for comparison. The probability of small early containment failure conditional of core damage is

also shown in Table 3.8. This quantity is analogous to the probability of large early containment

failure conditional on core damage reported previously, except that it accounts for only the cases

in which the containment fails by leaking. The change in SERF is shown in Table 3.9.

Table 3.7: Small Early Release Frequency (yx§ 1)

Case Mean 5% 50% 95%

Un-damaged (Reference) 4.65E-8 2.89E-10 1.36E-9 1.27E-8

Un-damaged (Current Study) 4.45E-8 2.89E-10 1.37E-9 2.23E-8

50% Corrosion near basemat 4.70E-8 2.89E-10 1.37E-9 2.23E-8

50% Corrosion at midheight 1. 15E-7 2.89E-10 1.37E-9 4.94E-7

65% Corrosion near basemat 4.70E-8 2.89E-10 1.37E-9 2.23E65% Corrosion at midheight 1 .46E-7 2.89E-10 1 .37E-9 32ETable 3.8: Probability of Small Early Containment Failure Conditional on Core Damage

Case Mean 5% 50% 95%

Un-damaged (Reference) 0.00113 4.24E-5 5.9 1E-5 9.74E-5

Un-damaged (Current Study) 0.00108 4.24E-5 5.96E-5 1.71E-4

50% Corrosion near basemnat 0.00115 4.24E-5 5.96E-5 1.71E-4

50% Corrosion at midheight 0.00280 4.24E-5 6.OOE-5 3.80E-3

65% Corrosion near basemat 0.00115 4.24E-5 5.96E-5 1.7 1E-4

65% Corrosion at midheight 0.00357 4.24E-5 6.01E-5 2.49E-2

Table 3.9: Change in the Small Early Release Frequency (yr-) due to Degradation

Case Mean 5% 50% 95%

50% Corrosion near basemnat 2.58E-9 0 0 0

50% Corrosion at midheight 7.03E-8 0 0 4.72E-7

65% Corrosion near basemnat 2.58E-9 0 0 0

65% Corrosion at midheight 1.02E-7 ,0 0O 3.21E-6

It is also instructive to evaluate another metric, designated here as the total early release

frequencies (TERF). This is simply the summation of LERF and SERF. TERF, the total

probability of early containment failure conditional on core damage, and the change in the total

early release frequencies are shown in Table 3. 10 through Table 3.12.

44
Table 3. 10: Total Early Release Frequency (yr-')

Case Mean 5% 50% 95%

Un-damaged (Reference) 1.56E-7 2.89E-10 1.72E-9 1.56E-6

Un-damaged (Current Study) 1.45E-7 2.89E-10 1.69E-9 1.1S5E-6

50% Corrosion near basemat 1.48E-7 2.89E-10 1.69E-9 1.15E-6

50% Corrosion at midheight 2.16E-7 2.89E-10 1.70E-9 1.62E-6

65% Corrosion near basemat I1.48E-7 2ý.89E-10 1.69E-9 1. 15E-6

65% Corrosion at midheight I2.47E-7 2.89E-10 1.70E-9 4.36E-6

Table 3.11: Probability of Total Early Containment Failure Conditional on Core Damage

Case Mean 5% 50% 95%

Un-damaged (Reference) 0.00381 4.24E-5 7.49E-5 0.0120

Un-damaged (Current Study) 0.00354 4.24E-5 7.33E-5 0.0088

50% Corrosion near basemat 0.00360 4.24E-5 7.33E-5 0.0088

50% Corrosion at midheight 0.00526 4.24E-5 7.38E-5 0.0124

65% Corrosion near basemat 0.00360 4.24E-5 7.33E-5 0.0088

65% Corrosion at midheight 0.00603 4.24E-5 7.39E-5 0.0335

Table 3.12: Change in the Total Early Release Frequency (yi§1) due to Degradation

Case Mean 5% 50% 95%

50% Corrosion near basemat {2.5 8E-9 0 0 0

50% Corrosion at mildheight 7.03E-8 0 0____ 4.72E-7

65% Corrosion near basemat 2.5 8E-9 0 0 0

65% Corrosion at midheight {1.02E-7 0 0 3.2 1E-6

When these additional risk metrics are evaluated, the effect of the degradation on the risk

becomes much clearer. In all of these cases, the risk measured in terms of SERF or TERF

increases as a result of liner corrosion. Because the liner corrosion only increases the risk of

small releases, ASERF and ATERE are equal. The risk of both small and large early releases is

still quite small, and the risk criteria of Regulatory Guide 1. 174 would be easily satisfied, even if

TERF and ATERF were used in place of LERF and ALERE.

The example plants examined here serve as good case studies indicating that one should be very

cautious about simply applying the ALERF criterion to evaluate the significance of containment

degradation. It is important to closely examine how degradation can increase the likelihood of

one failure mode while decreasing the likelihood of another, and evaluate the consequences of

these different modes. It cannot be stressed enough that the cases of degradation examined here

are extremely limited in scope. There are currently no means of predicting degradation prior to

its discovery. Since the location and specific nature of any degradation could dramatically affect

the containment capacity and risk, a detailed analysis of that scenario would be required. There

are also a number of assumptions that would require additional consideration when performing a

site specific analysis. The specific results reported in this study should in no way be applied to

making regulatory decisions on existing plants.

45
4. Risk Analysis of BWR Plant with Mark I Steel Containment

To investigate the effects of corrosion in a steel containment vessel, a typical boiling water

reactor (BWR) Ii~ant with a Mark I steel containment was chosen for study. Figure 4.1 shows a

schematic diagram of the containment at this plant, with the areas where the effects of corrosion

are investigated in this study. As was done for the RC containment, corrosion is assumed to

occur in areas where moisture is likely to collect, and where the presence of corrosion is likely to

weaken the containment. This is the same containment studied by Cherry and Smith (2000), and

the locations for postulated corrosion in the steel shell coincide with those assumed in that study.

Corrosion is assumed to occur at the knuckle between the spherical and cylindrical portions of the

drywell, which has the shape of an inverted light bulb. Corrosion is also considered in the region

of the sand pocket at the concrete floor inside the drywell, and in the wetwell at the waterline. In

addition, corrosion in one of the large bellows in the vent lines that connect the drywell and

wetwell is also considered. The effect of bellows corrosion was not considered by Cherry and

Smith.

Corrosion at

Drywell Knuckle

Corrosion at

Sand Pocket

-Corrosion at

Wetwell Waterline

Vent Line Bellows

Corrosion

Figure 4. 1: Postulated Corrosion in Liner of Steel Mark I Containment

4.1 Structural Model of Steel Mark I Containment

A combination of several different finite element models was used to model the steel Mark I

containment in its original state and with the presence of corrosion in the locations mentioned

previously. To model the global behavior of the containment, 3D models of a 22.5 degree slice of

the containment were created using shell elements. Four such models were created and analyzed

in this study. The first one contained the basic features of the containment. The second model of

46
the whole containment was used to model the effects of some of the larger penetrations, including

the equipment hatch and a wetwell access hatch. The third and fourth models of the whole

containment included the effects of corrosion. In addition to the global models of the

containment, a series of 3D models of the local regions around representative penetrations was

also created. In these models, the steel is modeled by continuum elements, rather than by shell

elements, as is the case in the coarser, global models.

The models of the steel Mark I containment use the same baseline material properties and

temperature/pressure relationship used by Cherry and Smith. The material properties are varied

in the parametric analyses that use the parameters generated by LHS.

4.1.1 Global Baseline Containment Model

As mentioned above, all of the global models of the containment model a 22.5 degree slice using

shell elements. The drywell, wetwell, and vent line are all included in a single model, as shown

in Figure 4.2. As can be seen in the detailed view of the vent line shown in Figure 4.3, the

bellows convolutions are explicitly modeled. This model differs somewhat from the model used

by Cherry and Smith for this containment. In that model, the drywell and wetwell were modeled

separately, and the forces transmitted through the vent line were estimated and applied as

boundary conditions to the two models. Because of increased computational power available at

the time of the current work, it seemed more practical to explicitly model the coupling between

the drywell and wetwell in a single model. This helped simplify the process of analyzing the

effects of corrosion in the vent line bellows.

The baseline model of the containment incorporates relatively few local features. The flanges in

the region of the head gasket, as well as the vent line details and the ring stiffeners in the region

of the wetwell supports. Any details such as penetrations that are not repetitive in nature are not

included. The thickness of the shell varies throughout the containment, and these changes are

incorporated into the model.

Along the edges of the slice, the containment model uses boundary conditions appropriate for the

symmetry assumptions made. The base of the drywell, which lies below the concrete floor, is not

included in the model. The drywell model begins at the edge of the concrete floor, which is in

roughly the same location as the sand pocket. The nodes along this bottom edge of the model are

fixed against displacement. As was the case in the analyses of Cherry and Smith, contact

between the drywell shell and the concrete shield building, which are separated by a 5.1 cm (2 in)

wide air gap, is neglected. This is a conservative assumption, because the shield building limits

further deformation of the steel shell once contact occurs.

47
A'

Figure 4.2: Finite Element Mesh of Drywell, Vent Line, and Wetwell

Figure 4.3: Detailed View of Mesh in Vent Line Region

48
4.1.2 Containment Penetration Models

Figure 4.4 shows the approximate locations of the local details modeled in this study. These

details include relatively large features, such as the equipment hatch and wetwell access hatch, as

well as smaller pipe penetrations. In addition to these, the vent line bellows are modeled with a

reasonable level of detail in all of the global models. Finally, the behavior of the drywell head

gasket is modeled using a separate computer program. While the details selected here are not allinclusive, it is believed that they provide a representative sample of the details present in all parts

of the containment. The models used to analyze these local details are described below.

Figure 4.4: Approximate Locations of Local.Details Analyzed in Steel Mark I

Containment

4.1.2.1 Global Model with Large Penetrations

The basic global model of the containment that was shown in Figure 4.2 was modified to include

two large features: an equipment hatch and a wetwell access hatch. These were not included in

the basic model because they are large enough that they could have a significant effect on the

response in the areas surrounding them, and would have unduly complicated the basic model.

Because of the large size of these penetrations, it is not reasonable to simply transfer boundary

conditions from the basic model to submodels of these features. Figure 4.5 shows a view of the

entire mesh of the model with these large penetrations.

49
..

Figure 4.5: Finite Element Mesh of Containment with Large Penetrations

Figure 4.6 shows a detailed view of the region around the equipment hatch, and Figure 4.7 shows

a similar detailed view of t he wetwell access hatch. The shaded regions in these figures represent

areas where the plate is thickened around the penetrations. Like the base model, the penetration

regions are modeled entirely with shell elements.

In the case of the equipment hatch, the thickened plate around the hatch is 4.45 cm (1.75 in) thick,

while the surrounding containment shell makes a transition from 1.91 cm (0.75 in) thick in the

upper area to 3.18 cm (1.25 in) thick in the lower area around the equipment hatch. While the

lower part of the stiffening plate is curved to ease the transition to the rest of the shell, there are

fairly sharp corners on the upper portion. This causes a stress concentration, and the mesh is

refined to a relatively high degree in that region to capture that. The stiffening plate around the

w .etwell access hatch is 4.45 cm (1.75 in) thick, while the wetwell shell surrounding that area is

2.86 cm (1. 125 in) thick.

50
Figure 4.6: Mesh Detail of Equipment Hatch Area

Figure 4.7: Mesh Detail of Wetwell Access Hatch Area

4.1.2.2 Detailed Models of Smaller Penetrations

The rest of the penetrations selected for study were modeled with detailed 3D finite element

models. These models, which use 3D continuum elements, represent the pipe, the stiffener

surrounding the penetration, the transition to the surrounding containment shell, and a section of

the surrounding containment large enough to reasonably contain the local effects. These models

are either half-symmetry or quarter-symmetry, depending on the geometric details. Strains were

taken from the global model at points corresponding to the locations of the penetrations, and used

to compute appropriate displacement boundary conditions. Temperatures were also applied to

coincide with those applied to the global model.

51
Figure 4.8 shows the mesh used to analyze the region around a steam line penetration, the

approximate location of which is shown in Figure 4.4, as are all of the penetrations studied here.

In this location, two identical pipes 1.66 mn (65.4 in) apart at their centers penetrate the drywell

shell side by side. The pipes are 3.81 cm (1.5 in) thick, and do not penetrate the containment

normal to the shell. The penetration angle is approximately 11I degrees from the vertical and 20

degrees from the horizontal. The finite element model uses half symmetry to include only one of

the pipes. While the orientations of the pipes are such that the penetrations are not exactly

symmetric, this simplification does not affect the results significantly. The thickened area around

the two pipes is 4.45 cm (1.75 in) thick, and the surrounding drywell shell is 1.91 cm (0.75 in)

thick. The transition from the thickened plate to the surrounding plate is made on a 1:4 slope on

either side. This is true of all of the penetrations modeled here. The thickened plate is 1. 17 mn (46

in) high by 2.83 mn (111.4 in) wide, measured from points before the transition begins to the

thinner material.

H. H1 1i!H11 111

. .1 . . . . . . $ .

Figure 4.8: Steam Line Penetration Submodel

The next penetration studied, a floor drain line penetration, is similar to the steam line penetration

in that there is again a pair of pipes penetrating the drywell shell side by side. These pipes

penetrate the drywell at a point lower than the steam lines, where the drywell shell is 3.18 cm

(1.25 in) thick. The pipes are much smaller than the steam lines, with outside diameters of 8.89

cm (3.5 in) and wall thicknesses of 0.76 cm (0.3 in). The thickening plate is 33.0 cm (13 in) high

and 94.0 cm (3 7 in) wide, and the pipes are spaced 6 1.0 cm (24 in) apart from center to center.

The pipes are horizontal, but because of the angle of the containment at that point, they penetrate

at about 29 degrees from normal. Similarly to the steam line penetration, half symmetry was

assumed to reduce the model size. Figure 4.9 shows the mesh used to model this penetration.

52
Figure 4.9: Floor Drain Penetration Submodel

The third drywell penetration chosen for study by a detailed finite element model is a

containment spray line penetration located just below the transition from a cylinder to a sphere.

This penetration is of particular interest because initial analyses indicated that under pressure

loads, this area experiences higher strain than other areas in the shell. The shell in this region is

1.91 cm (0.75 in) thick, and the thickened plate is 4.45 cm (1.75 in) thick. In this case, a single

pipe with outside diameter of 35.6 cm (14.0 in) and thickness of 1.91 cm (0.75 in) penetrates the

containment, at an angle of 34 degrees from normal. The stiffener plate is 68.6 cm (27 in) in

diameter. Figure 4. 10 shows the half symmetry mesh generated for this penetration.

Figure 4. 10: Containment Spray Line Penetration Submodel

To model a representative sampling of details located throughout the containment, two local

models of penetrations in the wetwell were also developed. One of these, a wetwell

instrumentation line penetration, is located'in the lower portion of the wetwell, and the other, a

53
high pressure coolant injection (HPCI) test line penetration, is located in the upper portion. In

both cases, a single pipe surrounded by a circular thickening plate is oriented normal to the

wetwell shell, making it possible to use quarter symmetry models. Figure 4.11 and Figure 4.12

show the models of these two penetrations.

Figure 4.11: Wetwell Instrumentation Line Penetration Submodel

Figure 4.12: Wetwell HPCI Test Line Penetration Submodel

The wetwell instrumentation line has an outside diameter of 6.03 cm (2.38 in) and a wall

thickness of 0.55 cm (0.22 in). The thickened plate around the penetration is 3.18 cm (1.25 in)

thick and 19.6 cm (7.7 in) in diameter, and the wetwell shell surrounding the penetration is 1.71

cm (0.675 in) thick.

54
The HPCI test line has an outside diameter of 27.31 cm (10.75 in), and the pipe wall is 1.51 cm

(0.59 in) thick. The circular thickened plate around this penetration is 3.81 cm (1.5 in) thick and

has a diameter of 109.6 cm (43.2 in). The wetwell shell surrounding this penetration is 1.53 cm

(0.604 in) thick.

4.1.3 Analysis of Drywell Head Gasket

In addition to considering tearing and rupture at local details, it is also important to consider the

possibility of leakage of seals. The drywell head gasket was analyzed for leakage in this study

because it is an important potential location for early leakage, and the drywell head is one of the

leakage locations specifically considered in the risk analysis of this plant.

Rather than use a detailed analytical model, the approach used here is to perform a basic

engineering calculation of the leakage area that results from opening of the head gasket due to

internal pressurization. In the process of obtaining expert judgment of the failure pressures for

this containment in the NUREG-1 150 study, expert C used a relatively simple FORTRAN

program to obtain probability distributions of the leakage and rupture pressures for the drywell

head gasket. The source code for this program appears in page 5.3-3 8 of NUREG/CR-455 1 Vol.

2, Rev. 1, Part 3 (Breeding et al., 1992). This code accounts for the amount of preload in the

drywell head bolts, the deformation of the head bolts and drywell shell in that region, the

temperature difference between the head bolts and the drywell shell, and the ability of the head

gasket to spring back to fill an opening.

The code was modified slightly to input and output the computed data in a different format, but

the intent was to leave the core parts associated with the leak area computation unchanged

because the underlying principles seemed reasonable. In the process of adapting this code,

however, two critical errors were discovered in the original code. In a part of the code that

interpolates over a table of temperature-dependent material properties, the interpolation is not

done properly. Also, in computing the leak area, the preload force for just one bolt is considered,

when that force should have been multiplied by the number of bolts. These two errors actually

tended to cancel each other out, resulting in fairly plausible results. The code used in the current

work corrects both of these errors.

The end result of running the head gasket code is an opening area vs. pressure curve. When the

opening reaches a size of 64.5 cm2 (10 in 2), it is considered a "leak", and when it reaches a size of

1672 cm2 (259 in 2), it is considered a "rupture".

4.1.4 Corroded Region Models

In the current work, corrosion is postulated in two locations in the drywell and one location in the

wetwell. The locations and sizes of these corroded zones are similar to those assumed by Cherry

and Smith. In addition to those regions, the current work also considers corrosion in one of the

plies of the vent line bellows. The corroded areas are modeled using modified versions of the

global shell model of the entire containment. The mesh is refined in the areas where corrosion is

postulated, and the shell elements are thinned to account for the corrosion. New models were

developed for the current work, and one difference between the models used in the current work

and those used by Cherry and Smith is that the boundaries of the corroded areas are made of

smooth curves and contain no sharp corners, which tend to increase the stresses and could cause

failure at a lower pressure. In the present work, corrosion is assessed with penetration depths of

25% and 50% through the containment shell in all areas investigated. In addition, corrosion is

investigated in the drywell vent bellows. In the plant under consideration, the drywell vent

55
bellows have two-ply construction. One of the bellows plies is assumed to have experienced

corrosion.

The original intent in the current work was to simply create a single model of the entire

containment that incorporated all of these corroded regions. The corroded regions are far enough

apart that negligible coupling is expected between them, meaning that a single model where all of

these regions are corroded would produce essentially the same results as separate models for each

of these cases would produce. When performing the parametric studies to generate probability

distributions of the failure pressures, it was found that because of the level of mesh refinement in

all of the corroded areas, the single model that incorporated all of the corroded areas required an

unreasonable amount of analysis time. Therefore, two models of the containment with corrosion

were developed. The first one only modeled the corrosion assumed in the drywell sand pocket

region, while the other model contained the corrosion in the drywell knuckle region, the wetwell,

and the bellows. This change resulted in more reasonable run times with very similar results.

4.1.4.1 Corroded Shell Models

Figure 4.13 shows a detail of the mesh in the region where corrosion is postulated in the drywell

knuckle region just below the point where the transition is made to a sphere from a cylinder. This

area was selected because it is a region of elevated strains under pressure because it is close to a

discontinuity. Water dripping down the outside of the drywvell could also accumulate here, and

the outside of the shell at this location is inaccessible for visual inspection because of the shield

building. The elements in the corroded area are shaded. The shell in this area has a thickness of

1.91 cm (0.75 in), and with the assumption of corrosion 25% through the depth, the corroded

elements have a thickness of 1.429 cm (0.563 in). In the model with corrosion 50% through the

depth, the corroded elements have a thickness of 0.953 cm (0.375 in). The assumed corrosion

region is about 38 cm (15 in) high and its 1.27 mn (50 in) width spans half of the 22.5 degree slice

of the containment. Accounting for the symmetry of the model, the actual width of the corroded

zone would be 2.54 mn (100 in).

Fiur 4.3 ehDti fDyelKukeCroinAe

56
The other region in the drywell where corrosion is studied is just above the sand pocket region.

This is also a difficult to inspect area where moisture could potentially accumulate. As for the

sand pocket area, a region extending half way across the slice was assessed with corrosion 25%

and 50% through the shell. The corroded region in the model (shown in Figure 4.14) is about 32

cm (13 in) high, and 1.07 mn (42 in) wide, meaning that with symmetry conditions, the region is

actually 2.14 mn (84 in) wide. The shell in this region is 3.18 cm (1.25 in) thick. In the model of

corrosion 25% through the depth, the corroded area is 2.38 cm (0.938 in) thick, while in the 50%

corrosion model, it is 1.59 cm (.63 in) thick.

Figure 4.14: Mesh Detail of Corroded Area at Sand Pocket

The final corroded region (Figure 4.15) in the containment shell was assumed to occur at the

water line in the wetwell. In the segments of the wetwell without vent line penetrations, which is

where this corrosion is assumed to occur, the shell is 1.53 cm (0.604 in) thick in the upper half,

and 1.71 cm (0.675 in) thick in the lower half. During normal operation, the water level in the

wetwell is very close to the transition point between these two thicknesses. A region of corrosion

25.4 cm (10 in) high is assumed to straddle this transition point. The corroded region assumed

here is centered on the outside of the torus between two ring stiffeners, and extends half of that

distance. The corroded zone in the model is 2.16 mn (85 in) wide, meaning that by symmetry, it is

actually modeling a zone 4.32 mn (170 in) wide. It is assumed that a uniform corrosion depth

occurs over the full corrosion region. The corrosion depth is expressed as a percentage of the

upper, thinner shell. Thus, with 25% corrosion, the upper shell is 1. 15 cm (0.453 in) thick and the

lower shell is 1.33 cm (0.524 in) thick. In the case where 50% corrosion is evaluated, the upper

shell is 0.767 cm (0.302 in) thick, and the lower shell is 0.947 cm (0.373 in) thick.

57
- , 7- 7 -

Figure 4.15: Mesh Detail of Corroded Area at Wetwell Waterline

4.1.4.2 Corroded Bellows Model

One of the objectives of the current study is to investigate the effects of bellows corrosion in a

risk-informed framework. Bellows can be found in both steel and concrete containments, but are

found more often in steel containments. Most bellows that form a part of the containment

pressure boundary are used in process piping penetrations to allow for relative movement

between the pipe and the containment. These process piping bellows are typically located on the

outside of the containment, so that as the containment expands due to intemnal pressurization, as

could potentially occur in an accident, the bellows would be compressed. The bellows may be

subjected to a combination of lateral and axial movements, depending on the orientation of the

pipe relative to the containment.

In addition to the process piping bellows, the second major use of bellows in nuclear power plant

containment vessels is in the vent lines that connect the drywell and wetwell in steel Mark I

containments, such as the one investigated here. These bellows typically have a larger diameter

than process piping bellows, and would not be subjected to relative movements as large as those

observed in process piping bellows.

Both process piping bellows and vent line bellows can have either a single ply or two plies. Twoply bellows are separated by a wire mesh, which allows for the region between the two plies to be

pressurized to check for leaks. The vent line bellows in the containment studied here have two

plies, but it is actually quite common for these bellows to only have a single ply.

Corrosion in bellows, which are made of stainless steel, is of a much different nature than

corrosion in the carbon steel that makes up the rest of the containment pressure boundary.

Because of the large residual stresses retained in the bellows during the forming process, they are

susceptible to transgranular stress corrosion cracking (TGSCC). Unlike corrosion in the liner

shell, which penetrates the steel to a certain depth, leaving the uncorroded material untouched,

TGSCC results in microscopic cracks that are difficult to detect and typically extend through the

depth of the material. Very little residual strength remains in the region of the bellows where this

has occurred. TGSCC is usually detected by leak rate tests rather than visual observation (Cherry

et al., 2001).

58
An experimental study conducted at Sandia National Laboratories (Lambert and Parks, 1995)

subjected a number of bellows to extreme conditions of pressure and displacement, and found

that before they have experienced any age-related degradation, bellows are generally very

resistant to leakage under these conditions. Leakage was only observed when the bellows were

subjected to displacements close to th~e point of full compression.

In addition to testing bellows in their original state, Lambert and Parks also attempted to induce

corrosion in bellows and determine how their capacity is reduced. Their goal was to induce

corrosion sufficient to potentially degrade the bellows performance in severe accident conditions,

but not so much that the bellows would fail a leak rate test prior to being subjected to those

extreme conditions. In attempting to do this, they found that because of the nature of stress

corrosion cracking, it is very difficult to control the amount of corrosion. Of the six corroded

bellows tested, three had no detectible leakage prior to being loaded, two had minor leakage, and

one had a significant amount of leakage.

Five of the corroded bellows tested were two-ply, and intended to be representative of process

piping bellows. The sixth bellows specimen had a single ply, and was typical of a vent line

bellows. All of the bellows were corroded from the outside, meaning that for the two-ply

bellows, the inner ply was not corroded. Great care was taken to not excessively corrode the

single ply bellows because breaking the pressure boundary would have made testing very

difficult.

In general, the findings of these tests were that for the two-ply bellows, large deformations of the

bellows caused the existing corrosion cracks to expand. When the bellows were highly

compressed, the leak rate tended to decrease due to the pressing together of the convolutions, but

when they were returned to their un-displaced configuration, the leak paths were allowed to open

up. The containments that exhibited minor leakage prior to the test had large leak rates, while

those that were initially leak-tight had small leak rates after the tests. The single ply bellows had

fairly minor corrosion, and did not leak after the test, although cracks had grown and it appeared

that it was on the verge of leaking.

The level of deformation required to initiate leaking in a corroded bellows is a very uncertain

quantity due to the nature of stress corrosion cracking. It appears that little would be gained by

performing detailed structural analyses of a degraded process piping bellows because of the

difficulty in developing a criterion for the initiation of leakage. In the Mark I containment

studied here, process piping bellows are not likely to experience very large deformation during

severe accident conditions because the drywell displacement is limited to about 5.1 cm (2 in)

because of contact with the shield building.

The vent line bellows in the Mark I containment seemed to be a better candidate for study. As

has been mentioned previously, the baseline shell model of the containment explicitly

incorporates the bellows with a reasonable level of detail. The two-ply bellows are approximated

as a single ply with twice the thickness of a single ply in the model. In the finite element model,

each 180-degree turn in the bellows convolutions is traversed by 6 elements, with an edge length

of about 0.8 cm (0.3 in), and the edge length of those elements in the other direction is about 14.5

cm (5.7 in). In the baseline analyses, the differential movement in the vent line bellows in the

late stages of the analysis is a small fraction of the original bellows length. Thus, it appears that

the ability of the vent line bellows to withstand high internal pressures is more important than

their ability to withstand large deformations.

59
The degraded vent line bellows are assumed to have corrosion in one of the plies. To model this,

it is assumed that the corroded region of the ply has lost all of its strength. Much like the other

corroded zones in the contaimnment shell, the elements in the corroded zone of the ply are assigned

half of the thickness of the surrounding bellows elements to simulate the loss of strength of one of

the plies. Shell elements are used throughout all parts of the bellows plies.

The vent line bellows are universal bellows, with two 26.4 cm (10.4 in) long sections of bellows

convolutions separated by a 15.3 cm (6 in) long center spool. The inside diameter of the bellows

is 226 cm (89 in), the convolution depth is 4.8 cm (1.9 in), and the convolution pitch is 5.9 cm

(2.3 in). The bellows are constructed of two 0.20 cm (0.08 in) thick plies of A240 Type 304

stainless steel.

Figure 4.16 shows a detailed view of the degraded portion of the bellows. The degraded area

covers an approximately 25 x 100 cm (10 x 40 in) elliptical area that spans the length of one of

the sets of convolutions at the lower part of the bellows. In the view of the mesh, the corroded

zone is shaded. The other set of convolutions shown in the figure illustrates the meshing scheme

used in the un-corroded bellows.

Figure 4.16: Mesh Detail of Corroded Bellows Area

The same methodology for checking for tearing in the containment shell is used in the bellows.

The report of Lambert and Parks provides a series of stress-strain curves taken from 40 specimens

at temperatures ranging from room temperature to 371 'C (700 OF). This data is used to develop

the statistical parameters describing the bellows material in this work. Bellows material is

extremely ductile at room temperature, with ultimate strains of around 0.7. At elevated

temperatures, the ductility is significantly decreased. At 218 'C (415 OF), the ultimate strain

drops to about 0.4.

One important consideration in the investigation of the bellows is whether a tear is likely to

develop into a hole large enough~ to be considered a "rupture". A series of experiments on

cracked bellows subjected to severe loading conditions is reported in Takenaka et al. (1989). In

these experiments, circumferential through-wall cracks of varying lengths were imposed on the

60
bellows with a machining process. The longest of these cracks extended 1200 around the

bellows. A rubber sealing material was used to prevent leakage to allow for the bellows to be

pressurized. Even in the bellows with the longest crack, no unstable crack growth was observed

when the bellows was subjected to high pressure and displacement conditions. In the specimen

with the longest crack,' unstable squirm of the bellows occurred under the loading conditions, but

no crack propagation was observed. These experiments confirm that bellows steel is extremely

tough and resistant to unstable crack propagation. Based on this, it is assumed in the current

work that a bellows tear results only in a "leak", and that "rupture" will not occur in the bellows.

4.1.5 Structural Analysis with Best Estimate Properties

In addition to the parametric analyses performed with the input parameters generated by LHS, a

baseline analysis of the BWVR Mark I containment was performed using mean values of those

parameters. The results of this analysis will be presented first because they help in the

understanding of the fragility analysis results. The containment analysis consists of a combined

study of the global and local models described in previous sections.

Figure 4.17 shows a plot of the potential for failure vs. pressure for all of the potential failure

locations considered in the current work for the un-degraded containment, as well as for the

locations with assumed 25% corrosion depth. The local details in the un-degraded containment

are shown in solid lines, the corroded areas are shown in dashed lines, and the head gasket is

shown in a dotted line. In this plot, the failure function is simply the quantity used to determine

when leakage occurs, divided by its limiting value. In the locations where tearing would cause

leakage, the magnified plastic strain is used to determine when leakage occurs. The limiting

value of the magnified plastic strain is the uniaxial failure strain. For the head gasket leak, the

failure function is obtained by dividing the opening area by the "leak" threshold area.

Pressure (psig)

050 100 150 200

2 1 i /I /

Equipment Hatch .

-Wetwell Access Hatch. -Bellows 1

-Steam Line Pen. .

-Floor Drain Pen.

_ Cont. Spray Pen. -Wetwell Inst. Pen.

O - ~HPCI Test Pen.. I .... Head Gasket Leak

C_ o 1 -- 25% Knuckle Corrosion

'2-25% Wetwell Corrosion/ r l Cr 

o

- - 259%/ Sand Pocket Corrosion/

LL 0.5

Pressure (MPa gauge)

Figure 4.17: Leakage Potential for All Penetration Details and 25% Corrosion

Locations

61
From this plot, it is clear that for the un-degraded containment, the head gasket is the dominant

cause of leakage. The bellows and several of the penetrations all appear to fail at about the same

point. The floor drain penetration is not likely to result in a failure, as the magnified strains are

very low even at the maximum analysis pressure. This is because it is located in a much thicker

section of the containment shell than the other penetrations. With 25% corrosion depth, two of

the corrosion locations postulated here (at the drywell knuckle and at the wetwell waterline)

experience tears at pressures below the failure pressure at any of the locations investigated in the

un-degraded containment. Corrosion 25% through the shell at the sand pocket is less critical than

tearing at other details of the containment, and does not occur before the time of analysis

termination at 1.38 MPa (200psig).

Figure 4.18 shows a plot very similar to that in Figure 4.17, except that the results for the 50%

corrosion depth cases are shown in place of the results for the 25% corrosion depth cases. The

results for the corrosion through 1 vent line bellows ply are also shown on this plot. The uncorroded detail results are also shown on this plot for comparison purposes, and are exactly the

same as those in Figure 4.17. Increasing the corrosion depth to 50% has a significant effect on all

of the locations considered. With corrosion 50% through the shell, leakage is now expected to

occur at the wetwell waterline before it would occur anywhere in the un-degraded containment.

The corroded bellows and drywell knuckle did not completely reach the failure criterion at the

time their analysis was terminated, but failure appears imminent, and the results can be

reasonably extrapolated to estimate a failure pressure in this case. That analysis terminated early

because large strains elsewhere in the model made it difficult to obtain a converged solution.

Pressure (psig)

50 100 150 200

2 1

Equipment Hatch

-Wetwell Access Hatch

-Bellows

-Steam Line Pen. ~ 1 ___Floor Drain Pen.

Cont. Spray Pen. co - Wetwell Inst. Pen. O - HPCI Test Pen. .... Head Gasket Leak

02 1 -- 5%Knuckle Corrosion __________________

-- Bellows Corrosion (1 ply)

Ct -- 50% Wetwell Corrosionply/ - 50% Sand Pocket Corrosion /

0 0.2 0.4 0.6 0.8 1 1.2

Pressure (MPa gauge)

Figure 4.18: Leakage Potential for All Penetration Details and 50% Corrosion

Locations (Including 1 Ply Bellows Corrosion)

Table 4.1 provides a summary of the "leak" and "rupture" pressures for the locations checked in

the current analyses. This table also provides a listing of the sizes of the features used as an

estimate of the crack size for the rupture criterion, as well as the length of the crack that would be

required for the containment to rupture given the stress level at the "leak" pressure. Finally, this

62
table provides a listing of the risk analysis failure modes to which the individual details are

assumed to contribute. A listing of the meanings of the abbreviations for these failure modes is

provided in

Table 4.2.

Table 4. 1: Summary of Locations and Failure Pressures

Location Leak Pressure Rupture Assumed Grit. Crack Risk Model

MiPa (psig) Pressure Feature Size at Mode

M~a(sg iemi)La ~n

Equipment Hatch 1.21 (176.9) 1.21 (176.9) 4.57 (180) 0.20 (7.8) DWL,

____________ DWvR

Wetwell Access tt3.05 (120) Vt WWLaW,

Hatch WWRaW,

CWVWR

Bellows tN/A N/A N/A WWLaW

Steam Line Pen. tt2.90(114) t DWL,

______ DWR

Floor Drain Pen. t t 1.02 (40) t DWL,

DWR

Cont. Spray Pen. t t 0.79 (31) t DWL, ________ ________ ______ DWR

Wetwell Inst. Pen. 1.56 (225.9)* 1.56 (225.9)* 0.25 (10) 0.09 (3.7) WWvLbW,

WWRbW,

______________ CWW~R

HPCI Test Pen. 1.37 (199.1) 1.37 (199.1) 1.19 (47) 0.05 (2.1) WWNLaW,

WW'RaW,

___________CWWNR

Head Gasket 1.00 (145.4) 1.68 (243.5) N/A N/A DWHL,

___________DWHR

Knuckle 1.18 (170.8) 1.18 (170.8) 2.54(100) 0.15(5.8) DWL,

Corrosion (25%) D WR

Knuckle 1. 04 (15 1.0)* 1.04 (151.0)* 2.54 (100) 0.18 (7.2)* D'WL,

Corrosion (50%) DWrR

Bellows 1.12 (162.4) N/A N/A N/A WWLaW

Corrosion

Wetwell 1.1-7 (169.6) 1.17 (169.6) 4.32 (170) 0.14 (5.3) WWLaW,

Corrosion (25%) VWWRaW

Wetwell 0.809 (117.4) 0.809 (117.4) 4.32 (170) 0.91 (36.0) VWVLaW,

Corrosion (50%) W~WRaW

Sand Pocket t t2.13 (84) tDWL,

Corrosion (25%) DWR

Sand Pocket 1.34 (194.5) 1.34 (194.5) 2.13 (84 1.5(11) DWL,

Corrosion (50%) _____ DWTR

*Failure pressure not reached in analysis. Result extrapolated from last analysis steps.

tFailure pressure not reached in analysis. Last step too far from failure point to reasonably

extrapolate result.

63
Table 4.2: Risk Model Failure Mode Abbreviations

Abbreviation Meaning

DWL Drwl eak

DWR Drywell Rupture

CDWR Catastrophic Drywell Rupture

DWHL Drywell Head Leak

DW*HR Drywell Head Rupture

WWLaW Wetwell Leak above Waterline

WWRaW Wetwell Rupture above Waterline

WWLbW Wetwell Leak below Waterline

WWRbW Wetwell Rupture below Waterline

CWWR Catastrophic Wetwell Rupture

From the analysis results, it is apparent that in most cases, the assumed crack length, based on the

size of the feature where it initiates, is far longer than the crack length required for unstable crack

growth at the loading pressure. This means that in most cases, the "leak" and "rupture" pressures

are identical. In the best estimate case presented here, there are no instances of the rupture

pressure being greater than the leak pressure. In the LHS analyses, however, it is likely that there

would be a few cases where a rupture does not form immediately upon tear initiation. As

mentioned previously, if a rupture occurs in the drywell, catastrophic rupture is precluded by the

presence of the shield wall. In the wetwell, however, a rupture will immediately grow into a

catastrophic rupture. In those locations, the pressures for "leak", "rupture", and "catastrophic

rupture" are identical in most cases.

It is interesting to note that for most of the penetrations, the critical crack length at the tearing

pressure is very small, and clearly below the size of the feature causing the strain localization.

For the cases of corrosion, however, the critical crack lengths at the tearing pressure are larger.

This is especially true in as the corrosion depth increases, because the tearing pressure is reduced

due to the thinning of the shell. If smaller zones of corrosion were assumed, the probability of

experiencing leak before rupture would be increased.

4.2 Fragility Analysis of Degraded Steel Mark I Containment

A procedure similar to that used for the reinforced concrete was used to generate fragility curves

for the Steel Mark I containment. After the global and local models of this containment were

finalized, random variables were chosen and LHS was used to generate a 30 sets of random input

parameters to develop fragility curves.

Table 4.3 shows a listing of the random parameters used in this analysis. Random parameters

were generated to approximate randomness in properties of the plate steel, bellows steel, and

drywell head gasket. In addition, random parameters were used to account for epistemic

uncertainty.

64
Table 4.3: Random Input Parameters

Property Median COV!f Distribution

Plate Steel

Ultimate Strength (f) 682 MiPa 0.09 Lognormal

(98.9 ksi) ______

Yield Strength Factor 1.0 0.07 Normal

Elastic Modulus (E,) 200 GPa 0.06 Normal

(29000 ksi)

Uniaxial Failure Strain (cfui) 0 .25 0.12 Normal

Fracture Mech. Cutoff]J 1.0 0.10 Lognormal

Corrosion Depth Uncertainty 1.0 0.10 Normal

Bellows Steel

Ultimate Strength ()719 MPa 0.12 Lognormal

(104.3 ksi)

Yield Strength Factor 1.0 0.07 Normal

Elastic Modulus (E,) 200 GPa 0.06 Normal

(29000 ksi)

Uniaxial Engineering Failure Strain (efait) 0.76 10.13 Normal

D rywell Head Gasket _____ _________

Temperature Difference 75 OF 0.28 Lognormal

Bolt Preload 445 kN 0.09 Lognormal

_______ _______ _______ _______ (100 kips) _ _ _ _ _ _ _ _ _

Gasket Resiliency 0.38 mm 0.49 Lognormal ______ _______ ______ ______ (0.015 in) _ _ _ __ _ _ _ _ _

Bolt Yield Strength Factor 1.0 0.07 Normal

Evistemic Uncertainty

ILocal 3D Model .Strain Factor (JFEM-u,)

ILocal Shell Model Strain Factor (JFEM-u,)

ICorrosion Factor Uncertainty ( f,-ý)

Stress/strain curves for the plate and bellows steel were generated in the same manner as was

done for steel components of the reinforced concrete containmnent. Random numbers were

generated for the ultimate strength strength, f, . The yield strength, fy is computed by

multiplying the ultimate strength by a second parameter, s, which has a mean value of 1.0, and a

factor to represent the average ratio of the yield to ultimate strength, denoted as r.

fy =srf. (4.6)

For the plate steel, r is 0.53, while for the bellows steel, a value of 0.39 is used for r.

The variability in the parameters describing the randomness in the A516 Gr. 70 plate steel used in

the steel containment shell is assumed to be the same as that in the steel liner of the reinforced

concrete containment. The parameters describing the bellows steel are taken from the results of a

series of coupon tests summarized by Lambert and Parks (1995).

A listing of the 10 failure modes for which conditional probabilities are required by the risk

analysis models has been provided in Table 4.2. These modes are comprised of failures of

various sizes at four location groupings: the drywell head (DWH), the rest of the drywell (DW),

65
the wetwell above the waterline (WWaW), and the wetwell below the waterline (WWbW). For

the drywell head, failure is assumed to only occur at the gasket. For all of the other location

groupings, multiple locations within those groupings were investigated. The raw and fitted

fragilities for the locations falling within these groupings are presented below. They are

organized by groupings, and the codes for the groupings in which they fall (e.g. DW, WWaW,

etc.) are shown in the legends of the plots for each of these locations.

Figure 4.19 shows the fragilities for the leak and rupture modes of the head gasket. As mentioned

previously, these were computed from a simple engineering analysis program written specifically

for this application rather than from a detailed simulation. Figure 4.20 shows the fragilities for all

of the locations within the drywell, and Figure 4.21 shows those for the 'wetwell both above and

below the waterline. The failure locations shown in these plots are all present in the containment

in its original condition. As noted in the figure captions, no failures were observed in the floor

drain penetration or the wetwell access hatch in the 30 samples that were run. If more samples

would have been run, it is possible that failures would have been observed, but these are clearly

not governing cases, and will thus have a very negligible effect onl the overall results. As a result,

these locations are not considered in the computation of the fragility curves.

It should also be noted that in almost all of the locations in the original containment without

corrosion, the rupture criterion is always met when the leak criterion is met. This means that the

conditional probability of leak given failure at a location is always zero for these cases. The

exceptions to this are the drywell head and the bellows failure. The head gasket fails by

controlled opening of the pressure unseating gasket rather than tearing, and as mentioned before,

it is assumed that a bellows failure can not be large enough to be considered a rupture. In the

drywell region, there is a small air gap between the steel drywell shell and the concrete shield

building. Because this would preclude a catastrophic rupture, as did the surrogate shield building

in the Sandia steel containment test (Luk et. al., 2000), it assumed that a catastrophic rupture

cannot occur in the drywell. On the other hand, a rupture in the wetwell shell is assumed to

immnediately grow to become a catastrophic rupture, because there is nothing to prevent a running

crack from stopping.

66
Pressure (psi)

150 300

U-

-o

.0

0

a.

0.8 1 1.2

Pressure (MPa)

Figure 4.19: Raw and Fitted Fragility Curves for the Drywell Head Region

Pressure (psi)

0 50 100 150 1.0 r200 250 300

0.8 VG--o Eq. Hatch Lk. & Rup. (DW)

o-a Steam Line Pen. Lk. & Rup. (DW)

Cont. Spray Pen. Lk. & Rup. (OW)

--Eq. Hatch Lk. & Rup. LN Fit

-- Steam Line Pen. Lk. & Rup. LN Fit

---Cont. Spray Pen. Lk. & Rup. LN Fit

.0

a.

0.6 II' I'

0.4 HDesign Pressure

0.2 k

0.0 I . I I . I

0 0.2 0.4 0.6 0.8 1 1.2

Pressure (MPa)

1.4 1.6 1.8 2

Figure 4.20: Raw and Fitted Fragility Curves for Individual Locations in the Drywell Region

(Note: No Observed Failures at Floor Drain Penetration)

67
Pressure (psi)

1.0~I

0-0o-. Bellows Leak (WWaW)

0-0 HPCI Test Line Leak & Rupture (WWaW),M

0.8-~- Inst. Line Leak & Rupture (WWbW)

-- Bellows Leak LN Fit

-- HPCI Test Line Leak & Rupture LN Fit

-- Inst. Line Leak & Rupture LN Fit

MU-0

__1 Design Pressure

0.4-

0.2-

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Pressure (MPa)

Figure 4.21: Raw and Fitted Fragility Curves for Individual Locations in the Wetwell Region

(Note: No Observed Failures at Wetwell Access Hatch)

Figure 4.22 shows the fragilities for failure at the corroded area in the drywell knuckle region for

25% and 50% corrosion depths. The leak and rupture pressures are the same in every case.

Figure 4.23 shows similar fragilities for failure in the drywell sand pocket region with 25% and

50% corrosion. This is the only location in this study where the tearing criterion was met before

the rupture criterion. A relatively small number of samples failed with 25% corrosion, so the

quality of the fitted curves is not as good as in other cases. Finally, Figure 4.24 shows the

fragility curves for the postulated corrosion areas within the wetwell above waterline grouping.

These include 25% and 50% corrosion at the wetwell waterline and corrosion of one of the vent

line bellows plies. As for the un-corroded bellows, a corroded bellows failure is assumed to not

constitute a rupture.

69
Pressure (psi)

0 50 100 150 200 250 300

1.I I

0.8 I0)

Cz

-0

0-

0.6 [--

Design

D resign 

2 %

Corr. LI

50% D Corr. LU

25% DX --- Corr. LI

50% DX

-- Corr. LI

0.4 [-

V. Knuckle

k. & Rp. (DW)

V. Knuckle

c. & Rp. (DW)

A]. Knuckle

k. & Rp. LN Fit

fV. Knuckle

k. & Rp. LN Fit

0.2 II . I A

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

Pressure (MPa)

2

Figure 4.22: Raw and Fitted Fragility Curves for Corrosion Location (25% and 50% depths) in

the Drywell Knuckle Region

Pressure (psi)

,0 50 100 150 200 250 300 1.

0.8 I

2?

CO

.0

2

CL

0.6 F

o-I 25IadPt Cr.L.(W

* -025% Sand Pkt. Corr. Lkp. (DW)

S50% Sand Pkt. Corr. Rup. (DW)

S50% Sand Pkt. Corr. Lkp. (DW)

--- 250% Sand Pkt. Corr. Rup. (DW)i

--25% Sand Pkt. Corr. Lkp. LN Fit

2--50% Sand Pkt. Corr. Rup. LN Fit

--50% Sand Pkt. Corr. Lkp. LN Fitj

Design

PressureA

0.4 I

0.2 I0.010 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Pressure (MPa)

1.8 2

Figure 4.23: Raw and Fitted Fragility Curves for Corrosion Location (25% and 50% depths) in

the Drywell Sand Pocket Region

69
Pressure (psi)

0 50 100 150 200 250 300

IA',. . ,

0.8 HUn0.4

2

(L

r- 25% Wetwl. Corr. -0Lk. & Rp. (WWaW)

50% Wetwl. Corr. M-aLk. & Rp. (WWaW)

Vent Bellows Corr.

Leak (WWaW)

25% Wetwl. Corr.

Lk. & Rup. LN Fit

50% Wetwl. Corr.

Lk. & Rup. LN Fit

Vent Bellows Corr.

Leak LN Fit

0.2 HSI I . I .

0 0.2 0.4 0.6 0.8 1 1.2

Pressure (MPa)

1.4 1.6 1.8 2

Figure 4.24: Raw and Fitted Fragility Curves for Corrosion Locations at Wetwell Waterline

(25% and 50% depths) and Vent Line Bellows (1 Ply Corroded)

Once the parameters for the fitted distributions presented above were computed, the procedure

outlined in Chapter 2 was applied to compute overall fragilities and conditional failure

probabilities for each of the cases investigated here. Figure 4.25 shows plots of the original

containment fragility along with the fragilities of the contaimnment in all of the degraded states

considered here. In many of the cases, the presence of degradation did not significantly affect the

overall fragility. This is due to the fact that there is already a large number of potential failure

locations present in the containment without corrosion. The case that had the most detrimental

effect on the overall fragility is that where 50% corrosion was assumed in a large area in the

wetwell waterline. The case with 50% corrosion at the drywell knuckle had the second most

severe effect, but its effect was much smaller.

70
Pressure (psi)

050 100 150 200 1

- Original Condition

- 25% Drywell Knuckle Corrosion

0.8- - 50% Drywell Knuckle Corrosion

- 25% Sand Pocket Corrosion - 50% Sand Pocket Corrosion

- 25% Wetwell Corrosion

0.6- - 50% Wetwell Corrosion

- Vent Line Bellows Corrosion

0.4- Design

Pressure

0.2-

0 11

0 0.2 0.4 0.6 0.8 1 1.2

Pressure (MPa)

Figure 4.25: Overall Fragilities for Original Condition and All Corroded States Investigated

Figure 4.26 through Figure 4.33 show the conditional probabilities of the failure modes required

by the risk analysis for the original containment and for all of the corroded cases. For each case,

the overall fragility is shown along with the conditional probabilities. Only the conditional

probabilities of those modes that have nonzero probabilities of failure are shown in these plots.

This data will be used as input into the risk analysis models.

71
Pressure (psi)

0 50 100 150 200 250

0.8

u16

.o0.4

2

a0.2I

Pressure (MPa)

Figure 4.26: Conditional Probabilities of Failure Modes for Original Containment

Pressure (psi)

50 100 150 200 250

Overall Fragility

__CWWR

0.8 DWR

-DWHL

i0.6-

20 0.4- 2 Design IL Pressure",

0.2 -/

0 _ _ _

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Pressure (MPa)

Figure 4.27: Conditional Probabilities of Failure Modes for Containment with 25% Corrosion at

Drywell Knuckle

72
Pressure (psi)

0 50 100o 150 200 250

1.8-

0.8-

a .6

.~0.4-

0

0- 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Pressure (MPa)

Figure 4.28:

CI

U-

.0

2-

Conditional Probabilities of Failure Modes for

Drywell Knuckle

Containment with 50% Corrosion at

Pressure (psi)

100 150 250

0.8 1

Pressure (MPa)

Figure 4.29: Conditional Probabilities of Failure Modes for Containment with 25% Corrosion at

Drywell Sand Pocket

73
Pressure (psi)

0.8

u-

.~0.4

0.

0~

0.8 1

Pressure (MPa)

Figure 4.30:

CO

.0

0-

Conditional Probabilities of Failure Modes for Containment with 50% Corrosion at

Drywell Sand Pocket

Pressure (psi)

100 150 250

0.8 1

Pressure (MPa)

Figure 4.3 1: Conditional Probabilities of Failure Modes for Containment with 25% Corrosion at

Wetwell Water Line

74
Pressure (psi)

0 50 100 150 200 250

1

0.81-

U.

.0

.0

0~

0.6 I-

.----. -

-- Overall Fragility

-CWWR

DWR

-DWHL

0.4 F- Design N Pressure\

0.2 -

0 0.2 0A4 0.6 0.8 1

Pressure (MPa)

1.2 1.4 1.6

Figure 4.32:

U-

.0

a.

Conditional Probabilities of Failure Modes for

Wetwell Water Line

Containment with 50% Corrosion at

200 250

Pressure (psi)

100 150

0.8 1

Pressure (MPa)

Figure 4.33: Conditional Probabilities of Failure Modes for Containment with Corrosion in One

of Vent Line Bellows Plies

75
4.3 Risk Analysis Results

Table 4.4 shows the CDF values from NIJREG-1 150. Because the containment response does

not affect the CDF for this plant, the results are the same for all of the cases studied.

Table 4.4: Core Damage Frequency (yr'1)

I Case Mean 15% 150% 195%1

1All 4.5E-6 3.5E-7 1.9E-6 1.3E-5

As for the PWVR with a reinforced concrete containment evaluated in Chapter 3, it is very

important to carefully consider which containment failure modes contribute to the risk metrics

being used. Characteristic 5 in the accident progression event tree for this plant tells which mode

of failure was experienced by the containment. The answer to this question can be: DWI{L,

DWL, WWL, DWHR, DWR, drywell melt-through (DWMTH), wetwell venting (WWVENT),

wetwell rupture (WWR), or no containment failure (NOCF). There are a number of ways that the

risk outcomes could potentially be grouped.

Table 4.5 shows the probabilities of early containme nt failure conditional on core damage for the

reference case (using NUREG- 1150 inputs), the un-damaged case using the inputs generated in

the current work, and all of the degradation cases investigated. The containment failures are

grouped into five categories. All of these categories bin together early containment failures that

occur after core damage from the same set of initiating events. The first of these categories, early

rupture, groups together all rupture failures (DWHR, DWR, WWR). The second, early drywell

leak, groups together all drywell leak failures (DWHL, DWVL). The early wetwell leak category

is listed separately for reasons that will be explained. It only contains the WWL failures. The

early venting category contains the WWNVENT failures, and the early melt-through category

contains the DWMTH failures.

Table 4.5: Mean Probabilities of Early Containment Failure Conditional on Core Damage

Early Early

Early Drywell Wetwell Early Early MeltCase: Rupture Leak Leak Venting thog

Un-damaged (Reference) 0.05951 0.0009426 0.002098 0.01771 0.3574

Un-damaged (Current Study 0.07016 0.002918 0 0.01771 0.3475

Bellow Corrosion 0.07016 0.001067 0.001321 .0.01771 0.3475

25% Corrosion at Knuckle 0.07180 0.002820 0 0.01771 0.3459

50% Corrosion at Knuckle 0.07492 0.001125 0 0.01771 0.3443

25% Corrosion at Sand Pocket 0.07082 0.002951 0 0.01771 0.3459

50% Corrosion at Sand Pocket 0.07082 0.002918 0 0.01771 0.3459

25% Corrosion at Wetwell Water Line 0.06131 0.001187 0 0.01771 0.3574

50% Corrosion at Wetwell Water Line 0,05688 0 10 10.-1011771 0.363 9

A very important feature of these results is that there is a very high probability of a melt-through

failure. The probability of an early melt-through failure given core damage is roughly 36% for all

cases. The probability of a failure in this mode is significantly higher than any of the other types

76
of failure. The next most significant mode is early rupture, with a probability of about 6-7%,

depending on the case, followed by wetwell venting, with a probability of about 2%. All of the

other failure modes are relatively insignificant. The summation of all of the mean conditional

probabilities for all of the modes listed in Table 4.5 is about 43.8% and changes very little as the

various types of degradation are introduced.

This dominance of the melt-through mode of containment failure was noted in NUREG-1 150. It

stems from the fact that the Mark I containment is relatively small, so that if the core were to

melt, it would spread out over a relatively confined area, making it much less likely to cool off

before penetrating the containment than it would be in a larger containment.

The wetwell leak failures are in a category separate from the drywell leak failures in Table 4.5

because the outcome is different. Any gasses released from the wetwell will have been scrubbed

by passing through the water in the wetwell, and the end outcome is arguably similar to wetwell

venting, in which the wetwell is intentionally vented to relieve pressure.

The effects of the various types of containment degradation can be best understood using the

categorizations of failure types shown in Table 4.5. In the case of bellows corrosion, the only

changes are in the probability of drywell leak and wetwell leak. The drywell leak failure

probability decreases, and the wetwell leak probability goes from 0 to .001321. The summation

of the probabilities of the two modes of failure is somewhat lower than the original wetwell leak

probability. It stands to reason that a weakened bellows would tend to draw failures away from

the drywell to the wetwell. Because a release through the vent line bellows would be scrubbed,

and the change in risk due to this type of degradation is miniscule compared to the risk of a meltthrough, it can be argued that a corroded vent-line bellows ply has a negligible effect on the risk.

The cases where the drywell knuckle is corroded 25% and 50% through the thickness result in an

increase in the probability of a drywell rupture, combined with a decrease in the probability of a

drywell leak or a drywell melt-through. These effects are more pronounced in the 50% corrosion

depth case, and follow the same trends observed in the 25% depth case. These results are

intuitive, because corrosion at this location was determined to lead immediately to rupture.

Scenarios that would have ended in drywell leakage or melt-through with the original

containment have a greater likelihood of ending with drywell rupture with the presence of this

type of corrosion.

With the presence of corrosion at the sand pocket, the changes are much less pronounced than

those due to those from corrosion at the knuckle. The sand pocket location is much less critical

than the drywell knuckle, and even with 50% corrosion depth, failure was likely to occur

elsewhere in the containment before occurring at this location.

Corrosion in the wetwell had the greatest influence on the risk of any of the degradation types

considered. The results at first seem somewhat counter-intuitive. Wetwell corrosion causes the

risk of a rupture (drywell or wetwell) as well as the risk of a drywell leak to drop. At the same

time, it causes the risk of a drywell melt-through to increase by roughly the same amount as the

decrease in the risk of failure in the other two modes. This appears to be caused by the fact that

failure at the corroded zone in the wetwell would result in a catastrophic rupture, and the cooling

water in the wetwell would be lost, resulting in a greater likelihood of a drywell melt-through.

To group these failure modes together for the computation of the risk metrics calculated for the

other containments, it was decided that early drywell ruptures and drywell melt-through failures

would be grouped together for computing LERIF. Drywell leakage is used to compute SERF, and

77
wetwell leakage and venting are excluded from the calculation because the release would be

scrubbed in those cases. The total early release frequency is the summation of LERF and SERF.

These results are presented in a manner consistent with that used for the other plants considered

in this study in the series of tables below. Table 4.6 shows the LERF results, and Table 4.7

shows the probability of large early containment failure conditional on core damage (using the

same groupings used for LERF). The change in LERF due to degradation is shown in Table 4.8.

Analagous results for SERF, the conditional probability of small early containment failure

conditional on core damage, and the change in SERF are shown in Table 4.9, Table 4. 10, and

Table 4.11, respectively. Finally, TERF, the conditional probability of all containment failures,

and the change in TERF are shown in Table 4.12, Table 4.13, and Table 4.14. These total risk

tables do not include wetwell leakage or venting, as noted previously.

Table 4.6: Large Early Release Frequency (yi§1

Case Mean 5% 50% 95%

Un-damaged (Reference) 1.876E-06 8.377E-13 7.335E-07 1.151lE-05

Un-damaged (Current Study) 1.880E-06 8.377E-13 7.335E-07 1.268E-05

Bellow Corrosion 1.880E-06 8.377E-13 7.335E-07 1.268E-05

25% Corrosion at Knuckle 1.880E-06 8.377E-13 7.335E-07 1.345E-05

50% Corrosion at Knuckle 1.886E-06 1.779E-12 7.335E-07 1.353E-05

25% Corrosion at Sand Pocket 1.875E-06 8.377E-13 7.335E-07 1.330E-05

50% Corrosion at Sand Pocket 1.875E-06 8.377E-13 7.335E-07 1.330OE-05

25% Corrosion at Wetwell Water Line 1.884E-06 8.377E-13 7.335E-07 1.151E-05

50% Corrosion at Wetwell Water Line 1.894E-06 8.377E-13 7.335E-07 1. 149E-05

Table 4.7: Probability of Large Early Containment Failure Conditional on Core Damage

Case Mean 5% 50% 95%

Un-damaged (Reference) 0.4169 2.393E-06 0.3861 0.8851

Un-damaged (Current Study) 0.4177 2.393E-06 0.3861 0.9754

Bellow Corrosion 0.4 177 2.393E-06 0.3861 0.9754

25% Corrosion at Knuckle 0.4 177 2.393E-06 0.386 1 1.0344

50% Corrosion at Knuckle 0.4192 5.082E-06 0.3861 1.0410

25% Corrosion at Sand Pocket 0.4 167 2.393E-06 0.386 1 1.0230

50% Corrosion at Sand Pocket 0.4167 2.393E-06 0.3861 1.0230

25% Corrosion at Wetwell Water Line 0.4187 2.393E-06 0.3861 0.8857

50% Corrosion at Wetwell Water Line 0.4208 2.393E-06 0.3861 0.8836

Table 4.8: Change in the Large Early Release Frequency (yr-) due to Degradation

Case Mean 5% 50% 95%

Bellow Corrosion 0 0 0 0

25% Corrosion at Knuckle 0 0 0 7.672E-07

50% Corrosion at Knuckle 6.639E-09 9.410E-13 0 8.525E-07

25% Corrosion at Sand Pocket -4.426E-09 0 0 6.1 80E-07

50% Corrosion at Sand Pocket -4.426E-09 0 0 6.180E-07

25% Corrosion at Wetwell Water Line 4.426E-09 0 0 -1. 166E-06

50% Corrosion at Wetwell Water Line 1 .402E-08 0 0 -1. 1 93E-06

78
Table 4.9: Small Early Release Frequency. (yr-1)

Case Mean 5% 50% 95%

Un-damaged (Reference) 4.242E-09 0 0 0

Un-damaged (Current Study) 1.3 13E-08 0 0 1.287E-07

Bellow Corrosion 4.802E-09 0. 0 0

25% Corrosion at Knuckle 1.269E-08 0 0 1.230E-07

50% Corrosion at Knuckle 5.06 1E-09 0 0 0

25% Corrosion at Sand Pocket 1.328E-08 0 0 1.287E-07

50% Corrosion at Sand Pocket 1.3 13E-08 0 0 1.287E-07

25% Corrosion at Wetwell Water Line 5.341E-09 0 0 5.733E-08

50% Corrosion at Wetwell Water Line 0 0 0 0

Table 4. 10: Probability of Small Early Containment Failure Conditional on Core Damage

Case Mean 5% 50% 95%

Un-damaged (Reference) 0.0009426 0 0 0

Un-damaged (Current Study) 0.0029 18 0 0 0.009902

Bellow Corrosion 0.00 1067 0 0 0

25% Corrosion at Knuckle 0.002820 0 0 0.009459

50% Corrosion at Knuckle 0.001125 0 0 0

25% Corrosion at Sand Pocket 0.00295 1 0 0 0.009902

50% Corrosion at Sand Pocket 0.0029 18 0 0 0.009902

25% Corrosion at Wetwell Water Line 0.001187 0 0 0.004410

50% Corrosion at Wetwell Water Line 0 0 0 0

Table 4.11: Change in the Small Early Release Frequency (yr-1) due to Degradation

Case Mean 5% 50% 95%

Bellow Corrosion -8.329E-09 0 0 -1.287E-07

25% Corrosion at Knuckle -4.426E-10 0 0 -5.75 1E-09

50% Corrosion at Knuckle -8.070E-09 0 0 -1.287E-07

25% Corrosion at Sand Pocket 1.475E-10 0 0 0

50% Corrosion at Sand Pocket 0 0 0 0

25% Corrosion at Wetwell Water Line -7.790E-09 0 0 -7.139E-08

50% Corrosion at Wetwell Water Line -1.3 13E-08 0 0 -1.287E-07

Table 4.12: Total Early Release Frequency (yr 1)

Case Mean 5% 50% 95%

Un-damaged (Reference) 1 .880E-06 8.377E- 13 7.335E-07 1.151 E-05

Un-damaged (Current Study) 1.893E-06 8.377E-13 7.335E-07 1.281E-05

Bellow Corrosion 1.884E-06 8.377E-13 7.335E-07 1.268E-05

25% Corrosion at Knuckle 1.892E-06 8.377E-13 7.335E-07 1.357E-05

50% Corrosion at Knuckle 1.891E-06 1.779E-12 7.335E-07 1.353E-05

25% Corrosion at Sand Pocket 1.889E-06 8.377E-13 7.335E-07 1.343E-05

50% Corrosion at Sand Pocket 1.888E-06 8.377E-13 7.335E-07 1.343E- 05

25% Corrosion at Wetwell Water Line 1.889E-06 8.377E-13 7.335E-07 1.157E-05

50% Corrosion at Wetwell Water Line Il.894E-06 8.377E-13 7.335E-07 1. 149E-05

79
Table 4.13: Probability of Total Early Containment Failure Conditional on Core Damage

Case Mean 5% 50% 95%

Un-damaged (Reference) 0.4178 2.393E-06 0.3861 0.8851

Un-damaged (Current Study) 0.4206 2.393E-06 0.386 1 0.9853

Bellow Corrosion 0.4188 2.393E-06 0.386 1 0.9754

25% Corrosion at Knuckle 0.4205 2.393E-06 0.386 1 1.0439

50% Corrosion at Knuckle 0.4203 5.082E-06 0.3861 1.0410

25% Corrosion at Sand Pocket 0.4197 2.393E-06 0.386 1 1.0329

50% Corrosion at Sand Pocket 0.4196 2.393E-06 0.3861 1.0329

25% Corrosion at Wetwell Water Line 0.4199 2.393E-06 0.3861 0.8901

50% Corrosion at Wetwell Water Line 0.4208 2.393E-06 0.3861 0.8836

Table 4.14: Change in the Total Early Release Frequency (yrf1) due to Degradation

Case Mean 5% 50% 95%

Bellow Corrosion -8.329E-09 0 0 -1.287E-07

25% Corrosion at Knuckle -4.426E-10 0 0 7.6 15E-07

50% Corrosion at Knuckle -1.43 1E-09 9.410E-13 0 7.237E-07

25% Corrosion at Sand Pocket -4.279E-09 0 0 6.180E-07

50% Corrosion at Sand Pocket -4.426E-09 0 0 6.180E-07

25% Corrosion at Wetwell Water Line -3.364E-09 0 0 -1.237E-06

50% Corrosion at Wetwell Water Line 8.852E-10 0 0 -1.322E-06

Even though the conditional probability of containment failure given core damage is quite high

for this plant, the LERF is reasonably low, having a value of about 1.88E-6 for all cases. The

change in LERF, or any of the other risk metrics, for that matter, is quite low, simply due to the

fact that the baseline probability of melt-through given core damage is so high that it dwarfs any

changes in the likelihood of rupture failures caused by corrosion.

Comparing the LERF and ALERF results with the guidelines of Regulatory Guide 1. 174 indicates

that any of the degradation cases studied here would be acceptable according to that criterion.

This is in large part due to the low value of CDF, which is also well within the bounds of

acceptability.

The example plants examined here serves as good case studies indicating that one should be very

cautious about simply applying the ALERF criterion to evaluate the significance of containment

degradation. It is important to closely examine how degradation, can increase the likelihood of

one failure mode while decreasing the likelihood of another, and evaluate the consequences of

these different modes. It cannot be stressed enough that the cases of degradation examined here

are extremely limited in scope. There are currently no means of predicting degradation prior to

its discovery. Since the location and specific nature of any degradation could dramatically affect

the containment capacity and risk, a detailed analysis of that scenario would be required. The

specific results reported in this study should in no way be applied to making regulatory decisions

on existing plants.

80
5. Risk Analysis of PWR Ice Condenser Containment

As with the BWR Mark I steel containment, the effects of corrosion are examined for a typical

pressurized water reactor (PWRa) Ice Condenser steel containment. Figure 5.1 shows a schematic

diagram of the PWR Ice Condenser Containment. The regions of corrosion are indicated in the

locations where moisture is likely to accumulate and weaken the containment. The corroded

locations remain consistent with the degraded PWR analyses performed by Cherry and Smith

(200 1). Corrosion at the basemat and upper floor locations are based on inspections summarized

by Shah, et al. (1994). Even though not accessible for inspection, corrosion in the ice basket

region is also examined due to the presence of water. All three corroded locations are examined

with and without corrosion to determine the effects of degradation. As defined by NUREG/CR455 1, SAND86-1309, Vol. 2, Rev. 1, Part 3, failure in these three locations would bypass the ice

condenser. Detailed analysis of the upper containment (region above the ice basket) is also

performed where failure is assumed not to bypass the ice condenser.

Steel

containment

Concrete

exaine in shiseStdy

Figue 5.: Crroion Potulaed n PW IceCondnserSteldShel

5. Srctra odl fPW IeCodesr onanm n

Sevra dffret inteeleetmdl r mlydt oe h W c odne

Cotimeti tsoiialadcrrddsats h goa ehvo s nlzdHiha3Dfnt

81
element model of a 53 degree slice of the containment using shell elements. The 53 degree slice

is selected to include the interface between the thickened plate region which contains multiple

penetrations and hatches, and the thinner plates which makeup a majority of the containment

circumference. The regions of stress and stress concentrations are expected at the thickness

transition between plates (Clauss, 1985; Greimann et al., 1987 Cherry and Smith, 2001). In

addition to the 53 degree global model, three "submodels" are examined to study the regions of

high stress and strain concentration with higher levels of mesh refinement. The effects of

corrosion are studied at locations within two of these submodels and at one location within the

global model.

The models of the steel PWR Ice Condenser containment use the same baseline material

properties as the BWM Mark I steel containment. The material properties are varied in the

parametric analysis with parameters generated by LHS.

5.1.1 Global Baseline Containment Model

The 53 degree slice of the global containment in Figure 5.2 resembles closely the model

employed by Cherry and Smith. The plate thickness, plate locations, horizontal stiffeners, and

vertical stringers remain identical to their model. Due to increases in computational power, the

level of mesh refinement has been increased substantially. The global model used by Cherry and

Smith contained 10125 four-noded shell elements (S4R ABAQUS elements) and 10335 nodes.

The current model includes 24911 shell elements and 25255 nodes. The majority of the additional

elements reside in the regions of high stress and strain concentrations or locations of postulated

corrosion.

In addition, Cherry and Smith modeled the sections of the anchorage system and anchor bolts.

These components are encased in the concrete basemat which was not modeled. Instead,

appropriate boundary conditions were applied to bolts and to the shell at the intersection with the

top of the concrete basemat. Figure 5.2 shows that the current model of the steel shell extends

only to the intersection of the concrete basemat and steel shell. The nodal degrees of freedom are

constrained against displacement and rotation along this line of intersection. The anchorage

system has been analyzed previously by Fanous et al. (1993) and is not studied here.

Penetrations were not explicitly modeled here since previous work (Miller, 1990; Greimann, et

al., 1984) determined that failures will occur in the thin plates near the interface with the thick

plate regions (Clauss, 1985; Greimann et al., 1987). Figure 5.3 illustrates the different plate

thicknesses for the PWR Ice Condenser containment. Though not explicitly modeled, a

significant number of penetrations pass through the thickest plate region (3.81 cm). The plate

thickness in the cylinder ranges from 1.27 cm below the springline to 3.18 cm near the basemat.

The dome thickness varies from 1.11 cm above the springline to 2.38 cm at the top of the dome.

As with the penetrations, the bellows are not explicitly modeled, but leak pressures are estimated

using previous experimental and analytical analyses of the bellows (Lambert, et al., 1995;

Greimann, et al., 199 1).1

82
Figure 5.2: Finite Element Mesh of PWR and Detailed View of the Basemat Region

-1

Figure 5.3: Illustration of the Variation in Shell Plate Thickness (cm) for the PWR

83
5.1.2 Containment Local Models

Figure 5.4 shows the approximate locations of the local regions of concern for the PW*R

containment. Three of the locations (upper containment, ice basket, and upper floor) highlighted

in Figure 5.4 contain regions of strain and stress concentration due to abrupt changes in plate

thickness. Each of these regions is analyzed in additional detail using submodels described in this

section. The fourth location near the basemat is studied in detail within the global model.

Figure 5.4: Regions of Stress and Strain Concentration for the PW`R

5.1.2.1 Basemnat Region

Figure 5.5 illustrates the high level of mesh refinement employed near the intersection of the steel

shell (3.02 cm plate thickness) and concrete basemat. As described earlier, the nodes along the

intersection are constrained against displacement and rotation.

While membrane action is the primary means of load resistance throughout the containment, the

strains near the basemat are dominated by bending caused by the outward expansion of the shell.

The bending strains are limited since membrane action will eventually resist the increasing

loading after the radial displacements become large enough. Cherry and Smith (2000) and

Ellingwood and Cherry (1999) increased the strain limit to cause a leak due to bending strains by

50% over the values used for membrane strains. This was introduced to account for the limited

nature of the bending strains and since a crack initiated by bending strains at the plate surface

would need to propagate through the thickness of the plate prior to leak formation. Cherry and

Smith also limited failure to surface (bending) strains above 5%, i.e., no failure was considered

possible for bending strains below 5%. This study does not employ the 5% minimum strain but

does increase the strain limit for bending strains by 75%. Due to significant bending at the

intersection, the mesh was refined in the vertical direction (darkened area at the intersection in

Figure 5.5) until obtaining convergence of the maximum plastic strain.

84
anr

ýemt Rgio (itesectionl Of Steel Shell and Concrete

Figure 5.5'. Detailed View Of the Baseitat egin ater

5.1.2.2 Ice BaSket Regijon 

ocusat the corners of the thick plate surrouddb .n 

ouiu e . nd moeed by

reinof high strain concentrations 

rein sShwCUXaabltisO

thine r maeri al i th re ion of the ice basket. This reiooidsowei 

i ngu 5.4 and dll edthe

addtioal etal uin th 5U nioel llstrated in Figure 5.6. The sub dlngcpbliiso

th n e atre a 

bm de 

the eg uQod l lS 

applies autom natc ly he

ABAQ ,US a eem ployed here to a ay e the su l ss e it re r m i d

correspondin g displacements generated from thraalyi fthegoa odlt h bud 

so

the s b n d lfor each load step. Th e pressure 

esd rem ai id nt ca to th

analysis Of the global model.-Edi 

uruddbyapaeOl 

h

(0.625~ ~ ~ o in)1 

thc.Temsacnpaetikeslas 

to significant strain concentrations 

Inth

thn e plate near th aon ~o h thickn s plt e.Te thickn s plate is 290 cm (114 in)wie nth

(06 5 n hi 

k 

r a tredgion ofig r. 6 f lo s a slope of14

vetichinn 

r ecin SInce shell element 

reue he ae srae, ion oFigurasto bewe n the, two

includedlinithetiub-odel. 

This region, ilutIn aditon, the corners of the transito

plates wa nl d di h s frode 3 .81 cm to 1.5dc

arunded" at the interface with the tiplae mateforalTh 

rounde corershav 

afradiu ofe

1.27 cm (05i)wih 

is assumed to be a reasonabl 

siefor aroundsedmn 

weld bead. the ionclusion

of.hes lc al d tis reduces the artifi al sr inmcnentraTion 

ms ~ h ID n g c pethe lmy -fo h

ofnt h ee e olem en t ai re r s ntation of the actual contai . otinentg T he nmesh w srge fnce d ne r thOo ne s o

the thik 'Plate (darkened areas'nFgr .)utl 0 tiig~~egneo 

h aiu lsi

strai85
Ithickness transiton between plates

Figure 5.6: Detailed View of the Ice Basket Region Submodel

5.1.2.3 Upper Floor Region

The second submodel includes the shell region at the location of the upper floor at the interface

between plates of varying thickness. Figure 5.4 indicates the location of the upper floor

submodel shown in Figure 5.7. This specific location contains a thin plate at 1.91 cm (0.75 in)

thickness surrounded on two sides by a plate 3.81 cm (1.5 in) thick. The finite element

procedures remain identical to those described for the ice basket region submodel. The plate

thickness transition follows the 1:4 slope and 1.27 cm (0.5 in) radius for the plate comer. As with

the ice basket region submodel, the mesh was refined until obtaining convergence of the

maximum plastic strain.

86
Figure 5.7: Detailed View of the Upper Floor Region Submodel

5.1.2.4 Upper Containment Region

The final submodel created for the analysis of the PWR Ice Condenser containment examines a

portion of the upper containment, where the upper containment describes the region above the ice

condenser. Failure in this region is assumed not to bypass the ice condenser. Figure 5.8 shows

the submodel for the upper containment with the global position outlined in Figure 5.4.

The upper containment submodel contains several plates of varying thickness. The plate at the

bottom left of the submodel is the same plate thickness, 3.81 cm (1.5 in), as the thickest plate in

the ice basket and upper floor submodels. As described previously, the thick plate contains

multiple penetrations for bellows and access hatches. The submodel includes three thinner plates

at 1. 11 cm (0.4375 in), 1.27 cm (0.5 in), and 1.59 cm (0.625 in), from top to bottom. The

springline is located at the bottom of the top plate. Due to the relatively small difference in

thickness between the three thinner plates, transition regions were not included. The transitions

between the three thin plates and the thick plate are modeled as shown in Figure 5.8. Several

locations include rounded corners with the adopted 1.27 cm (0.5 in) radius. As with the previous

submodels, the mesh was refined in the regions of strain concentration until obtaining

convergence of the maximum plastic strain.

87
Figure 5.8: Detailed View of the Upper Containment Region Submodel

5.1.3 Corroded Regions

Corrosion is postulated in three locations for the PWTR Ice Condenser containment. Figure 5.9

shows the three locations at the basemat, the upper floor, and ice basket region. These locations

and their sizes remain similar to the three locations studied by Cherry and Smith. Inspections

have observed corrosion in PWR Ice Condenser containments at the basemat and upper floor

locations (Shah, et al., 1994). The ice basket region is not accessible for inspection but has a high

potential for corrosion due to the presence of water. The finite element meshes are refined in the

areas of corrosions, with additional refinement in the regions of strain concentration. Corrosion is

introduced into the shell models by reducing the shell thickness in the postulated corroded

regions. Two nominal levels of corrosion are assumed for each region, 25% and 50% for the

basemat and ice basket regions, and 50% and 65% for the upper floor location.

Due to the relatively large distance between the three corroded regions, the global model is

analyzed with corrosion in all three locations. One analysis was performed with 50% corrosion in

the basemat region, 50% corrosion at the upper floor region, and 25% at the ice basket region. A

second analysis included 25% corrosion at the basemnat region, 65% corrosion at the upper floor

region, and 50% at the ice basket region. Since the existence of corrosion in one region of the

global model has only negligible effects on the strains in the other corroded regions, the solutions

for each region can be used independently. This also enables the use of the global models with

corrosion in all three locations to supply the boundary conditions for the submodels containing

corrosion. Two of the previously described submodels are used to model corrosion in the upper

floor and ice basket regions. The global analysis is used to determine the strains at the basemnat

with corrosion. These corroded regions are described in the following sections.

88
Figure 5.9: Locations of Corrosion Postulated for the PWR

5.1.3.1 Corroded Basemnat Region

Figure 5. 10 illustrates the postulated corrosion in the basemat region. The corroded region spans

428.5 cm (168.7 in) along the intersection between the containment shell and the concrete

basemat. The corrosion extends 10. 16 cm (4 in) in the verteical direction, with 3.81 cm (1. 5 in)

of that length fully corroded. As with the interface between plates of differing thickness in the

submodels, a 6.35 cm (2.5 in) transition in thickness is modeled between the uncorroded and

corroded plates. Corrosion at 25% and 50% of the original 3.02 cm (1. 19 in) thickness reduces

the nominal thickness to 2.27 cm (0.894 in) and 1.51 cm (0.594 in), respectively. The model

includes a high level of mesh refinement in the corroded region (darkened region in Figure 5. 10).

89
Figure 5. 10: Detailed View of the Corroded Basemat Region

5.1.3.2 Corroded lee Basket Region

Figure 5.11 shows the postulated region of corrosion within the ice submodel. This specific

location is not accessible during inspections but is susceptible to corrosion due to the presence of

water. The corrosion is placed in the thin plate at the interface with the thicker plate described in

the discussion of the ice basket submodel. The corroded region is highlighted in red with the

thickness transition in orange. The corrosion extends 12.5 cm (4.9 in) in the horizontal direction

and 25.6 cm (10. 1 in) in the vertical direction. The two corrosion levels, 25% and 50%, reduce

the original 1.59 cm (0.625 in) thickness to 1. 19 cm (0.469 in) and 0.79 cm (0.3 125 in),

respectively. The model includes a high level of mesh refinement in the corroded region with

additional refinement in the areas of strain concentration (darkened areas in Figure 5.11).

90
thickness transition between plates

and between corroded and

uncorroded regions I

Figure 5.11: Detailed View of the Corroded Ice Basket Region Submodel

5.1.3.3 Corroded Upper Floor Region

Figure 5.12 illustrates the postulated corrosion region within the upper floor submodel. The

corroded region was place in the thin plate at the location of the upper floor and is surrounded by

a thick plate along the bottom and left sides of the submodel. The postulated corrosion region

spans the entire length of the upper floor in the global model, as outlined in Figure 5.9. Here the

corroded region only reaches to the edge of the submodel. This does not affect the results for this

location since the maximum strains occur in the corner where the thin plate is surrounded by the

thicker plate. The corrosion extends 68 cm (27 in) in the vertical direction (typical concrete floor

thickness). The two corrosion levels, 50% and 65%, reduce the original 1.91 cm (0.75 in)

thickness to 0.953 cm (0.375 in) and 0.667 cm (0.2625 in), respectively. The model includes a

high level of mesh refinement in the corroded region with additional refinement in the area of the

strain concentration (darkened area in Figure 5.12).

91
Figure 5.12: Detailed View of the Corroded Upper Floor Region Submodel

5.1.4 Analysis of the Bellows

Previously, a detailed studied and finite element analysis of the bellows in the PWR Ice

Condenser containment was performed by Greimann et al. (199 1). They determined that the two

bellows most likely to leak due to large deformation are located just below the springline in the

thick plate region shown in Figure 5.13. These particular bellows supply the containment with

glycol and extend approximately 61 cm (24 in) in length with two 15.2 cm (6 in) convolution

sections. Greimann et al. concluded that the bellow would remain leak tight until as least 0.427

MfPa (62 psi). At this point, the end pipe and bellows wall come into contact with the possibility

of the rigid end pipe pushing through the bellow wall.

Figure 5.13: Approximate Bellows Location Relative to Upper

Containment Submodel

92
As discussed earlier for the bellow analysis of the BWR containment, typical bellows were tested

in an experimental study by Lambert and Parks (1994). The program included nine "like-new"

and six corroded bellows of various configurations, test conditions, lateral displacements, and

internal loadings. Of the nine like-new bellows, six did not leak even at 100% compression of the

convolution. The remaining three bellows leaked prior to 100% compression, but none prior to

86% compression. Since the bellows are not explicitly modeled for the MWR, the results of these

experiments are employed to develop a simple failure criterion for determining the point of leak

in the critical bellows (location shown in Figure 5.13). Conservatively assuming that the six

bellows which did not leak prior to 100% compression, do leak at 100% compression, an average

compression of 97% compression is assumed to cause leakage in the bellows. Here, the critical

bellow has 30.5 cm (12 in) of convolution. Therefore, leak in the bellow is predicted to occur

when the radial (outward) displacement of the containment at the bellow location reaches 97% of

30.5 cm (12 in) (in the average case). The variation (standard deviation) of the data set is used to

vary this percentage throughout the 30 LHS samples.

For the six corroded experiments, three leaked prior to any compression due'through-thickness

corrosion prior to any loading. Of the remaining three bellows, two leaked at 50% and 100%

compression, and one did not leak even at 100% compression. Since it can be assumed that

bellows with corrosion through the entire thickness of the bellow would be discovered and

repaired during inspections, the three bellows which leaked prior to compression where assumed

to leak at 50% compression (the next lowest value). As with the like-new procedure, the bellow

which did not leak at 100% compression was assumed to leak at 100% compression. Therefore,

the corroded bellow is assumed to leak when the compression reaches the average value of 67%

of the convolution length (30.5 cmn (12 in)). The uncertainty in the percent of compression is

reflected in the large variation (standard deviation) employed to generate the LHS samples.

Failure in the bellows is limited to leak since rupture is not considered likely to occur (see

discussion for bellows in the BWR containment).

5.1.5 Structural Analysis with Best Estimate Properties

As with the BWR containment, a baseline analysis was performed for the PWIR Ice Condenser

Containment using the median of each LHS input parameters. Figure 5.14 shows the potential for

failure vs. pressure for all locations considered in this study. This plot includes results for failures

at local details in both original and corroded conditions. For the basemat, upper floor, ice basket,

and upper containment, the failure function is defined as the magnified plastic strain divided by

the uniaxial failure strain. For the bellows failure, the failure function is defined as the radial

displacement at the bellows location divided by the critical compression length (97% of 30.5 cm

for no corrosion, and 63% (median value for assumed lognormal distribution) of 30.5 cm for

corrosion).

Figure 5.14 shows clearly that corrosion has a significant effect on the failure pressure. In the

original condition, failure is predicted to occur at the ice basket local detail, followed by the upper

containment, bellow, and upper floor location, respectively. Neither the bending or membrane

strains at the uncorroded basemnat reach values large enough to initiate failure prior to the finite

element analysis convergence limit (pressure at which the analysis failed to converge). The

introduction of 50% corrosion to the basemat region does lead to bending failure prior to the end

of the analysis. For this median (best estimate) analysis, 25% corrosion was not sufficient to

cause failure at the basemat. Failure is obtain in several of the LHS cases with 25% corrosion at

the basemat.

93
U2.0 Basemrat 50% Corrosion (bending) 20 -- Basemat 50% Corrosion (membrane)

-- Basemat 25% Corrosion (bending)

-- Basemat 25% Corrosion (membrane)

-Basemat No Corrosion (bending)

Basemat No Corrosion (membrane)

1.5 Ic- e Basket 50% Corrosion -- Ice Basket 25% Corrosion

-Ice Basket No Corrosion

-Upper Floor 65% Corrosion

Upper Floor 50% Corrosion

10 Upper Floor No Corrosion -Upper Containment

Bellow No Corrosion

-- Bellow Corrosion

0.5

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Pressure (MPa gauge)

Figure 5.14: PWVR Leakage Potential for All Locations and Corrosion Levels

Corrosion at the upper floor and ice basket locations causes a clear reduction in the failure

pressure. The differences in failure pressure between 25% and 50% corrosion for the ice basket

and 50% and 65% for the upper floor are relatively small compared to the analyses without any

corrosion. Lower failure pressure is also seen in the bellow with the introduction of corrosion.

Table 5.1 summarizes the failure pressures at each location and corrosion condition. Even though

the failures predicted in Figure 5.14 use the leakage failure criterion, the far field stresses are

sufficient to initiate catastrophic rupture immediately after the leak forms in most cases. The

catastrophic rupture criterion is based on the J integral exceeding the critical J at the point of leak

initiation. The J integral is calculated using the far field stress and an assumed crack length. At

the point of leak, the newly formed crack is assumed to immediately grow to the size of a nearby

feature, typically the length of the nearest plate edge. The distance between the concrete shield

building and the steel containment is assumed to be sufficiently large as to not prevent

catastrophic rupture. Therefore, rupture and catastrophic rupture are equivalent for the PWYR. In

many cases, the far field stresses, assumed to be the driving force for crack growth, are on the

order of the yield strength of the material at the point of leak. This further justifies the conclusion

that catastrophic rupture will occur immediately after reaching the leakage criterion. This holds

for the upper floor, ice basket, and upper containment locations, since none of the 30 LHS

analyses showed rupture at higher pressures than leak using the critical J integral criterion.

Therefore, catastrophic rupture is the only risk mode considered for these locations. Several of

the basemnat analyses do predict rupture at higher pressures than leak, and can therefore contribute

to the leak bypass mode. These cases have leaks occurring at relatively low pressures which do

not have sufficient far field stresses to propagate the assumed crack. Finally, the bellows are

assumed to leak and not transition to catastrophic rupture. Therefore, a leak in the bellow is

assumed to contribute to the leak no bypass mode.

94
Table 5. 1: Summary of Locations and Failure Pressures

Location Leak Pressure Rupture Feature Size

(Corrosion) MPa (psig) Pressure mn (in) Risk Model Mode

MPa (psig)

Basemat 0.560 0.560 4.285 m Bypass - Leak

(50% Corrosion) (81.2) (81.2) (168.7 in) Catastrophic Rupture

Basemat N/A* N/A 4.285 mn Bypass - Leak

(25% Corrosion) (168.7 in) Catastrophic Rupture

Basemat N/A* N/A N/A Bypass - Leak

(No Corrosion) Catastrophic Rupture

Upper Floor 0.414 0.414 2.896 Catastrophic Rupture

(65% Corrosion) (60.2) (60.2) (114)

Upper Floor 0.430 0.430 2.896 Catastrophic Rupture

(50% Corrosion) (62.4) (62.4) (114)

Upper Floor 0.590 0.590 2.896 Catastrophic Rupture

(No Corrosion) (85.6) 856(114)

Ice Basket 0.406 0.406 2.896 Catastrophic Rupture

(50% Corrosion) (58.9) (58.9) (114)

Ice Basket 0.429 0.429 2.896 Catastrophic Rupture

(25% Corrosion) (62.2) - (62.2) (114)

Ice Basket 0.462 0.462 2.896 Catastrophic Rupture

(No Corrosion) (67.0) (67.0) (114)

Upper 0.5 18 0.5 18 2.896 Catastrophic Rupture

Containment (75.2) (75.2) (114)

Bellows 0.530 N/A N/A No Bypass - Leak

(No Corrosion) (76.9)

Bellows0.486N/ N/A No Bypass - Leak

(Corrosion)(05 __________

*Failure not obtained prior to convergence limit.

5.2 Fragility Analysis of Degraded PWR Ice Condenser Containment

The PWR Ice Condenser Containment was analyzed with 30 sets of random input parameters

generated by LHS using the values in Table 5.2. The computation of the yield strength from the

yield strength factor for the BWR Mark I containment remains the same for the PWR. Fragility

curves were then created using the failure pressures for each of the 30 analyses for each local

detail.

Figure 5.15 illustrates the fragility distributions for the locations assumed to cause a bypass of the

ice condenser if a leak occurred. The top plot in Figure 5.15 shows the fragility distributions for

the basemat with and without corrosion. At low failure probabilities there does exist a small gap

between leak and catastrophic rupture. Each fragility distribution was fit with a lognormal

distribution and plotted against the raw distributions in Figure 5.15. Since no one distribution fit

the leak fragilities, two separate distributions are used to represent the 50% and 25% corrosion

cases.

A number of the 30 analysis did not reach failure prior to obtaining the convergence limit for

these two levels of corrosion. For these cases, failure pressures were extrapolated based on the

last values computed in the analysis. These extrapolated cases were not used in the lognormal fit

95
leading to poor curve fits at higher pressures, but enables better fits to the low probability failures

which are not extrapolated. All five points shown for the basemat case without corrosion were

extrapolated and therefore no curve fit is included.

Table 5.2: Random Input Parameters

LProperty Median COy!P Distribution

Plate Steel

Ultimate Strength (f) 682 MPa 0.09 Lognormal

(98.9 ksi)

Yield Strength Factor 1.0 0.07 Normal

Elastic Modulus (E,) 200 GPa 0.06 Normal

(29000 ksi)

Uniaxial Failure Strain (Sfaji) 0.25 0.12 Normal

Fracture Mech. Cutoff]J 1.0 0.10 Lognormal

Corrosion Depth Uncertainty 1.0 0.10 Normal

Bellows Leak ______ ___________

Percent of Convolution Length 97% T0.05 Normal

Percent of Convolution Length 63% 0.36 Lognormal

Epistemic Uncertainty__________________

Local Shell Model Strain Factor 1.0 0.35 Lognormal

(IFEM-u ) _____________

Corrosion Factor Uncertainty 1.0 0.20 Lognormal

The bottom plot in Figure 5.15 illustrates the fragility curves for the upper floor and ice basket

locations. Without corrosion, the ice basket region is by far the most critical region and the likely

failure location. Even though the original plate thickness at the upper floor location (1.91 cm) is

slightly larger than at the ice basket location (1.59 cm), 50% corrosion is required at the upper

floor to produce a similar fragility curve as the ice basket at 25% corrosion. The fragility curves

for 65% corrosion at the upper floor and 50% at the ice basket are also similar. As with the leak

fragilities for the basemnat location, two distributions were required to fit the ice basket fragility

with 50% corrosion.

The failures predicted for the upper floor and ice basket lead directly to catastrophic rupture since

the far field stresses in the shell are sufficiently large to cause unstable propagation of small leak

cracks.

Figure 5.16 shows the fragility curve for the locations assumed not to bypass the ice condenser

after developing a leak. Although a leak at the upper containment location would not bypass the

ice condenser, the current prediction shows that the upper containment failure proceeds directly to

catastrophic rupture (the risk model assumes that all catastrophic ruptures will bypass the ice

condenser). No corrosion was considered in this location since the upper containment is located

above the ice condenser. Figure 5.15 also includes the fragilities for the bellow assumed most

critical. The failure pressures at low probabilities are close to the lower bound pressure of 0.427

96
MIPa determined by Greimann et al. (199 1) through finite element analyses. Figure 5.16 also

shows the effects of corrosion in the bellows with a slight shift in the fragility.

1.0 _

a Basemnat 50% Corrosion - Leak

08 * Basemnat 50% Corrosion - Rupture

o Basemnat 25% Corrosion - Leak

* Basemnat 25% Corrosion - Rupture

U- 0.6 # Basemnat No Corrosion - Rupture

10.4

0

0

Design Pressure

a0.2- 0

0.0 Ar --Or :ý --

0.0 0.1 0.2 0.3 0.4 0.7 0.8 0.9 1.0

Pres

0.5 0.6

sure (MPa gauge)

1.0

0.8-

2!

~ 0.6 Design Pressure 06 1.9 *U

S0.4 Up

0.2 2

,Ic

0.0 A

0. 0.1 0.2 0.3 0.4 0.5 0.6

Pressure (MPa gauge)

per Floor 65% Corrosion - Rupture

per Floor 50% Corrosion - Rupture

per Floor No Corrosion - Rupture

eBasket 50% Corrosion - Rupture

eBasket 25% Corrosion - Rupture

eBaskete No Corrosion - Rupture

0.7 0.8 0.9 1.0

Figure 5.15: Fragility Curves for Locations Contributing to the Bypass Mode:

(top) Basemat Location, (bottom) Upper Floor and Ice Basket Locations

97
1.0

.Upper Containment - Rupture

0.8 -Bellow No Corrosion - Leak

VDBellow Corrosion - Leak

LL 0.6~

S0.4 Design Pressure

0.2

0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Pressure (MPa gauge)

Figure 5.16: Fragility Curves for Locations Contributing to the No Bypass

Mode

The fragility curves enable the determination of total cumulative probability of failure

distributions. Eight different "conditions" are considered for the PWR Ice Condenser

containment: 1) Original (No corrosion at any location), (2) 50% corrosion at the basemat, (3)

25% corrosion at the basemat, (4) 65% corrosion at the upper floor, (5) 50% corrosion at the

upper floor, (6) 50% corrosion at the ice basket, (7) 25% corrosion at the ice basket, and (8)

corrosion in the bellows. For each condition, no corrosion is present at any location other than

the location being considered. Since there are two similar bellows assumed to be equally critical,

conditions 1 through 7 include two statistically independent bellows. The corroded bellows

condition (8) also considers two statistically independent bellows with both corroded.

98
Figure 5.17 illustrates the cumulative probability of failure for each of the 8 conditions. Failure is

defined at the lowest pressure to cause leak or rupture (these occur simultaneously for most

conditions). At low failure probabilities, the pressures exhibit a large level of scatter between the

different conditions. This reflects the uncertainty in both material properties and modeling

accuracy that are introduced through the LHS method. Failure pressures at higher probabilities

show significantly less scatter since catastrophic rupture in a few critical locations dominates the

containment behavior (less influence from the corrosion location and level).

1.0 - -

-Original (No Corrosion)

-Basemnat 50% Corrosion

(D08 Basemnat 25% Corrosion

Upper Floor 65% Corrosion

Upper Floor 50% Corrosion 0 -Ice Basket 50% Corrosion

ý-0.6-Ice Baseket 25% Corrosion

-B~ellows Corrosion

S0.4

=0.2

0

0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Pressure (MPa gauge)

Figure 5.17: Cumulative Probability of Failure for Each Containment Condition

Figure 5.18 through Figure 5.25 show the conditional failure probabilities corresponding to the 8

conditions illustrated in Figure 5.17. The conditional probabilities reflect the probability of a

specific mode causing failure, given that a containment failure has occurred.

99
1 n

7 0.8 No Bypass - Leak

U - Catastrophic Rupture

0L

p0.6

0.4

0.0

± 0.4 . . . . . . .

Desig Pressur Prssr 

Figure 5.18: Conditional Probabilities for the Original Condition (No Corrosion)

For example, Figure 5.18 shows the conditional probabilities for the containment with no

corrosion in any location (original containment state). At low pressures (pressure < 0.32 MPa),

the conditional probability of catastrophic rupture is equal to 1. Figure 5.17 indicates that the

cumulative probability of failure for the containment without corrosion at pressures lower than

approximately 0.34 MPa are close to 0. At these low cumulative failure probabilities near 0, any

containment failure that occurs, would occur in the ice basket location which proceeds directly to

catastrophic rupture. As the pressure increases, leak in the bellows increases in probability and

contributes to the leak no bypass mode. At higher pressures (pressure > 0.6 MPa), the

catastrophic rupture conditional probability again reaches 1.

Figure 5.19 and Figure 5.20 contain the conditional probabilities for the two basemat corrosion

conditions. For these conditions, leak at the basemnat becomes possible at low pressures and

contributes to the leak bypass mode.

100
1.0

CD8 Bypass -Leak

-No Bypass -Leak

LI_ - Catastrophic Rupture

p0.6-

0.4

0.0

0. . 0.4 . . 0.- .

oPesr Desgnuresu) -~ 

Fiue51:Cniinl-rbblte o 0 Croina h aea

1.0 rCD

0

U_

cc

.0

2

CL

0

0.8 F -Bypass - Leak

-__No Bypass -Leak

Catastrophic Rupture

0.6 [

0.4 [

Design Pressure

0.2 F

I 0.0 1~

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Pressure (MPa gauge)

Figure 5.20: Conditional Probabilities for 25% Corrosion at the Basemnat

Corrosion in the upper floor and at the ice basket locations leads to conditional probabilities for

catastrophic ruptures near 1 at all pressures. Figure 5.21 through Figure 5.24 show that there is a

101
relatively small conditional probability for the leak no bypass mode due to the bellows in these

cases.

1.0F

0.8

U0.

a-7 0.6

.0

-oO

00

-No Bypass -Leak

- Catastrophic Rupture

Design Pressure

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Pressure (MPa gauge)

Figure 5.21: Conditional Probabilities for 65% Corrosion at the Upper Floor

1.0

0.8 -No Bypass -Leak

-Catastrophic Rupture cc'

0.

.~0.6

o .2

0.0

Design Pressure

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Pressure (MPa gauge)

Figure 5.22: Conditional Probabilities for 50% Corrosion at the Upper Floor

102
1.0

S0.8

0.6

-L 0.4 70

o0.2

-No Bypass -Leak7

- Catastrophic Ruptures

Design Pressure

0.0 . _ _

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Pressure (MPa gauge)

Figure 5.23: Conditional Probabilities for 50% Corrosion at the Ice Basket

1.0

S0.8

cc

0.

2'0

0.4

.0

±0.0

-No Bypass - Leak

-Catastrophic Rupture

Design Pressure

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Pressure (MPa gauge)

Figure 5.24: Conditional Probabilities for 25% Corrosion at the Ice Basket

Corrosion in the bellows causes the conditional probability of the leak no bypass mode to

increase significantly. At low pressures (pressure < 0.3 MPa), catastrophic rupture still

dominates, but the cumulative probability of failure is approximately 0 in this range.

103
1.0

-No Bypass -Leak

1±. -Catastrophic Rupture

~0.6

0.

ca

ao Design Pressure

0.2

0.2

0.0-------- ~ _

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Pressure (MPa gauge)

Figure 5.25: Conditional Probabilities for Bellows Corrosion

5.3 Computational Issues Discovered with the NUREG-1 150 Ice

Condenser PRA Model

While performing the risk analyses with the existing PRA model for the ice condenser

containments, several issues were encountered. First, the original conditional failure probabilities

were hard-coded into the accident progression event tree (APET) subroutine. Due to the multiple

failure modes and locations, an error was determined such that the array which stored the

conditional failure probabilities was accessed incorrectly. This led to the wrong conditional

failures being accessed and used in the PRA model, i.e., the probability of leak at location I was

being accessed when rupture at location 2 should have been. It would seem that this resulted

from a misinterpretation of how FORTRAN stores three-dimensional arrays. Since the code was

modified to read the conditional failure probabilities from an input file, this problem was

corrected by altering the input order for the conditional failure probabilities. In addition,

numerical problems were discovered with the steel PWYR ice condenser conditional failure

probabilities. It was determined that non-zero values are required for the conditional failure

probability in certain instances. Without finite values, specific accident scenarios do not proceed

through the correct path, leading to drastically inaccurate values for LERF. Additional analyses

showed that the values used for the conditional failure probability (10-6 ) did not affect LERF

when changed as long as then remained relatively small, but non-zero. These issues were

resolved prior to running the PRA analyses.

104
5.4 Risk Analysis Results

Table 5.3 shows the CDF values from NIJREG 1150. Because the containment response does not

affect the CDF for this particular plant, the results are the same for all of the cases studied.

Table 5.3: Core Damage Frequency (yr-')

Case IMean 15% 150% 195%

1All 5.7E-5 1.2E-5 3.7E-5 1.8E-4

Table 5.4 shows the LERF results, Table 5.5 shows the probability of large early containment

failure conditional on core damage, and Table 5.6 shows the change in LERF relative to the Undamaged (Current Study) case. The change in LERF is used with Figure 2.2 to assess the

acceptability of a given degradation state within the framework of Regulatory Guide 1. 174.

Table 5.6 indicates that none of the degraded cases cause an increase of LERF to exceed 10-7.

Since LERE does not exceed 5E-5, each of the degraded cases falls within Region III in Figure

2.2. Therefore, each of these cases would be acceptable by Regulatory Guide 1. 174.

Table 5.4 Large Early Release Frequency (yr'

Case Mean 5% 50% 95%

Un-damaged (Reference) 7.41E-7 0 1.32E-9 1.22E-5

Un-damaged (Current Study) 4.67E-7 0 1.62E-9 1.01E-5

Bellow Corrosion 4.61E-7 0 1.32E-9 1.01E-5

25% Corrosion at Basemat 4.57E-7 0 1.62E-9 1.01E-5

50% Corrosion at Basemat 4.41 E-7 0 9.29E-10 1.O1E-5

50% Corrosion at Upper Floor 5.14E-7 0 3.89E-9 1.02E-5

65% Corrosion at Upper Floor 5.37E-7 0 6.48E-9 1 .02E-5

25% Corrosion at Ice Basket 5.05E-7 0 3.89E-9 1.02E-5

50% Corrosion at Ice Basket 5*57E-7 0 5.55E-09 1.02E-05

Table 5.5: Probability of Large Early Containment Failure Conditional on Core Damage

Case Mean 5% 50% 95%

Un-damaged (Reference) 1.30E-02 0 1.O1E-5 6.75E-02

Un-damaged (Current Study) 8.19E-03 0 4.37E-05 5.61 E-02

Bellow Corrosion 8.08E-03 0 3.57E-05 5.61 E-02

25% Corrosion at Basemnat 8.02E-03 0 4.37E-05 5.62E-02

50% Corrosion at Basemat 7.73E-03 0 2.5 1E-05 5.62E-02

50% Corrosion at Upper Floor 9.0 1E-03 0 1 .05E-04 5.64E-02

65% Corrosion at Upper Floor 9.42E-03 0 1.75E-04 5.64E-02

25% Corrosion at Ice Basket 8.86E-03 0 1 .05E-04 5.64E-02

50% Corrosion at Ice Basket 9.78E-03 0 1.50E-04 5.65E-02

105
Table 5.6: Change in the Large Early Release Frequency (yr1) due to Degradation

Case Mean 5% 50% 95%

Bellow Corrosion -6.27E-09 0 -2.96E-10 0.OOE+0O

25% Corrosion at Basemat -9.69E-09 0 O.OOE+00 1 .80E-08

50% Corrosion at Basemnat -2.62E-08 0 -6.88E-10 1.80E-08

50% Corrosion at Upper Floor 4.67E-08 0 2.27E-09 5.40E-08

65% Corrosion at Upper Floor 7.0 1E-08 0 4.86E-09 5.40E-08

25% Corrosion at Ice Basket 3.82E-08 0 2.27E-09 5.40E-08

50% Corrosion at Ice Basket 9.06E-08 0 3.93E-09 7.20E-08

Further examination of the change in LERF for each of the degraded cases shows that LERF

actually decreases for three of the degraded cases. Each of these cases, bellows corrosion and the

two basemat corrosion cases, has significantly high leak conditional probabilities at lower

pressures. The four corrosion cases at the upper floor and ice basket are dominated by

catastrophic rupture. This behavior explains the trends in LERF since only ruptures and

catastrophic ruptures are included in LERF in the PRA model.

The decrease in LERF is possible for the three leak-dominant cases because leak outcomes are

included in the small release frequency (SERF). Table 5.7 through Table 5.9 show the SERF,

SERF conditional on core damage, and the change in SERF relative to the Un-damaged (Current

Study) case. Table 5. 10 through Table 5.12 show the total frequencies (LERF + SERF).

As expected, SERF increases for the leak-dominant cases and decreases for the catastrophic

rupture cases. It should be noted that if there were a table similar to

Table 3.4 for SERF, the 50% corrosion at the basemat case would fall within Region 11 with a

ASERF of 1 .67E-7. A change proposed under the Regulatory Guide 1.174 risk-informed

methodology must also satisfyi other design goals. It must still maintain defense in depth and

acceptable safety margins, and therefore, changes in SERF may need to be addressed.

Table 5.12 illustrates that any form of degradation increases the total release frequency.

Table 5.7: Small Early Release Frequency (yr-')

Case Mean 5% 50% 95%

Un-damaged (Reference) 1.O1E-07 0 4.51lE-10 2.09E-06

Un-damaged (Current Study) 1.04E-07 0 4.29E-10 2.09E-06

Bellow Corrosion 1. 17E-07 0 5.85E-10 2.79E-06

25% Corrosion at Basemat 1.34E-07 0 5.3 7E- 10 3.28E-06

50% Corrosion at Basemat 2.71E-07 0 1. 11 E-09 5.44E-06

50% Corrosion at Upper Floor 8.72E-08 0 4.07E- 10 1.20E-06

65% Corrosion at Upper Floor 8.72E-08 0 3.92E-10 1 .20E-06

25% Corrosion at Ice Basket 8.72E-08 0 4.29E-10 1.20E-06

50% Corrosion at Ice Basket 8.6 1E-08 10 3.92E- 10 1.20E-06

106
Table 5.8: Probability of Small Early Containment Failure Conditional on Core Damage

Case Mean 5% 50% 95%

Un-damaged (Reference) 1 .78E-03 0 1 .22E-05 1. 16E-02

Un-damaged (Current Study) 1.82E-03 0 1. 16E-05 1. 16E-02

Bellow Corrosion 2.05E-03 0 1.58E-05 1.55E-02

25% Corrosion at Basemat 2.35E-03 0 1 .45E-05 1 .82E-02

50% Corrosion at Basemat 4.75E-03 0 2.99E-05 3.02E-02

50% Corrosion at Upper Floor 1.53E-03 0 1. 1OE-05 6.66E-03

65% Corrosion at Upper Floor 1 .53E-03 0 1 .06E-05 6.66E-03

25% Corrosion at Ice Basket 1.53E-03 0 1. 16E-05 6.66E-03

50% Corrosion at Ice Basket 1.5 1E-03 0 1.06E-05 6.66E-03

Table 5.9: Change in the Small Early Release Frequency (yr-') due to Degradation

Case Mean 5% 50% 95%

Bellow Corrosion 1.3 1E-08 0 1.55E-10 7.02E-07

25% Corrosion at Basemat 3.02E-08 0 1.07E-10 1. 19E-06

50% Corrosion at Basemat 1.67E-07 0 6.77E-10 3.35E-06

50% Corrosion at Upper Floor -1.65E-08 0 -2.22E-1 1 -8.89E-07

65% Corrosion at Upper Floor -1.65E-08 0 -3.70E- 11 -8.89E-07

25% Corrosion at Ice Basket -1.65E-08 0 0.00E+00 -8.89E-07

50% Corrosion at Ice Basket -1.77E-08 0 -3.70E-11 -8.89E-07

Table 5. 10: Total Early Release Frequency (yr-1 )

Case Mean 5% 50% 95%

Un-damaged (Reference) 8.42E-07 0 8.25E-10 1.42E-05

Un-damaged (Current Study) 5.71E-07 0 2.05E-09 1.22E-05

Bellow Corrosion 5.77E-07 0 1.91E-09 1.29E-05

25% Corrosion at Basemat 5.91E-07 0 2.15E-09 1.34E-05

50% Corrosion at Basemat 7.11E-07 0 2.04E-09 1.56E-05

50% Corrosion at Upper Floor 6.01E-07 0 4.29E-09 1. 14E-05

65% Corrosion at Upper Floor 6.24E-07 0 6.87E-09 1. 14E-05

25% Corrosion at Ice Basket 5.92E-07 0 4.3 1E-09 1. 14E-05

50% Corrosion at Ice Basket 6.44E-07 0 5.94E-09 1. 14E-05J

Table 5.11: Probability of Total Early Containment Failure Conditional on Core Damage

Case Mean 5% 50% 95%

Un-damaged (Reference) 1.48E-02 0 2.23E-05 7.9 1 E-02

Un-damaged (Current Study) 1.OOE-02 0 5.53E-05 6.77E-02

Bellow Corrosion 1.O1E-02 0 5.15E-05 7.16E-02

25% Corrosion at Basemat 1 .04E-02 0 5.82E-05 7.44E-02

50% Corrosion at Basemat 1 .25E-02 0 5.50E-05 8.64E-02

50% Corrosion at Upper Floor 1.05E-02 0 1. 16E-04 6.3 1 E-02

65% Corrosion at Upper Floor 1. 1OE-02 0 1.86E-04 6.3 1E-02

25% Corrosion at Ice Basket 1.04E-02 0 1. 17E-04 6.3 1 E-02

50% Corrosion at Ice Basket 1.13E-02 0 1.61E-04 6.32E-02

107
Table 5.12: Change in the Total Early Release Frequency (yf-') due to Degradation

Case Mean 5% 50% 95%

Bellow Corrosion 6.84E-09 0 -1.41E-10 7.02E-07

25% Corrosion at Basemat 2.05E-08 0 1.07E-10 1.21E-06

50% Corrosion at Basemat 1.41 E-07 0 -1.1 lE-l1 3.37E-06

50% Corrosion at Upper Floor 3.02E-08 0 2.25E-09 -8.35E-07

65% Corrosion at Upper Floor 5.36E-08 0 4.82E-09 -8.35E-07

25% Corrosion at Ice Basket 2.17E-08 0 2.27E-09 -8.35E-07

50% Corrosion at Ice Basket 7.30E-08 0 3.90E-09 -8.17E-07

The example plants examined here serves as good case studies indicating that one should be very

cautious about simply applying the ALERF criterion to evaluate the significance of containment

degradation. It is important to closely examine how degradation can increase the likelihood of

one failure mode while decreasing the likelihood of another, and evaluate the consequences of

these different modes. It cannot be stressed enough that the cases of degradation examined here

are extremely limited in scope. There are currently no means of predicting degradation prior to

its discovery. Since the location and specific nature of any degradation could dramatically affect

the containment capacity and risk, a detailed analysis of that scenario would be required. The

specific results reported in this study should in no way be applied to making regulatory decisions

on existing plants.

108
6. Risk Analysis of PWR Plant with Prestressed Concrete

Containment

The final containment investigated in this study is a prestressed concrete containment vessel at a

PWR nuclear power plant. As for the other three plants investigated in this study, a risk model

was developed for this plant in the NUREG- 1150 study. The original intent was to develop

containment fragility curves for this containment and integrate those into the NUREG-1 150 risk

model for this plant, as was done for the other three cases. As this study progressed, however, it

became evident that for a number of reasons, it would not be possible to use the original risk

model for this plant.

Because of the large effort involved in developing a risk model for a plant from the ground up, it

was decided to pursue an alternative route to perform a representative risk analysis of a PWR

plant with a prestressed concrete containment. It was observed that the representative prestressed

concrete containment has a volume roughly 30% greater than that of the reinforced concrete

containment studied in Chapter 3, but that the design pressures of these two containments are

very similar, 0.324 MPa (47 psi) for the prestressed concrete containment, and 0.3 10 MIPa (45

psi) for the reinforced concrete containment. The greater volume of the prestressed concrete

containment is due to the fact that it houses a 4-loop PWR reactor, while the reinforced concrete

containment houses a smaller, 3-loop PWR reactor. The increased amount of steam produced in

a loss of coolant accident (LOCA) in the 4-loop system requires a larger containment volume to

resist that load while keeping the design pressure roughly constant.

Because the reinforced concrete and prestressed concrete containments have approximately the

same design pressure, it is reasonable to use the structural models of the prestressed concrete

containment together with the risk model for the plant with the reinforced concrete containment.

If a prestressed concrete containment were chosen in the original design of the 3-loop PWR plant

instead of the reinforced concrete containment that was acutally built, it would exhibit roughly

the same structural response as is seen in the prestressed containment in the 4-loop PWR plant.

The actual structural dimensions (wall thickenss, amount of prestressing and reinforcing steel,

etc.) are somewhat larger in the containment with a larger volume because the forces are larger as

a result of the increased volume. However, if two containments of differing size are built to the

same design codes and design pressure, they will experience leak, rupture, and catastrophic

rupture failures at approximately the same pressures. This was a key premise of the series of

scaled containment model tests conducted at Sandia National Laboratories.

The risk assessment of the PWR plant with a prestressed concrete containment studied here

should be viewed as a study of the plant investigated in Chapter 3, but with an alternative design

scenario where a prestressed concrete containment was chosen in place of a reinforced concrete

containment. This is clearly not an analysis of an actual plant, but that is not the intention of this

study. The goal is to demonstrate the risk significance of various types of degradation that might

be observed at typical U.S. nuclear power plants.

The analysis of the prestressed concrete containment assesses the effects of corrosion in the liner

as well as degradation of the prestres sing tendons. The effects of corrosion in the liner wall are

investigated near the wall-basemat juncture and at the mid-height of the containment. Two cases

109
of tendon degradation at the mid-height are also examined. Figure 6.1 shows these, degradation

locations on a schematic diagram of ,the containment building.

42.67 mConcrete

containment

~A~egradation

corrosion

64.62 m

.......................... 1-..Basemat

corrosion

................ ............ exmnd erdto

% ........ .ex miedin this study

Figure 6. 1: Postulated Degradation in Pre stressed Concrete Containment

The corrosion locations were chosen because they are regions of potentially high liner strains,

where corrosion has been observed in similar containments, or potential regions of corrosion. It

should be re-emphasized that although the dimensions and other properties of the containment

vessel were taken from the drawings of an actual plant, the corrosion assumed for this study is not

representative of actual corrosion observed at that plant.

6.1 Structural Model of Prestressed Concrete Containment

Experimental evidence from a pressurization test of a 1:4 scale model of a prestressed concrete

containment vessel with a steel liner (Hessheimer et al, 2003) indicates that this type of

containment tends to resist pressures well beyond its design pressure. In the 1:4 scale model test,

the containment exhibited limited structural damage on a global scale up to 3.3 times the design

pressure. At that point, the leak rate exceeded the capacity of the pressurization system. An

inspection of the liner revealed 26 discrete tears, nearly all located at fabrication defects. The

onset of linear tearing and leakage occurred at a pressure 2.5 times the design pressure with an

average hoop strain of 0. 18%. After applying a leak-resistant coating to the liner and

110
repressurizing the containmnent with water and nitrogen gas, the containment resisted a pressure

approximately 3.6 times the design pressure. At this point, the containment catastrophically

ruptured at the mid-height of the cylinder. The initial average hoop strain at peak pressure was

1.02% and increased to 1.65% just prior to rupture.

The procedure used in this study to analyze the prestressed containment is very similar to that

used by Cherry and Smith (2001). In that study, an axisymmetric model of the containment

structure was developed to find the global strains. This model included the effects of the liner,

the concrete, the reinforcing steel, and tendons. The global strains were then used as boundary

conditions for refined 2-D liner submodels with corrosion damage and a 3-D hatch submodel. An

area of the liner with a reduced thickness modeled corrosion damage. A strain criterion was used

to determine the point when tearing occurred. Factors were used in the failure criterion to

account for the multi-axial stress state, the level of model refinement, and the level of refinement

in the analytical model.

A second study by Smith (2001) reexamined the prestressed containment including degradation

of the prestressing tendons. The analysis used a 300 wedge segment of the containment, rather

than the axisymmetric model employed in the first study. Seventeen different tendon degradation

scenarios were considered including losses in prestressing and tendon cross-sectional area (due to

corrosion). Degradation of both the vertical and horizontal tendons was considered. The same

strain criterion was used to determine the point of tearing in the liner.

The approach of this study closely follows the work done by Cherry and Smith (200 1) and Smith

(2001), with a few notable exceptions. The global 3-D 300 wedge model of the containment has

essentially remained unchanged. Local 2-D models are also used to model the corroded regions

in the liner. However, the finite element meshes of the corroded areas have been modified to

more realistically model the shape of a corroded region. In the meshes used by Cherry and

Smith, the corroded regions were rectangular in shape, which resulted in stress concentrations at

the corners of those regions. The edges of the corroded regions have been rounded, and the

transition between the corroded and non-corroded areas has been made more gradual. In

addition, the 3-D model of the hatch used in the previous work was not analyzed here. Strain

concentrations caused by penetrations are taken into account with strain magnification factors

similar to those used in the reinforced concrete containment analysis.

The work of Cherry and Smith (2001) Smith (2001) was primarily focused on finding the failure

pressure of degraded containments. For the purposes of this study, it is important to not only

characterize the strength of degraded containments, but to find the difference between the

containment in its original and degraded conditions for the purposes of computing the change in

risk. For this reason, an additional effort has been made to account for the effects of local

penetrations, which are important contributors to early failure in the un-degraded model. In

addition, failure criteria are established for leak, rupture, and catastrophic rupture, whereas the

previous studies only considered leak in their failure estimates.

6.1.1 3-D Global Models

As mentioned previously, the global behavior of the containment is modeled with essentially the

same 3-D 30' wedge finite element model used by Smith (2001). The 3-D finite element mesh of

the containment is shown in Figure 6.2(a).

III
(a) Original Mesh (b) Deformed at 1.08 MPa (157 psi)

Figure 6.2: 3-D Wedge Finite Element Model of Prestressed Containment

The concrete is modeled using the ANACAP-U (ANATECH, 1997) constitutive model, which is

linked with the ABAQUS program. 20-node bricks are used to model the concrete components.

Nonlinear behavior of the concrete is modeled with a stress-strain law evaluated at element

integration points, so the effects of cracking and crushing are "smeared out" over an element.

When a tensile strain criterion, which takes multi-axial stress states into account, is met at an

integration point, a fixed smeared crack is initiated and softening occurs. A hardening-softening

model accounts for the nonlinear behavior of concrete in compression.

Reinforcing bars are modeled by embedding them within the concrete elements with the

ABAQUS *REBAR conmmand. A uniaxial model accounts for hardening in the reinforcing steel.

The hoop and dome tendons are also modeled using reinforcing bars, while the vertical tendons

are modeled with truss elements. The liner is modeled with 3-D, 8-node shell elements directly

attached to the concrete elements on the inside face of the containment. Nonlinear behavior of

the steel in the shell is modeled using a steel plasticity model. Nonlinear spring elements are used

to approximate the contact conditions between the containment and the soil below. The spring

elements have a high elastic stiffness in compression, and have no strength in tension.

The containment model is subjected to a monotonically increasing internal pressure loading. An

increasing temperature is applied to the containment in conjunction with the pressure loading.

Initially, the internal surface (liner) of the containment has a temperature of 2 10 Celsius (700

Fahrenheit). This increases to a maximum of 1800 Celsius (3560 Fahrenheit) at a pressure of 1.0

MPa (145 psi). Since concrete cracking and reinforcing bar yielding dissipate the liner strains,

the thermal loads do not have a significant effect. Because the analysis is performed using load

control, it reaches a point where small increases in the pressure result in very large deformations.

At this point, the analysis cannot continue because obtaining a converged solution becomes too

difficult. This generally occurs when the pressure load is around 1. 1 MPa (160 psi) for this

model, but varies depending on the input parameters.

112
Figure 6.2(b) shows the deformed shape of the 3-D model for a typical case near the end of the

analysis. Deformations have been magnified by a factor of 5 in this figure. It is evident from the

figure that hoop strains are very large near the mid-height of the containment. There are also

large bending deformations in the wall-basemat junction.

6.1.2 Local Models with Liner Corrosion

In the analysis of this containment, the strain magnification factors described in Section 2.4.2.1

are used to approximate strain concentrations in the liner at discontinuities, while detailed 2-D

finite element models are used to model regions of hypothetical corrosion. To determine the

relative significance of corrosion in different locations, two cases of liner corrosion are assumed:

at the mid-height of the containment, and in the wall just above the junction with the basemat.

In both cases, corrosion is evaluated at two depths of penetration : 50% and 65% of the liner

thickness. The finite element models for both cases are identical, with the corrosion assumed to

have occurred over a region 14 cmn (5.5 in) wide and 7.3 cm (2.9 in) high. The finite element

mesh of this region is shown in Figure 6.4. Figure 6.3 illustrates the full mesh, which covers a

95.3 cm (3 7.5 in) by 261 cm (105 in) region. At the boundaries of the mesh, the average length

of an element edge is 50 mmn (2 in), while in the corroded area, the mesh is refined considerably

and the average element length is approximately 2.54 mm (0. 1 in).

Displacements are extracted from the 3-D global analyses and used as boundary conditions for

the submodels. Symmetry conditions are set on the right side of the submodel, and displacements

imposed on the top, bottom, and left side. Displacements are also imposed at the location of Lsection steel anchors running in the vertical direction. These L-sections are modeled in the 2-D

mesh with beam elements.

113
displacements/

imposed Z symmetry

]I- region of

corrosion

Figure 6.3: Submodel Finite Element Mesh

In both of these cases, a 2.54 cm (I in) layer of elements surrounding the fully corroded region is

used to make a more gradual transition from the un-damaged area to the corrosion zone. In that

layer of elements, the corrosion is assumed to penetrate 25% and 32.5% of the wall thickness for

the 50% and 65% corrosion cases, respectively. In these models, the steel is modeled using a

plasticity model.

Figure 6.4: Corroded Region in Submodel Finite Element Mesh

The results from the local models are post-processed to deter-mine the point at which tearing

(leak), rupture, and catastrophic rupture occurs. For leak, the effective plastic strains are

multiplied by factors to account for the effects of the multiaxial stress state, corrosion, gauge

length, and modeling uncertainty, as described in Section 2.4. 1.1.

114
6.1.3 Degraded Tendon Analyses

In addition to examining the effects of corrosion in the liner, two cases of tendon degradation are

studied here. Smith (2001) examined 17 different tendon degradation cases. Here, two of these

cases are studied within the risk assessment framework. The first degraded case reduces the area

of 20% of the hoop tendons grouped at the midheight of the cylinder by 50%. It is assumed that

the area could have been reduced by general corrosion, pitting, stress corrosion cracking, or

hydrogen embrittlement (Smith, 2001). The second case reduces the prestressing force in the

same 20% of tendons at the midheight by 50%. Lower than expected levels of prestressing have

been observed in existing plants (Ashar et al., 1994) possibly due to improper calibration of the

jacks during initial post-tensioning, higher than expected prestressing losses, and failures in

quality control. The 3-D global model was modified to introduce these two cases of tendon

degradation.

6.1.4 Structural Analysis with Best Estimate Properties

The primary focus of the structural analysis in this study is to develop fragility curves to interface

with the risk model. However, it is instructive to study the results of a baseline analysis that uses

the median values of the input parameters that are randomly generated for the LHS analyses.

Six potential liner failure modes are considered: failure at the four locations of geometric

discontinuities for which magnification factors are used (see Section 2.4.2. 1), failure at a

corroded region at the wall midheight, and failure at a corroded region on the wall near the

basemat. In addition, two cases of tendon degradation are examined with failures determined at

the four locations of geometric discontinuities. To investigate the potential for failure (leak) at all

of these locations, the 3-D global model is analyzed, and results are extracted for use as

displacement boundary conditions for the two 2-D local corrosion models. The two local

corrosion models are run with 50% and 65% corrosion and post-processed to find the most

critical value of ýpat every loading step using the steel leak criterion (see Section 2.4. 1. 1). A

separate post-processing tool is applied to the results of the 3-D models to apply appropriate

magnification factors to find EPfor the four selected discontinuity locations at every loading

increment. The uniaxial plastic failure strain, 2 fau,' was assumed to be 25% for these analyses.

The gauge length factor was assumed to be 4.0 for the local corrosion models in this baseline

analysis.

Figure 6.5 shows the plot of the ratio of to toaiI (0.25) for the 4 discontinuities and 2 liner

corrosion locations as a function of internal pressure for the baseline analysis (no tendon

degradation). A horizontal line has been drawn at 1.0 to show the failure criterion. It is evident

that the failure condition is met first at the wall-basemat junction, and that the discontinuity at the

springline appears to be the least critical location. From this analysis, it appears that a

containment without any degradation would leak at 0. 744 MPa (107.8 psi) at the wall-basemat

junction. If the postulated corrosion were present at the basemat, it would fail at that location at

an internal pressure of 0.904 MIPa (131.1 psi) and 0.892 MIPa (129.4 psi) for 50% and 65%

corrosion, respectively. Leakage near the corroded midheight location does not occur until 1.070,

MPa (155.3 psi) and 1.030 MPa (149.4 psi) for 50% and 65% corrosion, respectively. Leakage

occurs at the wall-basemat junction prior to leak in the corroded basemat location. Table 6.1

summarizes the leak pressures for each location.

Although Cherry and Smith (2001) assumed somewhat different corrosion patterns, it is useful to

compare their failure pressures with those obtained in this study. For their best estimate model of

115
the containment, they found that the un-damaged containment failed at 0.99 MI~a (143 psi). Here,

we predict failure at the wall-basemat junction at 0.744 MIPa (107.8 psi). A possible reason for

the lower capacity in the current study is the use of the magnification factors (see Section 2.4.2. 1)

to determine failure at the discontinuities within global model. The magnification factors enable

the use of global models that do not include detailed modeling of discontinuities. The analysis by

Cherry and Smith did not use the magnification factor technique, but used the strains from a

coarsely meshed axisymmetric model to determine failure.

With corrosion 50% through the wall, Cherry and Smith (2001) found that the containment failed

at 0.93 MPa (135 psi) when the corrosion was at the mid-height and 0.92 M[Pa (134 psi) with

corrosion at the basemat. The failure pressures for the un-damaged model and midheight

corrosion obtained in the current study are somewhat higher than those found by Cherry and

Smith. This may be due to the fact that Cherry and Smith obtained the boundary conditions for

their submodel from an axisyrnmetric global model. Cherry and Smith also assumed a slightly

different corrosion shape and location. These are possible reasons for the higher capacity of the

corroded midheight area found in the current study.

20 - Leak Stearn Penetration 20 - Leak WaLt-Basemrat Juriction

-Leak Hatch

Leak Springline Crsoe

-- Leak Base 50% CorrosionCtrOw

-- Leak Base 65% Corrosion

1.5 -- Leak Midheight 50% Corrosion I

-- Leak Midheight 65% Corrosion

Rupture No Corrosion

-.- Rupture Baae 50% Corrosion

-- -Rupture Base 65% Corrosion

o1.0 Rupture Midrreight 50% Corrosion

.Rupture Miciheight 65% Corrosion/

-Catastrophic Rupture

LL 0.5 O inP sr

0.0

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Pressure (MPa gauge)

Figure 6.5: Failure Potential at Liner Corrosion and Discontinuity Locations

Figure 6.5 and Table 6.1 also include failure curves and pressures for five rupture cases: the

original containment with no corrosion, 50% corrosion at the basemat, 65% corrosion at the

basemat, 50% corrosion at the midheight, and 65% corrosion at the midheight. The procedure in

Section 2.4.2.2 is used to compute the ratio of the total rupture area, A total ý to the rupture area

limit of 0.028 m2 (0.3 ft2), as a function of pressure. The four features, steam penetration, wallbasemat junction, hatch, and springline, are each assumed to contain four cracks ( n,) each after

the leak criterion has been reached. The choice of four cracks at each location is somewhat

arbitrary, though based on the upper limit of the number of tears observed in the 1:6 scale

reinforced concrete containment testing at Sandia National Laboratories (Horschel, 1992). The

number of cracks at each location could have been introduced as a random variable, but due to the

approximate nature of the rupture estimate employed here, a random variable with a large

116
uncertainty is imposed on the total rupture area. One crack is assumed at the basemnat and

midheight locations for cases considering corrosion.

For the two midheight and two basemat corroded cases, leak occurs only slightly before the

overall rupture failure, if not after. This has only a negligible effect on the total rupture area,

since only one ciack is assumed to initiate at the corroded locations. Therefore, the rupture

curves for the original case with no corrosion and the two rnidheight corrosion cases and 50%

basemat corrosion case share the same curve. The 65% basemnat corrosion case increase diverges

slightly from the other rupture cases, but only after failure. Obviously, assuming more than one

corroded location for each case will increase the rupture area and lower the rupture pressure.

Variation in the total area assumed to cause rupture (0.028 m2

' or 0.3 ft2) will also affect the

rupture pressure. As mentioned previously, a large uncertainty is imposed on the total rupture

area to account for the approximate nature of the rupture criterion.

Finally, Figure 6.5 and Table 6.1 include the simple estimate for catastrophic rupture described in

Section 2.4.2.3. It is clear from the failure pressures that catastrophic rupture will occur prior to a

leak failure at many of the discontinuities and small regions of corrosion.

Table 6. 1: Summary of Locations and Failure Pressures without Tendon Degradation

Location Failure Pressure

MPa (psig)

Leak Steam Penetration 0.92 1 (133.6)

Leak Wall-Basemnat Junction 0.744 (107.8)

Leak Hatch 0.935 (135.7)

Leak Springline 1.035 (150.1)

Leak Base 50% Corrosion 0.904 (131.1)

Leak Base 65% Corrosion 0.892 (129.4)

Leak Midheight 50% Corrosion 1.070 (155.3)

Leak Midheight 65% Corrosion 1.030 (149.4)

Rupture No Corrosion 0.904 (131.1)

Rupture Base 50% Corrosion 0.900 (130.6)

Rupture Base 65% Corrosion 0.900 (130.6)

Rupture Midheight 50% Corrosion 0.904 (131.1)

Rupture Midheight 65% Corrosion 0.904 (13 1.1)

Catastrophic Rupture 0.980 (142.1)

Figure 6.6 and Table 6.2 show the failure functions and pressures for the case with 50% area loss

of 20% of the midheight tendons. With the exception of leak at the springline, a failure mode

which did not occur during the analysis, all of the discontinuities failed at lower pressures than in

the undegraded tendon case. The pressures at the steam and hatch penetrations were most

effected since they reside closest to the midheight of the containment. The rupture pressure also

decreases significantly. Most significant is the reduction in the catastrophic rupture pressure

which is now predicted to occur prior to leak or rupture in any location. This is due to the 50%

reduction in the area of the tendons when computing the catastrophic rupture pressure.

117
2.0

1.5

o 1.0 -

U.

u-0.5

0.0-

- Leak Steam penetration

- Leak WaII-Baaemat Junction

Leak Hatch

-Leak Springfine

Rupture

-Catastrophic Rupture

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Preaaure (MPa gauge)

Figure 6.6: Failure Potential at Discontinuity Locations for 50% Area Degradation

in the Midheight Tendons

Table 6.2: Summary of Locations and Failure Pressures with 50% Area Reduction of the

Midheight Tendons

Location Failure Pressure

MPa (psig)

Leak Steam Penetration 0.662 (96.0)

Leak Wall-Basemat Junction 0.733 (106.3)

Leak Hatch 0.642 (93.2)

Leak Springline No failure during analysis

Rupture 0.669 (97.0)

Catastrophic Rupture 0.608 (88.2)

Figure 6.7 and Table 6.3 show the failure functions and pressures for the case with 50% loss of

the prestressing for 20% of the midheight tendons. All of the discontinuities failured at lower

pressures than in the undegraded tendon case, but in general not as low as the 50% area reduction

case. The pressures at the steam and hatch penetrations were most affected since they reside

closest to the midheight of the contaimnment. The catastrophic rupture pressure remains the same

as the undegraded tendon case since the level of prestressing in not factored into the catastrophic

rupture criterion.

118
2.0

0 1.0

U.0.5

- Leak S tearn Penetration

-Leak WaU-Basemat Juncton

Leak Hatch

Leak Spdringline

Rupture

-Catastroptic Rupture 1/

I F Design Pressure

0.0

0.00 0.20 0.40 0.60 0.80

Pressure (MPa gauge)

1.00 1.20 1.40

Figure 6.7: Failure Potential at Discontinuity Locations for 50% Loss of

Prestressing of the Midheight Tendons

Table 6.3: Summary of Locations and Failure Pressures with 50% Prestressing Reduction of the

Midheight Tendons

Location Failure Pressure

NMa (psig)

Leak Steam Penetration 0.768 (111.4)

Leak Wall-Basemat Junction 0.731 (106.0)

Leak Hatch 0.894 (129.7)

Leak Springline 1.013 (146.9)

Rupture 0.806 (116.9)

Catastrophic Rupture 0.980 (142.1)

6.2 Fragility Analysis of Degraded Prestressed Concrete Containment

The principal goal of the current study is to integrate structural analyses of degraded

containments with risk analysis models to understand the significance of the degradation from a

risk-informed perspective. Fragility curves of containments under pressurization with and

without degradation serve as the interface between the structural and risk analyses. As explained

in Section 2.5, Latin Hypercube Sampling is used in this study to generate sets of random

variables to be used as input to the structural finite element analyses. For this containment, 23

input parameters were selected as random variables, and 30 samples of those parameters were

taken for analysis.

Of the 23 input parameters, 18 describe the inherent randomness, or aleatory uncertainty, in the

basic properties of concrete, reinforcing bars, and liner steel. The remaining 5 parameters

describe epistemnic uncertainty, or uncertainty in the ability to characterize the failure pressure.

Several of the random input parameters are correlated with others. For concrete, the tensile

119
strength, ft. and modulus of elasticity, E~, are correlated with the cylinder compressive

strength, f'. Likewise, there is correlation between the yield strength and ultimate strength of

steel.

Whenever possible, statistical test data was used as the basis for the probability distributions in

this study. When such data was unavailable, engineering judgment was used to provide

reasonable estimates of uncertainty. Based on as-built material properties from Butler and

Fugelso (1982), the elastic modulus of concrete in the containment is related to the compressive

strength as:

E, = c 70000 fP (6.1)

where c, is a random variable with a median of 1.0 and a coefficient of variation of 0.077. From

Mirza et al. (1979), f ', in the containment is computed as:

f, t= c2 8.31f_ýc (6.2)

where c., has a median of 1.0 and a coefficient of variation of 0. 196. Units of psi are used in

both of these equations. Under average control conditions, Mirza et al. suggest that a coefficient

of variation (COV) of 0. 15 can be assumed for f'c .

The concrete in the base slab varies from the concrete in the containment. The relationship

between the elastic modulus and tensile strengths with the compressive sirength follow as,

Ec = c 65000J ý, (6.3)

from Butler and Fugelso (1982) with a coefficient of variation of 0.077, and

f=c 8. 3 F,- (6.4)

from Mirza et al. (1979) with a coefficient of variation of 0. 196.

The prestressed containment investigated in this study has reinforcing bars and prestressed steel

tendons. For both materials, the elastic modulus, E, is assumed to be independent of the yield

strength, fy I and the ultimate strength, f, . Correlation is induced between fyand f,, in a

manner similar to that for concrete:

fy =s rf. (6.5)

where s is a random variable with a median of 1.0. The variable r is the ratio of the yield stress

to the ultimate stress, and differs depending on the type of steel. For the reinforcing bars, a value

of 0.63 was assumed for r (Weatherby, 1988). For tendons, this value was set at 0.875

(Weatherby, 1988), and for the liner steel, a value of 0.535 was used.

Additional uncertainties include the variation in the corrosion depth. This is applied to the

corroded thickness of the submodels of the liner and to the two degraded tendon cases. For the

50% reduced area tendons, the corrosion depth uncertiainty is multiplied by 50% of the normal

tendon area for the hoop tendons at the midheight thoughout the 30 analyses. For the 50% loss in

prestressing, the corrosion depth uncertainty is multiplied by the normal prestressing values for

the hoop tendons at the midheight of the containment thoughout the 30 analyses. The normal

prestressing levels for the tendons are 970 MPa for the hoop tendons, 1014 MPa for the

meridonal tendons, and 981 MPa for the dome tendons. Even for the undegraded tendon cases,

each of the prestressing levels is multiplied by a prestressing uncertainty with a median of 1.0 and

a COV of 0.03.

120
Five separate variables are used to describe the epistemic uncertainty. Variable describes the

uncertainty inherent in predicting the global strains, the local strains from the 2-D submodels with

corrosion, the strain magnification in the presence of corrosion, the calculation of the rupture

area, and the simple estimate for catastrophic rupture.

Each of these variables has a median value of 1.0. A COV of 0.3 was assumed for the global

strain prediction variable, IFEM-u, . The magnification factors for the liner discontinuities for the

prestressed containment (Figure 2. 10) are simply multiplied by the uncertainty factor in Equation

2.9.' Failures at the these discontinuities are determined from the undegraded containment

analyses and for both of the degraded tendon cases.

The COV of the local model uncertainty factor, JFEM-U , was set to 0.35 because it was felt that

there is more uncertainty in the local models than in the global models. For the local detailed

models, Equation 2.1 is used to compute the magnified strains. Since the local models contain

corrosion, the corrosion factor, f~equals 2 and is multiplied by an uncertainty factor, f~~with

a COV of 0.20.

The final two epistemic factors account for the uncertainty in the rupture area, fU,- and

catastrophic rupture pressure, fa- Since the calculation of the rupture area in Equation 2.12

contains several approximations, a large COV is employed, equal to 0.40. The simple method

used here to compute the catastrophic rupture pressure (Equation 2.13) should provide a

reasonable estimate, enabling the use of a low COV of 0. 10. This uncertainty is in addition to the

variation in the ultimate strengths random variables used in Equation 2.13.

Table 6.4 shows all of the random input parameters. This table shows the median values of the

parameters, a measure of the variation assumed for the parameter, and the type of distribution.

For variables with normal distributions, the COV is used as the measure of variation, while 83 is

used for variables represented with a lognormal distribution.

A total of 30 sets of these input parameters Were generated based on analyses using the specified

distribution functions. Once the analyses were run, the 30 leak pressures were used to develop

fragility curves for each of the four locations of linear discontinuity. Figure 6.8 shows the

fragility curves based on the sorted analyses values and associated lognormal curve fits for the

case with no tendon degradation. The fragility curves represent the leak pressure for the four

discontinuity locations. Figure 6.9 shows the fragility curves for leak at the two corroded

locations, basemat and midheight, at the two levels of corrosion, 50% and 65%. These plots

indicate that increasing the level of corrosion from 50% to 65% of the liner thickness has only a

minimal effect.

121
Table 6.4: Random Input Parameters

Property Median COV/, Distrib~ut~ion77

Compressive Strength (f) 45.0 MPa 0.15 Lognormal

(6.529 ksi) _____j________

Elastic Modulus factor (c,) 1.0 0.077 jNormal

Tensile Strength factor (c2 ) 1.0 0.196 Normal

Concrete (Base Region)404Ia 15 T L

[Compressive Strength (Jf'c 40.46 ksi) 01 Lognormal

Elastic Modulus factor (c,) 1 :o 0.077 Normal

Tensile Strength factor (c2 ) 1.0 0.196 Normal

Reinforcing Steel _______ ____ _______

Ultimate Strength (f. 721.2 MiPa [0.09 Lognormal ______________________(104.6 ksi) j____I______

Yield Strength Factor (s) 1.0 j0.07 Normal

Elastic Modulus (E,) 200 Gpa 0.06 Normal _________________________(29000 ksi) I_____I_______

Liner Steel

Ultimate Strength f)576.8 MiPa 0.09 Lognormal

________________________(83.66 ksi)

Yield Strength Factor (s) 1.0 0.07 Normal

Elastic Modulus (E,) 200 GPa 0.06 Normal

(29000 ksi)

Uniaxial Failure Strain (ejau) 0.25 0.12 Normal

Corrosion Depth Uncertainty 1.0 0.10 Normal

(also used for tendon

degradation)_____________________

Tendon Steel___________ _______

Ultimate Strength (f)1649 MiPa 0.09 Lognormal

________________________(239.1 ksi) ____ ______

Yield Strength Factor (s) 1.0 0.07 Normal

Elastic Modulus (E,) 200 Gpa 0.06 Normal

________________________(29000 ksi) ____________

Tendon Prestressing Factor 1.0 0.03 Normal

Epistemic Uncertainty

Axisymmetric Model Strain 1.0 0.30 Lognormal

Factor Uncertainty (JFEM, )

Sub-model Strain Factor 1.0 0.35 Lognormal

Uncertainty (JFEMu)

Corrosion Factor Uncertainty 1.0 0.20 Lognormal

Leak Area for Rupture 1.0 0.40 Lognormal

Uncertaint

Catastrophic Rupture 1.0 0.10 Lognormal

Uncertainty

122
1.0

0.8

2

uL 0.6

.0

2

(L

0.2

0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Figure 6.8: Fragility Curves for Leak at Discontinuity Locations

1.0

0.8 I2

a.

0.6 IDesign Pressure

o Leak - Base 50% Corrosion

" Leak - Base 65% Corrosion

" Leak - Midheight 50% Corrosion

" Leak - Midheight 65% Corrosion

0.4 I0.2 Ia ACIP

0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Pressure (MPa gauge)

1.4 1.6 1.8 2.0

Figure 6.9: Fragility Curves for Leak at Corroded Locations

As discussed previously, the rupture threshold is assumed to be reached when the total crack

opening caused by initiated leaks, exceeds 0.028 m2 (0.3 ft2) . Figure 6. 10 shows the rupture

fragility curves for the five cases examined in this study. Since no significant change in pressure

occurs for the both corroded midheight and the 50% basemat cases, the curves for these cases

remain identical. The crack opening near the basemnat with 65% corrosion are large enough to

cause a slight decrease in rupture pressure. Figure 6. 10 also illustrates the fragility curve for

catastrophic rupture. Since the criteria for catastrophic rupture is not affected by the corrosion in

the liner, the catastrophic rupture fragility remains the same for each of the 4 corroded cases as

well as the undegraded case.

123
1.0

0.8 I-

*Rupture - No Corrosion

*Rupture - Base 50% Corrosion

*Rupture - Base 65% Corrosion

*Rupture - Midheight 50% Corro,

*Rupture - Midheight 65% Corro~

*Catastrophic Rupture '0 u 0.6

0.4

2

0.2

0.0

IionV

sion

Design Pressure

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Pressure (MPa gauge)

1.4 1.6 1.8 2.0

Figure 6. 10: Fragility Curves for Rupture and Catastrophic Rupture

Figure 6.11 illustrates the fragility curves for leak at the 4 discontinuity locations, rupture, and

catastrophic rupture for the case with 50% area degradation in the midheight tendons.

Catastrophic rupture occurs at approximately the same pressure as the leak locations and rupture.

This is due to the leak and rupture pressures being set to the catastrophic rupture pressure if it is

smaller than the computed leak or rupture pressure.

1.0

0.8

2

LL 0.6

S0.4

2

aS.,-.

DeIg Pressure

" Leak - Steam Penetration

a Leak - Wall-Basemat Junction

-Leak - Hatch

* Leak - Springline

* Rupture

* Catastrophic Rupture

k

0.2 F00l

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Pressure (MPa gauge)

1.4 1.6 1.8 2.0

Figure 6.11: Fragility Curves for 50% Area Reduction in Midheight Tendons

124
Figure 6.12 shows the fragility curves for leak at the 4 discontinuity locations, rupture, and

catastrophic rupture for the case with 50% prestressing loss in the midheight tendons. Due to the

shape of the distribution for leak and the wall-basemat junction, the lognormal curve fits required

one curve fit for high probabilities and one curve fit for low probabilities.

1.0

0.8

2

.0

Design Press 0 , a + DO

a a (* *

0 0z C*

00o .

* Leak - Steam Penetration

* Leak - Wall-Basemat Junction

Leak - Hatch

* Leak - Springline

* Rupture

* Catastrophic Rupture

0.2 -

0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Pressure (MPa gauge)

1.4 1.6 1.8 2.0

Figure 6.12: Fragility Curves for 50% Prestressing Loss for the Midheight Tendons

The leak fragilites for the four discontinuity locations were used to develop a cumulative

probability of failure curve for the original, uncorroded, containment. Figure 6.13 shows the

cumulative probability of failure (leak-) curves obtained in the current study for the containment

with corrosion degradation at the midheight and at the base, tendon degradation, and the fragility

of the containment in its original condition. The drop in capacity due to corrosion at the

midheight and basemnat is negligible, while the shifts due to tendon degradation prove more

significant.

125
1.0

0.8

LL

S0.6

CL

~,0.4

E= 0.2 C-,

Design Press

kwre - ~~Original - J orso

-Base 50%Coosn

-Base 65%Coosn ___Midheight50Corsn

-Midheight65Corsn Tendon Ana50

'11Original, Base 50%, Base 65%,

MMidtheight 50%, Midheight 65%

o Corrosion

Corrosion

Corrosion

50% Corrosion

65% Corrosion aa 50%

stressing 50%

F

0.01

0.10 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Cumulative Probability of Failure Curves for Original and Degraded Prestressed

Containment

Figure 6.13:

The conditional probability of failure curves were computed for each of the seven cases and

shown in Figure 6. l4Figure 6.20. Since the rupture and catastrophic curves are relatively

constant throughout the liner corrosion cases, the conditional probability distributions are

extremely similar. At low pressures (P < 0.70 MPa), the probability of leak is equal to 1.0 with

the rupture and catastrophic rupture probabilities at 0.0. With increasing pressure, the rupture and

the catastrophic rupture conditional probabilities begin to rise. The leak probability decreases

quickly as the rupture probabilities increase. The rupture curve peaks at approximately 1.0 ML~a.

At this point, both the leak and rupture curves decrease gradually to probabilities of 0.0 and the

catastrophic curve increase to a probability of 1.0 at approximately 1.4 MPa.

Figure 6.19 shows the conditional probabilities for the 50% tendon area degradation case. These

curve are significantly different that the undegraded and liner corrosion curves. For one, there is

essentially no rupture probability, and the leak and catastrophic rupture curves are shifted to the

left (lower pressures). Figure 6.20 illustrates the 50% loss in tendon prestressing case. These

conditional probabilities are similar to the undegraded and liner corrosion curves, but with a

slightly larger peak rupture probability which occurs at a slightly lower pressure.

126
1.0

~ 0.8 Rupture

- Catastrophic Rupture

0L

p0.6

2

0.4 Design Pressurej

0.2

0.0 L--- ---L

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Figure 6.14: Conditional Probability of Failure for Original Containment (No Corrosion)

1.0

T

S0.8

LJL

0.

CL 0.6

Fa a

0

S0.2

0.0 1-

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Pressure (MPa gauge)

Figure 6.15: Conditional Probability of Failure for 50% Corrosion at Basemnat

2.0

127
1.0

0.8 Rupture

cc -Catastrophic Rupturee LL

P0.6

2

0- 0.4 Design Pressurle

S

(S 0.2

0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Pressure (MPa gauge)

Figure 6.16: Conditional Probability of Failure for 65% Corrosion at Basemnat

1.0

- Leak

2 Ruptur

2 0.8Rutr

. - Catastrophic Rupture

0L

P0.6

2

750.4 Design Pressure

C:

0

r

000.2

0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Pressure (MPa gauge)

Figure 6.17: Conditional Probability of Failure for 50% Corrosion at Midheight

2.0

2.0

128
1.0

20.8 Rupture

i -Catastrophic Rupture

0

p0.6

CO

-fi0.4 Design Pressure r

0

S0.2

0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Pressure (MPa gauge)

Figure 6.18: Conditional Probability of Failure for 65% Corrosion at Midheight

2.0

1.0

.~0.8

-Leak

0 Rptur 0.6 Design Pressure -Caastop

0.4

C

0.

*0

0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Pressure (MPa gauge)

1.4 1.6 1.8 2.0

Figure 6.19: Conditional Probability of Failure for 50% Area Reduction of the Midheight

Tendons

129
1.0

m~ 0.8

L. -Leak

0 Rupture

0.6 - Catastrophic Rupture

0

S0.4 Design Pressure

0.

0

0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Pressure (MPa gauge)

Figure 6.20: Conditional Probability of Failure for 50% Loss of Prestressing for the

Midheight Tendons

6.3 Risk Analysis Results

Table 6.5 shows the CDF results from NUREG 1150 for the reinforced concrete containment

analyzed in Section 3. As explained at the beginning of this chapter, because the risk model for

the prestressed containment was not available, the risk model for the PWR plant with a reinforced

concrete containment described in Chapter 3 is used instead. The two containments have roughly

the same design pressure, so this can be viewed as an assessment of the plant in Chapter 3, but

with a hypothetical prestressed concrete containment design option. Because the containment

response does not affect the CDF for the plant for the reinforced concrete containment, the results

are the same for all of the cases studied.

Table 6.5: Core Damage Frequency (yr-)

ICase IMean 15% 150% 195%1

1All 14.1E-5 I6.8E-6 I2.3E-5 I1.3E-4 I

Table 6.6 shows the LERE results obtained from the current study, Table 6.7 shows the

probability of large early containment failure conditional on core damage, and Table 6.8 shows

the change in LERE relative to the un-damaged state due to degradation for the degradation types

and extents evaluated here.

130
Table 6.6: Large Early Release Frequency (yrf')

Case Mean 5% 50% 95%

Un-damaged (Current Study) 1.50E-7 0 1.98E-10 2.23E-6

50% Corrosion near basemat 1.41E-7 0. 1.83E-10 2.04E-6

50% Corrosion at midheight 1.4 1E-7 0 1.83E-10 2.04E-6

65% Corrosion near basemat 1.41 E-7 0 1.83E-10 2.04E-6

65% Corrosion at midheight 1.4 1E-7 0 1.83E-10 2.04E-6

50% Tendon Area Reduction 6.97E-7 0 1.81E-9 1.45E-5

50% Tendon Prestressing Loss 1.51E-7 2.03E-10 2.23E-6

Table 6.7: Probability of Large Early Containment Failure Conditional on Core Damage

Case Mean 5% 50% 95%

Un-damaged (Current Study) 0.0037 0 8.61E-6 0.0171

50% Corrosion near basemat 0.0034 0 7.94E-6 0.0157

50% Corrosion at midheight 0.0034 0 7.94E-6 0.0 157

65% Corrosion near basemat 0.0034 0 7.94E-6 0.0 157

65% Corrosion at midheight 0.0034 0 7.94E-6 0.0 157

50% Tendon Area Reduction 0.0170 0 7.86E-5 0.1110

50% Tendon Prestressing Loss 0.0037 0 8.84E-6 0.0171

Table 6.8: Change in the Large Early Release Frequency (yr') due to Degradation

Case Mean 5% 50% 95%

50% Corrosion near basemat -8.79E-9 0 -1.54E-1 1 -1.86E-7

50% Corrosion at midheight -8.79E-9 0 -1.54E-l1 -1.86E-7

65% Corrosion near basemat -8.79E-9 0 -1.54E-1 1 -1.86E-7

*65% Corrosion at midheight -8.79E-9 0 -1.54E-1 1 -1.86E-7

50% Tendon Area Reduction 5.47E-7 0 1.61E-9 1.22E-5

50% Tendon Prestressing Loss 1. 17E-9 0 5.26E-12 0

The key risk criteria for acceptance of a proposed plant change in Regulatory Guide 1. 174

(USNRC, 2001) are the baseline values of CDF and LERIF, and the changes in those values due to

the proposed modification, denoted as ACDF and ALERF. The acceptance criteria must be met

for both the pairs of ACDF and CDF and of ALERIF and LERIF. Because CDF is unaffected by

the containment properties in this particular plant, ACDF is 0, so the effects of the change clearly

fall within Region III for the CDF acceptance criteria, which can be seen in Figure 2. 1. In Region

III, it is not actually necessary to compute the baseline CDF, although for these analyses, the

mean CDF was computed, and has a value of 4. 1E-5, which is clearly acceptable.

For both the lower bound and best estimate fragility curves, there is a reduction in LERIF relative

to the un-damaged containment in the case where corrosion exists near the basemat or the

midheight. Because LERIF is reduced by the increases in leak (leak is included in SERF, not

LERIF) in these particular case, ALER1F is negative, so the effects of the change are assumed to

fall within Region III for the LERF acceptance criteria, which can be seen in Figure 2.2.

Therefore, the corrosion cases investigated in this study would be permissible modifications from

a risk standpoint by Regulatory Guide L.174.

131
The two degraded tendon cases increase the probability of catastrophic rupture, which is included

in LERF. The slight increase in LERF for the 50% reduction in tendon prestressing case falls

within the acceptable Region 111. The increase in LERF for the 50% tendon area reduction case is

sufficient to reach Region II in Figure 2.2. This indicates that increased scrutiny would be

required, but the change would still be acceptable from the standpoint of the risk metrics.

There are other criteria for acceptance that also must be met. A change proposed under that riskinformed methodology must also satisfy' other design goals. It must still maintain defense in

depth and acceptable safety margins.

The small early release frequency (SERF) is included in Table 6.9 for comparison. The

probability of small early containment failure conditional of core damage is also shown in Table

6.10. The sum of the large and small release frequencies and conditional are shown in Table 6.12

and Table 6.13.

Table 6.9: Small Early Release Frequency (yrý')

Case Mean 5% 50% 95%

Un-damaged (Current Study) 1.96E-7 1.58E-10 8.77E-10 4.53E-6

50% Corrosion near basemnat 2.04E-7 1.58E-10 8.77E-10 5.07E-6

50% Corrosion at midheight 2.04E-7 1.58E-10 8.77E-10 5.07E-6

65% Corrosion near basemnat 2.07E-7 1.58E-10 8.81lE-10 5.07E-6

65% Corrosion at midheight 2.04E-7 1.58E-10 8.77E-10 5.07E-6

50% Tendon Area Reduction 2.26E-7 1.33E-10 8.25E-10 3.70E-6

50% Tendon Prestressing Loss 2.78E-7 1.58E-10 8.84E-l10 6.30E-6

Table 6. 10: Probability of Small Early Containment Failure Conditional on Core Damage

Case Mean 5% 50% 95%

Un-damaged (Current Study) 0.00477 2.33E-5 3.8 1 E-5 0.0349

50% Corrosion near basemat 0.00499 2.33E-5 3.8 1E-5 0.0390

50% Corrosion at midheight 0.00499 2.33E-5 3.81lE-5 0.0390

65% Corrosion near basemnat 0.00506 2.33E-5 3.83E-5 0.0390

65% Corrosion at midheight 0.00499 2.33E-5 3.81lE-5 0.0390

50% Tendon Area Reduction 0.0055 1 1.96E-5 3.59E-5 0.0284

50% Tendon Prestressing Loss 0.00679 2.33E-5 ,3.84E-5 0.0484

Table 6.11: Change in the Small Early Release Frequency (yr-1) due to Degradation

Case Mean 5% 50% 95%

50% Corrosion near basemat 8.79E-9 0 0 5.39E-7

50% Corrosion at midheight 8.79E-9 0 0 5.39E-7

65% Corrosion near basemnat l. 17E-8 0 3.29E-12 5.39E-7

65% Corrosion at midheight 8.79E-9 0 0 5.39E-7

50% Tendon Area Reduction 3.05E-8 0 -5.26E-1 I -8.36E-7

50% Tendon Prestressing Loss 8.26E-8 0 6.57E-12 1.76E-6

132
Table 6.12: Total Early Release Frequency (yr-)

Case Mean 5% 50% 95%

Un-damaged (Current Study) 3.46E-7 1 .58E-10 1 .08E-9 6.76E-6

50% Corrosion near basemat 3.46E-7 1.58E-10 1.06E-9 7.11 E-6

50% Corrosion at midheight 3.46E-7 1.58E-10 1.06E-9 7.11 E-6

65% Corrosion near basemnat 3 .49E-7 1 .58E- 10 1 .06E-9 7.11 E-6

65% Corrosion at midheight 3.46E-7 1.58E-10 1.06E-9 7.11 E-6

50% Tendon Area Reduction 9.23E-7 1.33E-10 2.63E-9 * 82E-5

50% Tendon Prestressing Loss 4.29E-7 1.58E-10 1.09E-9 8.52E-6

Table 6.13: Probability of Total Early Containment Failure Conditional on Core Damage

Case Mean 5% 50% 95%

Un-damaged (Current Study) 0.00843 2.33E-5 4.68E-5 0.0520

50% Corrosion near basemat 0.00843 2.33E-5 4.6 1E-5 0.0547

50% Corrosion at midheight 0.00843 2.33E-5 4.6 1E-5 0.0547

65% Corrosion near basemat 0.00850 2.33E-5 4.62E-5 0.0547

65% Corrosion at midheight 0.00843 2.33E-5 4.6 1E-5 0.0547

50% Tendon Area Reduction 0.02250 1.96E-5 1. 14E-4 0.1400

50% Tendon Prestressing Loss 0.0 1050 ,2.33E-5 4.73E-5 0.0656

Table 6.14: Change in the Total Early Release Frequency (yf') due to Degradation

Case Mean 5% 50% 95%

50% Corrosion near basemnat 0 0 -1.54E- 11 3.53E-7

50% Corrosion at midheight 0 0 -1.54E-1 1 3.53E-7

65% Corrosion near basemnat 2.93E-9 0 -1.22E-1I1 3.53E-7

65% Corrosion at midheight 0 0 -1.54E-11I 3.53E-7

50% Tendon Area Reduction 5.78E-7 -2.53E-11I -1.56E-9 1. 14E-5

50% Tendon Prestressing Loss 8.38E-8 0 1. 18E-1 1 1.76E-6

The example plants examined here serves as good case studies indicating that one should be very

cautious about simply applying the ALERF criterion to evaluate the significance of containment

degradation. It is important to closely examine how degradation can increase the likelihood of

one failure mode while decreasing the likelihood of another, and evaluate the consequences of

these different modes. It cannot be stressed enough that the cases of degradation examined here

are extremely limited in scope. There are currently no means of predicting degradation prior to

its discovery. Since the location and specific nature of any degradation could dramatically affect

the containment capacity and risk, a detailed analysis of that scenario would be required. The

specific results reported in this study should in no way be applied to making regulatory decisions

on existing plants.

133
7. Use of Regulatory Guide 1.174 and PRA Models in

Assessing Containment Degradation

7.1 Use of Regulatory Guide 1.174 Methodology Assessment

Regulatory Guide 1. 174 outlines the application of probabilistic risk assessment (PRA)

techniques to make risk-informed decisions regarding changes to a nuclear power plant's

licensing basis. The five principles to guide a risk-informed licensing basis change are outlined:

1 ) "The proposed change meets the current regulations unless it is explicitly related to a

requested exemption or rule change, i.e., a "specific exemption" under 10 CFR 50.12 or a

"4petition for rulemaking" under 10 CFR 2.802."

2) "The proposed change is consistent with the defense-in-depth philosophy."

3) "The proposed change maintains sufficient safety margins."

4) "When proposed changes result in an increase in core damage frequency (CDF) or risk,

the increases should be small and consistent with the intent of the Commission's Safety Goal

Policy Statement. " (USNRC, 1986)

5) "The impact of the proposed change should be monitored using performance

measurement strategies."

As mentioned in the fourth principle above, if a change results in an increase in risk, the increase

in risk must be small and fall within certain acceptance guidelines. In Regulatory Guide 1. 174,

core damage frequency and large early release frequency (LERF) have been designated as criteria

for determining the acceptance of a proposed change. If a proposed change in the licensing basis

results in an increase in either the CDF or LERF,' the change is only deemed acceptable if the

baseline values of CDF and LERF, as well as the change in those values due to the proposed

change, fall within certain bounds. Though we are not concerned with changes in CDF, many

accident scenarios could affect CDF. For example, damage to the reactor vessel, feedwater or

steam piping and supports due to the collapse of the bridge crane or other large section of

material could increase CDF. This would have additional effects on LERF that are not

considered in this study. Here, we assume that CDF is not affected due to containment

degradation, and therefore, we are only concerned with LERF. For this reason, among others,

this report should not be used for plant specific assessments.

The acceptance criteria for a proposed licensing basis change are shown graphically in terms of

LERF in Figure 2.2. This space is divided into three regions. In the area denoted as Region I, the

risk of the proposed change is deemed too high to be acceptable, and the change is not permitted.

In Region II, the risk increase is considered small, and the change is permitted. In Region III, the

risk increase is considered very small, and the change is permitted. A proposed change must

meet the acceptance guidelines for LERE to be deemed acceptable. If a change is deemed

acceptable, the cumulative impact of other plant changes on the risk over time must be monitored.

This study was successful in demonstrating a methodology to determine the change in LERF due

to containment degradation when the overall pressure capacity, or probability of catastrophic

rupture, of the containment was affected. The increase in risk due to the degradation has been

clearly illustrated. Although, several cases of degradation have been shown to not affect LERF,

and even decrease LERE in some scenarios. This could lead to the misleading conclusion that

degradation may be beneficial from a risk standpoint. This is obviously not acceptable and shows

134
that changes in LERF may not be the appropriate criteria to be applied in assessing containment

degradation.

The approach defined in Regulatory Guide 1. 174 for risk-informed decision-making is not

intended to relieve the duty of licensees to do things that they view as undesirable simply because

those things can be demonstrated to have a minimal impact on the risk. If a proposal results in a

risk increase, there must be clearly demonstrated benefits that outweigh the risk. If degradation is

shown to not affect risk (or decrease risk), additional scrutiny should be placed on the selected

risk parameter to determine if it is sufficient to base a regulatory decision upon.

Several cases of degradation explored in this study decrease the capacity of the containment to

resist internal pressure with little or no leaking prior to catastrophic failure. This could lead to a

release of radiation to the outside of the containment earlier than would have been the case had

the containment been in its original, un-degraded state. This could be in violation of maintaining

sufficient safety margins in the third principle above. Safety factors comparing the ratio of the

pressure capacity at 50% failure probability to the design pressure exceeds 2 for the 4 undegraded containments examined here. This ratio falls considerably below 2 for several cases of

degradation. A required safety margin should be determined for future implantation of this

methodology.

Additional structural performance criteria may also be essential to assessing the acceptability of

any modification, including degradation. In design codes, structures are typically required to

satisfyr appropriate safety factors, but also meet deflection criteria under those loads. Specifically,

nuclear containments have multiple penetrations, and may be in contact with other structure, etc.

Increased displacements due to degradation may cause failures not predicted in this study. Issues

related to other performance criterion could potentially be more significant to the increase in risk

than explored here. This could affect several of the principles above.

Arguably, the most important performance metric of a containment vessel undergoing

pressurization is its leak rate at a given pressure. For every type of containment vessel, there

exists a limiting pressure beyond which the structure can no longer be pressurized. This

structural capacity limit pressure is also an important performance characteristic, although it can

be of secondary importance simply because it is often far in excess of the pressure at which the

containment first begins to leak, especially for reinforced and prestressed concrete containment

vessels. The leak rate was not determined here due to the complexities in its prediction, though

SERF was determined for each case of degradation. The current Regulatory Guide 1. 174 does

not consider SERF directly. It could be argued that large increases in SERF are of significant

importance and would not be acceptable in a license basis change per the above principles.

In severe accident scenarios when the containment is subjected to pressures significantly higher

than the design pressure, translating structural response metrics such as strain and displacement

into crack initiation and propagation can be quite difficult, and dependent on the containment

design. Further research is needed to fully implement this methodology for several reasons. The

failure criterion used to predict crack initiation continues to be an open research topic. In

addition, the prediction of the propagation of the crack in a large scale 3D structure with a

multiaxial stress state is also an open area of research. The use of simple uniaxial tensile failure

strains to predict failure in three-dimensional finite element models with varying element sizes

remains an area of uncertainty. The division between leak, rupture, and catastrophic rupture are

definitions based on computation convenience. These were employed in large to remain

consistent with the NIJREG-1 150 PRA models. As far as the fragility analysis, the effect of

multiple penetrations also needs to be explored.

135
Overall, this methodology shows considerable promise in assessing the effects of degradation in

nuclear containments. Several items require fuirther study, including the quantification of limits

on SERF and TERF, reductions in the safety factor, increases in the deformation, and the criterion

used to predict crack initiation and propagation among others.

7.2 Limitations of PRA Models for Assessing the Effects of

Containment Degradation

The following description of the issues concerning the use of PRA models in the assessment of

containment performance was provided by Mark Leonard of Dycoda. These insights are based

on a review of the work performed in this study and the methods employed within the NUREG1150 PRA models (Leonard, 2006).

The common practice in Level 2 and Level 3 PRA is to define discrete outcomes (i.e.,

'bins' or groups) to various aspects of physical behavior. This is a practical necessity of

PRA due to the enormous range of scenarios and conditions being considered in a single,

integrated assessment or plant response to core damage accidents. This simplification of

actual plant behavior can restrict the ability of the PRA to discern subtle changes in risk

metrics. In the case of the NUREG-1 150 PRAs, the containment structural response to a

particular severe accident scenario must be categorized as resulting in one of four possible

outcomes: 'no failure', 'leakage', 'rupture' or 'catastrophic rupture.' Combinations of

these discrete outcomes representing changes as the accident progresses in time are

difficult to capture with high fidelity in a PRA. For example, containment leak rate during

a severe accident is likely to be a continuously changing parameter. The structure would

initially leak at (or below) the design basis leak rate, increase with time as containment

internal pressure increases and then increase more rapidly when an induced failure (e.g.,

crack) grows in size. Later in time, gross structural failure(s) might occur at entirely

different locations as different competing failure mechanisms become important. The PRA

analyst is challenged to fit this continuously changing containment leak rate into one of the

discrete outcomes with the PRA logic models.

A second simplification inherent to PR.A models concerns time. It is well known that the

time of "containment failure" has a first-order effect on radionuclide releases to the

environment. However, time itself is also discretized in PRA models. That is, the central

logic model of a PRA (e.g., the Accident Progression Event Tree, or APET, in NUREG1150) is typically divided into two or more time periods. The time at which a particular

event occurs along an actual severe accident timeline is assigned to one of these time

periods. In the NUREG-1 150 AIPETs, for example, an event can occur 'very early' (i.e.,

before the onset of core damage), 'early' (after the onset of core damage but before reactor

vessel lower head failure), or 'late' (long after the time of reactor vessel failure). The time

at which major changes in containment leakage occur must be fit into this discrete

representation of the accident time line in the same way that changes in the magnitude of

containment leakage are treated.

The loss of information caused by these simplifications is generally acknowledged as being

small and acceptable for the purposes of risk assessment. That is, frequency of scenarios

treated by a slight exaggeration in the size (or time) of containment leakage in one scenario

is balanced by the frequency of cases in which the leak rate is understated. Similarly, these

simplifications are often judged as a minor limitation in the fidelity of the Level 2/3 risk

136
models for measuring the risk importance of changes to underlying parameters - such as

the containment fragility curve(s) examined in this study. In this context, small calculated

changes in LERF are properly interpreted as meaning the effect of a proposed change to

the fragility curve(s) is within the modeling uncertainty of the PRA model itself.

However, for this conclusion to be valid the fundamental structure of the Level 2 PRA

models must faithfully represent contemporary understanding of containment

performance. It is not clear that this is the case in the NUREG-l 150 models, or in many

other contemporary Level 2 PRAs for that matter. The coarse discretization of

containment leak rate (or area) in PRA models is qualitatively consistent with the physical

behavior expected in free-standing steel containments, but not concrete containments.

Differences in the radiological source term using the simplified, discrete outcome approach

in the NUREG-1 150 models versus a more realistic, continuous containment response

model have not been characterized deterministically. Therefore, the quantitative

conclusions drawn from this study should be tempered by some concemn that the criteria

used to define conditions leading to a large, early release in the NUJREG-1 150 models may

not be accurate or complete.

This discussion of the limitations of PRA models in assessing containment performance should

be considered when interpreting the results of this study. Even with these limitations, it is

important to note that this study does provide a useful methodology and general information on

the effects of degradation in nuclear containments.

137
8. Summary and Conclusions

8.1 Program Overview

This study couples detailed structural analyses of degradation in 4 typical nuclear containments

with an existing series of Probabilistic Risk Assessment (PRA) models for each containment.

The 4 containments include two concrete containments, 1) a Pressurized Water Reactor (PWR)

with a large, dry reinforced concrete containment, and 2) a PWvR with a large, dry prestressed

concrete containment, and two steel containments, 1) a Boiling Water Reactor (BWR) with a

Mark I steel containment, and 2) a PWR with a steel ice condenser containment. The majority of

the degradation examined focuses on local corrosion of the steel liners in concrete containments

and the steel shells in steel containments.

Multiple finite element analyses of each containment within a Latin Hypercube Simulation (LHS)

framework enable the development of fragility curves for each containment under specific

degradation scenarios. The LHS framework introduces material property, construction,

modeling, and knowledge uncertainties into the deterministic structural analyses to produce the

fragility curves required in the coupling with the PRA model.

The fragility curves produced initially represent failures at one specific location and mode (leak,

rupture, etc) within a given containment. Fragility curves for various possible failure locations

are combined to determine cumulative probabilities of failure fragility curves and their

conditional failure probabilities with respect to leak, rupture, and catastrophic rupture. The

introduction of these curves into the existing PRA models produces values for the Large Early

Release Frequency (LERF) under each case of degradation. Finally, we assess the application of

Regulatory Guide 1. 174 to containment degradation using computed changes in LERF and other

risk metrics.

While actual plants are being used as examples in this study, it should be emphasized that the

analyses in this report are not intended to represent the actual condition of the plants. The

information concemning the plant systems and structures used in the analyses is not current, and

current operating conditions likely differ considerably from those assumed in the analyses. Most

important, degradation is assumed only to demonstrate an analytical methodology, and does not

represent actual degradation that has been observed at any of the plants. Any similarity between

the degradation assumed in this study and that observed in the plants used for these

demonstrations is purely coincidental. For these reasons along with the assumptions required to

conduct these analyses, the specific results of these analyses should not be used as a basis for

regulatory decisions.

8.2 Effects of Degradation on the Fragility, LERF, and other Risk

Metrics

The results of the fragility and PRA analyses for each plant with various forms of degradation can

be summarized easily due to the observed consistent trends. With magnitudes depending on the

depth and location, liner/shell corrosion significantly reduces the capacity of a given containment.

Only the 50% corrosion at the basemat case for the steel PWR ice condenser containment shows

leak possible near the design pressure at even low probabilities. Other degradation cases

throughout the containments studies here show shifts in the fragility curves, but not approaching

138
the design pressure even at low probabilities. It should be noted that the leaks predicted here are

based on geometrically idealized models. Even in regions of corrosion, the area is thinned

uniformly. In these cases, a definitive leak initiation is computed with an assumed criterion.

Experiments (Hessheimer, 2003) have shown (especially for concrete containments) that leaks

(though small) can occur at very low pressures near the design pressure and that the leak rate is a

continuous function of intemnal pressure (see Figure 2.3). These small leak rates at low pressures

often initiate at local details throughout the containment. The modeling of these local details

would require a model of significantly higher fidelity than the models created in this study. Even

though these early leaks are typically small compared to the leak initiations predicted in this

study, this should be considered when interpreting the results of this study.

This study adopted a step function failure progression to remain consistent with the NUREG1150 PRA models. From these PRA. model results, liner/shell degradation causes a small

increase in LERF in cases where catastrophic rupture dominates the failure mode. Containment

failure proceeds directly from leak to catastrophic rupture with little or no gap between the failure

modes. This is observed in the steel shell containments where sufficient energy exists within the

pressurized containment to propagate a crack after the initiation of a leak. Of the catastrophic

rupture dominated cases examined here with corrosion in the steel shell of a steel containment, all

remain within Region III of Figure 2.2.

Concrete containments also show increases in LERF with degradation when the overall capacity

is affected by the degradation. The two cases of tendon degradation of the prestressed concrete

containment show increases in LERF. The largest increase occurs when 50% of the area is

reduced for the midheight hoop tendons. The degradation of the tendons leads to a significant

probability of catastrophic rupture at low pressures. Here, LERF increases enough to enter

Region II of Figure 2.2.

Other cases actually show LERF remaining constant or even experiencing a reduction with

degradation. These cases were encountered when leak was the dominant failure mode at low

pressures. Specifically, these cases occurred in the basemat and bellows corrosion cases for the

steel PWR ice condenser and the two concrete containments with liner corrosion. The large

bending field at the base of the ice condenser containment causes leaks at low pressures prior to

catastrophic rupture. The concrete containment liners tear at relatively low pressures compared to

the overall capacity of the concrete vessel.

Since LERF was found to decrease in some cases where leaks dominates and would cause a

release, the Small Early Release Frequency (SERF) was included in the PRA results for each

containment. When leak dominates the failure, SERF increases and leads to the observed

decrease in LERF. In these cases, the leak site acts as a "vent" at low pressures, slowly releasing

material with the possibility of preventing or delaying a catastrophic rupture. In these scenarios,

the consequences of small early releases must be examined prior to the determination of

acceptability.

Since SERF decreases for the cases where catastrophic rupture dominates, the total early release

frequency (TERF = LERF + SERF) was computed for each containment at each degradation case.

TERF was included to illustrate that the total frequency increases or remains constant when,

introducing degradation regardless of the dominant failure mode.

If limits were placed on the increase in SERF or TERF that were analogous to those for LERF in

Figure 2.2, Region 11 would be reached for several additional degradation cases in this study. In

addition, the PRA models used here do not directly compute LERF or SERF. The binning

139
process is performed during the post-processing of the PRA results. It is at this point where the

results from the event tree analysis are placed into LERIF, SERF, and other "bins" depending on

the failure mode (e.g. leak, rupture, etc). This study places leak failures into the SERF bin, and

ruptures and catastrophic ruptures into the LERF bin. This was done assuming that a leak would

not depressurize the containment in less than two hours (NUREG-1 150 definition).

Obviously, this study has examined several simple cases of containment degradation. The

specific results presented here should not be applied to any existing plant since actual degradation

may be considerable more severe or widespread than examined here. This study also uses many

assumptions for miaterial properties and some of the procedures (e.g. failure criteria) are still the

subject of research. This study was conducted to demonstrate a methodology of applying a riskinformed assessment to structural degradation. This methodology could be applied to specific

degradation found in an existing plant, but significant care should be taken in selecting the failure

criteria, modeling assumptions, risk metrics, and the implementation of the containment behavior

in the PRA models or other risk analyses, among others.

140
9. References

ANATECH, 1997, "ANACAP-U User's Manual, Version 2.5" ANATECH Corp., San Diego,

CA.

Anderson, T.L., 1995, Fracture Mechanics. Fundamentals and Applications -2 nd ed., CRC

Press, Boca Raton, FL.

Ang, All-S. and Tang, W.H., 1975, Probability Concepts in Engineering Planning and Design,

Volume 1-Basic Principles, Wiley.

Ashar, H., Naus, D., and Tan, C.P., 1994, "Prestressed Concrete in U.S. Nuclear Power Plants

(Part I)." Concrete International, May 1994, 30-34.

Breeding, R.J., F.T. Harper, T.D. Brown, J.J. Gregory, A.C. Payne, E.D. Gorham, W. Murfin, and

C.N. Amos, 1992, "Evaluation of Severe Accident Risks: Quantification of Major Input

Parameters." NIJREG/CR-455 1, SAND86-1309, Vol. 2, Rev. 1, Part 3, Sandia National

Laboratories, Albuquerque, NM.

Breeding, R.J., J.C. Helton, W.B. Murfin, and L.N. Smith, 1990, "Evaluation of Severe Accident

Risks: Surry Unit 1." NUREG/CR-455 1, SAND86- 1309, Vol. 3, Sandia National Laboratories,

Albuquerque, NM.

Butler, T.A., and Fugelso, L.E, 1982, "Response of the Zion and Indian Point Containment

Building to Severe Accident Pressures." NUREG/CR-2569, LA-930 1-MS, Los Alamos, NM, Los

Alamos National Laboratory.

Castro, J.C., R.A. Dameron, R.S. Dunham, and Y.R. Rashid, 1993, "A Probabilistic Approach for

Predicting Concrete Containment Leakage." EPRI Report TR-102 176, TI, ANATECH Corp.,

San Diego, CA.

Cherry, J.L., J.M. Clauss, M. Pilch, J.J. Gregory, and J.A. Smith, 2001, "Aging Management and

Performance of Stainless Steel Bellows in Nuclear Power Plants." N-UREG/CR-6726,

SAND200l-1 147P, Sandia National Laboratories, Albuquerque, NM.

Cherry, J.L. and J.A. Smith, 2001, "Capacity of Steel and Concrete Containment Vessels with

Corrosion Damage." NUREG/CR-6706, SAND2000-1735, Sandia National Laboratories,

Albuquerque, NM.

Clauss, D.B., 1985, "Comparison of Analytical Predictions and Experimental Results for a 1:8-

Scale Steel Containment Model Pressurized to Failure." NUREG/CR-4209, SAND85-0679,

Sandia National Laboratories, Albuquerque, NM.

Clauss, D.B., 1985, "Pretest Predictions for the Response of a 1:8-Scale Steel LWR Containment

Building Model to Static Overpressurization." NIJREG/CR-49 13, SAND85-0891, Sandia

National Laboratories, Albuquerque, NM.

141
Clauss, D.B., 1987, "Round-Robin Pretest Analyses of a 1:6 scale Reinforced Concrete

Containment Model Subject to Static Internal Pressurization." NUREG/CR-49 13, SAND87-

089 1, Sandia National Laboratories, Albuquerque, NM.

Dameron, R.A., L. Zhang, Y.R. Rashid, and M.S. Vargas, 2000, "Pretest Analysis of a 1:4-Scale

Prestressed Concrete Containment Vessel Model." NIJREG/CR-6685, SAND2000-2093, Sandia

National Laboratories, Albuquerque, NM.

Eldred, M.S., A.A. Giunta, B.G. van Bloeman Waanders, S.F. Wojtkiewicz Jr., W.E. Hart, and

M.P. Alleva, 2002, "DAKOTA, A Multilevel Parallel Object-Oriented Framework for Design

Optimization, Parameter, Estimation, Uncertainty Quantification, and Sensitivity Analysis.

Version 3.0 Users Manual." SAND200l-3796, Sandia National Laboratories, Albuquerque, NM.

Ellingwood, B. R. and J.L. Cherry, 1999, "Fragility Modeling of Aging Containment Metallic

Pressure Boundaries." NIJREG/CR-663 1, ORNL/SUB/99-SP638V, Oak Ridge National

Laboratories, Oak Ridge, TN.

Gregory, J.J., W.B. Murfin, S.J. Higgins, R.J. Breeding, J.C. Helton, and A.W. Shiver, 1990,

"Evaluation of Severe Accident Risks: Sequoyah, Unit 1." NUREG/CR-4551, SAND86-1309,

Vol. 5, Sandia National Laboratories, Albuquerque, NM.

Greimann, L., F. Fanous, and D. Bluhm, 1984, "Final Report, Containment Analysis Techniques,

A State-of-the-Art Summary." NUREG/CR-3653, Ames Laboratory, IA.

Greimann, L., F. Fanous, J. Rogers, and D. Blubm, 1987, "An Evaluation of the Effects of Design

Details on the Capacity of LWR Steel Containment Buildings." NUREG/CR-4870, SAND87-

7066.

Greimann, L., W. Wassef, F. Fanous, and D. Bluhm, 199 1, "Analysis of Bellows Expansion

Joints in the Sequoyah Containment." NUREG/CR-5561, SAND9O-7020, Institute for Physical

Research and Technology, Iowa State University, Ames, IA.

Hancock, J.W. and A.C. Mackenzie 1976, "On the Mechanisms of Ductile Failure in HighStrength Steels Subjected to Multi-Axial Stress States," Journal of Mechanics and Physics of

Solids, 24, 147-169.

Hibbit, Karlsson and Sorenson, 2002, "ABAQUS/Standard User's Manual, Version 6.3,"

Hibbit, Karlsson and Sorenson, Inc, Pawtucket, RI.

Hessheimer, M.F., E.W. Kiamerus, L.D. Lambert, G.S. Rightley, and R.A. Dameron, 2003,

"Overpressurization Test of a 1:4-Scale Prestressed Concrete Containment Vessel Model."

NIJREG/CR-68 10, SAND2003-0840P, Sandia National Laboratories, Albuquerque, NM.

Horschel, D.S., 1992, "Experimental Results From Pressure Testing a 1:6-Scale Nuclear Power

Plant Containment." NUREG/CR-5 121, SAND88-0906, Sandia National Laboratories,

Albuquerque, NM.

International Standard Problem No. 48 Containment Capacity, Synthesis Report, Prepared by

Sandia National Laboratories, Nuclear Safety NEA/CSNI/R(2005)/Vol. 1, August 2005.

142
Lam, P.S. and R.L. Sindelar, 2000, "Flaw Stability in Mild Steel Tanks in the Upper-Shelf

Ductile Range - Part 11: J-Integral-Based Fracture Analysis." Journal of Pressure Vessel

Technology, ASME, 122, 169-173.

Lambert, L.D. and M.B. Parks, 1995, "Experimental Results 'from Containment Piping Bellows

Subjected to Severe Accident Conditions." NUREG/CR-6154, SAND94-171 1, Vol. 1&2, Sandia

National Laboratories, Albuquerque, NM.

Luk, V.K., M.F. Hessheimer, G.S. Rightley, L.D. Lambert, and E.W. Klamerus, 2000, "Design,

Instrumentation, and Testing of a Steel Containment Vessel Model." NUREG/CR-5679, SAND

98-270 1, Sandia National Laboratories, Albuquerque, NM 87185.

McKay, M.D., R.J. Beckman, and W.J. Conover, 1979, "A Comparison of Three Methods for

Selecting Values of Input Variables in the Analysis of Output from a Computer Code."

Technometrics, 21 (2),239-245.

Miller, J.D., 1990, "Analysis of Shell-Rupture Failure Due to Hypothetical Elevated-Temperature

Pressurization of the Sequoyah Unit I Steel Containment Building." NUREG/CR-5405,

SAND89-1650, Sandia National Laboratories, Albuquerque, NM.

Mirza, S.A., M. Hatzinikolas, and J.G. MacGregor, 1979, "Statistical Descriptions of Strength of

Concrete." Journal of the Structural Division, ASCE, 105 (6), 1021-1037.

Papaspyropoulus, V., C. Marschall, and M. Landow, "Predictions of J-R Curves with Large

Crack Growth from Small Specimen Data." NUREG/CR-4575, BMI-2 137, Battelle's Columbus

Division, Columbus, OH.

Rots, J. G., and J. Blaauwendraad, 1989, "Crack models for concrete: discrete or smeared?

Fixed, multidirectional or rotating?" Heron, 34(l), Delft University of Technology, The

Netherlands.

Shah, V.N., S.K. Smith, U.P. Sinha, 1994, "Insights for Aging Management of Light Water

Reactor Components." NUREG/CR-53 14, EGG-2562, Vol. 5, Idaho National Engineering

Laboratory, Idaho Falls, ID.

Shih, C.F., and J.W. Hutchinson, 1976, "Fully Plastic Solutions and Large Scale Yielding

Estimates for Plane Stress Crack Problems." Journal of Engineering Materials and Technology,

ASME, 98, 289-295.

Sindelar, R.L., P.S. Lam, G.R. Caskey, Jr., and L.Y. Woo, 2000, "Flaw Stability in Mild Steel

Tanks in the Upper-Shelf Ductile Range - Part I: Mechanical Properties." Journal of Pressure

Vessel Technology, ASME, 122, 169-173.

Smith, J.A., 2001, "Capacity of Prestressed Concrete Containment Vessels with Prestressing

Loss." SAND200I-1762, Sandia National Laboratories, Albuquerque, NM.

Takenaka, M., T. Omotani, T. Yamashita, and K. Tsukimori, 1989, "Surface Crack Propagation

and Stability of Through-Wall Crack of Bellows." Pressure Vessels and Piping Division

Publication, ASME, 168, 159-171.

143
Tang, H.T., R.A. Dameron, and Y.R. Rashid, 1995, "Probabilistic Evaluation of Concrete

Containment Capacity for Beyond Design Basis Internal Pressures," Nuclear Engineering and

Design, 157, 455-467.

Tronskar, J.P., M.A. Mannan, and M.O. Lai, 2003, "Correlation Between Quas-i-Static and

Dynamic Crack Resistance Curves," Engineering Fracture Mechanics, 70, 1527-1542.

United States Nuclear Regulatory Commission, 1986, "Safety Goals for the Operations of

Nuclear Power Plants; Policy Statement," Federal Register, Vol. 5 1, p. 30028 (51 FR 30028),

August 4, 1986.

United States Nuclear Regulatory Commission, 1990, "Severe Accident Risks: An Assessment

for Five U.S. Nuclear Power Plants," NURiEG-1 150.

United States Nuclear Regulatory Commission, 1995, "Use of Probabilistic Risk Assessment

Methods in Nuclear Activities: Final Policy Statement," Federal Register, Vol. 60, p. 42622, (60

FR 42622), August 16, 1995.

United States Nuclear Regulatory Commission, 2001, "An Approach for Using Probabilistic Risk

Assessment in Risk-Informed Decisions on Plant-Specific Changes to the Licensing Basis."

Regulatory Guide 1. 174 (Draft Regulatory Guide DG-1 1I10).

Weatherby, J.R., 1988, "Structural Assessments of the Surry and Zion Reactor Containments

Buildings for NIJREG- 1150," memorandum to R.J. Breeding, Sandia National Laboratories,

Albuquerque, NM.

144
NRIC FORM 335 U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT NUMBER

(9-2004) (Assigned by NRC, Add Vol., Supp., Rev.,

NRCMD 3.7 and Addendum Numbers, If any.)

BIBLIOGRAPHIC DATA SHEET NRGC-62

(See instructions on the reverse) SAN D2006-3772P

2. TITLE AND SUBTITLE 3. DATE REPORT PUBLISHED

Risk-Informed Assessment of Degraded Containment Vessels MONTH YEAR

November 2006

4. FIN OR GRANT NUMBER

Y6164

5. AUTHOR(S) 6. TYPE OF REPORT

Benjamin W. Spencer, Jason P. Petti, David M. KUnsman______________

7. PERIOD COVERED (inclusive Dates)

8. PERFORMING ORGANIZATION - NAME AND ADDRESS (If NRC, provide Division. Office or Region, U.S. Nuclear Regulatory Commission, and mailing address; if contra ctor,

provide name and mailing address.)

Sandia National Laboratories

P. 0. Box 5800

Albuquerque, NM 87185-0744

9. SPONSORING ORGANIZATION - NAME AND ADDRESS (if NRC, type 'Same as above', if contractor, provide NRC Division, Office or Region, U.S. Nuclear Regulatory Commission,

and mailing address.)

Division of Fuel, Engineering & Radiological Research

Office of Nuclear Regulatory Research

U. S. Nuclear Commssion

Washington, DC 20555-0001

10. SUPPLEMENTARY NOTES

Herman L. Graves, 111, NRC Project Manager

11. ABSTRACT (200 words or less)

Through the years, the containment vessels of operating nuclear power plants in the United States have exhibited various

forms of degradation, including corrosion of the steel shell or liner, reinforcing bars, and prestressing tendons; loss of

prestressing; and corrosion of bellows. Because the containment serves as the ultimate barrier against the release of

radioactive material into the environment, compromising the containment could increase the risk of a large release in the

unlikely event of an accident.

12. KEY WORDS/DESCRIPTORS (List words or phrases that will assist researchers in locating the report.) 13. AVAILABILITY STATEMENT

Degradation, assessment, containment, corrosion, loss of pretress, risk, bellows, steel liners unlimited

14. SECURITY CLASSIFICATION

(This Page)

unclassified

(This Report)

unclassified

15. NUMBER OF PAGES

16. PRICE

NRC FORM 335 (9-2004) PRINTED ON RECYCLED PAPER
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NUCLEAR REGULATORY COMMISSION

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OFFICIAL BUSINESS