NUREG-1806, Vol. 1 

 

Technical Basis for Revision of 

the Pressurized Thermal Shock 

(PTS) Screening Limit in the 

PTS Rule (10 CFR 50.61) 

Summary Report 

U.S. Nuclear Regulatory Commission 

Office of Nuclear Regulatory Research 

Washington, DC 20555-0001 
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 NUREG-1806, Vol. 1

 

 

 

ummary Report 

anuscript Completed: May 2006 

repared by 

irk, M. Junge, W. Arcieri, 

cher, 

 Woods, 

ivision of Fuel, Engineering and Radiological Research 

Technical Basis for Revision of 

the Pressurized Thermal Shock 

(PTS) Screening Limit in the 

PTS Rule (10 CFR 50.61) 

S

M

Date Published: August 2007 

P

M. EricksonK

B.R. Bass, R. Beaton, D. Bessette, 

T.H.J. Chang, T. Dickson, C.D. Flet

A. Kolaczkowski, S. Malik, T. Mintz, 

C. Pugh, F. Simonen, N. Siu, 

D. Whitehead, P. Williams, R.

S. Yin 

D

Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 

Washington, DC 20555-0001 
ii
iii

Abstract 

During plant operation, the walls of reactor pressure vessels (RPVs) are exposed to neutron radiation, 

resulting in localized embrittlement of the vessel steel and weld materials in the core area. If an 

embrittled RPV had a flaw of critical size and certain severe system transients were to occur, the flaw 

could very rapidly propagate through the vessel, resulting in a through-wall crack and challenging the 

integrity of the RPV. The severe transients of concern, known as pressurized thermal shock (PTS), are 

characterized by a rapid cooling of the internal RPV surface in combination with repressurization of the 

RPV. Advancements in our understanding and knowledge of materials behavior, our ability to 

realistically model plant systems and operational characteristics, and our ability to better evaluate PTS 

transients to estimate loads on vessel walls led the NRC to realize that the earlier analysis, conducted in 

the course of developing the PTS Rule in the 1980s, contained significant conservatisms. 

This report summarizes 21 supporting documents that describe the procedures used and results obtained 

in the probabilistic risk assessment, thermal hydraulic, and probabilistic fracture mechanics studies 

conducted in support of this investigation. Recommendations on toughness-based screening criteria for 

PTS are provided. 
iv
v

Foreword 

The reactor pressure vessel is exposed to neutron radiation during normal operation. Over time, the 

vessel steel becomes progressively more brittle in the region adjacent to the core. If a vessel had a 

preexisting flaw of critical size and certain severe system transients occurred, this flaw could propagate 

rapidly through the vessel, resulting in a through-wall crack. The severe transients of concern, known as 

pressurized thermal shock (PTS), are characterized by rapid cooling (i.e., thermal shock) of the internal 

reactor pressure vessel surface that may be combined with repressurization. The simultaneous occurrence 

of critical-size flaws, embrittled vessel, and a severe PTS transient is a very low probability event. The 

current study shows that U.S. pressurized-water reactors do not approach the levels of embrittlement to 

make them susceptible to PTS failure, even during extended operation well beyond the original 40-year 

design life. 

Advancements in our understanding and knowledge of materials behavior, our ability to realistically 

model plant systems and operational characteristics, and our ability to better evaluate PTS transients to 

estimate loads on vessel walls have shown that earlier analyses, performed some 20 years ago as part of 

the development of the PTS rule, were overly conservative, based on the tools available at the time. 

Consistent with the NRC’s Strategic Plan to use best-estimate analyses combined with uncertainty 

assessments to resolve safety-related issues, the NRC’s Office of Nuclear Regulatory Research undertook 

a project in 1999 to develop a technical basis to support a risk-informed revision of the existing PTS Rule, 

set forth in Title 10, Section 50.61, of the Code of Federal Regulations (10 CFR 50.61). 

Two central features of the current research approach were a focus on the use of realistic input values and 

models and an explicit treatment of uncertainties (using currently available uncertainty analysis tools and 

techniques). This approach improved significantly upon that employed in the past to establish the 

existing 10 CFR 50.61 embrittlement limits. The previous approach included unquantified conservatisms 

in many aspects of the analysis, and uncertainties were treated implicitly by incorporating them into the 

models. 

This report summarizes a series of 21 reports that provide the technical basis that the staff will consider in 

a potential revision of 10 CFR 50.61; it includes a description of analysis procedures and a detailed 

discussion of findings. The risk from PTS was determined from the integrated results of the Fifth Version 

of the Reactor Excursion Leak Analysis Program (RELAP5) thermal-hydraulic analyses, fracture 

mechanics analyses, and probabilistic risk assessment. These calculations demonstrate that, even through 

the period of license extension, the likelihood of vessel failure attributable to PTS is extremely low 

(≈10-8/year) for all domestic pressurized water reactors. Limited analyses are continuing to further 

evaluate this finding. Should the ≈10-8/year value be confirmed, this would provide a basis for significant 

relaxation, or perhaps elimination, of the embrittlement limit established in 10 CFR 50.61. Such changes 

would reduce unnecessary conservatism without affecting safety because the operating reactor fleet has little 

probability of exceeding the limits on the frequency of reactor vessel failure established from NRC guidelines 

on core damage frequency and large early release frequency through the period of license extension. 

 _______________________________ 

 Brian W. Sheron, Director 

 Office of Nuclear Regulatory Research 

U.S. Nuclear Regulatory Commission 
vi
vii

Contents 

Abstract........................................................................................................................................................iii 

Foreword.......................................................................................................................................................v 

Contents ......................................................................................................................................................vii 

Appendices...................................................................................................................................................xi 

Figures .........................................................................................................................................................xi 

Tables........................................................................................................................................................xvii 

Executive Summary ...................................................................................................................................xix 

Abbreviations...........................................................................................................................................xxix 

Nomenclature.........................................................................................................................................xxxiii 

Glossary .................................................................................................................................................xxxvi 

1 Motivation for and Objective of this Study.......................................................................................1-1 

1.1 Description of Pressurized Thermal Shock ..............................................................................1-1 

1.2 PTS Limits on the Licensable Life of a Commercial Pressurized Water Reactor....................1-1 

1.3 Technical Factors Suggesting Conservatism of the Current PTS Rule ....................................1-3 

1.4 Statement of Objective .............................................................................................................1-3 

1.5 Guide to this Report..................................................................................................................1-3 

2 Pressurized Thermal Shock Background ..........................................................................................2-1 

2.1 General Description of the Progression of a PTS Event...........................................................2-1 

2.1.1 Precursors.........................................................................................................................2-1 

2.1.2 Thermal-Hydraulic Response of the Vessel.....................................................................2-1 

2.1.3 Response of the Vessel to PTS Loading..........................................................................2-4 

2.2 Historical Incidence of PTS......................................................................................................2-5 

2.3 Summary of SECY-82-465 Findings .......................................................................................2-6 

2.4 Current Provisions of 10 CFR 50.61 ........................................................................................2-7 

2.4.1 Index Temperature Approach to Characterize Transition Fracture Toughness in Ferritic 

Steels................................................................................................................................2-7 

2.4.2 Irradiation Effects on Index Temperature........................................................................2-8 

2.4.3 Provisions of the Current Rule.........................................................................................2-8 

2.4.4 Evaluation of Operating Plants Relative to the Current PTS Screening Limits ..............2-9 

3 PTS Reevaluation Project..................................................................................................................3-1 

3.1 Model Used to Evaluate a Revised PTS Screening Limit ........................................................3-1 

3.1.1 Restrictions on the Model ................................................................................................3-1 

3.1.2 Overall Structure of the Model ........................................................................................3-1

3.2 Uncertainty Treatment..............................................................................................................3-5 

3.2.1 Recommended Framework ..............................................................................................3-5 

3.2.2 Implementation ................................................................................................................3-6 

3.3 Fundamental Assumptions and Idealizations .........................................................................3-12 

3.3.1 Probabilistic Risk Assessment .......................................................................................3-12 

3.3.2 Thermal-Hydraulics .......................................................................................................3-14 

3.3.3 Probabilistic Fracture Mechanics...................................................................................3-16 

3.4 Participating Organizations ....................................................................................................3-20 

3.5 External Review Panel............................................................................................................3-20 

4 Structure of this Report, and Changes Relative to Previous Reports ................................................4-1 
viii

4.1 Report Structure........................................................................................................................4-1 

4.2 Changes Relative to Previous Studies ......................................................................................4-1 

4.2.1 Studies Providing the Technical Basis of the Current PTS Rule.....................................4-1 

4.2.2 December 2002 Draft Report...........................................................................................4-4 

5 Probabilistic Risk Assessment and Human Reliability Analysis ......................................................5-1 

5.1 Introduction ..............................................................................................................................5-1 

5.2 Methodology.............................................................................................................................5-2 

5.2.1 Step 1: Collect Information..............................................................................................5-3 

5.2.2 Step 2: Identify the Scope and Features of the PRA Model ............................................5-5 

5.2.3 Step 3: Construct the PTS-PRA Models..........................................................................5-8 

5.2.4 Step 4: Quantify and Bin the PTS-PRA Modeled Sequences........................................5-12 

5.2.5 Step 5: Revise PTS-PRA Models and Quantification....................................................5-13 

5.2.6 Step 6: Perform Uncertainty Analyses...........................................................................5-14 

5.2.7 Step 7: Incorporate Uncertainty and Finalize Results....................................................5-15 

6 Thermal-Hydraulic Analysis.............................................................................................................6-1 

6.1 Introduction and Chapter Structure ..........................................................................................6-1 

6.2 Thermal-Hydraulic Analysis of PTS Transients.......................................................................6-1 

6.3 RELAP5 Code Description ......................................................................................................6-2 

6.3.1 RELAP5 Analysis Process...............................................................................................6-2

6.3.2 RELAP5 Numerics Issues ...............................................................................................6-7 

6.4 Plant Model Development........................................................................................................6-8 

6.5 Transient Event Simulations...................................................................................................6-13 

6.5.1 Loss of Coolant Accidents.............................................................................................6-13 

6.5.2 Reactor/Turbine Trips....................................................................................................6-13 

6.5.3 Main Steam Line Break .................................................................................................6-14 

6.5.4 Operator Actions............................................................................................................6-14 

6.6 RELAP5 Analysis Results......................................................................................................6-15 

6.7 RELAP5 Assessment Against Experimental Data .................................................................6-15 

6.7.1 Separate Effects Tests....................................................................................................6-16 

6.7.2 Integral System Response..............................................................................................6-19 

6.7.3 RELAP5 Assessment Conclusions ................................................................................6-41 

6.8 Sensitivity and Uncertainty Analysis .....................................................................................6-41 

6.8.1 Sensitivity Analysis .......................................................................................................6-41 

6.8.2 Treatment of Uncertainties ............................................................................................6-42 

7 Probabilistic Fracture Mechanics Analysis .......................................................................................7-1 

7.1 Interaction of PFM Model with PRA and TH models..............................................................7-1 

7.2 Components of the PFM Model ...............................................................................................7-1 

7.3 Objectives of this Chapter ........................................................................................................7-2 

7.4 Approach to Model Development and Uncertainty Characterization ......................................7-2 

7.5 Flaw Model...............................................................................................................................7-4 

7.5.1 Buried Flaws in Welds.....................................................................................................7-5 

7.5.2 Buried Flaws in Plates .....................................................................................................7-6 

7.5.3 Surface Flaws in Welds and Plates ..................................................................................7-6 

7.5.4 Comparison of the Current Flaw Distribution with that Proposed by the Marshall 

Committee........................................................................................................................7-7 

7.6 Neutronics Model .....................................................................................................................7-7 

7.6.1 ID Fluence........................................................................................................................7-8 

7.6.2 Through-Wall Fluence Attenuation .................................................................................7-8 

7.7 Crack Initiation Model..............................................................................................................7-8 

7.7.1 Key Features ....................................................................................................................7-8 

7.7.2 Major Changes...............................................................................................................7-10 
ix

7.8 Through-Wall Cracking Model ..............................................................................................7-13 

7.8.1 Key Features ..................................................................................................................7-13 

7.8.2 Major Changes...............................................................................................................7-14 

7.9 Probabilistic Fracture Mechanics Code FAVOR ...................................................................7-16 

7.9.1 Implementation of PFM Model .....................................................................................7-16 

7.9.2 Discretization of the Reactor Pressure Vessel ...............................................................7-18 

7.10 Experimental Validation of Linear Elastic Fracture Mechanics.............................................7-18 

8 Vessel Failure Frequencies Estimated for Oconee Unit 1, Beaver Valley Unit 1, and Palisades .....8-1 

8.1 Chapter Structure......................................................................................................................8-1 

8.2 Plant-Specific Features of Analysis..........................................................................................8-1 

8.2.1 PRA..................................................................................................................................8-1 

8.2.2 TH ....................................................................................................................................8-2 

8.2.3 PFM .................................................................................................................................8-3 

8.3 Estimated Values of FCI and TWCF........................................................................................8-4

8.3.1 Overall Results.................................................................................................................8-5 

8.3.2 Distribution Characteristics .............................................................................................8-5 

8.4 Material Factors Contributing to FCI and TWCF ..................................................................8-17 

8.4.1 Flaws Simulated by FAVOR, and Reference Temperature Metrics..............................8-17 

8.4.2 Effect of RPV Beltline Region on FCI and TWCF Values ...........................................8-24 

8.4.3 Embrittlement Normalization between Different Plants................................................8-26 

8.4.4 Changes in these Results Relative to those Reported in December 2002 .........................8-26 

8.5 Contributions of Different Transients to the Through-Wall Cracking Frequency .................8-26 

8.5.1 Overview........................................................................................................................8-26 

8.5.2 Primary Side Pipe Breaks ..............................................................................................8-35 

8.5.3 Stuck-Open Valves on the Primary Side (SO-1) ...........................................................8-44 

8.5.4 Large Diameter Secondary Side or Main Steam Line Breaks .......................................8-59 

8.5.5 Stuck-Open Valves on the Secondary Side (SO-2) .......................................................8-66 

8.5.6 Other Transient Classes .................................................................................................8-71 

8.6 Summary.................................................................................................................................8-71 

9 Generalization of the Baseline Results to All Pressurized-Water Reactors ......................................9-1 

9.1 Thermal-Hydraulic Sensitivity Studies ....................................................................................9-1 

9.1.1 Introduction......................................................................................................................9-1 

9.1.2 Sensitivity Studies Performed for Uncertainty Analysis .................................................9-2 

9.2 Fracture mechanics sensitivity studies .....................................................................................9-7 

9.2.1 Sensitivity Studies Performed To Assess the Robustness of the PFM Model.................9-7 

9.2.2 Sensitivity Studies Performed to Assess the Applicability of the Results in Chapter 8 to 

PWRs in General ...........................................................................................................9-13 

9.2.3 Summary and Conclusions ............................................................................................9-17 

9.3 Plant-to-Plant Differences in Design/Operational Characteristics that Impact PTS Transient 

Severity .......................................................................................................................................9-18 

9.3.1 Generalization Questionnaire.........................................................................................9-19

9.3.2 Analysis of Collected Information.................................................................................9-19 

9.3.3 Combined Observations and Overall Conclusion..........................................................9-33 

9.4 Consideration of External Events...............................................................................................9-34 

9.4.1 Introduction....................................................................................................................9-34 

9.4.2 Approach........................................................................................................................9-35 

9.4.3 Findings Based on the Reviews .....................................................................................9-35 

9.4.4 Additional Analyses.......................................................................................................9-36 

9.4.5 Overall Findings ............................................................................................................9-38 

9.5 Summary of Generalization Studies .......................................................................................9-39 

10 Risk-Informed Reactor Vessel Failure Frequency Acceptance Criteria .........................................10-1 
x

10.1 Introduction ............................................................................................................................10-1 

10.2 Current Guidance on Risk-Informed Regulation....................................................................10-1 

10.3 Containment Performance During PTS Accidents .................................................................10-2 

10.3.1 Previous Research Results .............................................................................................10-3 

10.3.2 Post-RPV Failure Scenarios Scoping Study ..................................................................10-4 

10.4 Acceptance Criteria Options.................................................................................................10-11 

10.5 Conclusions ..........................................................................................................................10-12 

11 Reference Temperature (RT)-Based PTS Screening Criteria..........................................................11-1 

11.1 Introduction ............................................................................................................................11-1 

11.2 Reference Temperature (RT) Metrics .....................................................................................11-2 

11.3 Relationship between RT Metrics and TWCF........................................................................11-3 

11.3.1 Weighted RT Values ......................................................................................................11-3 

11.3.2 Maximum RT Values .....................................................................................................11-6 

11.4 Proposed RT-Based Screening Limits ....................................................................................11-7 

11.4.1 Plate Vessels ..................................................................................................................11-7 

11.4.2 Forged Vessels.............................................................................................................11-11 

11.4.3 Need for Margin...........................................................................................................11-14 

11.4.4 Non-Best Estimate Aspects of the Model....................................................................11-15 

12 Summary of Findings and Considerations for Rulemaking ............................................................12-1 

12.1 Plant-Specific Baseline Analysis of the PTS Risk at Oconee Unit 1, Beaver Valley 

Unit 1, and Palisades...................................................................................................................12-1 

12.2 Applicability of these Plant Specific Results to Estimating the PTS Risk at PWRs in General.12-5 

12.3 An Anual Per-Plant Limit on Through-Wall Cracking Frequency Consistent with Current 

Regulatory Guidance on Risk-Informed Regulation ..................................................................12-7 

12.4 A Reference Temperature Based PTS Screening Criteria......................................................12-9 

12.5 Considerations for Rulemaking............................................................................................12-13 

13 References .....................................................................................................................................13-14 

13.1 Citations Summarized by this Report...................................................................................13-14 

13.1.1 Probabilistic Risk Assessment .....................................................................................13-14 

13.1.2 Thermal-Hydraulics .....................................................................................................13-14 

13.1.3 Probabilistic Fracture Mechanics.................................................................................13-15 

13.2 Literature Citations...............................................................................................................13-16 
xi

Appendices 

Appendix A Master Transient List and FAVOR 04.1 Results Summary.................................A-1 

Appendix B Peer Review .......................................................................................B-1 

Appendix C Flaw Distribution, Correspondence with Dr. Fredric Simonen of the Pacific Northwest 

National Laboratory...............................................................................C-1 

Appendix D Comparison of Plant-Specific Reference Temperature Values..............................D-1 

Appendix E Detailed Reply to Peer Review Comment 22..................................................E-1 

Appendix F Detailed Reply to Peer Review Comment 75..................................................F-1 

Appendix G Flaw Distributions for Forgings.................................................................G-1 

Figures 

Figure 1.1. Proximity of currently operating PWRs to the 10 CFR 50.61 screening limit for PTS.............1-2 

Figure 2.1. Schematic illustration of the main components of the primary (red) and secondary (blue) 

systems in a pressurized-water reactor ...................................................................................2-2 

Figure 2.2. Figure 2.13 from SECY-82-465, depicting the final temperatures for 32 PTS precursor 

events experienced in commercial reactor service prior to 1982 ...........................................2-6 

Figure 2.3. The empirical data used to establish the ASME KIc curve .....................................................2-8 

Figure 3-1. High-level schematic showing how a probabilistic estimate of through-wall cracking 

frequency (TWCF) is combined with a TWCF acceptance criterion to arrive at a proposed 

revision of the PTS screening limit. .......................................................................................3-2 

Figure 3-2. The three plants analyzed in detail in the PTS reevaluation effort.........................................3-4 

Figure 3.3. Characterization of TH uncertainties......................................................................................3-9 

Figure 3-4. Illustration of the magnitude of Kapplied values that contribute to TWCF because they have 

a conditional probability of crack initiation > 0. The top graph shows all Kapplied values with 

CPI > 0 overlaid on the KIc transition curve from an analysis of Beaver Valley Unit 1 at 60 EFPY. 

The bottom graph shows these same results expressed in the form of a cumulative distribution 

function.................................................................................................................................3-18 

Figure 3.5. Distribution of crack initiating depths generated by FAVOR Version 03.1.........................3-19 

Figure 4-1. Structure of documentation summarized by this report. When these reports are cited in the 

text, the citation appears in italicized boldface to distinguish them from literature citations.4-2 

Figure 5.1. Integrated technical analyses comprising the PTS reanalysis project ....................................5-1 

Figure 5.2. Diagrammatic representation of the PRA approach ...............................................................5-3 

Figure 5.3. Functional event tree as the basis for PTS PRA analysis .....................................................5-11 

Figure 6.1. Schematic of RELAP5 Input and Output Processing.............................................................6-5 

Figure 6.2. Schematic of RELAP5 Execution Processing........................................................................6-6

Figure 6.3. Palisades Reactor Vessel Nodalization ................................................................................6-10 

Figure 6.4. Palisades Coolant Loop Nodalization ..................................................................................6-11 

Figure 6.5. Palisades Main Steam System Nodalization ........................................................................6-12 

Figure 6.6. Mass Flow Rate at Nozzle Outlet (Marviken Test 22).........................................................6-17 

Figure 6.7. Pressure Rise (MIT Pressurizer Test ST4) ...........................................................................6-18 
xii

Figure 6.8. Reactor Vessel Downcomer Fluid Temperatures (ROSA-IV Test SB-CL-18)....................6-20 

Figure 6.9. Reactor Vessel Downcomer Temperatures (ROSA-IV Test SB-HL-06).............................6-21 

Figure 6.10. Reactor Vessel Downcomer Fluid Temperatures (ROSA/AP600 Test AP-CL-03).............6-22 

Figure 6.11. Reactor Vessel Downcomer Fluid Temperatures (ROSA/AP600 Test AP-CL-09).............6-23 

Figure 6.12. Reactor Vessel Downcomer Fluid Temperatures (Test APEX-CE-13) ...............................6-25 

Figure 6.13. Pressurizer Pressure (Test APEX-CE-13) ............................................................................6-25 

Figure 6.14. Reactor Vessel Downcomer Fluid Temperatures (Test APEX-CE-05) ...............................6-26 

Figure 6.15. Reactor Vessel Downcomer Fluid Temperatures (LOFT Test L3-7)...................................6-27 

Figure 6.16. Reactor Vessel Downcomer Fluid Temperatures (LOFT Test L2-5)...................................6-28 

Figure 6.17. Reactor Vessel Downcomer Fluid Temperatures (LOFT Test L3-1)...................................6-30 

Figure 6.18. Reactor Vessel Downcomer Fluid Temperatures (MIST Test 360499)...............................6-31 

Figure 6.19. Reactor Vessel Downcomer Fluid Temperatures (MIST Test 3109AA) .............................6-32 

Figure 6.20. Reactor Vessel Downcomer Fluid Temperatures (MIST Test 4100B2) ..............................6-32 

Figure 6.21. UPTF 1-21 DC Velocities at Bottom-Core Elevation Measured, Turbine Meters, 

Clockwise from Cold Leg 2, Filtered...................................................................................6-37 

Figure 6.22. UPTF 1-21 DC Velocities at Bottom-Core Elevation RELAP5 

 (Calculated, Clockwise from Cold Leg 2) .........................................................................6-38 

Figure 6.23. UPTF 1-21 Wall Temperature Minus Fluid Temperature Under Cold Leg 2 

at Core-Top Elevation ..........................................................................................................6-38 

Figure 6.24. UPTF Test 1-21 Wall Temperatures at 25 mm Depth Vessel Wall in Orientation of 

Cold Leg 2............................................................................................................................6-39 

Figure 6.25. APEX–CE–05 Measured and RELAP5 Fluid Temperatures 

4D below and centered on the Cold Leg 4 nozzle................................................................6-39 

Figure 6.26. APEX–CE–05 Measured and RELAP5 Wall Temperatures 

4D below and centered on the Cold Leg 4 nozzle................................................................6-40 

Figure 6.27. Creare Data Compared to Dittus-Boelter .............................................................................6-40 

Figure 6.28. Sensitivity parameter ranking of a 2.8-in. (7.18-cm) surge line break LOCA .....................6-51 

Figure 6.29. Confirmation of the Linearly Additive Assumption for a 2.8-in. (7.18-cm) surge line break LOCA

..............................................................................................................................................6-51 

Figure 6.30. Illustration of the Statistical Results for Downcomer Temperature Distribution.................6-51 

Figure 7.1. Illustration of the interrelationships between PFM model and the TH and PRA models, 

and the four principal sub-models that comprise the PFM model..........................................7-3 

Figure 7.2. Illustration of a root cause diagram showing how uncertainties in input variables (E, F, G, and 

H) propagate through models (nodes), themselves potentially having uncertainty, to produce 

uncertainty in a resultant value (A) ........................................................................................7-4

Figure 7.3. Comparison of the new flaw distribution to the Marshall flaw distribution...........................7-7 

Figure 7.4. Illustration of the impact of the flaw distribution adopted in this study (improved PNNL) with 

that used in previous PTS calculations (Marshall flaw characterization) [Dickson 02] 

(analysis performed on Oconee at 60 EFPY) .........................................................................7-7 

Figure 7.5. Number of flaws simulated that have a conditional probability of through-wall cracking that 

exceeds zero (Oconee at 60 EFPY)......................................................................................7-13 

Figure 7.6. Combined effects of allowing KIa to exceed 200 ksi√in and allowing for ductile crack reinitiation on the upper shelf. Open points show TWCF results when KIa is allowed to exceed 

200 ksi√in and ductile crack re-initiation is permitted. RTNDT* is defined in [Kirk 12-02].7-15 

Figure 7.7. Comparison of temperature separation between crack initiation and crack arrest toughness 

transition curves assumed in our current calculations (blue curve) with the constant separation 

of ~30°C (~86°F) assumed by previous calculations ...........................................................7-15 

Figure 7.8. FAVOR data streams flow through three modules: (1) FAVLoad, (2) FAVPFM, and (3) 

FAVPost ...............................................................................................................................7-16 

Figure 7.9. Flow chart for improved PFM model implemented in FAVPFM showing the four primary 

nested loops – (1) RPV Trial Loop, (2) Flaw Loop, (3) Transient Loop, and (4) Time Loop........7-17 
xiii

Figure 7.10. Rollout diagram of beltline materials and representative fluence maps for Oconee Unit 1.7-18 

Figure 7-11. Test vessels used in the ITV and PTSE test series (top) and in the TSE test series (bottom)......7-20 

Figure 8.1. Rollout diagram of beltline materials and representative fluence maps for Oconee............8-15 

Figure 8.2. Typical distribution of through-wall cracking frequency (as calculated for Beaver Valley at 

32 EFPY (blue circles) and for extended embrittlement conditions (red diamonds) ...........8-17 

Figure 8-3. TWCF distribution percentile corresponding to the mean value..........................................8-17 

Figure 8-4. Relationship between a reference temperature (RT) and various measure of resistance to 

fracture (fracture toughness). This is a schematic illustration of temperature dependence 

only; scatter in fracture toughness is not shown...................................................................8-19 

Figure 8-5. Location and orientation of flaws simulated by FAVOR to exist in different regions 

of the RPV beltline...............................................................................................................8-21 

Figure 8-6. Effect of flaw orientation on the bending experienced by a cylinder 

subjected to a cold thermal shock on the inner diameter......................................................8-21

Figure 8.7. Through-wall variation of crack driving force (KI): axially oriented flaws 

compared to circumferentially oriented flaws 

(Comparison is shown for an 8-inch diameter surge line break in Beaver Valley (Transient #7 

– see top plot) at a time 11 minutes after the start of the transient (see bottom plot).) ........8-22 

Figure 8-8. Contributions of the different transients to the TWCF in Oconee Unit 1 

(Numbers on the abscissa are the TH case numbers, see Appendix A) ...............................8-29 

Figure 8-9. Contributions of the different transients to the TWCF in Beaver Valley Unit 1 

(Numbers on the abscissa are the TH case numbers, see Appendix A) ...............................8-30 

Figure 8-10. Contributions of the different transients to the TWCF in Palisades 

(Numbers on the abscissa are the TH case numbers, see Appendix A) ...............................8-30 

Figure 8-11. Variation in percent contribution to the total TWCF of different transient classes 

with reference temperature (RT) as defined in Table 8.6. The contributions of feed-and-bleed 

LOCAs and steam generator tube ruptures were also assessed. These transient classes made no 

contribution to TWCF, with the exception that feed-and-bleed LOCAs contributed < 0.1% to 

the TWCF of the Palisades RPV. .........................................................................................8-34 

Figure 8-12. Comparison of the annual frequencies of various broad classes of events for full-power conditions

..............................................................................................................................................8-35 

Figure 8.13. Effect of surge line and hot-leg break diameter on the cooldown characteristics of Beaver 

Valley (top) and Oconee (bottom)........................................................................................8-37 

Figure 8.14. Effect of break location on the cooldown characteristics in Oconee (top) and Palisades 

(bottom)................................................................................................................................8-37 

Figure 8.15. Effect of season on the cooldown characteristics of cold leg breaks in Palisades..............8-38 

Figure 8.16. Effect of surge line and hot-leg break diameter on the depressurization characteristics of 

Beaver Valley (top) and Oconee (bottom) ...........................................................................8-38 

Figure 8.17. Effect of surge line and hot-leg break diameter on the heat transfer coefficient in Beaver 

Valley (top) and Oconee (bottom)........................................................................................8-38 

Figure 8.18. Comparison of the cooldown characteristics of the three plants modeled 

for a spectrum of break diameters ........................................................................................8-39 

Figure 8.19. Effect of pipe break diameter and break location on the conditional probability of throughwall cracking. (CPTWC taken at approximately equivalent embrittlement levels between 

plants (Beaver Valley and Palisades at 60 EFPY, Oconee at Ext-Ob)) .................................8-40 

Figure 8.20. Effect of pipe break diameter, break location, and season (S=Summer, W=Winter) on the 

conditional probability of through-wall cracking for Palisades ...........................................8-41 

Figure 8.21. Effect of pipe break diameter and break location on the conditional proportion of initiated 

flaws that propagate through the wall. (CPTWC/CPI ratios taken at approximately equivalent 

embrittlement levels between plants (Beaver Valley and Palisades at 60 EFPY, Oconee at ExtOb).) .....................................................................................................................................8-41 
xiv

Figure 8.22. Effect of LOCA break diameter and break location on the time at which through-wall 

cracking occurs (Break times taken at approximately equivalent embrittlement levels between 

plants (Beaver Valley and Palisades at 60 EFPY, Oconee at Ext-Ob).).................................8-42 

Figure 8.23. The TWCF attributable only to primary side pipe breaks in the three study plants ...........8-43 

Figure 8-24. Radial profile of arrested crack in TSE 6 [Cheverton 85a] (The crack in this experiment 

arrested after propagating 95% of the way through the cylinder wall.) ...............................8-43 

Figure 8-25. Effect of pipe break diameter on the pressure in the primary system at the most likely time 

of failure ...............................................................................................................................8-44 

Figure 8-26. Oconee SO-1 transients where the stuck-open SRVs reclose after 3,000 seconds. 

(Transients in the upper graphs initiate from full power, while transients in the lower graphs 

initiate from hot zero power.)...............................................................................................8-46 

Figure 8-27. Oconee SO-1 transients where the stuck-open SRVs reclose after 6,000 seconds (Transients 

in the upper graphs initiate from full power, while transients in the lower graphs initiate from 

hot zero power.)....................................................................................................................8-48 

Figure 8-28. Beaver Valley SO-1 transients where a single stuck-open SRV recloses after 6,000 seconds 

(Transients in the upper graphs initiate from full power, while transients in the lower graphs 

initiate from hot zero power.)...............................................................................................8-49 

Figure 8-29. Beaver Valley SO-1 transients where a two stuck-open SRVs reclose after 6,000 seconds. 

(Transients in the upper graphs initiate from full power, while transients in the lower graphs 

initiate from hot zero power.)...............................................................................................8-50 

Figure 8-30. Beaver Valley SO-1 transients where stuck-open SRVs recloses after 3,000 seconds 

(All transients initiate from hot zero power conditions. Transients in the upper graphs have one 

stuck-open valve, whereas transients in the lower graphs have two stuck-open valves.) ......8-51 

Figure 8-31. Comparison of SO-1 transients between different plants for transients initiated from 

HZP conditions, valve reclosure after 6,000 sec., and no HPI throttling .............................8-53 

Figure 8.32. The TWCF attributable solely to stuck-open valves on the primary side that later reclose8-58 

Figure 8.33. Power level effects on MSLB transients at Beaver Valley. Both breaks are in containment 

and have AUX feed continuing to the faulted generator for 30 minutes. The operator throttles 

HPSI 30 minutes after allowed.............................................................................................8-61 

Figure 8.34. Power level effects on MSLB transients at Palisades. Both breaks are in containment and 

include failures of both MSIVs to close. The operator takes no actions to either isolate AUX 

feed or to throttle HPI...........................................................................................................8-62 

Figure 8.35. Break location effects on MSLB transients at Beaver Valley. Both breaks include 

continuous AUX feed and are initiated from full-power conditions. In transient 106, the 

operator controls HPSI 30 minutes after allowed.................................................................8-62 

Figure 8.36. Break isolation effects on MSLB transients at Palisades. Both breaks occur inside 

 containment and are initiated from HZP conditions.............................................................8-63 

Figure 8.37. Effect of HHSI control on MSLB transients at Beaver Valley. In both breaks, AUX feed is 

 isolated 30 minutes after the break occurs. Both breaks are initiated from full-power 

conditions. ............................................................................................................................8-63 

Figure 8.38. Percentage of initiated cracks that propagate through-wall for MSLB transients..............8-65 

Figure 8.39. TWCF attributable to MSLB transients..................................................................................8-65 

Figure 8.40. Comparison of TWCF attributable to primary side stuck-open valves, primary side pipe 

 breaks, and MSLBs. Note that the contribution of MSLBs here overrepresents their actual 

 contributions to TWCF because of conservatisms in their modeling. On each graph, an 

upper-bound curve is hand drawn to the data originally presented in Figure 8.23, Figure 8.32, 

and Figure 8.39. On the left hand graph, all three upper-bound curves are placed together for 

easy comparison. ..................................................................................................................8-67 

Figure 8.41. The cooldown rate of various SO-2 transients, graphs (d) through (f), compared to MSLBs, 

graph (c), and primary side transients, graphs (a) and (b)....................................................8-68 
xv

Figure 8.42. Small steam line break simulated by sticking open all MSSVs in steam generator A 

with AFW continuing to feed affected generator for 30 minutes. Beaver Valley transient 111 

occurs at HZP, while Beaver Valley transient 118 occurs at full power..............................8-69 

Figure 8.43. Reactor/turbine trip with loss of MFW and EFW in Oconee. 

 Operator opens all TBVs to depressurize the secondary side. ............................................8-69 

Figure 8.44. Reactor/turbine trip with two stuck-open safety valves in Oconee. ....................................8-69 

Figure 8.45. Reactor/turbine trip with one or two stuck-open ADVs (P-019 and P-055, respectively) 

 in Palisades..........................................................................................................................8-70 

Figure 9.1. CPTWC Behavior for LOCAs of Various Break Diameters..................................................9-6 

Figure 9.2. Flaw dimension and position descriptors adopted in FAVOR ...............................................9-9 

Figure 9.3. Distribution of through-wall position of cracks that initiate...................................................9-9 

Figure 9.4. Flaw depths that contribute to crack initiation probability in Beaver Valley Unit 1 

when subjected to medium- and large-diameter pipe break transients at two different 

embrittlement levels .............................................................................................................9-10 

Figure 9.5. Flaw depths that contribute to crack initiation probability in Beaver Valley Unit 1 

when subjected to stuck-open valve transients at two different embrittlement levels .........9-10 

Figure 9.6. Comparison of embrittlement shift uncertainties simulated by FAVOR (blue line with X 

symbols) with the uncertainties in the experimental embrittlement shift database used by 

Eason to construct the model................................................................................................9-12 

Figure 9.7. Effect of different methods to artificially increase embrittlement on the predicted TWCF 

values....................................................................................................................................9-14 

Figure 9.8. Effect of vessel wall thickness on the variation of applied-KI vs. time for a 16-in. (40.64-cm) 

diameter hot leg break in Beaver Valley. The flaw has the following dimensions: L=0.35-in., 

2a=0.50-in., 2c=1.5-in. (L=8.89-mm, 2a=12.7-mm, 2c=38.1-mm).....................................9-17 

Figure 9.9. Distribution of RPV wall thicknesses for PWRs currently in service [RVID2]...................9-17 

Figure 9.10.Effect of vessel wall thickness on the TWCF of various transients in Beaver Valley (all analyses 

at 60 EFPY)..........................................................................................................................9-17 

Figure 10.1.Post-RPV failure accident progression tree..........................................................................10-6 

Figure 11-1.Correlation of through-wall cracking frequencies with weighted reference temperature 

metrics for the three study plants (°R = °F + 459.69) ..........................................................11-8 

Figure 11-2.Correlation of through-wall cracking frequencies with maximum reference temperature 

metrics for the three study plants (°R = °F + 459.69) ..........................................................11-9 

Figure 11-3. Comparison of FAVOR 04.1 TWCF estimates with TWCF values estimated using weighted 

RT values (Eq. 11-1)...........................................................................................................11-10 

Figure 11-4. Comparison of FAVOR 04.1 TWCF estimates with TWCF values estimated using maximum 

RT values (Eq. 11-2)...........................................................................................................11-10 

Figure 11-5. Weighted RT-based screening criterion for plate vessels based on Eq. 11-1 

(Left: Effect of RTCW value for a fixed TWCFTOTAL value of 1x10-6; 

Right: Effect of TWCFTOTAL for a fixed RTCW value of 300°F (149°C)).............................11-11 

Figure 11-6. Maximum RT-based screening criterion for plate vessels based on Eq. 11-2...................11-12 

Figure 11-7. Comparison of the maximum RT-based screening limit for plate vessels based on Eq. 11-2 

with assessment points for all operating PWRs at EOL (32 EFPY, 40 operating years) (left) 

and EOLE (48 EFPY, 60 operating years) (right) (Plant RT values estimated from 

information in [RVID2]. RTMAX-CW is 300°F (149°C) for both graphs, exceeding the calculated 

RTMAX-CW value for any plant at EOL or EOLE.).....................................................................11-12 

Figure 11-8. TWCF values for operating PWRs estimated using Eq. 11-1 at EOL (left) and EOLE (right) 

(Values for individual plants are reported in Appendix D.) ...............................................11-13 

Figure 11-9. Maximum RT-based screening criterion for forged vessels based on Eq. 11-1, illustrating the 

effect of TWCFTOTAL ...........................................................................................................11-14 
xvi

Figure 11-10. Comparison of maximum RT-based screening limit for forged vessels based on Eq. 11-2 

with operating PWRs at EOL (32 EFPY, 40 operating years) (left) and EOLE (48 EFPY, 60 

operating years) (right) (Plant RT values estimated from information in [RVID2]. RTMAX-PL is 

estimated based on forging properties.)..............................................................................11-14 

Figure 12-1. Comparison of RT-based screening limit (curves) with assessment points for operating 

PWRs at EOL in plate vessels (left) and forged vessels (right) .........................................12-12 
xvii

Tables 

Table 3.1. Summary of uncertainty treatment in the three major technical areas .................. 3-10 

Table 3.2. Participating organizations .................................................................................... 3-21 

Table 5.1. Comparison of PRA analyses used in this study 

 with the PRA analyses that supported 10 CFR 50.61.............................................. 5-6 

Table 5.2 General classes of human failures considered in the PTS analyses.........................5-9 

Table 6.1 Phenomena Identification and Ranking Table for Pressurized Thermal Shock in 

PWRs ....................................................................................................................... 6-4 

Table 6.2 Summary of PTS Sensitivity Studies..................................................................... 6-43 

Table 6.3 List of Combined Sensitivity Indicators Varied for LAA Verification ................. 6-49 

Table 6.4 Example of Representative Scenario Selection ..................................................... 6-51 

Table 7.1. Summary of sources of experimental data sources for the flaw distribution...........7-5 

Table 8.1. Summary of Plant Parameters Relevant to the PTS Evaluation............................... 8-7 

Table 8.2. Plant specific material values drawn from the RVID2 database [RVID2]............ 8-10 

Table 8.3. Summary of vessel specific inputs for the flaw distribution .................................8-12 

Table 8.4. Mean crack initiation and through-wall cracking frequencies estimated for Oconee 

 Unit 1, Beaver Valley Unit 1, using FAVOR Version 04.1 ................................. 8-16 

Table 8.5. Relative contributions of various flaw populations to the FCI and TWCF values 

 estimated by FAVOR Version 04.1....................................................................... 8-25 

Table 8.6. Reference temperature metric used in Section 8.5. ............................................... 8-27 

Table 8.7. Transients that contribute most significantly to the estimated TWCF of Oconee 

 Unit 1 .....................................................................................................................8-30 

Table 8.8. Transients that contribute most significantly to the estimated TWCF of Beaver 

 Valley Unit 1...........................................................................................................8-31 

Table 8.9. Transients that contribute most significantly to the estimated TWCF of Palisades 8-32 

Table 8.10. Transient severity indicators and estimated values of CPTWC for Oconee 

 at Ext-Ob embrittlement conditions........................................................................ 8-54 

Table 8.11. Mean operator action probabilities in our modeling of SO-1 transients................ 8-57 

Table 8.12. Factors contributing to the severity and risk-dominance of various transient 

 classes ...................................................................................................................8-73

Table 9.1. Summary of Oconee Downcomer Fluid Temperature Sensitivity Results for 

 LOCA.........................................................................................................................9-3 

Table 9.2. Summary of Beaver Valley Downcomer Fluid Temperature Sensitivity Results for 

 LOCA.........................................................................................................................9-3 

Table 9.3. Summary of Palisades Downcomer Fluid Temperature Sensitivity Results for 

 LOCA.........................................................................................................................9-4 

Table 9.4. Summary of Downcomer Fluid Temperature Sensitivity Results 

 for Stuck-Open Primary Side Valves......................................................................... 9-5 

Table 9.5. Plant list for generalization study ............................................................................ 9-21

Table 9.6 Important PTS scenarios and corresponding plant design and operational features9-22 

Table 9.7. Scenarios covered under the external event analyses .............................................. 9-37 

Table 9.8. Small-break LOCA internal event results................................................................ 9-37 
xviii

Table 9.9. Small-break LOCA TWCF comparison .................................................................. 9-39 

Table 10.1. Post-RPV-failure technical issues...........................................................................10-5 

Table 10.2. Potentially risk-significant post-RPV failure accident progression scenarios........10-8 

Table 10.3. Key APET scenarios............................................................................................. 10-11 

Table 11.1. Contributions of different flaw populations to the TWCF values estimated by FAVOR 

 Version 04.1 ............................................................................................................. 11-5 

Table 11.2. Non-best estimate aspects of the models used to develop the RT-based screening 

 limits for PTS shown in Figure 11-5 and Figure 11-9.......................................... 11-16 

Table 12.1. Factors contributing the severity and risk dominance of various transient 

 classes. ....................................................................................................................12-3 
xix

Executive Summary 

This report summarizes the results of a 5-year study conducted by the U.S. Nuclear Regulatory Commission 

(NRC), Office of Nuclear Regulatory Research (RES). The aim of this study was to develop the technical 

basis for revision of the Pressurized Thermal Shock (PTS) Rule, as set forth in Title 10, Section 50.61, 

of the Code of Federal Regulations (10 CFR 50.61), “Fracture Toughness Requirements for Protection 

Against Pressurized Thermal Shock Events,” consistent with the NRC’s current guidelines on risk-informed 

regulation. This report, together with other supporting reports documenting the study details and results, 

provides this basis. 

This executive summary begins with a description of PTS, how it might occur, and its potential consequences 

for the reactor pressure vessel (RPV). This is followed by a summary of the current regulatory approach 

to PTS, which leads directly to a discussion of the motivations for conducting this project. Following this 

introductory information, we describe the approach used to conduct the study, and summarize our key findings 

and recommendations, which include a proposal for revision of the PTS screening limits. We then conclude 

the executive summary with a discussion of the potential impact of this proposal on regulations other than 

10 CFR 50.61. 

Description of PTS 

During the operation of a nuclear power plant, the RPV walls are exposed to neutron radiation, resulting in 

localized embrittlement of the vessel steel and weld materials in the area of the reactor core. If an embrittled 

RPV had an existing flaw of critical size and certain severe system transients were to occur, the flaw 

could propagate very rapidly through the vessel, resulting in a through-wall crack and challenging the integrity 

of the RPV. The severe transients of concern, known as pressurized thermal shock (PTS), are characterized 

by a rapid cooling (i.e., thermal shock) of the internal RPV surface and downcomer, which may be 

followed by repressurization of the RPV. Thus, a PTS event poses a potentially significant challenge to 

the structural integrity of the RPV in a pressurized-water reactor (PWR). 

A number of abnormal events and postulated accidents have the potential to thermally shock the vessel 

(either with or without significant internal pressure). These events include a pipe break or stuck-open valve 

in the primary pressure circuit, a break of the main steam line, etc. During such events, the water level in 

the core drops as a result of the contraction produced by rapid depressurization. In events involving a break 

in the primary pressure circuit, an additional drop in water level occurs as a result of leakage from the break. 

Automatic systems and operators must provide makeup water in the primary system to prevent overheating of 

the fuel in the core. However, the makeup water is much colder than that held in the primary system. As 

a result, the temperature drop produced by rapid depressurization coupled with the near-ambient 

temperature of the makeup water produces significant thermal stresses in the thick section steel wall of the 

RPV. For embrittled RPVs, these stresses could be sufficient to initiate a running crack, which could 

propagate all the way through the vessel wall. Such through-wall cracking of the RPV could precipitate 

core damage or, in rare cases, a large early release of radioactive material to the environment. 

Fortunately, the coincident occurrence of critical-size flaws, embrittled vessel steel and weld material, 

and a severe PTS transient is a very low-probability event. In fact, only a few currently operating PWRs 

are projected to closely approach the current statutory limit on the level of embrittlement during their 

planned operational life. 
xx

Current Regulatory Approach to PTS 

As set forth in 10 CFR 50.61, the PTS Rule requires licensees to monitor the embrittlement of their RPVs 

using a reactor vessel material surveillance program qualified under Appendix H to 10 CFR Part 50, 

“Reactor Vessel Material Survellience Program Requirements.” The surveillance results are then used 

together with the formulae and tables in 10 CFR 50.61 to estimate the fracture toughness transition 

temperature (RTNDT) of the steels in the vessel’s beltline and how those transition temperatures increase 

as a result of irradiation damage throughout the operational life of the vessel. For licensing purposes, 

10 CFR 50.61 provides instructions on how to use these estimates of the effect of irradiation damage 

to estimate the value of RTNDT that will occur at end of license (EOL), a value called RTPTS. 10 CFR 50.61 

also provides “screening limits” (maximum values of RTNDT permitted during the plant’s operational life) 

of +270°F (132°C) for axial welds, plates, and forgings, and +300°F (149°C) for circumferential welds. 

These screening limits correspond to a limit of 5x10-6 events/year on the annual probability of developing 

a through-wall crack [RG 1.154]. Should RTPTS exceed these screening limits, 10 CFR 50.61 requires 

the licensee to either take actions to keep RTPTS below the screening limit (by implementing “reasonably 

practicable” flux reductions to reduce the embrittlement rate, or by deembrittling the vessel by annealing 

[RG 1.162]), or perform plant-specific analyses to demonstrate that operating the plant beyond the 10 CFR 50.61 

screening limit does not pose an undue risk to the public [RG 1.154]. 

While no currently operating PWR has an RTPTS value that exceeds the 10 CFR 50.61screening limit 

before EOL, several plants are close to the limit (3 are within 2°F, while 10 are within 20°F). Those plants 

are likely to exceed the screening limit during the 20-year license renewal period that is currently being 

sought by many operators. Moreover, some plants maintain their RTPTS values below the 10 CFR 50.61 

screening limits by implementing flux reductions (low-leakage cores, ultra-low-leakage cores), which are 

fuel management strategies that can be economically deleterious in a deregulated marketplace. Thus, 

the 10 CFR 50.61 screening limits can restrict both the licensable and economic lifetime of PWRs. 

Motivation for this Project 

It is now widely recognized that the state of knowledge and data limitations in the early 1980s 

necessitated conservative treatment of several key parameters and models used in the probabilistic 

calculations that provided the technical basis for the current PTS Rule. The most prominent of these 

conservatisms include the following factors: 

• highly simplified treatment of plant transients (very coarse grouping of many operational sequences 

(on the order of 105

) into very few groups (≈10), necessitated by limitations in the computational 

resources needed to perform multiple thermal-hydraulic calculations) 

• lack of any significant credit for operator action 

• characterization of fracture toughness using RTNDT, which has an intentional conservative bias 

• use of a flaw distribution that places all flaws on the interior surface of the RPV, and, in general, 

contains larger flaws than those usually detected in service 

• a modeling approach that treated the RPV as if it were made entirely from the most brittle of its 

constituent materials (welds, plates, or forgings) 

• a modeling approach that assessed RPV embrittlement using the peak fluence over the entire interior 

surface of the RPV 
xxi

These factors indicate the high likelihood that the current 10 CFR 50.61 PTS screening limits are 

unnecessarily conservative. Consequently, the NRC staff believed that reexamining the technical basis 

for these screening limits, based on a modern understanding of all the factors that influence PTS, 

would most likely provide strong justification for substantially relaxing these limits. For these reasons, 

RES undertook this study with the objective of developing the technical basis to support a risk-informed 

revision of the PTS Rule and the associated PTS screening limit. 

Approach 

As illustrated in the following figure, three main models (shown as solid blue squares), taken together, 

allow us to estimate the annual frequency of through-wall cracking in an RPV: 

• probabilistic risk assessment (PRA) event sequence analysis 

• thermal-hydraulic (TH) analysis 

• probabilistic fracture mechanics (PFM) analysis 

PRA Event

Sequence

Analysis

(SAPPHIRE)

Thermal

Hydraulic

Analysis

(RELAP)

Probabilistic

Fracture

Analysis

(FAVOR)

Sequence

Definitions

Sequence

Frequencies

freq

Conditional

Probability of

Thru-Wall

Cracking, CPTWC

P(t), T(t), &

HTC(t)

Yearly

Frequency of

Thru-Wall

Cracking

[CPTWC]

x

[freq]

Probabilistic Estimation of Through-Wall Cracking Frequency

Vessel damage, age, 

or operational metric

Yearly Frequency of

Thru-Wall Cracking

Screening 

Limit

Acceptance Criterion 

for TWC Frequency

Established consistent with

• 1986 Commission safety goal 

policy statement

• June 1990 SRM

• RG1.174

Screening Limit 

Development

Schematic showing how a probabilistic estimate of through-wall cracking 

frequency (TWCF) is combined with a TWCF acceptance criterion to arrive 

at a proposed revision of the PTS screening limit 

First, a PRA event sequence analysis is performed to define the sequences of events that are likely to cause 

a PTS challenge to RPV integrity, and estimate the frequency with which such sequences can be expected 

to occur. The event sequence definitions are then passed to a TH model that estimates the temporal variation 

of temperature, pressure, and heat-transfer coefficient in the RPV downcomer, which is characteristic of 

each sequence definition. These temperature, pressure, and heat-transfer coefficient histories are then 

passed to a PFM model that uses the TH output, along with other information concerning plant design 

and construction materials, to estimate the time-dependent “driving force to fracture” produced by a particular 

event sequence. The PFM model then compares this estimate of fracture driving force to the fracture toughness, 

or fracture resistance, of the RPV steel. This comparison allows us to estimate the probability that a crack 

could grow to sufficient size that it would penetrate all the way through the RPV wall if that particular 

sequence of events actually occured. The final step in the analysis involves a simple matrix multiplication 

of the probability of through-wall cracking (from the PFM analysis) with the frequency at which a 

particular event sequence is expected to occur (as defined by the event-tree analysis). This product 

establishes an estimate of the annual frequency of through-wall cracking that can be expected for a 

particular plant after a particular period of operation when subjected to a particular sequence of events. The 
xxii

annual frequency of through-wall cracking is then summed for all event sequences to estimate the total 

annual frequency of through-wall cracking for the vessel. Performance of such analyses for various 

operating lifetimes provides an estimate of how the annual frequency of through-wall cracking can be 

expected to vary over the lifetime of the plant. 

The probabilistic calculations just described are performed to establish the technical basis for a revised 

PTS Rule within an integrated systems analysis framework. Our approach considers a broad range of factors 

that influence the likelihood of vessel failure during a PTS event, while accounting for uncertainties 

in these factors across a breadth of technical disciplines. Two central features of this approach are a focus 

on the use of realistic input values and models (wherever possible), and an explicit treatment of uncertainties 

(using currently available uncertainty analysis tools and techniques). Thus, our current approach 

improves upon that employed in developing SECY-82-465, which included intentional and unquantified 

conservatisms in many aspects of the analysis, and treated uncertainties implicitly by incorporating them 

into the models. 

Key Findings 

The findings from this study are divided into the following five topical areas: (1) the expected magnitude 

of the through-wall cracking frequency (TWCF) for currently anticipated operational lifetimes, 

(2) the material factors that dominate PTS risk, (3) the transient classes that dominate PTS risk, (4) the 

applicability of these findings (based on detailed analyses of three PWRs) to PWRs in general, and (5) the 

annual limit on TWCF established consistent with current guidelines on risk-informed regulation. In this 

summary, the conclusions are presented in boldface italic, while the supporting information is shown in 

regular type. 

TWCF Magnitude for Currently Anticipated Operational Lifetimes 

• The degree of PTS challenge is low for currently anticipated lifetimes and operating conditions. 

o Even at the end of license extension (60 operational years, or 48 effective full-power years (EFPY) 

at an 80% capacity factor), the mean estimated TWCF does not exceed 2x10-8/year for the plants 

analyzed. Considering that the RPVs at the Beaver Valley Power Station and Palisades Nuclear 

Power Plant are constructed from some of the most irradiation-sensitive materials in commercial 

reactor service today, these results suggest that, provided that operating practices do not change 

dramatically in the future, the operating reactor fleet is in little danger of exceeding either 

the TWCF limit of 5x10-6/yr expressed by Regulatory Guide 1.154 [RG 1.154] or the value 

of 1x10-6/yr recommended in Chapter 10 of this report — even after license extension. 

Material Factors and their Contributions to PTS Risk 

• Axial flaws, and the toughness properties that can be associated with such flaws, control nearly all 

of the TWCF. 

o Axial flaws are much more likely than circumferential flaws to propagate through the RPV wall 

because the applied fracture driving force increases continuously with increasing crack depth 

for an axial flaw. Conversely, circumferentially oriented flaws experience a driving force peak 

mid-wall, providing a natural crack arrest mechanism. It should be noted that crack initiation 

from circumferentially oriented flaws is likely; it is only their through-wall propagation that is 

much less likely (relative to axially oriented flaws). 

o It is, therefore, the toughness properties that can be associated with axial flaws that control nearly 

all of the TWCF. These include the toughness properties of plates and axial welds at the flaw locations. 

Conversely, the toughness properties of both circumferential welds and forgings have little effect 

on the TWCF because these can be associated only with circumferentially oriented flaws. 
xxiii

Transients and their Contributions to PTS Risk 

• Transients involving primary side faults are the dominant contributors to TWCF, while transients 

involving secondary side faults play a much smaller role. 

o The severity of a transient is controlled by a combination of three factors: 

 initial cooling rate, which controls the thermal stress in the RPV wall 

 minimum temperature of the transient, which controls the resistance of the vessel to fracture 

 pressure retained in the primary system, which controls the pressure stress in the RPV wall 

o The significance of a transient (i.e., how much it contributes to PTS risk) depends on these three 

factors and the likelihood that the transient will occur. 

o Our analysis considered transients in the following classes (as shown in the following table): 

 primary side pipe breaks 

 stuck-open valves on the primary side 

 main steam line breaks 

 stuck-open valves on the secondary side 

 feed-and-bleed 

 steam generator tube rupture 

 mixed primary and secondary initiators 

Factors contributing to the severity and risk-dominance of various transient classes 

Transient Severity 

Transient Class 

Cooling Rate Minimum 

Temperature Pressure 

Transient 

Likelihood 

TWCF 

Contribution 

Large-Diameter Fast Low Low Low Large 

Medium-Diameter Moderate Low Low Moderate Large Primary Side 

Pipe Breaks 

Small-Diameter Slow High Moderate High ~0 

Stuck-Open Valve Recloses Slow Moderate High High Large 

Valves, 

Primary Side Valve Remains Open Slow Moderate Low High ~0 

Main Steam Line Break Fast Moderate High High Small 

Stuck-Open Valve(s), Secondary Side Moderate High High High ~0 

Feed-and- Bleed Slow Low Low Low ~0 

Steam Generator Tube Rupture Slow High Moderate Low ~0 

Mixed Primary & Secondary Initiators Slow Mixed Very Low ~0 

Color Key Enhances TWCF Contribution Intermediate Diminishes TWCF Contribution 

o The table above provides a qualitative summary our results for these transient classes in terms of 

both transient severity and the likelihood that the transient will occur. The color-coding of table 

entries indicates the contribution (or lack thereof) of these factors to the TWCF of the various 

classes of transients. This summary indicates that the risk-dominant transients (medium- and largediameter primary side pipe breaks, and stuck-open primary side valves that later reclose) all have 

multiple factors that, in combination, result in their significant contributions to TWCF. 

 For medium- to large-diameter primary side pipe breaks, the fast to moderate cooling rates 

and low downcomer temperatures (generated by rapid depressurization and emergency injection 

of low-temperature makeup water directly to the primary) combine to produce a high-severity 

transient. Despite the moderate to low likelihood that these transients will occur, their severity 

(if they do occur) makes them significant contributors to the total TWCF. 
xxiv

 For stuck-open primary side valves that later reclose, the repressurization associated with 

valve reclosure coupled with low temperatures in the primary combine to produce a highseverity transient. This, coupled with a high likelihood of transient occurrence, makes stuckopen primary side valves that later reclose significant contributors to the total TWCF. 

 The small or negligible contribution of all secondary side transients (main steam line break, 

stuck-open secondary valves) results directly from the lack of low temperatures in the primary 

system. For these transients, the minimum temperature of the primary for times of relevance 

is controlled by the boiling point of water in the secondary (212°F (100°C) or above). 

At these temperatures, the fracture toughness of the RPV steel is sufficiently high to resist 

vessel failure in most cases. 

Applicability of These Findings to PWRs in General 

• Credits for operator action, while included in our analysis, do not influence these findings in any 

significant way. Operator action credits can dramatically influence the risk-significance of individual

transients. Therefore, appropriate credits for operator action need to be included as part of a “best estimate” 

analysis because there is no way to establish a priori if a particular transient will make a large contribution 

to the total risk. Nonetheless, the results of our analyses demonstrate that these operator action credits 

have a small overall effect on a plant’s total TWCF, for reasons detailed below.

o Medium- and Large-Diameter Primary Side Pipe Breaks: No operator actions are modeled 

for any break diameter because, for these events, the safety injection systems do not fully refill 

the upper regions of the reactor coolant system (RCS). Consequently, operators would never 

take action to shut off the pumps. 

o Stuck-Open Primary Side Valves that May Later Reclose: Reasonable and appropriate credit 

for operator actions (throttling of the high-pressure injection (HPI) system) has been included 

in the PRA model. However, these credits have a small influence on the estimated values 

of vessel failure probability attributable to transients caused by a stuck-open valve in the primary 

pressure circuit (SO-1 transients) because the credited operator actions only prevent repressurization 

when SO-1 transients initiate from Hot Zero Power (HZP) conditions and when the operators 

act promptly (within 1 minute) to throttle the HPI. Complete removal of operator action credits 

from the model only slightly increases the total risk associated with SO-1 transients. 

o Main Steam Line Breaks: For the overwhelming majority of transients caused by a main steam line 

break (MSLB), vessel failure is predicted to occur between 10 and 15 minutes after transient initiation 

because the thermal stresses associated with the rapid cooldown reach their maximum within this 

timeframe. Thus, all of the long-term effects (isolation of feedwater flow, timing of HPSI control) 

that can be influenced by operator actions have no effect on vessel failure probability because 

such factors influence the progression of the transient after failure has occurred (if it occurs at all). 

Only factors affecting the initial cooling rate (i.e., plant power level at time of transient initiation, 

break location inside or outside of containment) can influence the conditional probability 

of through-wall cracking (CPTWC), and operator actions do not influence such factors in any way. 

• Because the severity of the most significant transients in the dominant transient classes is controlled 

by factors that are common to PWRs in general, the TWCF results presented herein can be used 

with confidence to develop revised PTS screening criteria that apply to the entire fleet of operating 

PWRs. 

o Medium- and Large-Diameter Primary Side Pipe Breaks: For these break diameters, the fluid 

in the primary cools faster than the wall of the RPV. In this situation, only the thermal conductivity 

of the steel and the thickness of the RPV wall control the thermal stresses and, thus, the severity 

of the fracture challenge. Perturbations in the fluid cooldown rate controlled by break diameter, 

break location, and season of the year do not play a role. Thermal conductivity is a physical property, 
xxv

so it is very consistent for all RPV steels, and the thicknesses of the three RPVs analyzed are typical 

of PWRs. Consequently, the TWCF contribution of medium- to large-diameter primary side 

pipe breaks is expected to be consistent from plant-to-plant and can be well represented for all PWRs 

by the analyses reported herein. 

o Stuck-Open Primary Side Valves that May Later Reclose: A major contributor to the risk-significance 

of SO-1 transients is the return to full system pressure once the valve recloses. The operating 

and safety relief valve pressures of all PWRs are similar. Additionally, as previously noted, 

operator action credits only slightly affect the total risk associated with this transient class. 

o Main Steam Line Breaks: Since MSLBs fail early (within 10–15 minutes after transient initiation), 

only factors affecting the initial cooling rate can have any influence on the CPTWC values. 

These factors, which include the plant power level at event initiation and the location of the break 

(inside or outside of containment), are not influenced by operator actions in any way. 

• Sensitivity studies performed on the TH and PFM models to investigate the effect of credible model 

variations on the predicted TWCF values revealed no effects significant enough to recommend 

changes to the baseline RELAP and FAVOR models, or to recommend cautions regarding 

the robustness of those models. 

• An investigation of design and operational characteristics for five additional PWRs revealed 

no differences in sequence progression, sequence frequency, or plant thermal-hydraulic response 

significant enough to call into question the applicability of the TWCF results from the three 

detailed plant analyses to PWRs in general. 

• An investigation of potential external initiating events (e.g., fires, earthquakes, floods) revealed 

that the contribution of those events to the total TWCF can be regarded as negligible. 

Annual Limit on TWCF 

• The current guidance provided by Regulatory Guide 1.174 [RG 1.174] for large early release 

is appropriately applied to setting an acceptable annual TWCF limit of 1x10-6 events/year. 

o While many post-PTS accident progressions led only to core damage (which suggests a TWCF limit 

of 1x10-5 events/year limit in accordance with Regulatory Guide 1.174), uncertainties in 

the accident progression analysis led to our recommendation to adopt the more conservative limit 

of 1x10-6 events/year based on LERF. 

Recommended Revision of the PTS Screening Limits 

We recommend using different reference temperature (RT) metrics to characterize an RPV’s resistance 

to fractures initiating from different flaws at different locations in the vessel. Specifically, we recommend 

a reference temperature for flaws occurring along axial weld fusion lines (RTAW or RTAW-MAX), 

another for flaws occurring in plates or in forgings (RTPL or RTPL-MAX), and a third for flaws occurring 

along circumferential weld fusion lines (RTCW or RTCW-MAX). In each of these reference temperature pairs, 

the first metric is a weighted value that accounts for the differences between plants in weld fusion line 

area or plate volume, while the second metric is a maximum value that can be estimated based only on 

the information in the NRC’s Reactor Vessel Integrity Database (RVID). We also recommend using 

different RT values together to characterize the fracture resistance of the vessel’s beltline region, 

in recognition of the fact that the probability of vessel fracture initiating from different flaw populations 

varies considerably in response to factors that are both understood and predictable. Correlations between 

these RT metrics and the TWCF attributable to axial weld flaws, plate flaws, and circumferential weld flaws 

show little plant-to-plant variability because of the general similarity of PTS challenges among plants. 
xxvi

RT-based screening limits were established by setting the total TWCF (i.e., that attributable to axial weld flaws 

and plate flaws and circumferential weld flaws) equal to the reactor vessel failure frequency acceptance 

criterion of 1x10-6 events per year. The following figures graphically represent these screening limits 

(for the maximum RT metrics), along with an assessment of all operating PWRs relative to these limits. 

In these figures, the region of the graphs between the red locus and the origin has TWCF values below 

the 1x10-6 acceptance criterion, so these combinations of reference temperatures would be considered 

acceptable and require no further analysis. By contrast, the region of the graph outside of the red locus 

has TWCF values above the 1x10-6 acceptance criterion, indicating the need for additional analysis 

or other measures to justify continued plant operation. Clearly, operating PWRs do not closely approach 

the 1x10-6/year limit. At EOL, at least 70°F, and up to 290°F, (39 to 161°C) separate plate-welded PWRs 

from the proposed screening limit; this separation between plant-specific values and the proposed 

screening limit reduces by 10–20°F (5.5 to 11°C) at end of license extension (EOLE, defined as 60 

operating years or 48 EFPY). Additionally, no forged plant is anywhere close to the limit of 1x10-6 events 

per year at either EOL or EOLE. This separation of operating plants from the screening limit contrasts 

markedly with the current situation, where the most embrittled plants are within 1°F (0.5°C) of the 

screening limit set forth in 10 CFR 50.61. These differences in the “proximity” of operating plants to the 

current (10 CFR 50.61) and proposed screening limits are illustrated by the bar graph on the next page. 

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300

RTMAX-AW [oF]

RTMAX-PL [oF]

Plate 

PWRs 

at EOL

1E-8

1E-7

5E-7 1E-6

Forged 

PWRs 

at EOL

0

50

100

150

200

250

300

350

-50 50 150 250 350 450

RTMAX-CW [

o

F]

Forging: RTMAX-PL [oF]

1E-8

1E-7

5E-7 1E-6

Comparison of RT-based screening limits (curves) 

with assessment points for operating PWRs at EOL 

(Left: plate vessels, Right: forged vessels) 
xxvii

0

4

8

12

16

Number of PWRs

Relative to RTPTS limits in 10CFR50.61

Relative to RT-MAX limits proposed in NUREG-1806 

400 80 120 160 200 240 280 320 360 400

oF from PTS Screening Limit after 40 Years of Operation

Relative to Current 10CFR50.61 Limits

Relative to NUREG-1806 Proposed Limits

0

4

8

12

16

Number of PWRs

Relative to RTPTS limits in 10CFR50.61

Relative to RT-MAX limits proposed in NUREG-1806 

400 80 120 160 200 240 280 320 360 400

oF from PTS Screening Limit after 40 Years of Operation

Relative to Current 10CFR50.61 Limits

Relative to NUREG-1806 Proposed Limits

Difference between the proximity of operating PWRs to the current RTPTS screening limits 

and to the screening limits proposed based on the work presented in this report. 

These RT-based screening limits (and similar limits described in the text for application to weighted 

RT values) apply to PWRs in general, subject only to the following provisos: 

• When assessing a forged vessel where the forging has a very high reference temperature (RTPL above 

225°F (107°C)) and the forging is believed to be susceptible to subclad cracking, a plant-specific 

analysis of the TWCF produced by the subclad cracks should be performed. However, no forging 

is projected to reach this level of embrittlement, even at EOLE. 

• When assessing an RPV having a wall thickness of 7-in. (18-cm) or less (7 vessels), the proposed 

RT limits are conservative. 

• When assessing an RPV having a wall thickness of 11-in. (28-cm) or greater, the proposed RT limits 

may be nonconservative. For the three plants meeting this criterion, either the RT limits would need 

to be reduced or known conservatisms in the current analysis would have to be removed to demonstrate 

compliance with the TWCF limit of 1x10-6 event/year. However, because these three plants 

are Units 1, 2, and 3 of the Palo Verde Nuclear Generating Station, which have vessels with very low 

embrittlement projected at EOL and EOLE, there is little practical need for such plant-specific analysis. 

Aside from relying on different RT metrics than 10 CFR 50.61, this proposed revision of the PTS screening limit 

differs from the current screening limit in the absence of a “margin term.” Use of a margin term is appropriate 

to account (at least approximately) for factors that occur in application but were not considered in the analysis 

upon which the screening limit is based. For example, the 10 CFR 50.61 margin term accounts for uncertainty 

in copper, nickel, and initial RTNDT. However, our model explicitly considers uncertainty in all of these 

variables, and represents these uncertainties as being larger (a conservative representation) than would be 

appropriate in any plant-specific application of the proposed screening limit. Consequently, use of 

the 10 CFR 50.61 margin term with the new screening limits is inappropriate. In general, the following 

additional reasons suggest that use of any margin term with the proposed screening limits is inappropriate: 
xxviii

(1) The TWCF values used to establish the screening limit represent 90th percentile values or greater. 

(2) The results from our three plant-specific analyses apply to PWRs in general, as demonstrated 

in Chapters 8 and 9 of this report. 

(3) Certain aspects of our modeling cannot reasonably be represented as “best estimates.” On balance, 

there is a conservative bias to these non-best-estimate aspects of our analysis because residual 

conservatisms in the model far outweigh residual nonconservatisms. 
xxix

Abbreviations 

1⁄4-T FLAW Surface-breaking flaw defined by ASME Boiler and Pressure Vessel Code 

as having a depth equal to one-quarter of the vessel wall thickness 

and a length equal to six times the flaw depth 

1D One-Dimensional 

ABAQUS Commercial finite element code developed by Hibbett, Karlsson, 

and Sorenson in Pawtucket, Rhode Island 

ACRS Advisory Committee on Reactor Safety (NRC) 

ADV Atmospheric Dump Valve 

AFW Auxiliary Feedwater 

APET Accident Progression Event Tree 

APEX Advanced Plant Experiment 

ASME American Society of Mechanical Engineers 

ASTM American Society for Testing and Materials 

ATWS Anticipated Transient without Scram 

B&W Babcock and Wilcox 

BWOG Babcock and Wilcox Owners’ Group 

BCC Body-Centered Cubic 

BWR Boiling-Water Reactor 

CDF Core Damage Frequency 

CE Combustion Engineering 

CEOG Combustion Engineering Owners’ Group 

CFD Computational Fluid Dynamics 

CL Cold Leg 

CFR Code of Federal Regulations

CFT Core Flood Tank 

CPI Conditional Probability of Crack Initiation 

CPTWC Conditional Probability of Through-Wall Cracking 

CSAU Code Scaling, Applicability, and Uncertainty Methodology 

CSNI Committee on the Safety of Nuclear Installations 

CST Condensate Storage Tank 

CVN Charpy V-Notch 

ECC Emergency Core Cooling 

ECCS Emergency Core Cooling System 

EFPY Effective Full-Power Years 

EFW Emergency Feedwater 

EOL End of License (40 operating years, 32 EFPY) 

EOLE End of License Extension (60 operating years, 48 EFPY) 
xxx

EPRI Electric Power Research Institute 

ESFAS Engineered Safety Features Actuation System 

F&B Feed-and-Bleed 

FAVOR Fracture Analysis of Vessels, Oak Ridge 

FCI Frequency of Crack Initiation 

GMAW Gas Metal Arc Weld 

H2TS Hierarchical, Two-Tiered Scaling 

HCLPF High Confidence of Low Probability of Failure 

HEP Human Error Probability 

HFE Human Failure Event 

HPI High-Pressure Injection 

HPSI High-Pressure Safety Injection 

HRA Human Reliability Analysis 

HSSI Heavy Section Steel Irradiation (Project) 

HZP Hot Zero Power 

IAEA International Atomic Energy Agency 

ID Inner Diameter 

IPE Individual Plant Examination 

IPEEE Individual Plant Examination of External Events 

IPTS Integrated Pressurized Thermal Shock 

ISLOCA Interfacing Systems Loss-of-Coolant Accident 

ITV Intermediate Test Vessel 

IVO Imatran Voima Oy 

LAS Low-Alloy Steel 

LBLOCA Large-Break Loss-of-Coolant Accident (pipe diameters above ~8-in. (~20-cm)) 

LEFM Linear Elastic Fracture Mechanics 

LER Licensee Event Report 

LERF Large Early Release Frequency 

LOCA Loss-of-Coolant Accident 

LOF Lack of Inter-Run Fusion 

LOFT Loss-of-Fluid Test facility 

LPI Low-Pressure Injection 

LPSI Low-Pressure Safety Injection 

MBLOCA Medium-Break Loss-of-Coolant Accident (pipe diameters of ~4 to 8-in. 

(~10 to 20-cm)) 

MFIV Main Feedwater Isolation Valve 

MFW Main Feedwater 

MIST Multi-loop Integral System Test 

MRJ Materials Reliability Project 

MSIV Main Steam Isolation Valve 

MSLB Main Steam Line Break 
xxxi

NDT Nil-Ductility Temperature 

NEA Nuclear Energy Agency (OECD) 

NRC U.S. Nuclear Regulatory Commission 

NRR Office of Nuclear Reactor Regulation (NRC) 

NUREG/CR NRC Technical Report Designator (Contractor-prepared Report 

published by the U.S. Nuclear Regulatory Commission) 

OD Outer Diameter 

OECD Organization for Economic Cooperation and Development 

ORNL Oak Ridge National Laboratory 

PFM Probabilistic Fracture Mechanics 

PIRT Phenomena Identification and Ranking Table 

PNNL Pacific Northwest National Laboratories 

PORV Power-Operated Relief Valve 

Ppb Parts per Billion 

PRA Probabilistic Risk Assessment 

PRODIGAL Probability of Defect Initiation and Growth Analysis 

PTS Pressurized Thermal Shock 

PTSE Pressurized Thermal Shock Experiment 

PVRUF Pressure Vessel Research Users’ Facility 

PWR Pressurized-Water Reactor 

QHO Quantitative Health Objective, as defined by the Commission’s Safety Goal 

Policy Statement [NRC FR 86] 

RCP Reactor Coolant Pump 

RCS Reactor Coolant System 

RELAP Reactor Leak and Power excursion code 

REMIX a computer program used to determine the temperature of a plume 

in the downcomer when the flow in the loops is stagnant 

RES Office of Nuclear Regulatory Research (NRC) 

RG Regulatory Guide 

RLE Review-Level Earthquake 

ROSA Rig of Safety Assessment 

RPS Reactor Protection System 

RPV Reactor Pressure Vessel 

RT Reference Temperature 

RVFF Reactor Vessel Failure Frequency 

RVID Reactor Vessel Integrity Database 

RWST Refueling Water Storage Tank 

SAPHIRE Systems Analysis Programs for Hands-on Integrated Reliability Evaluations 

SAW Submerged Arc Weld 

SBLOCA Small-Break Loss-of-Coolant Accident (pipe diameters below ~4-in. (~10-cm)) 

SCC Stress Corrosion Cracking 

SECY Secretary of the (U.S. Nuclear Regulatory) Commission 
xxxii

SEMISCALE a 1:1705 scaled experimental facility that simulates the primary system 

of a 4-loop PWR plant 

SG Steam Generator 

SGTR Steam Generator Tube Rupture 

SIAS Safety Injection Actuation Signal 

SIT Safety Injection Tank 

SMAW Submerged Metal Arc Weld 

SO-1 Stuck-open valve in the primary pressure circuit 

SO-2 Stuck-open valve in the secondary pressure circuit 

SQA Software Quality Assurance 

SRM Staff Requirements Memorandum 

SRV Safety/Relief Valve 

SSC System, Structure, or Component 

SSE Safe-Shutdown Earthquake 

SSRV Secondary System Relief Valve 

TBV Turbine Bypass Valve 

TH Thermal-Hydraulics 

TMI Three Mile Island 

TSE Thermal Shock Experiment 

TWCF Through-Wall Cracking Frequency 

UMD University of Maryland 

UPTF Upper Plenum Test Facility 

USE Charpy V-Notch Upper-Shelf Energy 

V&V Verification and Validation 

VCIF Vessel Crack Initiation Frequency 

(W) Westinghouse 

WOG Westinghouse Owners’ Group 

WPS Warm Pre-Stress 
xxxiii

Nomenclature 

Symbols Used in Thermal-Hydraulics 

α thermal diffusivity, m2

/s 

β bulk coefficient of expansion, 1/C

μ viscosity, kg/m-s 

ν kinematic viscosity, m2

/s 

ρ density, kg/m3

σ stress, kg/s2

τ characteristic time 

Cp heat capacity, m2

/s2-C 

g gravitational acceleration, m/s2

Gr Grashof Number 

h convective heat transfer coefficient, W/m2

-C

D diameter, m 

J joules, kg-m2

/s2

k conductivity, W/m-C

l length, m 

Nu Nusselt Number 

Pr Prandtl Number 

P pressure, kg/m-s2

q heat flux, W/m2

Re Reynolds Number 

Ri Richardson Number 

s seconds 

t thickness, m 

t time, s 

u velocity, m/s 

T temperature, C 

W watts, kg-m2

/s3
xxxiv

Symbols Used in Fracture Mechanics 

2a Flaw depth measured through the vessel wall thickness 

2c Flaw length measured parallel to the axial or circumferential direction 

of the vessel 

Cu Copper content, weight% 

JIc A fracture toughness measure defined by ASTM E1820, which quantifies 

the resistance of metals to crack initiation by the initiation, growth, 

and coalescence of microvoids 

J-R A fracture toughness measure defined by ASTM E1820, which quantifies 

the resistance of metals to ductile tearing 

KJc A fracture toughness measure defined by ASTM E1921, which quantifies 

the resistance of metals to crack initiation by cleavage mechanisms 

KIa A fracture toughness measure defined by ASTM E1221, which quantifies 

the ability of metals to arrest (stop) a running cleavage crack 

KIc A fracture toughness measure defined by ASTM E399, which quantifies 

the resistance of metals to crack initiation under plane strain conditions 

KIc(min) The minimum KIc fracture toughness possible at a particular temperature 

KAPPLIED Linear elastic crack driving force 

L For a buried defect, distance from the wetted clad surface on the vessel ID 

to the inner crack tip 

l The length of the fusion line of an axial weld 

Ni Nickel content, weight% 

P Phosphorus content, weight% 

RTAW A fracture toughness reference temperature, which characterizes the RPV’s 

resistance to fractures initiating from flaws found along the axial weld fusion 

lines. It corresponds to the maximum RTNDT of the plates/welds that lie 

to either side of the weld fusion lines, and is weighted to account for differences 

in weld fusion line length (and, therefore, number of simulated flaws) 

between vessel courses. 

RTPL A fracture toughness reference temperature, which characterizes the RPV’s 

resistance to fractures initiating from flaws found in plates that are not 

associated with welds. It corresponds to the maximum RTNDT occurring 

anywhere in the plate. 

RTCW A fracture toughness reference temperature, which characterizes the RPV’s 

resistance to fractures initiating from flaws found along the circumferential 

weld fusion lines. It corresponds to the maximum RTNDT of the plates/welds 

that lie to either side of the weld fusion lines. 

RTNDT Transition fracture toughness reference temperature defined by 

ASME NB-2331 

RTNDT(u) Unirradiated value of RTNDT

RTPTS RTNDT projected end of license to account for the effects of irradiation 

(defined in 10 CFR 50.61) 

tWALL Vessel wall thickness 

tCLAD Stainless steel cladding thickness 
xxxv

T30 The temperature at which the mean CVN energy is 30 ft-lbs (41J) 

T35/50 Charpy V-notch energy transition temperature defined as the temperature 

at which the CVN energy is at least 50 ft-lbs (68J) and the lateral expansion 

of the specimen is at least 0.035-in. (0.89-mm) [See the definition on page 2-

7]

TNDT Nil-ductility temperature defined by ASTM E-208 

ΔT30 The shift in the CVN 30 ft-lb (41J) transition temperature produced by 

radiation damage 

σflow Flow strength, average of tensile yield and tensile ultimate strength 

φt Fluence 
xxxvi

Glossary 

Terms Used in Probabilistic Risk Assessment 

Abnormal operating procedure A procedure (i.e., list of actions) used to address unique or special plant 

circumstances identified while using emergency operating procedures (EOPs). 

These abnormal operating procedures are usually called by EOPs, but may be 

indicated directly by some plant conditions. 

Accident progression event tree The event tree used to model the part of the accident sequence that follows 

the onset of core damage, including containment response to severe accident 

conditions, equipment availability, and operator performance. 

Binning The process of taking a large number of sequences and combining then into 

a smaller number of groups, that are expected to have similar characteristics 

(e.g., TH conditions), to allow effective utilization of limited resources. 

Core damage Uncovery and heatup of the reactor core to the point at which prolonged oxidation 

and severe fuel damage is anticipated and involving enough of the core to cause 

a significant release. 

Dominant scenario An accident sequence (scenario) that is usually represented by the top 10 or 20 events 

or groups of events modeled in a PRA, which accounts for a large fraction 

of the specified end state. 

Emergency operating procedure The primary procedure (i.e., list of actions) used to respond to a plant disturbance 

resulting from an initiating event. 

Event tree A logic diagram that begins with an initiating event or condition and progresses 

through a series of branches that represent expected system or operator performance 

that either succeeds or fails and arrives at either a successful or failed end state. 

Fault tree A deductive logic diagram that depicts how a particular undesired event can occur 

as a logical combination of other undesired events. 

Large Early Release The rapid, unmitigated release of airborne fission products from the containment 

to the environment occurring before the effective implementation of offsite 

emergency response and protective actions, such that there is a potential for 

early health effects. 

Latin Hypercube sampling A stratified sampling technique, in which the random variable distributions 

are divided into equal probability intervals, and probabilities are then randomly 

selected from within each interval. 

Mitigating equipment Systems or components, used to respond to an initiating event, of which 

successful operation prevents the occurrence of an undesired event or state. 

Pre-initiator human failure event Human failure events that represent the impact of human errors committed 

during actions performed prior to the initiation of an accident (e.g., during 

maintenance or the use of calibration procedures). 

Post-initiator human failure event Human failure events that represent the impact of human errors committed 

during actions performed in response to an accident initiator. 
xxxvii

Prompt fatality A fatality that results from substantial radiation exposures incurred during 

short time periods (usually within weeks, though up to 1 year for pulmonary 

effects). 

PTS bin A group of sequences that are expected to have similar TH characteristics 

and are represented by one unique set of TH characteristics during a FAVOR 

calculation. 

Risk-informed An approach to analyzing and evaluating activities, which bases decisions 

on the results of traditional engineering evaluations, supported by insights 

derived from the use of PRA methods. 

Scenario See Sequence. 

Screening The process of eliminating items from further consideration based on their 

negligible contribution to the probability of an undesired end state or its 

consequences. 

Sequence A representation in terms of an initiating event followed by a sequence 

of failures or successes of events (i.e., system, function, or operator performance) 

that can lead to undesired consequences, with a specified end state 

(e.g., potential for PTS). 

Terms Used in Thermal-Hydraulics 

Blowdown Rapid depressurization of a system in response to a break. 

Break flow Flow of water (liquid and vapor) out a pipe break or a valve. 

Break energy Energy content of the fluid flow out a break. 

Bottom-up To break up a complex system into its subsystems, and then break up each subsystem 

into its components, examine individual local phenomena and processes that 

most affect each component, and build up the total complex system from these 

individual pieces (like manufacturing a car). 

Coast down Time required for a pump to stop rotating once power is shut off due to inertia. 

Decay heat Heat generated from radioactive decay of fission products. 

Enthalpy Sum of internal energy and volume multiplied by pressure. 

Flash Change of phase from saturated liquid to vapor resulting from decrease in pressure. 

Flow quality Mass fraction of flow stream that is steam. Higher quality flow would have 

a high mass fraction of steam. 

Forced flow Flow driven by a pump. 

Inventory Mass of water. 

Loop flow Mass flow rate of coolant in a circuit. 

Makeup water Water reservoir available for inventory control. 

Natural circulation Flow driven by buoyancy (gravity). 

Pressure drop Change in pressure due to conversion of mechanical energy to internal energy. 

Protection system Electrical controls to actuate engineering safety features. 

Quality Mass fraction of steam in a two-phase steam-water mixture. 
xxxviii

Saturation temperature A temperature corresponding to phase change from liquid to vapor. 

Sensible heat The product of specific heat and temperature change of subcooled liquid. 

Subcooled A system is subcooled if it exists entirely in a liquid state. The degree 

of subcooling is the number of degrees that the temperature of the system 

would have to be raised to cause boiling. 

Throttled Operation of a control valve to regulate flow. 

Top-down To characterize a complex system by establishing the governing behavior, 

or phenomenon, that is most important, and then proceed from that starting point 

to successive lower levels, by identifying the processes that have the greatest 

influence on the top-level phenomenon. 

Trip A “trip” occurs when a breaker opens in response to its trip mechanism 

(an arm that holds the breaker closed moves to allow the breaker to open). 

When a reactor trips, all of the breakers that provide power to the rod control 

system open, causing the rods to be inserted in the core and stopping the nuclear 

reaction. When a pump trips, the breaker opens, thereby disconnecting power 

and causing the pump to stop. 

Water solid A situation in which there is no steam in the system (i.e., it is all liquid). 

A “water solid” system is subcooled. 

Terms Used in Fracture Mechanics 

Brittle Fracture occurring without noticeable macroscopic plastic deformation 

(stretching) of the material. 

Cleavage fracture Microscopically, cleavage is a fracture mode that occurs preferentially along 

certain atomic planes through the grains of the material. Cleavage can only 

occur in ferritic steels (i.e., steels having a body-centered cubic lattice structure). 

Macroscopically, cleavage fracture is often called “brittle” fracture because 

little noticeable plastic deformation (stretching) of the material occurs. 

(Note, however, that plastic flow at the micro-scale is a necessary precursor 

to cleavage.) Macroscopically, cleavage fracture is also characterized as being 

a sudden event, with cracks of very large dimensions developing over durations 

measured in fractional seconds. A useful, although inexact, analogue 

for cleavage fracture in common experience is the breaking of glass. 

Ductile fracture Microscopically, ductile fracture occurs through the initiation, growth, 

and eventual coalescence of micro-voids in the material into a macroscopic crack. 

These micro-voids tend to initiate at local heterogeneities in the material 

(e.g., inclusions, carbides, clusters of dislocations). Macroscopically, ductile fracture 

is associated with considerable plastic deformation (stretching) of the material. 

Relative to cleavage fracture, ductile fracture occurs very slowly, with crack 

growth rates measured in seconds rather than in micro-seconds (for cleavage). 

Fracture toughness A general term referring to a material’s resistance to fracture. The term may be 

modified to refer to fractures by different mechanisms: 

Arrest fracture toughness measures a material’s ability to stop a running 

cleavage crack. 

Cleavage fracture toughness measures a material’s ability to resist 

crack initiation in cleavage. 

Ductile fracture toughness measures a material’s ability to resist crack initiation 

attributable to ductile mechanisms on the upper shelf. 
xxxix

Lower shelf At low temperatures, the toughness behavior of steels occurs by transgranular 

cleavage and is said to be on the lower shelf. On the lower shelf, a fracture is 

unstable, and is often referred to as a “brittle” fracture. 

Reference temperature A characteristic temperature used to locate the transition curve of a ferritic steel 

on the temperature axis. 

Transition (or transition curve) Between lower shelf and upper shelf temperatures, the fracture behavior 

of a ferritic material is said to be in “transition.” At low temperatures in transition, 

fracture occurs by cleavage. As temperature increases through the transition regime, 

fracture occurs by ductile crack initiation and growth, a process which is terminated 

by cleavage. At still higher temperatures, cleavage cannot occur, and upper shelf 

conditions exist. 

Upper shelf At high temperatures, the toughness behavior of steels occurs by ductile mechanisms 

(micro-void initiation, growth, and coalescence) and is said to be on the upper shelf. 

On the upper shelf, afracture is stable and dissipates considerable amounts of energy. 

Terms Used in Uncertainty Analysis 

Aleatory Aleatory uncertainties arise as a result of the randomness inherent in a physical 

or human process. Consequently, aleatory uncertainties are fundamentally 

irreducible. If the uncertainty in a variable is characterized as being aleatory, 

the entire distribution of the variable is carried through each simulation run. 

Epistemic Epistemic uncertainties are caused by limitations in our current state of knowledge 

(or understanding) of a given process. Epistemic uncertainties can, in principle, 

be reduced by an increased state of knowledge. If the uncertainty in a variable 

is characterized as being epistemic in a probabilistic simulation, individual values 

of the variable are randomly selected from a distribution and propagated through 

the calculation. This procedure models the understanding that the “correct” value 

of the variable is knowable, at least in principal. Thus, for epistemic uncertainties, 

individual simulation runs are deterministic, while the totality of all simulation runs 

captures the uncertainty characteristic of the epistemic variable. 
1-1

1 Motivation for and Objective of this Study

1.1 Description of Pressurized 

Thermal Shock 

During the operation of a nuclear power plant, 

the walls of the reactor pressure vessel (RPV) 

are exposed to neutron radiation, resulting in 

localized embrittlement of the vessel steel 

and weld materials in the area of the reactor core. 

If an embrittled RPV had an existing flaw 

of critical size and certain severe system transients 

were to occur, the flaw could very rapidly 

propagate through the vessel, resulting in 

a through-wall crack and challenging the integrity 

of the RPV. The severe transients of concern, 

known as pressurized thermal shock (PTS), 

are characterized by a rapid cooling 

(i.e., thermal shock) of the internal RPV surface 

and downcomer, which may be followed by 

repressurization of the RPV. Thus, a PTS event 

poses a potentially significant challenge 

to the structural integrity of the RPV 

in a pressurized-water reactor (PWR). 

A number of abnormal events and postulated 

accidents have the potential to thermally shock 

the vessel (either with or without significant 

internal pressure). These events include 

a pipe break or stuck-open valve in the primary 

pressure circuit, or a break of the main steam line, 

among others. During such events, the water level 

in the core drops as a result of the contraction 

produced by rapid depressurization. In events 

involving a break in the primary pressure circuit, 

an additional drop in water level occurs as a 

result of leakage from the break. Automatic 

systems and operators must provide makeup water 

in the primary system to prevent overheating 

of the fuel in the core. However, the makeup water 

is much colder than that held in the primary system. 

As a result, the temperature drop produced by 

rapid depressurization coupled with the nearambient temperature of the makeup water produces 

significant thermal stresses in the thick section 

steel wall of the RPV. For embrittled RPVs, 

these stresses could be sufficient to initiate 

a running crack, which could propagate all the way 

through the vessel wall. Such through-wall 

cracking of the RPV could precipitate core damage 

or, in rare cases, a large early release of radioactive 

material to the environment. Fortunately, 

the coincident occurrence of critical-size flaws, 

embrittled vessel steel and weld material, 

and a severe PTS transient is a very low-probability 

event. 

1.2 PTS Limits on the Licensable 

Life of a Commercial 

Pressurized Water Reactor 

In the early 1980s, attention was focused on 

the possibility that PTS events could challenge 

the integrity of the RPV wall for two reasons: 

• Operational experience suggested 

that overcooling events, while not common, 

did in fact occur. 

• The results of in-reactor materials surveillance 

programs suggested that the steels used 

in RPV construction were prone to lossof-toughness over time as a result of neutron 

irradiation-induced embrittlement. 

This possibility of accident loading combined 

with degraded material conditions motivated 

investigations aimed at assessing the risk of 

vessel failure posed by PTS for the purpose of 

establishing the operational limits needed to ensure 

that the likelihood of RPV failures caused by 

PTS transients is kept sufficiently low. These efforts 

led to the publication of a Commission paper 

[SECY-82-465], which provided the technical basis 

for subsequent development of what has come 

to be known as the “PTS Rule,” as set forth in 

Title 10, Section 50.61, of the Code of Federal 

Regulations (10 CFR 50.61), “Fracture Toughness 
1-2

Requirements for Protection Against Pressurized 

Thermal Shock Events” [10 CFR 50.61]. 

Currently, 10 CFR 50.61 requires licensees 

to monitor the embrittlement of their RPVs 

using a reactor vessel material surveillance program 

qualified under Appendix H to 10 CFR Part 50, 

“Domestic Licensing of Production and Utilization 

Facilities.” The surveillance results are used 

together with the formulae and tables in 

10 CFR 50.61 to estimate the fracture toughness 

transition temperature (RTNDT

†

) of the steels 

in the vessel’s beltline and how those transition 

temperatures increase as a result of irradiation 

damage throughout the operational life of the 

vessel. For licensing purposes, 10 CFR 50.61 

provides instructions on how to use these estimates 

of the effect of irradiation damage to estimate 

the value of RTNDT that will occur at end of license 

(EOL), a value called RTPTS. 10 CFR 50.61 also 

provides “screening limits” (maximum values 

of RTNDT permitted during the plant’s operational 

life) of +270°F (132°C) for axial welds, plates, 

and forgings, and +300°F (149°C) for 

circumferential welds. These screening limits 

correspond to a limit of 5x10-6 events/year 

on the annual probability of developing 

a through-wall crack [RG 1.154]. Should RTPTS

exceed these screening limits, 10 CFR 50.61 

requires that the licensee to either take actions 

to keep RTPTS below the screening limit 

(by implementing “reasonably practicable” 

flux reductions to reduce the embrittlement rate, 

or by deembrittling the vessel by annealing 

[RG 1.162]), or perform plant-specific analyses 

to demonstrate that operating the plant beyond 

the 10 CFR 50.61 screening limit does not pose 

an undue risk to the public [RG 1.154]. 

While no currently operating PWR has an RTPTS

value that exceeds the 10 CFR 50.61screening limit 

before EOL, several plants are close to the limit 

 

†

 The RTNDT index temperature was intended 

to correlate with the fracture toughness transition 

temperature of the material. Fracture toughness, 

and how it is reduced by neutron irradiation 

embrittlement, are key parameters controlling 

the RPV’s resistance to any loading challenge. 

For a more detailed description of RTNDT

(in specific) and fracture toughness (in general), 

see [EricksonKirk PFM]. 

(3 are within 2°F while 10 are within 20°F, 

see Figure 1.1). Those plants that are close to 

are likely to exceed the screening limit during 

the 20-year license renewal period that is 

currently being sought by many operators. 

Moreover, some plants maintain their RTPTS values 

below the 10 CFR 50.61 screening limits 

by implementing flux reductions (low-leakage cores, 

ultra-low-leakage cores), which are fuel management 

strategies that can be economically deleterious 

in a deregulated marketplace. Thus, the 10 CFR 50.61 

screening limits can restrict the licensable and 

the economic lifetime of PWRs. As detailed 

in the next section, there is considerable reason 

to believe that these restrictions are not necessary 

to ensure public safety and, in fact, place 

unnecessary burden on licensees. 

0

20

40

60

80

0 50 100 150 200 250

o

F from Current 

10CFR50.61 PTS 

Screening Limit

Number of PWRs

Figure 1.1. Proximity of currently operating PWRs 

to the 10 CFR 50.61 screening limit for PTS 
1-3

1.3 Technical Factors Suggesting 

Conservatism of the Current 

PTS Rule 

It is now widely recognized that state of 

knowledge and data limitations in the early 

1980s necessitated conservative treatment 

of several key parameters and models used in 

the probabilistic calculations that provided 

the technical basis [SECY-82-465] of the current 

PTS Rule [10 CFR 50.61]. The most prominent 

of these conservatisms include the following factors: 

• highly simplified treatment of plant transients 

(very coarse grouping of many operational 

sequences (on the order of 105

) into very 

few groups (≈10), necessitated by limitations 

in the computational resources needed 

to perform multiple thermal-hydraulic 

calculations) 

• lack of any significant credit for operator action 

• characterization of fracture toughness using 

RTNDT, which has an intentional conservative 

bias [ASME NB2331] 

• use of a flaw distribution that places all

flaws on the interior surface of the RPV, 

and, in general, contains larger flaws than 

those usually detected in service 

• a modeling approach that treated the RPV 

as if it were made entirely from the most 

brittle of its constituent materials 

(welds, plates, or forgings) 

• a modeling approach that assessed RPV 

embrittlement using the peak fluence 

over the entire interior surface of the RPV 

These factors indicate the high likelihood that 

the current 10 CFR 50.61 PTS screening limits 

are unnecessarily conservative. Consequently, 

the staff of the U.S. Nuclear Regulatory 

Commission (NRC) believed that reexamining 

the technical basis for these screening limits, 

based on a modern understanding of all the factors 

that influence PTS, would most likely provide 

strong justification for substantially relaxing 

these limits. 

1.4 Statement of Objective 

For the reasons stated in Section 1.3, the NRC’s 

Office of Nuclear Regulatory Research (RES) 

undertook this study with the objective of developing 

the technical basis to support a risk-informed 

revision of the PTS Rule and the associated PTS 

screening limit, and thereby providing the basis 

for potential rulemaking. 

1.5 Guide to this Report 

As discussed in Chapter 4, this report summarizes 

a much larger documentary package, and updates 

a previous report [Kirk 12-02]. We begin 

in Chapter 2 by describing PTS, its potential 

precursors, and the historical occurrence of PTS 

in reactor operations. We also summarize the 

key findings on which the current rule is based, 

and we detail the provisions of the current rule. 

Chapter 3 describes this study in detail and discusses 

its guiding principles, our investigative approach, 

and our fundamental assumptions. Additionally, 

we detail the many organizations and individuals 

that have contributed to this project. Chapter 4 

provides a “map” to the documents from which 

this summary report was drawn and describes 

the information available in each of those 

detailed reports. In Chapters 5, 6, and 7, 

we synopsize the key features of our probabilistic 

risk assessment (PRA) and human reliability 

analysis (HRA), our thermal-hydraulic (TH) 

analysis, and our probabilistic fracture mechanics 

(PFM) analysis, respectively. Chapters 6 and 7 

also address experimental validation of our TH 

and PFM methodologies. Chapter 8 presents 

the results of our baseline plant-specific analysis 

of three PWRs, while Chapter 9 examines the 

general applicability of these results to the larger 

population of all commercial PWRs. In Chapter 10, 

we develop a limit on the risk posed by PTS 

that is consistent with current regulatory guidance. 

Chapter 11combines the information from 

Chapters 8 through 10 to develop a proposed 

revision to the 10 CFR 50.61 screening limit. 

Finally, Chapter 12 summarizes our findings 

and discusses some considerations for rulemaking.
2-1

2 Pressurized Thermal Shock Background 

In this chapter, we provide background 

information on PTS. We begin with a general 

description of the progression of a PTS event, 

including its precursors and their effect on both 

the primary pressure circuit and the RPV itself 

(Section 2.1). We then discuss the historical 

incidence of PTS (Section 2.2). Finally, 

we summarize the findings of SECY-82-465, 

which provide the technical basis for the current 

PTS Rule (Section 2.3), and we review the rule’s 

provisions (Section 2.4). 

2.1 General Description of 

the Progression of a PTS Event 

In the following sections, we describe the event 

sequence that can give rise to a PTS event 

(Section 2.1.1), the effect of those events on both 

the primary and secondary pressure circuits 

(Section 2.1.2), and the challenge that these 

transients can pose to the structural integrity 

of the RPV (Section 2.1.3). 

2.1.1 Precursors 

Normally, the RPV is very hot because of 

the high temperature of the water it contains 

(600°F 315°C)). Several types of malfunctions 

or accidents can cause the vessel to suddenly fill 

with cool water or cause the reactor coolant water 

temperature to decrease rapidly. Such rapid 

cooling causes the vessel to experience thermal 

shock. If the RPV is then subjected to high 

pressure, the phenomenon is referred to as PTS. 

Most significant PTS scenarios fall into one of 

the following two categories: 

• breaks in the primary side of the reactor 

coolant system (RCS) (see Sections 2.1.2.1 

and 2.1.2.2) 

• breaks in the secondary system 

(see Section 2.1.2.3). 

Here, we use the term “break” to refer to pipe breaks 

(e.g., hot leg break, cold leg break, main steam line 

break, steam generator tube rupture), as well as 

stuck-open valves. Initially, a stuck-open valve 

transient behaves much like a transient initiated 

by a pipe break. However, later in stuck-open 

valve transients the valve can unstick 

(and, therefore, reclose), so repressurization 

is possible. Our analysis considers potential 

failures of the following valves: 

• Primary Side/RCS: Power-operated relief 

valves (PORVs) and safety relief valves (SRVs) 

• Secondary Side: Main steam isolation valves 

(MSIVs), steam generator atmospheric dump 

valves (ADVs), main steam safety valves 

(MSSVs), and so on. 

Figure 2.1 illustrates the arrangement of the major 

components of both the primary and secondary 

systems in a PWR. 

2.1.2 Thermal-Hydraulic Response 

of the Vessel 

2.1.2.1 Pipe Breaks in the Primary 

System 

When a break occurs in the primary system, 

mass is lost from the RCS. The level of water 

in the pressurizer (PZR) decreases, thereby 

causing a decrease in RCS pressure. If the RCS 

pressure or PZR level decreases too far, the 

reactor protection system (RPS) will generate 

a reactor trip signal, which in turn will insert 

the control rods and stop the fission process. 

Additionally, the engineered safety features 

actuation system (ESFAS) will generate a safety 

injection actuation signal (SIAS). The SIAS 

will start the high-pressure injection (HPI) and 

low-pressure injection (LPI) pumps, which will 

start the supply of emergency core cooling (ECC) 

water to the RCS, as pressure allows.
2-2

Figure 2.1. Schematic illustration of the main components of the primary (red) and secondary (blue) systems 

in a pressurized-water reactor 

Steam

Dryer

Steam

Separator

SteamGenerator

Pressurizer

Hot Leg

Cold Leg RCP

SafetyInjectionAccumulator

CL

Core

HL

Another 

Steam Generator

LOCA Break Flow

Downcomer

to Quench Tank RWST

HPSI

LPSI

RPV

Containment

Main Feed Water

Auxiliary Feed Water

MainSteamLine

to Main Turbines

Main Steam

Isolation 

Valve (MSIV)

Exhaust to 

Atmosphere

Atmospheric 

Dump Valve 

(ADV)

Feed Water

Isolation 

Valve (FWIV)

Turbine-Driven 

Feed Pump

Motor-Driven A

Feed Pump

Exhaust t

Atmosphe

Refueling Water Storage Tank

High-Pressure 

Safety Injection

Low-Pressure 

Safety Injection

Containment

Sump

SurgeLine

Reactor Coolant Pump

Power Operated Relief Valve (PORV)

PORV Block Safety Valve Relief 

Valve

Containment 

Spray Pump

Component 

Cooling Water System

Containment Sprays

MainSteamSafetyValve (MSSV)

Exhaust to 

Main 

Condenser 

Turbine Bypass Valve (TBV)
2-3

Further progress of the transient depends upon 

the ability of HPI to make up for the mass lost 

through the break. 

For very small breaks (less than ~1.4-in. (3.5-cm) 

in diameter), HPI is sufficient to make up the 

lost mass and, thereby, maintain RCS mass 

and pressure control. For larger breaks, HPI 

is insufficient to replace the lost mass, so PZR 

level and RCS pressure continue to fall. As the 

pressure continues to fall, the safety injection 

tanks (SITs) discharge and, eventually, the LPI 

begins injecting colder water into the RCS. 

The ECC injection rates are substantially greater 

for large breaks (compared to small breaks), 

and result in much greater cooldown of the 

primary system and subsequently the RPV wall. 

The controlling feature of such loss-of-coolant 

accidents (LOCAs) is the size of the break. 

The larger the break, the faster the transient 

proceeds, and the more severe the cooldown. 

Larger breaks cause a greater pressure decrease, 

which results in larger ECC flows. This causes 

the downcomer temperature to drop rapidly. The 

rate of temperature decrease (which is controlled 

by the break size) and the minimum temperature 

achieved (which is controlled by the temperature 

of the ECC water and whether ECC water 

is recirculated from the sump) are the dominant 

TH factors that influence the severity of the transient. 

Since RCS pressure is low, it not a significant 

factor. 

2.1.2.2 Stuck-Open Primary Safety 

Relief Valves 

During stuck-open valve transients, a primary 

SRV is assumed to stick open as a result of 

mechanical binding or other possible causes. 

This binding of the valve may release later 

in the transient, resulting in valve reclosure. 

Phenomenologically, stuck-open valve scenarios 

are similar to small hot leg break LOCAs, until 

the valve recloses. The “break” areas of stuck-open 

valve scenarios are typically in the small-break 

LOCA range of ≈1.5 to 2+-in. (≈3.8 to 5+-cm). 

Following valve reclosure, HPI will gradually 

fill the RCS. As the RCS fills, the primary system 

pressure will increase above the saturation pressure 

of the coolant, thereby reestablishing subcooling 

in the loops. When operating procedures allow, 

the HPI can be controlled to avoid overfilling 

the RCS. If, however, the operator fails to 

attend to HPI control in a timely manner, 

the RCS can continue to fill until the primary 

system is water solid, meaning there is no longer 

any steam in the system. Since water is nearly 

incompressible, the RCS pressure rises very rapidly, 

and the pressure created by HPI will reopen 

the SRVs. RCS pressure will then remain 

at the SRV setpoint of 17.25 MPa (2500 psi) 

for as long as the HPI remains on. 

The controlling features of stuck-open valve 

scenarios are the length of time the valve is open, 

and the repressurization associated with 

the primary system becoming water solid. 

The longer the SRV stays open, the cooler 

the downcomer temperature becomes. Timely 

operator control of HPI is an important factor 

influencing transient severity because it determines 

the maximum pressure achieved in the primary 

system. Thus, for these scenarios, both downcomer 

temperature and RCS pressure are important. 

2.1.2.3 Breaks in the Secondary System 

Secondary side breaks can include both actual 

breaks of the steam line and the sticking-open 

of one or more of the numerous control and safety 

valves in the steam system. A stuck-open valve 

is, therefore, also referred to as a “break,” 

consistent with the terminology adopted 

to describe stuck-open valves in the primary 

system Break sizes can range from a single 

valve sticking open to a complete main steam line 

break (MSLB). Similar to LOCAs, time and 

break size are directly related. The larger 

the break, the faster the transient proceeds, 

and the more severe the cooldown. 

Following break initiation, the response of 

engineered safety features systems may result in 

safety injection actuation, actuation of main 

feedwater isolation valves (MFIVs) and/or MSIVs, 

as well as automatic control of auxiliary feedwater 

(i.e., through isolation of a turbine-driven pump). 

If the break is downstream of the MSIVs, 

the steam line break will be terminated 
2-4

when the MSIV shuts. For larger MSLBs, 

MSIV closure is automatic and occurs rapidly 

after break initiation. For smaller steam line 

breaks, however, the operators will isolate 

the affected steam generator by securing flow 

to the generator and manually isolating 

the MSIVs. Therefore, downstream breaks 

are not PTS-significant. However, the main 

steam SRVs and ADVs are upstream of 

the MSIVs and, consequently, are not affected 

by an MSIV closure. For breaks occurring 

upstream of the MSIVs, steam will continue 

to blowdown until the affected steam generator 

is completely depressurized. 

Steam generator depressurization causes cooling 

of the primary system. As steam continues 

leaking out of the break, the secondary side 

pressure continues to decrease, and the water 

in the generator remains saturated. Consequently, 

as the secondary side pressure decreases, 

the secondary side temperature also decreases. 

The primary side and secondary side remain 

“thermally coupled” during secondary side 

break scenarios, meaning that the primary system 

temperature will track the temperature of the 

affected steam generator. This primary system 

cooling increases the density of the primary water, 

so the volume of the water in the RCS shrinks. 

For sufficiently large secondary breaks, 

the shrinkage may be sufficient to actuate 

the emergency core cooling system (ECCS), 

causing direct injection of water at a temperature 

between that of external storage tanks (≈40°F 

(4.4°C)) and that of water recirculated from the 

sump (~120°F (49°C)). The flow of this colder 

water increases the cooling rate of the primary, 

thereby increasing transient severity. However, 

HPI does not reduce the minimum temperature 

of the primary below the boiling point of water 

in the secondary because the large heat transfer 

area in the affected steam generator (which is 

now at saturated conditions) is more than 

sufficient to bring the HPI water temperature 

up to the boiling point in the secondary system. 

If the break is outside of containment, the lowest 

temperature expected would be 212°F (100°C) 

(saturation for atmospheric pressure); however, 

the final temperature could be higher (~250°F 

(120°C)) if the break is in containment. In this 

case, the minimum temperature of the primary 

system depends on the final containment pressure 

following blowdown of the steam generator. 

The controlling features of steam line break 

scenarios are the size of the break, control of 

feedwater to the broken steam generator, proper 

steaming of the unaffected generator, and 

control of HPI if HPI is actuated. Large steam 

line breaks resemble large LOCAs in terms of 

the rate of downcomer cooling. The differences 

between large steam line breaks and primary 

system pipe breaks (LOCAs) are as follows: 

• The downcomer does not get as cold during 

secondary side breaks. Temperatures 

typically range from 212°F to 250°F 

(100°C to 121°C) for secondary side breaks, 

depending on whether the break is outside 

or inside of containment and, if inside, 

what the containment pressure is. By contrast, 

temperatures for primary system pipe breaks 

(LOCAs) can be as low as ≈40°F (4.4°C) 

for LOCAs because the minimum temperature 

is controlled by the boiling point of water, 

rather than ambient outside temperatures. 

• Natural circulation flow rates (characteristic 

of large steam line breaks) are higher than 

loop stagnation flow rates (characteristic 

of large LOCAs). This higher flow ensures 

thorough mixing in the downcomer 

of the reactor coolant and ECCS flow 

(provided that coolant flow is initiated). 

The need to consider thermal plumes 

or streaming effects can thus be eliminated 

a priori for breaks in the secondary system. 

2.1.3 Response of the Vessel 

to PTS Loading 

As detailed in Section 2.1.2, all PTS precursors 

cause rapid cooling of the primary system. 

Depending on the transient, this cooling may 

or may not be accompanied by significant pressure. 

Both of these factors (rapid cooling and pressure) 

produce stresses in the vessel wall. The thermal 

stresses are (approximately) equal both along 

the axis of the vessel and around its circumference 

because of its cylindrical geometry. At the 
2-5

beginning of the cooldown, the thermal stresses 

are tensile on the inner diameter (ID) of the vessel, 

and are equilibrated by compressive stresses 

on its outer diameter (OD). As the transient 

continues, these thermal stresses reduce to zero 

to the extent that isothermal conditions 

are achieved in the vessel wall. The pressure 

stresses are twice as large in the circumferential 

direction as they are in the axial direction (again 

as a direct consequence of the cylindrical vessel 

geometry). Also, pressure stresses are constant 

through the thickness of the RPV wall. 

The degree to which these stresses challenge 

the integrity of the vessel is controlled by 

a number of factors, the most important of which 

are as follows: 

• the existence of a crack in the RPV, as well as 

its location, orientation, and size 

• the material’s resistance to cracking 

at the location of the flaw, which is 

measured by its “fracture toughness.” 

Fracture toughness depends on a number 

of other factors (each defined at the flaw 

location), the most important of which 

are as follows: 

o temperature 

o irradiation damage (fluence) 

o chemical composition 

o fracture toughness before irradiation 

Qualitatively, when high stresses occur in the 

presence of a large crack at a low temperature, 

and when the material at the location of the crack 

has low fracture toughness, initiation of the crack 

becomes more likely. The likelihood that this 

initiated crack will propagate all the way through 

the vessel wall (thereby producing a breach 

in the primary system and leading to a condition 

we have defined as “failure”) again depends on 

the interplay between the applied stresses 

(and how they vary through the wall) 

with the material’s ability to stop a running crack 

(known as “arrest fracture toughness”). 

The factors that influence fracture toughness 

(listed above) also influence arrest fracture 

toughness. While arrest is by no means certain, 

it is true that as the crack propagates into the 

vessel wall, arrest becomes progressively more 

likely for transients where the stresses are 

primarily thermal. For these “mostly thermal” 

transients (medium- and large-diameter primary 

side pipe breaks, for example) arrest becomes 

more likely as the crack progresses into the vessel 

wall because temperature tends to increase while 

irradiation damage tends to decrease. (Both of these 

changes increase arrest fracture toughness.) 

Conversely, the progression of a crack initiated by 

a transient that produces both thermal and 

pressure stresses is fundamentally different. In 

this situation, the stresses remain higher through 

the wall because of the contribution of the 

pressure stress. Additionally, the fracture 

driving force tends to increase as the crack travels 

through the wall, as a result of the effect of 

primary system pressure on the crack faces. 

For these reasons, in transients that produce both 

thermal and pressure stresses, almost all cracks 

that initiate also propagate all the way through 

the vessel wall. 

2.2 Historical Incidence of PTS 

In the technical basis document written to support 

the current PTS Rule [SECY-82-465], the staff 

summarized the operational events that had, 

to that date, presented PTS challenges to 

operating plants. These events are depicted 

in Figure 2.2, which illustrates the three key 

operational parameters influencing event severity. 

Specifically, those parameters are the final RCS 

temperature, severity of the thermal shock 

(dT/dt) caused by the event, and existence 

(or lack thereof) of high pressure. A more recent 

search of licensee event reports (LERs) 

submitted between 1980 and 2000 reveals 

the occurrence of 128 “potentially PTS-significant” 

events. Approximately half of those LERs 

report the minimum temperature reached 

by the RCS, and the data suggest that the most 

recent transients are nearly all benign, with all 

but one having minimum RCS temperatures 

above 500°F (260°C). Thus, while overcooling 

events have occurred, they have only rarely been 

severe enough to challenge the structural integrity 

of the RPV.
2-6

750oF/hr

450oF/hr

380oF/hr

72oF/hr

63oF/hr

54oF/hr

dT/dt

380oF/hr

Loss of

Power

≈380oF/hr

Figure 2.2. Figure 2.13 from SECY-82-465, depicting the final temperatures for 32 PTS precursor events 

experienced in commercial reactor service prior to 1982 

(Cooling rates associated with the most significant transients have been superimposed on this graph.) 

2.3 Summary of SECY-82-465 

Findings 

In the early 1980s, the nuclear industry and 

the NRC staff performed a number of investigations 

to assess the risk of vessel failure posed by PTS, 

and to establish the operational limits needed 

to ensure that the likelihood of RPV failures 

caused by PTS transients is maintained at an 

acceptably low level. These efforts led to the 

publication of a Commission paper [SECY-82-

465] that provided the technical basis for 

subsequent development of what has come to be 

known as the “PTS Rule” [10 CFR 50.61]. The 

Commission paper included a number of 

probabilistic calculations performed to assess the 

influence of both contributory and mitigating 

factors (e.g., plant design, operator actions, 

operator training, material toughness, flaw 

population, and so on) on the outcome (vessel 

failure or non-failure) of a PTS event. The 

results of these calculations were used to 

develop a relationship between the probability of 

a through-wall crack developing in the RPV and 

the RTNDT index temperature of the RPV. 

Regulatory Guide 1.154 [RG 1.154] later used 

this relationship, together with the judgment that 

an annual through-wall cracking frequency of 

5x10-6 is acceptable, to establish “screening 

limits,” or maximum values of RTNDT permitted 

during the operating life of the plant. 

Specifically, the established limits were +270°F 

(132°C) for axial welds, plates, and forgings, 

and +300°F (149°C) for circumferential welds 

[10 CFR 50.61]. 

In the mid-1980s, the NRC conducted a number 

of follow-on studies concerning the risk 

associated with PTS events [ORNL 85a, 85b, 86]. 

These studies, featuring plant-specific analyses 

of H.B. Robinson Steam Electric Plant, Calvert 

Cliffs Nuclear Power Plant, and Oconee Nuclear 

Station, demonstrated that plants embrittled 

to the PTS screening limit of +270°F (132°C) 

had an annual probability of developing a throughwall crack below 5x10-6 events/reactor year. 

These plant-specific analyses demonstrate the 

conservatism of the generic analyses reported in 

SECY-82-465, which served as the basis for the 

provisions of 10 CFR 50.61. 
2-7

2.4 Current Provisions 

of 10 CFR 50.61 

As previously stated, 10 CFR 50.61 establishes 

“screening limits” (or maximum values of RTNDT

permitted during the operating life of the plant) 

of +270°F (132°C) for axial welds, plates, 

and forgings, and +300°F (149°C) for 

circumferential welds. Here, we discuss 

in greater detail the provisions of 10 CFR 50.61, 

as follows: 

• Section 2.4.1: why an index-temperature 

approach is adopted to characterize 

transition fracture toughness in ferritic steels 

• Section 2.4.2: the approach used to 

characterize irradiation effects on the index 

temperature 

• Section 2.4.3: the specific provisions of 

10 CFR 50.61 

• Section 2.4.4: an evaluation of currently 

operating PWRs, relative to the PTS 

screening limits In 10 CFR 50.61 

2.4.1 Index Temperature Approach 

to Characterize Transition Fracture 

Toughness in Ferritic Steels 

“Fracture toughness” is a measure of a material’s 

ability to deform without breaking in the presence 

of preexisting cracks. Physical evidence 

and numerous experimental observations 

demonstrate that the temperature dependence 

of the cleavage initiation fracture toughness 

of ferritic steels (KIc or KJc) does not depend 

on composition, heat treatment, material forming 

techniques (weld, plate, or forging), or irradiation 

conditions [Kirk 01a]. These factors influence 

only the position of the toughness transition curve 

on the temperature axis. This has led to widespread 

use of transition temperature approaches 

to characterize the cleavage fracture toughness 

of ferritic materials [WRC 175, Wallin 93a]. 

Such approaches employ empirical and/or physical 

evidence to establish the temperature dependence 

of fracture toughness that is common to all 

ferritic steels. Figure 2.3 shows the data used 

to establish the ASME KIc curve, one of the 

earliest transition temperature characterizations 

developed specifically using nuclear grade ferritic 

steels and weldments [WRC 175]. The formula 

for the curve in Figure 2.3 is as follows: 

Eq. 2-1 KIc = + ⋅ [ ] 02.0exp806.22.33 ( ) −⋅ RTT NDT +100

where

RTNDT is defined in accordance with 

ASME NB2331, as follows: 

RTNDT = { NDT TTMAX 50/35 − 60, }. 

TNDT is the nil-ductility temperature (NDT) 

determined by testing specimens 

in accordance with ASTM E208. 

T35/50 is the transition temperature at which 

Charpy-V notch (CVN) specimens 

tested in accordance with ASTM E23 

exhibit lateral expansion of at least 

0.035-in. (0.89-mm) and absorbed 

energy of at least 50 ft-lbs (68J). 

In Eq. 2-1, RTNDT serves as an “index temperature” 

(i.e., a single value that characterizes 

the combined effects of alloying heat treatment, 

irradiation, etc. on fracture toughness)‡

. 

Combining an index temperature with 

the (independently established) temperature 

dependence of fracture toughness (Eq. 2-1) 

defines the variation of toughness with temperature 

throughout the transition regime. The ease 

with which an index temperature can be 

experimentally established (relative to the much 

greater testing burden necessary to establish 

the complete toughness transition curve) 

makes transition temperature approaches 

attractive in applications where extensive 

material characterization is either economically 

infeasible or, for practical reasons, impossible. 

 

‡

 While RTNDT is an index temperature that has 

customarily been used along with a fracture 

toughness transition curve (i.e., the ASME KIc

curve), RTNDT is not a fracture toughness index 

temperature. As specified by ASME NB-2331 

(and as represented in Eq. 2-1), RTNDT is defined 

based on non-fracture toughness tests that can, 

at best, be correlated with fracture toughness. 

[EricksonKirk PFM] provides a more detailed 

description of RTNDT. 
2-8

The monitoring of neutron irradiation embrittlement 

falls into both categories because of the expense 

associated with the testing of irradiated materials 

and the limited volumes of material that can be 

irradiated as part of a surveillance program. 

0

50

100

150

200

-250 -200 -150 -100 -50 0 50 100

KIc ( MPa-m1/2 )

(T-RTNDT) (oC) 06/27/00.K1 ptw

ASME KIc Curve

ASME KIc Curve (extended)

EPRI NP-710-SR Database

Figure 2.3. The empirical data used to establish 

the ASME KIc curve 

2.4.2 Irradiation Effects 

on Index Temperature 

As part of their required reactor vessel material 

surveillance programs qualified under Appendix H 

to 10 CFR Part 50, licensees attach surveillance 

capsules to the inner diameter and/or internal 

structures of the RPV. These capsules, which 

contain Charpy V-notch (CVN) specimens 

[ASTM E23], are removed over the lifetime 

of the RPV [ASTM E185], and the CVN 

specimens are tested to establish the index 

temperature T30 (the temperature at which 

the energy consumed in fracturing the CVN 

specimen is 30 ft-lbs). The difference between 

T30 after some amount of irradiation and T30

before irradiation begins is called ∆T30, a metric 

which has long been used to assess the degree 

of irradiation damage imparted to the steel. 

(∆T30 is closely related to the irradiation-induced 

shift in fracture toughness transition temperature. 

See [Kirk 01b] and [EricksonKirk-PFM].) 

These ∆T30 values from RPV surveillance programs 

provide the empirical basis to establish 

embrittlement trend curves that correlate 

the effect of irradiation exposure and chemical 

composition on ∆T30. 10 CFR 50.61 adopts 

the following embrittlement trend curve 

[Randall 87]: 

Eq. 2-2 )log1.028.0(

30 )( f fCFT − =∆

where 

CF is a “chemistry factor” that 

characterizes the irradiation 

sensitivity of the steel. CF depends 

on copper content, nickel content, 

and product form. 10 CFR 50.61 

includes tables of CF values. 

f is the fast neutron fluence in 

neutrons per cm2

 (E>1Mev) 

divided by 1019. For the purposes 

of 10 CFR 50.61, f is defined as 

the peak fluence at the clad-to-base 

metal interface at EOL. 

2.4.3 Provisions of the Current Rule 

10 CFR 50.61 uses the RTNDT index temperature 

and the ∆T30 index temperature shift to estimate 

the effect of irradiation on RTNDT, as follows: 

Eq. 2-3 RT fNDT )( = RT uNDT )( ∆⋅R+ 30 + MT

where 

RTNDT (f) is the estimated RTNDT of the vessel 

material after irradiation to the 

fluence f. Toughness is determined 

from RTNDT(f) through its use as 

an index temperature for the ASME 

KIc and KIR curves. 

RTNDT(u) is the unirradiated RTNDT. It can be 

determined based on either ASME 

NB2331 or other alternative 

techniques [NRC MEMO 82, 

NRC MTEB 5.2]. 

R is 1 if ∆T30 is calculated from 

chemistry and fluence using Eq. 2-2. 

If ∆T30 is evaluated based on 

surveillance CVN data, R is the ratio 

of the CF value estimated from 

the chemistry of the surveillance 

capsule to the CF value estimated 

from the heat average chemistry. 
2-9

∆T30 is defined by Eq. 2-2. 

M is defined by Eq. 2-4. 

Eq. 2-4 22 2 M I += σσ ∆

where 

σI is the standard deviation in the value 

of RTNDT(u). 

σ∆ is the standard deviation in the value 

of ∆T30. 

According to 10 CFR 50.61, a nuclear power 

plant licensee is required to estimate RTNDT(f)

at EOL using Eq. 2-2 for all materials in the 

vessel beltline. The highest of these values, 

defined as RTPTS, is compared to the 10 CFR 50.61 

PTS screening limit of +300°F (149°C) 

for circumferential welds and +270°F (132°C) 

for all other materials. If RTPTS exceeds 

the screening limit, the licensee is required 

to either (1) implement flux reduction techniques 

to keep RTPTS below the screening limit, 

(2) anneal the vessel according to Regulatory 

Guide 1.162 [RG 1.162], or (3) submit a safety 

analysis to the NRC demonstrating that the plant 

is safe to operate beyond the screening limit. 

2.4.4 Evaluation of Operating Plants 

Relative to the Current 

PTS Screening Limits 

Figure 1.1 compares RTNDT values for all 

currently operating PWRs evaluated at the end 

of their originally licensed life (40 years) using 

Eq. 2-3 with the current 10 CFR 50.61 PTS 

screening limits. A number of points should 

be noted: 

• No plants currently exceed the screening limit. 

However, since the operators of the Yankee 

Rowe Nuclear Power Plant failed to persuade 

the staff to permit operation in excess of 

the screening limit using the probabilistic 

procedures outlined in Regulatory Guide 1.154 

[RG 1.154], all plants that have predicted 

that they would exceed the screening limit 

before EOL have elected to remain 

in statutory compliance by (1) implementing 

flux reduction, (2) pursuing new technological 

approaches coupled with exemption requests, 

or (3) using a combination of the two 

approaches. 

• Currently, 10 plants project an RTNDT at EOL 

(≡RTPTS) within 20°F of the screening limit. 

• While the most embrittled region in one-third 

of the operating PWRs is the circumferential 

weld, less than half of those plants (11 of 23) 

have their operation limited by 

the circumferential weld because of the higher 

PTS screening limit currently used to assess 

these plants (+300°F (149°C) vs. the +270°F 

(132°C) value used for axial welds, plates, 

and forgings). 
3-1

3 PTS Reevaluation Project 

This chapter describes the PTS Reevaluation 

Project, which the NRC’s Office of Nuclear 

Regulatory Research (RES) initiated in 1999. 

The chapter is structured as follows: 

• Model Structure: Section 3.1 provides 

an overview of the model used to evaluate 

the technical basis for a revised PTS 

screening limit. 

• Uncertainty Treatment: Since the objective 

of this study is to develop the technical basis 

for a risk-informed revision of 10 CFR 50.61, 

a systematic treatment of uncertainties is 

a central feature of this project. Section 3.2 

describes our framework for uncertainty 

treatment and propagation and provides 

an overview of how uncertainties were 

addressed in the PRA, TH, and PFM. 

• Assumptions: Section 3.3 summarizes 

the fundamental assumptions made 

in developing our model. 

• Contributors: Section 3.4 describes 

the organizations and individuals that have 

made key contributions over the course 

of this project. 

• Peer Review: Given the complex 

interdisciplinary nature of this project, 

and at the request of the NRC’s Advisory 

Committee on Reactor Safeguards (ACRS), 

the staff convened a panel of external experts 

to review the study’s methodologies, 

findings, and recommendations. Section 3.5 

describes the conduct of this review group 

and the staff’s approach to addressing their 

comments. 

3.1 Model Used to Evaluate 

a Revised PTS Screening Limit 

3.1.1 Restrictions on the Model 

The desired outcome of this study is to establish 

the technical basis for a new PTS screening limit. 

To enable all commercial PWR licensees to assess 

the state of their RPVs relative to such a new 

criterion without the need to make new material 

property measurements, the fracture toughness 

properties of the RPV steels need to be estimated 

using only information that is currently available 

(i.e., RTNDT values, upper-shelf energy values, 

and chemical composition of beltline materials). 

All of this information is summarized 

in the NRC’s Reactor Vessel Integrity Database 

[RVID2]. 

3.1.2 Overall Structure of the Model 

Our overall model involves three major components, 

which are illustrated (along with their interactions) 

in Figure 3-1: 

Component 1. Probabilistic Evaluation 

of Through-Wall Cracking Frequency: Estimate 

frequency of through-wall cracking as a result 

of a PTS event given the operating, design, 

and material conditions in a particular plant. 

Component 2. Acceptance Criterion 

for Through-Wall Cracking Frequency: 

Establish a value of reactor vessel failure frequency 

(RVFF) consistent with current guidance 

on risk-informed decision-making. 

Component 3. Screening Limit Development: 

Compare the results of the two preceding steps 

to determine if some simple, materials-based 

PTS screening limit can be established. 

Conceptually, plants falling below the screening 

limit would be deemed adequately resistant to 

a PTS challenge and would not require further 

analysis. Conversely, more detailed, plant-specific 
3-2

analysis would be needed to assess the safety 

of plant operation beyond the screening limit. 

Each of these components is described 

in the following subsections. 

PRA Event

Sequence

Analysis

(SAPPHIRE)

Thermal

Hydraulic

Analysis

(RELAP)

Probabilistic

Fracture

Analysis

(FAVOR)

Sequence

Definitions

Sequence

Frequencies

freq

Conditional

Probability of

Thru-Wall

Cracking, CPTWC

P(t), T(t), &

HTC(t)

Yearly

Frequency of

Thru-Wall

Cracking

[CPTWC]

x

[freq]

Probabilistic Estimation of Through-Wall Cracking Frequency

Vessel damage, age, 

or operational metric

Yearly Frequency of

Thru-Wall Cracking

Screening 

Limit

Acceptance Criterion 

for TWC Frequency

Established consistent with

• 1986 Commission safety goal 

policy statement

• June 1990 SRM

• RG1.174

Screening Limit 

Development

Figure 3-1. High-level schematic showing how a probabilistic estimate of through-wall cracking frequency 

(TWCF) is combined with a TWCF acceptance criterion to arrive at a proposed revision 

of the PTS screening limit. 

3.1.2.1 Component 1: Probabilistic 

Estimation of Through-Wall 

Cracking Frequency 

As illustrated in Figure 3-1, three main models 

(shown as solid blue squares), taken together, 

allow us to estimate the annual frequency 

of through-wall cracking in an RPV: 

• PRA event sequence analysis 

• TH analysis 

• PFM analysis 

In the following subsections, we first describe 

these three models and their sequential execution 

to give the reader an appreciation of 

their interrelationships and interfaces 

(Section 3.1.2.1.1). Secondly, we describe 

the iterative process we undertook, which involved 

repeated execution of all three models in sequence, 

to arrive at final models for each plant 

(Section 3.1.2.1.2). We then discuss the three 

specific plants we analyzed in detail 

(Section 3.1.2.1.3). Finally, we conclude with 

a discussion of the steps taken to ensure that 

our conclusions based on these three analyses 

apply to domestic PWRs in general

(Section 3.1.2.1.4). 

3.1.2.1.1 Sequential Description 

of How PRA, TH, and PFM 

Models are Used 

To Estimate TWCF 

First, a PRA event sequence analysis is performed 

to define the sequences of events that are likely 

to cause a PTS challenge to RPV integrity, 

and estimate the frequency with which such 

sequences can be expected to occur. The event 

sequence definitions are then passed to a TH model, 

which estimates the temporal variation 

of temperature, pressure, and heat-transfer 

coefficient in the RPV downcomer characteristic 

of each sequence definition. These temperature, 
3-3

pressure, and heat transfer coefficient histories 

are then passed to a PFM model that uses the TH 

output, along with other information concerning 

plant design and construction materials, 

to estimate the time-dependent “driving force 

to fracture” produced by a particular event 

sequence. The PFM model then compares this 

estimate of fracture driving force to the fracture 

toughness, or fracture resistance, of the RPV steel. 

This comparison allows us to estimate 

the probability that a crack would be created and 

would penetrate all the way through the RPV 

wall if that particular sequence of events actually 

occurred. The final step in the analysis involves 

a simple matrix multiplication of the probability 

of through-wall cracking (from the PFM analysis) 

with the frequency at which a particular event 

sequence is expected to occur (as defined by the 

event-tree analysis). This product establishes 

an estimate of the annual frequency of through-wall 

cracking that can be expected for a particular 

plant after a particular period of operation 

when subjected to a particular sequence of events. 

The annual frequency of through-wall cracking 

is then summed for all event sequences to estimate 

the total annual frequency of through-wall cracking 

for the vessel. Performance of such analyses 

for various operating lifetimes provides 

an estimate of how the annual through-wall 

cracking frequency can be expected to vary 

over the lifetime of the plant. 

3.1.2.1.2 Iterative Process Used 

To Establish Plant-Specific 

Models 

The set of transients used to represent a particular 

plant are identified using a PRA event-tree 

approach, in which many thousands of different 

overcooling sequences are “binned” together 

into groups of transients believed to produce 

similar thermal-hydraulic outcomes. Judgments 

regarding which transients to put into which bin 

were guided by such characteristics as similarity 

of break size, operator action, etc., and resulted 

in “bins” such as medium-break primary system 

LOCAs, MSLBs, etc. From each of the tens 

or hundreds of individual event sequences 

in each bin, a single sequence was then selected 

and programmed into the Reactor Leak 

and Power (RELAP) TH excursion code to define 

the variation of pressure, temperature, and heat 

transfer coefficient vs. time. These TH transient 

definitions were then passed to the Fracture 

Analysis of Vessels, Oak Ridge (FAVOR) 

PFM code, which estimated the conditional 

probability of through-wall cracking (CPTWC) 

for each transient. When multiplied by the bin 

frequency estimates from the PRA, these CPTWCs 

become TWCF values, which (when rank-ordered) 

estimate the degree to which each bin contributes 

to the total TWCF of the vessel. At this stage, 

many bins were found to contribute very little 

or nothing at all to the total TWCF, and so 

received little further scrutiny. However, some 

bins invariably dominated the TWCF estimate. 

These bins were further subdivided by 

partitioning the bin frequency, and selecting a 

TH transient to represent each part of the 

original bin. This refined model was then 

reanalyzed using FAVOR, and the bins that 

provide significant contributions to TWCF are 

again examined. This process of bin 

partitioning, and selection of a TH transient to 

represent each newly partitioned bin, continued 

until the total estimated TWCF for the plant no 

longer changes significantly. 

3.1.2.1.3 Plant-Specific Analyses 

Performed 

In this study, we performed detailed calculations 

for three operating PWRs (Oconee 1, Beaver 

Valley 1, and Palisades), as shown in Figure 3-2. 

Together, these three plants sample a wide range 

of design and construction methods, and they 

contain some of the most embrittled RPVs 

in the operating fleet. 

3.1.2.1.4 Generalization to All 

Domestic PWRs 

Since the objective of this study is to develop the 

technical basis for revision of the 10 CFR 50.61 

PTS screening limit that applies in general to all 

PWRs, we must understand the extent to which 

the three plant-specific analyses adequately address 

(in either a representative or a bounding sense) 

the range of conditions experienced by domestic 

PWRs in general. 
3-4

Beaver Valley 1

Palisades

• High embrittlement plant

• Westinghouse design

• High embrittlement plant

• Combustion Engineering design

Oconee 1

• Plant used in 1980s PTS study

• Babcox & Wilcox design

Figure 3-2. The three plants analyzed in detail in the PTS reevaluation effort. 

To achieve this goal, we have took the following 

measures: 

• We performed sensitivity studies on both 

the TH and PFM models to address the effect 

of credible changes to the models and/or 

their input parameters. The results of these 

studies provide insights regarding 

the robustness of our conclusions (based on 

three plants), when applied to the PWR 

population in general. 

• We examined plant design and operational 

characteristics of five additional plants. 

In so doing, our aim was to determine 

whether the design and operational features 

identified as being important in our three 

plant-specific analyses vary significantly 

enough in the population of PWRs to 

question the generality of our results. 

• In our three plant-specific analyses, 

we assumed that the only possible origins 

of PTS events are caused by events internal

to the plant. However, the PRA categorized 

external events (such as fires, floods, and 

earthquakes), which can also be PTS 

precursors. We, therefore, examined 

the potential for external initiating events 

to create significant additional risk relative 

to the internal initiating events we already 

modeled in detail. 

3.1.2.2 Component 2: Acceptance 

Criterion for Through-Wall 

Cracking Frequency 

Since the issuance of SECY-82-465 and the 

original PTS Rule, the NRC has established 

a considerable amount of guidance on the use 

of risk metrics and risk information in regulation 

[e.g., NRC FR 86, and RG 1.174]. To ensure 

consistency with this guidance, the PTS 

Reevaluation Project staff identified and assessed 

options for a risk-informed criterion for RVFF 

(which Regulatory Guide 1.154 currently 

specifies in terms of TWCF). 

As described in a May 2002 status report on risk 

metrics and criteria for PTS [SECY-02-0092], 

the options developed involved both qualitative 

concerns (the definition of RPV failure) 

and quantitative concerns (a numerical criterion 

for the reactor vessel failure frequency). 

These options reflected uncertainties in the margin 

between PTS-induced RPV failure, core damage, 

and large early release. The options also incorporated 

input received from the ACRS [NRC LTR 02], 

regarding concerns related to the potential 

for large-scale oxidation of reactor fuel 

in an air environment. 
3-5

Our assessment of the options involved identifying 

technical issues unique to PTS accident scenario 

development, developing an accident progression 

event tree to structure consideration of the issues, 

performing a scoping study of containment 

performance during PTS accidents, and reviewing 

the options in light of this information. 

The scoping study involved collecting 

and evaluating available information, performing 

a few limited-scope thermal-hydraulic 

and structural calculations, and conducting 

a semi-quantitative analysis of the likelihood 

of various accident progression scenarios. 

3.1.2.3 Component 3: Screening Limit 

Development 

As illustrated schematically in the lower left corner 

of Figure 3-1, a screening limit for PTS can be 

established based on a simple comparison 

of TWCF estimates as a function of an appropriate 

measure of RPV embrittlement with the TWCF

acceptance criterion (see Chapter 10). Beyond 

the work to establish both the TWCF vs. 

embrittlement curve and the limit value for 

TWCF, it is also necessary to establish a suitable 

vessel damage metric that, ideally, allows 

different conditions in different materials at 

different plants to be normalized. From 

a practical standpoint, “suitable” implies that 

the metric needs to be based on readily available 

information regarding plant operation and 

materials. 

3.2 Uncertainty Treatment 

At the outset of this project (1999), a staff member 

reviewed the NRC’s existing approach for PRA 

modeling, focusing on how uncertainties should 

be treated, how they were propagated through 

the PRA, TH, and PFM models, and how that 

approach compared with the NRC’s guidelines 

on work supporting risk-informed regulation 

[Siu 99]. This review established the general 

framework for model development and uncertainty 

treatment adopted in this study. In the following 

two sections, we first review this recommended 

framework (Section 3.2.1), and then discuss its 

actual implementation (Section 3.2.2). 

Section 3.2.2 provides an overview of 

the uncertainty treatment implemented in the 

PRA, TH, and PFM analyses and discusses how 

uncertainties are “passed” between these three 

main technical modules. Details of these 

implementations appear elsewhere in this report 

(Sections 5.2.6–5.2.7, 6.8.2, and 7.4, respectively) 

and in other documents [Whitehead-PRA, 

Chang, and EricksonKirk-PFM, respectively]. 

3.2.1 Recommended Framework 

In this study, we performed probabilistic calculations 

to establish the technical basis for a revised PTS 

Rule within an integrated systems analysis 

framework [Woods 01]. Our approach considers 

a broad range of factors that influence the likelihood 

of vessel failure during a PTS event, while 

accounting for uncertainties in these factors 

across a breadth of technical disciplines [Siu 99]. 

Two central features of this approach are a focus 

on the use of realistic input values and models 

(wherever possible), and explicit treatment 

of uncertainties (using currently available 

uncertainty analysis tools and techniques). 

Thus, our current approach improves upon that 

employed in developing SECY-82-465, in which 

many aspects of the analysis included intentional 

and unquantified conservatisms, and uncertainties 

were treated implicitly by incorporating them 

into the models (RTNDT, for example). 

Our probabilistic models distinguish between 

aleatory and epistemic uncertainties. Aleatory 

uncertainties arise as a result of the randomness 

inherent in a physical or human process, 

whereas epistemic uncertainties are caused by 

limitations in our current state of knowledge 

(or understanding) of a given process. 

A practical way to distinguish between aleatory 

and epistemic uncertainties is that the latter can, 

in principle, be reduced by an increased state 

of knowledge. Conversely, because aleatory 

uncertainties arise as a result of randomness 

at a level below which a particular process 

is modeled, they are fundamentally irreducible. 

The distinction between aleatory and epistemic 

uncertainties is an important part of PTS analysis 

because different mathematical and/or modeling 

procedures are used to represent these different 

types of uncertainty. 
3-6

3.2.2 Implementation 

In this section, we describe our implementation 

of the uncertainty framework synopsized 

in Section 3.2.1, focusing specifically 

on the following aspects: 

• How the framework was implemented in of 

the PRA, TH, and PFM analyses. Consistent 

with the framework, we systematically 

identify uncertainties and characterize 

their nature (as aleatory or epistemic). 

These uncertainties are then either quantified 

or addressed as part of the overall structure 

of the mathematical model. 

• How uncertainties are “propagated” through 

the major components of the computational 

model used to estimate the TWCF illustrated 

in the upper right corner of Figure 3-1. 

This includes propagating uncertainties from 

PRA to TH, PRA to PFM, and TH to PFM. 

• How the uncertainties considered in all three 

models (i.e., PRA, TH, and PFM) become 

manifest in the uncertainties in the estimated 

value of TWCF. 

The first two points are described in Sections 

3.2.2.1 through 3.2.2.3, for PRA, TH, and PFM, 

respectively. The final point is addressed 

in Section 3.2.2.4. Finally, Section 3.2.2.5 

addresses the uncertainties associated with the 

potential “incompleteness” of our mathematical 

model relative to the physical reality we are 

trying to represent. 

3.2.2.1 PRA 

As illustrated in Figure 3-1, the PRA analysis 

has two major outputs: 

• Bin Definition: the representation (or model) 

of the total PTS challenge using a finite 

number of event “bins,” each of which 

represents an assortment of TH scenarios 

(that are believed to be similar) 

• Bin Frequency: an estimate (central tendency 

and distribution) of the frequency with which 

the events represented by each bin 

are expected to occur 

Each of these outputs has an associated uncertainty, 

as described in the following sections. 

3.2.2.1.1 Bin Definition 

Each bin represents an assortment of TH scenarios 

(i.e., PTS sequences) for the following reasons: 

• Like most PRAs, ours includes the usual 

idealization that both equipment failures 

and operator actions are binary (i.e., a valve 

either sticks open or it does not, an operator 

either acts or fails to act)§

. Clearly, reality 

is continuous; valves may stick open 

by various amounts and operators may act, 

but after some delay. This idealization leads 

to the situation where our mathematical 

representation (a single bin) represents 

a spectrum of potential outcomes, with each 

outcome having a distinct TH characteristic. 

• Another common PRA feature that we adopt 

is to group “similar” transients together 

in a single bin. For example, all primary system 

pipe breaks having a break diameter of 8-in. 

(20-cm) and above are placed in a single bin 

called “large-break LOCAs.” This approach 

is motivated by previous experience indicating 

that transients grouped in this manner have 

“similar” severity. Nonetheless, such “similarity” 

is an approximation. To continue with 

the large-break LOCA example, hot leg 

and cold leg breaks have different severities 

for the same break diameter, break diameter 

changes above 8-in. (20-cm) cause slightly 

different severities, and so on. All of these 

unmodeled effects occur for well-recognized 

physical reasons. Again, this idealization 

leads to the situation where our model (a 

single bin) represents a spectrum of potential 

outcomes, with each outcome having a 

distinct TH characteristic. 

 

§

 As detailed in Section 5.2.6.1, this statement is 

not always true. When judged to be important, 

certain equipment failures and operator actions 

were further subdivided (e.g., 30% stuck-open 

valves, operator actions at 1 vs. 10 minutes, etc.). 

Nonetheless, the PRA model is still a discrete 

representation of a continuum, and each PRA bin 

still represents a spectrum of TH responses. 
3-7

Thus, the structure of the PRA representation 

of the PTS challenge contains within it 

an uncertainty that is random and (hence) 

aleatory, having to do with all the ways 

that a PTS challenge could occur (i.e., PTS 

sequences). Discretizing the continuum 

of potential PTS sequences (which number 

in the tens or hundreds of thousands) into 

a tractable number of bins for detailed analysis 

(~hundreds) means that each bin contains many 

sequences, each of which can (in principle) 

produce a different TH response and, thereby, 

a different effect on the vessel. 

As is often the case in PRA, only a portion 

of the entire aleatory uncertainty significantly 

affects the overall results of the analysis. 

The important part of the aleatory uncertainty is 

determined by the way the PRA model was 

developed and how the bins were defined. As 

described in Section 3.1.2.1.2, an initial PRA 

model is developed and individual TH sequences 

are selected to represent each bin. These TH 

definitions are then passed to the FAVOR PFM 

code, which estimates the CPTWC for each 

transient. When multiplied by the frequency 

estimates for each bin, these CPTWC values 

become TWCF values, which (when rankordered) estimate the degree to which each bin 

contributes to the total TWCF of the vessel. At 

this stage, many bins are found to contribute 

very little or nothing at all to the total TWCF. 

However, some bins invariably dominate the 

TWCF estimate. These bins are then further 

subdivided by partitioning the frequency of the 

bin, and selecting a TH transient to represent 

each part of the original bin. This refined model 

is then reanalyzed using FAVOR, and the bins 

that provide significant contributions to TWCF 

are again examined. This process of bin 

partitioning, and selection of a TH transient to 

represent each newly partitioned bin, continues 

until the total estimated TWCF for the plant no 

longer changes significantly. At this point, that 

portion of all possible PTS sequences (and, 

hence, the aleatory uncertainty) that significantly 

affects the overall results is determined and 

remains in the final model as representing the 

aleatory uncertainty associated with how a PTS 

challenge might occur. 

3.2.2.1.2 Bin Frequency 

For each bin, there is uncertainty regarding the 

true frequency of occurrence. The uncertainty 

in the frequency with which the events 

represented by each bin occurs depends upon the 

following three factors, each of which is also 

uncertain: 

• uncertainty in the initiating event and its 

associated frequency 

• uncertainty in the series of equipment 

successes and/or failures that may follow 

the initiating event, and the uncertainty 

in their associated probabilities 

• uncertainty in the operator actions that may 

or may not be taken following the initiating 

event, and the uncertainty in their associated 

probabilities 

Thus, the frequency of occurrence of each bin 

is a function of the frequencies and probabilities 

of these factors. (The bin frequency is estimated 

from the individual frequencies and probabilities 

using Latin Hypercube sampling techniques 

to develop the bin frequency histogram that is 

provided as input to the FAVOR post-processor 

(FAVPOST).) Each of these factors has an 

associated epistemic uncertainty, which is 

described by a distribution. These uncertainties 

are epistemic in nature because our belief as to 

the estimates of these frequencies and probabilities 

is influenced by our limited state of knowledge 

about these rare events; and better knowledge 

would clearly lead to reduced uncertainty. 

3.2.2.2 TH 

The approach used to address uncertainty 

in the TH analysis principally utilized sensitivity 

studies to quantify the effects of phenomenological 

and boundary condition uncertainties/variations 

on the severity of a TH sequence. The results 

of these studies were used in two ways: 

(1) They were combined with probability 

estimates of the sensitivity parameters being 

evaluated to adjust the bin frequencies from 

the PRA analysis. 
3-8

(2) They were used to justify further subdivision 

of the PRA bins. (See the discussion in 

Section 3.2.2.1.1.) 

In this way, the TH uncertainty analysis 

accounts for certain parameters that can affect 

the thermal-hydraulic response of the plant, 

which were not explicitly considered in the PRA 

analysis (e.g., season of the year). Because 

the uncertainty analysis also produced insights 

regarding the effects of various system 

parameters and TH models on event severity, 

it also helped to identify the transient used to 

represent each PRA bin to the PFM analysis. 

This method of accounting for TH uncertainty 

does not quantify the uncertainties associated 

with each TH sequence. Rather, it characterizes 

the uncertainties associated with each PRA bin. 

This is appropriate because, as illustrated in 

Figure 3.3, each TH sequence that is passed 

to the PFM analysis represents a much larger 

number of TH sequences that, together, 

constitute a PRA “bin.” Provided the combined 

effects of the TH parameter and modeling 

uncertainties on the severity of this one 

representative sequence is small relative to both 

• the uncertainty in the frequency of occurrence 

of all of sequences in the bin, and 

• the variability in severity between 

the different sequences in the bin 

then, the uncertainty associated with TH 

parameter and modeling uncertainties of the 

representative sequence can be considered 

negligible. The appropriateness of not 

accounting for these uncertainties because they 

are negligibly small is ensured by the iterative 

process used to define the PRA bins. 

As described in Section 3.2.2.1.1, PRA bins 

that contribute significantly to the estimated 

TWCF were continually partitioned (including 

appropriate partitioning of the bin frequencies 

and selection of new TH sequences to represent 

each partitioned bin) until the total estimated 

TWCF for the plant did not change significantly 

with continued partitioning. Thus, any errors 

caused by not explicitly accounting for the TH 

parameter and modeling uncertainties associated 

with the TH sequence used to represent each 

PRA bin are not expected to influence the outcome 

of the analysis (i.e., the estimated values of TWCF). 

3.2.2.3 PFM 

Development of the PFM model featured 

a comprehensive review of all model components 

(both sub-models and parameters) with the aim 

of identifying, classifying, and quantifying 

the uncertainties in each [EricksonKirk-PFM]. 

In the great majority of cases, the best-estimate 

models (and associated uncertainties) were 

quantified, and these were propagated through 

the calculation. In some cases, inadequate 

empirical and/or physical evidence existed 

to support creation of a best-estimate with 

uncertainties. In these cases, conservative 

models and parameters were adopted 

[EricksonKirk-SS]). The judgment to include 

these conservatisms as part of the overall model 

is itself a treatment of uncertainty, not through 

quantification, but rather by influencing 

the structure of the overall PFM model. 
3-9

PRA Bin

Many (E2 to E3)

specific fault

sequences 

believed to be 

similar

1 2

4

3

5

n

Uncertainty in the 

frequency of event 

occurrence

PRA Bin

Many (E2 to E3)

specific fault

sequences 

believed to be 

similar

1 2

4

3

5

n

PRA Bin

Many (E2 to E3)

specific fault

sequences 

believed to be 

similar

1 2

4

3

5

n

1 2

4

3

5

n

Uncertainty in the 

frequency of event 

occurrence

TH 

Sequences

1

2

n

.

.

.

Variability in the 

severity of different 

sequences

TH 

Sequences

1

2

n

.

.

.

TH 

Sequences

1

2

n

.

.

.

1

2

n

.

.

.

Variability in the 

severity of different 

sequences

Representative 

TH Sequence

TH parameter and 

modeling 

uncertainties

TH parameter and 

modeling 

uncertainties

Figure 3.3. Characterization of TH uncertainties 

The great majority of the parameters in the PFM 

model (e.g., RTNDT, Cu, Ni, fluence, flaw 

parameters) were determined to have epistemic 

uncertainties. Statistical distributions were 

developed to characterize these uncertainties 

from representative data. In some cases, 

physical models guided these characterizations. 

Conversely, the various fracture toughness 

parameters in the PFM model were all 

determined to have alleatory (irreducible) 

uncertainties. These alleatory uncertainties 

are a direct and natural consequence of the 

heterogeneity of the material at the same size 

scale as the crack-tip deformation fields. They 

also arise because the interaction of two factors 

(material resistance vs. applied loading) 

produces the measured parameter called fracture 

toughness (again, see [EricksonKirk-PFM] for 

full details). 

The output of the PFM model is distributions 

quantifying the CPTWC for each transient 

analyzed. (This value is termed “conditional” 

because occurrence of the transient is assumed 

in the PFM calculation.) These distributions 

account for the uncertainties in the various toughness 

parameters, non-toughness parameters, and submodels that together make up the PFM model. 

3.2.2.4 What the Uncertainties 

in TWCF Represent 

Sections 3.2.2.1, 3.2.2.2, and 3.2.2.3 described 

the uncertainties in the PRA, TH, and PFM 

models, respectively. Table 3.1 summarizes that 

discussion, and indicates that in each of these 

three areas, the important uncertainties have 

been either “accounted for” (in that they 

influenced the structure of the computational 

model) or “numerically quantified” (as part of 

the model). Thus, a description of what the 

uncertainties in the reported values of TWCF 

represent requires more than a strictly numerical 

answer. As described in a NUREG-series report 

on the theory and implementation of the 

FAVOR code [Williams], FAVPOST estimates 

the numerical value of TWCF by performing 

a matrix multiplication of the distribution of 

the frequency of each bin defined in the PRA 

analysis with the distribution of CPTWC 

estimated by the PFM analysis. However, these 
3-10

uncertainties and their quantifiable distributions 

arise as a direct consequence of the particular 

model we have used to calculate them and, as 

indicated in Table 3.1, the structure of the model 

itself accounts for a number of uncertainties 

that have not been numerically quantified. Thus, 

the uncertainties in our reported TWCF values 

represent all of the uncertainties discussed in this 

section and in the detailed companion reports 

[Whitehead-PRA, Chang, and EricksonKirk-PFM]. 

Table 3.1. Summary of uncertainty treatment in the three major technical areas 

Technical 

Area 

Uncertainty 

Type 

Uncertainties that were 

accounted for in the structure 

of the model 

Uncertainties that were 

numerically quantified 

Aleatory 

Discretization of all of the ways 

a PTS challenge could occur 

into a finite number of “bins” 

--- PRA 

Epistemic --- Bin frequency 

Aleatory Boundary condition uncertainties

The effects of certain boundary condition 

uncertainties are reflected in 

the frequencies assigned to certain 

PRA bins. 

TH 

Epistemic Model uncertainties --- 

Aleatory --- Uncertainties in fracture toughness 

values (e.g., KIc, KIa, JIc) 

PFM 

Epistemic 

Adoption of conservative models 

(e.g., RTNDT, flaw distribution, 

fluence attenuation) 

Uncertainties in non-toughness values 

(e.g., Cu, Ni) 

3.2.2.5 Incompleteness Uncertainty 

As with any attempt to represent a complex 

physical system using a mathematical model, 

the question of “incompleteness uncertainty” 

arises. That is, “What has been left out of 

the model and, as a result, how confident should 

a decision-maker be in using the results of 

the analysis?”. It is fundamentally impossible to 

quantitatively address uncertainties arising from 

unknown factors. However, our process for 

model building, verification and validation 

(V&V) of our computational models, 

conservatisms known to remain in the models, 

the various reviews to which our work has been 

subjected, and the potential implementation of 

our results in future rules all provide qualitative 

assurance that any incompleteness in the model 

should have a negligible effects on the results. 

We discuss each of these factors below: 

• Process for Model Building: The PRA, TH, 

and PFM models were developed and 

continually improved throughout this study. 

Licensees from the three study plants 

provided input and review of both the PRA 

and TH models. The commercial nuclear 

power industry, working under the auspices 

of the Electric Power Research Institute 

(EPRI) Materials Reliability Project, was 

involved in reviewing all three models from 

the inception of the study. Additionally, 

subject-matter experts from the industry 

played a key role in both developing and 

reviewing the PFM model. To address 

uncertainties in a manner consistent with the 

framework proposed by Siu and synopsized 

in Section 3.2.1, various new models of both 

flaws and fracture toughness behavior were 

created for the PFM model. These new 

models have been presented for review and 

comment in various public and international 

venues, and have been published in both peerreviewed journals and conference proceedings 

[Kirk 01a, Kirk 02a, Natishan 01, 

EricksonKirk 04]. 

• Computational V&V: Calculations made 

in PRA, TH, and PFM are performed using 

computer codes referred to as SAPHIRE, 

RELAP, and FAVOR, respectively. 

SAPHIRE and RELAP are commercially 

available programs and have been subjected 

to extensive review and V&V. The FAVOR 

PFM code was developed by RES for the 

express purpose of performing probabilistic 
3-11

simulations of PTS. Accordingly, we have 

performed and reported V&V of FAVOR 

according to the software quality assurance 

(SQA) guidance in NUREG/BR-0167 [Malik]. 

• Known Conservatisms: While we devoted 

considerable effort throughout this study 

to perform “best estimate” analyses, it is 

nonetheless true that a number of 

conservatisms remain. Primary among these 

is the decision to treat through-wall cracking 

of the RPV as equivalent to occurrence of 

a large early release of radioactivity to 

the atmosphere. Chapter 10 discusses 

the reason for, and conservatism implicit in, 

this assumption. Furthermore, throughout 

the development of all the PRA, TH, and 

PFM models, there has been a tendency 

to address uncertainties by adopting 

conservative models or input values 

when the weight of physical and empirical 

evidence was inadequate to construct 

a “best-estimate” model. These types of 

conservatisms are discussed throughout 

Chapters 5–7 and in the supporting detailed 

reports [Whitehead-PRA, Bessette, 

EricksonKirk-PFM], and are summarized 

in Section 11.4.4. 

• Reviews: As described under Process for 

Model Building above, our models were 

subjected to both internal and external review 

during their development. Additionally, 

we solicited and received reviews of 

the entire project from three sources. 

In December 2002, we published an interim 

report summarizing the results of computations 

performed up to that time [Kirk 12-02]. 

This report was reviewed by both 

the commercial nuclear power industry and 

staff from the NRC’s Office of Nuclear 

Reactor Regulation (NRR), with both groups 

providing written comments [NEI Comments, 

NRR Comments]. These reviews indicated 

the need for numerous minor revisions, 

remodeling of some Oconee transients, 

and (most significantly) a fundamental 

restructuring and expansion of 

the documentation to improve both clarity 

and completeness. Addressing these 

comments resulted in this document (and the 

supporting documents, see Section 4.1), 

which have been subjected to review by 

an international group of experts. 

The comments provided by this panel 

(see Section 3.5 and Appendix B) have, 

again, resulted in improvements in both 

our documentation and our mathematical 

models. It is important to recognize that 

the combined effect of all of these changes 

(i.e., changes made in response to NEI, 

NRR, and external review panel comments) 

to the TWCF results [Kirk 12-02] has been 

to reduce the total TWCF by, on average, 

approximately one-third. Thus, while the 

comments received from the review panels 

have improved both the clarity of our 

documentation and the overall completeness 

and correctness of our models, the changes 

have not substantially altered either the overall 

structure of the models or the TWCF results 

that could be used to establish a new numerical 

value for the PTS screening criterion. 

• Potential Implementation: Should NRR elect 

to use the information presented in this 

and supporting documents as the basis 

for rulemaking to revise the requirements 

of 10 CFR 50.61, it must be remembered 

that it is only a screening limit that is being 

revised. Exceeding a screening limit does not 

suggest that failure is imminent (or even likely). 

It merely signals the need for the licensee 

to take additional actions (either analytical 

or mitigative) to assure NRR that plant 

operation beyond the screening limit does not 

unduly increase the risk to the public. 

Additionally, the current structure of 

10 CFR 50.61 requires that these actions 

be taken three years before the limits are 

actually exceeded. It also requires 

continued surveillance (according to the 

requirements of Appendix H to 

10 CFR Part 50) to ensure the continued 

validity of assumptions made during 

development of the screening limit 

regarding irradiation embrittlement 

mechanisms. Maintenance of this rule 

structure mitigates the practical impact 

on the overall public risk posed by PTS, 

as a result of any incompleteness uncertainties 

associated with the recommended numerical 

value of the screening limit. 
3-12

3.3 Fundamental Assumptions 

and Idealizations 

Any mathematical model of a physical system 

inherently involves some level of assumption 

and/or idealization to make estimates of 

the parameters of interest tractable within 

the practical constraints associated with the 

particular problem of interest. As discussed in 

greater detail in Chapters 5, 6, and 7, the PRA, 

TH, and PFM models each involve a large 

number of sub-models and, thus, a large number 

of possible assumptions and/or idealizations. 

Assumptions and idealizations that occur within 

each of the PRA, TH, and PFM sub-models are, 

therefore, addressed in Chapters 5, 6, and 7, 

respectively, or within their supporting reports. In 

the following subsections, we discuss the 

fundamental assumptions and idealizations that 

pertain to the PRA, TH, and PFM sub-models as 

a whole. 

3.3.1 Probabilistic Risk Assessment 

As with any PRA or HRA, the analysis team 

found it necessary to make assumptions in this 

study. In addition to the typical assumptions 

made as part of a PRA (e.g., actual plant system 

configuration is represented by the as-built 

as-operated documented information), the 

analysis team made various additional 

assumptions during the detailed PTS analyses. 

These assumptions are grouped into seven 

categories, as follows: 

1. Project execution 

a. Lessons learned from the Oconee 

analysis and preliminary PFM 

calculations for Beaver Valley 

and Palisades were used to simplify 

the model construction for Beaver 

Valley and Palisades. 

2. Possible PTS Initiating Events 

a. Scenarios initiated by an anticipated 

transient without scram (ATWS) were 

screened from the PTS analyses for two 

reasons. First, ATWS events generally 

begin with severe undercooling 

(i.e., there is too much power for the 

heat removal capability) and likely 

involve other failures to achieve an 

overcooling situation. Second, with 

typical ATWS frequency estimates in 

the range of 10-5/yr to 10-6/yr combined 

with the need for other failures to occur 

to possibly cause a continuing and 

serious overcooling situation, ATWSinitiated sequences should not be 

significant contributors to PTS risk 

when compared to other modeled 

scenarios with initiator frequencies 

commonly in the range of 1/yr to 10-3/yr. 

b. Interfacing systems loss-of-coolant 

accidents (ISLOCAs) could involve 

overcooling from the start of the event. 

However, significant ISLOCAs often 

fail, or are assumed to fail, mitigating 

equipment in PRAs, which ultimately 

causes an undercooling event, rather 

than an overcooling event; thus, 

ISLOCAs were not analyzed. Also, 

similar to ATWS, frequency estimates 

for ISLOCAs of sufficient size to cause 

a sever cooldown are in the range of 10-

5

/yr to 10-6/yr. Therefore, ISLOCAs 

should not be significant contributors 

to PTS risk when compared to other 

modeled scenarios with initiator 

frequencies commonly in the range of 

1/yr to 10-3/yr. 

c. It was asssumed that the frequency of 

inadvertent reactor/turbine trips under 

hot zero power (HZP) conditions is 20% 

of that occuring under full power 

conditions. The basis of this 20% factor 

is as follows: 

i. The plant operates at HZP 

approximately 2% of the time. 

ii. Except for inadvertent 

reactor/turbine trips attributable to 

transient conditions that arise while 

purposely changing feedwater and 

steam conditions along with 

changing power and other 

parameters in the plant, a review of 

transients occurring while at HZP 

provided no evidence that initiators 
3-13

are significantly more prone to 

occur at HZP than at full power. 

While no statistical treatment of this 

observation was attempted, 

engineering judgment was used to 

suggest that reactor/turbine trips 

seem more likely under HZP than 

under full power conditions because 

operators are often adjusting 

feedwater and steam conditions 

during HZP, factors that increase the 

likleyhood of tripping the plant. On 

this baisis, a factor of 10 increase in 

the likelihood of trips under HZP 

(vs. full power condtions) was 

assumed. 

iii. 2% x 10 = 20% 

3. Scenario development 

a. Medium- and large-break LOCAs 

were modeled as leading directly to 

a significant thermal transient for 

the reactor vessel without the need 

to consider the response of mitigating 

systems. 

b. The status of pressurizer PORVs and 

SRVs (i.e., whether they were open or 

closed) was assumed to be unimportant 

in the development of small LOCA 

scenarios. The basis for this assumption 

was that the pressure drop resulting 

from the LOCA initiating event should 

preclude the demand to open a primary 

side PORV or SRV. 

c. The PTS models excluded certain 

systems, structures, and components 

(SSCs) (e.g., pressurizer sprays and 

heaters) because they typically were 

found to have little impact on PTS risk. 

d. The functions of some SSCs were 

simply assumed for certain scenarios 

(e.g., accumulators were assumed to 

inject their inventory if conditions in the 

primary were such that injection should 

occur—failure of accumulator check 

valves was not modeled). 

e. The analysts recognized the importance 

of when an operator action occurred or 

when a piece of equipment changed 

state to the degree of overcooling 

experienced during a PTS scenario. 

To account for this, the scenarios 

incorporated a limited set of important 

operator actions (e.g., operator fails 

to throttle high-pressure injection) 

and equipment state changes 

(e.g., stuck-open pressurizer SRV 

recloses). 

4. Systems analysis 

a. The impact of heating and ventilation 

failures on equipment performance can 

be ignored because of the relatively 

slow effects on PTS-relevant equipment 

(e.g., failure of a pump as a result of 

room cooling failure typically takes 

a few hours by which time the PTS event 

is most likely over). 

5. Data 

a. Engineering judgment was used to estimate 

the failure probabilities for some SSCs. 

The numerical values provided by these 

judgments were typically conservative 

(i.e., the values were chosen such that 

potential PTS scenarios would not be 

inadvertently eliminated). 

6. Human reliability analysis 

a. Pre-initiator human failure events (HFEs) 

were not explicitly modeled in the Oconee 

and Beaver Valley PTS PRAs. Such 

human events were assumed to be included 

in the industry-wide data that was used 

to model system unavailabilities. 

For the Palisades analysis, pre-initiator 

HFEs were left “as-is” (i.e., the existing 

pre-initiator HFEs in the Palisades PRA 

model used in the PTS analysis were not 

modified). 

b. The time at which operators perform an 

action is taken to be either the earliest 

the action can be performed or the latest 

the action can be performed, whichever 

exacerbates PTS conditions (e.g., if the 

action involves the operator successfully 

throttling a pump by 20 minutes, then 
3-14

the action would be modeled as occurring 

at 20 minutes). 

c. Given the uncertainty associated with 

the various plant conditions that could 

exist during hot shutdown, some human 

error probabilities (HEPs) were assumed 

to be greater than their corresponding 

full-power HEPs. 

7. PTS bin development 

a. The assignment of the large number 

of potential PTS scenarios (tens of 

thousands) to a more limited number of 

PTS TH bins (tens to over one hundred) 

involved the analysts’ judgments as to 

how various combinations of equipment 

and operator successes affected the TH 

response of the plant when compared to 

a limited set of initial TH calculations. 

If the analysts judged that a scenario’s 

response would be similar to an existing 

TH calculation, the scenario was “binned” 

into the existing calculation’s bin. If the 

analysts judged that a scenario’s response 

could be sufficiently different from 

the existing calculations, a new TH 

calculation was requested, thereby 

creating a new bin. 

b. Typically, the analysts estimated 

the impact of the various equipment 

and operator combinations on two 

parameters (i.e., minimum downcomer 

temperature and primary pressure). 

c. Minimum downcomer temperature was 

the most important parameter that 

the analysts used to decide whether 

an existing TH bin could represent 

a scenario, or whether a new TH bin 

should be created. 

d. If the analysts determined that a PTS 

scenario could “fit” into more than one 

TH bin having similar characteristics 

(i.e., minimum downcomer temperatures 

approximately the same), they assigned 

the scenario to the bin believed to be 

more conservative (i.e., the scenario 

was assigned to the bin with the highest 

primary pressure). 

3.3.2 Thermal-Hydraulics 

The appropriateness of the RELAP TH analysis 

to assess PTS rests on the validity of the following 

fundamental assumptions: 

• We assume that the TH methodology 

implemented in RELAP is appropriate 

to assess the conditions in the downcomer 

during a PTS event. RELAP estimates fluid 

temperatures and wall-to-fluid heat transfer 

coefficients that represent well-mixed 

conditions in the downcomer at the core 

elevation. This approach assumes that jets, 

thermal plumes, and thermal streaming 

are not significant factors for PTS-type 

loadings. 

• We assume that it is appropriate to use the 

variation of pressure, temperature, and heat 

transfer coefficient with time characteristic 

of a single TH transient to represent an entire 

PRA bin (which may contain many tens 

or hundreds of transients). 

In the following subsections, we discuss the 

appropriateness of each of these assumptions. 

3.3.2.1 Appropriateness of the RELAP 

TH Model, in General 

At the most basic level, a TH analysis requires 

calculation of conservation of mass and energy, 

from which pressure and temperature follow 

from the equation of state. From this information, 

the analysis then estimates the distribution of 

energy within the RCS. Within the downcomer, 

the interface between the thermal-hydraulic and 

fracture mechanics calculations is the heat flux 

between the downcomer fluid and the vessel wall. 

Heat flux quantifies the RCS energy distribution, 

which depends on both the temperature and heat 

transfer characteristics of the downcomer region. 

In this study, we used RELAP5/MOD3.2.2γ

to estimate the heat flux and pressure boundary 

conditions. RELAP5 is a best-estimate systems 

code that models heat transfer and hydrodynamic 

processes without any intentional conservative 

or nonconservative modeling features. The code 

has been extensively documented [RELAP 01]. 

Our specific validation of RELAP5 addressed 
3-15

its ability to accurately estimate pressure, 

downcomer fluid temperature, and wall-to-fluid 

heat transfer coefficients for PTS loading conditions 

[Fletcher]. In these validation studies, which 

are summarized in Section 6.2, we compared 

RELAP5/MOD3.2.2γ predictions of pressure 

and temperature to measurements made in 

the most ideally scaled integral systems test 

facilities. These comparisons demonstrate 

that RELAP5/MOD3.2.2γ predictions 

of pressure and temperature appropriately 

characterize PTS loading events. 

3.3.2.2 Appropriateness of the TH 

Model 

RELAP5 calculates fluid temperatures and 

wall-to-fluid heat transfer coefficients that 

are characteristic of a well-mixed downcomer 

(at the core elevation). Dickson evaluated 

the suitability of this assumption using a 

predecessor of FAVOR [Dickson 87]. In that 

study, the base-case calculation represented 

a hot leg break with a diameter of 2-in. (5-cm) 

and a “nominal” plume strength of 140°F 

(60°C). (Plume strength equals the temperature 

difference between the colder water below 

the cold legs and the balance of the downcomer.) 

It should be noted that this “nominal” plume 

strength greatly exceeds any plumes that have 

been measured, as detailed in the following 

paragraph, and this “nominal” plume had 

no discernable effect of (relative to no plume 

at all) on the probability of through-wall cracking 

estimated by FAVOR. Furthermore, a doubling 

of the nominal plume strength produces only 

a 30% increase in the estimated probability 

of through-wall cracking. This study provided 

an indication that the well-mixed downcomer 

assumptions made by both RELAP and FAVOR 

are appropriate. 

More recently, we have performed additional 

work to establish the adequacy of the assumption 

of a one-dimensional (1D) temperature boundary 

condition, as follows: 

• A new integral experimental program was 

conducted at the APEX-CE test facility 

at Oregon State University to study cold leg 

and downcomer mixing [Reyes-APEX]. 

• We reviewed existing experimental databases, 

including integral system tests in the Lossof-Fluid Test (LOFT) facility and the Rig 

of Safety Assessment (ROSA), as well as 

full-scale tests in the Upper Plenum Test 

Facility (UPTF), and reduced-scale mixing 

tests at Creare, Purdue University, 

and Imatron Voimy Oy (Finland). 

• We performed mixing calculations using 

the REMIX code and computational fluid 

dynamics (CFD) codes. 

In thermal-hydraulic evaluations of PTS 

[Bessette], we compare these experimental data 

and RELAP5/MOD3.2.2γ predictions 

of pressure and temperature to establish 

the adequacy of the uniform temperature 

approximation. As seen consistently in 

the experimental data, the downcomer is wellmixed. In integral system test data, 

the temperature variations seen in the in the axial 

or azimuthal directions is on the order of 9°F 

(5°C). Large temperature gradients (i.e., on the 

order of 180°F, or 100°C) are often seen in the 

cold leg following loop flow stagnation. 

However, temperature gradients in the cold leg 

do not translate to corresponding temperature 

variations in the downcomer because of the large 

eddy mixing occurring in the downcomer. 

In summary, the maximum plume measured 

in any integral test facility representation 

of a PTS transient is on the order of 9°F (5°C). 

Probabilistic fracture mechanics calculations 

show that much larger plumes (strengths of ≈

216°F, or 120°C) are needed to have even small 

effects on the estimated probability of throughwall cracking [Bessette, Section 5.5]. For these 

reasons, the modeling approaches of both 

the RELAP and FAVOR codes with regard to 

temperature uniformity throughout the downcomer 

are viewed as both appropriate and non-biasing 

for this application. 
3-16

3.3.2.3 Appropriateness of a Using 

a Single TH Transient To 

Represent an Entire PRA Bin 

In Section 3.1.2.1.2, we described the iterative 

process used to establish the single TH transient 

that represents an entire PRA bin (which may 

contain many tens or hundreds of transients). 

This process includes continual partitioning 

of the PRA bins that contribute significantly 

to the estimated TWCF until the total estimated 

TWCF for the plant does not change significantly 

with continued partitioning. Given that process, 

the appropriateness of using a single TH transient 

to represent an entire bin (which may contain 

tens or hundreds of sequences that can produce, 

in principal, a like number of different TH 

responses) is not justified based on the exact 

agreement of the representative TH transient 

to all of the other transients in the bin (which is 

not, and cannot, be guaranteed). Rather, the 

appropriateness is justified by the procedure 

detailed in Section 3.1.2.1.2, which ensures that 

further subdivision of the bins would not result 

in significant changes to the TWCF (the desired 

output of the analysis). 

3.3.3 Probabilistic Fracture Mechanics 

The appropriateness of the FAVOR PFM 

analysis to assess PTS rests on the validity 

of the following four fundamental assumptions: 

• We assume (in general) that linear elastic 

fracture mechanics (LEFM) is an appropriate 

methodology to use in assessing the 

structural integrity of RPVs subjected to 

PTS loadings, and (in particular) that FAVOR 

predictions of the fracture response of RPVs 

in response to PTS loading are accurate. 

• We assume that the effect of crack growth 

by subcritical mechanisms (i.e., environmentally 

assisted cracking and/or fatigue) is 

negligible and, consequently, the flaw 

population of interest is that associated with 

initial vessel fabrication. 

• We assume that the fracture toughness of 

the stainless steel cladding is adequately high, 

and remains so even after irradiation, 

so there is no possibility of cladding failure 

as a result of the loading imposed by PTS 

transients. 

• We assume that stresses are sufficiently low 

at locations in the vessel wall between 

3/8⋅twall from the vessel ID and the OD, 

so the probability of failure associated with 

postulated defects in this region does not 

have to be calculated because it is zero. 

• We assume that if a particular transient does 

not achieve a temperature in the downcomer 

below 400°F (204°C), it does not contribute 

to the vessel failure probability. 

In the following subsections, we discuss the 

appropriateness of each of these assumptions. 

3.3.3.1 Use of Linear Elastic Fracture 

Mechanics 

One fundamental assumption in constructing our 

PFM model is that a linear elastic stress analysis 

of the vessel, and consequent fracture integrity 

assessment using the techniques of linear elastic 

fracture mechanics (LEFM), are accurate. 

Evidence supporting the appropriateness of this 

assumption is available in the following areas: 

(1) In Section 7.10, we summarize the results 

of studies aimed at experimentally validating 

the appropriateness of LEFM techniques 

when applied to assessing the integrity 

of RPVs under thermal shock and PTS 

experiments. The results of three experimental 

series performed on scaled pressure vessels 

at ORNL in the 1970s and 1980s 

demonstrate the accuracy of LEFM

techniques in these applications. 

(2) One fundamental requirement for LEFM 

validity is that the dimensions of the plastic 

zone at the tip of a loaded crack must be 

very small compared with the dimensions of 

the crack being assessed and the structure in 

which the crack resides [Rolfe]. Under 

these conditions, the error introduced by 

plastic flow (which is not accounted for 

within LEFM theories) is acceptably small. 

To assess plastic zone sizes characteristic of 

the PTS problem, we had the FAVOR 

probabilistic fracture mechanics code report 
3-17

all of the applied driving force to fracture 

(Kapplied) values from an analysis of Beaver 

Valley Unit 1 at 60 EFPY, which contribute 

to the TWCF, (i.e., those that have 

a conditional probability of crack initiation 

greater than 0). The top graph in Figure 3-4 

shows these Kapplied values overlaid on the 

KIc transition curve, while the bottom graph 

shows these same values expressed in the 

form of a cumulative distribution function. 

The lower graph indicates that 90% of the 

Kapplied values that contribute to the TWCF

estimate lie between 20 and 35 ksi√in (22 – 

38.5 MPa√m). Using these stress intensity 

factor values together with Irwin’s equation 

for the plastic zone size under plane strain 

conditions [Rolfe] indicates that the plastic 

zone radii characteristic of PTS loading 

range from ~0.03 to ~0.13-in. (~0.76 to 

~3.30-mm) depending upon the value of 

Kapplied (here taken to range from 20 to 35 

ksi√in, or 22 – 38.5 MPa√m), and the value 

of the yield strengths (here taken to be 70 

ksi (on average) for unirradiated materials 

and 90 ksi (on average) for irradiated 

materials (483 and 621, respectively). 

These values of plastic zone radii are small 

compared with the thickness of a PWR 

reactor vessel, indicating the appropriateness 

of LEFM techniques. Moreover, it can be 

noted that as the vessel ages, irradiation 

damage causes the yield strength to increase. 

Thus, as vessels approach EOL and 

extended EOL conditions, LEFM techniques 

become, if anything, more appropriate. 

3.3.3.2 Assumption of No Subcritical 

Crack Growth 

3.3.3.2.1 Due to Environmental 

Effects on the Low-Alloy 

Pressure Vessel Steel 

Stress corrosion cracking (SCC) requires 

the presence of three factors: an aggressive 

environment, a susceptible material, and 

a significant tensile stress. If these three factors 

exist and SCC can occur, growth of intrinsic 

surface flaws in a material is possible. Since an 

accurate PTS calculation for the low-alloy steel 

(LAS) pressure vessel should address realistic 

flaw sizes, the potential for crack growth 

in the reactor vessel LAS as a result of SCC 

needs to be analyzed, in principle. However, 

for the reasons detailed in the following 

paragraphs, SCC for LAS in PWR environments 

is highly unlikely and, therefore, is appropriately 

assumed not to occur for the purposes of 

the FAVOR calculations reported herein. 

The first line of defense against SCC of LAS 

is the cladding that covers much of the LAS 

surface area of the reactor vessel and main 

coolant lines. This prevents the environment 

from contacting the LAS and, therefore, obviates 

any possibility of SCC of the pressure boundary. 

Additionally, several test programs have been 

conducted over the past three decades, all of 

which show that SCC in LAS cannot occur 

in normal PWR or boiling-water reactor (BWR) 

operating environments. SCC of LAS in the 

reactor coolant environment is controlled by 

the electrochemical potential (often called 

the free corrosion potential). The main variable 

that controls the LAS electrochemical potential 

is the oxygen concentration in the coolant. 

During normal operation of a PWR, the oxygen 

concentration is below 5ppb. The 

electrochemical potential of LAS in this 

environment cannot reach the value necessary to 

cause SCC [IAEA 90, Hurst 85, Rippstein 89, 

Congleton 85]. During refueling conditions, the 

oxygen concentration in the reactor coolant does 

increase. However, the temperature during an 

outage is low, rendering SCC kinetically 

unfavorable. During refueling outage conditions 

with higher oxygen concentrations but lower 

temperatures, the electrochemical potential of 

the LAS would still not reach the values 

necessary for SCC to occur [Congleton 85]. 
3-18

0

25

50

75

100

125

150

175

200

-200 -150 -100 -50 0 50 100

T-RTNDT [oF]

Kapplied [ksi*in0.5]

applied KI

K-0%

K-50%

K-99%

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

20 30 40 50 60 70

Applied KI [ksi*in0.5]

Cumulative Probability Provided that 

CPI>0

Figure 3-4. Illustration of the magnitude of Kapplied

values that contribute to TWCF because they have 

a conditional probability of crack initiation > 0. 

The top graph shows all Kapplied values with CPI > 0 

overlaid on the KIc transition curve from an analysis 

of Beaver Valley Unit 1 at 60 EFPY. The bottom 

graph shows these same results expressed 

in the form of a cumulative distribution function. 

3.3.3.2.2 Due to Environmental 

Effects on the Austenitic 

Stainless Steel Cladding 

As stated in Section 3.3.3.2.1, one assurance of 

the negligible effects of environmentally assisted 

crack growth on the low-alloy pressure vessel 

steel is the integrity of the austenitic stainless 

steel cladding that provides a corrosion-resistant 

barrier between the LAS and the primary system 

water. Under conditions of normal operation, 

the chemistry of the water in the primary 

pressure circuit is controlled with the express 

purpose of ensuring that SCC of the stainless 

steel cladding cannot occur. Even under 

chemical upset conditions (during which control 

of water chemistry is temporarily lost), the rate 

of crack growth in the cladding is exceedingly 

small. For example, Ruther et al. reported 

an upper bound crack growth rate of ≈10-5 mm/s 

(≈4x10-7 in/s) in poor-quality water (i.e., high 

oxygen) environments [Ruther 84]. The amount 

of crack extension that could occur during a 

chemical upset is therefore quite limited, 

and certainly not sufficient to compromise 

the integrity of the clad layer. 

3.3.3.2.3 Due to Fatigue 

Fatigue is a mechanism that initiates and 

propagates flaws under the influence of 

fluctuating or cyclic applied stress and can be 

separated into two broad stages: fatigue damage 

accumulation (potentially leading to crack 

initiation), and fatigue crack growth. 

Fatigue is influenced by variables that include 

mean stress, stress range, environmental 

conditions, surface roughness, and temperature. 

Thermal fatigue can also occur as thermal 

stresses develop when a material is heated 

or cooled. Generally, fatigue failures occur 

at stresses having a maximum value less than 

the yield strength of the material. The process 

of fatigue damage accumulation, crack initiation, 

and crack growth closely relates to the phenomenon 

of slip attributable to static shear stress. 

Following a period of fatigue damage accumulation, 

crack initiation will occur by the progressive 

development and linking of intrusions along 
3-19

slip bands or grain boundaries. Growth of these 

initiated cracks includes fracture deformation 

sequences, plastic blunting followed by 

resharpening of the crack tip, and alternate 

slip processes. 

The PWR vessel is specifically designed so that 

all of its components satisfy the fatigue design 

requirements in Section III of the Boiler and 

Pressure Vessel Code promulgated by the 

American Society of Mechanical Engineers 

(ASME), or equivalent. Several studies have 

shown that the 60-year anticipated fatigue 

“usage” of the vessel beltline region attributable 

to normal plant operations, including plant 

heatup/cooldown, design-basis transients, etc. 

is low, so fatigue-initiated cracks will not occur. 

Similarly, fatigue loading of the vessel is 

considered insufficient to result in propagation 

of any existing fabrication defects [EPRI 94, 

Kasza 96, Khaleel 00]. 

3.3.3.3 Assumption that the Stainless 

Steel Cladding will not Fail as 

a Result of the Loads Applied 

by PTS 

Stainless steel, even in the clad form, typically 

exhibits initiation fracture resistance (JIc and J-R) 

values that far exceed those of the ferritic steels 

from which the RPV wall is made (see [Bass 04] 

for cladding data, compared to [EricksonKirk 04] 

for ferritic steel data). This is especially true 

for the levels of embrittlement at which vessel 

failure becomes a (small) probability because, 

at the fluences characteristic of the vessel ID 

location, the fracture toughness of ferritic steels 

can be considerably degraded by neutron 

damage, while the fracture toughness of 

austenitic stainless steels are essentially 

unaffected by these same levels of irradiation 

damage [Chopra 06]. This high toughness of 

the stainless steel cladding coupled with 

the small characteristic size of defects found 

in the cladding [Simonen] justifies the assumption 

that the stainless steel cladding will not fail 

as a result of the loads applied by PTS. 

3.3.3.4 Non-Contribution of Flaws 

Deep in the Vessel Wall to 

Vessel Failure Probability 

In FAVOR, flaws simulated to exist further than 

3⁄8⋅twall from the inner diameter surface 

are eliminated, a priori, from further analysis. 

This screening criterion is justified based on 

deterministic fracture mechanics analyses, which 

demonstrate that for the embrittlement and loading 

conditions characteristic of PTS, such flaws 

have zero probability of crack initiation. 

As illustrated in Figure 3.5, in practice, crack 

initiation almost always occurs from flaws 

that having their inner crack tip located within 

0.125⋅twall of the inner diameter, further 

substantiating the appropriateness of eliminating 

cracks deeper than 3⁄8⋅twall from further analysis. 

0

2

4

6

8

0.000 0.125 0.250 0.375

Percent Wall Thickness from ID

% of Flaws Predicted to Initiate

Beaver Valley at 200 EFPY

Palisades at 500 EFPY

Figure 3.5. Distribution of crack initiating depths 

generated by FAVOR Version 03.1 

3.3.3.5 Non-Contribution of Certain 

Transients to Vessel Failure 

Probability 

When running a plant-specific analysis using 

FAVOR, we only calculated the CPTWC for 

TH transients that reach a minimum temperature 

at or below 400°F (204°C). This a priori

elimination of transients is justified based on 

experience and deterministic calculations, both 

of which demonstrate that such transients lack 
3-20

adequate severity to have non-zero values of 

CPTWC, even for very large flaws and very 

large degrees of embrittlement. Additionally, 

the results of our plant-specific analyses 

(reported in Chapter 8) show that a minimum 

transient temperature of 352°F (178°C) must be 

reached before CPTWC will rise above zero, 

validating that our elimination of transients 

with minimum temperatures above 400°F (204°C) 

does not influence our results in any way. 

3.4 Participating Organizations 

This study could not have succeeded without the 

cooperation of a large number of individuals 

both within and outside the NRC. From its 

inception, the commercial nuclear power 

industry, working under the auspices of EPRI, 

has been a key participant in this project. Table 

3.2 summarizes the key organizations 

and individuals, and their contributions to this 

study. 

3.5 External Review Panel 

In response to a letter [Bonaca 03] from the 

Chairman of the ACRS, the NRC’s Executive 

Director for Operations (EDO) [Travers 03] 

identified a need to conduct formal peer review 

of the technical basis developed for potential 

revision of the screening criteria in the PTS Rule 

(10 CFR 50.61). In response to the EDO’s 

direction, RES solicited a panel of experts 

to perform an independent review of this report, 

and all supporting documentation that comprises 

the basis for our recommended revisions to the 

PTS Rule. Two peer reviewers were selected 

from each of the three key technical areas (PRA, 

TH, and PFM). Each peer reviewer was asked 

to provide his or her individual comments on 

the entire PTS technical basis without developing 

a consensus on a unified set of comments, 

to satisfy the requirement that this peer review 

panel must not constitute a Federal advisory 

committee. The following individuals served on 

the peer review panel. 

• Dr. Ivan Catton: Professor at the University 

of California, Los Angeles. Prof. Catton 

is an internationally recognized expert 

in thermal-hydraulics, and has served as 

a member of the NRC’s ACRS. 

• Dr. David Johnson: Vice President 

of ABS Consulting Inc., Irvine, California. 

Dr. Johnson is an internationally recognized 

expert in PRA. He is involved in major risk 

studies and in using those studies to support 

decision-making. 

• Dr. Thomas E. Murley: The chair of this 

peer review panel, Dr. Murley is a former 

Director of the NRR. Dr. Murley played 

a key role in regulating the operation 

of nuclear power plants for many years 

in comprehensive, high-level, broad-scope 

management of programs on water-cooled 

nuclear reactor power plants’ safety and risk 

assessments. 

• Dr. Upendra Rohatgi: A researcher at 

the U.S. Department of Energy’s 

Brookhaven National Laboratory, Upton, NY. 

Dr. Rohatgi has been extensively involved 

in the development of thermal-hydraulic 

computer codes for nuclear power plant 

applications. In the mid-1980s, he reviewed 

the thermal-hydraulic analyses performed 

for two of the plants analyzed in developing 

the current PTS Rule. 

• Mr. Helmut Schulz: Head of the Department 

of Structural Integrity of Components 

at Gesellschaft fuer Anlagen-und 

Reaktorsicherheit (GRS), Cologne, Germany. 

As a senior manager, Mr. Schulz has been 

involved in directing the development of 

PFM methodologies and managing various 

international cooperative research projects 

concerning fracture mechanics under the 

auspices of the Committee on the Safety 

of Nuclear Installations (CSNI) and 

the Nuclear Energy Agency (NEA) 

of the Organization for Economic 

Cooperation and Development (OECD) 

in Europe. 

• Dr. Eric vanWalle: Head of the Reactor 

Materials Research Department, Belgian 

Nuclear Research Center (SCK-CEN), Mol, 

Belgium. Dr. vanWalle is extensively 

involved in irradiation embrittlement 

characterization of RPV materials, and 
3-21

various International Atomic Energy 

Agency (IAEA) and OECD/NEA 

cooperative research projects in fracture 

mechanics related to ensuring the structural 

integrity of nuclear power plants. 

Appendix B provides more details of the peer 

review, including both the reviewers’ comments 

regarding our technical basis and recommendations, 

and the staff’s responses to those comments. 

Table 3.2. Participating organizations 

Sponsor/Organization Individuals Responsibilities 

RES/DET/MEB 

Mark EricksonKirk, 

Shah Malik, Tanny 

Santos, Debbie 

Jackson, Todd Mintz 

Project management, 

materials, fracture 

mechanics 

RES/DRAA/PRAB 

Roy Woods, Nathan 

Siu, Lance Kim, Mike 

Junge 

PRA, human reliability 

analysis, event 

sequence analysis, risk 

goal 

RES/DSARE/SMSAB Dave Bessette Thermal-hydraulics 

analysis 

Oak Ridge National Laboratory Terry Dickson, Richard 

Bass, Paul Williams PFM Code FAVOR 

Pacific Northwest National Laboratory 

Fred Simonen, Steve 

Doctor, George 

Schuster 

Flaw distribution 

Brookhaven National Laboratory John Carew Fluence 

Sandia National Laboratories 

Donnie Whitehead, 

John Forester, Vincent 

Dandini 

PRA, human reliability 

analysis, event 

sequence analysis, 

external events 

analysis, generalization 

task 

SAIC 

Alan Kolaczkowski, 

Susan Cooper, Dana 

Kelly 

PRA, human reliability 

analysis, event 

sequence analysis, 

external events 

analysis, generalization 

task 

University of Maryland 

Mohammad Modarres, 

Ali Mosleh, Fei Li, 

James Chang 

Uncertainty analysis of 

PFM and TH 

The Wreathwood Group John Wreathall Human reliability 

analysis 

Buttonwood Consulting Dennis Bley Human reliability 

analysis 

INEEL William Galyean PRA, event sequence 

analysis 

NRC 

ISL Bill Arcieri, Robert 

Beaton, Don Fletcher 

Thermal-hydraulic 

calculations using 

RELAP 
3-22

Sponsor/Organization Individuals Responsibilities

EPRI Stan Rosinski Program Management 

EPRI Materials Reliability Program (MRP) 

RPV Integrity Issue Task Group Robert O. Hardies ITG Chairman – Constellation Nuclear 

Westinghouse Electric Company 

Ted Meyer, Bruce 

Bishop, Randy Lott, 

Steve Byrne, Robert 

Lutz, Barry Sloan, Eric 

Frantz 

PRA, risk goal, PFM 

Code FAVOR, Fracture 

mechanics, materials, 

uncertainty analysis of 

PFM and TH 

Framatome ANP Ken Yoon Materials, fracture 

mechanics 

Sartrex Corporation Ron Gamble PRA, risk goal, PFM 

Code FAVOR 

Phoenix Engineering Associates Marjorie EricksonKirk 

Uncertainty analysis of 

PFM, fracture 

mechanics 

Constellation Nuclear – Calvert Cliffs Robert O. Hardies Plant-specific PTS 

First Energy – Beaver Valley Dennis Weakland Plant-specific PTS 

Duke Energy – Oconee Jeff Gilreath, Steve 

Nadar Plant-specific PTS 

Nuclear Management Company – Palisades 

John Kneeland, Brian 

Brogan, Christer 

Dahlgren, Gary Pratt 

Plant-specific PTS 

EPRI 

Applied Reliability Engineering Dave Blanchard Palisades PRA 
4-1

4 Structure of this Report, 

and Changes Relative to Previous Reports

4.1 Report Structure 

This report summarizes information found in 

a collection of other documents. As illustrated 

in Figure 4-1, various reports that concern either 

procedures or calculated results are available 

in each of three main technical areas (PRA, TH, 

and PFM). In this report, we do not attempt to 

provide a comprehensive summary of all aspects 

of the PFM, TH, and PRA procedures or results. 

Rather, in Chapters 5, 6, and 7, we focus on 

the key features of the PRA, TH, and PFM 

models, respectively, placing particular emphasis 

on changes between these models and those that 

were used to establish the technical basis for 

the current PTS Rule [10 CFR 50.61]. Chapter 8 

goes on to detail the results of our “baseline” 

probabilistic calculations for Oconee Unit 1, 

Beaver Valley Unit 1, and Palisades. Chapter 9 

summarizes various studies we have performed 

that collectively demonstrate the applicability 

of the results in Chapter 8 to PWRs in general, 

rather than just to the specific conditions 

analyzed herein. In Chapter 10, we discuss 

considerations associated with selecting 

an acceptable annual limit on TWCF, while in 

Chapter 11, we compare this limit to the results 

from Chapter 8 to establish a revision to 

the RTPTS screening criteria currently expressed 

in 10 CFR 50.61. 

4.2 Changes Relative to Previous 

Studies 

To assist readers familiar with the details of 

calculations that form the basis for the current 

PTS rule [SECY-82-465] or the calculations 

previously reported from this effort [Kirk 12-02], 

we provide a guide to where our methodology 

and results differ from the previous studies, 

and provide pointers to locations in this 

and other documents where those changes 

are discussed in greater detail 

4.2.1 Studies Providing the Technical 

Basis of the Current PTS Rule 

As detailed in Section 3.2, one fundamental 

difference between our approach and that of 

SECY-82-465 is that here we consider all of 

the known factors that influence the likelihood 

of vessel failure during a PTS event, while 

accounting for uncertainties in these factors 

in a consistent manner across a breadth 

of technical disciplines (see [Siu 99] for details). 

Two central features of this approach are a focus 

on the use of realistic input values and models 

(wherever possible), and explicit treatment 

of uncertainties (using currently available 

uncertainty analysis tools and techniques). 

Thus, our current approach improves upon that 

employed in developing SECY-82-465, in which 

many aspects of the analysis included intentional 

and unquantified conservatisms, and 

uncertainties were treated implicitly

by incorporating them into the models. 

In addition to this overall change in modeling 

approach, the following specific changes were 

made in the three main technical areas: 

Modifications to PRA

Table 5.1 (in Section 5.2.2) summarizes 

the differences between the current PRA 

and that used to support the current PTS Rule. 

These differences fall into the following three 

major categories: 

(1) greater refinement and detail in the current 

PRA 

(2) more realistic treatment of operator actions 

in the current PRA 
4-2

Summary Report – NUREG-1806

• Procedures, Uncertainty, & Experimental 

Validation: EricksonKirk, M.T., et al., 

“Probabilistic Fracture Mechanics: 

Models, Parameters, and Uncertainty 

Treatment Used in FAVOR Version 04.1,”

NUREG-1807.

• FAVOR

• Theory Manual: Williams, P.T., et al., 

“Fracture Analysis of Vessels – Oak 

Ridge, FAVOR v04.1, Computer Code: 

Theory and Implementation of 

Algorithms, Methods, and 

Correlations,” NUREG/CR-6854.

• User’s Manual: Dickson, T.L., et al., 

“Fracture Analysis of Vessels – Oak 

Ridge, FAVOR v04.1, Computer Code: 

User’s Guide,” NUREG/CR-6855.

• V&V Report: Malik, S.N.M., “FAVOR 

Code Versions 2.4 and 3.1 

Verification and Validation Summary 

Report,” NUREG-1795. 

• Flaw Distribution: Simonen, F.A., et al., 

“A Generalized Procedure for Generating 

Flaw-Related Inputs for the FAVOR 

Code,” NUREG/CR-6817, Rev. 1.

• Baseline: Dickson, T.L. and Yin, S., 

“Electronic Archival of the Results of 

Pressurized Thermal Shock Analyses for 

Beaver Valley, Oconee, and Palisades 

Reactor Pressure Vessels Generated with 

the 04.1 version of FAVOR,”

ORNL/NRC/LTR-04/18.

• Sensitivity Studies: EricksonKirk, M.T., 

et al., “Sensitivity Studies of the 

Probabilistic Fracture Mechanics Model 

Used in FAVOR,” NUREG-1808. 

• TH Model: Bessette, D., “Thermal 

Hydraulic Analysis of Pressurized 

Thermal Shock,” NUREG/1809.

• RELAP Procedures & Experimental 

Validation: Fletcher, C.D., et al., 

“RELAP5/MOD3.2.2 Gamma Assessment 

for Pressurized Thermal Shock 

Applications,” NUREG/CR-6857.

• Experimental Benchmarks: Reyes, J.N., 

et. al., Final Report for the OSU APEX-CE 

Integral Test Facility, NUREG/CR-6856.

• Experimental Benchmarks: Reyes, J.N., 

Scaling Analysis for the OSU APEX-CE 

Integral Test Facility, NUREG/CR-6731

• Uncertainty: Chang, Y.H., et all., 

“Thermal Hydraulic Uncertainty Analysis 

in Pressurized Thermal Shock Risk 

Assessment,” University of Maryland.

• Baseline: Arcieri, W.C., “RELAP5 

Thermal Hydraulic Analysis to Support 

PTS Evaluations for the Oconee-1, 

Beaver Valley-1, and Palisades Nuclear 

Power Plants,” NUREG/CR-6858.

• Sensitivity Studies: Arcieri, W.C., et al., 

“RELAP5/MOD3.2.2Gamma Results for 

Palisades 1D Downcomer Sensitivity 

Study”

• Consistency Check: Junge, M., “PTS 

Consistency Effort”

• Procedures & Uncertainty: Whitehead, D.W. 

and Kolaczkowski, A.M., “PRA Procedures 

and Uncertainty for PTS Analysis,”

NUREG/CR-6859.

• Uncertainty Analysis Methodology: Siu, N., 

“Uncertainty Analysis and Pressurized 

Thermal Shock, An Opinion,” USNRC, 1999.

• Beaver: Whitehead, D.W., et al., “Beaver 

Valley PTS PRA”

• Oconee: Kolaczkowski, A.M., et al., “Oconee 

PTS PRA”

• Palisades: Whitehead, D.W., et al., 

“Palisades PTS PRA”

• External Events: Kolaczkowski, A.M., et al., 

“Estimate of External Events Contribution 

to Pressurized Thermal Shock Risk”

• Generalization: Whitehead, D.W., et al., 

“Generalization of Plant-Specific PTS Risk 

Results to Additional Plants”

Results Models, Validation, & Procedures

PFM TH PRA

Figure 4-1. Structure of documentation summarized by this report. When these reports are cited in the text, 

the citation appears in italicized boldface to distinguish them from literature citations. 

(3) Use of the latest available data on initiating 

event frequencies and equipment failure 

probabilities in the current PRA 

As noted in the table, since these improvements 

were made with the intent of increasing both the 

accuracy and comprehensiveness of the PRA 

representation of the plants, they neither 

systematically increase nor reduce the estimated 

risk from PTS. 

Modifications to TH

The first PTS study was performed during 

the early 1980s. In that study, TH calculations 

were performed for Oconee Unit 1 with 

RELAP5/MOD1.5 (circa 1982) and for H.B. 

Robinson Unit 2 with RELAP5/MOD1.6 (circa 

1984). The results of those calculations were 

documented in [ORNL 86, ORNL 85b]. 

By contrast, the TH calculations performed in 

the current study employed 

RELAP5/MOD3.2.2Gamma, which was 

released in 1999 [RELAP 99]. The changes 

in the RELAP5 code in the intervening 20 years 

have been extensive [RELAP 99]: 
4-3

• RELAP5/MOD3.2.2Gamma uses a revised 

treatment of non-equilibrium modeling, 

including wall heat transfer models 

and coupling of the wall heat transfer 

and vapor generation models. 

• Interphase friction models were revised, 

and now incorporate a new interphase drag 

model for the vertical bubbly and slug flow 

regimes. 

• A general cross-flow modeling capability 

was installed, allowing cross-flow 

connections between most types 

of components and among the cell faces 

on those components. 

Other changes were implemented as a result of 

the code assessments related to the RELAP5 

analysis for the AP600 advanced passive reactor: 

• The Henry-Fauske critical flow model 

was added to provide a standard-reference 

critical flow model upon which code 

calculations are based. 

• Changes were made in code numerics 

to greatly reduce recirculating flows 

within model regions nodalized with 

a multidimensional approach. 

• A mechanistic interphase heat transfer 

model was implemented to include 

the effects of noncondensible gases. 

This change greatly improved the simulation 

of condensation, preventing erratic behavior 

and code execution failures. This change 

is particularly important for situations where 

the plant accumulators empty and nitrogen 

is discharged into the reactor coolant system 

(a situation that typically led to code execution 

failure at the time of the first PTS study). 

In the current study, no major changes were 

made from the RELAP5 plant input modeling 

approach used in the first PTS study [ORNL 86, 

ORNL 85a]. With only a few exceptions, 

the plant input models use the same nodalization 

schemes as before. Those nodalization schemes 

reflect plant modeling recommendations 

and guidance for the general modeling of plant 

transients, which evolved over years of RELAP4 

and RELAP5 experimental assessments and 

plant applications preceding the first PTS study. 

However, the current study used capabilities 

in RELAP5/MOD3.2.2Gamma, including 

renodalization of the reactor vessel downcomer 

(using the general cross-flow modeling capability), 

conversion of the vessel/hot and cold leg 

connections and the hot leg-to-pressurizer 

surge line connection to the cross-flow format, 

and addition of junction hydraulic diameter 

input data as required by the conversion 

of the code to junction-based interphase drag. 

[Bessette, Fletcher document how these 

RELAP5/MOD3.2.2Gamma capabilities 

influence the models used in the current study.] 

Current computer calculation speeds and data 

storage capabilities exceed greatly those used 

during the first PTS study, allowing the number 

of transients that can be reasonably evaluated 

directly using RELAP5 to be expanded by more 

than an order of magnitude. In the first PTS 

study, budget and schedule considerations 

limited the number of transients evaluated per 

plant to about 10 to 15. By contrast, the current 

study used more than 500 RELAP5 transient 

calculations to characterize the risk of vessel 

failure. 

Enormous advances in analysis tools (automated 

processes and plotting and data extraction routines) 

have also occurred. These tools lead to more 

comprehensive analyses, better communication 

and sharing of data, and more effective reporting 

of results. 

Modifications to PFM

(1) A significant conservative bias in the 

unirradiated toughness index temperature 

(RTNDT) model was removed. (See item 3 

in Section 7.7.2.2 of this report and 

Section 3.2.2.3.1 of [EricksonKirk-PFM].) 

(2) The spatial variation in fluence was 

recognized. (See item 1 in Section 7.7.2.2 

of this report and Section 3.2.3.1 

of [EricksonKirk-PFM].) 

(3) Most flaws are now embedded, rather than 

on the surface, and are also smaller than 

before. (See Section 7.5 of this report 

and [Simonen].) 
4-4

(4) Material region-dependent embrittlement 

properties were used. (See item 1 in 

Section 7.7.2.2 and Table 8.2 of this report.) 

(5) Non-conservatisms in the crack arrest model 

were removed. (See item 2 in Section 7.8.2 

of this report, Section 4.1 of [EricksonKirkPFM], and [Kirk 02a].) 

(6) Non-conservatisms in the embrittlement 

model were removed. (See Section 3.2.3 

of [EricksonKirk-PFM]). 

(7) The possibility of fracture on the upper shelf 

has been accounted for. (See item 1 in 

Section 7.8.2 of this report, Section 4.2 of 

[EricksonKirk-PFM], and [EricksonKirk 04].) 

(8) The effect of warm pre-stress (WPS) has 

been accounted for. (See Section 7.7.1.1 

of this report, Appendix B to 

[EricksonKirk-PFM]) 

(9) Uncertainties on chemical composition and 

RTNDT(u), which bound all known individual 

materials, have been included. (See 

Appendix D to [EricksonKirk-PFM].) 

4.2.2 December 2002 Draft Report 

In December 2002, we issued a draft report 

that detailed the results of plant-specific 

analyses performed on Oconee Unit 1, Beaver 

Valley Unit 1, and Palisades [Kirk 12-02]. 

Since that report was issued, we have made 

the following significant changes to our model: 

Modifications to PRA

No significant changes were made to 

the PRA/HRA models since [Kirk 12-02]. 

Modifications to TH

The RELAP5 Oconee model was revised 

to incorporate comments received from Duke 

Power [Arcieri-Base]. In addition, momentum 

flux modeling in the downcomer was changed 

to avoid the erroneous prediction of recirculating 

flows in the downcomer that, for a small number 

of cases, were unphysically high. When 

erroneous predictions of recirculating flows 

occurred, the high liquid velocity resulted in 

correspondingly high calculations of the heat 

transfer coefficient. The entire set of Oconee 

cases was rerun. 

Modifications to PFM

We revised the FAVOR PFM code. 

The information presented in [Kirk 12-02] 

was generated with FAVOR Version 02.4, 

whereas the information presented herein 

was generated with FAVOR Version 04.1. 

We made the following significant changes 

to FAVOR between these versions: 

(1) As part of our V&V effort, we identified 

a bug in how FAVOR associated material 

properties with cracks that lie on the fusion 

line of welds. This bug was most significant 

when the toughness properties of the plates 

adjacent to the weld are lower and, thus, 

control the fracture response, as is the case 

with Beaver Valley Unit 1. Details of this 

bug fix can be found [Malik]. 

(2) FAVOR now considers the possibility 

of failure occurring by ductile tearing 

on the upper shelf. Section 7.8 of this report 

describes the upper-shelf model we used 

and our rationale for its introduction, 

while Section 4.2 of [EricksonKirk-PFM] 

and [Williams] provide full details of the 

FAVOR Version 04.1 upper-shelf model. 

(3) FAVOR now models the effects of crack 

face pressure loading, as described in 

[Williams]. 

(4) FAVOR now accounts for the temperature 

dependence of thermal-elastic material 

properties, as described in [Williams]. 
5-1

5 Probabilistic Risk Assessment 

and Human Reliability Analysis 

5.1 Introduction 

This section describes the analysis activities 

associated with performing the PRA and HRA 

portions of the PTS reanalysis project. 

As depicted in Figure 5.1, the PTS reanalysis 

project was a closely integrated effort among 

three primary technical disciplines: 

(1) PRA (including HRA), 

(2) TH modeling, and 

(3) PFM. 

PRA Event 

Sequence 

Analysis

Sequence

definitions

Sequence

frequencies, [fr]

Thermal

Hydraulic 

Analysis

PFM 

Analysis

Pressure & 

temperature 

vs. time

Conditional

probability of thruwall cracking, [CPF]Yearly

frequency

of thru-wall 

cracking

[CPF]x

[fr]

Figure 5.1. Integrated technical analyses 

comprising the PTS reanalysis project 

As such, while this section focuses on the PRA 

and HRA (hereafter referred to as PRA unless 

specifically dealing with HRA) aspects of the 

reanalysis, important interfaces with the other 

technical disciplines are noted and cannot be 

completely separated from what was done in 

the PRA portion of the PTS reanalysis project. 

A key final product of this reanalysis project is 

the estimation of TWCFs associated with severe 

overcooling scenarios. The PRA portion of the 

reanalysis project had three primary purposes: 

(1) Define the overcooling scenarios (sequences) 

with the potential for being PTS challenges. 

(2) Direct the TH analysis as to the specific 

sequences to be modeled to obtain plant TH 

response information to be forwarded to 

the PFM analysts. 

(3) Estimate the frequencies, including 

uncertainties, for those overcooling 

sequences that are potentially important to 

the PTS results and provide that information 

to the PFM analysts. 

In fulfilling the above purposes, the PRA 

analysts followed an iterative process. 

The iterations were the result of (1) additional 

information becoming available from the other 

disciplines as the analyses evolved, and 

(2) feedback from the licensees participating in 

the three plant analyses (Oconee Unit 1, Beaver 

Valley Unit 1, and Palisades Unit 1). 

For each purpose listed above, a specific product 

was produced. The first product, definition of 

the overcooling sequences, is in the form of 

event trees constructed by the PRA analysts 

for each of the three plant PTS analyses. 

Event tree construction is a well-known and 

well-established PRA modeling tool that has 

been used in identifying and analyzing core 

damage scenarios, such as in the Individual 

Plant Examination (IPE) program. In this case, 

the same tool was used to identify and model 

overcooling sequences, rather than core damage 

sequences that could occur as a result of 

undercooling events. The sequences depicted by 

the PTS event trees represent those 

combinations of initiating events that disrupt 

normal plant operation (e.g., turbine trip), and 
5-2

subsequent plant equipment and operator 

responses that are included in each plant model 

to represent overcooling sequences with the 

potential to be a PTS challenge. 

The second product, direction by the PRA 

analysts to the TH analysts as to specific 

sequences to be modeled in their phase of the 

overall PTS analyses, was provided in the form 

of written and oral communications among 

the analysts. Each TH-modeled sequence 

was assigned a “case” number for identification 

purposes. For a given plant analysis, each TH 

“case” is a scenario that broadly represents many 

possible sequences on the event trees for that 

plant whose characteristics are similar enough 

that the sequences can be collectively 

represented by a single TH sequence (case). 

The TH analysts modeled each case to derive 

the time histories for reactor coolant pressure, 

reactor vessel downcomer temperature, vessel 

wall heat transfer characteristics, and other 

parameters important to defining the plant 

TH response during each case. This response 

information was subsequently provided to 

the PFM analysts to determine the vessel wall 

response (i.e., crack initiation and propagation) 

for the TH conditions. The modeling of multiple 

event tree sequences by a smaller number of 

“case” sequences involved a manual binning

process that is summarized later in more detail. 

The third product, sequence frequencies 

including uncertainties, was provided to the 

PFM analysts by the PRA analysts for those 

overcooling “case” bins that are potentially 

important to the PTS results. This information 

was provided in the form of electronic files 

containing a “case” bin identifier and statistical 

frequency information associated with that bin. 

These bin frequencies correspond to the “case” 

sequences modeled by the TH analysts and 

represent the combined frequencies of all 

event tree sequences combined into each bin. 

The PFM analysts then used the statistical 

frequency information, along with the TH 

information representing each bin, to estimate 

the TWCFs. 

5.2 Methodology 

A multi-step approach was followed to produce 

the PRA products for the PTS reanalysis project. 

Figure 5.2 depicts the steps followed to define 

the sequences of events that may lead to PTS 

(for input to the TH model), as well as 

the frequencies with which these sequences 

are expected to occur (for combination with 

the PFM results to estimate the annual frequency 

of through-wall cracking). Although the approach 

is illustrated in a serial fashion, its implementation 

involved multiple iterative passes 

through the various steps as the analyses 

and mathematical representations of each plant 

evolved. The following sections describe seven 

steps that together comprise the PRA analysis: 

Step 1: Collect information (Section 5.2.1) 

Step 2: Identify the scope and features of the 

PRA model (Section 5.2.2) 

Step 3: Construct the PRA models (Section 5.2.3) 

Step 4: Quantify and bin the PRA modeled 

sequences (Section 5.2.4) 

Step 5: Revise PRA models and quantification 

(Section 5.2.5) 

Step 6: Perform uncertainty analysis (Section 5.2.6) 

Step 7: Incorporate uncertainty and finalize results 

(Section 5.2.7) 

The reader should recognize that the PRA 

models described in this section consider only

events internal to the operating plant (stuck-open 

valves, pipe breaks, etc.) as possible PTS 

precursors. A scoping study aimed at assessing 

the frequency and consequences of external 

initiating events (e.g., fires, floods, etc.) is detailed 

in a separate document [Kolaczkowski-Ext] 

and summarized in Section 9.4 of this report. 
5-3

5.2.1 Step 1: Collect Information 

During the initial phase of the PTS project, 

significant resources were expended to collect 

information regarding PTS in general and each 

plant in particular. General informationgathering activities included reviewing the basis 

for the current PTS Rule [10 CFR 50.61], and 

searching LERs for the years 1980–2000 to gain 

an understanding of the frequency and severity 

of real overcooling events[INEEL 00a]. Plantspecific information sources included the PRA 

analyses performed during the 1980s in support 

of the Integrated Pressurized Thermal Shock 

(IPTS) studies and the current PTS Rule 

[ORNL 85a, 85b, 86], as well as plant-specific 

design and operational information. Familiarity 

with all of this information provided the bases 

upon which the PRA analysis of each plant 

was conducted. 

5.2.1.1 Generic Information 

5.2.1.1.1 LER Review 

The LER review identified a total of 128 events, 

demonstrating that overcooling events, or at least 

their precursors, do occur from time to time. 

These events are dominated by failure 

to properly control or throttle secondary side feed, 

a precursor that leads to relatively minor overcooling. 

Still, a few events have been associated with 

actual or potential loss of portions of secondary 

pressure control. These events predominantly 

involve equipment failures in the main feedwater, 

feed and steam control, and main steam systems. 

The results of the LER review also demonstrate 

that both active and passive (i.e., latent) human 

errors play a role, as many of the equipment 

failures were caused by improper maintenance 

or testing. Additionally, equipment in non-normal 

configurations can be an aggravating factor 

because contributing equipment faults have 

occurred that operators must identify, 

and for which they must compensate, to prevent 

overcooling.

Step 1

Collect Information

Step 2

Identify Scope & 

Features of PRA 

Model

Step 3

Construct PRA Model

Step 4

Quantify & Bin the 

Modeled Sequences

Step 5

Revise PRA Models & 

Quantification

Step 6

Perform Uncertainty 

Analysis

Step 7

Incorporate 

Uncertainties and 

Finalize Results

Result

Binned Sequence 

Frequencies for Use 

with PFM Results

TH

Model

PRA

Sequence 

Definitions

Pressure & 

Temperature

PFM

Model

CPI & CPF

Figure 5.2. Diagrammatic representation of the PRA approach 
5-4

5.2.1.1.2 Initiator Frequency and 

Probability Data 

Initiator frequency and failure probability data 

are needed for initiating events, systems, and 

components as input to the PRA model. Since 

the goal of the PTS reevaluation project was to 

provide a PTS risk perspective for the operating 

fleet of PWRs, it was deemed appropriate 

to apply industry-wide PWR data for initiator 

frequencies and equipment failure probabilities 

in the plant-specific analyses. Hence, while 

the PRA model structure and the operational 

considerations it represented were based on 

plant-specific information, initiator frequencies 

and equipment failure probability data were 

generally based on industry-wide data. 

Generic PWR data were obtained from two main 

sources. The first source, NUREG/CR-5750 

[Poloski 99], summarizes industry-wide initiator 

experience for the years 1987–1995, along with 

failure probabilities for selected components. 

This information was updated twice. The first 

update was performed in an unpublished (at the 

time) addendum to NUREG/CR-5750 [Poloski 99], 

which extended the experience base through 1998. 

The second update dealt with loss-of-coolant 

initiators and was based on input intended to 

account for time-dependent material aging 

mechanisms that were not included in the 

experiential data [Tregoning 05]** The second 

source, NUREG/CR-5500 [Poloski 98], 

summarizes industry-wide experience for 

selected systems. 

5.2.1.2 Specific Information 

5.2.1.2.1 Previous PTS-PRA 

Analyses

Review of the PRA analyses performed in support 

of the IPTS studies and the current PTS Rule 

was another important input to the analyses. 

 

** Generic initiator frequency and system failure 

probability information (as described in Section 

5.2.1.1.2) was used for Oconee 1 and Beaver Valley 1, 

whereas the plant-specific PRA conducted by 

Consumers’ Energy personnel (for Palisades) 

incorporated plant-specific information. 

Of particular relevance were NUREG/CR-3770 

[ORNL 86] and WCAP-15156 [Westinghouse 99] 

(a more recent 1999 study) since these are past 

analyses of two of the plants covered in this work, 

Oconee 1 and Beaver Valley 1, respectively. 

Information in NUREG/CR-4183 [ORNL 85b] 

concerning H.B. Robinson, and NUREG/CR-4022 

[ORNL 85a] concerning Calvert Cliffs, was also 

considered since these documents provided 

additional perspectives and analytical 

considerations useful to this work. 

5.2.1.2.2 Plant-Specific Information 

At the outset of each plant-specific analysis, 

information was requested from the licensees 

pertaining to plant design, procedures, training, 

and other aspects of plant operation relevant to 

building a PRA model for analyzing PTS. 

Information provided in response to these requests 

was supplemented by information gained during 

plant visits and ongoing interactions (oral, written, 

and email exchanges) with each licensee 

as the analyses evolved. In total, plant-specific 

information was derived from the following 

sources: 

• summaries of any recent past actual 

overcooling events 

• current PRA model and write-ups 

• final safety analysis report sections 

• piping and instrument diagrams 

and electrical drawings 

• emergency and abnormal operating 

procedures 

• miscellaneous system design-basis 

information and related material 

• PTS-relevant training material 

• operational aspects associated with 

hot-shutdown conditions 

• observed multiple simulator exercises 

at each plant involving overcooling events 

that were setup and run as part of 

a collaborative effort between each licensee 

and the NRC contractor PRA analysts 

• periodic interactions with the licensees 

regarding modeling details as each analysis 

evolved 
5-5

• feedback from each licensee as interim 

results from the analyses became available 

5.2.2 Step 2: Identify the Scope and 

Features of the PRA Model 

The format, structure, and details considered 

in the current analyses draw considerably from 

the earlier PRA analyses of PTS. Aside from 

recognition of the results and the reasons 

for the results from these past analyses, 

limitations and conservatism associated with 

the past studies were identified and, 

to the greatest possible extent, alleviated. 

Other improvements were adopted with 

the intent of increasing both the accuracy 

and comprehensiveness of the PRA representations 

of the plants. Table 5.1 summarizes 

the differences between the current PRA 

and that used to support the current PTS Rule. 

These differences fall into the following three 

major categories: 

(1) greater refinement and detail 

in the current PRA 

(2) more realistic treatment of operator actions 

in the current PRA 

(3) use of the latest available data on initiating 

event frequencies and equipment failure 

probabilities in the current PRA 

As noted in the table, since these improvements 

were made with the intent of increasing both 

the accuracy and comprehensiveness of the PRA 

representations of the plants, they neither 

systematically increase nor reduce the estimated 

risk from PTS. 

In addition to identifying the areas for improvement 

of the PRA models that are addressed in Table 5.1, 

review of past PRA analyses of PTS provided 

information in four other areas: 

(1) identifying the types of sequences 

that needed to be included in the PRA 

(2) identifying what types of initiating events 

should be included 

(3) identifying what functions and equipment 

status needed to be included 

(4) identifying what human actions needed to be 

considered 

The following four subsections describe 

the general features of the PRA models in each area. 

These features were established by a team approach 

involving analysts skilled in both system/sequence 

considerations and HRA considerations. Thus, 

the process for building PRA models involved 

integrated consideration of both system/sequence 

and human reliability factors. 

5.2.2.1 Types of Sequences 

The following list details the types of sequences 

included in the PRA models: 

• overcooling scenarios 

o at full/nominal-power operation 

o under hot-shutdown conditions 

• loss of RCS pressure scenarios 

• virtually sustained RCS pressure scenarios 

(i.e., scenarios where RCS pressure initially 

decreases, necessitating start of HPI 

to restore pressure) 

• late repressurization scenarios 

• scenarios that provide immediate overcooling, 

as well as those that begin as loss-of-cooling 

scenarios (i.e., undercooling) and subsequently 

become overcooling scenarios 

Two types of scenarios commonly modeled in PRAs 

are not included in the current PTS analyses 

(as previously discussed in Section 3.3.1): 

(1) ATWS scenarios 

(2) ISLOCA scenarios 

Sequences resulting from such scenarios 

were not included, based on the following 

considerations. First, ATWS events generally 

initially begin as a severe undercooling event 

(i.e., there is too much power for the heat 

removal capability) and likely involve other 

failures to achieve an overcooling situation. 

While ISLOCAs, like the LOCAs modeled 

in the PTS study, could involve overcooling 

from the start of the event, significant ISLOCAs 

are often assumed to fail mitigating equipment 

in PRAs, which ultimately causes an undercooling 

event and core damage. Second, with typical 

ATWS and sizeable (not just small leaks), 

ISLOCA frequency estimates in the range of 

10-5/yr to 10-6/yr (or even lower) and with the need 
5-6

Table 5.1. Comparison of PRA analyses used in this study 

with the PRA analyses that supported 10 CFR 50.61 

Difference Between Current PRA Analyses 

and the PRA Analyses that Supported 10 CFR 50.61

Effect on 

Calculated 

Risk

Comments

1 Slight expansion of the types of 

sequences and initiators considered 

Increase 

2 

Slight expansion of support systems 

both as initiators and as dependencies 

affecting equipment response 

Increase 

3 

Less gross binning of TH sequences 

because there are more "cases" into 

which to bin individual TH runs 

Reduce Current work features 50–100 cases 

per plant whereas previous studies 

only considered about a dozen cases 

(e.g., small steamline breaks and the 

opening of 1–2 secondary valves 

were previously binned with a large 

guillotine steamline break, thereby 

treating the cooling effects of the 

smaller scenarios much too 

conservatively). 

4 

Refinement 

of Detail 

Considered 

by the 

Analysis 

External initiating events considered as 

potential PTS precursors 

Increase See Section 9.4. 

5 Credit for operator actions is based on 

detailed consideration of numerous 

contextual factors associated with the 

modeled sequences, on multiple 

simulator observations at each plant, 

on the latest procedures and relevant 

training, and on numerous discussions 

with operating and training staffs. 

Detrimental acts of commission are 

also considered based on these same 

inputs, including procedural steps that 

call for operator actions that can 

exacerbate overcooling in certain 

situations. 

Both 

Increase 

and Reduce 

6 

Treatment 

of Operator 

Actions 

A greater number of discrete operator 

action times are considered. 

Reduce Previous studies considered success 

or failure of operator action generally 

at 1 or 2 times after the start of the 

event. Currently, we consider up to 3 

discrete times for some operator 

action. 

7 Use of New 

Data 

Includes the latest industry-wide (and 

some plant-specific) data for initiating 

event frequencies, equipment failure 

probabilities, and common-cause 

considerations. 

Reduce Largest factor is the significant drop 

in the initiator frequencies as a result 

of the decrease in scram rates 

resulting from institutional programs 

executed in the 1980s and 1990s. 
5-7

for other failures to occur to possibly cause 

a continuing and serious overcooling situation, 

sequences involving ATWS or ISLOCAs should 

not be significant contributors to PTS risk. 

This is because other modeled scenarios that are 

likely to be significant contributors to PTS risk 

commonly have initiator frequencies in the 

range of 1/yr to 10-3/yr, including other LOCAs 

that are already modeled in the PTS study. 

5.2.2.2 Initiating Events 

The following internal initiating events were 

included in the PRA models: 

• small-, medium-, and large-break LOCAs 

• transients commonly modeled in PRA 

analyses, including: 

o reactor-turbine trip 

o loss of main feedwater 

o loss of main condenser 

o loss of offsite power (including station 

blackout) 

o loss of support systems, such as AC 

or DC buses 

o loss of instrument air 

o loss of various cooling water systems 

• steam generator tube rupture (SGTR) 

• small and large steam line breaks 

with and without subsequent isolation 

5.2.2.3 Functional/Equipment 

Considerations 

The event trees in the PRA models that depict 

potential overcooling sequences are based on 

the status and interactions of four plant functions 

and associated plant equipment. Figure 5.3 

presents a function-level event tree depicting 

the four functions and resultant general types 

of sequences treated in the PRA models. Each 

plant analysis features much more detailed event 

trees constructed at the initiator and equipment 

response level that incorporate the plant-specific 

design and operational features. These four 

functions (i.e., primary integrity, secondary 

pressure, secondary feed, and primary flow/ 

pressure) are important to treat in the PTS 

analyses for the following reasons: 

• Primary integrity: The status of this function 

influences the potential RCS pressure, which 

in turn influences the rate of cooldown 

(in some situations), the injection source 

capability, and the incoming and outgoing 

flow rates. All of these factors influence 

the vessel downcomer temperature. 

• Secondary pressure: The status of this function 

influences the pressure and temperature 

in the RCS, since the RCS and the secondary 

side of the plant are thermal-hydraulically 

coupled in most scenarios. For example, 

a rapid drop in secondary pressure can cause 

rapid cooling of the RCS, affecting both 

the downcomer temperature and, potentially, 

the RCS pressure (depending on subsequent 

RCS injection flow and heat removal). 

• Secondary feed: The status of this function 

influences the pressure and temperature 

in the RCS, since the RCS and the secondary 

side of the plant are thermal-hydraulically 

coupled in most scenarios. For example, 

overfeed can contribute to enhanced cooling 

of the RCS, affecting both the downcomer 

temperature and, potentially, the RCS 

pressure (depending on subsequent RCS 

injection flow and heat removal). 

• Primary pressure/flow: The status of this 

combination of conditions influences 

the RCS pressure and flow conditions 

(forced flow or natural circulation) during 

the overcooling event as well as the nature 

of the injection that can add cooling 

to the vessel wall. The flow characteristics 

either exacerbate or mitigate flow stagnation, 

which can also affect the downcomer 

temperature. 

In the plant event trees, the status of equipment 

relevant to each function is modeled in each PRA. 

This means that for each plant, the status of 

equipment relevant to each function is identified 

and included in the sequence modeling. 

For illustrative purposes, the following list 

summarizes the equipment associated with each 

function in the PRA models: 

• Primary integrity: Status of pipe breaks, 

PORVs and associated block valves, 
5-8

pressurizer SRVs, and pressurizer heaters 

and spray considerations where appropriate. 

• Secondary pressure: Status of steam line 

breaks, MSIVs and associated non-return 

valves, as well as related bypass and drain 

valve considerations where appropriate, 

turbine throttle and governor valves, steam 

dump/turbine bypass valves and associated 

isolation valves (if any), ADVs and associated 

isolation valves, and secondary steam relief 

valves (SSRVs). 

• Secondary feed: Status of main feedwater 

(MFW), condensate, and auxiliary/emergency 

feedwater (AFW/EFW) systems. 

• Primary pressure/flow: Status of high head 

safety injection, charging pumps and 

letdown considerations, accumulators/safety 

injection tanks, low head safety injection, 

and reactor coolant pumps (RCPs). 

The status of other equipment that is relevant 

because of interactions with the equipment 

in this list is also modeled as appropriate. 

Such equipment includes the actuation 

and protection/isolation circuitry associated with 

the equipment in the preceding list, and support 

systems including cooling water, instrument air, 

and electric power and instrumentation. Heating 

and ventilation equipment was not considered 

in the analyses because of the slow effects 

of such a loss, and since the loss can often be 

easily identified and recovered. 

5.2.2.4 Human Action Considerations 

Plant records of overcooling events that have 

actually occurred demonstrate that operator 

actions and inactions can significantly influence 

the degree of overcooling and the RCS pressure 

for many types of overcooling events. 

Consequently, operator action directly influences, 

in both beneficial and detrimental ways, 

the potential for many types of event sequences 

to become serious PTS challenges. For example, 

early operator action to isolate the feed to a faulted 

(depressurizing or already depressurized) 

steam generator directly affects the amount 

of overcooling that occurs and/or how long 

such cooling is sustained. 

Consequently, any “realistic” PTS analysis 

needs to consider operator actions and inactions 

that influence overcooling sequences. 

Therefore, consistent with the guiding principles 

of this project to adopt best-estimate models 

and treat uncertainties explicitly whenever 

practicable, a rigorous treatment of human actions 

is included in the PRA models. The process 

to identify, model, and probabilistically quantify 

human factors derives largely from NUREG-1624, 

Revision 1 [NRC 00], which uses an expert 

elicitation approach. In this study, the experts 

included both NRC contractors and licensees. 

These individuals considered both errors 

of omission and acts of commission. This process 

identified several general classes of human failures 

(see Table 5.2), which have been incorporated 

into the PRA models. Table 5.2 also details 

which of the four primary functions (identified 

in Section 5.2.2.3) these failures most affect. 

5.2.3 Step 3: Construct the PTS-PRA 

Models 

The well-known and well-established event treefault tree PRA methodology was adopted 

as the basis for all plant-specific analyses. 

However, the modeling approach varied somewhat 

from plant-to-plant because of the order in 

which the plants were analyzed (lessons learned 

in the Oconee analysis impacted the Beaver Valley 

and Palisades modeling approach, for example). 

Additionally, the availability of information 

from TH and PFM at the time PRA modeling 

began influenced how the PRA model evolved. 

A summary is provided below of the modeling 

approaches for Oconee, Beaver Valley, 

and Palisades. 
5-9

Table 5.2 General classes of human failures considered in the PTS analyses 

Primary Integrity Control Secondary Pressure 

Control

Secondary Feed Control Primary Pressure/ 

Flow Control

I. Operator fails to 

isolate an isolable 

LOCA in a timely 

manner (e.g., close a 

block valve to a stuckopen PORV) 

II. Operator induces a 

LOCA (e.g., opens a 

PORV) that 

induces/enhances a 

cooldown 

I. Operator fails to 

isolate a 

depressurization 

condition in a timely 

manner 

II. Operator isolates 

when not needed (may 

create a new 

depressurization 

challenge, lose heat 

sink...) 

III. Operator isolates 

wrong path/SG 

(depressurization 

continues) 

IV. Operator creates an 

excess steam demand 

such as opening 

turbine 

bypass/atmospheric 

dump valves 

I. Operator fails to 

stop/throttle or 

properly align feed in 

a timely manner 

(overcooling enhanced 

or continues) 

II. Operator feeds wrong 

(affected) SG 

(overcooling 

continues) 

III. Operator 

stops/throttles feed 

when inappropriate 

(causes underfeed, 

may have to go to feed 

and bleed possibly 

causing overcooling) 

I. Operator does not 

properly control 

cooling and 

throttle/terminate 

injection to control 

RCS pressure 

II. Operator trips RCPs 

when not appropriate 

and/or fails to restore 

them when desirable 

III. Operator does not 

provide sufficient 

injection or fails to 

trip RCPs 

appropriately (failure 

to provide sufficient 

injection is modeled as 

leading to core 

damage; thus, such 

sequences are not 

PTS-relevant)
5-10

5.2.3.1 PRA Modeling Differences 

Attributable to the Organization 

Constructing the Model 

Both the Oconee and Beaver Valley PTS 

analyses use the same large event tree-small 

fault tree modeling format adopted by the PRAs 

that formed the technical basis for the current 

PTS Rule. This approach makes best use 

of the earlier work in constructing updated PRA 

models. Since the desired outputs do not require 

the explicit component faults for some systems 

included in the model, very simple system fault 

trees were used with corresponding system-level 

failure data to represent the failure 

or unavailability of these systems. 

In contrast, a plant-specific PRA model 

developed by the licensee was used to provide 

the starting point for the PRA model 

of the Palisades plant used in this project. 

The licensee’s PRA includes more detailed 

component-level fault trees for all the systems 

included in the PTS-PRA model. However, 

in all three analyses, the level of resolution 

in the results is sufficient for the purposes 

of assessing the PTS risk. 

5.2.3.2 PRA Modeling Differences 

Attributable to the Order 

of Plant Analysis 

The PRA model of Oconee was constructed first 

(at a time when feedback information from 

the TH analysis and from the PFM analysis 

was not yet available). Consequently, it was not 

possible to screen out of the model overcooling 

sequences having a benign TH response 

or very low estimated conditional probabilities 

of through-wall cracking (from the PFM analysis). 

Hence, the Oconee PRA model contains 

virtually all the possible overcooling sequences 

with virtually no a priori screening out 

of “low significance” sequences. Subsequent 

feedback from both TH and PFM verified that 

many of the sequences included in the Oconee 

model could justifiably been omitted from 

the PRA model. 

Work on the Beaver Valley PRA model 

was initiated after the Oconee model had been 

constructed, at a time when the Oconee analysis 

results, while still evolving, were generally 

well-understood. Also, as the Beaver Valley 

PRA model was being constructed, some 

advanced TH and PFM results were already 

available for Beaver Valley sequences 

(identified from “lessons learned” from 

the Oconee analysis). Consideration of this 

TH/PFM information on Beaver Valley 

permitted a priori screening of the following 

general categories of sequences from the Beaver 

Valley PRA model: 

• Sequences involving certain combinations 

of stuck-open pressurizer PORVs or SRVs 

were not modeled. 

• Sequences involving certain combinations 

of secondary valve and simultaneous 

pressurizer PORV/SRV stuck-open events 

were not modeled. 

• Sequences involving only secondary valve 

(single or multiple) stuck-open events 

were not modeled. 

• Sequences involving overfeed of various 

steam generator (SG) combinations 

were not modeled. 

• Sources of secondary depressurization 

downstream of the MSIVs were not 

explicitly modeled. 

• SGTR sequences (including those involving 

lack of proper feed control and even with 

RCPs shutdown, possibly inducing RCS 

loop stagnation) were not modeled. 

• Other sequences were screened from modeling 

on a case-by-case basis if the sequence 

frequency could be conservatively estimated 

as less than ~10-8/yr. This screening limit 

was used because, when coupled with 

the maximum CPTWC (i.e., failure) 

calculated for any type of sequence (in the 

10-3 range) a TWCF of <10-11/yr would be 

generated. Such frequencies would clearly 

not be important to the overall PTS results, 

since some other sequences were known 

to involve TWCFs in the 10-8/yr range. 
5-11

Figure 5.3. Functional event tree as the basis for PTS PRA analysis

INITIATOR PRIMARY_INTEGRITY SECONDARY_PRESSURE SECONDARY_FEED PRIMARY_INTEGRITY_(F&B) PRIMARY_FLOW-PRESSURE 

OK

OKDepressurizing

OKOverfeedUnderfeed

OK/ControlledInjection overfeed/RCP flow sInjection underfeed

Primary integrity CLOSED.Feed and bleed not possible.

Not isolated (i.e., overfeed)Underfeed

CLOSED

OK/ControlledInjection overfeed/RCP flow sInjection underfeed

Break or stuck open valveIncreased potential for PTS

(1) Not considered a PTS concern regardless of primary flow/ pressure(2) Not analyzed as part of PTS analysis since sequence leads to (possible) core damage(3) CLOSED primary integrity (i.e., no opening) results in (possble) core damage; thus, not analyzed as part of PTS analysis.(4) For cases where the initial primary breach is large enough (e.g., large LOCA), the "CLOSED" branch of the F&B top event is not applicable since sufficient bleed is already present; thus, the sequence logic simply "passes through" the F&B top event to the PR

OK/ControlledInjection overfeed/RCP flow sInjection underfeed

Primary integrity OPENfor feed and bleed

OK/ControlledInjection overfeed/RCP flow sInjection underfeed

OPENSecondary depressurization furtherlowers RCS temperature(4)(4)

 FUNCTIONAL-ET - PTS Functional Event Tree 2004/
5-12

Because the Palisades model was built starting 

with an already established licensee componentlevel PRA model with overcooling sequences, 

it is the most detailed model of the three. This 

preexisting Palisades model was augmented 

by the licensee, on the basis of NRC contractor 

review and input, to include possible scenarios 

and other factors not already in the preexisting 

model. Consequently, the “lessons learned” 

from the Oconee PRA also influenced 

the Palisades PRA model. In general, 

the Palisades PRA model addresses the same 

types of initiators and sequences, as do 

the Oconee and Beaver Valley models. 

However, the initiating event frequencies, 

equipment failure probability data, and human 

failure estimates are specific to Palisades. 

5.2.4 Step 4: Quantify and Bin the 

PTS-PRA Modeled Sequences 

For each plant, two conditions were modeled: 

full operating power and hot zero power (HZP). 

As identified in Section 5.2.3.2, little information 

was available to screen out potential PTS 

sequences for Oconee. Thus, because of 

a SAPHIRE code [SAPHIRE] limitation 

(i.e., the inability to store more than 100,000 

sequences in a database); it became necessary 

to produce separate SAPHIRE models for 

full-power and HZP. Once the models 

(i.e., the event trees and fault trees) 

were constructed, the SAPHIRE code was used 

to generate the sequence logic for each event tree, 

and to solve the resulting sequences (90,629 

sequences for each model) with no truncation 

attributable to frequency. 

Given the number of potential PTS sequences 

for Oconee (181,258), it was necessary to group 

(i.e., bin) sequences with like characteristics 

into representative TH cases that could be 

analyzed with the RELAP TH code [RELAP]. 

Initial bins were constructed by developing 

event tree partitioning rules in SAPHIRE, 

and then applying those rules to produce 

the TH bins. Development of the partitioning 

rules required the analysts to examine the TH 

information available from preliminary analyses 

to identify the characteristics that would be 

important to the binning process. 

Using this information, the analysts then made 

judgments as to whether existing TH characteristics 

could be used to represent new groups 

of sequences. If the analysts judged that existing 

characteristics were appropriate, either because 

they matched the examined sequences exactly 

or because the TH conditions from the new 

sequences were expected to be similar to, but not 

be worse than, the conditions from the existing 

analysis, the uniquely defining characteristics 

associated with the existing TH analyses were 

written in rule form for application in SAPHIRE. 

For those cases where the analysts were 

sufficiently unsure as to the appropriateness 

of using existing characteristics, new TH 

characteristics were identified. These new sets 

of characteristics were discussed with the TH 

analysts. If those discussions led to the conclusion 

that the expected TH conditions could be 

sufficiently different from prior TH analyses 

and the frequency of occurrence of the conditions 

was such that they could not be “added” to some 

existing TH bin without being unnecessarily 

conservative, a new TH calculation (and hence, 

TH “case”) was identified. The TH characteristics 

associated with this new calculation were then 

written in rule form for subsequent application 

in SAPHIRE. 

This iterative process continued until all 

accident sequence cut sets were associated with 

a specific TH bin. Thus, the final application 

of the developed rules involved the examination 

of each sequence cut set to determine which rule 

the cut set met, the subsequent “tagging” of 

the cut set, and the gathering of like-tagged 

cut sets into initial TH bins. Once all cut sets 

were gathered into the initial TH bins, the bins 

were re-quantified using a truncation limit of 10-

10/yr. 

For Beaver Valley, essentially the same process 

was followed. The major difference between 

the Oconee and Beaver Valley analyses was in 

the number of sequences developed and solved 

(a total of 8,298 sequences for Beaver Valley 

for power and HZP). As discussed in the previous 

subsection, knowledge about what was and was not 
5-13

important in the Oconee analysis was used with 

preliminary sequence frequency estimates 

and CPTWC results from early Beaver Valley 

TH and PFM calculations to minimize 

the number of sequences actually modeled 

in the corresponding SAPHIRE databases. 

Given the significantly lower number 

of sequences, no truncation was performed 

on the initial TH bins. 

For Palisades, the process was somewhat different, 

in that the SAPHIRE model included both power 

and HZP sequences in the same database 

(only 3,425 sequences total) and the sequences 

were solved using truncation value of a 10-9/yr. 

Another difference between the Palisades 

and Oconee or Beaver Valley analyses was how 

the TH bins were created. In the Palisades analysis, 

each sequence end state was defined to a specific 

TH bin and all resulting cut sets were placed in 

the defined bin. (Note: use of this binning process 

rather than the one used in the Oconee or Beaver 

Valley analyses did not have any significant impact 

on the results, which are similar across the three 

plant analyses. It is simply that the binning process 

was somewhat less refined for bins that, based 

on experience with Oconee and Beaver Valley, 

were not expected to significantly influence the 

estimated TWCF values.) 

5.2.5 Step 5: Revise PTS-PRA Models 

and Quantification 

With preliminary results available, reviews were 

conducted by both licensee and internal project 

staff. This allowed for formal feedback from 

the licensee with regard to the PTS-PRA models, 

inputs, assumptions, and results, and gave 

the analysts an opportunity for self-review 

of the PRA performed to date. The purposes of 

the reviews were to determine the following: 

• whether inaccuracies existed in the models, 

and whether additional potential PTS 

sequences needed to be modeled 

• whether additional TH bins should be created 

to reduce unnecessary conservatism based on 

new or updated information obtained from 

preliminary CPTWC calculations or needs 

identified by the uncertainty analysis 

• which human actions were associated with 

the important TH bins 

• which of those human actions should be 

reexamined to produce even more realistic 

(i.e., less conservative) HEPs 

• what combination of the above could be 

accomplished within the constraints of 

the project 

For Oconee, the reviews identified the following 

needs: 

• to add one more type of potential PTS sequence 

• to add more TH bins to address uncertainty 

issues and reduce conservatism (note that 

conservatism is reduced by not having 

too many sequences represented by a bin 

that is described by plant conditions that are 

too conservative for the actual conditions 

of the sequences) 

• to reexamine some human actions to produce 

updated HEPs to account for more specific 

conditions 

The Beaver Valley reviews identified the following 

needs: 

• to add more TH bins to address uncertainty 

issues and reduce conservatism 

• to reexamine some human actions to produce 

updated HEPs to account for more specific 

conditions 

Because the Palisades analysis was performed 

by the utility, the results of the review described 

here dealt only with issues identified by the NRC 

review of the licensees’ PTS model. The review 

identified the following needs: 

• to add more break sizes to the LOCA class 

of initiating events 

• to modify probabilities for a few selected 

basic events 

• to add more TH bins to address uncertainty 

issues 

It should be mentioned that while formal reviews 

were performed, such as during the second plant 
5-14

visits at both Oconee and Beaver Valley, 

informal periodic reviews were conducted 

through frequent written and oral communications 

among the licensees and project staff. 

Appropriately, the models were revised and 

requantification was performed on the basis 

of these licensee inputs and as a result of 

self-evaluations by the project staff. 

5.2.6 Step 6: Perform Uncertainty 

Analyses 

The primary objective of the PRA portion 

of the PTS analyses was to produce frequencies 

of the set of representative plant responses 

to plant upsets (i.e., scenarios). These scenarios 

involve mitigating equipment successes 

and failures, as well as operator actions 

that result in various degrees of overcooling 

of the internal reactor vessel downcomer wall. 

The major areas of uncertainty associated with 

the PRA can be grouped into two broad categories: 

• modeling of the representative plant scenarios 

• estimation of the frequency of each modeled 

scenario 

These areas of uncertainty and the techniques 

used to deal with the uncertainties are discussed 

in the following two subsections. 

5.2.6.1 Modeling of Representative 

Scenarios to Characterize 

Aleatory Uncertainty 

Each scenario in the PRA is represented by 

a collection of events described by the logic 

of the event tree and relevant fault trees for each 

initiating event identified in the analysis. 

The model initially assumed binary logic 

(e.g., the valve either fully recloses or sticks 

wide open with no intermediate states) for the 

events. The only explicit modeling of event 

timing involved the timing of operator actions 

(i.e., failure to take an action is modeled 

as failure to take that action in multiple discrete 

times — for example, by 10 minutes, 

by 20 minutes — each with a probability). 

Most uncertainties with regard to model structure 

(e.g., completeness, intermediate states) were 

not quantified. However, where deemed 

potentially important, a few aleatory 

uncertainties were addressed by purposely 

changing the model and assigning a probability 

to the applicability of the model change. Each 

of these changes became a different scenario 

(TH bin) with an associated frequency (e.g., area 

associated with a stuck-open SRV reduced 30%, 

timing of enclosure of a stuck-open SRV (3,000 

s vs. 6,000 s), actual break size of small and 

medium LOCAs). Since it is unknown which 

scenario will occur following an initiating event, 

the complete set of scenarios, as represented by 

the event trees, characterize a large part 

of the aleatory uncertainty associated with 

the occurrence of a PTS challenge. The most 

important of these uncertainties that were 

explicitly handled in the analyses are addressed 

further in the next step, Step 7. 

In addition, there is the overall uncertainty 

regarding the completeness of the PRA 

model(i.e., have all scenarios that potentially 

lead to PTS conditions been identified and 

modeled). This uncertainty issue was addressed 

non-quantitatively through both internal (i.e., 

NRC and its contractors) and external (i.e., 

licensee) reviews of the PRA model. As a result 

of this peer review process, the models are 

expected to produce a sufficiently complete set 

of potential PTS sequences and thus, any 

incompleteness in the models is expected to 

have a negligable effect on the results. 

5.2.6.2 Quantification of Scenario 

Frequencies to Characterize 

Epistemic Uncertainty 

Each scenario from the set of modeled scenarios 

is the interaction of what are treated as random 

events: 

• initiating event (plant upset) 

• series of mitigating equipment successes/failures 

(e.g., MFW trips, AFW starts, ADV 

challenges when one sticks open) 

• operator actions (e.g., fails to close the ADV 

isolation valve by 20 minutes after the ADV 

sticks open) 
5-15

Thus, the occurrence of each scenario is random, 

and the frequency of each scenario is obtained 

using the following equation: 

Eq. 5-1 

scenario initiating event Pyequipment response PyOperator sActions )( ff − − − = ⋅ ⋅

where f denotes a frequency and Py denotes 

a probability. 

Each of the variables used to obtain the scenario 

frequency has an epistemic uncertainty 

described by a distribution. The source of this 

information came primarily from the input data 

used in the analysis (i.e., the addendum to 

NUREG/CR-5750 [Poloski 99] for Oconee and 

Beaver Valley, and the plant-specific data used 

in the Palisades analysis). For a few specific 

model inputs, other data sources were also used 

to derive these uncertainty estimates. For the HEPs, 

both best-estimate values and uncertainty ranges 

and distributions were derived through 

the expert elicitation processes carried out 

in the human reliability analyses. Latin Hypercube 

sampling techniques were used to propagate 

these epistemic uncertainties to generate 

a probability distribution for each scenario 

frequency. Thus, the frequencies provided by 

the PRA analysts to the PFM analysts were 

described by histograms representing 

the resulting frequency distributions. In this way, 

these PRA uncertainty distributions were 

propagated through and combined with the PFM 

uncertainties to ultimately derive uncertainty 

distributions in the estimated TWCFs. 

5.2.7 Step 7: Incorporate Uncertainty 

and Finalize Results 

This section discusses important uncertainties 

(largely aleatory in nature) specifically 

addressed in the PRA and describes how each 

was handled. As described in the previous 

subsection, epistemic uncertainty in the frequency 

for each of the final TH bins was estimated 

using Latin Hypercube sampling techniques 

and is not described in this subsection. 

The uncertainties discussed below were dealt with 

quantitatively; however, the degree of resolution 

associated with each specific uncertainty 

was limited. These uncertainties include: 

• size of the LOCA within a LOCA category 

plus other factors (e.g., initial injection 

water temperature) 

• size of the opening associated with single 

or multiple stuck-open SRV(s) 

• time at which a stuck-open SRV recloses 

• time at which operators take or fail to take 

action 

These uncertainties were highlighted for specific 

treatment in the analysis based on (1) the scenarios 

found to be most important to the PTS results, 

and (2) a series of uncertainty analyses 

performed by the University of Maryland (UMD) 

project team members on many of the inputs 

and parameters potentially affecting the PTS results 

to see which uncertainties would most affect 

those results. The specific UMD analyses are 

discussed in [Chang]. The results of that work 

concluded that the above uncertainties are 

sufficiently important that they needed to be 

treated explicitly in the PRA model. These 

uncertainties and how they were addressed 

are discussed in the following paragraphs. 

The actual break size of a LOCA for a specific 

LOCA class (i.e., small, medium, or large) can 

be any point on the spectrum of sizes defined by 

the two end points for that class. In addition, 

other factors (e.g., initial injection water 

temperature, break location, and injection flow rate) 

can contribute to the overall PTS model uncertainty, 

since these factors along with the specific break 

size affect the rate of cooling and subsequent 

plant response. Numerical probability results 

from the UMD uncertainty analysis were used 

to model and estimate the importance of the various 

modeling uncertainties examined in the UMD 

analysis, including different break sizes within 

a given class (which were assumed to be 

uniformly distributed). These numerical analyses 

provided a spectrum of different plant TH responses 

arising from uncertainties in these key parameters 

including break size. This spectrum of results 

was then represented by a number of discrete cases 

to cover the total spectrum of results (typically, 

five cases for small LOCAs, three for medium 
5-16

LOCAs, and one for large LOCAs). Each case 

was assigned a probability by the UMD analysts 

based on how much of the total spectrum 

the discrete case represented. Each discrete case 

was assigned a new TH case number with 

corresponding TH curves, and the frequency 

of each new case was adjusted using the UMD 

assigned probability for that case. This was 

accomplished through the following steps: 

• gather all cut sets from all sequences 

generated for a specific LOCA class 

into one bin 

• reproduce the gathered cut sets a specified 

number of times corresponding to 

the number of discrete cases defined 

to represent the spectrum of results 

• modify each set of reproduced cut sets 

to include the probability assigned to 

that discrete case 

Thus, the new modified cut sets account for 

the uncertainty associated with various 

parameters examined in the UMD analysis, 

including possible variation of break sizes 

within a given LOCA class. 

Just as with the LOCAs, the size of the opening 

associated with a stuck-open SRV can vary from 

sizes that are not PTS-significant to the valve 

fully stuck open. To deal with this and other 

relevant issues examined in the UMD analysis, 

the cut sets (and their associated frequencies) 

from stuck-open SRV sequences were modified 

to include a fraction that represented the uncertainty 

from the UMD work. In this case, it was assumed 

that the SRV opening size is uniformly distributed 

(any specific opening is equally likely) 

and the resulting fraction was included in 

the sequence frequency estimates to account for 

that fraction of possible SRV size openings that 

would be sufficient, from a cooling perspective, 

to be potentially important. 

The time at which a stuck-open SRV recloses 

is unknown and can occur at any point after 

the valve sticks open. To approximate this, 

the frequencies associated with stuck-open SRV 

sequences with subsequent closure of the SRV 

were divided equally between two specific SRV 

reclosure times (i.e., 3,000 s and 6,000 s). These 

two time points were chosen after reviewing 

stuck-open SRV TH conditions. The 6,000 s 

point was chosen to coincide with the time when 

the change in downcomer wall temperature had 

“flattened out.” The 3,000 s point was chosen 

to coincide with the time when sufficient cooling 

had occurred to the downcomer wall such that 

PTS could become an issue. Use of these two times 

provides a mechanism for determining some 

measure of the uncertainty associated with 

reclosure of stuck-open SRVs. Each case was 

assigned a 50% chance of occurring††. 

Just as the time at which a stuck-open SRV 

recloses is unknown, so too are the times at which 

operators perform actions. To address this issue, 

the times at which selected operator actions 

(i.e., those believed to be relatively important 

to PTS) were performed was varied. Typically, 

two or three different times were chosen 

to represent the uncertainty in when the action 

would be performed. Once the times were defined, 

typically (1) as early as could be expected, 

(2) as late as possible that would still affect 

the outcome, and (3) for some actions, some 

intermediate time, the probability of failing 

to perform the action by the specified time 

was developed. Use of these operator action times 

provides a means of estimating the uncertainty 

associated with when the operators actually 

perform their actions. 

For the Oconee analysis, all issues identified 

above were incorporated into the analysis. 

For the Beaver Valley and Palisades analyses, 

results from the UMD analysis indicated that 

little uncertainty came from the sequences 

involving stuck-open SRVs that remained stuck 

open; thus, no modifications were made to those 

types of sequences in the Beaver Valley 

and Palisades analyses. However, all other 

 

†† Subsequent sensitivity analyses demonstrated that 

the 6,000 s time is nearly the worst time from a PTS 

challenge point of view. The worst conditional 

probabilities of vessel failure typically occur 

if the SRV is assumed to close at 7,000 s or a little 

beyond, but the vessel failure probabilities are within 

a factor of ~2 of those calculated for 6,000 s. 

See also the discussion in Section 8.5.3.3.2 

and Comment #76 in Appendix B. 
5-17

modifications were made for the analyses 

of Beaver Valley and Palisades.
6-1

6 Thermal-Hydraulic Analysis 

6.1 Introduction and Chapter 

Structure 

This section describes the thermal-hydraulic 

analysis performed on the Oconee-1, Beaver 

Valley-1, and Palisades nuclear power plants: 

• The Oconee-1 coolant system is a loweredloop, Babcock & Wilcox design with two 

steam generators, two hot legs, and four 

cold legs. 

• The Beaver Valley-1 coolant system is 

a Westinghouse design with three steam 

generators, three hot legs, and three cold legs. 

• The Palisades coolant system is a Combustion 

Engineering design with two steam generators, 

two hot legs, and four cold legs. 

The discussion in this section begins in Section 6.2 

with a general discussion of thermal-hydraulic 

issues for transients that contribute to the risk 

of vessel failure attributable to reactor coolant 

system overcooling. This section is followed by 

a description of the RELAP5 code and its 

implementation in the TH analysis in Section 6.3. 

The general structure of the RELAP5 code 

and an overview of the physical models contained 

in RELAP5 are included in this section. 

The modeling of the plant primary and secondary 

systems including model initialization is discussed 

in Section 6.4. Section 6.5 presents an overview 

of the types of transients simulated, while 

Section 6.6 presents an overview of the results. 

A summary discussion of the experimental 

validation of RELAP5 is presented in Section 6.7. 

Section 6.8 presents a discussion of sensitivity 

analysis and the analysis of uncertainty. 

6.2 Thermal-Hydraulic Analysis 

of PTS Transients 

The PTS analysis combines the thermal-hydraulic 

response of the reactor coolant system with 

the thermal response of the reactor vessel. 

These parameters, when combined with the PFM 

analysis, are used to estimate the probability 

of unstable crack propagation leading to possible 

vessel failure. The principal purpose of the TH 

analysis is to generate the time histories for key 

parameters for use in the FAVOR fracture 

mechanics analysis code, for various plant transients. 

The parameter responses passed to the FAVOR 

code are the reactor vessel downcomer fluid 

temperature, primary system pressure, and heat 

transfer coefficient on the inside of the vessel wall. 

A wide variety of transients that could contribute 

to the risk of vessel failure were analyzed. 

These transients include reactor system overcooling 

attributable to a LOCA or a stuck-open primary 

side relief valve, a component failure that results 

in an uncontrolled release of steam from 

the secondary side (e.g., MSLB or stuck-open 

secondary side relief valve), or a control system 

failure that results in overfilling the steam generators. 

Combinations of failures are also of concern 

and were analyzed. The transients analyzed 

were defined from an event and fault tree analysis 

to determine possible transients (or accident 

sequences) and their frequencies of occurrence 

(see Chapter 5). Each transient and its associated 

frequency of occurrence are factored into the PFM 

analysis to estimate the risk of vessel failure. 

As part of the analysis, key parameters 

and processes that affect the reactor vessel 

downcomer fluid temperature, primary system 

pressure and heat transfer coefficient on the inside 

of the vessel wall were defined. The Phenomena 

Identification and Ranking Table (PIRT) 

methodology was used to identify the most 
6-2

important processes that impact reactor system 

thermal-hydraulic response to a transient [Shaw 

88, Zuber 89]. 

The PIRT methodology considered number of 

phenomenological processes and reactor system 

and plant boundary condition parameters. 

Examples of phenomenological processes 

include wall-to-fluid heat transfer in the downcomer, 

natural circulation flow, and steam generator 

heat transfer. Boundary condition examples 

include ECCS water injection temperature, 

break location (in the case of a LOCA), 

and timing of valve reclosure (for transients 

involving a stuck-open relief valve). 

The PIRT methodology has been applied to 

the Yankee Rowe and H.B. Robinson plants 

for PTS events. In the case of Yankee-Rowe, 

the PIRT is based on a 1.3-in. [3.3-cm] cold leg 

break. This break is approximately equivalent to 

a 2.8-in. [7.1-cm] break when scaled up to 

the larger diameter of the three current plants. 

The H.B. Robinson PIRT was based on a 2-in. 

[5.08-cm] hot leg break. A PIRT was also 

performed as part of the assessment of 

RELAP5/MOD3.2.2Gamma against data from 

tests performed at experimental facilities 

that considered the wide variation in thermalhydraulic conditions that can occur in PTS 

transients. This assessment is discussed in 

the RELAP5 PTS Assessment Report [Fletcher]. 

Table 6.1, excerpted from that report, provides 

a list of the parameters and processes considered 

and their ranking. This list considers a broader 

view of the types of transients that were analyzed, 

rather than focusing on a single transient. 

The PIRT table presented in Table 6.1 was used 

to focus the RELAP5/MOD3.2.2Gamma 

assessment on the following parameters that can 

be observed in the experiments: 

• break flow 

• primary system pressurization 

• natural circulation/flow stagnation 

• boiler-condensation mode and reflux 

condensation 

• mixing in the downcomer 

• condensation, mixing, and stratification 

in the cold leg 

• integral system response 

These parameters were selected because of their 

primary or secondary importance on downcomer 

conditions. The following three phenomena 

were deemed to be most important to downcomer 

conditions during PTS events: 

• natural circulation/flow stagnation 

• integral system response 

• primary system pressurization 

Natural circulation/flow stagnation is important 

because if loop flow continues (or restarts during 

a transient), warm water at the average coolant 

system temperature will be flushed through the 

reactor vessel downcomer, increasing the 

downcomer fluid temperature. In contrast, if the 

loop flow is stagnant, the cold ECCS water will 

not be mixed with water from other parts of the 

reactor system and the downcomer temperature 

will be colder relative to the natural circulation 

case. Integral system response is important 

because the ECCS injection behavior (flow 

rates, timing, and to some extent temperatures) 

are functions of the overall system behavior. 

System pressurization is itself a primary figure 

of merit in the PTS analysis. The other 

phenomena listed above were considered 

because of their effect on these main phenomena 

or because they potentially impact downcomer 

conditions. Fluid mixing in the downcomer is 

among these phenomena. These phenomena as 

well as the overall RELAP5/MOD3.2.2Gamma 

assessment are further discussed in Section 6.7. 

6.3 RELAP5 Code Description 

6.3.1 RELAP5 Analysis Process 

The RELAP5/MOD3.2.2Gamma computer code 

released in June 1999 was used for transient 

analysis to determine downcomer fluid 

conditions. The RELAP5 code was developed 

for best-estimate transient simulation of lightwater reactor coolant systems during postulated 

accidents and transients. The code models the 

coupled behavior of the reactor coolant system, 

core, and secondary side system for loss-ofcoolant accidents and operational transients such 

as anticipated transients without scram, loss of 
6-3

offsite power, loss of feedwater, and loss of 

flow. With RELAP5, a generic modeling 

approach is used that permits simulating a 

variety of thermal-hydraulic systems. Control 

system and secondary system components are 

included to permit modeling of plant controls, 

turbines, condensers, and secondary feedwater 

and steam systems. 

Figure 6.1 and Figure 6.2 present top-level 

schematics of the RELAP5 modeling process 

and code structure. 

The RELAP5 model input development process 

is portrayed on the left side of Figure 6.1. When 

modeling fluid systems with RELAP5, the 

physical systems are subdivided into networks 

of fluid cells that are interconnected by 

junctions. The RELAP5 model represents the 

fluid volumes, flow areas, path lengths and other 

characteristics of the physical system using a 

nodalization scheme of the fluid cells and 

junctions. 

A RELAP5 input model is developed by 

assembling data that describes the thermalhydraulic parameters of the physical system, 

such as pipe lengths, flow areas, volumes, and 

coefficients that simulate the pressure losses for 

flow through irregular geometry. The input 

model also requires the user to select various 

modeling options appropriate for the specific 

application, such as the critical flow model to be 

used and the locations in the model where it is to 

be activated. 

The user must specify the initial conditions 

(pressures, temperatures, flow rates, etc.) for 

every model feature. In practice, RELAP5 plant 

transient event simulations begin from 

conditions that represent steady-state conditions. 

The initial condition input specifications cannot 

be made to an acceptable degree of accuracy 

using a manual approach. Instead, the user 

typically enters initial conditions that only 

approximate the desired ones and executes the 

plant model with RELAP5 in a steady-state 

mode until a smooth solution is attained with 

initial conditions that acceptably represent 

steady-state conditions. RELAP5 transient 

event simulations are then begun, starting from 

the accurate set of RELAP5-calculated steadystate initial conditions. 

The user must specify the thermo-physical 

properties (such as thermal conductivity and 

heat capacity) for the materials of the model 

features that represent structures. 

The user also defines the timing information for 

the calculation. This includes the problem start 

time, problem end time, a range of time step size 

and the interval between data points for the 

calculation printed and plotted output. 

The RELAP5 code is executed using the input 

model described above and the code execution 

process is summarized in Figure 6.2. RELAP5 

simultaneously solves the equations for the 

conservation of mass, momentum and energy for 

the fluid conditions and flows among the cells 

and junctions in the nodalization grid. 

The code employs a set of steam tables to 

represent the steam, water and noncondensible 

gas physical properties (pressure, temperature, 

void fraction, quality, density, internal energy, 

etc.) in each cell as the transient calculation 

proceeds. 

The transient calculation is advanced in time 

using discrete time steps, the selection of which 

is made to assure a stable solution. The code 

automatically makes this selection of time step 

size within the minimum and maximum time 

step range that is defined by the user via the 

input. 
6-4

Table 6.1 Phenomena Identification and Ranking Table for Pressurized Thermal Shock in PWRs 

Rank Description Comments 

1 Break flow/diameter 

(or valve capacity) 

Importance of LBLOCA has increased, pressure is less 

important 

2 ECCS flow rate 

(Accumulator, HPI, LPI) 

State on/off, shutdown head of pumps, accumulator initial 

pressure 

3 Operator actions Includes operating procedures, RCP trip, HPI throttling, 

feedwater isolation, etc. 

4 Time of stuck valve reclosure Pressurizer safety relief valves which reclose after sticking open 

5 Plant initial state Hot full power vs. hot zero power operation 

6 Break location Primary LOCA (hot leg, cold leg), MSLB (inside/outside 

containment, upstream/downstream MSIVs), SGTR 

7 Unique plant features/design Difference in steam generator design, number of loops, 

vent valves, etc. 

8 Vessel to downcomer fluid heat 

transfer 

Affects the rate at which heat is transferred from the vessel wall 

to the downcomer fluid. Affects risk of vessel failure in nonconduction limited situations. 

9 ECCS injection temperatures Seasonal/operational variations 

10 Sump recirculation ECCS temperature/flow changes after RWST drained 

11 Feedwater control (or failure) Post trip main feedwater behavior, steam generator overfeed 

events 

12 Feedwater temperature Oconee (using AFW instead of MFW during transient). 

13 Reactor vessel wall heat conduction In conjunction with vessel to downcomer fluid heat transfer, 

affects the rate at which heat is transferred from the vessel wall 

to the downcomer fluid. Important particularly on those 

situations where heat transfer from the wall is conduction 

limited. 

14 Loop flow upstream of HPI Scenario dependent, not as important for LBLOCAs 

15 ECCS – RCS mixing in cold legs Affects potential for formation of cold plumes in the downcomer 

16 Flow distribution in downcomer Affects mixing and potential for formation of cold plumes in the 

downcomer 

17 Jet behavior, cold leg pipe to 

downcomer 

18 Loop injection upstream of safety 

injection 

Scenario dependent, important for MSLB, not for LBLOCA 

19 Steam generator energy exchange 

20 Timing of manual RCP trips Risk of vessel failure lower if pumps remain on. Operator 

assumed to trip RCPs in accordance with plant procedures. 

21 Interphase condensation and noncondensibles RELAP5 overprediction of condensation 

22 DC to core inlet bypass Less important for LBLOCAs 

23 Downcomer to upper plenum bypass Less important for LBLOCAs 

24 Upper head heat transfer coefficient 

under voided conditions 

Less important for LBLOCAs 
6-5

Figure 6.1. Schematic of RELAP5 Input and Output Processing 
6-6

Figure 6.2. Schematic of RELAP5 Execution Processing 

RELAP5 is based on a hydrodynamic model for 

single-phase and two-phase systems involving 

steam-water-noncondensible fluid mixtures in 

enclosed regions. The model is non-homogeneous 

(that is, the liquid and vapor phases at the same 

location may flow at different velocities) and 

non-equilibrium (that is, the liquid and vapor 

phases within the same region may exist at 

different temperatures). 

The RELAP5 solution is based on a staggeredmesh arrangement in which the conditions 

representing the fluid state (pressures, 

temperatures, void fractions, etc.) are calculated 

at the center of each cell and the fluid flow 

behavior (liquid and vapor velocities and mass 

flow rates) is calculated at the junctions between 

the cells. The RELAP5-calculated behavior, 

therefore, represents flow of liquid and vapor 

from the center of one cell, through one-half 
6-7

of the length of that cell to the interconnecting 

junction, and through one-half of the length 

of the adjacent cell to the center of the adjacent 

cell. 

The flow through the cell regions of the flow 

path is subjected to the influence of losses 

attributable to wall friction, and the flow through 

the junctions may be subjected to the influence 

of losses attributable to the presence of irregular 

configurations, such as pipe bends, valves, and 

orifices. In addition, the model considers the 

effects of friction between the liquid and vapor 

phases. 

Flow regime maps that provide characteristics 

for fluid behavior in vertical and horizontal cell 

orientations are used to determine the 

distribution of steam and liquid within each cell. 

This distribution is considered consistently 

throughout the RELAP5 model (for example, 

influencing interphase friction, liquid and steam 

velocities, condensation, and vaporization and 

fluid-to-wall heat transfer). 

The RELAP5 heat structure model is used to 

represent the structures of the physical system, 

such as fuel rods, steam generator tubes, and 

piping walls. Heat structures may include the 

effects of internal heating, such as with fuel rods 

or electrically powered pressurizer heaters. Heat 

structures are connected to the fluid cells and 

may be “single-sided” (connecting to a fluid cell 

on only one side, for example when modeling a 

cold leg piping wall) or “two-sided” (connecting 

to fluid on both sides, for example, when 

modeling the passage of heat from the primary 

to secondary coolant system through the steam 

generator tubes). 

RELAP5 calculates wall-to-fluid heat transfer on 

a consistent basis, with the heat transfer based 

on the wall surface temperature and the fluid 

conditions (pressure, temperatures, velocities) in 

the fluid cell connected to the wall. The flow of 

heat within the heat structure is based on the 

wall surface temperature and a solution of the 

one-dimensional conduction heat transfer 

equation. A wall heat transfer mode map 

(analogous to the flow regime map described 

above) is used to determine the fluid-to-wall 

heat transfer process based on the wall 

temperature and fluid conditions (pressure, 

steam and liquid temperatures, void fraction, 

steam and liquid velocities). 

RELAP5 capabilities include trip and control 

functions that allow the system model to 

represent the functions of automatic and 

operator actions in a plant. Examples of these 

actions include reactor trips, feedwater 

termination, relief valve operation, reactor 

coolant pump trips, and initiation of emergency 

core coolant flows. The RELAP5 trip and 

control features are also particularly important 

because they provide great flexibility for linking 

the hydrodynamic and heat structure models 

together and using them for simulating transient 

events that realistically represent the expected 

behavior the prototype plant systems. 

RELAP5 output, as portrayed on the right side 

of Figure 6.1, includes both printed and plotted 

output. The printed output consists of a 

snapshot of the RELAP5 solution for the 

conditions of every model feature at userselected times during the transient calculation. 

The plotted output consists of a file containing 

the time histories of the calculated solutions for 

every condition in every model feature. The 

user specifies the data interval of the plotted 

output. For the PTS application, it is the 

RELAP5-calculated time histories for reactor 

vessel downcomer fluid temperature, pressure, 

and wall heat transfer coefficient that are passed 

to the fracture mechanics analysts for use as 

boundary conditions in their analyses. 

The RELAP5 plant and code assessment 

calculations for the PTS project were performed 

consistently using the same version of the code, 

which is RELAP5/MOD3.2.2Gamma. 

Complete documentation regarding the RELAP5 

code and its application is found the RELAP5 

Code Manuals [RELAP, various citations]. 

6.3.2 RELAP5 Numerics Issues 

Two potential RELAP5 problems related to 

unphysical flow circulations exist that are 

significant for PTS analysis. These problems 

are discussed as follows. 
6-8

The first potential problem relates to circulations 

for plants with two cold legs per coolant loop 

during event sequences that result in complete 

stagnation of the coolant loops (LOCAs with 

break diameters larger than 2 inches). Potential 

flow networks exist for these plants, consisting 

of the two common cold legs and the steam 

generator outlet plenum on each coolant loop 

and the reactor vessel downcomer. Circulating 

flows within these networks have been observed 

in RELAP5 calculations during periods when 

cold ECC injection water is injected into the 

cold legs. The calculated solution initially 

becomes unstable, resulting in the onset of a 

continuous flow through the network (with 

forward flow through one of the cold legs and 

reverse flow through the other cold leg). 

Recirculating cold leg flows are believed to be 

numerically initiated as a result of round-off 

error, although once initiated, physically based 

buoyancy forces are created that could sustain 

such flows. The data from certain MIST and 

APEX tests used in the RELAP5 assessments 

(discussed later) provide potential, but 

inconclusive, evidence of circulating flows in 

cold leg networks in the test facilities. If 

present, cold leg network flow increases the 

downcomer fluid temperature as a result of 

mixing of the ECC injection water before it 

enters the downcomer. Because cold leg 

network flow is nonconservative for PTS, and 

because it is not clear whether such flows are 

physical, large artificial reverse flow loss 

coefficients were added in the cold legs near the 

reactor coolant pumps in the Oconee and 

Palisades models used for the LOCA cases. 

These artificial flow loss coefficients prevent 

negative flow in either of the two cold legs, 

thereby preventing circulating flows within the 

cold network and ensuring a solution for PTS 

that is conservative in this respect. 

The second potential problem relates to large 

circulating flows calculated by RELAP5 to exist 

within the reactor vessel downcomer region that 

are not physically realistic. As with cold leg 

network circulation (described above), 

downcomer circulations were noted for LOCA 

sequences with break diameters greater than 2-

in. (5-cm). The source of the circulation was 

traced to the application of the RELAP5 

momentum flux model within downcomer 

regions that are represented using twodimensional nodalization schemes (in the axial 

and azimuthal directions). The root cause of this 

problem in the RELAP5 code has not yet been 

determined; however, it was found that 

deactivating momentum flux for the junctions 

within the downcomer region prevented these 

physically unrealistic circulating flows. As a 

result, momentum flux was deactivated in the 

downcomer regions of the plant models used for 

the LOCA cases. 

6.4 Plant Model Development 

For all three plants examined, the thermalhydraulic analysis methodology is similar. For 

each plant, the best available RELAP5 input 

model was used as the starting point. For 

Oconee, the base model was that used in the 

code scaling, applicability, and uncertainty 

[CSAU] study. For Beaver Valley, the base 

model was the H.B. Robinson-2 model used in 

the original PTS study in the mid-1980s. This 

model was reviewed by Westinghouse and 

revised and updated based on the review 

comments to reflect the Beaver Valley plant 

configuration. For Palisades, the base model 

was obtained from CMS Energy Corporation, 

the operators of the Palisades plant. This model 

was originally developed and documented by 

Siemens Power Corporation to support analysis 

of the loss of electrical load event for Palisades. 

The RELAP5 models are detailed 

representations of the power plants and include 

all major components for both the primary and 

secondary plant systems. RELAP5 heat 

structures are used throughout the models to 

represent structures such as the fuel, vessel wall, 

vessel internals, and steam generator tubes. The 

reactor vessel nodalization includes the 

downcomer, lower plenum, core inlet, core, core 

bypass, upper plenum and upper head regions. 

Plant-specific design features, such as the 

Oconee reactor vessel vent valves, are included. 

To illustrate the model features and level of 

detail, a nodeing diagram for the Palisades plant 

is included in Figure 6.3, Figure 6.4, and Figure 

6.5. The modeling approaches used for Oconee 

and Beaver Valley are similar. 
6-9

The downcomer model used in each plant was 

revised to use a two-dimensional nodalization. 

This approach was used to capture the possible 

temperature variation in the downcomer 

resulting from the injection of cold ECCS water 

into each cold leg. Capturing this temperature 

variation in the downcomer is not possible with 

a one-dimensional downcomer nodalization. In 

the revised models, the downcomer is divided 

into six azimuthal regions for each plant. The 

reason for choosing six azimuthal regions is to 

match the geometry of the hot and cold legs 

around the circumference of the reactor vessel 

and so that water from each of the cold legs 

would flow into a separate downcomer node. 

The safety injection systems modeled for the 

Oconee, Palisades, and Beaver Valley plants 

include high-pressure injection (HPI), lowpressure injection (LPI), other ECCS 

components (e.g., accumulators, core flood tanks 

(CFTs), and/or safety injection tanks (SITs), 

depending on the plant designation), and 

makeup/letdown as appropriate. The secondary 

coolant system models include steam generators, 

main and auxiliary/emergency feedwater, steam 

lines, safety valves, main steam isolation valves 

(as appropriate) and turbine bypass and stop 

valves. Each of the models was updated to 

reflect the current plant configuration, including 

updating system setpoints (to best estimate 

values) and modifying control logic to reflect 

current operating procedures. Other model 

changes include adding control blocks to 

calculate parameters for convenience or 

information only (e.g., items such as minimum 

downcomer temperature). 

Detailed information regarding the specific 

individual RELAP5 input models for the 

Oconee, Beaver Valley and Palisades plants can 

be found in [Arcieri-Base]. 

The RELAP5 model does not include an explicit 

containment model. A volume held at constant 

atmospheric pressure is used to represent the 

containment. This approach was used for the 

simulation of adverse containment conditions 

during a main steam line break in the 

containment. In this situation, the reactor 

coolant pumps are tripped because of high 

containment pressure. 

The RELAP5 analysis considers the increase in 

injection water temperature resulting from 

switchover of the ECCS suction from the 

refueling water storage tank (RWST) to the 

containment sump. This switchover occurs 

when the water inventory in the RWST is 

depleted as a result of the combined pumping of 

the ECCS and containment spray pumps. After 

switchover, the ECCS and containment sprays 

operate in a recirculation mode, taking suction 

from the containment sump. At the point of 

suction switchover, ECCS injection water 

temperature will increase from a typical range of 

283 to 305 K (50 to 90°F) to 325 to 335 K (120 

to 140°F) or higher. Increase in ECCS injection 

temperature resulting from switchover to the 

containment sump is modeled to reflect the 

change in ECCS injection temperatures. 
6-10

Figure 6.3. Palisades Reactor Vessel Nodalization
6-11

Figure 6.4. Palisades Coolant Loop Nodalization
6-12

Figure 6.5. Palisades Main Steam System Nodalization
6-13

6.5 Transient Event Simulations 

Transient events were selected for evaluation 

based on probabilistic risk assessment (PRA) 

analysis. Since each plant possesses unique 

thermal-hydraulic, hardware failure, and 

operational characteristics, there necessarily was 

variation in the transients events analyzed for the 

three plants. Examples of plant-to-plant 

differences important for PTS that affect 

transient selection include variations in shutoff 

heads for HPI pumps; initial pressure and 

temperature conditions in the accumulator 

(safety injection tank, core flood tanks); initial 

ECCS fluid temperature and allowed range; 

initial steam generator (SG) water masses; sizes 

and configurations of various valves and 

automatic controllers; and plant-specific 

operating procedures. 

The development of the transient case list for 

each plant was an evolutionary process defined 

by the transient or sequence definition analysis. 

Generally, transients were selected based on the 

rate of primary system cooldown after transient 

initiation. Most transient event cases simulated 

generally fell into the categories of LOCAs and 

reactor/turbine trips with various complicating 

hardware and operator failures. Scenarios that 

consider stuck-open relief valves that either 

remain open or subsequently reclose later in the 

transient, system failures that cause steam 

generator overfeed, main steam line breaks, and 

others were analyzed. Evaluations were also 

performed for other types of events, such as 

steam generator tube rupture, recovery from a 

loss-of-all-feedwater event, and feed-and-bleed 

recovery from a LOCA with HPI failure. 

The transient event simulations were run as 

RELAP5 restart calculations beginning from 

steady plant operating conditions. Total 

simulation time is 15,000 seconds for Palisades 

and Beaver Valley. For Oconee, the total 

simulation time is 10,000 seconds. . 

6.5.1 Loss of Coolant Accidents 

The smallest LOCA break size evaluated was 

1.0-in. (2.54-cm) in diameter. Larger break 

diameters were also evaluated where the break 

flow area was progressively doubled, up to 

22.63-in. (57.47-cm) in diameter. Break 

diameters considered in the analysis, therefore, 

range over the full break spectrum. The breaks 

for most LOCA cases are assumed to be on the 

hot side of the reactor coolant system (in the 

pressurizer surge line for smaller breaks and in 

the hot leg for larger breaks). The hot leg break 

location was selected for most evaluations 

because it results in the greatest reactor coolant 

system cooldown rate, an intentionally 

conservative treatment. The ECCS injection 

rates are also maximized in this situation. 

Evaluation of cold leg break LOCAs was also 

performed. 

 

For all LOCA cases, the discharge and flow loss 

coefficients used for break junctions are 

assumed to be equivalent to those used in AP600 

work. While these coefficients may not be 

appropriate for a specific break, the wide 

spectrum of break diameters accounts for any 

uncertainties in loss coefficients. 

6.5.2 Reactor/Turbine Trips 

The majority of cases analyzed are initiated by a 

reactor/turbine trip followed by various primary 

or secondary side failures. These failures 

include relief valve failures, steam generator 

level control failures, and others. In the 

RELAP5 model for all cases, a reactor trip is 

considered the same as a turbine trip. In reality, 

if a reactor trip signal is generated, there is a 

small delay before a turbine trip is generated. 

Since the long-term downcomer temperature and 

pressure are of interest, this delay is considered 

negligible. There are numerous cases where 

stuck-open valves (pressurizer or steam 

generator PORVs, safety relief valves, etc.) are 

modeled as failures following a reactor/turbine 

trip. In these cases, the valve is assumed to 

spuriously open at transient initiation. Primary 

side stuck valves (pressurizer SRVs or PORVs) 

are similar to LOCAs where the “break” is 

located at the top of the pressurizer, rather than 
6-14

in the surge line, hot leg, or cold leg. In most 

cases, the RELAP5 models use a single valve 

component to model several valves in parallel. 

For example, in Beaver Valley, three pressurizer 

PORVs are modeled with a single RELAP5 

valve component. In order to have a single 

PORV fail by sticking open, the RELAP5 valve 

component is opened to one-third of the full 

flow area. 

In a number of cases, the valve that stuck open 

was assumed to reclose at some later time. 

The time of reclosure was defined as either 

3,000 seconds or 6,000 seconds depending on 

the transient definition from the PRA analysis. 

(Occasionally, a different time was chosen.) 

Various times were chosen since it would not be 

known when the valve would reclose (if it were 

to reclose). The 6,000-second reclosure time 

was selected as a point far enough out in time 

where the primary pressure and temperature 

reached a minimum. 

Another set of failures is overfeeding of 

the steam generators. As with other cases, 

the initiating event is the reactor/turbine trip. 

These cases will result in an overcooling event. 

The failure could be anything from 

equipment/component failure to control failure 

or operator error. Cases have been run where 

a single steam generator is filled to the top, and 

the water level is maintained at that level. There 

are cases where multiple steam generators are 

filled to the top. Cases were run where the 

steam generator was filled to the top, then 

feedwater was stopped and the steam generator 

was allowed to boil dry. 

6.5.3 Main Steam Line Break 

Main steam line break cases were selected 

because they cause rapid depressurization of the 

steam generator. This rapid depressurization is 

one of the most limiting overcooling transients 

from a single failure on the secondary side. 

Large breaks considered were modeled as 

double-ended guillotine breaks. These breaks 

were assumed to occur at the connection of the 

steam line to the steam generator (upstream of 

the main steam isolation valves). Smaller steam 

line breaks were simulated with stuck secondary 

side valves (SRVs, ADVs, etc.) Turbine bypass 

valves were also assumed to stick open. In 

plants with main steam isolation valves, some of 

these stuck valves (breaks) were isolated by the 

MSIVs. 

6.5.4 Operator Actions 

Various operator actions are considered in the 

RELAP5 analyses based on the transient 

definition from the PRA analysis. For cases 

involving a primary system LOCA, the operator 

is assumed to take no action since automatic 

systems are presumed to operate and provide 

the core and primary system cooling. In these 

situations, the primary operator function is to 

monitor system conditions. For various 

transients involving reactor/turbine trips 

combined with component failures that lead to 

primary system overcooling, operator actions are 

a major factor and were modeled. Generally, the 

two categories of operator actions considered are 

(1) the operator correctly diagnoses the plant 

situation and performs the correct actions based 

on the emergency operating procedures, and 

(2) the operator fails to correctly diagnose the 

situation or takes an incorrect action. 

A significant operator action for the plants 

analyzed is HPI control/throttling. Depending 

on the transient scenario, continued HPI 

injection can cause the system to refill and 

repressurize to the HPI pump shutoff pressure 

and/or the pressurizer PORV opening setpoint 

pressure. A good example of a transient where 

system repressurization can occur is a stuckopen primary safety valve that recloses after the 

system has depressurized. Continued HPI will 

cause the primary system to repressurize in this 

case unless the operator recognizes that the 

faulted valve has reclosed and takes action to 

control HPI injection. 

Different plants have different HPI control 

methods. In Oconee, the operator can throttle 

HPI flow to obtain a desired flow rate and 

maintain a certain pressurizer water level. 

In Beaver Valley, however, the operator can 

either have a pump running or not. There is no 

“throttling”; rather, pumps are turned off if 

conditions are met. In Palisades, the operator 
6-15

can throttle HPI if auxiliary feedwater is 

operating with the steam generator wide-range 

level greater than -84% and the reactor coolant 

system subcooling greater than 13.9 K (25°F). 

In this case, HPI is throttled to maintain 

pressurizer level between 40 and 60%. 

HPI control is a crucial component in the overall 

PTS risk. An event where there is no HPI 

control can produce a much greater challenge to 

vessel integrity because of primary system 

repressurization than would the same event with 

HPI control because system repressurization 

does not occur. One significant variable in the 

HPI control is operator timing. Since the time 

that the operator will take control of the HPI is 

variable depending on the transient situation, 

several times are analyzed based on PRA input 

to determine the variation in overall system 

(downcomer) conditions. As an example, 

for Beaver Valley, cases were run where the 

operator does not control HPI, controls HPI 

1 minute after the criteria for control are met, 

and controls HPI 10 minutes after the criteria are 

met. 

Another example of an operator action is control 

of the reactor coolant pumps. The different 

plants use different criteria for tripping the RCP. 

At Oconee, the operator is assumed to trip the 

RCPs on low subcooling. At Beaver Valley, the 

RCP trip criterion is based on the difference 

between steam generator and pressurizer 

pressures. At Palisades, RCP trip criteria are 

based on primary system pressure and 

subcooling margin. In some events, the RCPs 

were not predicted to trip; however, various 

operating procedures could have caused the 

operators to trip the pumps. Therefore, in some 

cases, the RCPs were set to trip as an operator 

action. An additional note about RCPs is that 

they will be tripped if there are adverse 

containment conditions (i.e., main steam line 

break). Since the RELAP5 models used do not 

include the containment, the pumps were tripped 

manually if it was deemed necessary. 

Failure of the operator to correctly diagnose the 

situation and take the correct action was also 

considered in the transient analysis. Failure to 

isolate the auxiliary/emergency feedwater to a 

faulted steam generator during a steam line 

break is an example of an operator failure 

considered in this analysis. This failure will 

result in an overcooling event where the faulted 

generator continues to remove heat, thus 

lowering the primary temperature. Timing of 

operator action was also analyzed. As an 

example, analyses were performed assuming 

that the operator stops AFW/EFW to the faulted 

generator (at 30 minutes for Beaver Valley). 

Time of operator action was determined by PRA 

analysis. 

6.6 RELAP5 Analysis Results 

The parameters that are used in the probabilistic 

fracture mechanics analysis are the reactor 

vessel downcomer fluid temperature, primary 

system pressure and reactor vessel wall heat 

transfer coefficient as a function of transient 

time. Post-processing of the RELAP5 results is 

performed to generate files that are transmitted 

to ORNL for analysis. Averaged values for the 

downcomer fluid temperature, system pressure, 

and downcomer fluid to vessel wall heat transfer 

coefficient were provided. 

A large number of cases were analyzed for the 

Oconee, Beaver Valley, and Palisades plants to 

meet the requirements of the PRA analysis. A 

total of 177 cases were run for Oconee, 67 cases 

for Palisades, and 130 cases for Beaver Valley. 

These cases were needed to support the PRA 

model, particularly to support the development 

of transient bins needed to categorize the large 

number of transients that must be considered in 

developing a nuclear plant risk model. Because 

of the large number of cases, the results that are 

used in the probabilistic fracture mechanics 

analysis are separately presented in [Arcieri-Base]. 

6.7 RELAP5 Assessment Against 

Experimental Data 

Assessments are performed to establish the 

suitability of the RELAP5/Mod 3.2.2Gamma 

code for analyzing plant transients that are 

significant risk contributors for PTS. The 

RELAP5 code version used for the assessment 

calculations is the same that is used for the PTS 

plant calculations. Assessment principally 
6-16

consists of performing an analysis for a 

particular experimental facility for a specific 

transient test. The results from a RELAP5 

simulation of the test are compared against 

measurements from the experiment and 

conclusions are drawn regarding the code 

capabilities for predicting the physical behavior 

of the test. 

Prior assessments of RELAP5 have been 

performed for a wide variety of transients over 

the 20-year development history of the code. 

Many of those assessments focused on tests 

representing LOCAs, for which the key system 

response is the integrity of the reactor core. It is 

noted that LOCAs as an event category are also 

an important vessel failure risk contributor for 

PTS, and so the extensive LOCA experimental 

database remains relevant and very useful for 

PTS applications. However, in contrast to the 

focus on core behavior during LOCAs, the focus 

for PTS-related transients is on the temperature 

and pressure conditions in the reactor vessel 

downcomer. Hence, the assessments discussed 

here focus on comparing RELAP5 results to 

experimental data for conditions in the 

downcomer. 

The assessment of RELAP5/MOD3.2Gamma 

for representing PTS behavior, performed in the 

context of the PIRT discussion presented in 

Section 6.2, are summarized in the following 

sections. The assessments are documented in 

detail in the RELAP5 PTS Assessment Report 

[Fletcher]. 

6.7.1 Separate Effects Tests 

RELAP5 was assessed against separate-effects 

experiments to evaluate RELAP5 capabilities for 

predicting specific localized behavior that is 

relevant for PTS. These separate-effects 

experiments included Marviken tests for 

assessing critical flow models, MIT pressurizer 

facility tests for assessing steam condensation 

and RCS pressurization behavior, UPTF fullscale tests for assessing condensation and steamwater flow phenomena and semiscale tests for 

assessing coolant loop natural circulation flow 

behavior. These assessments are discussed in 

this section. 

6.7.1.1 Marviken Tests 

Critical flow assessments were performed using 

data obtained from two experiments conducted 

at the Marviken facility. Marviken is a full-scale 

test facility fabricated from the 14,830-ft3

(420-m3

) pressure vessel that was part of the 

Marviken nuclear power plant. RELAP5 is 

assessed against Marviken Tests 22 and 24. 

During the experiments, the vessel is pressurized, 

the desired temperatures and liquid levels are 

established, and the break is opened, allowing a 

blowdown of the vessel to occur through a 

discharge pipe. The two tests differ mainly in 

the length of the discharge pipe that is employed. 

The RELAP5 code utilizes the Henry-Fauske 

critical flow model to determine the break flow 

rate during periods when critical flow occurs. 

A comparison of the measured and RELAP5-

calculated vessel discharge flow rates for 

Marviken Test 22 is presented in Figure 6.6. 

The RELAP5 prediction of mass flow rate is in 

excellent agreement with the test data. The 

comparison of results for Test 24 is similar. 

The Marviken assessments indicate that 

RELAP5 is capable of predicting critical break 

flow in an experimental system of the prototype 

scale. However, issues related to the exact 

configuration of breaks in PWR piping result in 

an additional general break flow prediction 

uncertainty. In order to account for this general 

uncertainty, the PTS plant calculations were 

performed using a spectrum of break diameters 

and locations. Break diameters from 1-in. 

(2.54-cm) to 22.63-in. (57.5-cm) in equal flow 

area increments were analyzed in the PTS plant 

evaluations. 

6.7.1.2 MIT Pressurizer Test ST4 

The MIT test facility is a small-scale, lowpressure representation of a PWR pressurizer. 

The insulated test vessel is 3.74-ft (1.14-m) tall 

with an inner diameter of 0.667-ft (0.203-m). 

Test ST4 was initialized with 1.41-ft (0.432-m) 

of saturated water in the bottom of the vessel at 
6-17

a pressure of 0.493 MPa [71.5 psia]. During the 

test, subcooled water is injected into the bottom 

of the vessel, increasing both the water level and 

pressure. 

The capabilities of RELAP5 for simulating the 

steam condensation and the interfacial heat 

transfer between the stratified liquid and the 

vapor above the liquid were tested using 

comparisons to the measured data from this test. 

The mixing of the cold incoming water with hot 

water initially in the tank affects the prediction 

of the pressure increase, which for PTS is an 

important phenomenon. The simulation of this 

test is included in the set of standard problems 

that is executed routinely for RELAP5 

developmental assessment. 

A comparison of the measured and RELAP5-

calculated pressure behavior is shown in Figure 

6.7. The pressure increases as a result of the 

compression of the steam volume above the 

water surface. As the pressure increases, so too 

does the saturation temperature, leading to 

condensation of steam on the tank walls and 

liquid interface. RELAP5 predicted the trend of 

the pressure increase well, but somewhat 

0 10 20 30 40 50

Time (s)

0

5000

10000

15000

Mass Flow Rate (kg/s)

mflowj−6000000 (RELAP5) 

FAVE (Data) 

0 10 20 30 40 50

0

11023

22046

33069

Mass Flow Rate (lbm/s)

Figure 6.6. Mass Flow Rate at Nozzle Outlet (Marviken Test 22) 

overpredicted the pressure. The pressure 

overprediction is attributed to an underprediction 

of the environmental heat losses with the model. 

Heat losses in a small facility like the MIT test 

facility can have a significant impact on system 

parameters such as pressure. Overall, the 

assessment indicates that RELAP5 is capable of 

well-predicting the pressure increases 

experienced when steam regions within the RCS 

of a PWR are compressed. 

6.7.1.3 Upper Plenum Test Facility 

The Upper Plenum Test Facility (UPTF) is a 

full-scale model of a four-loop 1,300 MWe 

PWR. Components included in this facility are 

the reactor vessel, downcomer, lower plenum, 

core simulator, upper plenum, and four coolant 

loops, each with reactor coolant pump and steam 

generator simulators. The test vessel, core 

barrel, and internals are a full-size representation 

of a PWR reactor vessel. 
6-18

RELAP5 assessment was performed for 

Run 131 of UPTF Test 6. This test represents 

the interaction of steam and water in the reactor 

vessel downcomer and lower plenum regions of 

a PWR during the end-of-blowdown and refill 

portions of a large cold-leg break LOCA. The 

test investigates the behavior as the ECC water 

injected into the cold legs penetrates downward 

into the reactor vessel downcomer. 

The test is run by injecting steam at a constant 

rate through the core and steam generator 

simulators at pressure and temperature 

conditions of 0.258 MPa [37.4 psia] and 458 K 

(364°F). The steam flows in the reverse 

direction, upward through the reactor vessel 

downcomer, toward the broken cold leg. 

When the steam flow behavior becomes steady, 

slightly subcooled emergency core cooling water 

at 392 K [246°F] is injected into the cold legs 

of the three intact loops. 

0 10 20 30 40 50

Time (s)

0.48

0.50

0.52

0.54

0.56

0.58

0.60

Pressure (MPa)

p−3100001 (RELAP5) 

Data 

0 10 20 30 40 50

69.6

72.5

75.4

78.3

81.2

84.1

87.0

Pressure (psia)

Figure 6.7. Pressure Rise (MIT Pressurizer Test ST4) 

The RELAP5 simulation for UPTF Test 6, 

Run 131 indicates that the code well-predicts the 

measured downcomer pressure, lower plenum 

liquid level, and downcomer fluid temperature 

responses during the test. RELAP5 

under predicted the downcomer fluid 

temperature by an average of 8 K (15°F) 

over the test period. 

6.7.1.4 Semiscale Tests 

Experiments were performed in the Semiscale 

Mod-2A test facility to evaluate single-phase, 

two-phase, and reflux steady-state coolant loop 

natural circulation behavior. This facility is a 

small-scale model of the primary coolant system 

of a four-loop PWR. The scaling factor between 

the test facility and full-scale plant is 1:1705. 

Two Semiscale Mod-2A tests, S-NC-2 and 

S-NC-3, are used for RELAP5 assessment. 

The test facility represents the major 

components of a PWR, including, steam 

generators, reactor vessel, downcomer, reactor 

coolant pumps, pressurizer, and loop piping. 

The natural circulation experiments conducted at 

the facility utilized a single-loop configuration 

where the intact loop pump was replaced with a 
6-19

spool piece containing an orifice that simulated 

the hydraulic resistance of a locked pump rotor. 

The reactor vessel was also modified for these 

experiments to ensure a uniform heatup of the 

entire system and to avoid condensation in the 

vessel upper head region. 

In Test S-NC-2, the steady-state loop natural 

circulation flow rate is measured as a function of 

the primary-side mass inventory. Single-phase, 

two-phase, and reflux steady-state modes were 

examined by varying the primary-side system 

mass while holding the SG secondary side 

conditions constant. During the test, a total of 

17 separate steady-state conditions with different 

primary-side inventories ranging from 100 % to 

61.2% of the full or maximum inventory were 

evaluated. 

The RELAP5-calculated loop flow rates for 

Test S-NC-2 compare well with the test data for 

primary system inventories above 97% (singlephase liquid circulation and low-void two-phase 

circulation) and below 70% (reflux cooling 

circulation). For two-phase loop circulation, 

RELAP5 tended to overpredict the measured 

circulation rate for inventories between 70% and 

90% and to underpredict it for inventories 

between 90% and 97%. The disagreement 

between the calculated and measured flow rates 

for inventories between 70% and 97% is 

attributed to overprediction of interphase drag 

by RELAP5. 

In Test S-NC-3, the SG secondary side 

inventory is varied and the primary-side natural 

circulation flow rate is measured as a function of 

the reduced effective SG heat transfer area. As 

the SG inventory declines, the SG heat removal 

capability and the driving potential for primaryside loop circulation (the density difference 

between the core and the SG) is diminished, 

causing the primary flow rate to decline. 

RELAP5 well-predicted the measured primaryside flow at effective SG heat transfer areas 

above 55% but overpredicted the primary-side 

flow at lower inventories. 

In summary, RELAP5 well-predicted the two 

semiscale natural circulation tests for the 

conditions associated with high primary- and 

secondary-side coolant system inventories. The 

code also well-predicted the transitions to lower 

primary-side flow rates resulting from reduced 

primary- and secondary-side inventories. 

However, at reduced primary- and secondaryside inventories, the code generally tended to 

overpredict the primary-side flow rate and these 

overpredictions are believed to result from an 

overprediction of interphase drag. 

Overpredicting the primary-side flow rate 

generally is nonconservative from the viewpoint 

of PTS analysis. Since the temperature of the 

coolant loop flow typically is much higher than 

the ECCS injection temperature, faster loop 

flows result in warmer temperatures for coolant 

entering the reactor vessel. The assessments 

indicate that under degraded inventory 

conditions, the primary-side flow rate may be 

overpredicted by a factor of about two. The 

maximum downcomer fluid temperature 

uncertainty that results from overpredicting the 

loop flow is estimated to be 19 K (34°F). 

However, it is noted that this uncertainty applies 

only during simulation of event sequences 

involving natural circulation, and then only 

during specific time periods within them when 

the primary or secondary system inventories are 

degraded. This uncertainty is evaluated as part 

of the integral system assessments that follow. 

6.7.2 Integral System Response 

RELAP5 was assessed against integral-effects 

experiments to evaluate code capabilities for 

predicting the system response in facilities 

scaled to pressurized water reactors. The 

assessments focus on the code capabilities for 

predicting the behavior of the reactor vessel 

downcomer conditions, which are of greatest 

significance for PTS analysis. The integraleffects experiments address phenomena in 

coolant system configurations specifically 

representing the geometries of Westinghouse, 

Combustion Engineering, and Babcock & 

Wilcox PWR plant designs. The integral-effects 

tests simulated PWR behavior under conditions 

expected during small, medium, and large break 

LOCAs; stuck-open pressurizer SRV events; and 

feed-and-bleed cooling operation scenarios. 
6-20

These sequence categories make up the majority 

of the risk-dominant sequences in the PTS 

evaluation study for the Oconee-1, Beaver 

Valley-1 and Palisades PWRs. 

The integral tests used in the assessments were 

performed in the ROSA-IV, ROSA/AP600, 

OSU-APEX, LOFT, and MIST experimental 

facilities. Comparisons of pressures and 

temperatures measured in these experiments to 

those predicted by RELAP are made in Sections 

6.7.2.1 through 6.7.2.5. Section 6.7.2.6 makes 

comparisons between heat transfer coefficient 

estimates from these and other experimental data 

and those predicted by RELAP. 

6.7.2.1 ROSA-IV Experiments 

The ROSA-IV facility is a 1/48 volume-scaled, 

full-pressure representation of a Westinghouse 

3,423 MWt four-loop PWR. The facility utilizes 

a full-height electrically heated core. The four 

PWR coolant loops are represented with two 

equal-volume loops. Components included in 

the loops are the hot leg, steam generator, 

reactor coolant pump, cold leg, pressurizer 

(on the intact loop) and ECCS systems (HPI, 

LPI, and accumulators). 

RELAP5 was assessed against two ROSA IV 

experiments, SB-CL-18 and SB-HL-06. 

ROSA-IV Test SB-CL-18 represents a 5% 6-in. 

(15.24-cm) equivalent diameter scaled break on 

the side of a cold leg with the reactor in fullpower operation. The HPI and AFW systems 

are assumed to fail and a LOOP is assumed to 

occur at the time of the reactor trip. 

0 200 400 600 800 1000

Time (s)

400

450

500

550

600

Liquid Temperature (K)

tempf−108030000 (RELAP5, Upper) 

tempf−108100000 (RELAP5, Lower) 

TE−W000C−DC (Data, Upper) 

TE−W036C−DC (Data, Lower) 

0 200 400 600 800 1000

260

350

440

530

620

Liquid Temperature (F)

Figure 6.8. Reactor Vessel Downcomer Fluid Temperatures (ROSA-IV Test SB-CL-18) 

The assessment of RELAP5 against the test data 

from ROSA-IV Test SB-CL-18 indicates that 

the code is capable of acceptably simulating the 

experiment behavior including the parameters of 

key importance for PTS (RCS pressure, coolant 

loop flow, and reactor vessel downcomer 

temperatures). Figure 6.8 compares the 

measured and RELAP5-calculated reactor vessel 

downcomer fluid temperatures. The data shown 

are for elevations within the downcomer 

corresponding to the top and bottom of the 

reactor core. RELAP5 overpredicted the 
6-21

downcomer fluid temperature by a maximum of 

13 K (23°F) and underpredicted it by a 

maximum of 23 K (41°F). Over the test period, 

RELAP5 overpredicted the downcomer fluid 

temperature by an average of 0.16 K (0.29°F). 

ROSA-IV Test SB-HL-06 represents a 0.5% 

2-in. (5.08-cm) equivalent diameter scaled break 

on the top of the hot leg with the reactor in fullpower operation. The HPI and AFW systems 

are assumed to fail and a LOOP is assumed to 

occur at the time of the reactor trip. When the 

core uncovered and the heatup began, the 

pressurizer PORV was opened to depressurize 

the primary system and initiate accumulator 

injection. 

The assessment of RELAP5 against the test data 

from ROSA-IV Test SB-HL-06 indicates that 

the code is capable of acceptably simulating the 

experimental behavior including the parameters 

of key importance for PTS (RCS pressure, 

coolant loop flow, and reactor vessel 

downcomer temperatures). Figure 6.9 compares 

the measured and RELAP5-calculated reactor 

vessel downcomer fluid temperatures. The data 

shown are for elevations within the downcomer 

corresponding to the top and bottom of the 

reactor core. The large drop in the measured 

downcomer temperature at about 8,000 s 

resulted from a condensation-driven rapid 

movement of water into the pressurizer; this 

water movement was not seen in the RELAP5 

calculation. Condensation is an expected 

uncertainty in code calculations and the current 

state of the art in thermal-hydraulic modeling 

does not allow accurate predictions of extreme 

transient condensation events. RELAP5 

underpredicted the downcomer fluid temperature 

by a maximum of 70 K (126°F) and by an 

average of 10 K (18°F) over the test period.

0 2000 4000 6000 8000 10000

Time (s)

400

450

500

550

600

Liquid Temperature (K)

tempf−108030000 (RELAP5, Upper) 

tempf−108100000 (RELAP5, Lower) 

TE−W000C−DC (Data, Upper) 

TE−W036C−DC (Data, Lower) 

0 2000 4000 6000 8000 10000

260

350

440

530

620

Liquid Temperature (F)

Figure 6.9. Reactor Vessel Downcomer Temperatures (ROSA-IV Test SB-HL-06) 

6.7.2.2 ROSA AP-600 Experiments 

The ROSA-AP600 facility is a 1/30 volumescaled, full-pressure representation of a 

Westinghouse AP600 PWR. The facility utilizes 

a full-height electrically heated core. The two 

AP600 coolant loops are represented with two 

equal-volume loops in the test facility. 

Components represented in the loops are the hot 

leg, steam generator, one reactor coolant pump 

(compared with two pumps in the plant design), 
6-22

one cold leg (compared with two in the plant 

design), pressurizer (on one loop), and core 

makeup tanks (CMTs) on the other loop. The 

passive residual heat removal (PRHR) system, 

ADS, and IRWST are also represented in the test 

facility. 

While there are configuration differences 

between the designs of AP600 and currently 

operating PWRs, assessments against 

ROSA/AP600 data are useful for PTS because 

the cold leg and reactor vessel downcomer 

regions of the facility are particularly wellinstrumented and activation of the ADS 

effectively causes a transition from a smallbreak LOCA event sequence to a large-break 

LOCA event sequence, both of which are of 

interest for the PTS application. RELAP5 was 

assessed against two ROSA-AP600 

experiments, AP-CL-03 and AP-CL-09. 

Test AP-CL-03 represents a 0.1% 1-in. (2.54-cm) 

diameter scaled break on the bottom of a cold 

leg in the CMT loop. The reactor is operating at 

full power when the break opens. An additional 

failure, where one of the two ADS-4 valves on 

the CMT loop fails to open, is also assumed. 

The comparisons of RELAP5-calculated and 

measured data for this experiment show that the 

complex system behavior and timing of the test 

are well-predicted with RELAP5. The RELAP5 

prediction of coolant loop flow stagnation and 

draining are in good agreement with the test data. 

0 2000 4000 6000 8000

Time (s)

300

350

400

450

500

550

600

Liquid Temperature (K)

tempf−106090000 (RELAP5) 

TE−S000C−DC (Data) 

0 2000 4000 6000 8000

80

170

260

350

440

530

620

Liquid Temperature (F)

Figure 6.10. Reactor Vessel Downcomer Fluid Temperatures (ROSA/AP600 Test AP-CL-03) 

The test exhibits thermal stratification within the 

cold legs; a layer of cold ECCS water resides 

under a layer of warmer water within the 

horizontal cold leg pipes. This thermalstratification behavior cannot be represented 

with a one-dimensional computer code such as 

RELAP5. However, the assessment indicates 

only minimal effects of this code limitation on 

the calculated reactor vessel downcomer 

prediction. Figure 6.10 compares the RELAP5-

calculated and measured reactor vessel 

downcomer fluid temperatures on the 

pressurizer-loop side of the downcomer at an 

elevation corresponding to the bottom of the 

reactor core. The fluid temperature code-data 

comparisons at other locations in the 

downcomer are similar. RELAP5 overpredicted 

the downcomer fluid temperature by a maximum 

of 59 K (106°F) and underpredicted it by a 
6-23

maximum of 72 K (130°F). RELAP5 

underpredicted the downcomer fluid temperature 

by an average of 4 K (7°F) over the test period. 

Test AP-CL-09 also represents a 0.1% 1-in. 

(2.54-cm) diameter scaled break on the bottom 

of a cold leg in the CMT loop. The reactor is 

operating at full power when the break opens. 

Although similar to Test AP-CL-03, Test APCL-09 represents additional passive safety 

system failures: 

• Both CMT discharge valves fail closed. 

• Half of the valves in each ADS stage fail 

closed. 

• ADS (normally activated by low CMT level) 

activated 30 minutes after a low-low 

pressurizer pressure signal is generated. 

• Check valve in accumulator discharge line 

on the CMT loop fails closed. 

• Check valve in the IRWST discharge line on 

the CMT loop fails closed. 

• Only one-half of the PRHR heat exchanger 

capability is available. 

The comparisons of RELAP5-calculated and 

measured data for this experiment show that the 

complex system behavior and timing of the test 

are well-predicted with RELAP5. 

0 2000 4000 6000 8000 10000

Time (s)

300

350

400

450

500

550

600

Liquid Temperature (K)

tempf−106090000 (RELAP5) 

TE−S000C−DC (Data) 

0 2000 4000 6000 8000 10000

80

170

260

350

440

530

620

Liquid Temperature (F)

Figure 6.11. Reactor Vessel Downcomer Fluid Temperatures (ROSA/AP600 Test AP-CL-09) 

As in Test AP-CL-03, thermal stratification 

behavior within the horizontal cold legs (which 

cannot be represented with RELAP5) is 

observed in Test AP-CL-09. Because of cold 

leg thermal stratification effects, the sequence 

order in which two loops stagnated in the 

RELAP5 calculation was the reverse of that seen 

in the test. However, good agreement is seen 

between the calculated and measured first-loop 

and second-loop stagnation times. The 

assessment indicates only minimal effects of this 

code limitation on the prediction of vessel 

downcomer fluid temperatures. Figure 6.11 

compares the RELAP5-calculated and measured 

reactor vessel downcomer fluid temperatures on 

the pressurizer-loop side of the downcomer at an 

elevation corresponding to the bottom of the 

reactor core. The fluid temperature code-data 

comparisons at other locations in the 

downcomer are similar. RELAP5 overpredicted 
6-24

the downcomer fluid temperature by a maximum 

of 39 K (71°F) and underpredicted it by a 

maximum of 49 K (88°F). RELAP5 

overpredicted the downcomer fluid temperature 

by an average of 1 K (2°F) over the test period. 

6.7.2.3 APEX Tests 

A series of tests specific for plants of 

Combustion Engineering (CE) design was 

conducted at the APEX facility operated by 

Oregon State University. The APEX facility is a 

1⁄4-height scale low-pressure integral systems 

facility that has been configured to model the 

thermal-hydraulic phenomena of CE plants. The 

purpose of these tests was to investigate mixing 

of high-pressure injection fluid in the cold leg 

and the downcomer and to evaluate the onset of 

coolant loop flow stagnation, which can lead to 

low temperatures in the reactor vessel downcomer. 

Two APEX tests were used for RELAP5 

assessment, APEX-CE-13 and APEX-CE-05. 

Test APEX-CE-13 represents a stuck-open 

pressurizer safety relief valve event with the 

reactor operating at full power. The stuck-open 

valve is subsequently assumed to reclose. This 

type of transient event is a significant 

contributor to PTS risk event because the RCS is 

first significantly cooled and then repressurized 

after the relief valve closes. To start the test, the 

ADS-2 valve atop the pressurizer was opened to 

simulate a stuck-open pressurizer safety relief 

valve. Simultaneously, two reactor coolant 

pumps were tripped, the HPI system was 

actuated and reactor core power was tripped. 

The ADS-2 valve was closed at 1 hour into the 

test and the test was terminated about 20 

minutes later after the RCS had refilled. 

The comparisons of RELAP5-calculated and 

measured data from Test APEX-CE-13 indicate 

that the code is capable of acceptably simulating 

the behavior of the key PTS parameters for this 

test. RELAP5 overpredicted the RCS cooldown 

rate during the period when the relief valve is 

open as shown in Figure 6.12. RELAP5 

predicted a delayed onset of the repressurization 

and underpredicted the pressurization rate after 

the relief valve closed as seen in Figure 6.13. 

These differences between the calculated and 

measured responses are considered to be 

moderate and to result from difficulties in 

adequately modeling the system heat losses of 

small-scale facilities such as APEX. RELAP5 

underpredicted the downcomer fluid temperature 

by an average of 2 K (4o

F) over the test period. 

Test APEX-CE-05 was performed to provide 

baseline mixing data for the injection of cold 

ECC water into the cold legs of the RCS. 

During the test, RCS temperatures and pressures 

consistent with full-power plant operation are 

first established and then the steam generators, 

RCPs and reactor core heaters are secured to 

create stagnant conditions in the RCS. Highpressure injection is initiated into the four cold 

legs and a pressurizer drain valve is opened to 

accommodate the injected fluid and control the 

pressurizer level and RCS pressure. For this 

test, the behavior of interest is the manner in 

which the cold water entering the vessel through 

the cold legs spreads downward and around the 

reactor vessel downcomer annulus. The 

thermocouple instrumentation of the facility was 

upgraded in order to observe this behavior. 

The test data exhibit only very small variations 

in the downcomer temperatures around the 

periphery of the downcomer. The maximum 

azimuthal downcomer temperature variations are 

9 K (16°F) at the elevation corresponding to the 

top of the core and are 5 K (9°F) at the elevation 

corresponding to the bottom of the core. No 

significant plumes were observed in the 

downcomer based on the temperature results of 

this test. Larger variations are seen in the axial 

direction in the downcomer, but these variations, 

which are related to the time required for fluid to 

transit though the downcomer, are short-lived. 

The downcomer temperature variations observed 

in the RELAP5 simulation of the test similarly 

are small. 
6-25

0 1000 2000 3000 4000 5000

Time (s)

400

450

500

550

600

Liquid Temperature (K)

tempf−101050000 (RELAP5) 

tempf−104050000 (RELAP5) 

TF−130 (Data) 

TF−131 (Data) 

0 1000 2000 3000 4000 5000

260

350

440

530

620

Liquid Temperature (F)

Figure 6.12. Reactor Vessel Downcomer Fluid Temperatures (Test APEX-CE-13) 

0 1000 2000 3000 4000 5000

Time (s)

1.00

1.50

2.00

2.50

3.00

Pressure (MPa)

p−440010000 (RELAP5) 

PT−604 (Data) 

0 1000 2000 3000 4000 5000

145

218

290

363

435

Pressure (psia)

Figure 6.13. Pressurizer Pressure (Test APEX-CE-13) 

Figure 6.14 compares the RELAP5-calculated 

and measured reactor vessel downcomer fluid 

temperature responses for Test APEX-CE-05 at 

a representative location (directly under one of 

the cold legs at an elevation corresponding to the 

top of the core). The figures show that RELAP5 

predicts the downcomer fluid temperature 

excellently up to about 2,000 s, but then 

underpredicts it afterward. Over the test period, 

RELAP5 underpredicted the downcomer fluid 
6-26

temperature by an average of 5 K (9°F). The 

underprediction is attributed to more 

involvement of warm fluid residing within the 

cold legs in the mixing process in the 

experiment than in the calculation. 

A second sensitivity RELAP5 calculation for 

Test APEX-CE-05 was performed in which 

large artificial flow loss coefficients for reverse 

flow were added in the reactor coolant pump 

suction regions of each cold leg. This modeling 

approach is used in PTS plant calculations to 

suppress circulations through the cold legs on 

the same coolant loop (in the forward direction 

through one cold leg and in the reverse direction 

in the other) for certain types of PTS events. 

This model change resulted in RELAP5-

calculated reactor vessel downcomer fluid 

temperatures that were additionally lower 

(compared with the above calculation) by an 

average of 8 K (14°F) over the test period. This 

difference represents the expected downcomer 

temperature conservatism resulting from using 

the high artificial reverse flow loss coefficient 

modeling approach. 

0 1000 2000 3000 4000 5000

Time (s)

250

300

350

400

450

500

Temperature (K)

tempf−102050000 (RELAP5) 

TF−101−8D−2 (Data) 

0 1000 2000 3000 4000 5000

−9.7

80.3

170.3

260.3

350.3

440.3

Temperature (F)

Figure 6.14. Reactor Vessel Downcomer Fluid Temperatures (Test APEX-CE-05) 

6.7.2.4 LOFT Tests 

The Loss-of-Fluid Test Facility (LOFT) is a 

50-MWt volumetrically scaled PWR system. 

The LOFT facility was designed to obtain data 

on the performance of the engineered safety 

features of a commercial PWR system for 

postulated accidents, including LOCAs. 

The LOFT nuclear core is approximately 5.51-ft 

(1.68-m) tall and 2-ft (0.61-m) in diameter, and 

is composed of nine fuel assemblies containing 

1,300 nuclear fuel rods of representative PWR 

design. Three intact loops are simulated using a 

volume/power ratio scaling by the single 

circulating (intact) loop in the LOFT primary 

system. The broken loop is simulated by the 

scaled LOFT blowdown loop. 

An ECCS is provided to simulate the engineered 

safety features in PWRs. An HPI system 

centrifugal pump and a nitrogen-pressurized 

accumulator supply emergency core cooling. 

The LPIsystem and accumulator discharge lines 

are orificed as required to simulate the delivery 

characteristics of various PWR emergency core 

cooling systems. 
6-27

RELAP5 assessment was performed using three 

LOFT experiments, Test L3-7, Test L2-5 and 

Test L3-1. 

Loft Test L3-7 represents plant recovery actions 

following a 1-in. (2.54-cm) equivalent diameter 

break in the cold leg of a PWR operating at full 

power. The primary purpose of this test is to 

establish a break flow approximately equal to 

the HPI flow at an RCS pressure of 

approximately 6.9 MPa [1,000 psia], to isolate 

the break and to demonstrate the stabilization of 

the plant at cold shutdown conditions. 

During Test L3-7, the break was opened, the 

reactor and reactor coolant pumps were tripped, 

leading to coolant loop natural circulation flow. 

At 1,800 s, the AFW and HPI flows were 

terminated to hasten the loss of RCS fluid 

inventory and to establish the conditions leading 

into the system recovery to cold shutdown 

conditions. At 3,603 s, the AFW flow was 

reinstated and a SG steam bleed operation begun 

to effect a controlled depressurization of the 

intact loop SG secondary system. The HPI flow 

was reinstated at 5,974 s, and the test was 

terminated at 7,302 seconds. 

The assessment indicates that RELAP5 is 

capable of acceptably simulating the behavior of 

the key PTS parameters for LOFT Test L3-7. 

The RELAP5 prediction of the RCS pressure is 

in good-to-excellent agreement with the 

measured data. The RELAP5 prediction of the 

reactor vessel downcomer fluid temperature is in 

good agreement with the measured data. Figure 

6.15 shows a comparison of the measured and 

calculated reactor vessel downcomer fluid 

temperatures for this test at representative 

locations in the downcomer (on the broken loop 

and intact loop sides of the downcomer and at 

elevations in the downcomer corresponding to 

the elevations of the top and middle of the core). 

Over the test period, RELAP5 underpredicted 

the downcomer fluid temperature by an average 

of 8 K (14°F). 

0 2000 4000 6000 8000

Time (s)

450

500

550

600

Temperature (K)

tempf−210010000 (RELAP5, Upper) 

tempf−210030000 (RELAP5, Middle) 

TE−1ST−001 (Data, Upper, Broken) 

TE−2ST−001 (Data, Upper, Intact) 

TE−1ST−005 (Data, Middle, Broken) 

TE−2ST−005 (Data, Middle, Intact) 

0 2000 4000 6000 8000

350

440

530

620

Temperature (F)

Figure 6.15. Reactor Vessel Downcomer Fluid Temperatures (LOFT Test L3-7) 

Test LOFT L2-5 represents a double-ended 

offset guillotine break LOCA in the cold leg of a 

PWR operating at full power. The primary 

purpose of this test was to evaluate the 

performance of the ECCS for cooling the core. 

For the purposes of the PTS assessment, this test 
6-28

provides data for the very rapid blowdown and 

refilling of the RCS with cold ECCS which 

accompanies a very large break in the RCS. 

During the test, the break was opened and the 

reactor and reactor coolant pumps were tripped. 

Accumulator injection began when the RCS 

pressure had declined below the initial 

accumulator pressure and delayed injection of 

HPI and LPI ECC coolant began at 24 s and 

37 s, respectively after the break opened. 

The assessment indicated no major differences 

between the RELAP5-calculated and measured 

responses for LOFT Test L2-5. The RELAP5 

predictions of the reactor vessel downcomer 

fluid temperature and RCS pressure are in good 

agreement with the measured data. Figure 6.16 

shows a comparison of the measured and 

calculated reactor vessel downcomer fluid 

temperatures for this test at representative 

locations in the downcomer (on the broken loop 

side of the downcomer at elevations in the 

downcomer corresponding to the elevations of 

the top, middle and bottom of the core). Over 

the test period, RELAP5 underpredicted the 

downcomer fluid temperature by an average of 

4 K (7°F). 

0 20 40 60 80 100

Time (s)

350

400

450

500

550

600

Fluid Temperature (K)

tempf−714010000 (RELAP5, Top) 

tempf−716010000 (RELAP5, Middle) 

tempf−718010000 (RELAP5, Bottom) 

TE−1ST−001 (Data, Top) 

TE−1ST−005 (Data, Middle) 

TE−1ST−009 (Data, Bottom) 

0 20 40 60 80 100

170

260

350

440

530

620

Fluid Temperature (F)

Figure 6.16. Reactor Vessel Downcomer Fluid Temperatures (LOFT Test L2-5) 

LOFT Test L3-1 represents an equivalent 4-in. 

(10.16-cm) diameter break LOCA in the cold leg 

of a PWR operating at full power. The primary 

purpose of this experiment was to evaluate the 

performance of the ECCS for cooling the core. 

During the experiment, the reactor and the 

reactor coolant pumps were tripped and ECC 

flows from the HPI and accumulator systems 

were initiated as the RCS pressure declined. 

The accumulator water inventory was fully 

discharged and the experiment was continued 

until 3,623 s using the HPI ECC flow alone. 

At that time a feed-and-bleed SG cooling 

process was implemented; the experiment was 

concluded at 4,368 s. 

For the purposes of the PTS assessment, this test 

provides data for the rapid blowdown and 

stabilization of the RCS with ECCS injection for 

a break diameter that is toward the larger end of 

the small-break LOCA spectrum. 

Test L3-1 also provides data useful for 

comparing RELAP5 simulation capabilities 

when using one-dimensional and two-
6-29

dimensional reactor vessel downcomer modeling 

approaches. RELAP5 PTS plant simulations 

have shown considerable variation in calculated 

downcomer temperatures for cold leg LOCAs 

with break diameters near 4-in. (10.2-cm), 

depending upon whether the 1-dimensional or 

2-dimensional RELAP5 downcomer modeling 

approach is used. RELAP5 calculations for 

LOFT Test L3-1 are performed using both 

downcomer modeling approaches in order to 

judge which approach is better for simulating 

cold leg breaks of this approximate size. 

The assessment indicated that the behavior in the 

reactor vessel downcomer region is particularly 

difficult to predict for a break of this size and 

location. Accumulator injection has a potential 

for directly influencing the downcomer 

temperature, but mixing within the cold leg and 

upper downcomer regions significantly affects 

that influence. The prediction of mixing within 

the thermally stratified cold leg regions is 

beyond the capability of RELAP5. The break is 

large enough that the RCS depressurizes 

sufficiently to result in accumulator injection, 

but not so large as to allow for an accumulator 

discharge that is insensitive to the RCS pressure. 

Finally, the break location in the cold leg adds to 

the prediction difficulty because the most direct 

path for steam to reach the break is upward 

through the downcomer, against the downward 

flow of cold accumulator water. Therefore, 

interphase condensation modeling, known to be 

a weakness of RELAP5, appears to be 

particularly important for predicting the 

behavior for this particular break size and 

location 

The assessment indicates that RELAP5 is 

capable of acceptably predicting the reactor 

coolant system parameters for this test. The 

downcomer fluid temperatures in the test were 

underpredicted using both the 1- and 

2-dimensional downcomer modeling 

approaches. Over the test period, the 

underprediction is by an average of 7 K (13°F) 

when using the one-dimensional downcomer 

modeling scheme and by an average of 13 K 

(23°F) when using the 2-dimensional 

downcomer modeling scheme. Figure 6.17 

compares the measured and calculated fluid 

temperatures for Test LOFT L3-1 at a 

representative location in the reactor vessel 

downcomer. The data shown are for a location 

on the broken loop side of the downcomer at an 

elevation corresponding to the middle of the 

reactor core. The code-data comparisons at 

other locations in the downcomer are similar. 

The 2-dimensional reactor vessel downcomer 

modeling approach is judged to be the more 

appropriate approach for RELAP5 PTS 

applications because of (1) the better 

accumulator injection behavior it produced, 

(2) the ability it provides for predicting different 

fluid behavior in the intact and broken-loop 

sides of the reactor vessel downcomer, which 

has the potential to affect break flow and 

downcomer mixing, and (3) the more 

conservative downcomer fluid temperature 

predictions it produced. 

More detailed information regarding the 

assessment of RELAP5 for LOFT Test L3-1 is 

found in Section 3.9 of [Fletcher]. 

6.7.2.5 MIST Tests 

The Multi-loop Integral System Test (MIST) 

facility is a scaled full-pressure experimental 

facility that represents the B&W lowered-loop 

plant design with two hot legs and four cold 

legs. The plant-to-facility power scaling factor 

is 817, and the plant-to-facility volume scaling 

factor is 620 for the total primary system 

volume, excluding the core flood tanks. Major 

components include two once-through steam 

generators with full length tubes, two hot leg 

pipe segments, four cold leg pipe segments, four 

coolant pumps, a reactor vessel with an external 

downcomer, a pressurizer with spray and PORV 

connections, and one core flood tank. Boundary 

systems provide simulation of the HPI, auxiliary 

feedwater, and various types of failures such as 

steam generator tube ruptures and LOCAs. 
6-30

0 1000 2000 3000 4000

Time (s)

400

450

500

550

600

Temperature (K)

tempf−210030000 (RELAP5−1D) 

tempf−810030000 (RELAP5−2D) 

TE−1ST−005 (Data) 

sattemp−415060000 (RELAP5−2D Saturation) 

0 1000 2000 3000 4000

260

350

440

530

620

Temperature (F)

Figure 6.17. Reactor Vessel Downcomer Fluid Temperatures (LOFT Test L3-1) 

RELAP5 assessment was performed for three 

MIST experiments, Test 360499, Test 3109AA, 

and Test 4100B2. 

MIST Test 360499 is a HPI-power operated 

relief valve (HPI-PORV) feed-and-bleed 

simulation, starting from 110% flow, 10% 

scaled-power conditions. The system behavior 

for this test resembles a stuck-open pressurizer 

PORV event sequence with continued HPI 

injection and operator throttling based upon the 

RCS subcooling margin. Events such as this are 

significant contributors to the risk of PTS vessel 

failure. 

The assessment for this test indicated that the 

RELAP5 prediction of the RCS pressure was 

excellent. However, the assessment indicated 

major differences between the calculated and 

measured responses within the cold legs on the 

two coolant loops. RELAP5 overpredicted the 

cold leg temperature in Loop A, and did not 

predict the coolant loop flow stagnation seen in 

the test. RELAP5 underpredicted the cold leg 

temperature in Loop B and did predict the 

coolant loop flow stagnation seen in the test. 

Despite these difficulties, the RELAP5 

prediction of the reactor vessel downcomer fluid 

temperature, which represents a mixture of the 

cold leg temperatures, was judged to be good. 

Figure 6.18 compares the calculated and 

measured reactor vessel downcomer fluid 

temperatures for MIST Test 360499 at a 

representative location in the downcomer (at an 

elevation corresponding to the bottom of the 

core). The code-data comparisons at other 

downcomer locations are similar. Over the test 

period, RELAP5 overpredicted the downcomer 

fluid temperature by an average of 3 K (5°F).
6-31

0 5000 10000 15000 20000 25000 30000

Time (s)

400

450

500

550

600

Temperature (K)

tempf−330030000 (RELAP5) 

DCTC42 (Data) 

DCTC44 (Data) 

0 5000 10000 15000 20000 25000 30000

260

350

440

530

620

Temperature (F)

Figure 6.18. Reactor Vessel Downcomer Fluid Temperatures (MIST Test 360499) 

MIST Test 3109AA represents a 1.6-in.2

(10-cm2

) break in the RCP discharge section of a 

PWR cold leg. This break size corresponds to a 

1.4-in. (3.59-cm) diameter break in the PWR 

and is sufficiently small that HPI flow can 

compensate for break flow. At the start of the 

test, the facility is operating under naturalcirculation loop flow conditions, with the RCP 

rotors locked. 

The assessment indicated no major differences 

between the calculated and measured data for 

MIST Test 3109AA. The RELAP5 prediction 

of the RCS pressure is in good agreement with 

the measured data. The code well-predicted the 

interruption of loop natural circulation flow in 

both of the coolant loops. RELAP5 

overpredicted the reactor vessel downcomer 

fluid temperature after about 1,000 s. Figure 

6.19 compares the calculated and measured 

reactor vessel downcomer fluid temperatures for 

MIST Test 3109AA at a representative location 

in the downcomer (at an elevation corresponding 

to the top of the core). The code-data 

comparisons at other downcomer locations are 

similar. Over the test period, RELAP5 

overpredicted the downcomer fluid temperature 

by an average of 10 K (18°F). 

MIST Test 4100B2 represents a 15.5-in.2

(100-cm2

) [4.4-in. (11.2-cm) diameter] 

equivalent break in the RCP discharge section of 

a PWR cold leg. The break size is sufficiently 

large that HPI cannot compensate for the break 

flow. The test is initiated at conditions 

representing 3.5% scaled power and coolant 

loop natural circulation conditions with the 

RCPs tripped and their rotors locked. During 

the test, the core power is tripped and HPI and 

EFW flows are initiated. 

The assessment for MIST Test 4100B2 shows 

moderate differences between the calculated and 

measured data for the most important parameters 

for PTS (RCS pressure and downcomer fluid 

temperature). Following the RCS blowdown, 

basic limitations of RELAP5 resulted in an 

underprediction of the stable RCS pressure by 

about 0.68 MPa [98 psi]. RELAP5 slightly 

underpredicted the downcomer fluid 

temperatures during the blowdown period, up to 

about 2,100 s. However, during the refill period 

RELAP5 overpredicted the reactor vessel
6-32

0 1200 2400 3600 4800

Time (s)

480

500

520

540

560

Temperature (K)

tempf−330010000 (RELAP5) 

DCTC21 (Data) 

DCTC23 (Data) 

0 1200 2400 3600 4800

404

440

476

512

548

Temperature (F)

Figure 6.19. Reactor Vessel Downcomer Fluid Temperatures (MIST Test 3109AA) 

0 1200 2400 3600 4800

Time (s)

300

350

400

450

500

550

600

Temperature (K)

tempf−330010000 (RELAP5) 

DCTC21 (Data) 

DCTC23 (Data) 

0 1200 2400 3600 4800

80

170

260

350

440

530

620

Temperature (F)

Figure 6.20. Reactor Vessel Downcomer Fluid Temperatures (MIST Test 4100B2) 

downcomer fluid temperature by up to 32 K 

(58 °F). Figure 6.20 compares the calculated 

and measured reactor vessel downcomer fluid 

temperatures for MIST Test 4100B2 at a 

representative location in the downcomer (at an 

elevation corresponding to the top of the core). 

The code-data comparisons at other downcomer 

locations are similar. Over the test period, 
6-33

RELAP5 overpredicted the downcomer fluid 

temperature by an average of 0.37 K (0.67°F). 

6.7.2.6 Reactor Vessel Wall InsideSurface Heat Transfer 

Coefficient 

For the reactor vessel wall heat transfer 

coefficient, quantitative assessment comparisons 

are more difficult than for RCS pressures and 

downcomer fluid temperatures because heat 

transfer coefficients are not directly measured in 

the experiments. Further, since most of the test 

facilities were designed to study core-coolability 

safety issues and not vessel downcomer 

overcooling issues, experimental 

instrumentation related to downcomer wall heat 

transfer (wall and fluid thermocouples, wall heat 

fluxes and downcomer fluid velocities) is 

generally limited. Quantitative assessments of 

RELAP5 capabilities for predicting the vessel 

wall heat transfer coefficient and other heat 

transfer-related parameters are provided in this 

section to the extent feasible considering the 

limited available data. Other investigations into 

reactor vessel wall heat transfer in general and 

RELAP5 capabilities in particular are also 

presented here to support the assessment 

conclusions regarding the wall heat transfer 

coefficient. The information in this section 

summarizes that presented in greater detail 

elsewhere [Bessette]. 

As described below, for the PTS application, the 

wall heat transfer regime of greatest interest is 

for wall-to-fluid convection for Reynolds 

numbers toward the low end of the turbulent 

range. This regime corresponds to the reactor 

vessel downcomer situation during periods with 

low coolant-loop natural circulation flow or 

periods after the coolant-loop flows have 

stagnated as a result of voiding in the upper 

regions of the RCS (as is caused by draining 

during LOCA events). Other heat transfer 

regimes are also experienced during portions of 

the PTS transient accident scenarios. Highly 

turbulent forced convection is experienced when 

reactor coolant pumps are operating or when 

there is robust coolant-loop natural circulation 

flow. Saturated and subcooled nucleate boiling 

are generally experienced for events where the 

RCS rapidly depressurized, the fluid saturation 

temperature quickly drops and the hot vessel 

wall passes heat to a flashing and boiling fluid. 

The attention is given here to the regime for 

convection because it (1) is frequently 

encountered in the PTS scenarios, and (2) results 

in a relatively low heat transfer coefficient. The 

other regimes (highly turbulent convection and 

boiling) result in large heat transfer coefficients. 

A detailed assessment of the accuracy of 

RELAP’s heat transfer models is not warranted 

in these other regimes because the process of 

wall-to-fluid heat transfer is dominated by the 

surface boiling transport mechanism and not by 

the convective movement of fluid. Therefore, 

the heat transfer is less influenced by details of 

bulk fluid motion 

6.7.2.6.1 Effect of Heat Transfer 

Coefficient on Wall Heat 

Flux 

During normal steady plant operation, the 

reactor vessel wall temperature is the same as 

the downcomer fluid temperature (which is core 

inlet temperature). During PTS scenarios, the 

fluid temperature falls. The wall-to-fluid heat 

transfer processes from the hotter vessel wall to 

the colder fluid in the downcomer are of 

significance. The RCS cooldowns experienced 

in the PTS accident scenarios generally fall into 

three categories of (1) secondary-side events, 

such as main steam line breaks, (2) small 

primary-side LOCAs, such as hot or cold leg 

breaks or stuck-open pressurizer relief valve 

events, and (3) large primary-side LOCAs, such 

as double-ended hot or cold leg breaks. Each of 

these event categories is separately discussed in 

the following subsections. 

6.7.2.6.1.1 Secondary Side Events 

For secondary-side events, the RCS is rapidly 

cooled by overcooling to the steam generators 

but the RCS remains at high pressure and, often, 

forced flow of coolant through the RCS loops 

continues. The RCS fluid cools, but the extent 

of the cooldown is limited because the ultimate 

heat sink temperature is the saturation 
6-34

temperature at atmospheric pressure, which 

represents the final state in the secondary 

coolant system. The reactor vessel wall heat 

transfer coefficient remains high as a result of 

pump-forced flow or a robust coolant-loop 

natural circulation flow for cases where the 

reactor coolant pumps are tripped. As a result, 

the wall-to-fluid heat transfer process is 

controlled by heat conduction through the 

reactor vessel wall. 

6.7.2.6.1.2 Small Primary Side LOCAs 

For small primary-side LOCA events, the RCS 

depressurizes at a rate that is proportional to the 

break size. Fluid flashing caused by the RCS 

depressurization cools the RCS fluid as the 

saturation temperature falls. The ECC systems 

add cold water to the RCS at rates that increase 

with decreasing RCS pressure. This pressure 

dependency results because the ECC systems are 

made up of (1) tanks (accumulators, core flood 

tanks, and safety injection tanks) with cold water 

inventory stored at intermediate pressures, and 

(2) centrifugal pump systems (HPI, LPI, etc.) for 

which no flow is delivered above the pump 

shutoff heads and for which lower RCS 

pressures lead to greater cold water injection 

flow rates. 

For the small LOCAs, the system pressure is 

defined by the RCS mass and energy balances 

associated with core heat addition, cold water 

injection, steam generator heat removal, and 

break flow. There is much interdependence 

among the PTS parameters of interest (pressure, 

fluid temperature, and heat transfer coefficient). 

Larger break sizes lead to lower pressures 

(which tend to mitigate the PTS risk) while at 

the same time leading to higher ECC injection 

rates and lower fluid temperatures (which tend 

to increase the PTS risk). Further, the variations 

in the injection flow rate can directly affect the 

break flow (which, in turn, affects RCS 

pressure) and the RCS inventory, which affects 

tripping of reactor coolant pumps, coolant loop 

natural circulation and stagnation, vessel 

downcomer velocities and wall heat transfer 

coefficients. For small primary-side LOCA 

events, the potential for vessel failure as a 

consequence of PTS arises as a result of 

incomplete RCS depressurization and RCS 

draining, which causes the stagnation of the 

coolant-loop natural circulation flows and leads 

to pooling of cold water in the cold leg and 

downcomer regions. 

Because for small breaks, the injection of cold 

ECC water is at a low rate, the RCS cooldown 

experienced for this category of LOCA events is 

relatively slow and there is a feedback between 

the heat transfer from the wall to the fluid and 

the fluid temperature itself. For this category of 

events, the downcomer wall heat transfer 

regimes generally fall into the range of turbulent 

forced convection from wall to subcooled liquid 

(even following coolant loop flow stagnation, 

the downcomer flow rates remain sufficiently 

high to resemble forced convection). 

6.7.2.6.1.3 Large Primary Side LOCAs 

For large primary-side LOCA events, the RCS 

completely depressurizes and the injections of 

cold ECC water from the HPI, LPI, and 

accumulator systems are at very high rates. The 

rapid decline in the fluid saturation temperature 

leads to limited periods of fluid flashing and 

boiling on the hot vessel wall. Heat transfer 

coefficients are very high for conditions of 

nucleate boiling. As a result of the large break 

size, the RCS cannot repressurize from the ECC 

injection. The high injection rate floods the cold 

legs and vessel downcomer regions with cold 

water and this quickly terminates the boiling 

process. 

6.7.2.6.2 Comparison of Measured 

and RELAP5-Calculated 

Reactor Vessel Wall Heat 

Transfer Data 

Only limited pertinent data are available from 

integral system tests for assessing RELAP5 

reactor vessel wall-to-fluid heat transfer for 

geometries consistent with the plants and the 

conditions present in the PTS accident scenarios. 

Instruments are often not available for directly 

measuring heat transfer coefficient or heat flux. 

However, downcomer fluid and vessel wall 
6-35

thermocouple data along with fluid velocity data 

are occasionally available that permit a 

quantified comparison between the measured 

and RELAP5-calculated wall heat transfer 

process. This section summarizes vessel wallto-fluid heat transfer comparisons pertinent for 

the PTS for tests performed in the UPTF, 

APEX-CE, and Creare test facilities. 

6.7.2.6.2.1 UPTF Test 1 Run 21 

The UPTF featured a full-scale representation of 

the reactor vessel, downcomer, and cold legs of 

a PWR. Test 1 Run 21 consisted of injecting 

cold HPI water into one of the four cold legs 

(Cold Leg 2) into a system that was initially 

filled with hot pressurized water. The 

experimental conditions are comparable to those 

experienced in a PWR following stagnation of 

the coolant loop natural circulation flow. This 

experimental facility and test were modeled with 

RELAP5 and the calculated results were 

compared with the measured test data. The 

RELAP5 model included a 2-dimensional 

nodalization scheme, comparable to those 

employed in the PTS plant analyses. 

The measured velocity data at the core-bottom 

elevation in the downcomer exhibited a 

downward flow below Cold Leg 2 and upward 

flows through other azimuthal sectors of the 

downcomer as shown in Figure 6.21. (The 

direction of positive velocity is downward.) The 

RELAP5 simulation also showed a downward 

water flow below Cold Leg 2 (Figure 6.22), but 

with the cold water spreading into sectors 

adjacent to Cold Leg 2 by the time the flow 

reached the core bottom elevation. As a result, 

the RELAP5-calculated velocities are seen in 

these figures to be lower than the measured 

velocities. The fluid velocities in the 

downcomer (in both the test and calculation) 

were much greater than the superficial fluid 

velocity based on only the HPI flow in the 

downcomer. The test data indicated that the 

downcomer velocity is ~16 times the 

downcomer HPI superficial velocity. 

An assessment of the RELAP5-calculated vessel 

wall heat transfer coefficient was made using 

fluid and wall thermocouple data. In 

downcomer regions away from Cold Leg 2, 

RELAP5 was found to underpredict the rates of 

decline in both the fluid and vessel wall 

temperatures by a similar extent and therefore to 

predict the heat transfer coefficient well (within 

~15%). Below Cold Leg 2, RELAP5 was found 

to underpredict the wall-to-fluid differential 

temperature of the test as shown in Figure 6.23 

and to also underpredict the wall-to-fluid heat 

flux (as indicated by the slower cooldown rate at 

the location of a thermocouple embedded 1-in. 

(25-mm) into the vessel wall at the core top 

elevation; see Figure 6.24). Since the RELAP5 

underprediction of the differential temperature 

was much greater than the RELAP5 

underprediction of the heat flux, RELAP5 was 

found to overpredict the wall-to-fluid heat 

transfer coefficient under Cold Leg 2 for UPTF 

Test 1-21 by a factor of ~2. 

6.7.2.6.2.2 APEX-CE Test 5 

The Advanced Plant Experiment facility 

(APEX-CE) is a reduced-height, pressure, and 

temperature facility scaled to Palisades, a 

CE-designed plant. The test consisted of 

injecting cold HPI water into all four cold legs 

of a system that was initially filled with hot 

pressurized water. The experimental conditions 

are comparable to those experienced in a 

pressurized water reactor following stagnation of 

the coolant loop natural circulation flow. This 

experimental facility and test were modeled with 

RELAP5 and the calculated results were 

compared with the measured test data. The 

RELAP5 model included a two-dimensional 

nodalization scheme, comparable to those 

employed in the PTS plant analyses. 

The RELAP5 assessment concentrated on the 

first 1,700 s of the test period. There was 

excellent agreement between measured and 

calculated fluid and wall temperatures as shown 

in Figure 6.25 and Figure 6.26. The excellent 

match between the measured and calculated wall 

temperatures indicated that RELAP5 also 

predicts the wall heat flux well. However, a 

comparison between the measured and 

calculated wall-to-fluid differential temperatures 

indicated that RELAP5 underpredicted the test 

differential temperature by a factor of ~2 and, 
6-36

therefore, overpredicted the wall-to-fluid heat 

transfer coefficient for APEX-CE-5 by the same 

factor. 

There are no direct measurements for 

downcomer flow velocity in the APEX-CE 

facility, but flow velocity indications were 

derived from thermocouple data. The 

calculations indicated that the RELAP5 and 

measured flow velocities are in good agreement 

and that (after scaling up for a full-height 

downcomer) the data indicate that the 

downcomer circulating flow velocity is a factor 

of ~20 greater than the superficial velocity of the 

HPI flowing alone in the downcomer region. 

6.7.2.6.2.3 Creare Fluid Mixing Tests 

Creare performed experiments in a one-half 

linear scale facility to investigate fluid mixing in 

a downcomer region for a stagnant coolant-loop 

situation. The facility represents the region of a 

single cold leg and one-fourth of the reactor 

vessel downcomer. The downcomer 

configuration included a thermal shield installed 

in the center of the downcomer span. Two NRC 

tests, MAY105 and MAY106 were performed to 

simulate cold water injection into an initially hot 

downcomer (RELAP5 simulations for these tests 

were not performed). Velocity measurements 

for two tests indicated velocity ratios 

(downcomer velocity to superficial downcomer 

velocity based on HPI flow) of 21 and 26. The 

downcomer flow was found to contain regions 

of up-flow and down-flow, with the down-flow 

velocities greater than the up-flow velocities. 

The downcomer flow pattern was found to be 

buoyancy induced. 

Figure 6.27 shows that the heat transfer data for 

the Creare tests are proportional to the DittusBoelter correlation. An enhancement of the heat 

transfer by a factor of ~1.55 above the DittusBoelter correlation is seen in the figure for down 

flow regions but not elsewhere. The 

enhancement is attributed to entrance effects to 

which the thermal shield configuration may 

contribute. In modeling convective heat 

transfer, RELAP5 applies the maximum of 

Churchill-Chu for free convection and DittusBoelter for forced convection. At low flow 

velocities (e.g., < ~1 m/s), Churchill-Chu 

provides higher heat transfer coefficients than 

Dittus-Boelter. 

6.7.2.6.2.4 Summary and Discussion 

Three sets of experiments related to injection of 

cold water into stagnant initially hot water in the 

reactor vessel downcomer region of a 

pressurized water reactor have been described in 

this section. The situation represented by these 

tests is consistent with that following coolantloop stagnation in many of the PTS accident 

scenario categories. The experiments all 

indicate that the buoyancy effects of cold water 

entering the downcomer through the cold legs 

set up a circulation within the downcomer 

region. The downcomer circulation velocities 

are seen to be larger than the superficial velocity 

(that which would result in the downcomer from 

the ECC injection flow alone) by factors of ~16 

to 26. 

In the UPTF and APEX-CE assessments, 

RELAP5 with a two-dimensional downcomer 

nodalization is seen to be able to capture on a 

first-order basis the flow pattern and velocities 

in the downcomer region. Based on comparison 

between measured and RELAP5-calculated wall 

and fluid temperature data, RELAP5 is seen to 

provide reasonable representations of the vessel 

wall inside surface heat transfer coefficient. For 

the UPTF test, RELAP5 is seen to provide a 

good representation (within ~15%) of the heat 

transfer coefficient for downcomer regions away 

from Cold Leg 2 (the only cold leg through 

which the cold water enters the vessel) and to 

overpredict the heat transfer coefficient by a 

factor of ~2 for the region under Cold Leg 2. 

For the APEX-CE test (for which cold water 

enters the vessel through all cold legs), RELAP5 

is seen to overpredict the heat transfer 

coefficient for all downcomer regions, again by 

a factor of ~2. Creare data corroborate UPTF 

and APEX-CE data in showing enhanced large 

eddy circulating flows in the downcomer. The 

relatively high velocities result in good heat 

transfer as seen in the data and predicted by 

RELAP5. The integrated assessment of 

RELAP5 for downcomer heat transfer shows the 
6-37

predictions of the RELAP code to be either 

realistic or conservative. 

6.7.2.6.3 Comparison of RELAP5-

Calculated and CFDCalculated Downcomer 

Flows 

A comparison was made between RELAP5 and 

COMMIX CFD code solutions for the flow 

patterns experienced in the reactor vessel 

downcomer. The comparison was made during 

the coolant-loop flow stagnation period 

following a 2-inch (5.1-cm) hot-side break 

accident scenario in a three-loop Westinghouse 

plant. 

The comparison indicated that RELAP5 

adequately captured the overall flow patterns but 

not finer-scale eddy-flow behavior seen in the 

COMMIX run. The flow velocities from the 

COMMIX and RELAP5 calculations were 

similar and on the order of 19.7 to 39.4 in/s (0.5 

to 1.0 m/s). 

0 1000 2000 3000

Time (s)

−1

0

1

2

Flow Velocity (m/s)

UPTF 1−21 DC Velocities at Bottom−Core Elevation 

Measured, Turbine Meters, Clockwise from Cold Leg 2

1A06SV075 CL2

1A06SV055 HL2

1A06SV035 HL1

1A06SV015 CL1

1A06SV155 CL4

1A06SV135 HL4

1A06SV115 HL3

1A06SV095 CL3

Figure 6.21. UPTF 1-21 DC Velocities at Bottom-Core Elevation Measured, Turbine Meters, 

Clockwise from Cold Leg 2, Filtered 
6-38

0 1000 2000 3000

Time (s)

−2

−1

0

1

2

Liquid Velocity (m/s)

UPTF 1−21 DC Velocities at Bottom−Core Elevation 

RELAP5−Calculated, Clockwise from Cold Leg 2

velf−123080000 CL2

velf−122080000 HL2

velf−112080000 HL1

velf−113080000 CL1

velf−114080000 CL4

velf−115080000 HL4

velf−125080000 HL3

velf−124080000 CL3

Figure 6.22. UPTF 1-21 DC Velocities at Bottom-Core Elevation RELAP5 

(Calculated, Clockwise from Cold Leg 2) 

0 1000 2000 3000

Time (s)

0

5

10

15

20

Volume Liquid Temperature (K)

UPTF 1−21 Inside Wall Temperature Minus Fluid Temperature

Under Cold Leg 2 at Core−Top Elevation 

Measured

RELAP5 Calculated

Figure 6.23. UPTF 1-21 Wall Temperature Minus Fluid Temperature Under Cold Leg 2 

at Core-Top Elevation 
6-39

0 1000 2000 3000

Time (s)

360

380

400

420

440

460

Wall Temperature (K)

UPTF Test 1−21 Wall Temperatures at 25 mm Depth

Vessel Wall in Orientation of Cold Leg 2

httemp−123100205 RELAP5

1A17TW072 Measured

Figure 6.24. UPTF Test 1-21 Wall Temperatures at 25 mm Depth Vessel Wall in Orientation of Cold Leg 2 

0 1000 2000 3000 4000 5000

Time (s)

300

350

400

450

500

Temperature (K)

APEX−CE−05 Measured and RELAP5 Fluid Temperatures

4D below and centered on the Cold Leg 4 nozzle

tempf−106030000 RELAP5

TF−104−4D−2 Measured

Figure 6.25. APEX–CE–05 Measured and RELAP5 Fluid Temperatures 

4D below and centered on the Cold Leg 4 nozzle 
6-40

0 1000 2000 3000 4000 5000

Time (s)

300

350

400

450

500

Temperature (K)

APEX−CE−05 Measured and RELAP5 Wall Temperatures

4D below and centered on the Cold Leg 4 nozzle

httemp−100302201 RELAP5

TW−104−3.5D−2 Measured

Figure 6.26. APEX–CE–05 Measured and RELAP5 Wall Temperatures 

4D below and centered on the Cold Leg 4 nozzle 

Figure 6.27. Creare Data Compared to Dittus-Boelter 
6-41

6.7.3 RELAP5 Assessment Conclusions 

An assessment has been performed of the 

RELAP5/MOD3.2.2Gamma computer code 

capabilities for predicting the parameters of 

importance for evaluating PTS risk during PWR 

plant accident scenarios, focusing on the RCS 

pressure and the temperature of the fluid in the 

reactor vessel downcomer region. The 

assessment is performed by comparing the 

results from RELAP5 simulations of pertinent 

separate-effects and integral-effects tests with 

measured test data for experiments in facilities 

scaled to PWRs. Qualitative judgments are 

made regarding the overall fidelity of the 

RELAP5 test predictions. Quantitative 

estimates also are made of the average 

uncertainties in the RELAP5 predictions for the 

important PTS parameters. 

The RELAP5 PTS assessment uses data from 

six experiments in four different separate-effects 

experimental facilities and from eleven 

experiments in five different integral-effects 

experimental facilities. 

The separate-effects experiments specifically 

address (1) pressurizer draining and filling; 

(2) critical break flow; (3) steam and water 

behavior in the reactor vessel lower plenum and 

downcomer regions during the end-of-blowdown 

and refill periods of LBLOCAs; and (4) singlephase, two-phase, and reflux cooling mode loop 

natural circulation phenomena under primaryside and secondary-side degraded inventory 

conditions. These represent phenomena that are 

significant for the prediction of the important 

PTS parameters. 

The results of the 18 assessment cases generally 

indicated good and excellent agreement between 

the RELAP5 calculations and the measured test 

data. The conclusion from the 

RELAP5/MOD3.2.2Gamma PTS assessment is 

that the code is capable of well-predicting the 

phenomena of importance for evaluating PTS 

risk in PWRs. The average uncertainty in the 

RCS pressure prediction is characterized as 

±0.2 MPa (±29 psi). The average uncertainty in 

the reactor vessel downcomer fluid temperature 

prediction is characterized as ±10 K (±18°F). 

6.8 Sensitivity and Uncertainty 

Analysis 

Sensitivity studies were performed to evaluate 

the effect of key parameters on the RELAP5 

prediction of downcomer conditions. These 

sensitivity studies formed the basis for the 

assessment of uncertainty in the thermalhydraulic analysis. The purpose of the 

uncertainty analysis was to provide adjustments 

to PRA bin probabilities based on key thermalhydraulic parameters that significantly affect 

downcomer conditions, principally temperature. 

6.8.1 Sensitivity Analysis 

 

Table 6.2 presents a summary of the results of 

the sensitivity studies performed as part of the 

thermal-hydraulic analysis. Many of these 

sensitivity studies were used to guide the 

definition of the transients analyzed in this study 

and to guide the uncertainty assessment 

discussed later in this section. In addition to the 

sensitivity studies listed in Table 6.2, 

evaluations were performed on convective heat 

transfer from the reactor vessel to the 

downcomer fluid and on the effect of the 

in-vessel circulation flows on downcomer 

conditions. 

The heat transfer coefficient model for mixed 

convection used in RELAP5/MOD3.2.2Gamma 

is computed as the maximum of the forced 

convection, laminar convection, and natural 

convection values. The correlations used are by 

Dittus-Boelter, Kays, and Churchill-Chu. 

However, the flow and heat transfer in the 

downcomer during flow stagnation conditions 

are more accurately described as buoyancy 

opposed mixed convection. In this situation, 

heat transfer is from the hot walls to subcooled 

fluid flowing downward under low flow 

conditions. Under these conditions, heat transfer 

may be enhanced compared to free convection 

as modeled in RELAP5, which would promote 

more rapid cooling of the vessel walls. 

Sensitivity studies utilizing the Petukhov 

correlation for parallel plates (known as the 

ORNL ANS Interphase Model in 
6-42

RELAP5/MOD3.2.2Gamma) in lieu of the 

Dittus-Boelter correlation were performed. 

Additionally, RELAP5/MOD3.2.2Gamma was 

modified to apply a multiplier to compensate for 

buoyancy effects in forced turbulent convection 

published by Swanson and Catton [Swanson 87]. 

This model was later refined to utilize the 

Petukhov-Gnielinski heat transfer correlation 

along with the multiplier proposed by Swanson 

and Catton. 

Other studies were performed where the heat 

transfer coefficient calculated by RELAP5 was 

varied by ±30%. The results of these RELAP5 

calculations were analyzed using FAVOR to 

determine the direct impact of heat transfer 

uncertainty on vessel failure probability. The 

results of the heat transfer coefficient sensitivity 

studies are discussed in Chapter 9. 

In-vessel circulation flows that deliver water 

from the upper plenum region to the upper 

downcomer can occur during a transient 

(particularly a LOCA). Such flows would tend 

to warm the water in the upper downcomer and 

the cold legs. Experiments and CFD studies 

have shown that there can be significant counterflow of warm water from the upper downcomer, 

and energy exchange in the cold leg between the 

warm stream and the cold ECC injection. These 

in-vessel flows tend to increase the downcomer 

temperature. 

The B&W vent valve design allows for 

significant in-vessel circulation once the reactor 

coolant pumps are tripped. While the pumps are 

on, the vent valves are held shut by differential 

pressure. After the pumps are tripped, flow 

stagnation conditions can occur, and the 

resulting pressure difference between the upper 

plenum and the downcomer will cause the vent 

valves to open, resulting in significant flow of 

warm water from the upper plenum to the 

downcomer. The impact of vent valve function 

on the downcomer fluid temperature is transientdependent, but can be on the order of 50 K 

(90°F) based on a 2.83-in. (7.18-cm) surge line 

break, as seen in the next section. 

While Westinghouse and CE plants do not have 

vent valves, they do have a bypass flow path 

between the upper downcomer and the upper 

plenum. The area of this path is generally not 

precisely characterized in power plants, but 

amounts to approximately 3% of the total core 

flow during normal plant operation. Assuming 

typical values of entrance and exit loss 

coefficients, the approximate flow area becomes 

0.580-ft2

 (0.054-m2) (10-in. [25.4-cm] diameter 

equivalent). This value is about 7% of the flow 

area of the Oconee vent valves, which is 8.45-ft2

(0.785-m2

). The RELAP5 results were reviewed 

to evaluate bypass flows, for a large number of 

Palisades and Beaver Valley transients. The 

calculations indicate that the flow through the 

bypass region is small compared to the B&W 

vent valve flow, implying that the effect of 

bypass flow on downcomer temperature is small 

for Westinghouse and CE plants. 

6.8.2 Treatment of Uncertainties 

6.8.2.1 Overview 

The approach used to address uncertainty in the 

thermal-hydraulic analysis principally utilized 

sensitivity studies to quantify the effect of 

phenomenological and boundary condition 

uncertainties/variations on the severity of a TH 

sequence. The results of these studies were used 

in either of the following two ways: 

(1) They were combined with probability 

estimates on the sensitivity parameters being 

evaluated to adjust the bin probabilities from 

the PRA analysis. 

(2) They were used to justify further subdivision 

of the PRA bins. 

In this way, the TH uncertainty analysis 

accounted for certain parameters that can affect 

the thermal-hydraulic response of the plant that 

were not explicitly considered in the PRA 

analysis (e.g., season of the year). Because the 

uncertainty analysis also produced insights 

regarding the effects of various system 

parameters and TH models on event severity, it 

also helped to identify the transient used to 

represent each PRA bin to the PFM analysis. 
6-43

Table 6.2 Summary of PTS Sensitivity Studies 

Parameter Significance Sensitivity Evaluation Results 

Break flow (or 

valve capacity) 

Most important factor in 

determining the RCS 

cooldown and 

depressurization rate. 

Directly impacts ECCS 

injection flow. 

Break spectrum analysis 

performed for the three plants 

analyzed. Range of break 

diameters considered is 1-in. 

(2.54-cm) to 22-in. (56-cm), 

sequentially increasing the 

flow area by a factor of 2. 

Analyses where the flow area 

was varied by ±30% were also 

performed. 

Significant effect on 

downcomer 

conditions. 

Can be significant 

contributor to vessel 

failure risk. 

Uncertainty in break 

flow for a given break 

area is small, given the 

range of break areas 

evaluated. 

Break location Downcomer temperature 

generally warmer for cold 

leg breaks vs. hot leg 

breaks. 

Hot leg breaks generally 

result in lower 

downcomer temperatures 

because the break flow 

enthalpy is higher for a 

hot leg break than for the 

same size cold leg break. 

In addition, for cold leg 

breaks, the ECC flow into 

the broken cold leg tends 

to flow out the break. 

Therefore, less cold ECC 

water is delivered to the 

downcomer. 

Effect of break location 

evaluated by analyzing both 

cold leg and hot leg breaks. 

Significant effect on 

downcomer 

conditions. Either hot 

leg or cold leg breaks 

can be significant 

contributors to vessel 

failure risk. 

HPI Flow (BC) ECCS flow rates are 

specified from pump flow 

curves which are pressure 

dependent. 

HPI flow rate varied by ±10%. 

Evaluations also done 

considering HPI pump failure. 

Effect of flow rate 

sensitivity found to 

have an insignificant 

impact on downcomer 

conditions and is not a 

significant contributor 

to vessel failure risk. 

Transients involving 

pump failure resulted 

in warmer downcomer 

temperatures, but are 

generally small 

contributors to vessel 

failure risk. 

 
6-44

Parameter Significance Sensitivity Evaluation Results 

Accumulator 

Injection 

Temperature 

Injection of large volume 

of cold water as the 

system pressure reaches 

the injection pressure of 

the accumulators. 

Injection temperature is 

dependent upon the 

season (winter or 

summer) assumed. 

Temperature varied from 

294 K (70°F) to 314 K (105°F) 

depending on the plant 

analyzed and season assumed. 

Significant effect on 

downcomer 

conditions, principally 

temperature in 

conjunction with HPI 

and LPI injection 

temperature sensitivity 

evaluation. 

Can be significant 

contributor to vessel 

failure risk. 

Accumulator 

Injection Rate 

Injection of large volume 

of cold water as the 

system pressure reaches 

the injection pressure of 

the accumulators. 

The effect of pressure on flow 

was examined by varying the 

initial pressure from 3.8 MPa 

[550 psi], 4.1 MPa [600 psi] 

(nominal) and 4.5 MPa 

[650 psi]. 

Insignificant effect on 

downcomer 

conditions. 

HPI and LPI 

Injection 

Temperature 

Seasonal effect on the 

injection water 

temperature, which 

affects the downcomer 

water temperature. Done 

in conjunction with the 

accumulator injection 

temperature sensitivity. 

Oconee – Temperature range 

considered is 278 K (40°F) to 

303 K (85°F). 

Palisades – Temperature range 

considered is 278 K (40°F) to 

311 K (90°F). 

Beaver Valley – summer 

temperature of 286 K (55°F) 

considered. Note that Beaver 

Valley maintains ECC water 

temperature at a constant 

300 K (50°F) in accordance 

with Technical Specifications. 

Significant effect on 

downcomer 

conditions. Affected 

transients can be 

significant 

contributors to vessel 

failure risk. 

Decay Heat 

Load 

Decay heat load directly 

affects downcomer 

conditions. 

Hot full power conditions and 

hot zero power conditions 

considered. Hot zero power 

defined as 0.2% of full core 

power (~5.2 MWth). 

Uncertainties in decay 

heat load small 

compared to the range 

of conditions 

considered. 

HPI Flow 

Control 

Direct impact of HPI 

flow rate on downcomer 

conditions. HPI 

throttling generally 

reduces downcomer 

temperature and system 

pressure. 

For transients involving either 

closure of a stuck-open 

pressurizer SRV or main steam 

line break, the RCS may reach 

conditions for which operating 

procedures require HPI 

throttling or termination. For 

these transients, the scenarios 

analyzed varied the timing and 

conditions under which the 

operator controlled HPI flow. 

Significant effect on 

downcomer 

conditions, principally 

temperature. Affected 

transients can be 

significant 

contributors to vessel 

failure risk. 
6-45

Parameter Significance Sensitivity Evaluation Results 

Feedwater 

Control 

Direct impact on 

downcomer conditions 

particularly if the steam 

generator is overfilled. 

Various feedwater control 

scenarios ranging from normal 

control of steam generator 

level to failure of level control 

or operator error, resulting in 

filling of the steam generators 

until water entered the steam 

lines. 

Range of sequences 

analyzed covers 

uncertainty in 

feedwater control. 

Generally, effects are 

insignificant unless 

combined with a valve 

failure or MSLB. 

Secondary 

Pressure Control 

Direct impact on 

downcomer conditions 

for MSLB or stuck-open 

secondary relief valve 

sequences. 

A spectrum of PRA sequences 

were analyzed for failures of 

secondary side valves, 

including steam dump, steam 

generator safety/relief, and 

atmospheric release valves. 

The failures were combined in 

some instances with failure of 

feedwater control such that the 

faulted steam generator 

continued to be fed with 

auxiliary feedwater. 

Significant effect on 

downcomer 

conditions. Affected 

transients can be 

significant 

contributors to vessel 

failure risk. 
6-46

This method of accounting for TH uncertainty 

does not quantify the uncertainties associated 

with each TH sequence; rather, it characterizes 

the uncertainties associated with each PRA bin. 

This is appropriate because, as illustrated in 

Figure 3.3, each TH sequence that is passed on 

to the PFM analysis represents a much larger 

number of TH sequences that, together, 

constitute a PRA “bin.” Provided the combined 

effects of the TH parameter and modeling 

uncertainties on the severity of this one 

representative sequence is small relative to both 

• the uncertainty in the frequency of occurrence 

of all of the sequences in the bin, and 

• the variability in severity between the 

different sequences in the bin, then 

the uncertainty associated with TH parameter 

and modeling uncertainties of the representative 

sequence can be considered negligible. The 

appropriateness of not accounting for these 

uncertainties because they are negligibly small is 

ensured by the iterative process used to define 

the PRA bins. PRA bins that contribute 

significantly to the estimated TWCF were 

continually partitioned (including appropriate 

partitioning of their frequencies and selection of 

new TH sequences to represent each partitioned 

bin) until the total estimated TWCF for the plant 

did not change significantly with continued 

partitioning. Thus, any errors caused by not 

explicitly accounting for the TH parameter and 

modeling uncertainties associated with the TH 

sequence used to represent each PRA bin are not 

expected to influence the outcome of the 

analysis (i.e., the estimated values of TWCF). 

The following section summarizes the TH 

uncertainty analysis. Full details can be found in 

a companion report [Chang]. 

6.8.2.2 Approach 

The TH uncertainty characterization begins with 

identification of the event categories 

(e.g., LOCAs) that are expected to significantly 

challenge vessel integrity. If necessary, each of 

these event categories was then subdivided. For 

example, the LOCA event category called was 

subdivided as follows: 

• Small LOCA: between 1.5-in. (3.8-cm) and 

approximately 4-in. (10-cm) 

• Medium LOCA: approximately 4-in. 

(10-cm) and approximately 8-in. (20-cm) 

• Large LOCA: greater than approximately 

8-in. (20-cm) 

• Stuck-open pressurizer safety relief valves 

• Without subsequent reclosure 

• With subsequent reclosure, resulting in 

system repressurization 

The aim of event category subdivision was to 

better bound the uncertainty by not having one 

category attempt to represent too broad a range 

of thermal-hydraulic conditions. However, even 

within these subdivided event categories the 

response of the plant can vary due to sequence to 

sequence differences within each subdivision. 

To quantify this, the following uncertainties 

were identified: 

• Aleatory Uncertainties 

(1) Break diameter (1- to 22-in. (2.5- to 

56-cm)): variation of ±30% considered.

(2) Break location (surge line or hot leg, 

cold leg) 

(3) Decay heat level (full power, 

low (hot zero) power) 

(4) Reactor coolant pump status (tripped vs. 

operating) 

(5) Heat structure sensible heat (variation of 

±30% considered) 

(6) HPI state (normal operation, failed) 

(7) HPI flow rate (±10%) 

(8) Accumulator pressure ± 345 kPa (±50 

psi), accumulator temperature: 21°C, 

43°C (70°F, 110°F) 

(9) Effect of seasonal variation on 

downcomer temperature (summer, 

winter) 

• Epistemic Uncertainties 

(1) In-vessel circulation attributable to vent 

valve function in Oconee (cases where 

valves failed were considered) 

(2) Vessel wall-to-downcomer fluid heat 

transfer 

(3) Flow resistance (loop flow) 

(4) Break flow 
6-47

6.8.2.2.1 Break Diameter and 

Location (Aleatory 1 and 2) 

Downcomer conditions are strongly influenced 

by the break diameter (break flow) and break 

location. Various diameters (1.5-in. (3.8-cm) 

to 22-in. (56-cm)) and break locations (surge 

line, hot leg, and cold leg) are considered. 

The thermal-hydraulic response of the reactor 

system is considerably different as the break 

diameter increases from 2-in. (5.08-cm) to 16-in. 

(40.64-cm). For the larger break cases of 8-in. 

(20.32-cm) or more, maximum ECCS delivery 

will occur (the HPI and LPI systems will be 

operating at pump runout conditions), resulting 

in the maximum rate of reactor coolant system 

(downcomer) cooldown and depressurization. 

For smaller breaks in the range of 5.6-in 

(14.37-cm) or less, ECCS delivery flow will be 

limited by the break flow so that the rate at 

which reactor coolant system cooldown and 

depressurization will occur is more strongly tied 

to break diameter and location. In this range, the 

rate of reactor system cooldown and 

depressurization decreases with break diameter. 

Transients involving stuck-open primary side 

safety valves fall into this category. 

ECCS performance is also affected by the break 

location. For hot leg or surge line breaks, the 

ECCS will flow from the cold legs through the 

downcomer to the break. For cold leg breaks, 

some of the ECCS flow will be discharged 

through the break. 

Inherently, the rate of reactor system cooldown 

and depressurization is more uncertain in this 

range relative to break diameters greater than 

8-in. (20.32-cm). Hence, the uncertainty 

analysis focused on break diameters less than 

5.6-in (14.37-cm). A ±30% variation on break 

area to account for break flow uncertainty was 

considered for LOCA and stuck-open primary 

safety valve transients. 

6.8.2.2.2 Heat Sources (Aleatory 3, 4, 

and 5) 

Heat sources affecting downcomer conditions 

include the decay heat load, reactor coolant 

pump status, and the sensible heat in the reactor 

plant heat structures. 

In the case of decay heat load, three sets of 

decay heat data corresponding to full-power 

operation, 0.7% of full-power operation, and 

0.2% of full-power operation were analyzed. 

Later in the analysis, the low-power operations 

were combined into the hot zero power initiating 

state. Probabilities assigned to these states are 

0.98 for hot full-power conditions and 0.02 for 

hot zero power conditions. Uncertainties in heat 

load due to RCP operation were considered by 

evaluating transients where the pumps are 

tripped vs. when they remain operating. 

The principal effect of sensible heat in the heat 

structures is the rate at which heat is transferred 

from the system structure to the system fluid. A 

range of ±30% is considered in the uncertainty 

analysis. 

6.8.2.2.3 High-Pressure Injection 

(Aleatory 6 through 9) 

 

ECCS performance considered four factors, 

including (1) failure on demand, (2) injection 

flow rate, (3) injection temperature, and 

(4) injection timing. System failures include a 

partial or full system failure, where the injection 

flow at the required rate is not delivered. 

Failures of this type result in warmer 

downcomer temperatures. Transients involving 

HPI failure have been considered in the 

uncertainty analysis. Flow rate uncertainty was 

assessed using a ±10% variation in HPI flow. 

Flow rate uncertainties in the LPI or 

accumulators (or core flood tank) were also 

considered. 

Uncertainty in injection temperature considers 

the effect of seasonal variations on the injection 

water source, which is the refueling water 

storage tank located outdoors. Table 6.2 lists the 

values used. Probabilities assigned to the 
6-48

seasonal variation are 0.25 for summer and 

winter and 0.50 for fall/spring. Uncertainty in 

injection timing of the accumulators was 

considered by varying the injection pressure 

over a range of ±50 psi. The pressures at which 

high- and low-pressure injection is initiated are 

judged to have a small uncertainty. Uncertainty 

in the RCS coolant loop total flow resistance 

focuses on the loop flow resistance. A 100% 

increase in flow resistance was considered. 

6.8.2.2.4 Vent Valves (Epistemic 1) 

Uncertainty in the in-vessel circulation, which 

affects the energy distribution in the reactor 

coolant system, focuses principally on Oconee 

because of the presence of the vent valves. For 

the uncertainty evaluation, failure of the valves 

to open was considered. 

6.8.2.3 Definition of Sensitivity 

Indicator 

Sensitivity analyses were performed with 

RELAP5 for each of the parameters discussed in 

Section 6.8.2.2. Downcomer temperature is the 

most important of the three thermal-hydraulic 

boundary conditions in the fracture analysis and 

therefore is the focus of the sensitivity analysis. 

The sensitivity indicator is the effect on the 

average downcomer temperature due to the 

change in a single sensitivity parameter over the 

transient time of interest, which is 10,000 

seconds for this analysis. Each sensitivity 

indicator has an associated probability of 

occurrence determined from the parameter being 

varied. The following equation is used to 

compute the sensitivity indicator: 

∆T T = − sen T nom 

where T sen is the sensitivity case downcomer 

temperature averaged over the 10,000 seconds 

interval and T nom is the base case 

downcomer temperature averaged over the 

10,000 second interval. To compute the 

sensitivity indicator, each sensitivity parameter 

is varied (one at a time) to an upper and lower 

bound and the average temperature difference is 

determined. This approach is called the nominal 

range sensitivity analysis and is described in 

more detail in [Chang]. 

The impact on the sensitivity indicator of a 

given sensitivity parameter depends strongly on 

the transient and therefore a large number of 

transients that include the types of transients 

considered in the PTS analysis (LOCAs, stuckopen primary safety valves, MSLBs, etc.) need 

to be considered. 

6.8.2.4 Example of Results for a Surge 

Line Break 

The case of a 2.83-in. (7.18-cm) surge line break 

LOCA for Oconee is used to illustrate the 

development of the sensitivity indicator. Figure 

6.28 presents the sensitivity parameter ranking 

for the 2.83-in. (7.18-cm) surge line break 

LOCA for Oconee. For this case, the sensitivity 

indicator ranges from an increase of 100K 

(180°F) when HPI is assumed to fail to a 

decrease of 35 K (63°F) for hot zero power 

initialization. The sensitivity indicator depends 

on the transient being considered and sensitivity 

indicators were developed for the range of 

transients considered in the PTS analysis. 

The uncertainty evaluation requires 

consideration of the effect of multiple 

parameters on the downcomer conditions. As an 

example, a transient may be initiated from hot 

zero power during the summertime. The 

sensitivity studies only evaluated the effect of 

increasing or decreasing a single parameter. To 

combine the effect of multiple parameters on the 

downcomer fluid temperature, the sensitivity 

indicators are added together. This approach is 

based on the assumption that the effect of any 

sensitivity parameter is independent of the effect 

of any other parameter so that the sensitivity 

indicators become linearly additive. Application 

of the linearly additive assumption avoids 

performing RELAP5 sensitivity studies on the 

large number of sensitivity parameter 

combinations. The linear additive assumption 

was applied to the various types of transients 

considered in the uncertainty analysis. 
6-49

Validation of the linear additive assumption 

(LAA) was done by varying multiple sensitivity 

parameters in a single RELAP5 run based on a 

2.83-in. (7.18-cm) surge line break LOCA 

model for Oconee. Five different combinations 

of sensitivity parameters were selected to cover 

a downcomer temperature range of 111 K 

(200°F). 

Table 6.3 lists the five combinations of 

sensitivity parameters considered and the results 

of Tsens computed applying the linear additive 

assumption compared to direct computation 

using RELAP5. A plot of the results is shown in 

Figure 6.29. The 45-degree line in Figure 6.29 

represents the perfect scenarios in which the 

expected values are same as the RELAP5 

calculated values. The solid dots represent the 

realities. The difference between the solid dots 

and the squares on the 45-degree line is the 

deviation of the LAA from the RELAP5 results. 

Figure 6.29 shows that downcomer temperature 

computed using the linear additive assumption is 

in good agreement with the RELAP5 calculated 

results. 

Given the important sensitivity indicators and 

associated probabilities, a statistical analysis is 

carried out to finalize selection of representative 

transients for each bin and to refine the 

frequencies for the bins defined during the frontend risk modeling. This statistical analysis is 

performed in two parts. First, the downcomer 

temperature is determined by adjusting the 

nominal downcomer temperature for each 

subcategory identified in Step 5 by the 

sensitivity indicator (downcomer temperature 

adjustment) for all combinations of sensitivity 

parameters being considered for that 

subcategory using the linear additive approach. 

Then, the probability of occurrence for each 

combination of sensitivity parameters is 

determined. Note that thousands of temperature 

points are generated for all of the combinations 

of sensitivity parameters considered. 

Table 6.3 List of Combined Sensitivity Indicators Varied for LAA Verification 

No. Sensitivity Parameters Varied 

Tsens 

using 

LAA 

Tsens (°K) 

using 

RELAP5 

Tsens, RELAP5

– Tsens, LAA

(°K) 

1 Winter conditions; p(CFT) +50 psi; 70% Abrk; 

RVVVs Close; 70% HTC 331.7 345.3 13.6 

2 Summer; vent valves failed closed; 200% loop 

flow resistance 360.0 362.3 2.7 

3 

p(CFT) +50 psi; 110% nominal HPI mass flow; 

70% nominal break area; 130% nominal heat 

transfer coefficient 

387.6 391.4 3.8 

4 

Summer conditions; p(CFT) +50 psi ; 90% 

nominal HPI mass flow; 130% nominal break 

area; normal vent valve function; 200% loop flow 

resistance 

415.5 406.9 -8.6 

5 

Summer conditions; 90% nominal HPI mass flow; 

70% nominal break area; normal vent valve 

function; 130% nominal heat transfer coefficient. 

438.2 448.8 10.7 

Given the downcomer temperature and 

corresponding probability, a probability density 

function is constructed. The development of this 

function is illustrated in Figure 6.30 for Oconee 

for LOCAs between 1.5-in. (3.81-cm) and 4-in. 

(10.16-cm) in diameter. This figure shows the 

resulting cumulative distribution function found 

from integrating the probability density function 

that is used to obtain the probabilities used to 

adjust the bin frequencies. 
6-50

The representative scenarios are determined 

from the probability density function by 

subdividing the probability into five bands 

between the 0.05 and 0.95 probability levels and 

determining the temperature at the median point 

in each band. The probabilities in the two 

regions near the tails are increased by 0.05. This 

adjustment is made because of potentially large 

errors in the sensitivity indicator in the tails of 

the probability density function (below 0.05 and 

above 0.95 probability level). In Figure 6.30, 

there are five bands shown on the cumulative 

density function plots along with the median 

values identified and the downcomer 

temperature corresponding to each median. 

Selection of the representative scenario 

corresponding to the median temperature in each 

probability band in the cumulative density 

distribution plot is done by picking the 

sensitivity indicator result that corresponds to 

the median temperature and using the 

corresponding set of RELAP5 results for 

probabilistic fracture mechanics analysis. 

An example of the selection of representative 

scenarios along with the corresponding 

probabilities is presented in Table 6.4. 

The uncertainty analysis was performed for the 

transients considered for the Oconee, Beaver 

Valley, and Palisades plants. There were some 

variations in the thermal-hydraulic categories 

considered, the sensitivity indicators evaluated 

and in the set of representative transients 

selected. These variations are attributable to 

differences principally in plant design and plant 

operating conditions. Otherwise, the approach 

used is the same for the three plants. 

Adjustments were made to the bin probabilities 

and representative sequences were selected 

based on the uncertainty analysis conducted for 

the three plants. Details can be found in [Chang]. 

1 100% HPI fail 

2 50% HPI fail 

2 50% HPI fail 

3 25% HPI fail 

4 RVVVs Open 

5 CL LOCA 

6 90% m(HPI) 

7 130% CHTC 

8 Summer 

9 P(CFT) -= 50 psi 

10 Nominal 

11 P(CFT) += 50 psi 

12 110% m(HPI) 

13 70% CHTC 

14 Winter 

15 High CL rev. K 

16 RVVV Close 

17 HZP 
6-51

Figure 6.28. Sensitivity parameter ranking of a 2.8-in. (7.18-cm) surge line break LOCA 

Figure 6.29. Confirmation of the Linearly Additive Assumption for a 2.8-in. (7.18-cm) surge line break LOCA 

 

Figure 6.30. Illustration of the Statistical Results for Downcomer Temperature Distribution 

Table 6.4 Example of Representative Scenario Selection 

# TH Bin # Probability Scenario Specification Descriptions 

1 145 0.23 1E-3 m2

 cold leg LOCA with increased 30% break area 

(Winter)*

 

2 142 0.18 4E-3m2 surge line with 30% reduced break area 

3 141 0.18 4E-3m2 surge line with 30% increased break area 

4 172 0.18 8E-3m2 cold leg LOCA 

5 154 0.23 8E-3m2

 surge line LOCA with 30% reduced break area 

RPV vent valves closed 
7-1

7 Probabilistic Fracture Mechanics Analysis 

7.1 Interaction of PFM Model with 

PRA and TH models 

Figure 7.1 illustrates how the PFM model 

connects to both the PRA and TH models 

discussed in Chapters 5 and 6, respectively. 

Specifically, the PFM model takes as input from 

TH the pressure, temperature, and heat transfer 

coefficient time histories that have been defined 

by TH for the sequences defined by PRA. The 

PFM model uses this TH information along with 

other information concerning plant design and 

materials of construction to estimate the timedependent driving force to fracture produced by 

a particular event sequence. The PFM model 

compares this estimate of fracture driving force 

to the fracture toughness, or fracture resistance, 

of the RPV steel. This comparison allows us to 

estimate the probability that a particular 

sequence of events will produce a crack all the 

way through the RPV wall were that sequence of 

events actually to occur. The final step in the 

analysis involves a matrix multiplication of 

these through-wall cracking frequency estimates 

with the frequency at which a particular event 

sequence is expected to occur (as defined by 

PRA). This product establishes an estimate of 

the annual frequency of through-wall cracking 

that can be expected for a particular plant after a 

particular period of operation when subjected to 

a particular sequence of events. The annual 

frequency of through-wall cracking is then 

summed for all event sequences specified by 

PRA to estimate the total annual frequency of 

through-wall cracking for the vessel. 

Performance of such analyses for various 

operating lifetimes provides an estimate of how 

the annual through-wall cracking frequency can 

be expected to vary over the lifetime of the 

plant. 

7.2 Components of the PFM Model 

Figure 7.1 also shows that the PFM model is 

itself composed of four major sub-models 

(which themselves are composed of yet more 

sub-models and parameter inputs). The four 

major sub-models that make up the PFM model 

are as follows: 

• A flaw distribution model: see Section 7.5 

for an overview and [Simonen] for details. 

• A neutronics model: see Section 7.6 for an 

overview and [EricksonKirk-PFM] for 

details. 

• A crack initiation model: see Section 7.7 for 

an overview and [EricksonKirk-PFM] for 

details. 

• A through-wall cracking model: see Section 7.8 

for an overview and [EricksonKirk-PFM] 

for details. 

Together, these four sub-models provide the 

information necessary to estimate both the 

fracture driving force (Kapplied) generated by the 

PTS loading and the resistance of the material to 

fracture (KResistance). Kapplied depends upon the 

thermal-hydraulic inputs of pressure, 

temperature, and heat transfer coefficient (all vs. 

time), on the vessel dimensions, and on the 

location and size of the flaws that are quantified 

by the flaw distribution model. KResistance, more 

commonly called “fracture toughness,” depends 

upon the chemical composition of the steel, the 

downcomer temperature from the thermalhydraulics calculations combined with the heat 

conduction properties of the steel, and on the 

degree of neutron irradiation exposure 

experienced by the steel. Our calculations 

consider the potential for cracks to initiate in 

either a brittle manner by cleavage or in a ductile 

manner by microvoid initiation and coalescence. 

(The type of crack initiation that occurs depends 

upon the temperature.) We also consider the 
7-2

potential for cleavage cracks to stop, which is 

a phenomenon referred to as “crack arrest.” 

These different failure modes all have different 

characteristics fracture toughness (Resistance) 

values, as follows: 

• KIc quantifies the resistance of the material 

to crack initiation in cleavage. 

• JIc and J-R quantifies the resistance of the 

material to crack initiation by micro-void 

coalescence. Furthermore, the J-R curve 

describes the resistance of the material to 

further ductile crack growth. 

• KIa quantifies the ability of the material to 

stop (arrest) a running cleavage crack. 

These various values of KResistance (KIc, JIc, J-R, 

and KIa) and their dependencies on chemical 

composition, temperature, and neutron 

irradiation exposure are estimated by a 

combination of the neutronics model, the crack 

initiation model, and the through-wall cracking 

model. Also, the crack initiation model and the 

through-wall cracking models estimate, 

respectively, the probability of crack initiation 

and the probability of through-wall cracking by 

comparing the value of Kapplied to the appropriate 

value of KResistance. 

7.3 Objectives of this Chapter 

The objectives of this chapter are as follows: 

(1) Section 7.4: Describes our approach to 

model development and uncertainty 

characterization. 

(2) Sections 7.5 through 7.8: Provide a 

summary discussion of the four major 

sub-models that make up the PFM model. 

(3) Section 7.9: Provides a summary discussion 

of how all of these sub-models are 

implemented in the FAVOR probabilistic 

fracture mechanics code. (See [Dickson-UG] 

and [Williams] for details.) 

(4) Section 7.10: Provides a summary 

discussion of an experimental validation of 

the linear elastic fracture mechanics (LEFM) 

techniques that underlie our approach. 

(See Appendix A of [EricksonKirk-PFM] 

for details.) 

7.4 Approach to Model 

Development and Uncertainty 

Characterization 

As discussed in Section 3.2, our approach to 

developing a risk-informed revision of 

10 CFR 50.61 requires explicit identification of 

the type of uncertainty (aleatory or epistemic) 

to enable the development of an appropriate 

mathematical model. To do so, it is first 

necessary to establish independent, physically 

motivated, models that account for the effects of 

irradiation damage and temperature. We achieved 

this goal by the following three-step process: 

(1) Uncertainty Identification: We began by 

constructing a graphical description of the 

current toughness model. This description, 

called a “root cause diagram,” is illustrated 

schematically in Figure 7.2. Diagrams of 

this type show all of the parameters (shaded 

boxes) and all of the relationships (nodes) 

used to estimate the fracture toughness for a 

particular set of conditions. Decomposing 

the toughness / embrittlement model in this 

way permitted identification of individual 

sources of uncertainty, both in the 

parameters and in the relationships assumed 

between the parameters. 

(2) Uncertainty Classification: Uncertainties 

were classified through an understanding of 

the basic physical mechanisms responsible 

for crack initiation, for crack arrest, and for 

irradiation damage. Without this physical 

understanding, it was impossible to 

distinguish the irreducible (i.e., aleatory) 

uncertainties associated with variability of 

the material from reducible (i.e., epistemic) 

uncertainties caused by limited data, 

imperfect models, and so on. 

(3) Uncertainty Quantification: The physical 

understanding developed to classify 

uncertainty types also played a pivotal role 

in uncertainty quantification because a 

model of fracture toughness that can be 

regarded as representing the true behavior 
7-3

Figure 7.1. Illustration of the interrelationships between PFM model and the TH and PRA models, 

and the four principal sub-models that comprise the PFM model 

Flaw density, location,

Length, & depth

Flaw

Distributio

Model

Pressure vs. time

Temperature vs. time

Thermal

Hydraulics

Model

Fluence on Vessel ID Nucleonic

Model

Material Property &

Composition Data

Crack

Initiation

Model

Conditional

Probability of

Crack Initiation

Through Wall 

Cracking

Model

Conditional

Probability of

Thru-Wall Cracking

Matrix

Multiply

Yearly

Frequency of

Thru-Wall

Cracking

Probabilistic Fracture MechanicsModel
7-4

of the material is needed to quantify the 

uncertainties present in any other model. 

Therefore, uncertainty quantification was 

achieved by comparing the RTNDT-based 

toughness model developed for use in the 

PTS reevaluation project to this bestestimate model. 

To be consistent with LEFM principles, LEFMvalid KIc and KIa values were used to calibrate 

the parameters of this best estimate model. 

However, the best-estimate model cannot be 

constructed as a purely empirical fit to these KIc

and KIa values. Without the insights available 

from a physically based understanding it was 

impossible to discern if the trends demonstrated 

by the laboratory data can be expected to apply 

to the material and loading conditions of interest 

in commercial PWRs. Consequently, the “best 

estimate models” each had a form motivated by 

the physical processes responsible for the 

underlying phenomena. 

A

D

C

B

A = f (B,C,D)

F

E

H

G

D = G if G>H

B = E or F

Equation, Correlation

Choice

Comparison

Equation, Exact

Relationship Types

Parameter

Equation, Correlation

Choice

Comparison

Equation, Exact

Relationship Types

Parameter

Equation, Correlation

Choice

Comparison

Equation, Exact

Relationship Types

Parameter

Comparison

Equation, Exact

Relationship Types

Parameter

Figure 7.2. Illustration of a root cause diagram 

showing how uncertainties in input 

variables (E, F, G, and H) propagate 

through models (nodes), themselves 

potentially having uncertainty, to 

produce uncertainty in a resultant 

value (A) 

7.5 Flaw Model 

The flaw model provides estimates of the 

density (flaws per unit area or volume), size, and 

location in the vessel wall of initial fabrication 

defects‡‡. This flaw distribution, reported in 

 

‡‡ Growth of initial fabrication defects attributable to 

sub-critical cracking mechanisms does not need 

to be considered; see Section 3.3.3.2. 

detail by [Simonen], represents a major 

improvement in realism relative to that adopted 

in previous studies of PTS risk. Indeed, one of 

the major unknowns/uncertainties identified in 

the last comprehensive evaluation of PTS 

[SECY-82-465] was the distribution of flaws 

assumed to exist in the RPV wall. SECY-82-465 

used flaw models based on the Marshall study, 

which included data from a limited population of 

nuclear vessels and from many non-nuclear 

vessels [Marshall 82]. These flaw 

measurements were part of routine pre-service 

NDE examinations performed 25 or more years 

ago at vessel fabrication shops. Given the 

limitations of the NDE technology available at 

the time, the Marshall flaw distribution provides 

a reasonable representation only for flaws 

having depth dimensions larger than ≈1-in. 

(2.54-cm). The Marshall distribution was 

nonetheless applied in SECY-82-465 and in the 

IPTS studies [ORNL 85a, 85b, 86] by 

extrapolating fits to the data to the much smaller 

flaws of concern in PTS calculations (less than 

≈0.25-in. (0.64-cm)). Additionally, all flaws in 

the Marshall distribution were assumed to break 

the inner-diameter surface of the RPV despite 

the fact that the observations rarely, if ever, 

revealed surface breaking flaws in nuclear grade 

construction. 

Table 7.1 summarizes the various sources of 

experimental data used by Simonen et al. to 

develop the flaw distributions used in FAVOR. 

While the volume of material represented in 

Table 7.1 improve greatly on the Marshall flaw 

distributions [Marshall 82], an inescapable 

conclusion is also that the quantity of available 

data is also quite small compared with the 

volume of RPV material in service. 

Consequently, it is not possible to ensure on an 

empirical basis alone that the flaw distributions 

developed based on these data apply to all 

PWRs in general. However, the flaw 

distributions proposed in [Simonen] rely on the 

experimental evidence gained from inspections 

of the materials summarized in Table 7.1 do not 

rest solely on this empirical evidence. Along 

with these data Simonen et al. used both 

physical models and expert opinions when 

developing their recommended flaw 

distributions. Additionally, where detailed 
7-5

information was lacking Simonen et al. made 

conservative judgments (for example, all NDE 

indications were modeled as cracks and, 

therefore, potentially deleterious to RPV 

integrity). This combined use of empirical 

evidence, physical models, expert opinions, and 

conservative judgments allowed Simonen et al. 

to propose flaw distributions for use in FAVOR 

that are believed to be appropriate/conservative 

representations of the flaw population existing in 

PWRs in general. (See Appendix C and 

[Simonen] for details.) 

Table 7.1. Summary of sources of experimental 

data sources for the flaw 

distribution 

Vessel Weld Plate Clad 

PVRUF 9150 855 1650 

Shoreham 10375 975 -- 

Hope Creek 245 550 -- 

River Bend 2440 1465 -- 

Table entries represent volume of material examined in in3. 

In the following sections, we summarize the 

findings of this study for buried flaws in welds 

(Section 7.5.1), buried flaws in plates 

(Section 7.5.2), and surface flaws in both plates 

and welds (Section 7.5.3). Section 7.5.4 

contrasts our flaw distribution the results with 

the Marshall distribution used in SECY-82-465. 

7.5.1 Buried Flaws in Welds 

The Simonen study made the following 

observations regarding flaws that form as part of 

the axial or circumferential weld fabrication 

process: 

(1) Flaws in welds are distributed uniformly 

through the thickness of the RPV weld. 

There is no tendency for a greater density of 

flaws to occur either near the root or cap 

passes. 

(2) No surface breaking flaws were identified in 

all of the weld material examined, nor was a 

credible physical mechanism for surface 

flaw generation identified. Consequently, 

the flaw distributions used herein contain 

only buried flaws. This is a significant 

change from the Marshall flaw distribution, 

which contained only surface breaking 

flaws. 

(3) Virtually all non-volumetric flaws found in 

welds were lack of side-wall fusion defects 

that exist on the fusion line between the 

deposited weld metal and the plate or 

forging being joined. Consequently, the 

number of flaws in a particular weld scales 

in proportion to the fusion line area. 

Additionally, this observation implies that 

axial welds contain only axially oriented 

flaws whereas circumferential welds contain 

only circumferentially oriented flaws. 

(4) Data on flaw density exhibited statistically 

significant differences depending upon the 

welding process used (SAW, SMAW, 

GMAW, or repair weld). However, it is 

difficult in practice to ascertain from records 

precisely where different weld processes 

were used, or where repair welds were 

made. For this reason, we decided that the 

flaw distributions used in this study would 

represent blended combinations of the SAW, 

SMAW, and REPAIR flaw distributions. 

Percentages of SAW and SMAW were 

established on a vessel specific basis. The 

percentage of repair weld was assumed to be 

2% for all vessels analyzed. A repair weld 

volume of 2% exceeds slightly the repair 

percentage of 1.5% that was observed by 

PNNL for both the Shoreham and PVRUF 

vessels. 

(5) Flaw densities exhibited statistically 

significant differences depending upon the 

vessel examined (PVRUF or Shoreham). 

Since Simonen did not establish a model 

capable of explaining why the density and 

size of flaws can be expected to vary from 

vessel to vessel, it was decided to adopt for 

FAVOR calculations flaw densities based 

only on observations of the Shoreham vessel 

because the Shoreham welds had a higher 

flaw density than the PVRUF welds. 

(6) Flaw depth dimensions did not exhibit 

statistically significant differences for the 

different welding process and vessels 

examined, so in this case the data from the 

different processes and vessels were pooled. 
7-6

There was, however, clear differences in the 

distributions of flaws length depending on 

the welding processes and vessels examined, 

so the flaw length distributions were 

established on a case-by-case basis. 

It should also be noted that the empirical data 

used as the primary evidence to establish the 

distribution of embedded weld flaws do not, and 

cannot, provide any information about the 

maximum size a flaw can be. For this reason, 

it was decided to truncate the non-repair flaw 

distribution at 1-in. (2.54-cm) and the repair 

flaw distribution at 2-in. (5.08-cm). In both 

cases, the selected truncation limit exceeds the 

maximum observed flaw size by a factor of 2. 

We performed a sensitivity study with FAVOR 

and ascertained that, within reasonable bounds 

on truncation limit dimension, the estimated 

through-wall cracking frequency is not 

influenced in any significant way by the 

truncation limit [Dickson 03]. 

7.5.2 Buried Flaws in Plates 

As reflected by the information in Table 7.1, the 

empirical evidence available to support a plate 

flaw distribution is much more limited than the 

available information for welds. Data on flaw 

rates and sizes from these sources agree well 

with two flaw distributions for plates derived by 

applying flaw density adjustment factors to weld 

flaw distributions. These adjustment factors, 

which were proposed by a group of experts 

[Simonen], are as follows: 

• The density of plate flaws of depth less than 

0.24-in. (6-mm) is 10% of that for weld flaws. 

• The density of plate flaws of depth above 

0.24-in. (6-mm) is 2.5% of that for weld flaws. 

Since reasonable agreement exists between the 

limited experimental data on plate flaws and the 

adjusted weld distributions it was decided to use 

the adjusted weld distributions as input to 

FAVOR. A truncation limit of 0.43-in. 

(1.09-cm) was selected because it exceeds the 

largest observed plate flaw by a factor of 2. 

Again, a FAVOR sensitivity study demonstrates 

that this truncation limit does not influence 

significantly the estimated TWCF [Dickson 03]. 

Finally, the data reported by [Simonen] failed to 

reveal any preferred orientation for plate flaws. 

To model this finding in the most accurate way 

possible without performing mixed-mode 

fracture calculations, half of the simulated plate 

flaws are orientated axially, while the remaining 

half are oriented circumferentially in the vessel. 

7.5.3 Surface Flaws in Welds and Plates 

The entire inner-diameter of a nuclear RPV is 

clad with a thin layer of stainless steel to prevent 

corrosion of the underlying ferritic steel. Lack 

of inter-run fusion (LOF) can occur between 

adjacent weld beads, resulting in 

circumferentially oriented cracks. (All cladding 

in RPVs was deposited circumferentially.) 

While the data in [Simonen] shows a high 

probability (1 to 10 flaws per meter of deposited 

cladding weld bead) of obtaining very shallow 

LOF defects (1% of the clad layer thickness), 

only two deep LOF defects, having depths of 

~50% and ~63% of the clad layer thickness, 

were found in all of the cladding inspected. 

Simonen found no evidence of LOF defects that 

completely compromised the clad layer. 

The only flaws we expect to challenge the 

integrity of the RPV during PTS loading are 

those that completely penetrate the clad layer 

because it is only in this situation that the crack 

has its tip residing in the ferritic RPV steel, 

which is subject to neutron irradiation 

embrittlement. Despite the lack of empirical 

evidence for such deep flaws, it was not believed 

appropriate to completely exclude such flaws 

from the flaw model used in our PFM analysis 

owing to the limited amount of clad material 

examined. For this reason, we developed a 

distribution for small buried cladding flaws 

based on a combination of the data available, 

expert judgment, and the predictions of the 

PRODIGAL weld flaw simulation code 

[PRODIGAL]. This distribution was adjusted as 

follows to estimate the number of the clad flaws 

that fully penetrate the cladding thickness: 

• We estimated that only 1/1000th of the 

observed density of buried cladding flaws 

would fully penetrate the cladding thickness. 
7-7

• We assumed that these surface breaking 

defects exist only in single layer cladding. 

Multi-layer cladding was assumed to have 

no surface breaking flaws because the 

likelihood of two LOF defects aligning in 

two different weld layers is quite remote. 

• Based on the physical mechanism of their 

formation, all LOF defects are aligned with 

the clad welding direction (circumferential). 

In FAVOR, these surface-breaking 

circumferential flaws in the cladding can be 

simulated to occur anywhere in the vessel 

(i.e., in any weld, plate, and forging). 

7.5.4 Comparison of the Current Flaw 

Distribution with that Proposed by 

the Marshall Committee 

Figure 7.3 compares of the Marshall flaw 

distribution with the three components of the 

flaw distribution developed by Simonen. 

The following observations can be made: 

• In general, the individual contributions to 

the new flaw distribution contain more flaws 

than the Marshall distribution, but the flaws 

in the new distribution are considerably 

smaller. 

• While all of the flaws in the Marshall 

distribution are surface-breaking, only flaws 

associated with the cladding are surfacebreaking in our new distribution, and these 

comprise only a small percentage of the 

total. Also, these cladding flaws are all 

circumferentially oriented because they 

follow the direction of weld deposition. 

• The Marshall distribution focused on flaws 

in welds and did not distinguish between 

flaws in different product forms. The new 

distribution does, and it demonstrates that 

flaws in base metal are considerably smaller 

and occur less frequently than flaws in welds. 

As illustrated in Figure 7.4, Dickson and 

Simonen report that the estimated TWCF drops 

by a factor of between 20 and 70 when the new 

flaw distribution is adopted instead of the 

Marshall distribution [Dickson 03]. 

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

0 5 10 15 20 25 30

a = Flaw Depth, Percent Wall

Number of Flaws per Cubic Foot 

having Depth > a

 Weld metal flaws

 Base metal flaws

 Surface/Clad Flaws

 Marshall

W

B

S/C M

Figure 7.3. Comparison of the new flaw 

distribution to the Marshall flaw 

distribution 

limiting RTPTS (F) 

220 240 260 280 300 320 340 360 380

Ratio: frequency of RPV crack initiation (Marshall / PNNL) 

Ratio of frequency of RPV failure (Marshall / PNNL) 

0

10

20

30

40

50

60

70

80

ratio: frequency of RPV failure

(Marshall / improved PNNL) 

ratio: frequency of RPV crack initiation

(Marshall / improved PNNL) 

Figure 7.4. Illustration of the impact of the flaw 

distribution adopted in this study 

(improved PNNL) with that used in 

previous PTS calculations (Marshall 

flaw characterization) [Dickson 02] 

(analysis performed on Oconee at 60 

EFPY) 

7.6 Neutronics Model 

The neutronics model is itself composed of two 

major components: 

• a calculation of the fluence on the ID of the 

vessel performed according to NRC 

Regulatory Guide 1.190 [RG 1.190] 

• attenuation of this fluence through the wall 

of the vessel to the location of the crack of 
7-8

interest using the attenuation formula in 

Regulatory Guide 1.99 [RG 1.99]. 

7.6.1 ID Fluence 

The variation of fluence over the inner diameter 

of the vessel is estimated using modeling 

procedures based on the guidance provided in 

the NRC Regulatory Guide 1.190 [RG 1.190], 

“Calculational and Dosimetry Methods for 

Determining Pressure Vessel Neutron Fluence.” 

Fluences so calculated are considered best 

estimates because they are based on the most 

up-to-date calculational procedures. 

While procedures used to calculate fluence have 

been updated from those that provided the basis 

of the current PTS Rule, the more significant 

change in our fluence treatment has been the 

refinement of our discretization of the 

circumferential and azimuthal variation of 

fluence. In previous studies, each major region 

in the beltline of the vessel (i.e., each weld, 

plate, or forging) was assigned a value of 

fluence equal to the peak value estimated to 

occur anywhere in the region. In contrast, our 

models capture the detailed azimuthal and axial 

variation of fluence, resulting in a much more 

realistic model of the fluence variation in the 

beltline region. 

7.6.2 Through-Wall Fluence 

Attenuation 

Similar to previous PTS calculations [SECY-82-

465, ORNL 85a, ORNL 85b, ORNL 86] 

FAVOR adopts the Regulatory Guide 1.99, 

Revision 2, model of fluence attenuation through 

the thickness of the vessel [RG 1.99]. This 

model assumes that the fluence (and thus the 

damage caused by irradiation) drops 

exponentially as the through-wall distance from 

the inner radius of the RPV increases. The 

exponential coefficient adopted (-0.24) assumes 

that fluence attenuates at the same rate as 

displacements per atom (DPA) (a conservative 

assumption). A recent review of attenuation 

models [English 02] concluded that while the 

RG1.99R2 attenuation model is widely regarded 

as conservative, no better alternative model 

exists at the current time. 

7.7 Crack Initiation Model 

The crack initiation model is itself composed of 

the following major components: 

• Fracture driving force model 

o LEFM driving force 

o Warm pre-stress 

• Crack initiation resistance model 

o Unirradiated cleavage crack initiation 

toughness index temperature 

o Irradiation-induced shift in the cleavage 

crack initiation toughness index 

temperature 

o Cleavage crack initiation fracture 

toughness transition behavior 

The probability of a crack initiating is 

determined by comparing the fracture driving 

force (Kapplied) and the crack initiation resistance 

(KIc). If Kapplied for a given set of conditions 

(i.e., a particular TH transient and a particular 

flaw) exceeds the minimum value of the KIc

distribution, the conditional probability of crack 

initiation (CPI) takes on a value greater than 

zero, which is calculated by FAVOR. 

Conversely, if Kapplied for a given set of 

conditions falls below the minimum value of the 

KIc distribution then CPI=0 (exactly zero, not a 

very small number). 

In the following two subsections, we discuss the 

key features of the crack initiation model 

(Section 7.7.1) and the major differences 

between the current crack initiation model and 

that used in previous investigations of PTS risk 

(Section 7.7.2) [SECY-82-465, ORNL 85a, 

ORNL 85b, ORNL 86]. [EricksonKirk-PFM] 

provides a detailed discussion of the crack 

initiation model. 

7.7.1 Key Features 

7.7.1.1 Fracture Driving Force Model 

Warm pre-stress (WPS) effects were first noted 

in the literature in 1963 [Brothers 63]. These 

investigators reported (as have many since them) 
7-9

that the apparent fracture toughness of a ferritic 

steel can be elevated in the fracture mode 

transition regime if the specimen is first 

“pre-stressed” at an elevated temperature. Once 

a specimen is subjected to a certain Kapplied and 

has not failed, the temperature can be reduced 

and the specimen will remain intact despite the 

fact that the process of reducing the temperature 

has also reduced the initiation fracture toughness 

(KIc or KJc) to values smaller than Kapplied. In the 

past four decades, the physical mechanisms 

responsible for the WPS effect have been 

identified, studied extensively, and validated. 

The types of loading that produce PTS 

challenges are characterized (generally) by a 

rapid cooldown on the inside the RPV. This 

type of loading produces values of Kapplied that 

initially increase, but later decrease as the 

transient progresses. Thus, depending upon the 

specifics of the transient (temperature gradients, 

flaw location, and so on) WPS may be effective, 

thereby preventing initiation of a cleavage crack 

even though Kapplied exceeds KIc. Nonetheless, to 

date, investigations of PTS have not included 

WPS as part of the PFM model [SECY-82-465, 

ORNL 85a, ORNL 85b, ORNL 86] for the 

following two reasons: 

(1) TH transients were previously represented 

as smooth variations of both pressure and 

temperature with time. However, data taken 

from operating nuclear plants demonstrate 

that actual TH transients are not always so 

well behaved. This created the possibility 

that the short duration fluctuations of 

pressure and/or temperature with time 

characteristic of real transients might nullify 

the beneficial effect of WPS while the 

companion idealized transient might show 

WPS to be effective. 

(2) In the past, the probabilistic risk assessment 

(PRA) models of human reliability (HR) 

were not sufficiently sophisticated to capture 

the potential for plant operators to 

repressurize the primary system as part of 

their response to an overcooling event. 

Since such a repressurization would usually 

nullify the benefit of WPS, it was viewed as 

nonconservative to account for the benefit 

produced by WPS within a model that may 

also ignore the potentially deleterious effects 

of operator actions. 

This reevaluation of the PTS Rule features both 

more realistic representations of the TH 

transients and a much more sophisticated 

PRA/HR models that consider explicitly both 

acts of omission and commission on the part of 

plant operators. Consequently, we have 

incorporated WPS effects into the PFM model. 

Thus, in this model the following two 

requirements must both be met for a crack to 

initiate: 

Eq. 7-1 Kapplied ≥ KIc(min)

dKapplied/dt > 0

7.7.1.2 Crack Initiation Resistance 

Model 

Our model of the resistance of ferritic steels to 

cleavage crack initiation includes the following 

characteristics: 

• a temperature dependency of fracture 

toughness that is universal to all ferritic 

steels and is uninfluenced by irradiation 

• a scatter in fracture toughness that is 

universal to all ferritic steels and is not 

influenced by irradiation 

• a finite lower bound to the distribution of 

(scatter in) crack initiation toughness values 

(i.e., a value of fracture driving force below 

which cleavage fracture cannot occur) 

• an irradiation damage model that recognizes 

that the effects of irradiation are purely 

athermal (i.e., affecting only the position of 

the fracture toughness transition curve on 

the temperature axis) 

These characteristics are all motivated by an 

understanding of the physical processes 

responsible for cleavage fracture. While the 

numerical coefficients of our model are obtained 

empirically (i.e., obtained by fitting toughness 

data) the functional forms of the fits are 

physically motivated. This physical basis 

provides an additional benefit in that it helps 

provide assurance that the models apply to all 
7-10

conditions of interest (i.e., to a variety of RPV 

steels and welds subject to range of irradiation 

conditions. 

Our physical understanding of cleavage fracture 

also provides important guidance regarding how 

the uncertainty in fracture toughness should be 

modeled. Specifically, it is recognized that the 

distribution of non-coherent particles throughout 

the BCC iron lattice establishes the scatter in KIc

and KJc data [Natishan 01, EricksonKirk 04]. 

It is possible, at least in principle, to know if a 

non-coherent particle exists at a particular point 

in the matrix, or not. This might suggest an 

epistemic nature to KIc and KJc scatter, were it 

not for the fact that KIc and KJc do not exist as 

point properties. KIc and KJc values always have 

an associated size scale, that being the 

plastically deformed volume. Upon loading, 

the presence of the crack elevates the stress state 

along the entire length of the crack front to the 

point that dislocations begin to move in the 

surrounding volume of material, which contains 

a distribution of dislocation barriers (e.g., noncoherent particles, grain boundaries, twin 

boundaries, etc.). Sufficient accumulation of 

dislocations at a barrier can elevate the local 

stress-state sufficiently to initiate a crack in the 

barrier, and, if the criteria for fracture are 

satisfied, propagate the crack through the entire 

surrounding test specimen or structure. Thus, 

the existence of a particular dislocation barrier at 

a particular location does not control KIc and KJc. 

Rather KIc and KJc are controlled by the 

distribution of these barriers throughout the 

lattice, and how this distribution interacts with 

the elevated stresses along the crack front. Since 

the distribution of these barriers throughout the 

lattice is random and occurs at a size-scale 

below that considered by the crack initiation 

toughness model, the uncertainty in KIc and KJc

is irreducible. For this reason, the uncertainty in 

KIc is modeled as aleatory in FAVOR 

[Williams]. 

Beyond the aleatory uncertainty in KIc, our 

model of crack initiation toughness accounts for 

uncertainties in both the model and in the input 

parameters that are epistemic in nature. The 

major epistemic model uncertainty is the RTNDT

bias correction, which is discussed in the next 

section, because this represents a major change 

in the crack initiation model relative to that 

adopted in previous investigations of PTS. 

Epistemic uncertainties in input data (i.e., Cu, 

Ni, and P content, initial RTNDT, and unirradiated CVN upper-shelf energy) are 

accounted for and propagated through the 

FAVOR calculation. While the mean values of 

these distributions are the values the licensees 

have docketed [RVID2], the statistical 

distributions assumed to exist around these mean 

values were derived from all data available for 

the entire population of RPV-grade ferritic steels 

and their weldments. Consequently, these 

distributions overestimate (sometimes 

significantly so) the degree of uncertainty in 

these input variables relative to that which 

would characterize a particular weld, plate, or 

forging that would exist in the beltline of a 

particular PWR. While plant-specific studies 

might appropriately adopt less-scattered 

distributions, we have used generic distributions 

of the input variables to support our goal of 

developing a revision to 10 CFR 50.61 that 

applies to all PWRs. 

7.7.2 Major Changes 

In this section, we summarize the major changes 

between the calculational models adopted here 

and those used to support the current version of 

10 CFR 50.61. 

7.7.2.1 Fracture Driving Force Model 

As discussed in Section 7.7.1.1, our models 

incorporate the effects of WPS, whereas 

previous studies of PTS have not. Adopting a 

WPS model can reduce the TWCF estimated for 

certain classes of transients. For example, the 

TWCF estimated for a primary side pipe break 

will be significantly smaller when the effects of 

WPS are considered, while the TWCF estimated 

for a stuck-open valve that recloses later during 

the transient (thereby repressurizing the primary 

system) may not be affected by WPS at all. In 

plant analyses of Oconee Unit 1 based on a 

complete set of transients (i.e., considering the 

potential for vessel failure from all potential PTS 
7-11

precursors), inclusion of WPS in the model 

reduces the estimated TWCF by between a 

factor of 21⁄2 and 3 [Dickson 03]. Dickson’s 

results show that while the degree of “benefit” 

associated with adopting a WPS model depends 

on the transients considered to produce PTS risk 

it is reasonably insensitive to the degree of 

embrittlement. 

7.7.2.2 Crack Initiation Resistance 

Model 

Relative to the models used in the studies that 

established the technical basis to the current PTS 

Rule [SECY-82-465, ORNL 85a, ORNL 85b, 

ORNL 86], our model has the following major

differences (see [EricksonKirk-PFM] for a 

comprehensive discussion of all differences): 

(1) Consideration of Systematic Material 

Property and Fluence Variations throughout 

the Beltline Region: In previous studies, the 

known systematic variations of material 

properties and fluence throughout the 

beltline region were treated in a highly 

simplified fashion. Specifically, the effect 

of radiation damage on each major region 

(i.e., each plate, weld, or forging) of the 

vessel was assessed assuming that the entire 

region was subjected to the maximum 

fluence occurring anywhere in the region. 

This approach led to significant 

overpredictions of the embrittlement of the 

vessel, and consequent overestimates of the 

PTS risk. These conservatisms are absent 

from our model. 

(2) Treatment of Fracture Toughness Scatter as 

Aleatory: The aleatory model of fracture 

toughness uncertainty described in 

Section 7.7.1.2 differs from the epistemic 

treatment of toughness uncertainty adopted 

in all pervious probabilistic studies of PTS. 

In these studies the result of a particular trial 

in the calculation was the prediction that the 

vessel had or had not failed. While this 

epistemic treatment is inconsistent with our 

current understanding of the physics of 

cleavage fracture, the difference in the mean 

TWCF estimates produced by these two 

different approaches is small (all other 

factors being held constant). 

(3) RTNDT Bias Correction: While the 

restrictions on model development detailed 

in Section 3.1.1 require that the basis of our 

model be non-toughness metrics (i.e., 

RTNDT) our model recognizes that RTNDT is 

not a direct measure of the fracture 

toughness transition temperature. Indeed 

RTNDT is by intention a conservative 

approximation to the true fracture toughness 

transition temperature, overestimating this 

value (an implicit conservatism) by 65°F 

(18°C) on average, and up to 200°F (93°C) 

in some cases. Our model removes this 

conservative bias (on average), but in the 

process, introduces a non-physical model 

uncertainty. This model uncertainty, which 

cannot be removed as long as we rely on 

RTNDT -based metrics, should be regarded as 

an implicit conservatism in our results. This 

bias correction significantly reduces the 

estimated annual through-wall cracking 

frequency. 

7.7.2.3 Method for Estimating Vessel 

Crack Initiation Probability 

from the Probability of 

Initiation of Individual Cracks 

in the Vessel 

Our treatment of the uncertainty in crack 

initiation fracture toughness (KIc) as aleatory 

necessitates use of a different methodology for 

estimating the probability of crack initiation in 

the vessel from the probabilities of initiation of 

the many individual cracks throughout the vessel 

from that adopted in the calculations used in 

[SECY-82-465]§§. In previous probabilistic 

studies of PTS, the uncertainty in KIc was 

modeled as being epistemic, meaning that for 

any individual simulation, there existed a single 

value of KIc. Consequently, if the probabilistic 

computer code simulated that the applied 

fracture driving force (Kapplied) resulting from a 

PTS transient ever exceeded KIc for any of the 

 

§§ The discussion in this section also applies to the 

mathematical combination the probability of 

individual cracks propagating through-wall to 

estimate the probability of the vessel developing 

a through-wall crack. 
7-12

flaws in the vessel, the vessel failure probability 

was set to 1 (a certainty) and further calculations 

for that vessel were not performed because a 

vessel cannot fail twice. When KIc uncertainty 

is correctly modeled as being aleatory (as it is in 

our model), a different approach is needed 

because the result of each simulation run is not 

vessel non-failure (probability 0) or vessel 

failure (probability 1), but rather vessel 

non-failure (probability 0) or vessel failure 

probability (0 < probability ≤ 1; in practical 

terms vessel failure probability is usually a very 

small number that is not close to 1). In this 

situation, the appropriate representation of the 

vessel failure probability is the complement 

(meaning the difference from 1) of the joint 

(meaning combined) probability of non-failure 

of all of the flaws in the vessel [Fang 03], which 

can be expressed mathematically as follows: 

Eq. 7-2 ∏( ) =

−−=

n

j

PFAIL VESSEL P jFAIL

1

)( )( 11

where n is the total number of flaws simulated to 

exist in the pressure vessel. This equation can 

be stated in words as follows: the probability 

that the vessel will fail is 1 minus the probability 

that all of the cracks in the vessel do not fail, or, 

even more simply: in order for the vessel to not 

fail all of the cracks in it must not fail. 

During the many public meetings that have been 

held during the course of the PTS reevaluation 

project, concerns have been expressed that this 

methodology for estimating the vessel failure 

probability is both inappropriate and overly 

conservative. The following alternative 

probability formula has been proposed: 

Eq. 7-3 ( ))(

1

)( jFAIL

n

j

PFAIL VESSEL MAX P ==

This equation states that the failure probability 

of the vessel is the maximum of the individual 

failure probabilities associated with the many 

individual cracks in the vessel. The 

appropriateness of Eq. 7-2 rather than Eq. 7-3 

when estimating the total probability associated 

with system failures (vessels) that might result 

from many individual causes (cracks) can be 

easily understood by way of analogy. Consider 

the “system” to be an individual human life and 

consider the “failure” to be death. Below, we 

provide two examples to illustrate the 

differences between Eq. 7-2 and Eq. 7-3, and the 

appropriateness of Eq. 7-2: 

Example 1: Hypothetical individual #1 leads a 

very controlled life and (so) is subject to only 

one cause of death (cancer). The individual’s 

annual risk of dying of cancer is 2%. In this 

situation, this individual’s total annual risk of 

death is estimated to be 2% by either Eq. 7-2 or 

by Eq. 7-3. 

Example 2: Hypothetical individual #2 is less 

careful than hypothetical individual #1 and (so) 

is at risk from more than one cause of death. 

The individual’s annual risk of dying from any 

one of four causes is as follows: cancer=2%, 

AIDS=1%, skydiving=1⁄2%, gunshot=1⁄4%. 

Clearly individual #2 has a greater annual death 

risk than individual #1, yet Eq. 7-3 estimates 

their annual death risks to be identical: 

MAX(2%, 1%, 1⁄2%, 1⁄4%), or 2%. Conversely, 

Eq. 7-2 estimates individual #2’s annual death 

risk to be {1-(1-0.02)*(1-0.01)*(1-0.005)*(1-

0.0025)}, or 3.7%. 

It can also be noted that for the particular 

situation of interest here (PTS-induced failures 

of nuclear RPVs containing cracks), the 

numerical differences between the failure 

probabilities estimated by Eq. 7-2 and Eq. 7-3 is 

actually very small because, as illustrated in 

Figure 7.5, for the great majority of the time, 

only one crack in a vessel has a probability of 

through-wall cracking that exceeds zero. It was 

for this reason, that Meyer assessed the 

differences between Eq. 7-2 and Eq. 7-3 to be 

practically insignificant [Meyer 03]. 
7-13

0

25

50

75

100

0 2 4 6 8 10

Number of Flaws Having a 

Conditional Probability of 

Through Wall Cracking Above 0

% of Vessels Simulated

Figure 7.5. Number of flaws simulated that have 

a conditional probability of throughwall cracking that exceeds zero 

(Oconee at 60 EFPY). 

7.8 Through-Wall Cracking Model 

Provided that the results of a particular trial for a 

particular simulated flaw result in an estimation 

of CPI > 0, FAVOR will check to see how far 

the simulated crack will propagate into the 

vessel wall before it arrests permanently (if it 

arrests at all). The through-wall cracking model 

is itself composed of the following component 

models: 

• Fracture driving force 

o LEFM driving force 

• Crack growth resistance 

o cleavage crack arrest 

o upper shelf ductile tearing model 

o property gradient model 

The probability of through-wall cracking is 

determined by comparing the fracture driving 

force (Kapplied) to the resistance to further crack 

growth, which is expressed as a value of 

cleavage crack arrest toughness (KIa). 

Additionally, once a propagating crack has 

arrested the potential for re-initiation at some 

later time in the transient is assessed relative to 

the material’s resistance to crack initiation in 

either cleavage (KIc) or by ductile tearing 

(K{JIc}, and the associated J-R curve). For each 

simulation where FAVOR calculates a value of 

CPI > 0, it then conducts 100 deterministic 

through-wall cracking analyses. The outcome of 

each of these deterministic simulations is either 

that the crack propagates all the way through the 

thickness of the vessel***, or that the crack 

arrests before it reaches the outer diameter. The 

percentage of the trials that result in throughwall cracking is then multiplied by the CPI

value to estimate the CPTWC. 

In the following two subsections, we discuss the 

key features of the through-wall cracking model 

(Section 7.8.1) and the major differences 

between our model and that used in previous 

investigations of PTS risk (Section 7.8.2) 

[SECY-82-465, ORNL 85a, ORNL 85b, ORNL 

86]. These sections address only the crack 

growth resistance models because the fracture 

driving force models are the same as used for 

crack initiation. [EricksonKirk-PFM] provides 

a detailed discussion of the through-wall 

cracking model. 

7.8.1 Key Features 

Our model of the resistance of ferritic steels to 

through-wall cracking includes both a cleavage 

crack arrest model and a model for re-initiation 

of a crack by ductile tearing on the upper 

shelf†††. These models include the following 

characteristics: 

• Crack arrest toughness model 

o a temperature dependency of crack 

arrest toughness that is universal to all 

ferritic steels and is not influenced by 

irradiation 

o a scatter in crack arrest toughness that is 

universal to all ferritic steels and is not 

influenced by irradiation 

 

*** In practice, when the crack extends 90% of the 

way through the wall thickness the vessel is 

considered to have failed. 

††† The through-wall cracking model also accounts 

for the possibility of re-initiation in cleavage, but 

for these purposes the crack initiation model 

described previously in Section 7.7 is used. 
7-14

o a finite lower bound to the distribution 

of (scatter in) crack arrest toughness 

values (i.e., a value of fracture driving 

force below which cleavage fracture 

cannot occur) 

o a model that positions the crack arrest 

transition temperature depending on the 

crack initiation transition temperature, 

and recognizes that the temperature 

differential between the crack initiation 

and crack arrest transition temperatures 

depends on the amount of prior 

hardening (i.e., irradiation damage) 

experienced by the material 

• Upper shelf ductile initiation and tearing 

model 

o a temperature dependency of uppershelf toughness that is universal to all 

ferritic steels and is not influenced by 

irradiation 

o a scatter in upper-shelf toughness that is 

universal to all ferritic steels and is not 

influenced by irradiation 

o a linkage between the magnitude of the 

fracture toughness on the upper shelf 

and the fracture toughness transition 

temperature 

These characteristics are all motivated by an 

understanding of the physical processes 

responsible for both cleavage crack arrest and 

for ductile crack initiation on the upper shelf. 

While the numerical coefficients of our models 

are obtained empirically (i.e., obtained by fitting 

toughness data), the functional forms of the fits 

are physically motivated. This physical basis 

provides an additional benefit in that it helps 

provide assurance that the models apply to all 

conditions of interest (i.e., to a variety of RPV 

steels and welds subject to range of irradiation 

conditions). 

Our physical understanding of both cleavage 

crack arrest and of ductile crack initiation also 

provides important guidance regarding how the 

uncertainty in fracture toughness should be 

modeled. As was the case for cleavage crack 

initiation toughness, it is recognized that the 

physical processes responsible for both cleavage 

crack arrest and for ductile crack initiation make 

the uncertainty in these toughness values 

aleatory in nature [EricksonKirk-PFM], and it is 

so modeled in FAVOR [Williams]. 

7.8.2 Major Changes 

Relative to the models used in the studies that 

established the technical basis to the current PTS 

Rule [SECY-82-465, ORNL 85a, ORNL 85b, 

ORNL 86], our model has the following major

differences (see [EricksonKirk-PFM] for a 

comprehensive discussion of all differences): 

(1) Allowance of Ductile Tearing and Inclusion 

of Crack Arrest Resistance at Kapplied Values 

Above 200 ksi√in (220 MPa√m): In all 

former studies of PTS (including our own 

study reported in [Kirk 12-02]) the 

resistance to crack arrest was truncated at 

200 ksi√in (220 MPa√m) because this is the 

highest value allowed by the ASME code 

KIa curve. However, ample evidence from 

large-scale experiments exists demonstrating 

that crack arrest above 200 ksi√in (220 

MPa√m) does occur, indicating the 

inappropriateness and over-conservatism of 

the 200 ksi√in (220 MPa√m) limit. 

Moreover, no allowance was ever made in 

former studies of the possibility for an 

arrested crack to re-initiate by ductile tearing 

on the upper shelf despite the fact that the 

resistance to crack initiation on the upper 

shelf ranges between 100 and 200 ksi√in 

(110-220 MPa√m) for ferritic RPV steels 

both before and after irradiation. We have 

eliminated this apparent oversight in our 

through-wall cracking model. As shown in 

Figure 7.6, the combined effect of these two 

changes is a reduction in the TWCF by a 

factor of 4–5 (at lower levels of 

embrittlement) down to a reduction factor of 

~1.5 as embrittlement increases. Allowing 

cracks to arrest at Kapplied values above 

200 ksi√in has resulted in cracks being 

arrested at shallower depths, which in turn 

makes re-initiation by either cleavage or 

ductile fracture more difficult. Thus, 

removing the conservatism of the 200 ksi√in 

(220 MPa√m) limit on KIa more than 
7-15

compensated for the non-conservatism 

associated with assuming that re-initiation in 

a ductile mode cannot occur. 

(2) A Separation between the KIc and KIa Curves 

that Depends on the Degree of Irradiation 

Embrittlement: In all studies of PTS risk 

predating this reevaluation, the temperature 

separation between the KIc and KIa transition 

curves was held fixed irrespective of the 

material condition, as has always been the 

practice for the ASME KIc and KIa curves. 

However, because ferritic steels harden to an 

absolute limit [Wagenhofer 01], the 

separation between the two curves depends 

upon the degree to which the material is 

hardened, with more hardened (more 

irradiated) materials having smaller 

separations [Kirk 02a]. This is also 

supported by ample empirical evidence 

[Wallin 98b]. We have not performed a 

sensitivity study to assess the effect of this 

model change. However, comparison of the 

temperature differential between the KIc and 

KIa curves adopted by our current model (see 

curve of Figure 7.7) with the constant 

temperature differential of ~30°C (~86°F) 

previously assumed (i.e., the temperature 

separation between the ASME KIc and KIa

curves) demonstrates our new model 

reduces the crack arrest capacity of higher 

toughness materials (i.e., materials having a 

To value of ~60°C (~140°F) or less) because 

the greater KIc to KIa curve separation 

adopted by our model reduces the of value 

of KIa at a fixed KIc. Conversely, the crack 

arrest capacity of more embrittled materials 

(i.e., materials having a To value of ~60°C 

(~140°F) or more) is greater in our model 

than it is in the ASME model. 

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

0 100 200 300 400

RT NDT * [o

F]

Mean TWCF / Year

Beaver (F03.1), Old Thru-Wall Propagation Model

Beaver (F03.1), New Thru-Wall Propagation Model

Palisades (F03.1), Old Thru-Wall Propagation Model

Palisades (F03.1), New Thru-Wall Propagation Model

Figure 7.6. Combined effects of allowing KIa to 

exceed 200 ksi√in and allowing for 

ductile crack re-initiation on the 

upper shelf. Open points show 

TWCF results when KIa is allowed to 

exceed 200 ksi√in and ductile crack 

re-initiation is permitted. RTNDT* is 

defined in [Kirk 12-02]. 

0

50

100

150

-200 -100 0 100 200

T o [o

C]

∆RTARREST = 

TKIa - To [

oC]

 All Wallin Data

 HSST 02, 72W, 73W

Figure 7.7. Comparison of temperature 

separation between crack initiation 

and crack arrest toughness 

transition curves assumed in our 

current calculations (blue curve) 

with the constant separation of 

~30°C (~86°F) assumed by previous 

calculations 

Separation of ASME 

KIc and KIR Curves 
7-16

7.9 Probabilistic Fracture 

Mechanics Code FAVOR 

7.9.1 Implementation of PFM Model 

As shown in Figure 7.8, FAVOR is composed of 

three computational modules: (1) a deterministic 

load generator (FAVLoad), (2) a Monte Carlo 

PFM module (FAVPFM), and (3) a postprocessor (FAVPost). Figure 7.8 also indicates 

the nature of the data streams that flow through 

these modules. 

Figure 7.8. FAVOR data streams flow through 

three modules: (1) FAVLoad, (2) 

FAVPFM, and (3) FAVPost 

FAVLoad takes as input the time histories of 

pressure, temperature, and heat transfer 

coefficient defined by the RELAP TH analysis. 

These inputs are used along with a 1D transient 

heat conduction equation to estimate the timedependent variation of temperature through the 

vessel wall. These time-dependent temperature 

profiles are used, along with the RELAP 

pressure history, in a linear elastic stress analysis 

to estimate the time history of applied-KI, which 

is passed to FAVPFM for further analysis. 

The FAVPFM module implements the logical 

specification of the PFM model within a series 

of nested loops illustrated in Figure 7.9. These 

loops step through the TH time history and 

implement the Monte-Carlo trials necessary to 

estimate the conditional probabilities of crack 

initiation and of though wall cracking. The 

probabilities estimated by FAVOR (complete 

with uncertainties) are conditional in the sense 

that, within the FAVPFM module, the TH 

transients are assumed to occur. 

The FAVPFM module provides the capability to 

model the variation of radiation damage in the 

beltline region of an RPV with as much detail as 

the analyst considers necessary. Only that 

portion of the beltline that is proximate to the 

active core need be modeled because the fastneutron flux, and thus the radiation damage, 

drops to nearly zero within a foot beyond the 

fuel region. Within this region (active core 

±1-ft. (0.3-m), the vessel is represented as a 

combination of “major regions,” with each 

major region representing a different plate, weld, 

or forging each having (potentially) a unique 

combination of mean copper content, mean 

nickel content, mean phosphorus content, and 

unirradiated RTNDT. Each major region may be 

divided into as many “sub-regions” as the 

analyst feels are necessary to represent 

accurately both the axial and azimuthal variation 

of fluence. Sufficient discretization is adopted 

so that each sub-region is effectively subjected 

to the same fluence throughout. In this way, the 

complex variation of embrittlement throughout 

the vessel wall that is caused by variations in 

both material and radiological conditions is 

represented to the model. It should be noted that 

this material/radiological model is a 

considerably more accurate representation of 

reality than the models adopted in the 

calculations performed to support SECY-82-465 

and the IPTS studies. In these earlier 

calculations, the entire vessel was presumed to 

be made out of the most irradiation-sensitive 

material, and all of this material was assumed to 

be subjected to the peak fluence that occurred 

anywhere in the vessel. 

The last FAVOR module, FAVPost, combines 

the conditional initiation and through-wall 

cracking probabilities and combines these, 

through a matrix multiplication, with the 

frequency histograms for each TH sequence 

provided by the PRA analyses. In this way, the 

complete distribution of TWCF (per operating 

year) is estimated. 
7-17

Figure 7.9. Flow chart for improved PFM model implemented in FAVPFM showing the four primary 

nested loops – (1) RPV Trial Loop, (2) Flaw Loop, (3) Transient Loop, and (4) Time Loop
7-18

7.9.2 Discretization of the Reactor 

Pressure Vessel 

FAVOR utilizes discretizes the RPV beltline 

into one “major regions” for each axial weld, 

circumferential weld, plate, and forging. The 

major regions are further subdivided into isofluence “subregions.” To model accurately the 

complex variation of fluence with azimuth and 

axial location (see Figure 7.10) a large number 

of sub-regions was necessary (15280, 19651, 

and 67076 subregions for Beaver Valley, 

Oconee, and Palisades, respectively). The 

neutron fluence maps were provided for 32 and 

40 EFPY were used, and were linearly 

extrapolated to estimate fluence for longer 

operational durations. 

Figure 7.10. Rollout diagram of beltline materials and representative fluence maps for Oconee Unit 1 

7.10 Experimental Validation of 

Linear Elastic Fracture 

Mechanics 

Extensive experimental/analytical investigations 

performed at ORNL during the 1970s and 1980s 

examined the accuracy with which LEFM 

models could be expected to predict the failure 

of nuclear RPVs subjected to both simple 

loadings (pressure only) and to much more 

complex loadings (PTS conditions) [Cheverton 

85a, Cheverton 85b]. These investigations all 

featured tests on thick-section pressure vessels 

(see Figure 7-11), and aimed to reproduce, 

as closely as practical in a laboratory setting, the 

conditions that characterize thermal shock of a 

nuclear RPV. These conditions include the 

following: 

• fracture initiation from small flaws 

• severe thermal, stress, and material 

toughness gradients 

• biaxial loading 

• effects of cladding (including residual 

stresses) 

• conditions under which warm pre-stress may 

be active 
7-19

• combined stress and toughness gradient 

conditions that can promote crack initiation, 

arrest, re-initiation, and re-arrest all during 

the same transient 

• due to these various gradients, the 

possibility of conversion of fracture mode 

from cleavage to ductile and back again all 

during the same TH transient 

The three test series were as follows: 

• The first series of tests employed ten 

intermediate test vessels (ITVs), three with 

cracks located at a cylindrical nozzle and 

seven with cracks located remote from any 

geometric discontinuities. These tests were 

aimed at investigating the ability of LEFM 

to predict the fracture response of thick 

section vessels containing relatively deep 

flaws (20 to 83% of the 6-in. (152.4 mm) 

vessel wall) at test temperatures ranging 

from lower shelf to upper shelf. A variety of 

nuclear grade RPV plates, forgings, and 

weldments were tested. 

• The second series of tests comprised eight 

thermal-shock experiments (TSEs). The 

purpose of these experiments was to 

investigate the behavior of surface cracks 

under thermal-shock conditions similar to 

those that would be encountered during a 

large-break loss of coolant accident 

(LBLOCA) (i.e., a rapid cooldown in the 

absence of internal pressure). 

• The third series of tests included two 

experiments that subjected ITV specimens 

to concurrent pressure and thermal 

transients. These “pressurized thermal 

shock experiments,” or PTSEs, sought to 

simulate the effects of a rapid cooldown 

transient combined with significant internal 

pressure. Thus, these experiments simulated 

TH conditions characteristic of smaller 

break LOCAs. 

These investigations support the following 

conclusions: 

• ITV Experiments: 

o LEFM analyses very closely predicted 

actual fracture pressures for thick-wall 

pressure vessels. 

o Methods for calculating fracture 

toughness from small specimens were 

successfully used in applications of 

fracture analysis of thick flawed vessels. 

• Thermal Shock Experiments (TSEs): 

o Multiple initiation-arrest events with 

deep penetration into the vessel wall 

were predicted and observed. 

o Surface flaws that were initially short 

and shallow were predicted and 

observed to grow considerably in length 

before increasing significantly in depth. 

o Warm pre-stress was observed to limit 

crack extension through the wall under 

LOCA conditions. 

o Small-specimen fracture mechanics data 

successfully predicted the fracture 

behavior of thick pressure vessels. 

o Crack arrest occurred in a rising stress 

field. 

• Pressurized Thermal Shock Experiments 

(PTSEs): 

o Warm pre-stress is effective at inhibiting 

crack initiation for conditions under 

which crack initiation would otherwise 

be expected (i.e., Kapplied > KIc). 

o Crack arrest toughness values (KIa) 

inferred from conditions prototypic of 

PTS loading agree well with other 

experimental measurements, suggesting 

the transferability of laboratory 

toughness data to structural loading 

conditions. 
7-20

o LEFM predictions of crack initiation, 

growth, and arrest behavior successfully 

captured the response of the vessel to 

the transient; however some details were 

not exactly predicted (two initiation-runarrest events were predicted whereas 

one was observed). 

With regard to this final bullet item, it should be 

noted that exact agreement between 

deterministic predictions and individual 

experiments cannot be expected when the 

physical processes that underlie those 

experiments produce large aleatory uncertainties 

(as is the case with KIc and KIa data; see 

Sections 7.7.1.2 and 7.8.1, respectively). Such 

disagreement does not in itself condemn the 

methodology, but rather reveals that the 

precision of any single prediction is limited by 

the precision in our knowledge of the controlling 

material properties. 

Figure 7-11. Test vessels used in the ITV and 

PTSE test series (top) and in the 

TSE test series (bottom) 
8-1

8 Vessel Failure Frequencies Estimated for Oconee Unit 1, 

Beaver Valley Unit 1, and Palisades 

8.1 Chapter Structure 

In this chapter, we describe the results of our 

probabilistic calculations for Oconee Unit 1, 

Beaver Valley Unit 1, and Palisades. 

Section 8.2 details the plant-specific features of 

each analysis, including both methodology and 

input variables. In Section 8.3, we present the 

values of frequency of crack initiation (FCI) and 

through-wall cracking frequency (TWCF) that 

we have estimated for these three plants, and we 

discuss the characteristics of the distributions 

from which these values are derived. 

In Section 8.4, we examine the material features 

that contribute most significantly, and those that 

do not contribute at all, to the magnitude of the 

FCI and TWCF values. A key output of this 

section is a methodology to express the 

embrittlement level of different plants on an 

equivalent basis. In Section 8.5, we both 

identify the classes of transients (e.g., LOCAs, 

MSLBs, and so on) that contribute most 

significantly, and those that do not contribute 

at all, to the level of PTS challenge at a 

particular plant. Using this information along 

with methodology developed in Section 8.4 

allows us to determine if plant-specific factors 

need to be considered when assessing the level 

of challenge posed to plants by different 

transient classes. The chapter concludes with 

Section 8.6, which summarizes our findings and 

indicates factors that need to be considered if 

these findings are to be considered generally 

applicable to all PWRs. Issues of general 

applicability are examined in more detail in 

Chapter 9. 

8.2 Plant-Specific Features of 

Analysis 

8.2.1 PRA 

8.2.1.1 Analysis Methodology 

In the case of both the Oconee and Beaver 

Valley PRA analyses, NRC contractors were 

responsible for both constructing the PRA 

models and binning the overcooling sequences 

into “case” sequences. The PRA models were 

constructed from scratch, largely based on 

information learned from the 1980s PTS work, 

but with numerous improvements. The HRA 

portion of the PRA was also initially performed 

by the NRC contractors. The corresponding 

licensees provided information about each plant 

and answered both written and verbal questions 

as the PRA model and the PRA/HRA evolved. 

In each case, two plant visits took place: one 

early in the process to gather plant information, 

and a second when interim results were available 

to allow licensee review and input. 

In contrast, the PRA/HRA analysis for Palisades 

derived mostly from an existing licensee PRA 

model that already included overcooling 

sequences. NRC contractors provided 

comments on the existing PRA model, a model 

that was subsequently modified by the licensee 

in response to these comments. Once the 

revised PRA model was satisfactory to both the 

licensee and NRC contractors, the HRA portion 

of the analysis was conducted as a collaborative 

effort. This HRA information was included in 

the Palisades PRA model, and sequence binning

and frequency estimates were subsequently 

performed primarily by the licensee with NRC 

contractor review, input, and slight modification. 

Two plant visits were also conducted for the 

Palisades analysis: the first for initial project and 
8-2

plant familiarization, and the second for 

conducting the collaborative HRA. As for the 

other two plant analyses, numerous discussions 

were held between the Palisades staff and NRC 

Contractors as the PRA model and PRA/HRA 

evolved. Hence, while the same overall 

approach was followed to construct all three 

PRA/HRA models, the origin of these models 

and the key personnel responsible for 

constructing them varied from plant-to-plant 

8.2.1.2 Inputs 

The plant-specific PRAs described in Section 

8.2.1.1 led to the definition of a master list of 

thermal-hydraulic transients. A sub-set of these 

transients from this list was defined as the “base 

case” for each plant, which represents our best 

mathematical description of the conditions at the 

plant that could produce a PTS challenge to 

vessel integrity. TH cases from the master list 

were eliminated from the base case for a number 

of reasons, including the following: 

• Certain transients were binned together, 

making some TH runs redundant, or 

• Sensitivity studies revealed that certain TH 

cases did not need to be passed on, or 

• The minimum temperature remained above 

400°F (204°C) within the first ≈170 minutes. 

Experience gained from previous analysis of 

PTS has repeatedly demonstrated that 

transients need to be at least this severe to 

make any contribution at all to the 

calculated through-wall cracking frequency. 

Later examination of TWCF estimates for 

all base case transients revealed that many 

transients having lower minimum 

temperatures still made no contribution to 

TWCF, thus demonstrating the 

appropriateness of this screening limit. 

The details of each plant-specific PRA are 

summarized in other reports [KolaczkowskiOco, Whitehead-BV, Whitehead-Pal]. 

Appendix A provides the master list of transients 

for all three plants, and also lists the frequency 

values for the base-case transients. 

8.2.2 TH 

This section describes the RELAP5 models 

developed for the Oconee-1, Beaver Valley Unit 1, 

and Palisades plants. The TH analysis 

methodology is similar for the three plants. 

In each case, the best available RELAP5 input 

model was used as the starting point to expedite 

the model development process. For Oconee, 

the base model was that used in the code scaling, 

applicability and uncertainty (CSAU) study. For 

Beaver Valley, the base model was the H.B. 

Robinson-2 model used in the original PTS 

study in the mid 1980s. This model was revised 

by Westinghouse to reflect the Beaver Valley 

plant configuration. For Palisades, the base 

model was obtained from Nuclear Management 

Corporation, the operators of the Palisades plant. 

This model was originally developed and 

documented by Siemens Power Corporation to 

support analysis of the loss of electrical load 

event for Palisades. 

The RELAP5 models for the Oconee, Beaver 

Valley, and Palisades plants are detailed 

representations of the power plants and include 

all major components for both the primary and 

secondary plant systems. RELAP5 heat 

structures are used throughout the models to 

represent structures such as the fuel, vessel wall, 

vessel internals, and steam generator tubes. The 

reactor vessel nodalization includes the 

downcomer, lower plenum, core inlet, core, core 

bypass, upper plenum and upper head regions. 

Plant-specific features, such as the reactor vessel 

vent valves, are included as appropriate. 

The downcomer model used in each plant 

utilizes a two-dimensional nodalization. This 

approach was used to capture the possible 

temperature variation in the downcomer due to 

the injection of cold ECCS water into each of 

the cold legs. Capturing this temperature 

variation in the downcomer is not possible with 

the original one-dimensional downcomer. In the 

revised models, the downcomer is divided into 

six azimuthal regions for each plant. 

The safety injection systems modeled for the 

Oconee, Palisades, and Beaver Valley plants 

include high-pressure injection (HPI), 
8-3

low-pressure injection (LPI), other ECCS 

components (e.g., accumulators, core flood tanks 

(CFTs), safety injection tanks (SITs) depending 

on the plant designation), and makeup/letdown, 

as appropriate. 

The secondary coolant system models include 

steam generators, main and auxiliary/emergency 

feedwater, steam lines, safety valves, main 

steam isolation valves (as appropriate), and 

turbine bypass and stop valves. 

Each of the models was updated to reflect the 

current plant configuration including updating 

system setpoints (to best estimate values) and 

modifying control logic to reflect current 

operating procedures. Other changes to the 

models include the addition of control blocks to 

calculate parameters for convenience or 

information only (e.g., items such as minimum 

downcomer temperature). The Oconee, Beaver 

Valley, and Palisades models were then 

initialized to simulate hot full power and hot 

zero power plant operation for the purpose of 

establishing satisfactory steady-state conditions 

from which the PTS transient event sequence 

calculations are started. 

In RELAP5 simulations of LOCA event 

sequences for the Oconee and Palisades plants 

during which all of the reactor coolant pumps 

are tripped and the loss of primary coolant 

system inventory is sufficient to interrupt 

coolant loop natural circulation flow, a 

circulating flow was observed between the two 

cold legs on the same coolant loop. The 

circulations mix coolant in the reactor vessel 

downcomer, cold leg and SG outlet plenum 

regions. These RELAP5 cold-leg circulations 

were originally reported during the first PTS 

evaluation study [Fletcher 84, Spiggs 85] and 

are significant for the PTS application. When 

the circulation is present the calculated reactor 

vessel downcomer fluid temperature benefits 

from the warming effects created by mixing the 

cold HPI fluid with the warm steam generator 

outlet plenum fluid. When the circulation is not 

present the calculated reactor vessel downcomer 

fluid temperature more directly feels the 

influence of the cold HPI fluid. Note that both 

the Oconee and Palisades plants have a “2x4" 

configuration with two cold legs and one hot leg 

in each coolant loop. In contrast, the Beaver 

Valley plant has a single hot and cold leg per 

coolant loop and this type of circulating flow is 

not seen. (See Section 6.3.2 for a further 

discussion of this issue.) 

Certain experiments used in the assessment 

exhibited apparent indications of cold leg 

circulations very similar to those simulated with 

RELAP5. However, the experimental evidence 

was not judged to be conclusive and concerns 

(related to circulation initiation and the 

scalability of the behavior from the sub-scale 

experiment to full-scale plant configurations) 

remain regarding the veracity of these 

circulations. Because of these concerns and 

because the effect of including cold leg 

circulations in the RELAP5 simulations is 

nonconservative for PTS (i.e., it results in 

warmer reactor vessel downcomer 

temperatures), same-loop cold leg circulations 

were prevented in the RELAP5 PTS plant 

simulations for LOCA events. The cold leg 

circulations were prevented by implementing 

large reverse flow loss coefficients (1.0E5, 

based on the cold leg pipe flow area) in the 

reactor coolant pump regions of the RELAP5 

model. The model change is implemented at the 

time during the event sequence when the reactor 

coolant pump coast-down is complete. 

A tabulation of the key parameters for the three 

study plants relevant to PTS is presented in 

Table 8.1, while [Arcieri-Base] explains the TH 

models in detail. 

8.2.3 PFM 

A separate report [Dickson-Base] provides full 

details of the plant-specific input values for each 

of the three plants. These inputs include the 

following: 

• Composition and Mechanical Property Data: 

As detailed in Section 7.7.1.2 of this report 

and in Appendix D of [EricksonKirk-PFM] 

FAVOR models the uncertainty in the input 

variables of Cu, Ni, P, unirradiated RTNDT, 

and unirradiated Charpy upper shelf energy. 

The data on which the distributions that 
8-4

FAVOR samples are based are drawn from 

all data available for the entire population 

of RPV-grade ferritic steels and their 

weldments. Consequently, these 

distributions overestimate (sometimes 

significantly so) the degree of uncertainty in 

these input variables relative to that 

characteristic of a particular weld, plate, or 

forging in a particular PWR. The mean 

values of Cu, Ni, P, unirradiated RTNDT, and 

unirradiated Charpy upper shelf energy 

about which these distributions are located 

are modeled as being specific to the 

particular welds, plates, and forgings in the 

particular plants. These input values, which 

are summarized in Table 8.2 are drawn from 

the NRC’s Reactor Vessel Integrity 

Database [RVID2]. RVID2 was developed 

based on information obtained from licensee 

responses to NRC Generic Letter 92-01, 

Revision 1 and its 1995 supplement 

[GL9201R1, Strosnider 94, GL9201R1S1]. 

GL-92-01 was issued to resolve questions 

arising out of the staff’s review of the 

Yankee Rowe PWR in the early 1990s. In 

reviewing the licensee’s submittal, the staff 

noted that chemical composition and 

reference temperature information was not 

available for the specific materials from 

which Yankee was constructed. To prevent 

occurrence of this problem at other plants 

GL-92-01 required licensees to provide to 

the NRC all of their vessel-specific 

composition and mechanical property data. 

The 1995 supplement to GL-92-01 

[GL9201R1S1] continued and broadened 

this data collection effort when the staff 

noted that licensees were not always able to 

consider all pertinent data in their submittals 

because of both proprietary issues associated 

with some data sets and because no single 

source of all the material property data 

needed to support reactor vessel integrity 

evaluations existed. As the consolidation of 

all the data obtained in response to GL-92-

01 Rev. 1 (and its 1995 supplement) the 

information in RVID2 (and, consequently, 

in Table 8.2) provides a sound basis for the 

compositional and mechanical property 

models adopted in FAVOR. 

• Flaw Data: As described in Section 7.5 and 

detailed by [Simonen], flaw distributions 

have been derived that apply to domestic 

PWRs in general. Nonetheless, these 

distributions have certain plant-specific 

aspects. Table 8.3 summarizes the variables 

that quantify the plant-specific features of 

the flaw distribution, and the basis for these 

variables. 

• Locations of Welds, Plates, and Forgings 

within the Vessel Beltline, and Fluence: 

Plant-specific information is needed 

regarding the spatial arrangement of the 

different welds, plates, and forgings and on 

the variation of fluence throughout the 

beltline region of the vessels. Figure 8.1 

provides an example of such information for 

Oconee Unit 1; see [Dickson-Base] for full 

details. Information regarding the spatial 

arrangement of the different welds, plates, 

and forgings is taken from construction 

drawings while fluence estimates are based 

on RG1.190 procedures. (See Section 7.6 of 

this report and [EricksonKirk-PFM] for 

details.) 

Only those factors discussed above are defined 

on a plant-specific basis in this analysis. All 

other features not mentioned are justified as 

generic and treated as such. Details on models 

and variables treated generically can be found in 

Chapter 7, as well as in [EricksonKirk-PFM, 

EricksonKirk-SS]. 

8.3 Estimated Values of FCI and 

TWCF 

This section begins with a presentation of our 

estimates of the annual frequencies of crack 

initiation (FCI) and through-wall cracking 

(TWCF) resulting from PTS for our three study 

plants for a range of embrittlement conditions 

(Section 8.3.1). We then examine the 

characteristics of the distributions that underlie 

these FCI and TWCF values (Section 8.3.2). 
8-5

8.3.1 Overall Results 

Table 8.4 presents FAVOR Version 04.1 

estimates of the mean annual FCI and mean 

annual TWCF for Oconee Unit 1, Beaver Valley 

Unit 1, and Palisades at 32 and 60 EFPY‡‡‡. 

To estimate values of these metrics close to the 

TWCF limit of 1x10-6 events/year proposed in 

Chapter 10, it was necessary to increase the 

amount of irradiation damage beyond that likely 

during operational lifetimes currently considered 

possible. To do so, we performed analyses for 

some very long operating lifetimes (designated 

as Ext-A and Ext-B in the table), thereby 

increasing the fluence and, consequently, the 

irradiation damage. The range of irradiation 

exposures examined includes conditions both 

below and above the current 10 CFR 50.61 

RTPTS screening limits. 

The results in Table 8.4 demonstrate that even at 

the end of license extension (60 operational 

years, or 48 EFPY at an 80% capacity factor) the 

mean estimated through-wall cracking frequency 

(TWCF) does not exceed 2x10-8/year. 

Considering that the Beaver Valley and 

Palisades RPVs are constructed from some of 

the most irradiation-sensitive materials in 

commercial reactor service today, these results 

suggest that, provided operating practices do not 

change dramatically in the future, the operating 

reactor fleet is in little danger of exceeding the 

TWCF acceptance criterion of 5x10-6/yr 

expressed by Regulatory Guide 1.154 [RG 

1.154]§§§, even after license extension. 

 

‡‡‡ The table also includes a number of different 

reference temperature metrics, the significance 

of which is discussed in Section 8.4. 

§§§ Specifically, Section 9 of Regulatory Guide 

1.154 makes the following statement: “This 

Regulatory Guide outlines the analyses that 

should be performed in support of any request to 

operate at RTPTS values in excess of 270°F ... 

and states that the staff’s primary acceptance 

criterion will be licensee demonstration that 

through-wall cracking frequency will be below 

5x10-6 per reactor year for such operation.” 

8.3.2 Distribution Characteristics 

To present our analysis results for all three 

plants in as compact a format as possible, we 

report only mean values of FCI and TWCF in 

Table 8.4. Nonetheless, since a systematic 

treatment of uncertainties is key to our objective 

of developing a risk-informed revision to 

10 CFR 50.61, it is important to examine the 

characteristics of the distributions that underlie 

these mean values. As illustrated in Figure 8.2 

using Beaver Valley as a characteristic example, 

the TWCF distributions are both very broad and 

highly skewed toward zero. As described in the 

following sections, both the skewness and the 

spread in these results are expected because both 

of these characteristics result directly from the 

physical features of cleavage fracture. 

8.3.2.1 Skewness in the TWCF 

Distribution 

The skewness in the TWCF distributions 

illustrated in Figure 8.2 results directly from the 

physical nature of cleavage crack initiation and 

arrest. The crack initiation (KIc) and crack arrest 

(KIa) toughness distributions both have finite 

lower bound values that are physically justified 

[EricksonKirk-PFM]. The following three 

mathematical conditions all lead to a likelihood 

of through-wall cracking that is zero by 

definition (not just a very small number): 

• If the applied-KI value for a particular 

FAVOR simulation run (i.e., a particular 

crack in a particular location subjected to a 

particular TH transient) never exceeds the 

0th percentile KIc value, then the crack has 

zero probability of crack initiation and 

(consequently) zero probability of throughwall cracking. 

• If the applied-KI value for a particular 

simulation run exceeds the 0th percentile KIc

value, but exceeds it at a time when the 

applied-KI value is dropping with time (i.e., 

dKI/dt ≤ 0), then warm pre-stress has 

occurred and the crack has zero probability 

of crack initiation and (consequently) zero 

probability of through-wall cracking. 
8-6

• If the applied-KI value for a particular 

simulation run exceeds the minimum KIc at a 

time when the applied-KI value is increasing 

with time (i.e., dKI/dt > 0), then the crack 

has a non-zero probability of crack 

initiation. However, if while the crack is 

propagating through the RPV wall, the 

applied-KI value falls below the minimum 

KIa value then the crack arrest must occur. 

Such a crack would provide no contribution 

to the through-wall cracking frequency. 
8-7

Table 8.1. Summary of Plant Parameters Relevant to the PTS Evaluation 

Description Oconee Beaver Valley Palisades

Reactor thermal 

power 

2568 MWt 2660 MWt 2530 MWt

Primary code 

safety valve 

opening pressure

17.34 MPa (2515 psia) 17.27 MPa (2505 

psia)

Three valves with 

staggered opening 

setpoints of 17.24, 17.51 

and 17.79 MPa (2500, 

2540 and 2580 psia).

Primary code 

safety valve 

capacity

Two valves each with a 

capacity of 43.47 kg/s 

(345,000 lbm/hr) at 16.89 

MPa (2450 psia).

Three valves each 

with a capacity of 

62.77 kg/s (498,206 

lbm/hr) at 17.24 MPa 

(2500 psia).

Three valves each with a 

capacity of 28.98 kg/s 

(230,000 lbm/hr) at 17.75 

MPa (2575 psia).

Pressurizer 

PORV opening 

pressure

17.0 MPa (2465 psia) The first PORV is 

controlled by a 

compensated error 

signal. The error 

[pressurizer pressure 

– 15.51 MPa (2250 

psia) is processed 

with a proportional 

plus integral 

controller. This 

PORV begins to 

open when the 

compensated error is 

> 0.69 MPa (100 psi) 

and closes when the 

compensated 

pressure error < 0.62 

MPa (90 psi). The 

second and third 

PORVs open when 

the pressurizer 

pressure is > 16.2 

MPa (2350 psia) and 

close when pressure 

< 16.1 MPa (2340 

psia).

Two valves, both with an 

opening setpoint 

pressure of 16.55 MPa 

(2400 psia). Note that 

closed block valves 

prevent the function of 

pressure relief through 

these valves during 

normal plant operation.

PORV capacity Estimated flow rate is 

16.03 kg/s (127,000 

lbm/hr) at 16.9 MPa 

(2450 psia).

Three valves each 

with a capacity of 

26.46 kg/s (210,000 

lbm/hr) at 16.2 MPa 

(2350 psia)

Two valves each with a 

capacity of 61.46 kg/s 

(487,800 lbm/hr) at 16.55 

MPa (2400 psia).
8-8

Description Oconee Beaver Valley Palisades

LPI injection 

actuation setpoint

3.89 MPa (550 psig). SIAS signal: 

pressurizer pressure 

< 12.72 MPa (1845 

psia), high steamline 

DP (steamline 

pressure < header 

pressure by 0.69 

MPa (100 psi) or 

more), or steamline 

pressure < 3.47 MPa 

(503 psia).

Pressurizer pressure less 

than 10.98 MPa (1593 

psia) with a 27-second 

time delay.

LPI pump shutoff 

head 

1.48 MPa (214 psia) 1.48 MPa (214.7 

psia)

1.501 MPa (217.7 psia).

LPI pump runout 

flow

504.5 kg/s (1110 lbm/s) 

total for two pumps. 

313.4 kg/s (690.84 

lbm/s) total for the 

three loops.

433.5 kg/s (955.7 lbm/s) 

total for the four loops.

HPI injection 

actuation setpoint

11.07 MPa (1605 psia) SIAS signal: 

pressurizer pressure 

<12.72 MPa (1845 

psia), high steamline 

DP (steamline 

pressure < header 

pressure by 0.69 

MPa (100 psi) or 

more), or steamline 

pressure <3.47 MPa 

(503 psia).

Pressurizer pressure less 

than 10.98 MPa (1593 

psia) with a 27-second 

time delay.

HPI pump shutoff 

head 

> 18.61 MPa (2700 psia) >17.93 MPa (2600 

psia)

8.906 MPa (1291.7 psia).

HPI pump runout 

flow

80.9 kg/s (178.2 lbm/s) 

total for the four loops.

61.12 kg/s (134.7 

lbm/s) total for the 

three loops.

86.49 kg/s (190.7 lbm/s) 

total for the four loops.

Reactor coolant 

pump trip setpoint

No automatic trips on the 

reactor coolant pump. 

Operator is assumed to 

trip RCPs at 0.28 K 

(0.5EF) subcooling.

No automatic trips on 

the reactor coolant 

pumps. Operator is 

assumed to trip 

RCPs when the 

differential pressure 

between the RCS 

and the highest SG 

pressure was less 

than 2.59 MPa (375 

psig).

No automatic pump trips. 

Procedures instruct the 

operators to trip two 

RCPs (one in each loop) 

if pressurizer pressure 

falls below 8.96 MPa 

(1300 psia) and to trip all 

pumps if RCS subcooling 

falls below 13.9 K (25EF) 

or if containment 

pressure exceeds 0.127 

MPa (18.4 psia).

SG safety valve 

bank opening 

pressure

The lowest relief valve 

setpoint is 6.76 MPa 

(980 psia).

The lowest relief 

valve setpoint is 7.51 

MPa (1090 psig).

The lowest MSSV 

opening setpoint 

pressure is 7.097 MPa 

(1029.3 psia).

SG atmospheric 

steam dumps 

opening criteria

Not included in the 

RELAP5 model. 

Opening pressure of 

7.24 MPa (1050 

psia).

Open to control the RCS 

average temperature to 

551 K (532EF)
8-9

Description Oconee Beaver Valley Palisades

Number of main 

steam isolation 

valves

None. One per steam line. One per steam line.

Location of 

steamline flow 

restrictors

None. Located in SG outlet 

nozzles. 

Located in SG outlet 

nozzles.

Isolation of 

turbine-driven 

EFW/AFW pump 

during MSLB

Isolated during MSLB by 

isolation circuitry

Requires manual 

operator action and 

would be done if 

needed to maintain 

SG level

Requires manual 

operator action and 

would be done if needed 

to maintain SG level.

Analyzed range of 

SI water 

temperature 

Base case model 

assumptions for HPI and 

LPI nominal feed 

temperature is 294.3 K 

(70°F). CFT temperature 

is 299.8 K (80°F). 

Sensitivity cases for 

ECCS temperature due 

to seasonal variation: 

Summer Conditions 

 HPI, LPI - 302.6 K 

(85°F) 

 CFT - 310.9 K (100°F) 

Winter Conditions 

 HPI, LPI - 277.6 K 

(40°F) 

 CFT - 294.3 K (70°F) 

Base case model 

assumptions for HPI 

and LPI nominal feed 

temperature is 

283.1 K (50°F). CFT 

temperature is 

305.4 K (90°F). 

Sensitivity cases for 

ECCS temperature 

due to seasonal 

variation: 

Summer Conditions 

HPI, LPI – 285.9 K 

(55°F) 

CFT – 313.7 K 

(105°F) 

Base case model 

assumptions for HPI and 

LPI nominal feed 

temperature is 304.2 K 

(87.9°F). SIT 

temperature is 310.9 K 

(100°F). 

Sensitivity cases for 

ECCS temperature due 

to seasonal variation: 

Summer Conditions 

 HPI, LPI - 310.9 K 

(100°F) 

 SIT - 305.4 K (90°F) 

Winter Conditions 

 HPI, LPI - 277.6 K 

(40°F) 

 SIT - 288.7 K (60°F) 

Refueling water 

storage tank 

water volume 

Borated water storage 

tank water volume is 

327,000 gallons 

(1,237,695 l) 

Tank's useable 

volume is between 

1627.7 and 1669.4 

m3

 (430,000 and 

441,000 gallons).

889.5 m3 (235,000 

gallons)

Containment 

spray actuation 

setpoint and flow 

rate

Total containment spray 

flow rate is 3,000 gpm 

(11355 lpm (1500 

gpm/pump, 5678 

lpm/pump) 

Total containment 

spray flow is 334.4 

liter/s (5300 gpm)

Containment spray is 

activated on high 

containment pressure at 

0.127 MPa (18.4 psia). 

Total containment spray 

rate is 229.8 liters/s 

(3643 gpm).

CFT/accumulator 

water volume

2 tanks each with a water 

volume of 28,579 liters 

(7550 gallons)

3 accumulators each 

with a liquid volume 

of 29,299 liters (7740 

gallons)

4 SITs each with a water 

volume of 29450 liters 

(7780 gallons).

CFT/SIT/ 

accumulator 

discharge 

pressure

4.07 MPa (590 psia) 4.47 MPa (648 psia) 1.48 MPa (214.7 psia)
8-10

Table 8.2. Plant specific material values drawn from the RVID2 database [RVID2] 

RTNDT(u) [

o

F] Composition(2)

Product 

Form Heat Beltline σflow(u)

 [ksi] RTNDT(u)

Method 

RTNDT(u)

Value 

σ(u)

Value Cu Ni P 

USE(u) 

[ft-lb] 

Beaver Valley 1, (Designer: Westinghouse, Manufacturer: CE) 

Coolant Temperature = 547°F, Vessel Thickness = 7-7/8-in. 

C4381-1 INTERMEDIATE SHELL B6607-1 83.8 MTEB 5-2 43 0 0.14 0.62 0.015 90

C4381-2 INTERMEDIATE SHELL B6607-2 84.3 MTEB 5-2 73 0 0.14 0.62 0.015 84

C6292-2 LOWER SHELL B7203-2 78.8 MTEB 5-2 20 0 0.14 0.57 0.015 84

PLATE 

C6317-1 LOWER SHELL B6903-1 72.7 MTEB 5-2 27 0 0.2 0.54 0.01 80

305414 LOWER SHELL AXIAL WELD 

20-714 LINDE 75.3 Generic -56 17 0.337 0.609 0.012 98

1092 

WELD 305424 INTER SHELL AXIAL WELD 19-

714 79.9 Generic -56 17 0.273 0.629 0.013 112

LINDE 

0091 

WELD 

90136 CIRC WELD 11-714 76.1 Generic -56 17 0.269 0.07 0.013 144

Oconee 1, (Designer and Manufacturer: B&W) 

Coolant Temperature = 556°F, Vessel Thickness = 8.44-in.

FORGING AHR54 

(ZV2861) LOWER NOZZLE BELT (4) B&W Generic 3 31 0.16 0.65 0.006 109

C2197-2 INTERMEDIATE SHELL (4) B&W 

Generic 1 26.9 0.15 0.5 0.008 81

C2800-1 LOWER SHELL (4) B&W 

Generic 1 26.9 0.11 0.63 0.012 81

C2800-2 LOWER SHELL 69.9 B&W 

Generic 1 26.9 0.11 0.63 0.012 119

C3265-1 UPPER SHELL 75.8 B&W 

Generic 1 26.9 0.1 0.5 0.015 108

PLATE 

C3278-1 UPPER SHELL (4) B&W 

Generic 1 26.9 0.12 0.6 0.01 81

1P0962 INTERMEDIATE SHELL AXIAL 

WELDS SA-1073 79.4 B&W Generic -5 19.7 0.21 0.64 0.025 70

299L44 INT./UPPER SHL CIRC WELD 

(OUTSIDE 39%) WF-25 (4) B&W Generic -7 20.6 0.34 0.68 (3) 81

61782 NOZZLE BELT/INT. SHELL CIRC 

WELD SA-1135 (4) B&W Generic -5 19.7 0.23 0.52 0.011 80

71249 INT./UPPER SHL CIRC WELD 

(INSIDE 61%) SA-1229 76.4 ASME NB2331 10 0 0.23 0.59 0.021 67

72445 UPPER/LOWER SHELL CIRC 

WELD SA-1585 (4) B&W Generic -5 19.7 0.22 0.54 0.016 65

8T1762 LOWER SHELL AXIAL WELDS 

SA-1430 75.5 B&W Generic -5 19.7 0.19 0.57 0.017 70

8T1762 UPPER SHELL AXIAL WELDS SA1493 (4) B&W 

Generic -5 19.7 0.19 0.57 0.017 70

LINDE 80 

WELD 

8T1762 LOWER SHELL AXIAL WELDS 

SA-1426 

75.5 B&W 

Generic -5 19.7 0.19 0.57 0.017 70

Palisades, (Designer and Manufacturer: CE) 

Coolant Temperature = 532°F, Vessel Thickness = 81⁄2-in.

A-0313 D-3803-2 (4) MTEB 5-2 -30 0 0.24 0.52 0.01 87

B-5294 D-3804-3 (4) MTEB 5-2 -25 0 0.12 0.55 0.01 73

C-1279 D-3803-3 (4) ASME NB2331 -5 0 0.24 0.5 0.011 102

C-1279 D-3803-1 74.7 ASME NB2331 -5 0 0.24 0.51 0.009 102

C-1308A D-3804-1 (4) ASME NB2331 0 0 0.19 0.48 0.016 72

PLATE 

C-1308B D-3804-2 (4) MTEB 5-2 -30 0 0.19 0.5 0.015 76
8-11

RTNDT(u) [

o

F] Composition(2)

Product 

Form Heat Beltline σflow(u)

 [ksi] RTNDT(u)

Method 

RTNDT(u)

Value 

σ(u)

Value Cu Ni P 

USE(u) 

[ft-lb] 

LINDE 

0124 

WELD 

27204 CIRC. WELD 9-112 76.9 Generic -56 17 0.203 1.018 0.013 98

34B009 LOWER SHELL AXIAL WELD 3-

112A/C 76.1 Generic -56 17 0.192 0.98 (3) 111

W5214 LOWER SHELL AXIAL WELDS 3-

112A/C 72.9 Generic -56 17 0.213 1.01 0.019 118

LINDE 

1092 

WELD 

W5214 INTERMEDIATE SHELL AXIAL 

WELDS 2-112 A/C 72.9 Generic -56 17 0.213 1.01 0.019 118

Notes:

(1) Information taken directly from the July 2000 release of the NRC’s Reactor Vessel Integrity 

(RVID2) database. 

(2) These composition values are as reported in RVID2. In FAVOR calculations these values should 

be treated as the central tendency of the Cu, Ni, and P distributions detailed in [EricksonKirk-PFM]. 

(3) No values of phosphorus are recorded in RVID2 for these heats. A generic value of 0.012 should 

be used, which is the mean of 826 phosphorus values taken from the surveillance database used 

by Eason et al. to calibrate the embrittlement trend curve. 

(4) No values strength measurements are available in PREP4 for these heats [PREP]. A value of 

77 ksi should be used, which is the mean of other flow strength values reported in this Table.
8-12

Table 8.3. Summary of vessel specific inputs for the flaw distribution 

Variable Oconee Beaver 

Valley Palisades Calvert Cliffs Notes 

Inner Radius (to cladding) [in] 85.5 78.5 86 86 Vessel specific info 

Base Metal Thickness [in] 8.438 7.875 8.5 8.675 Vessel specific info 

Total Wall Thickness [in] 8.626 8.031 8.75 8.988 Vessel specific info 

Variable Oconee Beaver 

Valley Palisades Calvert Cliffs Notes 

Volume fraction [%] 97% 100% - SMAW% - REPAIR% 

Thru-Wall Bead 

Thickness [in] 0.1875 0.1875 0.1875 0.1875 All plants report plant-specific 

dimensions of 3/16-in. 

Truncation Limit [in] 1 

Judgment. Approx. 2X the 

size of the largest non-repair 

flaw observed in PVRUF & 

Shoreham. 

Buried or Surface -- All flaws are buried Observation 

Orientation -- Circ flaws in circ welds, axial flaws in axial 

welds. 

Observation: Virtually all of 

the weld flaws in PVRUF & 

Shoreham were aligned with 

the welding direction because 

they were lack of sidewall 

fusion defects. 

Density basis -- Shoreham density Highest of observations 

Aspect ratio 

basis -- Shoreham & PVRUF observations 

Statistically similar 

distributions from Shoreham 

and PVRUF were combined 

to provide more robust 

estimates, when based on 

judgment the amount data 

were limited and/or 

insufficient to identify different 

trends for aspect ratios for 

flaws in the two vessels. 

SAW 

Weld 

Depth basis -- Shoreham & PVRUF observations 

Statistically similar 

distributions combined to 

provide more robust 

estimates 

Variable Oconee Beaver 

Valley Palisades Calvert Cliffs Notes 

Volume fraction [%] 1% 

Upper bound to all plantspecific info provided by 

Steve Byrne (Westinghouse – 

Windsor). 

Thru-Wall Bead 

Thickness [in] 0.21 0.20 0.22 0.25 

Oconee is generic value 

based on average of all 

plants specific values 

(including Shoreham & 

PVRUF data). Other values 

are plant-specific as reported 

by Steve Byrne. 

SMAW 

Weld 

Truncation Limit [in] 1 

Judgment. Approx. 2X the 

size of the largest non-repair 

flaw observed in PVRUF & 

Shoreham. 
8-13

Buried or Surface -- All flaws are buried Observation 

Orientation -- Circ flaws in circ welds, axial flaws in axial 

welds. 

Observation: Virtually all of 

the weld flaws in PVRUF & 

Shoreham were aligned with 

the welding direction because 

they were lack of sidewall 

fusion defects. 

Density basis -- Shoreham density Highest of observations 

Aspect ratio 

basis -- Shoreham & PVRUF observations 

Statistically similar 

distributions from Shoreham 

and PVRUF were combined 

to provide more robust 

estimates, when based on 

judgment the amount data 

were limited and/or 

insufficient to identify different 

trends for aspect ratios for 

flaws in the two vessels. 

Depth basis -- Shoreham & PVRUF observations 

Statistically similar 

distributions combined to 

provide more robust 

estimates 

Variable Oconee Beaver 

Valley Palisades Calvert Cliffs Notes 

Volume fraction [%] 2% 

Judgment. A rounded 

integral percentage that 

exceeds the repaired volume 

observed for Shoreham and 

for PVRUF, which was 1.5%. 

Thru-Wall Bead 

Thickness [in] 0.14 

Generic value: As observed 

in PVRUF and Shoreham by 

PNNL. 

Truncation Limit [in] 2 

Judgment. Approx. 2X the 

largest repair flaw found in 

PVRUF & Shoreham. Also 

based on maximum expected 

width of repair cavity. 

Buried or Surface -- All flaws are buried Observation 

Orientation -- Circ flaws in circ welds, axial flaws in axial 

welds. 

The repair flaws had complex 

shapes and orientations that 

were not aligned with either 

the axial or circumferential 

welds; for consistency with 

the available treatments of 

flaws by the FAVOR code, a 

common treatment of 

orientations was adopted for 

flaws in SAW/SMAW and 

repair welds. 

Repair 

Density basis -- Shoreham density Highest of observations 
8-14

Aspect ratio 

basis -- Shoreham & PVRUF observations 

Statistically similar 

distributions from Shoreham 

and PVRUF were combined 

to provide more robust 

estimates, when based on 

judgment the amount data 

were limited and/or 

insufficient to identify different 

trends for aspect ratios for 

flaws in the two vessels. 

Depth basis -- Shoreham & PVRUF observations 

Statistically similar 

distributions combined to 

provide more robust 

estimates 

Variable Oconee Beaver 

Valley Palisades Calvert Cliffs Notes 

Actual Thickness [in] 0.188 0.156 0.25 0.313 Vessel specific info 

# of Layers [#] 1 2 2 2 Vessel specific info 

Bead Width [in] 1 

Bead widths of 1 to 5-in. 

characteristic of machine 

deposited cladding. Bead 

widths down to 1⁄2-in. can 

occur over welds. Nominal 

dimension of 1-in. selected 

for all analyses because this 

parameter is not expected to 

influence significantly the 

predicted vessel failure 

probabilities. May need to 

refine this estimate later, 

particularly for Oconee who 

reported a 5-in bead width. 

Truncation Limit [in] Actual clad thickness rounded to the nearest 

1/100th of the total vessel wall thickness 

Surface flaw 

depth in FAVOR [in] 0.259 0.161 0.263 0.360 

Judgment & computational 

convenience 

Buried or Surface -- All flaws are surface breaking 

Judgment. Only flaws in 

cladding that would influence 

brittle fracture of the vessel 

are brittle. Material properties 

assigned to clad flaws are 

that of the underlying 

material, be it base or weld. 

Orientation -- All circumferential. 

Observation: All flaws 

observed in PVRUF & 

Shoreham were lack of interrun fusion defects, and 

cladding is always deposited 

circumferentially 

Density basis -- 

No surface flaws observed. Density is 

1/1000th that of the observed buried flaws in 

cladding of vessels examined by PNNL. If 

there is more than one clad layer then there 

are no clad flaws. 

Judgment 

Aspect ratio 

basis -- Observations on buried flaws Judgment 

Cladding 

Depth basis -- 

Depth of all surface flaws is the actual clad 

thickness rounded up to the nearest 1/100th

of the total vessel wall thickness. 

Judgment. 
8-15

Variable Oconee Beaver 

Valley Palisades Calvert Cliffs Notes 

Truncation Limit [in] 0.433 

Judgment. Twice the depth 

of the largest flaw observed in 

all PNNL plate inspections. 

Buried or Surface -- All flaws are buried Observation 

Orientation -- Half of the simulated flaws are 

circumferential, half are axial. 

Observation & Physics: No 

observed orientation 

preference, and no reason to 

suspect one (other than 

laminations which are benign. 

Density basis -- 1/10 of small weld flaw density, 1/40 of large 

weld flaw density of the PVRUF data 

Judgment. Supported by 

limited data. 

Aspect ratio 

basis -- Same as for PVRUF welds Judgment 

Plate 

Depth basis -- Same as for PVRUF welds Judgment. Supported by 

limited data. 

Figure 8.1. Rollout diagram of beltline materials and representative fluence maps for Oconee 
8-16

Table 8.4. Mean crack initiation and through-wall cracking frequencies estimated for Oconee Unit 1, 

Beaver Valley Unit 1, using FAVOR Version 04.1 

Axial Weld Fusion Line 

Reference Temperatures 

[

o

F] 

Reference 

Temperatures 

Evaluated at 

Max Fluence 

on Vessel ID 

[

o

F] Plant EFPY1 RTPTS

[

o

F] 2

Max 

RTNDT

in an 

Axial 

Weld 

Max 

RTNDT

in a 

Plate 

Weld 

Length 

Weighted 

Max 

RTNDT

Plate Circ 

Weld 

Mean 

FCI 

[events/

year] 

Mean 

TWCF 

[events/ 

year] 

32 221 152 76 134 79 175 1.29E-10 2.30E-11

60 250 171 86 149 89 193 1.02E-09 6.47E-11

Ext-Oa 323 232 131 200 136 251 1.01E-07 1.30E-09 Oconee 

Ext-Ob 329 263 161 227 170 281 5.24E-07 1.16E-08

32 280 155 192 171 243 83 1.32E-07 8.89E-10

60 299 175 210 188 272 102 5.19E-07 4.84E-09

Ext-Ba 308 188 225 203 301 121 1.71E-06 2.02E-08

Beaver 

Valley 

Ext-Bb 312 207 250 226 354 155 8.87E-06 3.00E-07

32 283 212 180 210 189 201 5.22E-08 4.90E-09

60 311 230 196 227 205 215 1.23E-07 1.55E-08

Ext-Pa 358 277 246 271 259 254 7.46E-07 1.88E-07 Palisades 

Ext-Pb 372 333 316 324 335 301 4.47E-06 1.26E-06

1. All plants were analyzed for operational durations of 32 and 60 EFPY (or 40 and 75 operational 

years, respectively, at an 80% capacity factor. Each plant was also analyzed at two extended 

embrittlement levels (Ext-Oa and Ext-Ob for Oconee, for example) with the aim of obtaining 

mean through-wall cracking frequency values closer to the 1x10-6 limit proposed in Chapter 10. 

2. RTPTS is defined as per the equations and procedures of 10 CFR 50.61. Limiting materials in 

Oconee, Beaver Valley, and in Palisades are circumferential weld SA-1229, plate 6317-1, and 

axial weld 2-112 A/C, respectively. 

In practice, these mathematical conditions are 

satisfied most of the time in the Monte Carlo 

simulations conducted using FAVOR (78% of 

the time in Beaver Valley at 32 EFPY, for 

example) because the simulated crack is small, 

the simulated toughness is high, and the 

simulated TH transient does not produce a very 

severe stress state in the RPV wall. However, 

on rare occasions, a larger crack will be 

simulated in a lower toughness material and 

subjected to a more severe transient. In these 

situations, the likelihood of developing a 

through-wall crack is higher. However, this 

combined sampling of the upper tails of many 

distributions happens only rarely. 

8.3.2.2 Large Spread in the TWCF 

Distribution 

The TWCF distributions illustrated in Figure 8.2 

are very broad, spanning three or mode orders of 

magnitude from minimum to maximum. This 

characteristic again relates to the physics of 

cleavage fracture. As discussed in Section 

8.3.2.1, the absolute lower bounds associated 

with both the KIc and KIa distributions leads to a 

large number of the Monte Carlo simulations 

producing a through-wall cracking probability 

that is, by definition, zero. However, on rare 

occasions, the tails of many distributions are 

sampled in the same simulation run, resulting in 

a larger crack being simulated to occur in a 

lower toughness material. This combined 
8-17

possibility of both zero and higher probabilities 

of TWCF leads to TWCF distributions that are 

naturally broad. As illustrated in Figure 8.2, 

the TWCF distributions tend to compress as the 

plants age because the more embrittled materials 

in these plants are less likely to produce 

through-wall cracking frequencies that are either 

very low, or zero. 

0.00

0.25

0.50

0.75

1.00

1E-11 1E-09 1E-07 1E-05 1E-03

Thru-Wall Cracking Frequency, TWCF

% Contribution to TWCF

16.5 95 2.3

78.4% at Zero

78.4% at

TWCF=0

Figure 8.2. Typical distribution of through-wall 

cracking frequency (as calculated 

for Beaver Valley at 32 EFPY 

(blue circles) and for extended 

embrittlement conditions 

(red diamonds) 

0

10

20

30

40

50

60

70

80

90

100

100 200 300 400

Maximum RTNDT Along Axial Weld 

Fusion Line [o

F]

Percentile of Mean TWCF Value

Oconee

Beaver Valley

Palisades

Figure 8-3. TWCF distribution percentile 

corresponding to the mean value 

Because of the skewness characteristic of the 

TWCF distributions, the mean values reported in 

Table 8.4 do not lie close to the median value of 

the underlying distributions. In fact, as 

illustrated in Figure 8-3, mean TWCF values 

generally correspond to the ~90th percentile (and 

usually higher) over the range of embrittlement 

studied. Thus, the mean TWCF values are 

appropriately used to establish a revised PTS 

screening limit suitable for regulatory use. 

8.4 Material Factors Contributing 

to FCI and TWCF 

This section begins (in Section 8.4.1) with a 

discussion of the flaws simulated by FAVOR to 

exist in the RPV and the toughness properties 

that control the behavior of those flaws (i.e., if 

the flaw initiates, if the flaw propagates through 

the RPV wall). These considerations lead to 

several proposed “reference temperature 

metrics” that are can be used to correlate and/or 

predict the likelihood of fracture occurring in the 

various regions (axial weld, circumferential 

weld, plate) of the RPV beltline. We then 

discuss (in Section 8.4.2) the contribution of the 

various RPV beltline regions to the estimated 

FCI and TWCF values. In Section 8.4.3, we 

propose a procedure that accounts, at least 

approximately, for the different embrittlement 

levels in the three study plants to enable the 

comparison of similar transients at different 

plants presented in Section 8.5. We conclude in 

Section 8.4.4 with a discussion of how these 

results differ from those reported in December 

2002 [Kirk 12-02]. 

8.4.1 Flaws Simulated by FAVOR, and 

Reference Temperature Metrics 

When performing a structural flaw assessment, 

the location of the flaw or flaws being assessed 

needs to be known (along with many other 

factors) so that the resistance to fracture of the 

material at the flaw location can be either 

measured or estimated. The situation in this 

study differs somewhat from a routine flaw 

assessment because the flaws are simulated, and 

because hundreds upon thousands of flaws are 

being assessed. Nonetheless, the objective here 
8-18

is to correlate and/or predict the metrics that 

quantify the vessel’s resistance to fracture: 

CPI Conditional Probability of Crack 

Initiation. This is the probability that 

a crack will grow from its original 

size, conditioned on the assumed 

occurrence of a particular transient. 

CPTWC Conditional Probability of ThroughWall Cracking. This is the probability 

that a crack will grow from its original 

size to the point that it propagates 

completely through the vessel wall, 

conditioned on the assumed 

occurrence of a particular transient. 

FCI Frequency of Crack Initiation. This is 

the matrix product of the CPI value 

for each transient (including its 

uncertainty distribution) with the 

estimated frequency of that transient 

occurring (including its uncertainty 

distribution). FCI values are 

expressed per year. 

TWCF Through-Wall Cracking Frequency. 

This is the matrix product of the 

CPTWC value for each transient 

(including its uncertainty distribution) 

with the estimated frequency of that 

transient occurring (including its 

uncertainty distribution). TWCF 

values are expressed per year. 

In order to correlate and/or predict these metrics 

to quantify the vessel’s resistance to fracture, 

some measure of the resistance of the materials 

in the vessel to fracture at the location of these 

many flaws is needed. A reference temperature 

(RT) establishes the resistance of a material to 

fracture, the variability in this resistance, and 

how this resistance varies with temperature. 

As described in [EricksonKirk-PFM] and as 

illustrated schematically in Figure 8-4, 

a reference temperature is commonly thought of 

as positioning the cleavage fracture toughness 

transition curve on the temperature axis. 

However, because relationships exist that 

establish the position of the arrest transition 

curve and of the upper shelf curve with respect 

to the cleavage reference temperature 

(see [EricksonKirk-PFM] for a full discussion), 

the toughness of ferritic steels can be fully 

descried by this single reference temperature. 

Since RT values can be estimated from 

information on vessel materials available in the 

RVID database [RVID2] and from information 

available from surveillance programs 

implemented under Appendix H to 

10 CFR Part 50, they provide a way to estimate 

the resistance of vessel materials to fracture and 

how this resistance diminishes with increased 

neutron irradiation. 

Figure 8-5 illustrates the location and orientation 

of the flaws that are simulated to exist in the 

RPV and the relationship between these flaw 

locations and the azimuthal and axial variations 

of fluence. (See [EricksonKirk-PFM] and 

[Simonen] for a more detailed explanation of the 

technical bases for these flaw locations and 

orientations.) The information in Figure 8-5 

is summarized as follows for each of the 

simulated flaw populations: 
8-19

Temperature

Fracture Toughness

Ref Temp

Cleavage 

Fracture 

Toughness

Ductile (or Upper Shelf) 

Fracture Toughness

Arrest 

Fracture 

Toughness

Figure 8-4. Relationship between a reference temperature (RT) and various measure of resistance to fracture 

(fracture toughness). This is a schematic illustration of temperature dependence only; 

scatter in fracture toughness is not shown. 

• Embedded Axial Weld Flaws: The 

overwhelming majority of flaws in axial 

welds are lack of fusion defects, which 

occur on the weld fusion lines. 

Consequently, all of these flaws are oriented 

axially. The behavior of these flaws 

(i.e., if the flaw initiates, if the flaw 

propagates through the RPV wall) 

is controlled by the less tough of the plate 

or weld that lie on either side of the flaws. 

As illustrated in Figure 8-5, the axial fluence 

variation is relatively minor along most of 

the axial weld fusion line length. However, 

the large azimuthal fluence variation can 

expose each axial weld fusion line to have 

different fluences. The likelihood of vessel 

fracture from axial weld flaws depends upon 

(1) the total number of axial weld flaws 

(which scales with fusion line area), and 

(2) the fluence to which these flaws are 

subjected. Consequently, an appropriate 

metric to correlate/predict the likelihood of 

fracture from axial weld flaws would be 

weighted to account for variations in axial 

weld length and fluence level. 

Mathematically, the reference temperature 

metric for axial welds (RTAW) is defined as 

follows:

Eq. 8-1 

∑

∑

=

=

− ⋅

= nfl

i

i

FL

nafl

i

i

FL

i

AWMAX

AW

RT

RT

1

1

l

l

where 

nafl is the number of axial weld fusion lines in the vessel beltline region, 

lFL is the length of a particular fusion line in the vessel beltline region, and 

RTMAX-AW is evaluated for each of the axial weld fusion lines using the following formula. 

In the formula the symbol φtFL refers to the maximum fluence occurring along a 

particular axial weld fusion line, and ∆T30 is the shift in the Charpy V-Notch 

30-ft-lb energy produced by irradiation at φtFL. 

{( ( )) ( ( ) FL )} axialweld axialweld

FL uNDT

plate plate

AWMAX uNDT RT − ≡ RTMAX )( ∆+ 30 φ , RTtT )( ∆+ 30 φtT
8-20

• Embedded Circumferential Weld Flaws: 

The overwhelming majority of flaws in 

circumferential welds are lack of fusion 

defects, which occur on the weld fusion 

lines. Consequently, all of these flaws are 

oriented circumferentially. The behavior 

of these flaws (i.e., if the flaw initiates, 

if the flaw propagates through the RPV 

wall) is controlled by the less tough of the 

plate or weld that lie on either side of the 

flaws. As illustrated in Figure 8-5, the 

azimuthal fluence variation ensures that 

these circumferential weld cracks will 

somewhere be subjected to the maximum 

fluence that occurs anywhere on the vessel ID. 

Flaws are equally likely to occur at any 

position around the circumference of the 

RPV, and the initiation / propagation of 

fracture from such flaws is more likely 

at higher fluences. Consequently, an 

appropriate metric to correlate/predict the 

likelihood of fracture from circumferential 

weld flaws would be a weighted average of 

the largest RTNDT value associated with each 

circumferential weld fusion line when 

irradiated to the maximum ID fluence. 

Mathematically, the reference temperature 

metric for circumferential welds (RTCW) 

is defined as follows:

Eq. 8-2 ncfl

RT

RT

ncfl

i

i

CWMAX

CW

∑=

−

= 1

where 

ncfl is the number of circumferential weld fusion lines in the vessel beltline region, 

RTMAX-CW is evaluated for each of the circumferential weld fusion lines using the following 

formula. In the formula the symbol φtMAX refers to the maximum fluence 

occurring over the ID in the vessel beltline region, and ∆T30 is the shift in the 

Charpy V-Notch 30 ft-lb energy produced by irradiation at φtMAX. 

{( ( )) ( ( ) MAX )} circweld circweld

MAX uNDT

plate plate

CWMAX uNDT RT − ≡ RTMAX )( ∆+ 30 φ , RTtT )( ∆+ 30 φtT

It should be noted that at an equivalent 

embrittlement level, the likelihood of a 

circumferential weld flaw leading to 

through-wall cracking of the vessel is much 

lower than for an axial weld flaw. Even 

though circumferential and axial weld flaws 

are the same size because they are drawn 

from the same distribution, the variation of 

crack driving force through the wall of a 

cylindrical RPV differs considerably for 

circumferential and for axial flaws. 

Cheverton et al. describe how the 

application of a cold thermal shock to the 

inner diameter of a cylinder containing a 

flaw produces bending of the cylinder wall 

[Cheverton 85a]. This bending, originating 

from the contraction of the cold metal at and 

near the ID and the resistance to this 

contraction provided by the hotter metal 

deeper into the thickness of the cylinder, 

tends to be much larger for infinite length 

axial flaws than for infinite length 

circumferential flaws. A cylindrical 

geometry with an infinite axial flaw is 

asymmetric while a cylindrical geometry 

with an infinite circumferential flaw is 

symmetric. The asymmetry associated with 

the axial flaw degrades the cylinder's 

resistance to bending much more than the 

symmetric circumferential flaw (see Figure 8-6). 

It is for this reason that the applied-KI of an 

axially oriented flaw continues to increase 

for cracks extending much deeper into the 

vessel wall than does the applied-KI for a 

circumferentially oriented flaw (see Figure 

8.7). The driving force peak that occurs for 

circumferential cracks provides a natural 

crack arrest mechanism that occurs in all 

RPVs because of their cylindrical geometry. 

Conversely, the applied driving force for 

axial flaws continues to increase as their 

depth increases, which leads directly to the 

ability of axial flaws to propagate all the 

way through the RPV wall. 
8-21

A

A

B B

Azimuthal fluence variation along B-B

Axial fluence variation along A-A

Axial Weld: Embedded flaws 

occur only along fusion line 

(edges of region)

Circumferential Weld: Embedded flaws occur only 

along fusion line (edges of 

region)

Plate: Embedded flaws occur anywhere within region, axial or 

circumferential.

Cladding: Surface breaking 

defects occur anywhere within 

region, all circumferential

Figure 8-5. Location and orientation of flaws simulated by FAVOR to exist in different regions 

of the RPV beltline 

Figure 8-6. Effect of flaw orientation on the bending experienced by a cylinder 

subjected to a cold thermal shock on the inner diameter. 
8-22

 

0

100

200

300

400

500

600

0

0.5

1

1.5

2

2.5

0 50 100 150 200 250 300

coolant temperature (F) 

pressure (ksi) 

transient time (minutes) 

T(t) 

P(t) 

RPV through-wall location (inches) 

0 2 4 6 8 10

KI (ksi in1/2) 

0

50

100

150

200

250

300

350

400

KI for circumferentially oriented 

360 degree continuous inner surface 

breaking flaw 

KI for axially oriented 

infinite length inner surface 

breaking flaw 

Figure 8.7. Through-wall variation of crack driving force (KI): axially oriented flaws 

compared to circumferentially oriented flaws 

(Comparison is shown for an 8-inch diameter surge line break in Beaver Valley (Transient #7 – see top plot) 

at a time 11 minutes after the start of the transient (see bottom plot).) 
8-23

• Embedded Plate Flaws: Flaws in plates 

occur predominantly due to no-metallic 

inclusions. These can occur anywhere 

within the plate; they have no preferred 

orientation (i.e., they are equally likely to be 

axial or circumferential). As illustrated in 

Figure 8-5, the azimuthal fluence variation 

makes it certain that every plate will 

somewhere be subjected to the maximum 

fluence occurring on the vessel ID. Plate 

flaws are equally likely to occur at any 

position in the plate, so initiation / 

propagation of fracture from such flaws is 

more likely at higher fluences. 

Consequently, an appropriate metric to 

correlate / predict the likelihood of fracture 

from plate flaws would be a weighted 

average of the largest RTNDT value 

associated with each plate when irradiated to 

the maximum ID fluence. Mathematically, 

the reference temperature metric for plates 

(RTPL) is defined as follows:

Eq. 8-3 

∑

∑

=

=

− ⋅

= npl

i

i

PL

npl

i

i

PL

i

PLMAX

PL

V

VRT

RT

1

1

where 

npl is the number of plates in the vessel beltline region, 

VPL is the volume of each of these plates, 

RTMAX-PW is evaluated for each plate using the following formula. In the formula the 

symbol φtMAX refers to the maximum fluence occurring over the ID in the vessel 

beltline region, and ∆T30 is the shift in the Charpy V-Notch 30 ft-lb energy 

produced by irradiation at φtMAX. 

( ) MAX

plate plate

PLMAX uNDT RT − RT )( ∆+≡ 30 φtT

It should be noted that at an equivalent 

embrittlement level, the likelihood of a plate 

flaw leading to through-wall cracking of the 

vessel is much lower than for an axial weld 

flaw for two reasons. First, half of all 

simulated plate flaws are oriented 

circumferentially, which reduces their 

driving force relative to axial flaws 

(see Figure 8.7). Additionally, plate flaws 

are generally much smaller than weld flaws. 

However, the azimuthal variation of fluence 

makes it virtually certain that some region 

of the plates will be subjected to a higher 

fluence (often a much higher fluence) than 

will the axial weld fusion lines. At some 

point, this added embrittlement to which the 

plate flaws are subjected will overcome the 

smaller plate flaw driving force caused by 

their smaller size (vs. axial weld flaws), 

causing the fracture of plate flaws to become 

more likely than the fracture of axial weld 

flaws. 

• Surface-Breaking Flaws in the Stainless 

Steel Cladding: The only flaws simulated to 

break the inner diameter surface of the RPV 

occur because of lack of inner-run fusion 

between adjacent beads of weld-deposited 

stainless steel cladding. Since this cladding 

is always deposited circumferentially, these 

flaws are always oriented circumferentially, 

and they can occur anywhere over the entire 

ID surface of the vessel. All of the 

simulated flaws have a crack depth equal to 

the thickness of the cladding layer, so the 

toughness properties that control the 

behavior of these flaws (i.e., if the flaw 

initiates, if the flaw propagates through the 

RPV wall) are those of the axial weld, 

circumferential weld, or plate region that lie 

under the simulated location of the surface 

flaw. As discussed later in this section, 

FAVOR reports the contribution of these 

flaws to FCI and TWCF along with the 

contribution of the underlying axial weld, 
8-24

circumferential weld, or plate region. Thus, 

the contribution of these flaws to FCI and 

TWCF is addressed by the combination of 

RTAW, RTCW, and RTPL making an 

independent reference temperature metric 

for flaws in cladding unnecessary. 

Furthermore, the circumferential orientation 

of these flaws makes their contribution to 

FCI and TWCF very small****.

8.4.2 Effect of RPV Beltline Region 

on FCI and TWCF Values 

As illustrated in Figure 8-5, the beltline region 

of a nuclear RPV is fabricated from different 

material product forms. All three vessels 

analyzed here are plate vessels and, therefore, 

are fabricated from heavy section ferritic steel 

plates roll formed to produce 120° or 180°

degree segments. These segments are joined by 

axial welds to form a shell course, and then 

different shell courses are joined by 

circumferential welds to make the vessel. 

Two to three shell courses generally make up 

the beltline region of the vessel. An alternative 

fabrication practice, which avoids the need 

for axial welds, is to join ring-forged cylinders 

with circumferential welds. In Section 9.2, 

we address application of the results presented in 

this chapter (for plate vessels) to forged vessels. 

In this report, we use the term “regions” to refer 

to the different product forms (i.e., plates, axial 

welds, circumferential welds, and forgings) that 

make up each RPV. As detailed in Table 8.2, 

each region has unique properties of chemical 

composition (which controls susceptibility to 

irradiation embrittlement), strength, and toughness. 

These properties also vary within the each 

region, see [EricksonKirk-PFM] and [Williams], 

respectively, for a description of our bases for 

characterizing this variation and of the statistical 

 

**** At the extremely high embrittlement level 

simulated by the Ext-Ob analysis of Oconee 

Unit 1, cladding flaws contributed only 2.5% 

and 0.01% to the total FCI and TWCF 

(respectively). At the more realistic 

embrittlement levels represented by the 32 

and 60 EFPY analyses, these flaws made no 

contribution to either FCI or TWCF. 

models we have adopted in FAVOR for this 

purpose. Table 8.5 details the relative 

contributions these different regions make to the 

FCI and TWCF values reported in Table 8.4, 

demonstrating that these different regions (and 

their associated flaw populations) make widely 

varied contributions to the FCI and TWCF 

values, as follows: 

• Circumferential Flaws: Circumferential 

flaws are responsible for a large portion of 

the FCI because the maximum ID fluence 

always interacts with a potential location of 

a circumferential flaw, but almost never 

with the potential location of an axial flaw. 

The consequential higher embrittlement 

frequently associated with circumferential 

flaws (RTCW > RTAW) leads directly to their 

role as dominant initiators††††. However, 

as illustrated in Figure 8.7, differences in 

how the driving force to fracture varies 

through-wall in a cylindrical vessel causes 

most of these initiated circumferential 

cracks to arrest before they propagate 

completely through the vessel wall and 

contribute to the TWCF. For this reason, 

circumferential cracks do not contribute to 

TWCF except in a very minor way at very 

high RTCW values. 

• Axial Flaws: Axial flaws are responsible for 

nearly all of the TWCF. In both Oconee and 

in Palisades, the toughness associated with 

the axial weld flaws is less than the 

toughness associated with the plate flaws 

(RTAW > RTPL) so the axial weld flaws 

control nearly all of the TWCF. In Beaver 

Valley, the toughness associated with the 

plate flaws is less than the toughness 

associated with the axial weld flaws 

 

†††† This observation regarding the general 

dominance of circumferential flaws in 

controlling FCI does not apply to Palisades. 

In Palisades, the toughness along the axial 

weld fusion line is less than the toughness 

along the circumferential weld fusion line 

(i.e., RTAW > RTCW). This occurs because the 

chemistry of the axial welds in Palisades is 

more irradiation-sensitive than that of the 

circumferential welds, increasing their 

embrittlement despite the lower fluence along 

the axial weld fusion lines. 
8-25

(RTPL > RTAW). Thus, in Beaver Valley, the 

plate flaws are responsible for some portion 

of the TWCF. However, they do not 

completely control the TWCF because weld 

flaws are much larger than plate flaws. 

Nonetheless, it is always the toughness 

properties that can be associated with axial 

flaws (i.e., the toughness properties of either 

the plate or of the axial weld: RTAW and/or 

RTPL) that control the TWCF. The toughness 

properties of the circumferential weld 

(RTCW) play only a minor role and this only 

for highly embrittled materials (high RTCW).

Table 8.5. Relative contributions of various flaw populations to the FCI and TWCF values 

estimated by FAVOR Version 04.1 

Apportionment by Originating Flaw Population 

Reference 

Temperatures [o

F] FCI(1) TWCF(1)

EFPY 

RTAW RTCW RTPL

Mean 

FCI 

Mean 

TWCF 

Axial 

Welds 

Circ 

Welds Plates Axial 

Welds 

Circ 

Welds Plates 

Oconee Unit 1 

32 134 136 72 1.29E-10 2.30E-11 33.83% 66.16% 0.00% 100.00% 0.00% 0.00% 

60 149 156 83 1.02E-09 6.47E-11 18.64% 81.35% 0.01% 99.90% 0.10% 0.00% 

Ext-Oa 200 207 134 1.01E-07 1.30E-09 8.82% 90.82% 0.35% 99.83% 0.16% 0.00% 

Ext-Ob 227 229 164 5.24E-07 1.16E-08 8.52% 90.78% 0.71% 99.81% 0.11% 0.08% 

Beaver Valley Unit 1 

32 171 243 217 1.32E-07 8.89E-10 2.37% 96.01% 1.61% 68.44% 0.33% 31.23% 

60 188 272 244 5.19E-07 4.84E-09 3.01% 94.26% 2.73% 39.19% 0.72% 60.09% 

Ext-Ba 203 301 273 1.71E-06 2.02E-08 2.64% 93.04% 4.33% 15.69% 1.74% 82.55% 

Ext-Bb 226 354 324 8.87E-06 3.00E-07 2.23% 91.02% 6.75% 9.21% 6.18% 84.62% 

Palisades 

32 210 201 165 5.22E-08 4.90E-09 93.79% 6.22% 0.00% 99.95% 0.05% 0.00% 

60 227 215 181 1.23E-07 1.55E-08 92.56% 7.44% 0.00% 99.97% 0.04% 0.00% 

Ext-Pa 271 259 231 7.46E-07 1.88E-07 84.45% 15.41% 0.15% 99.91% 0.02% 0.08% 

Ext-Pb 324 335 293 4.47E-06 1.26E-06 60.24% 38.58% 1.18% 98.62% 0.01% 1.37% 

Note: (1) FCI and TWCF percentages may not add to 100% due to rounding. 
8-26

8.4.3 Embrittlement Normalization 

between Different Plants 

Section 8.5 examines the classes of transients 

that have the greatest contribution to FCI and 

TWCF. Part of this discussion focuses on the 

similarity/difference of the severity associated 

with the same type of transient at different plants 

(e.g., does a 4-in. hot leg break have a similar 

severity at the different analyzed plants, or must 

plant-specific factors be considered to accurately 

predict the severity of the transient?). 

These discussions form the beginning of our 

assessment of the general applicability of our 

results to all PWRs — a topic that Chapter 9 

addresses in more detail. To perform these 

plant-to-plant comparisons of transient severity 

on an equivalent basis, it is important to be able 

to account for the differences in embrittlement 

level between the different analyses we 

performed. We use the reference temperature 

metrics RTAW, RTCW, and RTPL introduced in 

Section 8.4.2 for this purpose. 

As discussed in Section 8.4.2, the development 

of a single reference temperature to serve as an 

embrittlement metric for all plants is 

complicated by the following two factors: 

• The fracture toughness varies widely 

throughout the pressure vessel (because of 

the combined influences of different 

chemistries in different regions and the 

fluence variation over the vessel ID). 

• The distribution of flaws throughout the 

vessel; their size, location, and orientation; 

is non-homogeneous (for physically 

understood reasons). 

Nonetheless, the toughness properties associated 

with axial cracks control the 

likelihood of developing a throughwall crack. In Oconee and in 

Palisades, these properties are 

described completely by RTAW

because ~100% of the TWCF is 

associated with the axial weld flaw 

population in these plants, 

irrespective of embrittlement level. 

The situation in Beaver Valley is 

more complex because the high 

fluence levels remote from the axial 

weld fusion lines and the high 

irradiation susceptibility of the 

Beaver Valley materials create a 

situation where plate flaws and (at 

very high levels of embrittlement) 

circumferential weld flaws 

contribute to the TWCF. To reflect 

this, the reference temperature for 

Beaver Valley should lie between 

RTAW and RTPL. These 

considerations are reflected in the 

final column of 

Table 8.6, which provides the reference 

temperature values used in Section 8.5. 

It should be noted this approach to obtaining 

a single reference temperature is developed here 

only to support the transient comparisons 

performed in Section 8.5. Embrittlement metrics 

useful for estimating the level of PTS risk in PWRs 

in general are discussed and developed 

in Chapter 11. 

8.4.4 Changes in these Results Relative 

to those Reported in December 2002 

While the specific numerical results reported 

herein differ from those in our interim report 

[Kirk 12-02], the general trends discussed in this 

section have not changed substantively from 

those reported earlier. 

8.5 Contributions of Different 

Transients to the Through-Wall 

Cracking Frequency 

8.5.1 Overview 

As a first step toward assessing the transients 

that contribute most prominently to the overall 

TWCF, we divided the transients analyzed for 

each plant (see Appendix A for a complete list) 

into the following transient classes: 
8-27

Table 8.6. Reference temperature metric used in Section 8.5. 

Reference 

Temperatures [o

F] 

TWCF Apportioned by 

Originating Flaw Population Plant EFPY 

RTAW RTCW RTPL

Axial 

Welds 

Circ 

Welds Plates 

Reference 

Temperature for 

Section 8.5 

Comparisons [o

F] 

32 134 136 72 100.00% 0.00% 0.00% 134 (=RTAW) 

60 149 156 83 99.90% 0.10% 0.00% 149 (=RTAW) 

Ext-Oa 200 207 134 99.83% 0.16% 0.00% 200 (=RTAW) 

Oconee 

Ext-Ob 227 229 164 99.81% 0.11% 0.08% 227 (=RTAW) 

32 171 243 217 68.44% 0.33% 31.23% 185 (=RTAW + 

0.31⋅{RTPL-RTAW}) 

60 188 272 244 39.19% 0.72% 60.09% 222 (=RTAW + 

0.61⋅{RTPL-RTAW}) 

Ext-Ba 203 301 273 15.69% 1.74% 82.55% 262 (=RTAW + 

0.85⋅{RTPL-RTAW}) 

Beaver 

Valley 

Ext-Bb 226 354 324 9.21% 6.18% 84.62% 315 (=RTAW + 

0.91⋅{RTPL-RTAW}) 

32 210 201 165 99.95% 0.05% 0.00% 210 (=RTAW) 

60 227 215 181 99.97% 0.04% 0.00% 227 (=RTAW) 

Ext-Pa 271 259 231 99.91% 0.02% 0.08% 271 (=RTAW) 

Palisades 

Ext-Pb 324 335 293 98.62% 0.01% 1.37% 324 (=RTAW) 

Note: In Section 8.5, when the TWCFs of different plants are compared at “roughly equivalent” 

embrittlement levels, the results associated with the shaded rows are used. 

LOCA Pipe breaks of any diameter on the 

primary side (see Tables A.1 and A.2) 

SO-1 Stuck-open valves (that may later 

reclose) on the primary side (see Tables 

A.3 and A.4) 

F&B Feed & bleed “LOCA” (see Table A.8) 

MSLB Large diameter (or “main”) steam line 

break (see Table A.5) 

SO-2 Smaller diameter secondary side 

breaks, including stuck-open valves 

(see Table A.7) 

SGTR Steam generator tube rupture 

(see Table A.8) 

OVR Overfeed (see Table A.8) 

MIX Mixed primary and secondary initiators 

(see Table A.9) 

Figure 8-8, Figure 8-9, and Figure 8-10 illustrate 

the contribution to the total TWCF of each 

transient analyzed for Oconee, Beaver Valley, 

and Palisades, respectively. (Descriptions of the 

transients that contribute more than 1% to the 

total TWCF are provided in Table 8.7, Table 

8.8, and Table 8.9 for each plant.) These 

graphical depictions demonstrate that many of 

the transients analyzed contribute little or 

nothing to the TWCF while a limited number of 

transients dominate TWCF. In general, the 

contributions of primary side pipe breaks 

(LOCAs) and stuck-open valves on the primary 

side that may later reclose (SO-1) are the most 

important, collectively accounting for 70% or 

more of the total risk (see Figure 8-11). Stuckopen valves on the secondary side (SO-2) and 

breaks in the main steam line (MSLB) also 

contribute to TWCF, but to a more limited 

extent. Feed-and-bleed LOCAs (F&B) and 

steam generator tube ruptures (SGTR) do not 

contribute to TWCF in any significant way. 

Figure 8-12 illustrates the annual frequencies of 

occurrence of the most risk-significant classes of 
8-28

events, where risk-significance is based on the 

information in Figure 8-8 through Figure 8-10. 

In Figure 8-12 the division between small and 

medium and medium and large break LOCAs 

occurs at approximately 4 and 8-inches 

(10.16 and 20.32-cm), respectively. Based on 

this information, the following observations 

can be made: 

• Plant Effects on Frequency: The 

frequencies associated with Oconee and 

Beaver Valley are identical because these 

frequencies were established by the NRC’s 

PRA contractors based on industry-wide 

data [INEEL99, INEEL00b] and based on 

limited plant-specific data. It was the view 

of these analysts that there were not enough 

differences between these plants and/or 

plant-specific data to support adoption of 

plant-specific frequencies. The Palisades 

frequencies differ slightly from those 

adopted for the other two plants for several 

reasons. Different analysts performed the 

Palisades PRA, so some differences are 

attributable to different interpretations of 

available data. Secondly, the Palisades PRA 

analysts adopted slightly different models to 

represent PTS risk than were used for the 

other two plants. Finally, the Palisades PRA 

analysis made use of some Palisadesspecific information. Taken together, the 

small plant-to-plant frequency differences 

shown in Figure 8-12 arise, in part, because 

of both real differences between the plants 

and differences in modeling or judgment. 

• Event Effects on Frequency: SO-2 events 

occur with the greatest frequency; 

approximately 0.02/yr. MSLB and SO-1 

events are the next most frequent, but are 

approximately 10 times less likely than SO2 events. All LOCA events are less likely 

still, as illustrated in Figure 8-12. The least 

likely event class is large-break LOCAs, 

which are approximately 3,000 times less 

likely than SO-2 events. 

In the following subsections, we examine in 

further detail the four classes of transients that 

collectively account for virtually all of the 

TWCF: LOCA, SO-1, MSLB, and SO-2. 

Sections 8.5.2 through 8.5.5 

are structured as follows: 

Step 1. Each section begins with a general 

description of transients in the class, how the 

transient progresses, what actions the operators 

take, and so on. 

Step 2. We then review of all of the transients in 

the class that were modeled in each of the three 

study plants with the aim of describing how each 

transient class has been modeled. Additionally, 

this discussion points out plant-specific 

similarities/differences in our treatment of the 

transient class as regards the specific transients 

selected to represent the class as a whole. 

Step 3. We then examine relationships between 

the systems-based characteristics of the 

transients in the class (e.g., break size, break 

location, HPI throttling at 1 vs. 10 minutes, etc.) 

and their thermal-hydraulic signature (i.e., their 

temporal variation of pressure, temperature, and 

heat transfer coefficient in the downcomer). 

Step 4. The probabilistic fracture mechanics 

results are then discussed within the context of 

the thermal-hydraulic understanding developed 

in Step #2. Specifically we overlay on the TH 

transients the predicted times at which the vessel 

fails. This focuses attention on the part of the 

transient where differences in the TH signature 

can influence whether the vessel is predicted to 

fail or not. Particular attention is paid to determining 

the importance of operator actions in controlling 

the transient severity, and identifying if the 

results from these three study plant can be 

considered to apply to all PWRs in general. 

Step 5. The discussion of each transient class 

concludes with a comparison of our current 

findings to those reported previously [Kirk 12-02] 

and those that established the basis for the current 

provisions of 10 CFR 50.61 [SECY-82-465]. 

Finally, in Section 8.5.6, we discuss classes 

of transients that do not contribute in any 

significant way to the total TWCF. These 

include SGTR, feed-and-bleed LOCAs, and 

transients that include a combination of failures 

in both the primary and secondary pressure 

circuits. 
8-29

Oconee

0

10

20

30

40

50

60

70

80

90

100

LOCA, 110LOCA, 119LOCA, 120LOCA, 142LOCA, 154LOCA, 160LOCA, 172

LOCA, 44

LOCA,15

MSLB, 101

MSLB, 89MSLB, 99

SGTR, 127

SO-1, 112SO-1, 114SO-1, 116SO-1, 121SO-1, 123SO-1, 125SO-1, 146SO-1, 148SO-1, 165SO-1, 169SO-1, 171

SO-2, 29SO-2, 31SO-2, 37SO-2, 90

% Contribution to TWCF

32 EFPY

60 EFPY

Ext-Oa

Ext-Ob

Figure 8-8. Contributions of the different transients to the TWCF in Oconee Unit 1 

(Numbers on the abscissa are the TH case numbers, see Appendix A) 

Beaver

0

10

20

30

40

50

60

70

80

90

100

LOCA, 2LOCA, 7

LOCA, 56

LOCA, 114LOCA, 116

MSLB, 74MSLB, 81

MSLB, 103MSLB, 105MSLB, 107MSLB, 109MSLB, 111MSLB, 113

SO-1, 14SO-1, 34SO-1, 60SO-1, 62SO-1, 65SO-1, 67SO-1, 69SO-1, 71SO-1, 73SO-1, 92SO-1, 94

SO-1, 119SO-1, 121SO-1, 123SO-1, 125SO-1, 127SO-1, 129

SO-2, 78

% Contribution TWCF

32 EFPY

60 EFPY

Ext-Ba

Ext-Bb
8-30

Figure 8-9. Contributions of the different transients to the TWCF in Beaver Valley Unit 1 

(Numbers on the abscissa are the TH case numbers, see Appendix A) 

Palisades

0

10

20

30

40

50

60

70

80

90

100

F&B, 31F&B, 32

LOCA, 2

LOCA, 40LOCA, 58LOCA, 59LOCA, 60LOCA, 61LOCA, 62LOCA, 63LOCA, 64

MSLB, 22MSLB, 24MSLB, 26MSLB, 27MSLB, 29MSLB, 34MSLB, 49MSLB, 50MSLB, 51MSLB, 54

SO-1, 42SO-1, 48SO-1, 53SO-1, 65SO-2, 16SO-2, 18SO-2, 19SO-2, 52SO-2, 55

% Contribution to TWCF

32 EFPY

60 EFPY

Ext-Pa

Ext-Pb

Figure 8-10. Contributions of the different transients to the TWCF in Palisades 

(Numbers on the abscissa are the TH case numbers, see Appendix A) 

Table 8.7. Transients that contribute most significantly to the estimated TWCF of Oconee Unit 1 

Class TH# System Failure Operator Action HZP? %1

SO-1 122 Stuck-open pressurizer safety 

valve. Valve recloses at 6,000 secs. 

Operator throttles HPI at 10 minutes after 2.7 K 

[5°F] subcooling and 100-in. (254-cm) 

pressurizer level is reached. (Throttling criteria 

is 27.8 K [50°F] subcooling.) 

Yes 47% 

SO-1 165 

Stuck-open pressurizer safety 

valve. Valve recloses at 6,000 

secs [RCS low-pressure point]. 

None Yes 13% 

SO-1 124 Stuck-open pressurizer safety 

valve. Valve recloses at 3,000 secs. 

Operator throttles HPI at 10 minutes after 2.7 K 

[5°F] subcooling and 100-in. (254-cm) 

pressurizer level is reached. (Throttling criteria 

is 27.8 K [50°F] subcooling.) 

Yes 6% 

SO-1 168 

TT/RT with stuck-open pzr SRV. 

SRV assumed to reclose at 3,000 

secs. Operator does not throttle 

HPI. 

None Yes 1% 

LOCA 160 

5.66-in. (14.37-cm) surge line 

break. ECC suction switch to the 

containment sump included in the 

analysis. 

None No 15% 

LOCA 164 

8-in. (20.32-cm) surge line break. 

ECC suction switch to the 

containment sump included in the 

None No 12% 
8-31

Class TH# System Failure Operator Action HZP? %1

analysis. 

LOCA 156 

16-in. (40.64-cm) hot leg break. 

ECC suction switch to the 

containment sump included in the 

analysis. 

None No 3% 

LOCA 141 

3.22-in. (8.19-cm) surge line break 

[Break flow area increased by 30% 

from 2.83-in. (7.18-cm) break]. 

None No 1% 

Note: 1. The column headed “%” indicates the contribution of this transient to the TWCF averaged across all four 

embrittlement levels analyzed. 

Table 8.8. Transients that contribute most significantly to the estimated TWCF of Beaver Valley Unit 1 

Class TH# System Failure Operator Action HZP? %1

SO-1 126 

Reactor/turbine trip w/one stuck-open 

pressurizer SRV which recloses at 

6,000 s and operator controls HHSI 

10 minutes after allowed. 

None No 10% 

SO-1 60 

Reactor/turbine trip w/one stuck-open 

pressurizer SRV which recloses at 

6,000 s. 

None. No 7% 

SO-1 130 

Reactor/turbine trip w/one stuck-open 

pressurizer SRV which recloses at 

3,000 s at HZP and operator controls 

HHSI 10 minutes after allowed. 

None Yes 6% 

SO-1 97 

Reactor/turbine trip w/one stuck-open 

pressurizer SRV which recloses at 

3,000 s. 

None. Yes 2% 

SO-1 129 

Reactor/turbine trip w/one stuck-open 

pressurizer SRV which recloses at 

6,000 s at HZP and operator controls 

HHSI 10 minutes after allowed. 

None Yes 1% 

SO-1 123 

Reactor/turbine trip w/two stuck-open 

pressurizer SRVs which reclose at 

3,000 s at HZP and operator controls 

HHSI 10 minutes after allowed. 

None Yes 1% 

LOCA 56 4-in. (10.16-cm) surge line break None No 35% 

LOCA 7 8-in. (20.32-cm) surge line break None. No 20% 

LOCA 9 16-in. (40.64-cm) hot leg break None. No 6% 

MSLB 102 

Main steam line break with AFW 

continuing to feed affected generator 

for 30 minutes. 

Operator controls HHSI 30 minutes after 

allowed. Break is assumed to occur inside 

containment so that the operator trips the 

RCPs as a result of adverse containment 

conditions. 

No 4% 

MSLB 104 

Main steam line break with AFW 

continuing to feed affected generator 

for 30 minutes. 

Operator controls HHSI 60 minutes after 

allowed. Break is assumed to occur inside 

containment so that the operator trips the 

RCPs as a result of adverse containment 

conditions. 

No 3% 

MSLB 103 

Main steam line break with AFW 

continuing to feed affected generator 

for 30 minutes. 

Operator controls HHSI 30 minutes after 

allowed. Break is assumed to occur inside 

containment so that the operator trips the 

RCPs as a result of adverse containment 

conditions. 

Yes 3% 
8-32

Class TH# System Failure Operator Action HZP? %1

Note: 1. The column headed “%” indicates the contribution of this transient to the TWCF averaged across all four 

embrittlement levels analyzed. 

Table 8.9. Transients that contribute most significantly to the estimated TWCF of Palisades 

Class TH# System Failure Operator Action HZP? % 

SO-1 65 

One stuck-open pressurizer SRV that recloses at 

6,000 sec after initiation. Containment spray is 

assumed not to actuate. 

None. Operator does not 

throttle HPI. Yes 35% 

SO-1 48 

Two stuck-open pressurizer SRVs that reclose at 

6,000 sec after initiation. Containment spray is 

assumed not to actuate. 

None. Operator does not 

throttle HPI. Yes 1% 

SO-1 53 

Turbine/reactor trip with two stuck-open pressurizer 

SRVs that reclose at 6,000 sec after initiation. 

Containment spray is assumed not to actuate. 

None. Operator does not 

throttle HPI. No 1% 

LOCA 40 16-in. (40.64-cm) hot leg break. Containment sump 

recirculation included in the analysis. 

None. Operator does not 

throttle HPI. No 23% 

LOCA 58 

4-in. (10.16-cm) cold leg break. Winter conditions 

assumed (HPI and LPI injection temp = 40°F 

(4.44°C), Accumulator temp = 60°F (15.56°C)) 

None. Operator does not 

throttle HPI. No 10% 

LOCA 62 

8-in. (20.32-cm) cold leg break. Winter conditions 

assumed (HPI and LPI injection temp = 40°F 

(4.44°C), Accumulator temp = 60°F (15.56°C)) 

None. Operator does not 

throttle HPI. No 4% 

LOCA 64 

4-in. (10.16-cm) surge line break. Summer 

conditions assumed (HPI and LPI injection temp = 

100°F (37.78°C), Accumulator temp = 90°F 

(32.22°C)) 

None. Operator does not 

throttle HPI. No 3% 

LOCA 60 

2-in. (5.08-cm) surge line break. Winter conditions 

assumed (HPI and LPI injection temp = 40°F 

(4.44°C), Accumulator temp = 60°F (15.56°C)) 

None. Operator does not 

throttle HPI. No 2% 

LOCA 63 

5.66-in. (14.37-cm) cold leg break. Winter conditions 

assumed (HPI and LPI injection temp = 40°F 

(4.44°C), Accumulator temp = 60°F (15.56°C)) 

None. Operator does not 

throttle HPI. No 2% 

LOCA 59 

4-in. (10.16-cm) cold leg break. Summer conditions 

assumed (HPI and LPI injection temp = 100°F 

(37.78°C), Accumulator temp = 90°F (32.22°C)) 

None. Operator does not 

throttle HPI. No 1% 
8-33

Class TH# System Failure Operator Action HZP? % 

MSLB 54 

Main steam line break with failure of both MSIVs to 

close. Break assumed to be inside containment 

causing containment spray actuation. 

Operator does not isolate 

AFW on affected SG. 

Operator does not throttle 

HPI. 

No 2% 

MSLB 27 

Main steam line break with controller failure resulting 

in the flow from two AFW pumps into affected steam 

generator. Break assumed to be inside containment 

causing containment spray actuation. 

Operator starts second AFW 

pump. 

No 1% 

SO-2 55 

Turbine/reactor trip with 2 stuck-open ADVs on SG-A 

combined with controller failure resulting in the flow 

from two AFW pumps into affected steam generator. 

Operator starts second AFW 

pump. 

No 12% 

SO-2 19 Reactor trip with 1 stuck-open ADV on SG-A. None. Operator does not 

throttle HPI. Yes 5% 

Note: 1. The column headed “%” indicates the contribution of this transient to the TWCF averaged across all four 

embrittlement levels analyzed. 
8-34

0%

20%

40%

60%

80%

100%

134149200227

0%

20%

40%

60%

80%

100%

193239286342

SO-2

MSLB

LOCA

SO-1

0%

20%

40%

60%

80%

100%

210 210227 22

271 271

324 324

Oconee

Palisades

Beaver

RT [oF]

% Contribution to Total TWCF

Figure 8-11. Variation in percent contribution to the total TWCF of different transient classes 

with reference temperature (RT) as defined in 

Table 8.6. The contributions of feed-and-bleed LOCAs and steam generator tube ruptures were also assessed. 

These transient classes made no contribution to TWCF, with the exception that feed-and-bleed LOCAs 

contributed < 0.1% to the TWCF of the Palisades RPV. 
8-35

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

SB

LOCA

MB

LOCA

LB

LOCA

SO-1 MSLB SO-2

Event Class

Yearly Frequenc

y

Palisades

Oconee and Beaver Valley

Figure 8-12. Comparison of the annual frequencies of various broad classes of events for full-power conditions 

8.5.2 Primary Side Pipe Breaks 

8.5.2.1 General Description of a Pipe 

Break Transient 

Following a pipe break, the primary system cools 

by two mechanisms. The rapid depressurization 

caused by the break produces a rapid drop in 

system temperature because, under the saturated 

conditions that exist once a break occurs, 

pressure is linked to temperature via the 

ideal gas law. For large-diameter breaks, 

this pressure-induced temperature decrease 

dominates the primary system cooldown. 

As break size decreases, another cooling 

mechanism (the temperature and volume 

of the ECC injection water) becomes important. 

As indicated in Figure 2.1, ECCS pumps 

(e.g., HPSI, LPSI, etc.) all inject into the cold leg. 

Consequently, for cold leg breaks, some of the 

injection water is lost out of the break, never 

reaching (or cooling) the downcomer. In this 

situation, the volume of the cooling water lost 

is approximately proportional to the number of 

cold legs. (For example, in a 3-loop plant, 

if one cold leg breaks, the injection flow reaching 

the downcomer is diminished by one-third.) 

Conversely, no cooling water is lost if the break 

occurs in either the hot leg or in the surge line. 

For this reason, cold leg breaks tend to be 

somewhat less severe (at an equivalent diameter) 

than hot leg or surge line breaks. 

The minimum temperature to which the 

injection water cools the primary can depend on 

the ambient temperature outside the plant 

because both the HPSI and LPSI pumps draw 

from the RWST. In plants where the RWST is 

outside and uninsulated, the temperature of the 

cooling water is subject to seasonal temperature 

variations, which directly impact the portion of 

the downcomer cooling controlled by safety 

injection. The effect of seasonal temperature 

variations on cooling water temperature is a 

more important factor for smaller diameter 

breaks. 
8-36

Additionally, factors such as the total volume of 

the inventory in the RWST and the pressures at 

which the safety injection pumps start can differ 

from plant-to-plant. These features influence the 

cooldown characteristics of pipe break transients 

for the following reasons: 

• The total volume of the inventory in the 

RWST controls the time interval over which 

the ECCS can draw water from this source. 

If the transient continues after this time, the 

ECCS has to switch over to recirculation 

from the containment sump. Since the water 

in the sump has flowed out of the break, it is 

generally warmer (~120°F (48.9°C)) than 

water drawn from the RWST (as low as ~ 

40°F (4.4°C) during the winter). 

• For breaks of medium to small diameter 

(approximately 4-in. (10.16-cm) and below) 

the cooldown rate is sufficiently gradual that 

it can be influenced by the pressure at which 

the safety injection pumps start. Plantspecific differences can, therefore, influence 

the cooldown rate. Differences of this type 

occurred among the three study plants. Both 

Oconee and Beaver Valley have high-head 

HPSI that injects water immediately upon 

receiving a safety injection actuation signal 

(at ~ 1,700 psi). In contrast, Palisades has 

low-head HPSI pumps that inject water 

when the pressure falls below 1,300 psi. 

8.5.2.2 Model of this Transient Class 

As detailed in Appendix A, Tables A.1 

(break diameters above 3.5-in. (8.9-cm)) and 

A.2 (break diameters below 3.5-in. (8.9-cm)) 

our modeling of primary side pipe breaks 

includes a spectrum of break diameters ranging 

from 1.4- to 16-in. (3.6- to 40.6-cm) because 

break size is the single most important factor 

that controls the rate of system depressurization 

and (thereby) the severity of the transient. 

No operator actions are modeled for any break 

diameter exceeding ≈3-in. (≈7.6-cm) because for 

these events, the safety injection systems do not 

fully refill the upper regions of the RCS. 

Consequently, operators would never take action 

to shut off the pumps. Other factors modeled 

include the following: 

• break location (for smaller diameter breaks) 

• season of the year (for smaller diameter breaks) 

• total volume of the RWST inventory 

(controls the time at which cooling water 

begins to draw from the sump, which is 

warmer than the water stored in the RWST) 

• pump start setpoints 

8.5.2.3 Relationships between System 

Characteristics and ThermalHydraulic Response 

8.5.2.3.1 Dominant vs. Secondary 

Factors 

Primary side pipe breaks characteristically cause 

both a rapid cooldown and a rapid depressurization 

of the primary system. At long times, 

the temperature of the primary approaches 

the temperature of the injection water, which can 

be as low as 35°F (1°C) because it is stored in 

external tanks. As described in the previous 

section, the break area (i.e., π⋅(DBREAK/2)2

) is the 

main factor controlling the initial cooldown rate 

because break area controls the depressurization 

rate and the two are linked through the ideal gas 

law. Figure 8.13 illustrates this point for a 

spectrum of hot leg/surge line breaks in both 

Beaver Valley and Oconee. 
8-37

0 2000 4000 6000

Time (s)

250

350

450

550

650

Temperature (K)

16.0" (BV−009) 

8.0" (BV−007) 

4.0" (BV−056) 

2.828" (BV−114) 

2.0" (BV−003) 

1.414" (BV−002) 

0 2000 4000 6000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000

Time (s)

250

350

450

550

650

Temperature (K)

16.0" (OC−156) 

8.0" (OC−164) 

5.7" (OC−160) 

3.4" (OC−154) 

2.4" (OC−142) 

1.7" (OC−145) 

0 2000 4000 6000−10

170

350

530

710

Temperature (F)

Figure 8.13. Effect of surge line and hot-leg break 

diameter on the cooldown characteristics 

of Beaver Valley (top) and Oconee (bottom) 

Factors other than break size can alter the 

cooldown signature somewhat, but are generally 

less important than the dominating influence of 

break area. For example: 

• Break Location: As described in the 

previous section, cold leg breaks are 

expected to be less severe than hot leg 

breaks at equivalent break diameter due to 

loss of injection water out of the break. 

However, as illustrated in Figure 8.14 the 

effect of break location is not so great as to 

take a break out of severity order as 

indicated by break size. 

• Injection Water Temperature: Variations in 

injection water temperature occur both at the 

time in the transient when the volume of the 

RWST is exhausted and the HPSI/LPSI 

pumps start drawing off the sump and as a 

consequence of seasonal variations. The 

sudden increase in downcomer temperature 

evident at approximately 2000 sec. on the 8- 

and 16-in. diameter break curves in the top 

graph in Figure 8.13 indicates the time at 

which the switchover to sump occurs. 

Figure 8.15 illustrates the effect of seasonal 

variations on cold leg breaks in Palisades. 

Again, break diameter is seen to be the 

dominant factor controlling the initial 

cooldown rate with seasonal factors playing 

a less important role. 

Relative to differences in cooldown rate between 

different break sizes, differences in primary 

system pressure are more modest because safety 

injection flow cannot fully compensate for the 

loss of inventory out of these breaks. Figure 

8.16 illustrates this point for a range of break 

sizes in both Oconee and Beaver Valley. 

Similarly, the effect of break size on differences 

in the heat transfer coefficient between different 

breaks is more modest, see Figure 8.17. 

0 2000 4000 6000

Time (s)

250

350

450

550

650

Temperature (K)

5.7" Surge (OC−160) 

4.0" Cold (OC−172) 

2.4" Surge (OC−142) 

0 2000 4000 6000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000

Time (s)

250

350

450

550

650

Temperature (K)

5.7" Cold (P−063) 

4.0" Surge (P−064) 

4.0" Cold (P−059) 

2.8" Cold (P−061) 

0 2000 4000 6000−10

170

350

530

710

Temperature (F)

Figure 8.14. Effect of break location 

on the cooldown characteristics in Oconee (top) 

and Palisades (bottom) 
8-38

0 2000 4000 6000

Time (s)

250

350

450

550

650

Temperature (K)

5.7" Winter (P−063) 

4.0" Winter (P−058) 

4.0" Summer (P−059) 

2.0" Winter (P−060) 

0 2000 4000 6000−10

170

350

530

710

Temperature (F)

Figure 8.15. Effect of season on the cooldown 

characteristics of cold leg breaks in Palisades 

0 2000 4000 6000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

16.0" (BV−009) 

8.0" (BV−007) 

4.0" (BV−056) 

2.828" (BV−114) 

2.0" (BV−003) 

1.414" (BV−002) 

0 2000 4000 60000

725

1450

2176

2901

Pressure (psia)

0 2000 4000 6000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

16.0" (OC−156) 

8.0" (OC−164) 

5.7" (OC−160) 

3.4" (OC−154) 

2.4" (OC−142) 

1.7" (OC−145) 

0 2000 4000 60000

725

1450

2176

2901

Pressure (psia)

Figure 8.16. Effect of surge line and hot-leg break 

diameter on the depressurization characteristics 

of Beaver Valley (top) and Oconee (bottom) 

0 2000 4000 6000

Time (s)

0

5000

10000

15000

20000

25000

Heat Transfer Coefficient (W/m2*K)

16.0" (BV−009) 

8.0" (BV−007) 

4.0" (BV−056) 

2.828" (BV−114) 

2.0" (BV−003) 

1.414" (BV−002) 

0 2000 4000 60000.00

0.24

0.49

0.73

0.98

1.22

Heat Transfer Coefficient (Btu/s*ft2*F)

0 2000 4000 6000

Time (s)

0

5000

10000

15000

20000

25000

Heat Transfer Coefficient (W/m2*K)

16.0" (OC−156) 

8.0" (OC−164) 

5.7" (OC−160) 

3.4" (OC−154) 

2.4" (OC−142) 

1.7" (OC−145) 

0 2000 4000 60000.00

0.24

0.49

0.73

0.98

1.22

Heat Transfer Coefficient (Btu/s*ft2*F)

Figure 8.17. Effect of surge line and hot-leg 

break diameter on the heat transfer coefficient 

in Beaver Valley (top) and Oconee (bottom) 

8.5.2.3.2 Plant-Specific Effects 

Figure 8.18 compares the cooldown characteristics 

of different break sizes across the three plants 

modeled. For nominally identical conditions 

between plants (i.e., break size, break location, 

power level at transient initiation), the response 

of the three study plants is similar across the 

entire break size spectrum. This is because 

the cooldown rate is controlled (mostly) 

by the size of the break and the overall size, 

temperature, and pressure of the RPV in which 

the break occurs. In Figure 8.18, these factors 

are consistent plant-to-plant.
8-39

0 2000 4000 6000

Time (s)

250

350

450

550

650

Temperature (K)

Beaver Valley (009) 

Oconee (156) 

Palisades (040) 

0 2000 4000 6000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000

Time (s)

250

350

450

550

650

Temperature (K)

Beaver Valley Surge (007) 

Oconee Surge (164) 

Palisades Cold Winter (062) 

0 2000 4000 6000−10

170

350

530

710

Temperature (F) (a) 16-in. hot leg breaks (b) 8-in. breaks 

0 2000 4000 6000

Time (s)

250

350

450

550

650

Temperature (K)

Oconee Cold (172) 

Palisades Cold Winter (058) 

Palisades Cold Summer (059) 

0 2000 4000 6000−10

170

350

530

710

Temperature (F)

(c) 4-in. cold line breaks 

0 2000 4000 6000

Time (s)

250

350

450

550

650

Temperature (K)

Beaver Valley Cold (115) 

Palisades Cold (061) 

0 2000 4000 6000−10

170

350

530

710

Temperature (F) 0 2000 4000 6000

Time (s)

250

350

450

550

650

Temperature (K)

Beaver Valley Surge (003) 

Palisades Surge Winter (060) 

0 2000 4000 6000−10

170

350

530

710

Temperature (F)

(d) 2.8-in. cold line breaks (e) 2-in. surge line breaks 

Figure 8.18. Comparison of the cooldown characteristics of the three plants modeled 

for a spectrum of break diameters 

8.5.2.4 Estimates of Vessel Failure 

Probability 

In Section 8.5.2.3, we identified break size 

as the factor that most significantly influenced 

the cooldown rate that results from a pipe break, 

with break location and season of the year 

playing more limited roles. We examine these 

factors in the following subsections. 

Additionally, we discuss differences between 

the number of cracks initiated by pipe break 

transients vs. those that propagate through 

the wall, and information concerning the time 

differential between transient initiation (i.e., pipe 

break) and vessel failure. The section concludes 

with an assessment of the applicability of these 
8-40

findings to assessing the probability of vessel 

failure due to pipe breaks in general. 

In the following subsections, we compare values 

of CPTWC for different transients taken from 

Tables A.1 and A.2. To obtain an approximately 

equivalent level of embrittlement across all 

plants these comparisons use results for Beaver 

Valley and for Palisades at 60 EFPY, while 

Oconee results are taken at the Ext-Ob 

embrittlement level (see 

Table 8.6). 

8.5.2.4.1 Break Size Effects 

Figure 8.19 shows the effect of break size on the 

CPTWC results for all three plants. Up to a 

break diameter of ~4- to 5-in. (~10.16- to 12.7-cm), 

CPTWC depends strongly on break diameter. 

By comparison, for larger break diameters, 

the CPTWC is essentially independent of further 

increases in break diameter. For these larger 

diameter breaks, the RCS fluid cools faster than 

the wall of the RPV. In this situation, 

only the thermal conductivity of the steel 

and the thickness of the RPV wall control 

the thermal stresses and, thus, the severity of 

the fracture challenge, perturbations to the fluid 

cooldown rate controlled by the break diameter, 

break location, and season of the year do not 

play a role. Thermal conductivity is a physical 

property, so it is very consistent for all RPV 

steels. Consequently, the single factor 

controlling the severity of the fracture challenge 

for large diameter pipe breaks is the thickness of 

the RPV wall because higher thermal stresses 

can develop in thicker walls. This effect of wall 

thickness is seen in Figure 8.19, where the 

CPTWC for the thinner vessel (Beaver Valley: 

7.875-in (20-cm) thick) is consistently below 

that of the thicker vessels (Palisades and Oconee 

both have wall thicknesses of 81⁄2-in) for break 

sizes above 4- to 5-in. (~10.16- to 12.7-cm). 

In Section 9.2, we discuss the effects of thickness 

on vessel failure probability in greater detail. 

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

0 4 8 12 16

Break Diameter [in]

CPTW

C

Oconee:

Surge/Hot

Oconee:

Cold

Beaver:

Surge/Hot

Beaver:

Cold

Palisades:

Surge/Hot

Palisades:

Cold

Figure 8.19. Effect of pipe break diameter 

and break location on the conditional probability 

of through-wall cracking. 

(CPTWC taken at approximately equivalent 

embrittlement levels between plants (Beaver Valley 

and Palisades at 60 EFPY, Oconee at Ext-Ob)) 

8.5.2.4.2 Break Location and 

Seasonal Effects 

Figure 8.19 also illustrated the effect of break 

location. As discussed in Section 8.5.2.2 and 

illustrated in Figure 8.14, cold leg breaks are 

less severe than hot leg breaks across the entire 

break size spectrum because some portion of the 

ECC flow is lost out of a cold leg break. The 

magnitude of the influence of break location on 

CPTWC is negligible for conduction limited 

conditions (i.e., for large breaks) and increases 

with decreasing break size because it is for 

smaller breaks that differences in injection flow 

can have a significant effect on the fluid cooling 

rate. In the Palisades analysis the combined 

effects of break size and of seasonal variations 

were modeled in more detail than in the other 

two plants: Figure 8.20 shows these results. 

Focusing on the 4-in. (10.16-cm) diameter breaks, 

we see that the surge line break (summer conditions) 

has a CPTWC approximately 300 times greater 

than that of a 4-in. (10.16-cm) diameter cold leg 

break. The effects of seasonal variations are less 
8-41

important: at the 4-in. (10.16-cm) break size, 

a cold line break in winter has a CPTWC 

approximately 20 times greater than a cold line 

break in summer. It should be noted that 

seasonal variations are not important at all 

plants. Some plants have insulated RWSTs 

which mitigate the effect of outside temperature 

on the temperature of the ECC injection water. 

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

0 4 8 12 16

Break Diameter [in]

Conditional Probability of Throu

g

Wall Cracking

Palisades

Surge/Hot

Palisades

Cold

W

S

W

W

W

S

S

Figure 8.20. Effect of pipe break diameter, 

break location, and season (S=Summer, 

W=Winter) on the conditional probability 

of through-wall cracking for Palisades 

8.5.2.4.3 Differences Between Crack 

Initiation and Vessel 

Failure for Pipe Break 

Transients 

Because of the lack of a significant pressure 

component during a pipe break (see Figure 8.16), 

these transients cause many more crack 

initiations than they do complete failure of the 

vessel wall. This is quantified in Figure 8.21 

by the ratio of the conditional probability 

of through-wall cracking to the conditional 

probability of crack initiation. A ratio of 100% 

would indicate that all initiated cracks also 

propagated through the vessel wall. 

The maximum ratio for any pipe break analyzed 

is 12%. while the ratios for the large diameter 

breaks that contribute most significantly to the 

through-wall cracking frequency are ~1% for 

Oconee and Beaver Valley, and ~4% for Palisades. 

The lower ratios for Oconee and Beaver Valley 

are caused by the greater dominance of 

circumferential cracks as initiators in these 

plants (see Table 8.5). 

0%

4%

8%

12%

16%

0 4 8 12 16

Break Diameter [in]

CPTWC / CPI Rati

o

Oconee:

Surge/Hot

Oconee:

Cold

Beaver:

Surge/Hot

Beaver:

Cold

Palisades:

Surge/Hot

Palisades:

Cold

Figure 8.21. Effect of pipe break diameter 

and break location on the conditional proportion 

of initiated flaws that propagate through the wall. 

(CPTWC/CPI ratios taken at approximately equivalent 

embrittlement levels between plants (Beaver Valley 

and Palisades at 60 EFPY, Oconee at Ext-Ob).) 

8.5.2.4.4 Time Between Pipe Break 

and Vessel Failure 

As illustrated Figure 8.22, there is very little time 

(particularly for large breaks) between the 

initiating event (i.e., the pipe breaking) and 

vessel failure. If failure is going to occur 

as a consequence of a pipe break, it will happen 

within ~30 min. (1800 sec.) for 4-in. (10.16-cm) 

breaks. Vessel failures resulting from larger 

breaks occur even faster: if an 8-in. (20.32-cm) 

break fails the vessel, it does so within ~15 min. 

(900 sec.). These short failure times limit the 

influence of thermal-hydraulic variations that 

occur at much longer times (see the plots in 

Section 8.5.2.3); they also limit the time in 

which operator action can occur. Additionally, 

it should be noted that operator actions are not 
8-42

a factor for pipe break transients because for 

breaks of diameter ~2-in. (5.08-cm) and greater, 

there is no action that the operator can take: 

ECCS flow must continue to keep the core 

covered. 

0

20

40

60

80

0 4 8 12 16

Break Diameter [in]

Time to Most Frequent Failur

e

[min]

Oconee:

Surge/Hot

Oconee:

Cold

Beaver:

Surge/Hot

Beaver:

Cold

Palisades:

Surge/Hot

Palisades:

Cold

Figure 8.22. Effect of LOCA break diameter 

and break location on the time at which 

through-wall cracking occurs 

(Break times taken at approximately equivalent 

embrittlement levels between plants (Beaver Valley 

and Palisades at 60 EFPY, Oconee at Ext-Ob).) 

8.5.2.4.5 Applicability of Findings 

to PWRs in General 

While the information presented in this section 

pertains specifically to the three plants analyzed, 

the following three factors suggest that these 

results can be used with confidence to assess 

the risk of vessel failure arising from pipe break 

transients for PWRs in general: 

(1) Larger break sizes control the contribution 

of pipe breaks to the total estimated TWCF. 

In the three plants studied break diameters 

above 5-in. (12.7-cm) account for more than 

50% of the TWCF attributable to pipe 

breaks, with break diameters of 3.5- to 5-in. 

(8.9- to 12.7-cm) accounting for nearly all 

of the remainder. As discussed in this 

section, the severity of larger breaks is more 

consistent from plant-to-plant than for 

smaller break diameters. 

(2) Operator actions do not play a major role in 

pipe break transients. Consequently, the 

transferability of these results to other plants 

cannot be questioned on the basis of differences 

in operator training, experience, and so on. 

(3) At an equivalent embrittlement level, 

the TWCF is fairly consistent among 

the three plants modeled. As a direct 

consequence of factors 1 and 2, the TWCF 

attributable only to primary side pipe breaks 

is reasonably consistent from plant-to-plant 

(see Figure 8.23). 

In Section 9.3, we discuss the applicability 

of these results to PWRs in general in greater 

detail. 

8.5.2.5 Comparison with Previous 

Studies 

8.5.2.5.1 As Reported by [Kirk 12-02] 

While the specific numerical results reported 

herein differ from those in our interim report 

[Kirk 12-02] the general trends discussed in this 

section have not changed substantively from 

those reported earlier. 

8.5.2.5.2 Studies Providing the 

Technical Basis of the 

Current PTS Rule 

Our results demonstrating that pipe breaks, 

particularly large diameter pipe breaks, are 

dominant contributors to PTS risk represent 

a substantial change relative to earlier PTS 

studies [SECY-82-465, ORNL 85a, 86b, 86]. 

It should, however, be noted that in these earlier 

studies, large diameter pipe breaks could not 

contribute to the through-wall cracking 

frequency because they were excluded a priori

from the analysis. This exclusion resulted from 

erroneous assumptions made about the need 

for significant pressure to drive through-wall 

cracking, and erroneous interpretation of largescale tests [Cheverton 85a, Cheverton 85b] 

as 1:1 surrogates for full-scale PWRs. 
8-43

(See Appendix A to [EricksonKirk-PFM].) 

Specifically, a series of thermal shock 

experiments (TSEs) performed at Oak Ridge 

National Laboratory in the late 1970s and early 

1980s demonstrated that thermal shock alone 

(no pressure was or could be applied to these 

open-ended cylinders) could drive a cleavage 

crack almost entirely through the wall of a 

scaled RPV. (Figure 8-24 shows a post-test 

photograph of the crack in TSE #6, wherein the 

crack arrested after propagating 95% of the way 

through the cylinder wall.) While 95% throughwall cracking is not vessel failure, we do not feel 

that this evidence adequately justifies the 

previous judgment that thermal shock alone 

cannot fail a pressure vessel for the following 

reasons: 

(1) The cylinders tested by ORNL were much 

thicker (in comparison to their diameter) 

than commercial PWRs. This increased 

stiffness makes crack arrest more likely in 

the experiment than in the actual structure. 

(2) The cylinders tested in the ORNL TSEs 

were fabricated from forgings that tended to 

have material on the outer diameter that was 

tougher (lower fracture toughness transition 

temperature) than on the inner diameter. 

This toughness gradient, which resulted 

from the processes used to fabricate the 

forgings, is not typical of the axial welds 

that contribute the most to PTS failure 

frequencies. Again, qualitatively, crack arrest 

in the TSEs is more likely than in the actual 

structure. 

(3) Because the ORNL TSEs used open-ended 

cylinders, the pressure component of the 

loading was zero, by definition. However, 

the results of our PFM calculations 

(see Figure 8-25) demonstrate that, 

while low, some pressure is retained within 

the primary system, even for large diameter 

breaks. 

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

100 150 200 250 300 350 400

RT from Table 8.5 [oF]

TWCF due to Primary Side Pipe Break

s

Oconee - LOCA

Beaver - LOCA

Palisades - LOCA

Figure 8.23. The TWCF attributable only to 

primary side pipe breaks in the three study plants 

Figure 8-24. Radial profile of arrested crack 

in TSE 6 [Cheverton 85a] 

(The crack in this experiment arrested 

after propagating 95% of the way through 

the cylinder wall.) 
8-44

0

250

500

750

1000

0 5 10 15 20

LOCA Break Diameter [inches]

Primary System Pressure at 

Failure Time [psi]

Oconee

Beaver Valley

Palisades

Figure 8-25. Effect of pipe break diameter 

on the pressure in the primary system 

at the most likely time of failure 

8.5.3 Stuck-Open Valves on the Primary 

Side (SO-1) 

8.5.3.1 General Description of an SO-1 

Transient 

An SO-1 transient begins with a demand of one 

or more pressurizer SRVs. In some cases, 

the SRV opens in response to a real demand, 

but more often, SRVs open because of a false 

demand (for example, setpoint drift). Opening of 

an SRV causes depressurization and consequent 

rapid cooldown of the RCS. At this stage, other 

plant equipment actuates and the operators 

respond in accordance with operating procedures, 

injecting makeup water to address the loss 

of primary system coolant caused by the open 

SRV. Since the makeup water is stored in 

external tanks at ambient temperature, 

emergency injection further cools the 

downcomer wall. At some (random) later time, 

the stuck-open SRV recloses. When the valve 

recloses the continued charging and highpressure injection causes the RCS to begin to 

refill. For the first ~15 minutes following valve 

reclosure, both RCS pressure and temperature 

are stable or increase slightly. During this time, 

it is unlikely that the primary injection throttling 

criteria will be met because the primary system 

is still saturated (i.e., there is no subcooling) 

and the level in the pressurizer is inadequate to 

satisfy the throttling criteria. After ~15 minutes, 

the RCS pressure will rise very quickly (over 

just a few minutes) as the pressurizer fills as a 

result of the combined effects of continued 

primary injection and system heatup. During 

this rapid repressurization, the primary system 

throttling criteria will be met, thereby allowing

the operators to act to control the 

repressurization rate. The ability of operators to 

throttle injection once they are allowed to 

depends upon how quickly they are able to 

recognize and react to rapid changes in plant 

conditions, from a saturated system before 

bubble collapse to a nearly solid system as and 

after the bubble collapses. The rapidity of 

operator response once the throttling criteria are 

met controls whether, and for how long, 

the RCS becomes fully repressurized. 

8.5.3.2 Model of this Transient Class 

Transients modeled in this class (see Table A.3 

in Appendix A) include one or more stuck-open 

pressurizer SRVs or PORVs that may reclose 

(unstick) later in the transient. The initial 

cooling rate in these transients is similar to that 

of a small (~2-in. (5.08-cm) diameter) pipe break, 

so it is not so rapid as to generate a considerable 

challenge to the RPV (see Figure 8.19). 

However, the potential for valve reclosure 

at some point in the transient leads to the 

possibility of system repressurization, and this 

coupled with the thermal stresses from the 

cooldown and the lowered fracture toughness of 

the vessel (because of the reduced temperature 

in the primary system) dramatically increases 

the severity of this transient class over that 

associated with small diameter pipe breaks. 

Our modeling of this transient class includes 

the following factors: 

• plant power level at transient initiation 

(full-power vs. hot zero power) 

• the random time at which valve reclosure 

is assumed to occur (the possibility of 

reclosure after both 3,000 and 6,000 seconds 

was modeled) 
8-45

• the timing of operator action (i.e., pump 

throttling) after valve reclosure (modeling 

considered action taken 1 minute, 

10 minutes, and never after the throttling 

criteria were met)‡‡‡‡

• seasonal variations 

• more than one valve sticking open 

• less than the total number of stuck-open 

valves subsequently reclosing, or valves 

only partially sticking open 

Scoping analyses revealed the first three of these 

factors to be of primary importance in 

establishing the severity of the loading 

challenge, while the last three factors played 

very minor roles. Attention, therefore, focused 

on a more detailed analysis of the first three 

factors, the effects of which are described in the 

following section. 

8.5.3.3 Relationships between System 

Characteristics and ThermalHydraulic Response 

The following three sections (8.5.3.3.1 through 

8.5.3.3.3) examine the effects of the following 

factors, based on the results of a systematic 

study of these variables performed for Oconee 

(see Figure 8-26 and Figure 8-27): 

• valve reclosure time 

• plant power level at transient initiation 

• timeliness of operator action once the 

throttling criteria are met 

The results of a somewhat more limited study 

performed for the Beaver Valley plant can be 

found in Figure 8-28 through Figure 8-30. 

Finally, we discuss how well these trends 

can be expected to apply to other PWRs

 

‡‡‡‡ This statement applies only to the models of 

Beaver Valley and Oconee. Because of 

hardware differences Palisades was modeled 

differently (see Section 8.5.3.4.2). 
8-46

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

O−149: HPI never throttled 

O−114: HPI throttled after 1 minute 

O−115: HPI throttled after 10 minutes 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000 8000 10000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

O−149: HPI never throttled 

O−114: HPI throttled after 1 minute 

O−115: HPI throttled after 10 minutes 

0 2000 4000 6000 8000 100000

725

1450

2176

2901

Pressure (psia)

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

O−168: HPI never throttled 

O−123: HPI throttled after 1 minute 

O−124: HPI throttled after 10 minutes 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000 8000 10000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

O−168: HPI never throttled 

O−123: HPI throttled after 1 minute 

O−124: HPI throttled after 10 minutes 

0 2000 4000 6000 8000 100000

725

1450

2176

2901

Pressure (psia)

Figure 8-26. Oconee SO-1 transients where the stuck-open SRVs reclose after 3,000 seconds. (Transients in 

the upper graphs initiate from full power, while transients in the lower graphs initiate from hot zero power.) 

8.5.3.3.1 Effect of Valve Reclosure 

Time on SO-1 Response 

Valve reclosure is a random event that can occur 

at any time after the transient begins. In our 

model, we have discretized this continuum into 

the two possibilities of reclosure at 3,000 and 

6,000 seconds. These possibilities were selected 

based on the recognition that the severity of the 

transient varies with valve reclosure time. Up to 

some time, transient severity increases with 

increasing time before reclosure because the 

temperature of the primary system is dropping 

(which reduces the fracture toughness) while the 

thermal stresses are still climbing (because the 

cooldown is continuing). However, once the 

RCS has reached its minimum temperature 

(established by the temperature of the HPI 

water), the severity of the event begins to reduce 

because the thermal stresses begin to decline. 

The 6,000-second reclosure time was selected to 

coincide (approximately) with the time of 

maximum transient severity because it is 

(approximately) at this time that the RCS 

temperature reaches its minimum value. 

The 3,000-second reclosure time was selected 

because it is not reasonable to assume that all 

valve reclosures will occur at the worst possible 

time. The potential for valve reclosure after 

very long times (in excess of 7,200 seconds, 

or 2 hours) were not considered because by that 

time, operators would have initiated new 

procedures. Since the operators’ objective is to 

stop the transient (i.e., stop dumping irradiated 

primary system water into containment), they 

would likely depressurize the steam generators 

by opening the steam dump valves to cool the 

secondary side, and they would start lowpressure injection and cool down the RCS to 

saturation conditions. These actions change the 

nature of the transient, making it more benign. 
8-47

Also, they change the probability of operator 

error. Additional information on valve reclosure 

times can be found in response to Peer Reviewer 

Comment #76 in Appendix B to this report. 

Figure 8-26 through Figure 8-30 illustrate the 

effect of valve reclosure at 3,000 vs. 6,000 

seconds in both Oconee (Figure 8-26 and Figure 

8-27) and Beaver Valley (Figure 8-28 through 

Figure 8-30). The primary difference between 

these two reclosure times is that the system 

temperature at the time of repressurization is 

lower for the 6,000-second case. Because the 

valve has been open for a longer time, HPI of 

cold water has continued for a longer time, 

leading to the colder temperatures in the 

downcomer. The temperature at the time of 

repressurization is ≈ 50–75°F (27.7 – 41.7 

°C)colder when reclosure occurs after 6,000 sec. 

vs. when reclosure occurs after only 3,000 sec. 

in Oconee (compare Figure 8-26 to Figure 8-27). 

In Beaver Valley, the effect of a longer time 

before reclosure on the temperature at 

repressurization is more modest (≈25°F or 

13.9°C) compare Figure 8-30 to Figure 8-28 and 

Figure 8-29). Additionally, comparing similar 

conditions between plants (Figure 8-27 for 

Oconee vs. Figure 8-28 for Beaver Valley) 

reveals that Beaver Valley cools faster and 

reaches lower temperatures than Oconee. The 

origins of these differences between plants are 

threefold: 

• The presence of vent valves at Oconee 

allows recirculation of water in the 

downcomer area, leading to higher 

temperatures in B&W plants. 

• The mass flow rate of the PORV in Beaver 

Valley is 65% greater than that at Oconee 

(see Table 8.1). Thus, more cooling water is 

injected into the Beaver Valley RPV in a 

fixed amount of time, leading to more rapid 

cooling of the primary system. 

• The temperature of the injection water is 

warmer at Oconee (70°F (21°C)) than it is at 

Beaver Valley (50°F (10°C)), which leads 

directly to lower minimum temperatures at 

Beaver Valley. 

Other features of the transient that contribute 

significantly to its severity (e.g., repressurization 

or not) are not influenced by valve reclosure 

time. Whether a plant repressurizes following 

valve reclosure depends on the plant power level 

at event initiation, as well as the timeliness of 

operator action, as discussed in the following 

two sections.
8-48

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

O−109: HPI never throttled 

O−112: HPI throttled after 1 minute 

O−113: HPI throttled after 10 minutes 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000 8000 10000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

O−109: HPI never throttled 

O−112: HPI throttled after 1 minute 

O−113: HPI throttled after 10 minutes 

0 2000 4000 6000 8000 100000

725

1450

2176

2901

Pressure (psia)

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

O−165: HPI never throttled 

O−121: HPI throttled after 1 minute 

O−122: HPI throttled after 10 minutes 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000 8000 10000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

O−165: HPI never throttled 

O−121: HPI throttled after 1 minute 

O−122: HPI throttled after 10 minutes 

0 2000 4000 6000 8000 100000

725

1450

2176

2901

Pressure (psia)

Figure 8-27. Oconee SO-1 transients where the stuck-open SRVs reclose after 6,000 seconds (Transients in 

the upper graphs initiate from full power, while transients in the lower graphs initiate from hot zero power.) 
8-49

0 3000 6000 9000 12000

Time (s)

250

350

450

550

650

Temperature (K)

BV−060: HPI never throttled 

BV−125: HPI throttled after 1 minute 

BV−126: HPI throttled after 10 minutes 

0 3000 6000 9000 12000−10

170

350

530

710

Temperature (F)

0 3000 6000 9000 12000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

BV−060: HPI never throttled 

BV−125: HPI throttled after 1 minute 

BV−126: HPI throttled after 10 minutes 

0 3000 6000 9000 120000

725

1450

2176

2901

Pressure (psia)

0 3000 6000 9000 12000

Time (s)

250

350

450

550

650

Temperature (K)

BV−071: HPI never throttled 

BV−127: HPI throttled after 1 minute 

BV−129: HPI throttled after 10 minutes 

0 3000 6000 9000 12000−10

170

350

530

710

Temperature (F)

0 3000 6000 9000 12000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

BV−071: HPI never throttled 

BV−127: HPI throttled after 1 minute 

BV−129: HPI throttled after 10 minutes 

0 3000 6000 9000 120000

725

1450

2176

2901

Pressure (psia)

Figure 8-28. Beaver Valley SO-1 transients where a single stuck-open SRV recloses after 6,000 seconds 

(Transients in the upper graphs initiate from full power, while transients in the lower graphs initiate from 

hot zero power.) 
8-50

0 3000 6000 9000 12000

Time (s)

250

350

450

550

650

Temperature (K)

BV−062: HPI never throttled 

BV−119: HPI throttled after 1 minute 

BV−120: HPI throttled after 10 minutes 

0 3000 6000 9000 12000−10

170

350

530

710

Temperature (F)

0 3000 6000 9000 12000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

BV−062: HPI never throttled 

BV−119: HPI throttled after 1 minute 

BV−120: HPI throttled after 10 minutes 

0 3000 6000 9000 120000

725

1450

2176

2901

Pressure (psia)

0 3000 6000 9000 12000

Time (s)

250

350

450

550

650

Temperature (K)

BV−070: HPI never throttled 

BV−122: HPI throttled after 1 minute 

BV−124: HPI throttled after 10 minutes 

0 3000 6000 9000 12000−10

170

350

530

710

Temperature (F)

0 3000 6000 9000 12000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

BV−070: HPI never throttled 

BV−122: HPI throttled after 1 minute 

BV−124: HPI throttled after 10 minutes 

0 3000 6000 9000 120000

725

1450

2176

2901

Pressure (psia)

Figure 8-29. Beaver Valley SO-1 transients where a two stuck-open SRVs reclose after 6,000 seconds. 

(Transients in the upper graphs initiate from full power, while transients in the lower graphs initiate from 

hot zero power.) 
8-51

0 3000 6000 9000 12000

Time (s)

250

350

450

550

650

Temperature (K)

BV−097: HPI never throttled 

BV−128: HPI throttled after 1 minute 

BV−130: HPI throttled after 10 minutes 

0 3000 6000 9000 12000−10

170

350

530

710

Temperature (F)

0 3000 6000 9000 12000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

BV−097: HPI never throttled 

BV−128: HPI throttled after 1 minute 

BV−130: HPI throttled after 10 minutes 

0 3000 6000 9000 120000

725

1450

2176

2901

Pressure (psia)

0 3000 6000 9000 12000

Time (s)

250

350

450

550

650

Temperature (K)

BV−069: HPI never throttled 

BV−121: HPI throttled after 1 minute 

BV−123: HPI throttled after 10 minutes 

0 3000 6000 9000 12000−10

170

350

530

710

Temperature (F)

0 3000 6000 9000 12000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

BV−069: HPI never throttled 

BV−121: HPI throttled after 1 minute 

BV−123: HPI throttled after 10 minutes 

0 3000 6000 9000 120000

725

1450

2176

2901

Pressure (psia)

Figure 8-30. Beaver Valley SO-1 transients where stuck-open SRVs recloses after 3,000 seconds 

(All transients initiate from hot zero power conditions. Transients in the upper graphs have one stuck-open valve, 

whereas transients in the lower graphs have two stuck-open valves.) 

8.5.3.3.2 Effect of Plant Power Level 

on SO-1 Response 

If a plant experiences an SO-1 transient at HZP 

rather than at full-power conditions, the rate of 

system cooldown will be more rapid because 

there is less heat in the system initially. This can 

be seen in Figure 8-26 and Figure 8-27 by 

comparing the top graphs (which are initiated 

from full-power conditions) vs. the bottom 

graphs (which are initiated from HZP 

conditions). The cooling rate for the HZP 

transients is considerably more rapid than for the 

full-power transients. This more rapid cooling 

rate for HZP transients coupled with the fact that 

HZP transients begin at lower temperatures than 

full-power transients makes the temperature at 

the time or repressurization much lower for HZP 

transients than it is for full-power transients. 

These observations are true regardless of the 

plant considered, and can be expected to hold for 

all PWRs because of differences in system heat 

characteristic of HZP vs. full-power conditions. 

For these reasons, SO-1 transients are always 

more severe when initiated under HZP conditions. 

8.5.3.3.3 Effect of Timing of 

Operator Action on SO-1 

Response 

Operators are allowed to limit the injection of 

water to the primary system once certain 

“throttling criteria” are met. The specific 

throttling criteria vary from plant-to-plant and 

from manufacturer to manufacturer, but 

generally include the following items: 

• The subcooling margin must be above some 

specified minimum to prevent boiling in the 

primary. 

• The level of inventory in the pressurizer 

must be maintained at or above a certain 

elevation to keep the pressurizer heaters 

submerged. 
8-52

• There may be requirements that the pressure 

not be falling, to ensure that the operators 

have regained pressure control of the system 

(and so can safely begin to reduce injection 

flow). 

These conditions generally cannot be met in an 

SO-1 transient until the stuck-open valve 

recloses. As previously noted, how quickly the 

operator responds after the throttling criteria are 

satisfied has a significant effect on whether the 

system repressurizes. Our model considers three 

possibilities for operator action: 1 minute after 

the throttling criteria are met, 10 minutes after 

the throttling criteria are met, and never 

(no throttling). 

The information in Figure 8-26 through Figure 

8-30 demonstrates that operator action must be 

very rapid to prevent the primary from returning 

to full system pressure for at least some period 

of time. In all of our analyses, throttling 

10 minutes after the throttling criteria were met 

was too late to prevent rapid repressurization 

shortly after valve reclosure. When operators 

throttled 1 minute after the throttling criteria 

were met and the transient was initiated from 

full power, the rate of repressurization was 

sometimes reduced or the time of 

repressurization delayed, but full system 

pressure was ultimately regained. It was only in 

cases where operators throttled within 1 minute 

and the transient initiated from HZP that the 

operator action prevented system 

repressurization§§§§. This effect of power level 

on the repressurization response occurs because 

for HZP there is less heat in the system initially, 

and because the system is colder at the time of 

valve reclosure. Pressure and temperature are 

linked, so the need to heat up the colder water 

 

§§§§ Figure 8-30 (bottom graphs, transient 121) illustrates 

one case for Beaver Valley at variance with this trend. 

In this case, rapid operator action has significantly delayed 

repressurization, but has not stopped it. However, this long 

delay before repressurization occurs permits considerable 

warming of the water in the primary system, which reduces 

significantly the probability of vessel failure. Thus, 

significant delay of repressurization is nearly as effective as 

preventing repressurization entirely. 

and having less heat to do so inhibits the sudden 

repressurization. 

Certain plant-specific features also influence the 

effectiveness of operator action. Comparing the 

results for Oconee (Figure 8-26 and Figure 8-27) 

and with those for Beaver Valley (Figure 8-28 

through Figure 8-30) reveals that, for a fixed 

throttling time, repressurization is delayed 

somewhat longer at Beaver Valley than at 

Oconee. This is a direct consequence of the 

differences in PORV mass flow rate (65% 

greater at Beaver Valley) and differences in the 

injection water temperature (20°F (11°C) colder 

because of the reduced thermal energy in the 

RCS (of Beaver Valley relative to Oconee) at 

the time of value reclosure. Consequently, a 

given throttling action will be more effective in 

preventing repressurization at Beaver Valley 

because throttling limits the reintroduction of 

thermal energy to the primary, thereby delaying 

the time at which water solid conditions, and 

therefore repressurization, occur. It should, 

however, be noted that these plant-specific 

differences do not alter significantly the risksignificance of the transient because their most 

important feature is the return to full system 

pressure (or not), not small (5–10 minute) 

variations in when return to full system pressure 

occurs. Section 8.5.3.4 discusses the risksignificance of SO-1 transients in greater detail. 

8.5.3.3.4 Other Factors 

In principle, factors other than the time of valve 

reclosure, the power level at transient initiation, 

and the timeliness of operator throttling of HPI 

can affect the TH response of the plant to an 

SO-1 transient. These factors can include, 

for example, seasonal variations, more than one 

valve sticking open, less than the total number 

of valves that stuck-open reclosing, valves that 

only partially stick open, and so on. We 

considered a number of these factors (see Table 

A.3 of Appendix A), but found their combined 

likelihood and consequence to be very small 

relative to the three factors discussed here in 

detail. 
8-53

8.5.3.3.5 Plant-Specific Effects on 

SO-1 Transients 

In Sections 8.5.3.3.1 through 8.5.3.3.3, attention 

focused on transients in Oconee and in Beaver 

Valley because these plants modeled first and, 

consequently, the most detailed parametric study 

was performed on these plant. The plant-specific 

effects of vent valves, PORV mass flow rate, 

and injection water temperature have already 

been discussed. Certain combinations of events 

were eliminated from the later analyses of 

Palisades because the insights gained from 

earlier analysis suggested that the eliminated 

transients contributed very little or nothing at all 

to the overall PTS risk. Nonetheless, it is 

important to assess the degree to which the 

observations made in Sections 8.5.3.3.1 through 

8.5.3.3.3 based on Oconee and Beaver Valley 

apply to Palisades. Figure 8-31 shows that the 

cooling rate in the Palisades transient initiated 

from HZP is less than that at either Oconee or 

Beaver Valley because the low-heat HPSI 

pumps at Palisades don’t inject as much water as 

the high-head HPSI pumps at Beaver Valley and 

Oconee. Nonetheless, this plant-to-plant difference 

does not alter the trends noted in Sections 

8.5.3.3.1 through 8.5.3.3.3 based on Oconee and 

Beaver Valley results (e.g., HZP transients cool 

more rapidly than full-power transients, only 

rapid operator actions taken for transients 

initiated under HZP conditions can prevent 

(or significantly delay) repressurization, etc.). 

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

O−165: HPI never throttled 

BV−071: HPI never throttled 

P−065: HPI never throttled 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000 8000 10000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

O−165: HPI never throttled 

BV−071: HPI never throttled 

P−065: HPI never throttled 

0 2000 4000 6000 8000 100000

725

1450

2176

2901

Pressure (psia)

Figure 8-31. Comparison of SO-1 transients between different plants for transients initiated from 

HZP conditions, valve reclosure after 6,000 sec., and no HPI throttling
8-54

8.5.3.4 Estimates of Vessel Failure 

Probability 

8.5.3.4.1 General Observations 

In this section, we examine the effect that the 

time of valve reclosure, the power level at 

transient initiation, and the timeliness of 

operator throttling of HPI have on estimated 

values of CPTWC and on the predicted time of 

vessel failure during the transient. In Table 8.10, 

we examine the Oconee transients illustrated 

in Figure 8-26 and in Figure 8-27 focusing on 

various indicators of transient severity 

(i.e., cooling rate, if repressurization occurs or not, 

and the temperature at the time of repressurization), 

as well as the CPI, CPTWC, and time of failure 

values estimated by FAVOR. The following 

observations follow from the information in the 

table (these observations also apply to SO-1 

transients at other plants):

Table 8.10. Transient severity indicators and estimated values of CPTWC for Oconee 

at Ext-Ob embrittlement conditions 

Transient Initiated from 

Full Power 

Transient Initiated from 

HZP 

HPI 

Throttling Item Valve 

Recloses 

after 3,000 

sec 

Valve 

Recloses 

after 6,000 

sec 

Valve 

Recloses 

after 3,000 

sec 

Valve 

Recloses 

after 6,000 

sec 

Transient # 149 109 168 165 

Average cooling rate over first 2,000 

seconds (o

F/hr) 308 308 486 486 

Time of repressurization (seconds) 4200 7100 4000 7100 

Temperature at repressurization (oF) 390 270 180 90 

Conditional probability of crack 

initiation (CPI) 0 1.83E-07 1.10E-04 1.24E-04 

Conditional probability of through-wall 

cracking (CPTWC) 0 1.83E-07 1.09E-04 1.24E-04 

Never 

Time of most failures (seconds) #N/A 7140 4080 7200 

Transient # 115 113 124 122 

Average cooling rate over first 2,000 

seconds (o

F/hr) 308 308 486 486 

Time of repressurization (seconds) 4200 7100 4050 7100 

Temperature at repressurization (oF) 390 270 190 90 

Conditional probability of crack 

initiation (CPI) 0 1.42E-07 9.38E-05 1.44E-04 

Conditional probability of through-wall 

cracking 0 1.31E-07 9.37E-05 1.44E-04 

10 minutes 

after 

throttling 

criteria 

satisfied 

Time of most failures (seconds) #N/A 7140 4140 7260 

Transient # 114 112 123 121 

Average cooling rate over first 2000 

seconds (o

F/hr) 308 308 486 486 

Time of repressurization (seconds) 4000 – 4400 7100 - 7800 None None 

Temperature at repressurization (oF) 400 – 440 300 - 405 #N/A #N/A 

Conditional probability of crack 

initiation (CPI) 0 0 2.06E-07 2.06E-07 

Conditional probability of through-wall 

cracking 0 0 1.28E-08 1.28E-08 

1 minute 

after 

throttling 

criteria 

satisfied 

Time of most failures (seconds) #N/A #N/A 1620 1620 
8-55

• The occurrence of repressurization does not 

lead to a non-zero probability of vessel 

failure unless the temperature of the vessel 

at the time of repressurization is low enough. 

The information in Table 8.10 substantiates 

the general observation that the vessel 

temperature must be below 400°F (204°C) 

to produce a non-zero value of CPTWC. 

• If a failure occurs, it most often happens 

between 5 and 20 minutes after the time of 

valve reclosure, closely following the time 

of repressurization. 

• If repressurization occurs and a crack 

initiates, the initiated crack fails the vessel 

almost every time (i.e., the CPTWC is equal 

to or only slightly less than the CPI). 

This crack initiation/through-wall crack 

propagation behavior contrasts sharply with 

that associated with primary side pipe breaks 

(see Figure 8.21) where only 5–10% of 

initiated cracks propagated through-wall. 

The combination of thermal stresses and 

pressure in SO-1 transients makes cracks, 

once initiated, much more likely to 

propagate all the way through the RPV wall. 

• SO-1 transients initiated from HZP conditions 

have CPTWC values that are ~1000 times 

higher than the same transient initiated from 

full-power conditions, this occurring as a 

consequence of the faster cooling rates 

and lower temperatures achieved during 

transients initiated from HZP. 

• Valve reclosures after 6,000 seconds exhibit 

slightly higher CPTWC values than valve 

reclosures at 3,000 seconds. The effect of 

higher thermal stresses (for 3,000-second 

valve reclosures) seems to approximately 

offset the effect of lower toughness 

(for 6,000-second valve reclosures). 

• For transients initiated from HZP, operator 

action within 1 minute of reaching the 

throttling criteria prevents a return to full 

system pressure, thereby reducing the 

CPTWC by a factor of ~10,000 relative to 

the CPTWC generated by repressurization. 

8.5.3.4.2 Influence of Operator 

Actions 

The final observation made in the preceding 

section indicates the potentially significant 

influence of operator action on the risksignificance of the transient. Consequently, 

in this section we review the basis for the 

probabilities assigned to represent the likelihood 

of operator action in response to this type of 

transient. 

The probabilities assigned to reflect the likelihood 

of operator action (throttling HPI in this case) 

after certain times were established based on the 

expert views of three PRA analysts, with the 

individual analyst’s judgments averaged to 

provide the consensus view used in our models 

[Kolaczkowski-Oco, Whitehead-BV, 

Whitehead-Pal]. Table 8.11 summarizes the 

factors that both favor and impede successful 

throttling considered by these analysts in 

formulating their opinions. Table 8.11 also 

provides the mean probabilities for operator 

action taken from the consensus distribution. 

These numbers reflect the analysts’ view that 

throttling within 1 minute of meeting the 

throttling criteria is somewhat more likely in 

Oconee than in Beaver Valley, a difference 

motivated mostly by differences in the simulator 

observations and procedures followed at the 

different plants. The numerical throttling 

probabilities for Palisades are somewhat 

different from those of Oconee and Beaver 

Valley because of differences in hardware. 

At Palisades, HPSI can only charge to 

approximately 1,250 psi while pressurization 

between 1,250 psi and full system pressure is 

achieved via charging pumps. The analysts’ 

took the view that successful throttling of HPSI 

was very unlikely, whereas successful throttling 

of charging pumps was very likely. 

The plots of pressure vs. time (see for example 

Figure 8-26 and Figure 8-27) indicate that HPI 

must be throttled within 1 minute of meeting the 

throttling criteria to prevent repressurization to 

full system pressure for a HZP transient. Thus, 

in our model, operators have a 68% chance of 

preventing repressurization in Oconee, and a 

40% chance in Beaver Valley (see Table 8.11). 
8-56

Our model for Palisades deviates from that 

suggested by the PRA information in Table 8.11. 

While the PRA information suggests that 

repressurization to 1,250 psi is certain and 

further repressurization is unlikely (happening 

only 1 time out of 100, on average), the TH 

sequences selected to represent stuck-open valve 

transients for Palisades credit no operator 

actions***** and, so, all have repressurization to 

full system pressure. Thus, the TH sequences 

run and passed to PFM for analysis reflect the 

following operator action credits for successful 

throttling of HPI: 

• Oconee operators successfully throttle HPI 

and, thereby, prevent return to full system 

pressure (on average) 68% of the time, 

provided that the transient initiates from 

HZP. Since approximately 20% of SO-1 

transients occur under HZP conditions, 

this means that at Oconee operators prevent 

return to full system pressure for 

approximately 14% of SO-1 transients. 

• Beaver Valley operators successfully 

throttle HPI and, thereby, prevent return 

to full system pressure (on average) 40% of 

the time, provided that the transient initiates 

from HZP. Since approximately 20% of 

SO-1 transients occur under HZP conditions, 

this means that at Beaver Valley operators 

prevent return to full system pressure for 

approximately 8% of SO-1 transients. 

• Palisades operators never successfully 

throttle HPI; therefore, all stuck-open valve 

transients return to full system pressure once 

the valve recloses. 

These observations indicate that while 

reasonable and appropriate credit for operator 

actions has been included in the PRA model, the 

actual influence of these credits on the estimated 

values of vessel failure probability attributable 

to SO-1 transients is small because the operator 

actions credited only prevent repressurization 

 

***** The Palisades model does not subdivide the 

PRA bins to account for “credit” vs. “no credit” 

because of our understanding (at the time the 

model was built) that the estimated TWCF 

values would be sufficiently low even with this 

implicit conservatism. 

when SO-1 transients initiate from HZP 

conditions. Complete removal of operator 

action credits from the model changes the total 

risk associated with SO-1 transients only 

slightly. 

8.5.3.4.3 Applicability of these 

Findings to PWRs in 

General 

While the information presented in this section 

pertains specifically to the three plants analyzed, 

the following factors suggest that these results 

can be used with confidence to assess the risk of 

vessel failure arising from pipe break transients 

for PWRs in general. 

(1) A major contributor to the risk-significance 

of SO-1 transients is the return to full system 

pressure once the valve recloses. The 

operating and SRV pressures of all PWRs 

are similar. 

(2) While our model includes reasonable and 

appropriate PRA credits for operator action 

to throttle HPI, these credits have only a 

small effect on the estimated probability of 

vessel failure because the operator actions 

credited only prevent repressurization when 

SO-1 transients initiate from HZP conditions. 

Complete removal of operator action credits 

from the model changes the total risk 

associated with SO-1 transients only 

slightly. 

At an equivalent embrittlement level, the TWCF 

is fairly consistent between the three plants 

modeled. As a direct consequence of these 

factors, the TWCF attributable solely to stuckopen primary side valves that later reclose is 

reasonably consistent from plant-to-plant (see 

Figure 8.32). In Chapter 9, we discuss the 

applicability of these results to PWRs in general

in greater detail. 
8-57

Table 8.11. Mean operator action probabilities in our modeling of SO-1 transients 

Mean Prob

throttling w

throttling 

Plant Factors that favor successful throttling Factors against successful throttling 

x = 1 

minute 

x = 

min

Crew is in loss of subcooling procedure (EP-501). Procedure contains many cautions on PTS 

Crew might have adopted a LOCA mindset and, therefore, not be attentive to the possibility of rapid repressurization. 

Simulator observations confirm that crews are sensitized to PTS, and that they carefully monitor PTS parameters. 

Emergency safeguards logic must be reset before HPI can be throttled, so throttling might be delayed while logic is being reset. 

High pressure alarms would indicated the need to throttle HPI 

Crew might not immediately throttle if they perform additional investigation to confirm that the event they are responding to is a stuck-open valve (for which throttling is appropriate) vs. a pipe break (for which throttling is not appropriate. 

Oconee 

Crew would be alerted to changing plant conditions by the slow pressure rise that follows valve reclosure and precedes the rapid pressure increase. 

68% 27

Before valve reclosure the crew has successfully stabilized a SLOCA, and they remain in a SLOCA condition until the valve recluses. SLOCA procedures make it reasonable to expect that the crew is thinking about PTS and is carefully monitoring plant parameters. 

Simulator observations suggest that the crews do not have a sense of urgency associated with throttling/terminating HHSI. Rather, they trust that their procedures will tell them to throttle in time. 

Simulator observations confirm that procedures are attended to and the crew carefully monitors critical parameters. 

Crew might have adopted a LOCA mindset and therefore not be attentive to the possibility of rapid repressurization. Emergency safeguards logic must be reset before HPI can be throttled, so throttling might be delayed while logic is 

Beaver Valley being reset. 

Crew might not immediately throttle if they perform additional investigation to confirm that the event they are responding to is a stuck-open valve (for which throttling is appropriate) vs. a pipe break (for which throttling is not appropriate. 

40% 56

0% for thrott

HPSI within 

minutes 

Palisades Throttling of the charging system (pressurizes from 1,250 psi to full system pressure) is very likely because it is a simple action that is linked procedurally to securing HPSI. Throttling of HPSI (pressurizes to 1,250 psi) is unlikely because the time available in which to throttle is very short. 99% for thrott

charging syst

within 5 minu
8-58

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

100 150 200 250 300 350 400

RTAW [oF]

TWCF due to SO-1 Transient

Oconee - SO-1

Beaver - SO-1

Palisades - SO-1

Figure 8.32. The TWCF attributable solely 

to stuck-open valves on the primary side 

that later reclose 

8.5.3.5 Comparison with Previous 

Studies 

8.5.3.5.1 As Reported by [Kirk 12-02] 

Previously, we reported that stuck-open valves 

on the primary side were dominant contributors 

to TWCF only in Oconee; in both Beaver Valley 

and Palisades, the contribution of such transients 

was 20% or less [Kirk 12-02]. Figure 8-11 and 

Figure 8.32 demonstrate that stuck-open valves 

on the primary side now contribute significantly 

to the TWCF of all three plants. This change 

results from an inadequacy in our previous 

approach to determining the group of transients 

we use in FAVOR to represent the behavior of 

the plant. Previously, we performed our first 

FAVOR calculation for each plant for a highly 

embrittled condition, determined which 

transients contributed ~1% or more to the 

TWCF, and conducted analyses at lower 

embrittlement levels using only this limited set 

of transients. As shown in Figure 8-11, our 

previous filtering strategy eliminated transients 

that provide significant contributions to PTS risk 

at lower embrittlement levels. Therefore, in this 

study, FAVOR analyses were performed on all 

transients at all embrittlement levels. 

8.5.3.5.2 Studies Providing the 

Technical Basis of the 

Current PTS Rule 

In analyses performed to establish the technical 

basis for the current PTS Rule, the three plants 

analyzed were Oconee, H.B. Robinson, and 

Calvert Cliffs. Analyses of Oconee and H.B. 

Robinson (which were performed first) did not 

consider the class of scenarios referred to herein 

as SO-1 [ORNL 85b, ORNL 86]. The Calvert 

Cliffs analysis, which was the last analysis 

performed, considered the possibility of both 

PORV and SRV reclosures, although not to the 

level of detail achieved in the current study 

[ORNL 85a]. Furthermore, all valve reclosure 

cases were binned together in the Calvert Cliffs 

study, which made it impossible to characterize 

the effects of power level, valve reclosure time, 

and operator action as we have in this study. 

Putting everything into one bin usually produces 

a conservative characterization; however, not 

investigating or understanding how various 

factors influence transient severity can lead to 

nonconservatisms when significant effects are 

not recognized and, therefore, not modeled. 

In the 1986 analysis of Calvert Cliffs, SO-1 

transients were among the two most important 

PTS scenarios (the other being small LOCAs) 

for the Calvert Cliffs analysis. This is in contrast 

to the 1985–1986 findings for Oconee and H.B. 

Robinson, which found secondary failures 

(either MSLBs or secondary valve openings) 

to be most important. 

With regard to frequency estimates for SO-1 

transients, our estimates rely on data that are 

representative of current operating practice. 

These estimates are lower than those used 

in the 1980s. 
8-59

8.5.4 Large Diameter Secondary Side 

or Main Steam Line Breaks 

8.5.4.1 General Description of MSLB 

Transients 

MSLB transients all begin with a break in one of 

the main steam lines. As main steam lines are 

large pipes with diameters of multiple feet, 

the steam generator rapidly blows down (loses 

steam through the break). Because of the break, 

the affected steam generator can no longer 

maintain pressure above that existing at the 

break location. The depressurization of the 

generator from its 860 psi (5.92 MPa) operating 

pressure to the pressure at the break location 

causes a temperature drop in the primary from 

550°F (288°C) to the saturation temperature at 

the pressure that exists at the break location 

(212°F (100°C) if the break is outside of 

containment, ~250°F (~121°C) if the break is 

inside of containment because containment is 

pressurized to ~50psi (345 kPa) by the steam 

escaping from the break). The temperature 

inside the still sealed primary system tracks that 

of the broken steam generator because of the 

very large heat transfer area provided by the 

steam generator tubes. (That is, the primary and 

secondary systems are coupled, so the 

temperature in the primary rapidly approaches 

that of the largest heat sink, which in this case, is 

the broken steam generator.) Thus, the 

inventory in the primary circuit cools rapidly to 

the temperature of the water boiling in the 

broken steam generator (as previously mentioned, 

212°F (100°C) if the break is outside of 

containment, ~250°F (~121°C) if the break is 

inside of containment) for all durations of 

interest from a PTS perspective†††††. 

As explained below, this is true despite the fact 

that both the makeup water to the primary and 

the feedwater to the faulted generator are 

 

††††† When the primary remains at approximately 

isothermal conditions for a long period of time, 

the temperatures of the ID and the OD of the 

RPV become approximately equal. Under these 

conditions, there is no thermal stress and, 

consquently, no risk of vessel failure 

attributable to PTS. 

supplied at temperatures far below the boiling 

point of water: 

• The rapid cooling of the primary in response 

to the MSLB shrinks the primary system 

inventory, causing a pressure drop. To 

compensate for the pressure drop, the 

ESFAS (an automatic function) initiates 

safety injection, causing the HPI pumps to 

supply makeup water to the primary system. 

HPI flow then refills and repressurizes the 

primary system. Even though the makeup 

water is drawn from external tanks and, so, 

is injected at a temperature far below the 

range of 212°F (100°C) to ~250°F (~121°C), 

the temperature of the primary remains at or 

above that of the broken steam generator 

because the heat transfer area provided by 

the steam generator tubes is so large that it 

overwhelms the lower temperature of the 

makeup water. At a later time, operators 

may be allowed to throttle HPI injection. 

• At very long times after the beginning of 

an MSLB transient, the temperature in the 

primary system approaches that of the feed 

water to the faulted steam generator, or 

about 100°F (38°), because the reactor is no 

longer generating enough heat to boil the 

water in the faulted generator. This drop to 

temperatures below 212°F (100°C) does not 

occur until several hours or more have 

passed, long after isothermal conditions 

have been achieved in the RPV. 

The primary aim of operators responding to an 

MSLB is to isolate the break (that is, to stop the 

feed to the faulted generator and/or to stop the 

flow out of the break). The steps the operators 

take to achieve this goal depends on the location 

of the break relative to both the main steam 

isolation valve and the containment structure 

(see Figure 2.1 for the arrangement of major 

plant components and a definition of the terms 

used in the following description): 

• Break downstream of the MSIV: In this 

case, the operators’ response is simply to 

isolate the affected generator by closing both 

the FWIV and MSIV. This reseals the 

secondary system and ends the transient. 

At this point, the temperature of the steam 
8-60

generator is controlled by the temperature of 

the primary. 

• Break upstream of the MSIV outside of 

containment: In this case, the break flow 

cannot be stopped by shutting the MSIV, so 

the operators close both the FWIV and 

MSIV to isolate the affected generator. 

Without feedwater, the generator eventually 

boils dry, and the unaffected generator 

becomes the primary heat sink, thereby 

ending the transient. 

• Break upstream of the MSIV inside of 

containment: The operators’ response to 

this event is the same as when the break is 

upstream of the MSIV and outside of 

containment: the FWIVs are closed, 

stopping feed to the faulted generator. 

However, the venting of steam from the 

break inside the containment structure 

increases pressure inside of containment, 

causing an “adverse containment” condition. 

As a result of the increase in pressure inside 

of containment, the ESFAS generates a 

containment isolation signal. This signal 

automatically isolates all containment 

penetrations that could (potentially) lead to a 

radioactive release; however, the source of 

cooling water to the RCPs is one of these 

penetrations. Without cooling water, the 

RCPs would seize, so operators must secure 

(stop) the RCPs. Without RCPs to circulate 

water in the cold leg, the mixing of cooler 

and hotter water in the downcomer reduces 

significantly, resulting in lower downcomer 

temperatures. 

Given the relative length of pipe runs, the 

ruggedness of the piping, and the pipe support 

system, MSLBs are most likely to occur 

downstream of the MSIVs. Also, as was the 

case with stuck-open valve transients (see 

Section 8.5.3), MSLBs can occur from either 

full power or HZP conditions. 

8.5.4.2 Model of this Transient Class 

As detailed in Table A.4 of Appendix A, our 

modeling of MSLB transients includes delayed 

operator actions, such as the following 

examples: 

• allowing feed to continue to the faulted 

steam generator for 30 minutes or 

indefinitely 

• throttling HPI to the primary, but only 30–

60 minutes after the throttling criteria have 

been met 

The model also includes exacerbating equipment 

failures, such as the following: 

• failure of MSIVs to close 

Additionally, the model adopts physically 

unrealistic temperatures, such as: 

• Most MSLBs in Beaver Valley and Oconee 

are assumed to occur inside containment 

(worst case). When a main steam line 

breaks inside of containment, the 

containment building is pressurized to 

~50psi (345 kPa), which elevates the boiling 

point of water to ~260°F (127°C). 

However, our model does not account for 

pressurization of containment by the break 

flow, so the boiling point of the secondary 

(and, consequently, the minimum 

temperature in the primary) is 212°F 

(100°C). This lower temperature increases 

the severity of the thermal shock to which 

the RPV wall is subjected and reduces the 

RPV’s resistance against this thermal shock. 

This conservative modeling approach was taken 

because PFM calculations performed early in the 

project indicated that even with these 

conservative assumptions, the contribution of 

MSLB transients to the total vessel risk was very 

small relative to the contribution of primary side 

pipe breaks and stuck-open primary side valves. 

Further refinement of the MSLB model to 

achieve increased realism would only reduce the 

risk-significance of the transients, and this 

refinement was not viewed as being necessary. 

Consequently, when considering the results 

presented in the following sections, the reader is 

reminded to view them as representing an upper 

bound to the vessel integrity challenge actually 

posed by MSLB transients. 
8-61

8.5.4.3 Relationships between System 

Characteristics and ThermalHydraulic Response 

In this section, we examine the effects of a 

variety of factors on the pressure and 

temperature transients associated with MSLBs: 

• Effect of plant power level at event 

initiation: Figure 8.33 and Figure 8.34 show 

the effect of an MSLB initiating from full 

power vs. HZP conditions. The initial 

cooldown rate associated with the HZP 

transients is more rapid than for the fullpower transients expected as a result of a 

lack of heat in the system, but only slightly 

so. The rapidity of the cooldown caused by 

the large break area of the main steam line 

mitigates the potential cooling rate boost 

associated with transient initiation from HZP. 

• Effect of break location: Figure 8.35 shows 

that MSLBs occurring inside containment 

experience considerably faster cooldown 

rates than when the break is outside of 

containment. As previously discussed, 

the break of a main steam line inside 

containment is expected to produce more 

rapid cooling of the downcomer because the 

RCPs will be shut down, resulting in less 

mixing of the hot and cold water in the 

downcomer. 

• Isolation of feedwater flow: Figure 8.36

shows that failure to isolate feedwater flow 

allows temperatures in the primary to 

continue to drop because feedwater flowing 

to the affected generator is still steaming 

and, therefore, still cooling the primary. 

• Timing of HHSI control: Safety injection 

flow initiates automatically following 

an MSLB to repressurize the primary. 

Figure 8.37 shows that when the operators 

throttle HHSI effects directly how long 

high pressures are maintained. 

In terms of plant-specific effects on MSLB 

transients, B&W plants (Oconee) differ from 

other plants because of the much smaller steam 

generator volume in the B&W design than in 

Combustion Engineering or Westinghouse 

designs. Consequently, the blowdown from 

an MSLB at Oconee concludes almost 

instantaneously, whereas the blowdown in 

Beaver Valley and Palisades takes 

approximately 250 seconds. The rapid 

blowdown in Oconee produces a much more 

rapid cooling rate than in the other two plants, 

but the minimum temperature associated with 

this rapid cooling is so high (far above 400°F 

(204°C)) that the risk of vessel failure is very 

very low. Thus, the vessel failure probability 

estimates discussed in the following section 

arise almost exclusively from the non-B&W 

plants. 

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

BV−102 (Full Power) 

BV−103 (Hot Zero Power) 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000 8000 10000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

BV−102 (Full Power) 

BV−103 (Hot Zero Power) 

0 2000 4000 6000 8000 100000

725

1450

2176

2901

Pressure (psia)

Figure 8.33. Power level effects on MSLB 

transients at Beaver Valley. Both breaks are in 

containment and have AUX feed continuing to the 

faulted generator for 30 minutes. The operator 

throttles HPSI 30 minutes after allowed. 
8-62

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

P−054 (Full Power) 

P−051 (Hot Zero Power) 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000 8000 10000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

P−054 (Full Power) 

P−051 (Hot Zero Power) 

0 2000 4000 6000 8000 100000

725

1450

2176

2901

Pressure (psia)

Figure 8.34. Power level effects on MSLB 

transients at Palisades. Both breaks are in 

containment and include failures of both MSIVs 

to close. The operator takes no actions to either 

isolate AUX feed or to throttle HPI. 

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

BV−106 (break in containment) 

BV−074 (break outside containment) 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000 8000 10000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

BV−106 (break in containment) 

BV−074 (break outside containment) 

0 2000 4000 6000 8000 100000

725

1450

2176

2901

Pressure (psia)

Figure 8.35. Break location effects on MSLB 

transients at Beaver Valley. Both breaks include 

continuous AUX feed and are initiated from fullpower conditions. In transient 106, the operator 

controls HPSI 30 minutes after allowed. 
8-63

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

P−049 (AFW isolated at 30 minutes) 

P−029 (AFW never isolated) 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000 8000 10000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

P−049 (AFW isolated at 30 minutes) 

P−029 (AFW never isolated) 

0 2000 4000 6000 8000 100000

725

1450

2176

2901

Pressure (psia)

Figure 8.36. Break isolation effects on MSLB 

transients at Palisades. Both breaks occur inside 

containment and are initiated from HZP 

conditions. 

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

BV−102 (HHSI controlled after 30 minutes) 

BV−104 (HHSI controlled after 60 minutes) 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000 8000 10000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

BV−102 (HHSI controlled after 30 minutes) 

BV−104 (HHSI controlled after 60 minutes) 

0 2000 4000 6000 8000 100000

725

1450

2176

2901

Pressure (psia)

Figure 8.37. Effect of HHSI control on MSLB 

transients at Beaver Valley. In both breaks, AUX 

feed is isolated 30 minutes after the break occurs. 

Both breaks are initiated from full-power 

conditions. 
8-64

8.5.4.4 Estimates of Vessel Failure 

Probability 

8.5.4.4.1 General Observations 

In the preceding section the effect of the 

following factors on the pressure and 

temperature transients associated with main 

steam line breaks was examined: 

• effect of plant power level at event initiation 

• effect of break location 

• isolation of feedwater flow 

• timing of HHSI control 

All of the long-time effects (isolation of 

feedwater flow, timing of HSSI control) have no 

effect on the vessel failure probability because 

these factors influence the progression of the 

thermal-hydraulic transient after failure has 

occurred (if it occurs). In almost all of the 

transients discussed in the previous section, 

vessel failure is predicted to occur between 

10 and 15 minutes after transient initiation 

(rare cases have failures as late as 30 minutes 

after initiation). Thus, operator actions 

(as modeled) cannot affect vessel failure 

probability. Only factors affecting the initial 

cooling rate can have any influence on CPTWC 

values. These factors include the plant power 

level at event initiation and the location of the 

break (inside or outside of containment). As 

shown in Figure 8.33 and Figure 8.34, the plant 

power level has only a slight influence on the 

initial cooling rate, and (so) only a slight 

influence on the CPTWC (less than a factor of 2 

increase). The location of the break (inside or 

outside of containment, see Figure 8.35) has a 

somewhat larger effect. For this comparison, 

the break inside containment has a CPTWC 

~3 times higher than the break outside of 

containment. 

Figure 8.38 presents a distribution describing the 

percentage of cracks initiated by MSLB transients 

that subsequently propagate through-wall. 

The large thermal component to the loading 

at the time of failure (10–15 minutes into the 

transient) allows a large percentage of the 

initiated cracks to experience a stable arrest. 

However, because there is a pressure component 

to MSLB transients (the relative proportion of 

pressure loading to thermal loading depends on 

the time of failure experienced by a particular 

simulation), in some situations, once the cracks 

initiate they almost always propagate entirely 

through the vessel wall. 

8.5.4.4.2 Applicability of these 

Findings to PWRs in 

General 

These results can be applied with confidence 

to PWRs in general for the following reasons: 

• Even though our model of MSLBs is 

intentionally conservative, the estimated 

conditional failure probabilities are low (10-9

to 10-5); realistic estimates can be expected 

to be lower (perhaps considerably so) 

because of the physically unrealistic aspects 

of our modeling (e.g., we have not modeled 

the pressure buildup inside of containment 

attributable to the MSLB, which would raise 

the minimum temperature of the primary 

system, thereby reducing the severity of the 

transient). 

• Operator actions (as modeled) have no 

influence whatsoever on the estimated 

failure probabilities reported here. 

• The part of the MSLB transient responsible 

for the reported failure probabilities is the 

rapid initial cooldown caused by 

depressurization of the secondary through 

the break. Since main steam lines are so 

large, the rapidity of this cooldown should 

not vary much from plant-to-plant, nor 

should it be influenced by other factors 

(plant power level at event initiation, 

operator actions, etc.) 

Figure 8.39 compares the portion of the TWCF 

attributable to MSLBs at the three study plants. 

Based on the factors discussed above, the plantto-plant consistency in the level MSLBs 

challenge is expected. 
8-65

0%

10%

20%

30%

40%

50%

0-10

10-2020-3030-4040-5050-6060-7070-8080-90

90-100

% of Initiated Cracks that 

Propigate Thru-Wall

% of MSLB Transient

s

Figure 8.38. Percentage of initiated cracks 

that propagate through-wall for MSLB transients 

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

100 150 200 250 300 350 400

RT from Table 8.5 [oF]

TWCF due to MSL

B

Oconee - MSLB

Beaver - MSLB

Palisades - MSLB

Figure 8.39. TWCF attributable to MSLB transients 

8.5.4.5 Comparison with Previous 

Studies 

8.5.4.5.1 As Reported by [Kirk 12-02] 

While the specific numerical results reported 

herein differ from those in our interim report 

[Kirk 12-02], the general trends discussed in this 

section have not changed substantively from 

those reported earlier. 

8.5.4.5.2 Studies Providing the 

Technical Basis of the 

Current PTS Rule 

In analyses performed to establish the technical 

basis for the current PTS Rule three plants were 

analyzed: Oconee, H.B. Robinson, and Calvert 

Cliffs [ORNL-86, ORNL-85b, ORNL-85a, 

respectively]. Analyses of Oconee and H.B. 

Robinson revealed secondary failures (either 

MSLBs or secondary valve openings) to be the 

most dominant class of transient (following the 

“residual” categorization in Oconee), in contrast 

to the information reported here, which shows 

the contribution of MSLBs to be much less than 

that associated with either primary side pipe 

breaks or with stuck-open primary side relief 

valves that reclose after a significant cooling 

period. (See Figure 8.40 for a summary of current 

TWCF predictions divided by transient class.) 

In the previous analyses of Oconee and H.B. 

Robinson, MSLBs had to be more risk-significant 

than either (1) medium–large diameter pipe 

breaks or (2) stuck-open relief valves on the 

primary side that reclose after a significant 

cooling period simply because these classes of 

transients were not modeled in the earlier studies. 

At the time of these previous analyses, the 

prevalent technical belief regarding vessel 

failure was that “rapid depressurization will 

severely limit the potential for a vessel failure” 

[ORNL-85b]. Consequently, no breaks larger 

than 2.5-in. (6.4-cm) in diameter were 

considered in these analyses. Further, while 

stuck-open primary side valve scenarios were 

analyzed, and early isolation of stuck-open 

pressurizer pilot-operated relief valve scenarios 

were also examined, late reclosures of primary 
8-66

side valves after significant cooling has occurred 

were not analyzed in the Oconee and H.B. 

Robinson analyses. 

In the Calvert Cliffs analysis [ORNL-85a], the 

LOCAs considered included pipe diameters only 

up to 3-in. (7.6-cm). However, for Calvert Cliffs, 

“late” reclosures of stuck-open pressurizer relief 

valves (i.e., reclosures occurring 11⁄2 hours into 

the transient) were analyzed. In the 1985 ORNL 

analysis of Calvert Cliffs, such a reclosure event 

(similar to those we analyzed in this updated 

study), especially at HZP, was found to be 

the highest or among the top three highest 

“dominant risk sequences” depending on the 

EFPY of the vessel (including being more 

important than steam line breaks, as we have 

found in this updated study). Hence, the early 

Calvert Cliffs analysis [ORNL-85a] shows 

trends similar to those reported herein. 

Additionally, even though our treatment of 

MSLBs has been conservative, it is still more 

refined than in previous studies largely because 

of the evolution of computer capabilities and the 

ability to analyze many more scenarios more 

completely today than was available more than 

20 years ago. For example, the secondary side 

break models adopted in the previous analyses 

often represented a full spectrum of secondary 

side breaks from small breaks and valve opening 

scenarios through a break of the main steam line 

using the bounding pressure/temperature vs. 

time transient characteristic of an MSLB. This 

approach overestimated both the severity of 

many secondary side events and the frequency 

of their occurrence. Furthermore, many of the 

TH profiles (e.g., for downcomer temperature 

vs. time) were based, in part, on extrapolations 

of the early timing profile trends and other hand 

calculations that tended to conservatively predict 

the degree of cooling in the downcomer region. 

Based on the above along with advances in our 

technical understanding and modeling of cooling 

scenarios, the associated thermal-hydraulics, and 

vessel fracture mechanics, it is understandable 

that the early belief that secondary failures 

dominate PTS risk has changed to that provided 

in this study. 

8.5.5 Stuck-Open Valves on the 

Secondary Side (SO-2) 

8.5.5.1 General Description of SO-2 

Transients 

The steam supply system contains several valves 

to control pressure. All of these valves have 

opening areas much smaller than the main steam 

line, so opening any one (or even several) of 

them does not produce nearly as rapid a 

depressurization rate (and consequently cooling 

rate) as that associated with MSLB transients 

(see Section 8.5.4). The general progress of a 

transient associated with one (or many) 

secondary side valves sticking open is, therefore, 

similar to that described for MSLBs (see Section 

8.5.4.1), with the exception that all of these 

valves are outside of containment, so the 

considerations associated with a break in 

containment discussed in Section 8.5.4.1 do not 

apply to stuck-open secondary side valves. 
8-67

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

100 150 200 250 300 350 400

TWCF due to SO-1 Transient

Oconee - SO-1

Beaver - SO-1

Palisades - SO-1

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

100 150 200 250 300 350 400

TWCF due to Primary Side Pipe Breaks

Oconee - LOCA

Beaver - LOCA

Palisades - LOCA

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

100 150 200 250 300 350 400

TWCF due to MSLB

Oconee - MSLB

Beaver - MSLB

Palisades - MSLB

Reference Temperature [oF]

SO-1

M&L LOCA

MSLB

M&L LOCA

MSLB

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

100 150 200 250 300 350 400

TWCF due to SO-1 Transient

Oconee - SO-1

Beaver - SO-1

Palisades - SO-1

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

100 150 200 250 300 350 400

TWCF due to Primary Side Pipe Breaks

Oconee - LOCA

Beaver - LOCA

Palisades - LOCA

1.E-14

1.E-13

1.E-12

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

100 150 200 250 300 350 400

TWCF due to MSLB

Oconee - MSLB

Beaver - MSLB

Palisades - MSLB

Reference Temperature [oF]

SO-1

M&L LOCA

MSLB

M&L LOCA

MSLB

Figure 8.40. Comparison of TWCF attributable to primary side stuck-open valves, primary side pipe breaks, 

and MSLBs. Note that the contribution of MSLBs here overrepresents their actual contributions to TWCF 

because of conservatisms in their modeling. On each graph, an upper-bound curve is hand drawn to the data 

originally presented in Figure 8.23, Figure 8.32, and Figure 8.39. On the left hand graph, all three 

upper-bound curves are placed together for easy comparison. 

8.5.5.2 Model of this Transient Class 

Tables A.5 and A.6 in Appendix A detail the 

transients analyzed as SO-2s. The transients in 

Table A.5 include the sticking open of all main 

steam safety valves (MSSVs) or turbine bypass 

valves (TBVs). The opening of all TBVs is an 

action taken to depressurize the secondary in 

response to complete loss of both main and 

emergency feedwater to a single steam 

generator. Different scenarios are selected to 

assess the effect of smaller breaks of the steam 

line than those discussed in Section 8.5.4, 

including all MSSVs sticking open, one MSSV 

sticking open, or an ADV sticking open. The 

transients in Table A.6 begin with the trip of the 

reactor/turbine. This is followed by one or two 

of the TBVs or ADVs being opened to purge 

energy from the system. If these valves stick 

open, an overcooling transient begins. In both 

sets of transients (Table A.5 and A.6), the effects 

of operator actions and plant power level 

at event initiation are modeled. 

Our modeling of this class of transients is not 

“best estimate.” Rather, we have tended to 

examine bounding cases. This approach was 

motivated by the knowledge that MSLB 

transients (which are more severe than SO-2 

transients because of the larger break area) 

contribute very little to the overall TWCF. 

(See Figure 8.41 for a comparison of cooldown 

rates of all transient classes.) Consequently, 

detailed analysis of SO-2 transients was not 

viewed as being warranted. When considering 

the results presented for SO-2 transients, the 

reader is reminded (1) to view them as 

representing an upper bound to the vessel 

integrity challenge actually posed by SO-2 

transients, and (2) to expect a greater apparent 

risk-significance of SO-2 transients in Palisades 

than in the other two plants as a result of the lack 

of refinement in the Palisades model of this 

transient class. 
8-68

 0 2000 4000 6000

Time (s)

250

350

450

550

650

Temperature (K)

16.0" (BV−009) 

8.0" (BV−007) 

4.0" (BV−056) 

2.828" (BV−114) 

2.0" (BV−003) 

1.414" (BV−002) 

0 2000 4000 6000−10

170

350

530

710

Temperature (F) 0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

O−113: HPI throttled after 10 minutes, 6000 s, full power 

BV−126: HPI throttled after 10 minutes, 6000 s, full power 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

(a) Primary pipe breaks (b) Primary stuck-open valves 

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

P−054 (Full Power) 

P−051 (Hot Zero Power) 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

BV−111 

BV−118 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

(c) MSLB (d) All MSSVs Stuck Open 

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

O−098 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

P−019 

P−055 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

(e) all TBVs stuck open (f) 1 or 2 ADVs stuck open 

Figure 8.41. The cooldown rate of various SO-2 transients, graphs (d) through (f), compared to MSLBs, 

graph (c), and primary side transients, graphs (a) and (b). 

8.5.5.3 Relationships between System 

Characteristics and ThermalHydraulic Response 

As illustrated in Figure 8.41, the cooling rate 

associated with SO-2 transients is slower than 

for MSLBs and, in general, decreases with 

decreasing valve opening area. Additionally, 

while the minimum temperature experienced 

when MSSVs are open is the same as during an 

MSLB, the minimum temperature produced by 

opening TBVs or ADVs is higher (nearly 100°F 

(55.5°C) higher), further redacting the severity 

of these transients relative to MSLBs. Figure 
8-69

8.42 through Figure 8.45 show both the 

temperature and pressure characteristics of a 

variety of different transients in the SO-2 

category. These graphs show that for a number 

of different reasons (HHSI into the primary and 

failure to throttle same, AUX feed, etc.) SO-2 

transients generally experience some (or even 

full) system pressure in the primary. 

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

BV−111 

BV−118 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000 8000 10000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

BV−111 

BV−118 

0 2000 4000 6000 8000 100000

725

1450

2176

2901

Pressure (psia)

Figure 8.42. Small steam line break simulated by sticking open all MSSVs in steam generator A 

with AFW continuing to feed affected generator for 30 minutes. Beaver Valley transient 111 occurs at HZP, 

while Beaver Valley transient 118 occurs at full power. 

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

O−098 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000 8000 10000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

O−098 

0 2000 4000 6000 8000 100000

725

1450

2176

2901

Pressure (psia)

Figure 8.43. Reactor/turbine trip with loss of MFW and EFW in Oconee. 

Operator opens all TBVs to depressurize the secondary side. 

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

O−031 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000 8000 10000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

O−031 

0 2000 4000 6000 8000 100000

725

1450

2176

2901

Pressure (psia)

Figure 8.44. Reactor/turbine trip with two stuck-open safety valves in Oconee. 
8-70

0 2000 4000 6000 8000 10000

Time (s)

250

350

450

550

650

Temperature (K)

P−019 

P−055 

0 2000 4000 6000 8000 10000−10

170

350

530

710

Temperature (F)

0 2000 4000 6000 8000 10000

Time (s)

0.0

5.0

10.0

15.0

20.0

Pressure (MPa)

P−019 

P−055 

0 2000 4000 6000 8000 100000

725

1450

2176

2901

Pressure (psia)

Figure 8.45. Reactor/turbine trip with one or two stuck-open ADVs (P-019 and P-055, respectively) 

in Palisades. 

8.5.5.4 Estimates of Vessel Failure 

Probability 

The CPTWC of SO-2 transients tends to be very 

low, consistent with the more 

gradual cooling rates caused by 

these transients relative to other 

transient classes (see Figure 8.41). 

Ranges of SO-2 CPTWC values for 

different transients are as follows 

(different plants are compared at 

roughly equivalent levels of 

embrittlement, see 

Table 8.6): 

• Many stuck-open valves: CPTWC ranges 

from E-13 to E-10. 

• One or two stuck-open valves: CPTWC 

ranges from E-13 to E-7. 

Comparing these values with the E-5 to E-4 

CPTWC values associated with the significant 

transients in the dominant classes (primary side 

pipe breaks and stuck-open valves on the 

primary side) provides a perspective on the 

limited influence of SO-2 transients to the total 

TWCF estimated for a vessel. As stated earlier, 

it is only the conservative binning of Palisades 

transients, this leading to high estimates of bin 

frequencies (see section 8.5.5.2), that has led 

SO-2 transients to contribute non-negligibly to 

the percentage total TWCF in Palisades (see 

Figure 8-11). More refined analysis of SO-2 

transients for Palisades would reduce their 

influence to the point of being immeasurable, as 

was the case for Beaver Valley and Oconee. 

Two factors in our analysis suggest that these 

findings can be applied to PWRs in general: 

• the conservative modeling of SO-2 

frequencies in Palisades 

• the fact that the CPTWC values that result 

from all secondary side valves sticking open 

produces values that are negligible (E-13 to 

E-10) relative to significant transients in the 

dominant classes (E-5 to E-4). 

Section 9.3 provides further discussion of the 

similarities and differences between the SO-2 

modeling employed here and the general 

conditions in the operating fleet. 

8.5.5.5 Comparison with Previous 

Studies 

8.5.5.5.1 As Reported by [Kirk 12-02] 

While the specific numerical results reported 

herein differ from those in our interim report 

[Kirk 12-02], the general trends discussed in this 

section have not changed substantively from 

those previously reported. 

8.5.5.5.2 Studies Providing the 

Technical Basis of the 

Current PTS Rule 

In the preceding analysis of the Oconee plant 

[ORNL 86], relevant operator action HEPs were 

applied to a wide spectrum of scenarios (i.e., not 

so scenario-specific). This analysis used generic 
8-71

probabilities for a limited number of operator 

events and did not consider all of the various 

times that we investigated. Thus, the preceding 

analysis of the Oconee plant for SO-2 transients 

should be viewed as being conservative relative 

to that reported herein. In the preceding analyses 

of Robinson and Calvert Cliffs [ORNL 85b, 

ORNL 85a], the HRA became more 

sophisticated, in that the HEPs were assigned on 

a more scenario-specific basis than for Oconee. 

However, these analyses still did not model 

different action times, as was done in our 

analysis. For these reasons, the preceding 

analysis of both Oconee and or H.B. Robinson 

for SO-2 transients should be viewed as being 

conservative relative to that reported herein. 

Other generic factors contribute to the conservatism 

of the preceding analyses: 

• Today, we have more industry experience, 

providing a larger data basis upon which to 

establish initiating event frequency 

estimates. The number of initiating events 

per year has declined since the earlier 

analyses were performed. 

• Procedures and training have improved 

considerably. 

• Modern PRA and HRA techniques have 

allowed us to do more refined analyses and 

model industry improvements. 

• Increased computational ability has enabled 

finer subdivision of the challenges to the 

plant (more bins). This has considerably 

reduced the conservatism inherent to the 

binning process. 

8.5.6 Other Transient Classes 

Tables A.7 and A.8 in Appendix A summarize 

the transients analyzed in the following classes: 

• feed-and-bleed 

• steam generator tube rupture 

• overfeeds 

• mixed primary and secondary side failures 

In all cases, the combination of the low 

probability of these events occurring with the 

low consequence of the event produces 

transients that are not risk-significant. 

8.6 Summary 

This chapter provides the results of plantspecific analyses of Oconee Unit 1, Beaver 

Valley Unit 1, and Palisades. In the following 

list, which summarizes the information 

presented in this chapter, the conclusions are 

shown in bold italics while supporting 

information is shown in regular type: 

• The degree of PTS challenge for currently 

anticipated lifetimes and operating

conditions is low. 

o Even at the end of license extension 

(60 operational years, or 48 EFPY at an 

80% capacity factor), the mean estimated 

through-wall cracking frequency (TWCF) 

does not exceed 2x10-8/year for the 

plants analyzed. Considering that the 

Beaver Valley and Palisades RPVs are 

constructed from some of the most 

irradiation-sensitive materials in 

commercial reactor service today, these 

results suggest that, provided that 

operating practices do not change 

dramatically in the future, the operating 

reactor fleet is in little danger of 

exceeding either the limit on TWCF of 

5x10-6/yr expressed by Regulatory 

Guide 1.154 [RG 1.154] or the 1x10-6/yr 

value recommended in Chapter 10, even 

after license extension. 

• Mean TWCF values are in fact upper 

bounds. 

o Because of the skewness characteristic 

of the TWCF distributions that arise as a 

result of the physical processes 

responsible for steel fracture, mean 

TWCF values correspond to the 90th

percentile (or higher) of the TWCF

distribution. Thus, the mean TWCF values 

we report in this chapter are appropriately 

regarded as upper bounds to the 

uncertainty distribution on TWCF. 
8-72

• Axial flaws, and the toughness properties 

that can be associated with such flaws, 

control nearly all of the TWCF. 

o Axial flaws are much more likely to 

propagate through-wall than 

circumferential flaws because the 

applied driving force to fracture 

increases continuously with increasing 

crack depth for an axial flaw. 

Conversely, circumferentially oriented 

flaws experience a driving force peak 

mid-wall, providing a natural crack 

arrest mechanism. It should be noted 

that crack initiation from 

circumferentially oriented flaws is 

likely; it is only their through-wall 

propagation that is much less likely 

(relative to axially oriented flaws). 

o It is, therefore, the toughness properties 

that can be associated with axial flaws 

that control nearly all of the TWCF. 

These include the toughness properties 

of plates and axial welds at the flaw 

locations. Conversely, the toughness 

properties of both circumferential welds 

and forgings have little effect on TWCF 

because these can be associated only 

with circumferentially oriented flaws. 

• Transients involving primary side faults 

are the dominant contributors to TWCF. 

Transients involving secondary side faults 

play a much smaller role. 

o The severity of a transient is controlled 

by a combination of three factors: 

 the initial cooling rate, which 

controls the thermal stress in the 

RPV wall 

 the minimum temperature of the 

transient, which controls the 

resistance of the vessel to fracture 

 the pressure retained in the primary 

system, which controls the pressure 

stress in the RPV wall 

o The significance of a transient (i.e., how 

much it contributes to PTS risk) depends 

on these three factors and on the 

likelihood of the transient occurring. 

o Our analysis considered transients in the 

following classes: 

 primary side pipe breaks 

 stuck-open valves on the primary side 

 main steam line breaks 

 stuck-open valves on the secondary side 

 feed-and-bleed 

 steam generator tube rupture 

 mixed primary and secondary initiators 

o Table 8.12 summarizes our results for 

these transient classes in terms of both 

transient severity indicators and the 

likelihood of the transient occurring. 

The color-coding of table entries 

indicates the contribution (or not) 

of these factors to the TWCF of the 

different classes of transients. 

This summary indicates that the riskdominant transients (medium- and largediameter primary side pipe breaks, and 

stuck-open primary side valves that later 

reclose) all have multiple factors that, 

in combination, result in their significant 

contribution to TWCF. 

 For medium- to large-diameter 

primary side pipe breaks, the fast to 

moderate cooling rates and the low 

downcomer temperatures (generated 

by the rapid depressurization and 

emergency injection of lowtemperature makeup water directly 

to the primary) combine to produce 

a high-severity transient. Despite 

the moderate to low likelihood of 

transient occurrence, the severity of 

these transients (if they occur) 

makes them significant contributors 

to the total TWCF. 

 For stuck-open primary side valves 

that later reclose, the repressurization 

associated with valve reclosure 

coupled with low temperatures in 

the primary combine to produce a 

high-severity transient. This 

coupled with a high likelihood of 

transient occurrence makes stuckopen primary side valves that later 

reclose significant contributors to 

the total TWCF. 
8-73

Table 8.12. Factors contributing to the severity and risk-dominance of various transient classes 

 

Transient Severity 

Transient Class Cooling 

Rate 

Minimum 

Temperature Pressure 

Transient 

Likelihood 

TWCF 

Contribution 

Large-Diameter Fast Low Low Low Large 

Medium-Diameter Moderate Low Low Moderate Large 

Primary 

Side Pipe 

Breaks Small-Diameter Slow High Moderate High ~0 

Primary Valve Recloses Slow Moderate High High Large 

Stuck-Open 

Valves 

Valve Remains 

Open Slow Moderate Low High ~0 

Main Steam Line Break Fast Moderate High High Small 

Stuck-Open Valve(s), 

Secondary Side Moderate High High High ~0 

Feed-and-Bleed Slow Low Low Low ~0 

Steam Generator Tube Rupture Slow High Moderate Low ~0 

Mixed Primary & Secondary 

Initiators Slow Mixed Very Low ~0 

Color Key Enhances TWCF Contribution Intermediate Diminishes TWCF 

Contribution 
8-74

 The small or negligible contribution 

of all secondary side transients 

(MSLBs, stuck-open secondary 

valves) results directly from the lack 

of low temperatures in the primary 

system. For these transients, the 

minimum temperature of the 

primary for times of relevance is 

controlled by the boiling point of 

water in the secondary (212°F (100°C) 

or above). At these temperatures, 

the fracture toughness of the RPV 

steel is sufficiently high to resist 

vessel failure in most cases. 

• Credits for operator action, while included 

in our analysis, do not influence these 

findings in any significant way. Operator 

action credits can dramatically influence the 

risk-significance of individual transients. 

Appropriate credits for operator action, 

therefore, need to be included as part of a 

“best estimate” analysis because there is no 

way to establish a priori if a particular 

transient will make a large contribution to 

the total risk. Nonetheless, the results of our 

analyses demonstrate that the overall effect

of these operator action credits on the total 

TWCF for a plant is small, for the following 

reasons:

o Medium- and Large-Diameter Primary 

Side Pipe Breaks: No operator actions 

are modeled for any break diameter 

because, for these events, the safety 

injection systems do not fully refill 

the upper regions of the RCS. 

Consequently, operators would never 

take action to shut off the pumps. 

o Stuck-Open Primary Side Valves that 

May Later Reclose: Reasonable and 

appropriate credit for operator actions 

(throttling of HPI) has been included in 

the PRA model. However, the influence 

of these credits on the estimated values 

of vessel failure probability attributable 

to SO-1 transients is small because the 

operator actions credited only prevent 

repressurization when SO-1 transients 

initiate from HZP conditions and when 

the operators act promptly (within 

1 minute) to throttle HPI. Complete 

removal of operator action credits from 

the model increases the total risk 

associated with SO-1 transients only 

slightly. 

o Main Steam Line Breaks: For the 

overwhelming majority of MSLB 

transients, vessel failure is predicted to 

occur between 10 and 15 minutes after 

transient initiation because it is within 

this timeframe that the thermal stresses 

associated with the rapid cooldown 

reach their maximum. Thus, all of the 

long-time effects (isolation of feedwater 

flow, timing of HSSI control) that can 

be influenced by operator actions have 

no effect on vessel failure probability 

because these factors influence the 

progression of the transient after failure 

has occurred (if it occurs). Only factors 

affecting the initial cooling rate (i.e., 

plant power level at transient initiation, 

break location inside or outside of 

containment) can influence the CPTWC 

values. These factors are not influenced 

in any way by operator actions. 

• Because the severity of the most significant 

transients in the dominant transient classes 

are controlled by factors that are common 

to PWRs in general, the TWCF results 

presented in this chapter can be used with 

confidence to develop revised PTS 

screening criteria that apply to the entire 

fleet of operating PWRs. 

o Medium- and Large-Diameter Primary 

Side Pipe Breaks: For these break 

diameters, the fluid in the primary cools 

faster than can the wall of the RPV. 

In this situation, only the thermal 

conductivity of the steel and the 

thickness of the RPV wall control the 

thermal stresses and, thus, the severity 

of the fracture challenge. Perturbations 

to the fluid cooldown rate controlled by 

break diameter, break location, and 

season of the year do not play a role. 

Thermal conductivity is a physical 

property, so it is very consistent for all 
8-75

RPV steels, and the thicknesses of the 

three RPVs analyzed are typical of 

PWRs. Consequently, the TWCF 

contribution of medium- to largediameter primary side pipe breaks is 

expected to be consistent from plant-toplant and can be well-represented for all 

PWRs by the analyses reported herein. 

o Stuck-Open Primary Side Valves that 

May Later Reclose: A major 

contributor to the risk-significance of 

SO-1 transients is the return to full 

system pressure once the valve recloses. 

The operating and safety relief valve 

pressures of all PWRs are similar. 

Additionally, as previously noted, 

operator action credits affect the total 

risk associated with this transient class 

only slightly. 

o Main Steam Line Breaks: Since MSLBs 

fail early (within 10–15 minutes after 

transient initiation), only factors 

affecting the initial cooling rate can 

have any influence on CPTWC values. 

These factors include the plant power 

level at event initiation and the location 

of the break (inside or outside of 

containment). These factors are not 

influenced in any way by operator 

actions. 

 
9-1

9 Generalization of the Baseline Results 

to All Pressurized-Water Reactors 

In Chapter 8, we presented the results of three 

plant-specific analyses of Oconee Unit 1, Beaver 

Valley Unit 1, and Palisades. These analyses 

quantified the variation with material 

embrittlement level of the annual risk of 

developing a through-wall crack in an RPV. 

Since the objective of this project is to develop 

a revision to the PTS screening limit expressed 

in 10 CFR 50.61 that applies in general to all 

PWRs, it is critical that we understand the extent 

to whixh our analyses adequately address the 

range of conditions experienced by domestic 

PWRs. In this chapter, we therefore examine 

the generality of our results, focusing on four 

topics that address this goal: 

• Sections 9.1 and 9.2 describe sensitivity 

studies performed on the TH and PFM 

models, respectively. These studies address 

the effect of credible changes to the model 

and/or its input parameters on the output of 

the model. Such results are needed to 

engender confidence in both the robustness 

of the results presented in Chapter 8 and 

their applicability to PWRs in general. 

• Section 9.3 describes an effort in which we 

examine the plant design and operational 

characteristics of five additional plants. 

Our aim is to determine whether the design 

and operational features that are the key 

contributors to PTS risk (see Section 8.6) 

vary significantly enough in the general 

plant population to question the generality 

of our results. 

• Throughout our analysis, we have assumed 

that the only possible causes of PTS events 

have origins that are internal to the plant. 

However, external events such as fires, 

floods, earthquakes, and so on, can also be 

PTS precursors. Therefore, in Section 9.4, 

we examine the potential for external 

initiating events to create significant 

additional risk relative to the internal initiating 

events we have already modeled in detail. 

9.1 Thermal-Hydraulic Sensitivity 

Studies 

9.1.1 Introduction 

This section addresses the results and observations 

of the thermal-hydraulic analyses and sensitivity 

studies performed to support the PTS analysis. 

The sensitivity studies were performed to evaluate 

the effects of variations in parameters that can 

affect the downcomer conditions used as 

boundary conditions to the probabilistic fracture 

mechanics analysis. These conditions are the 

average downcomer fluid temperature, the 

system pressure and the average downcomer 

fluid to wall heat transfer coefficient. 

The sensitivity studies were performed 

to achieve the following purposes: 

(1) Determine the effect on average downcomer 

fluid temperature range attributable to 

variation of system parameters such as break 

size, break location, season, and others. 

(2) Evaluate the impact of downcomer heat 

transfer coefficient on the downcomer 

conditions and, ultimately, on conditional 

probability of through-wall cracking 

(CPTWC). 

The thermal-hydraulic analysis was performed 

using RELAP5/MOD3.2.2Gamma. Chapter 6 

presents a discussion of RELAP5 as used in this 

analysis, along with a comparison of RELAP 

predictions of pressure, temperature, and heat 

transfer coefficient to the results of both separate 

effects and integral systems and tests (see 

Section 6.7). A discussion of how uncertainty 

was factored into the analysis is also presented 

in Chapter 6 (see Section 6.8.2). 
9-2

9.1.2 Sensitivity Studies Performed for 

Uncertainty Analysis 

Selection of sensitivity studies that were 

performed is based largely on previous 

experience with the types of transients being 

analyzed combined with variations in plant 

operating states that can affect the downcomer 

conditions. Sensitivity studies were performed 

for the Oconee, Beaver Valley, and Palisades 

plants to support the thermal-hydraulic 

uncertainty analyses. As previously noted, the 

uncertainty analysis approach is discussed in 

Chapter 6. This section focuses on the results of 

the sensitivity studies conducted to support the 

uncertainty analysis. [Chang] discusses the 

sensitivity and uncertainty analyses in detail. 

9.1.2.1 LOCAs 

Sensitivity analyses were performed on LOCAs 

ranging from 1.4-in. (3.59-cm) to 8-in. (20.32-cm) 

for the Oconee, Beaver Valley, and Palisades 

plants. Various sensitivity parameters were 

defined and a RELAP5 run was made for a 

selected parameter, changing only that 

parameter. The average downcomer fluid 

temperature over a 10,000-second period was 

then computed. The downcomer temperature 

difference between the nominal case 

(no parameters varied) and the cases where a 

parameter is varied is used in the uncertainty 

analysis. 

Table 9.1, Table 9.2, and Table 9.3 present a 

summary of the key sensitivity parameters and 

the effects on downcomer temperature for the 

Oconee, Beaver Valley, and Palisades plants, 

respectively. The nominal temperatures are 

based on RELAP5 runs with no change in 

sensitivity parameters, while the other 

temperatures listed are the differences between 

the temperature results for the changed 

sensitivity parameter and the nominal 

temperature results. Several parameters were 

considered in the sensitivity analysis, including 

season of the year, decay heat load, heat transfer 

coefficient, break area, and break location. 

Season of the year considered the impact of 

winter and summer on the ECCS injection water 

temperature. Typically, the RWST (or equivalent), 

which is the source of HPI and LPI injection 

water, is located outdoors. The temperature 

range analyzed is listed below: 

• Oconee: The HPI and LPI injection 

temperature used is 303 K [85°F], and the 

core flood tank temperature is 311 K 

[100°F] during the summer. During the 

winter, the HPI and LPI injection 

temperature used is 278 K [40°F], and the 

core flood tank temperature is 294 K [70°F]. 

For the nominal case, the HPI and LPI 

injection temperature used is 294 K [70°F], 

and the core flood tank temperature is 300 K 

[80°F]. 

• Beaver Valley: HPI and LPI injection 

temperature used is 286 K [55°F], and core 

flood tank temperature is 314 K [105°F] 

during the summer. During the winter, the 

HPI and LPI injection temperature used is 

281 K [45°F], and the core flood tank 

temperature is 297 K [75°F]. For the 

nominal case, the HPI and LPI injection 

temperature used is 283 K [50°F], and core 

flood tank temperature is 305 K [90°F]. 

Note that Beaver Valley currently cools the 

RWST to meet LOCA safety limits. 

• Palisades: The HPI and LPI injection 

temperature used is 311 K [100°F], and the 

safety injection tank temperature is 305 K 

[90°F] during the summer. During the 

winter, the HPI and LPI injection 

temperature used is 278 K [40°F], and the 

safety injection tank temperature is 289 K 

[60°F]. For the nominal case, the HPI and 

LPI injection temperature used is 304 K 

[87.9°F], and the safety injection tank 

temperature is 300 K [80°F]. 
9-3

Table 9.1. Summary of Oconee Downcomer Fluid Temperature Sensitivity Results for LOCA 

Break Diameter 

Parameter 3.6-cm 

[1.4 in] 

5.1-cm 

[2 in] 

7.2-cm 

[2.8 in] 

10.2-cm 

[4 in] 

14.4-cm 

[5.7 in] 

20.3-cm 

[8 in] 

Nominal 414 K 

[285°F] 

394 K 

[250°F] 

388 K 

[239°F] 

363 K 

[194°F] 

329 K 

[133°F] 

317 K 

[111°F] 

Winter -12 K 

[-22°F] 

- -14 K 

[-25°F] 

- -15 K 

[-27°F] 

-3 K 

[-5°F] 

Summer - - 7 K 

[13°F] 

- 7 K 

[13°F] 

0 K 

[0°F] 

0.7% Decay Heat Load -16 K 

[-29°F] 

- -39 K 

[-70°F] 

- -8 K 

[-14°F] 

-5 K 

[-9°F] 

130% Heat Transfer Coeff - 6 K 

[11°F] 

8 K 

[14°F] 

- 2 K 

[4°F] 

- 

70% Heat Transfer Coeff - -7 K 

[-13°F] 

-8 K 

[-14°F] 

- -5 K 

[-9°F] 

- 

Cold Leg Break 61 K 

[110°F] 

24 K 

[43°F] 

13 K 

[23°F] 

16 K 

[29°F] 

0 K 

[0°F] 

Note: The nominal temperatures listed above are based on RELAP5 runs with no change in sensitivity parameters. Other temperatures 

listed are the difference between the temperature results for the changed sensitivity parameter and the nominal temperature results. 

Table 9.2. Summary of Beaver Valley Downcomer Fluid Temperature Sensitivity Results for LOCA 

Break Diameter 

Parameter 3.6-cm 

[1.4 in] 

5.1-cm 

[2 in] 

7.2-cm 

[2.8 in] 

10.2-cm 

[4 in] 

14.4-cm 

[5.7 in] 

20.3-cm 

[8 in] 

Nominal 459 K 

[367°F] 

377 K 

[219°F] 

336 K 

[145°F] 

319 K 

[115°F] 

313 K 

[104°F] 

300 K 

[80°F] 

Winter -2 K 

[-4°F] 

-11 K 

[-20°F] 

-3 K 

[-5°F] 

-1 K 

[-2°F] 

3 K 

[5°F] 

-3 K 

[-5°F] 

Summer 1 K 

[2°F] 

-7 K 

[-13°F] 

8 K 

[14°F] 

12 K 

[22°F] 

5 K 

[9°F] 

3 K 

[5°F] 

0.7% Decay Heat Load -99 K 

[-178°F] 

-29 K 

[-52°F] 

-11 K 

[-20°F] 

-7 K 

[-13°F] 

-9 K 

[-16°F] 

-1 K 

[-2°F] 

0.2% Decay Heat Load -106 K 

[-191°F] 

-40 K 

[-72°F] 

-16 K 

[-29°F] 

-10 K 

[-18°F] 

-11 K 

[-20°F] 

-2 K 

[-4°F] 

130% Heat Transfer Coeff 3 K 

[5°F] 

-3 K 

[-5°F] 

6 K 

[11°F] 

5 K 

[9°F] 

 0 K 

[0°F] 

70% Heat Transfer Coeff -4 K 

[-7°F] 

-15 K 

[-27°F] 

-5 K 

[-9°F] 

2 K 

[4°F] 

 

130% Break Area -48 K 

[-86°F] 

-11 K 

[-20°F] 

-12 K 

[-22°F] 

-13 K 

[-23°F] 

1 K 

[2°F] 

70% Break Area -18 K 

[-32°F] 

23 K 

[41°F] 

4 K 

[7°F] 

-7 K 

[-13°F] 

6 K 

[11°F] 

Cold Leg Break -4 K 

[-7°F] 

76 K 

[137°F] 

79 K 

[142°F] 

50 K 

[90°F] 

34 K 

[61°F] 

40 K 

[72°F] 

Note: The nominal temperatures listed above are based on RELAP5 runs with no change in sensitivity parameters. Other temperatures 

listed are the difference between the temperature results for the changed sensitivity parameter and the nominal temperature results. 
9-4

Table 9.3. Summary of Palisades Downcomer Fluid Temperature Sensitivity Results for LOCA 

Break Diameter 

Parameter 3.6-cm 

[1.4 in] 

5.1-cm 

[2 in] 

7.2-cm 

[2.8 in] 

10.2-cm 

[4 in] 

14.4-cm 

[5.7 in] 

20.3-cm 

[8 in] 

Nominal 482 K 

[408°F] 

427 K 

[309°F] 

391 K 

[244°F] 

350 K 

[170°F] 

320 K 

[116°F] 

310 K 

[98°F] 

Winter -6 K 

[-11°F] 

-8 K 

[-14°F] 

-17 K 

[-31°F] 

-16 K 

[-29°F] 

-16 K 

[-29°F] 

-16 K 

[-29°F] 

Summer 8 K 

[14°F] 

10 K 

[18°F] 

13 K 

[23°F] 

14 K 

[25°F] 

13 K 

[23°F] 

15 K 

[27°F] 

0.7% Decay Heat Load -32 K 

[-58°F] 

-21 K 

[-38°F] 

-27 K 

[-49°F] 

-17 K 

[-31°F] 

-1 K 

[-2°F] 

0 K 

[0°F] 

0.2% Decay Heat Load -66 K 

[-119°F] 

-47 K 

[-85°F] 

-40 K 

[-72°F] 

-20 K 

[-36°F] 

-2 K 

[-4°F] 

-1 K 

[-2°F] 

130% Heat Transfer Coeff 4 K 

[7°F] 

6 K 

[11°F] 

11 K 

[20°F] 

5 K 

[9°F] 

 

70% Heat Transfer Coeff -3 K 

[-5°F] 

-2 K 

[-4°F] 

-2 K 

[-4°F] 

-4 K 

[-8°F] 

 

130% Break Area 13 K 

[23°F] 

24 K 

[43°F] 

20 K 

[36°F] 

14 K 

[25°F] 

3 K 

[5°F] 

70% Break Area -9 K 

[-16°F] 

-18 K 

[-32°F] 

-12 K 

[-22°F] 

-6 K 

[-11°F] 

-1 K 

[-2°F] 

Cold Leg Break 9 K 

[16°F] 

38 K 

[68°F] 

39 K 

[70°F] 

23 K 

[41°F] 

32 K 

[58°F] 

22 K 

[40°F] 

Note: The nominal temperatures listed above are based on RELAP5 runs with no change in sensitivity parameters. Other temperatures 

listed are the difference between the temperature results for the changed sensitivity parameter and the nominal temperature results. 

As listed in Table 9.1 through Table 9.3, the two 

levels of decay heat considered were 0.7% and 

0.2% of full power. The heat transfer coefficient 

was varied by 70% and 130% of the RELAP5 

computed value in the primary system except for 

the core and the steam generator tubes. The 

nominal break area was varied by a factor of 0.7 

and 1.3 to evaluate possible uncertainty in the 

break flow. Finally, breaks of various sizes in 

the cold leg as well as the hot leg are considered. 

Some overall trends in the results are seen from 

the results in Table 9.1, through Table 9.3. First, 

the magnitude of the variation from nominal 

generally decreases with increasing break size 

for all three plants regardless of the parameter 

being evaluated, because of the combined effects 

of increased break and ECCS flow that occurs as 

the break size increases. For break diameters of 

4-in. (10.2-cm) or more, ECCS flow is at a 

maximum since the HPI and LPI pumps are 

generally operating at pump runout conditions. 

For breaks diameters less than 2.8-in. (7.2-cm), 

the pump flow begins to become limited by the 

break flow, with decreasing pump flow as the 

break diameter is decreased. In this range of 

break diameters, the downcomer fluid 

temperature is more sensitive to changes in 

break diameter. 

Cold leg breaks generally show the greatest 

increase in downcomer fluid temperature for the 

three plants, principally because of partial ECCS 

bypass through the break. 

The assumed decay heat load between hot full 

power and hot zero power cases shows the 

greatest decrease in downcomer fluid 

temperature. These sensitivity parameters are 

part of the definition of the boundary conditions 

that typically are provided as part of the 

transient definition. 

Parameters that involve model sensitivity such 

as change in break area, change in heat transfer 

coefficient (system-wide) also significantly 

affect the downcomer fluid temperature. Of the 

two parameters, downcomer fluid temperature is 

more sensitive to changes in break flow. As a 

result, a number of transients with adjustments 
9-5 

in break area were included in the baseline 

models discussed in Chapter 8. 

 

9.1.2.2 Stuck-Open Pressurizer SRVs 

That Reclose 

Sensitivity cases for stuck-open primary side 

SRVs considered the following parameters: 

• Number of valves stuck open (i.e., one or 

two valves) 

• Timing of valve reclosure (Reclosure times 

of 3,000 s, 6,000 s, and no reclosure were 

analyzed. Additional sensitivity studies 

were conducted for longer reclosure times; 

see response to Peer Review Comment #76 

in Appendix B.) 

• Time for operator to start HPI throttling 

(i.e., 1 minute, 10 minutes, and not throttled) 

• Decay heat (i.e., full-power and HZP) 

The number of stuck-open valves analyzed for 

the three plants depended on the plant 

characteristics. For Oconee, analysis was 

performed for one stuck-open SRV, since the 

probability of two stuck-open valves was 

screened out on the basis of low probability. For 

Palisades, sensitivity analysis was not performed 

on the stuck-open valve scenarios. 

For Beaver Valley, sensitivity studies were 

performed for one and two stuck-open valves 

considering various parameters, similar to the 

approach used for LOCA transients. The range 

used for each parameter is the same as used for 

the LOCA. The sensitivity of downcomer fluid 

temperature to each parameter is listed in Table 

9.4. As in the LOCA case, the nominal 

temperatures are based on RELAP5 runs with no 

change in sensitivity parameters while the other 

temperatures listed are the difference between 

the changed and the nominal sensitivity 

parameter. 

Table 9.4. Summary of Downcomer Fluid 

Temperature Sensitivity Results 

for Stuck-Open Primary Side Valves 

Number of Stuck-Open SRVs

1 valve 2 valves 

Nominal 393 K 

[248°F] 

349 K 

[169°F] 

Winter -5 K 

[-9°F] 

-3 K 

[-5°F] 

Summer 0 K 

[0°F] 

6 K 

[11°F] 

0.7% Decay 

Heat Load 

-42 K 

[-76°F] 

-15 K 

[-27°F] 

0.2% Decay 

Heat Load 

-52 K 

[-93°F] 

-27 K 

[-49°F] 

130% Heat 

Transfer Coeff

3 K 

[-5°F] 

6 K 

[-11°F] 

70% Heat 

Transfer Coeff

-8 K 

[-14°F] 

-4 K 

[-7°F] 

130% Valve 

Flow Area 

 -22 K 

[-40°F] 

70% Valve 

Flow Area 

 10 K 

[18°F] 

Some overall trends in the results are seen in 

Table 9.4. The largest change in temperature 

is from the variation in decay heat, a finding 

consistent with the observations made in 

Section 8.5.3.3.2 concerning the differences 

between HZP and full-power transients. This 

sensitivity parameter is part of the definition of 

the transient boundary conditions that are part of 

the definition of the transient being analyzed. 

Changes in valve flow area also significantly 

affect the downcomer fluid temperature. 

Parameters that involve model sensitivity such 

as change in break area, change in heat transfer 

coefficient (system-wide) also significantly 

affect the downcomer fluid temperature. Of the 

two parameters, downcomer fluid temperature is 

more sensitive to changes in break flow. 

Changes in these parameters are considered in 

defining the transients used in the risk 

assessment. 
9-6 

9.1.2.3 CPTWC Sensitivity During 

LOCA Transients 

One of the trends identified in the sensitivity and 

uncertainty analysis performed in [Chang] is the 

relationship between the conditional probability 

of vessel failure (CPF) and the LOCA break 

diameter; see the related discussion in 

Sections 8.5.2.4.1 and 8.5.2.4.2. Figure 9.1 

presents the Oconee, Beaver Valley, and 

Palisades CPTWC results at an approximately 

equivalent embrittlement level. The CPTWC 

data presented in Figure 9.1 for Oconee and 

Beaver Valley are for surge line or hot leg 

breaks with the indicated diameter. The 

transients were initiated from hot full-power 

conditions. The data presented for Palisades are 

for cold leg breaks, with the exception of the 

16-in. (40.6-cm) results which represent a hot 

leg break. All of the Palisades cases are initiated 

from full-power conditions. 

The results in Figure 9.1 show that CPTWC is 

relatively insensitive to thermal-hydraulic 

conditions in the primary system during LOCAs 

with a break diameter greater than 5.656-in. 

(14.4-cm). For these break diameters, the 

primary system cooldown rate is governed by 

the high rate of break and ECCS injection flow, 

which is a maximum at this break size range. 

The safety injection tanks discharge within a few 

minutes of accident initiation. Additionally, the 

high pressure and low-pressure injection systems 

will be at or near pump runout conditions. The 

combined flow of the injection systems and 

safety injection tank discharge will fill the 

downcomer with subcooled water after the 

initial blowdown for the duration of the 

transient. In this range of break sizes, the 

blowdown flow of the break is much greater 

than the ECCS flow delivery rate. The 

downcomer fluid temperature will be determined 

principally by the flow from the high and lowpressure injection systems, the safety injection 

tank discharge, and the initial temperature of the 

water used in the injection systems. In this 

range of break sizes, CPTWC reaches a 

maximum. 

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

0 4 8 12 16 20

Break Diameter [in]

CPTWC

Oconee

Beaver Valley

Palisades

Figure 9.1. CPTWC Behavior for LOCAs 

of Various Break Diameters 

The sensitivity of CPTWC to break size 

increases for break sizes below 5.656-in. 

(14.4-cm). This trend is seen for all of the 

results presented in Figure 9.1. For these 

smaller break diameters, the balance between 

break flow and the ECCS injection flow governs 

the primary system cooldown and depressurization 

rates. System depressurization is slower relative 

to the larger breaks (greater than 5.656-in. 

(14.4-cm)). As a result, safety injection tank 

discharge and initiation of low-pressure system 

injection begins later in the transient, and the 

injection rate is lower. At the lower end of this 

break diameter range (i.e., ≈2.5-in. or ≈5-cm), 

low-pressure system injection flow may not 

even be initiated, and the safety injection tanks 

may not totally discharge. In this range of break 

sizes, the depressurization limits the rate of 

high- and low-pressure injection system 

injection to the reactor system. The downcomer 

fluid temperature is principally determined by 

the break diameter (break flow), the flow from 

the high- and low-pressure injection systems, 

the safety injection tank discharge, and the 

initial temperature of the water used in these 

systems as in the larger breaks. However, water 

is injected at a slower rate, resulting in a slower 

cooldown and relative to the larger breaks. 
9-7 

One significant aspect of the results shown in 

Figure 9.1 is that there is a limit to the CPTWC 

value for each plant and, hence, to the risk of 

vessel failure produced by a primary side pipe 

break. Additionally, this limiting CPTWC 

behavior would be similar for any plant because 

the designs of the different vendors all have 

similar ratios of initial energy to RCS volume 

and core power to RCS volume. 

The observations on CPTWC behavior suggest 

that the same CPTWC trend will occur for any 

plant with a shift in the break diameter at which 

the CPTWC curve bends over and reaches a 

maximum. This behavior is expected to occur 

regardless of plant power level given that the 

ECCS system for any plant is designed to cool 

the core under a wide variety of LOCA 

conditions. This observation is relevant to the 

applicability of these results to PWRs in general. 

9.2 Fracture mechanics sensitivity 

studies 

We have performed sensitivity studies on our 

PFM model (and on PFM-related variables) with 

two aims in mind: 

• To provide confidence in the robustness of 

our PFM model, we assessed the effect of 

credible model and input perturbations on 

TWCF estimates. 

• To provide confidence that the results of our 

calculations for three specific plants can be 

generalized to apply to all PWRs, we 

performed sensitivity studies to assess the 

influence of factors not fully considered in 

our baseline TWCF estimates (see Chapter 8). 

Full details of sensitivity studies of our PFM 

model are available in a companion report 

[EricksonKirk-SS]. This section provides a 

brief summary of that information. 

9.2.1 Sensitivity Studies Performed 

To Assess the Robustness 

of the PFM Model 

9.2.1.1 Approach 

The model used to generate TWCF estimates is 

a complex assemblage of many sub-models and 

parameter inputs. These combine to produce 

intermediate calculated results that, upon 

passing through yet more sub-models, 

eventually become an estimated distribution of 

TWCF. The existence of each sub-model and 

parameter input in the PFM model, and their 

arrangement with respect to one another, 

represents a decision to structure the overall 

model in a particular way. Changing any one of 

these decisions can, in principal, change the 

estimated output of the model (i.e., the 

distribution of TWCF values). Therefore, we 

investigated the degree to which the selection of 

credible alternative sub-models may influence 

the TWCF estimates. Additionally, many of the 

inputs parameters to the PFM cannot be known 

precisely. Therefore, we also investigated the 

degree to which credible variations in the input 

parameters change the TWCF estimates. This 

approach of basing sensitivity studies on 

credible alternative sub-models and/or on 

credible variations of the input parameters 

follows directly from two principles of our overall 

approach to model building (see Section 3.2): 

• the use of realistic input values 

and sub-models 

• an explicit treatment of uncertainties 

These principles permitted calculation of TWCF 

estimates that are systematically biased neither 

high nor low (i.e., values that represent a “best 

estimate”) to the greatest extent practicable. 

By basing sensitivity studies on credible

alternative sub-models and credible variations of 

the input parameters, we maintain these 

principals and, thereby, allow our TWCF 

estimates to maintain their “best estimate” label. 
9-8 

This approach to performing sensitivity studies 

deviates from that taken previously [SECY-82-

465], wherein sensitivity studies either focused 

on “important” parameters and sub-models 

(i.e., those to which the TWCF was believed to 

be sensitive), or were performed seemingly 

without consideration of either the technical 

justification for the baseline sub-model or the 

credibility of the alternative sub-model used to 

motivate the sensitivity study. We feel it is, in 

most cases, important to avoid such ad hoc

justifications for performing sensitivity studies. 

Low sensitivity of the output TWCF to a change 

in a sub-model or input having an inadequate 

technical justification does not provide a rational 

basis for accepting that sub-model or input as 

part of the overall model. Similarly, high 

sensitivity of the output to a well justified 

sub-model or input does not provide a basis for 

either condemning that sub-model/input or 

adopting arbitrary margins in an effort to 

compensate for the high sensitivity. 

9.2.1.2 Sensitivity Studies Performed 

As detailed in [EricksonKirk-SS], the following 

sensitivity studies were performed to provide 

confidence in the robustness of the PFM model: 

• flaw distribution (size and density of 

simulated flaws) 

• residual stresses assumed to exist in the 

RPV wall 

• embrittlement shift model used 

and treatment of uncertainties 

• re-sampling of chemical composition 

variables at the 1⁄4T, 1⁄2T, and 3⁄4T locations 

for welds 

• crack face pressure 

• upper shelf toughness model 

The results of these sensitivities are summarized 

in the following sections. 

9.2.1.2.1 Flaw Distribution 

As detailed in Appendix C, the distributions of 

flaws that FAVOR simulates provide a 

conservative representation of both the sizes and 

densities of crack-like defects that exist in the 

general population of PWRs. Additionally, 

these flaw distributions were based on what is 

generally regarded as among the most 

comprehensive studies of flaws in RPV 

fabrication that is currently available [Simonen]. 

Consequently, it is difficult to find a credible

alternative flaw model on which to motivate a 

sensitivity study. Nonetheless, it is informative 

to understand the characteristics of the flaws 

drawn from these distributions that contribute 

most significantly to the estimated values of FCI 

and TWCF. For example, the information 

presented in Figure 8.7 indicated that only axial 

flaws can contribute significantly to the TWCF 

atributable to differences in the through-wall 

variation of crack driving force between axial 

and circumferentially oriented flaws. Two other 

general statements can be made regarding the 

flaws that contribute most significantly to the 

estimated TWCF values: 

(1) They are located close to the inner diameter 

surface of the vessel. The tensile thermal 

stresses produced by rapid cooling along the 

vessel ID do not penetrate far into the wall 

thickness of the RPV. A natural 

consequence of this, which is illustrated in 

Figure 9.3, is that the great majority of the 

cracks that are predicted to initiate and 

subsequently propagate through the vessel 

wall lie very close to the inner diameter 

surface. The information in Figure 9.3 

indicates that almost all flaws that initiate lie 

less than 1/8-T from the vessel ID. Since 

they are driven by the thermal stresses 

characteristic of cooldown transients, these 

observations hold true independent of 

embrittlement level. 

(2) They have a small through-wall dimension. 

This again occurs as a direct consequence of 

the fact that cooldown transients produce 

thermal stresses that (together with the 

pressure stresses) are only high enough to 

initiate cracks at locations close to the inner 

diameter of the vessel. Consequently, larger 
9-9 

flaws (which would generally be considered 

more deleterious in a fracture evaluation 

than would small flaws) tend to not initiate 

very frequently because their crack tips lie 

too far away from the inner diameter surface 

and, so, are subjected to low tensile loads, or 

even to compressive loads. In Figure 9.4 

and Figure 9.5, we examine the effect of 

duration of irradiation exposure, flaw 

location (in plate or weld), and transient type 

on the flaw sizes that initiate fracture in our 

analyses. This information demonstrates 

that the combined effects of the duration of 

irradiation exposure and flaw location are 

small, and are entirely as expected for they 

correlate well with relative embrittlement 

levels. Transient type plays a minor role, 

with predominantly thermal transients such 

as large pipe breaks generally initiating 

fracture from smaller flaws while transients 

that involve a significant pressure 

component (such as stuck-open valves that 

may later reclose) tend to initiate fracture 

from larger flaws. Nonetheless, the flaws 

that contribute to the estimated through-wall 

cracking frequency are small, having median 

depths ranging from 0.1 to 0.3-in. (2.54 to 

7.62-mm). 

In combination, these observations help to allay 

concerns that the flaw distributions sampled in 

FAVOR do not simulate enough flaws of large 

dimensions, or that the postulated future 

discovery of a large (previously undetected) 

flaw in service could invalidate the results of 

this study. Neither of these concerns is valid 

because, given the dominant effects of thermal 

stresses in controlling crack driving force, large 

flaws do not play a role in establishing the risk 

of RPV failure attributable to PTS. 

tWALL

tCLAD

2a

ID OD

L

2c

Figure 9.2. Flaw dimension and position 

descriptors adopted in FAVOR 

0

2

4

6

8

0.000 0.125 0.250 0.375

Distance of Inner Crack Tip 

from Clad/Base Interface, 

L/twall

% of Flaws Predicted to Initiate

Beaver Valley at Ext-Bb

Palisades at Ext-Pb

Figure 9.3. Distribution of through-wall position 

of cracks that initiate 
9-10 

0%

20%

40%

60%

80%

100%

0.0 0.5 1.0 1.5 2.0

Flaw Depth (2a) [in]

% of Flaws with Non-Zero CPI 

Having Depth < 2a

Weld flaws that initiate from

LOCAs at 60 EFPY

Plate flaws that initiate from

LOCAs at 60 EFPY

0.0 0.5 1.0 1.5 2.0

Flaw Depth (2a) [in]

Weld flaws that initiate from

LOCAs at Ext-Bb

Plate flaws that initiate from

LOCAs at Ext-Bb

Figure 9.4. Flaw depths that contribute to crack initiation probability in Beaver Valley Unit 1 

when subjected to medium- and large-diameter pipe break transients at two different embrittlement levels 

0%

20%

40%

60%

80%

100%

0.0 0.5 1.0 1.5 2.0

Flaw Depth (2a) [in]

% of Flaws with Non-Zero CPI 

Having Depth < 2a

Weld flaws that initiate from

SO-1s at 60 EFPY

Plate flaws that initiate from

SO-1s at 60 EFPY

0.0 0.5 1.0 1.5 2.0

Flaw Depth (2a) [in]

Weld flaws that initiate from

SO-1s at Ext-Bb

Plate flaws that initiate from

SO-1s Ext-Bb

Figure 9.5. Flaw depths that contribute to crack initiation probability in Beaver Valley Unit 1 

when subjected to stuck-open valve transients at two different embrittlement levels 

9.2.1.2.2 Residual Stresses 

FAVOR assumes that a single distribution 

quantifies the residual stresses produced by 

welding in both axial and circumferential welds 

[Williams]. These residual stresses were 

estimated from measurements made of how the 

width of a radial slot cut in the longitudinal weld 

in a shell segment from an RPV change with cut 

depth. These measurements were processed 

through a finite element analysis to determine 

the residual stress profile used by FAVOR 

[Dickson 99]. FAVOR also assumes that this 

residual stress distribution is not relieved by 

cracking of the vessel, (i.e., the residual stresses 

in the figure to the right are applied equally 
9-11 

irrespective of a/t). Since residual stresses 

would have to be relieved were a crack to 

develop through the weld in an RPV, the effect 

of this conservative assumption was be assessed 

by performing a sensitivity study wherein the 

weld residual stresses are retained in the crack 

initiation calculation but are removed from the 

through-wall cracking calculation. In this 

sensitivity study, we performed analyses of both 

the Beaver Valley and the Palisades RPVs at 

two embrittlement levels each (32 EFPY and the 

Ext-B embrittlement conditions). The effect of 

relieving the residual stresses in the throughwall cracking calculations was to entirely 

negligible, reducing the TWCF values by less 

than 1% (on average). This limited sensitivity of 

the TWCF values on residual stresses occurs 

because the crack driving force cause by the 

residual stress is very small relative to that 

caused by the combination of thermal and 

pressure loading. 

9.2.1.2.3 Embrittlement Shift Model 

The embrittlement shift model relates 

compositional and neutron exposure variables to 

the amount by which irradiation shifts the 

Charpy V-notch (CVN) transition temperature 

curve to higher temperatures. FAVOR adopts a 

model developed under an NRC Research 

contract by Eason in 2000 [Eason]. Since that 

time a similar, albeit not identical, embrittlement 

trend curve had been adopted by the American 

Society for Testing and Materials in the E900-02 

standard [ASTM E900]. A sensitivity study 

was, therefore, performed to assess the effect of 

adopting the ASTM embrittlement trend curve, 

rather than that proposed by Eason (again 

analyzing Beaver Valley and Palisades at two 

different embrittlement levels). The ASTM 

E900-02 embrittlement shift model produces 

TWCF estimates that are systematically lower 

(approximately one-third) of those estimated 

using the Eason shift model. This reduction in 

TWCF is almost entirely attributable to the 

existence of a “long-term bias” in the Eason 

model that does not exist in the ASTM E900-02 

model. Activity is currently underway within 

ASTM Committee E10.02 to revise the E900 

model. Representatives of both the industry and 

the NRC are involved in this code committee 

work, and the committee is expected to publish a 

revised model that incorporates features of both 

the current Eason and E900-02 relationships. 

Thus, for the purposes this report, we have 

continued to use the Eason correlation and 

accepted this approach as slightly conservative. 

At such time as a consensus emerges from the 

E10.02 Code committee process, it will be a 

simple matter to assess the effect of the new 

embrittlement shift model on the TWCF values 

reported herein. However, based on this 

sensitivity study, we expect this effect to be 

small (less than a factor of 3 reduction in 

TWCF). 

9.2.1.2.4 Embrittlement Shift 

Uncertainty Treatment 

In FAVOR, the uncertainty of the embrittlement 

shift model is not sampled. As argued in 

[EricksonKirk-SS], this approach is appropriate 

because the uncertainty in the embrittlement 

shift model arises as a result of uncertainties in 

the input variables to the embrittlement shift 

model (i.e., copper content, nickel content, 

phosphorus content, and fluence), which are 

sampled in FAVOR. This is demonstrated by 

the results in Figure 9.6, which were generated 

as follows: 

(1) Median values were assigned to all of the 

input variables to the Eason embrittlement 

shift equation (except for fluence). 

(2) The FAVOR uncertainty distributions for 

Cu, Ni, P, and fluence were sampled about 

these medians for fluence medians ranging 

from 0.25x1019 to 5x1019 n/cm2

. 

(3) At each different fluence value, 1,000 sets 

(Cu, Ni, P, and fluence) were simulated. 

Each set was used to estimate a value of 

embrittlement shift using the Eason 

embrittlement model. The standard 

deviation of these 1,000 embrittlement shift 

estimates was calculated and plotted in 

Figure 9.6. 

The uncertainties simulated by FAVOR agree 

well with those in the embrittlement shift data 

used by Eason to develop the model. The lower 

uncertainties associated with lower fluence 
9-12 

values results from FAVOR setting to zero 

simulations of embrittlement shift that are 

negative, which is physically unrealistic. 

This information confirms the appropriateness of 

the FAVOR approach to uncertainty simulation 

for this model. Simulation of both the 

embrittlement shift model uncertainties and the 

uncertainties in the input variables would 

produce a model that simulated a greater 

magnitude of uncertainty in embrittlement shift 

than is observed in test data. 

0

5

10

15

20

25

012345

Fluence / 1019 [n/cm2]

Standard Deviation [oF]

Standard deviation of simulated

embrittlement shift values

Standard deviation of Eason

model for welds

Standard deviation of Eason

model for plates

Figure 9.6. Comparison of embrittlement shift 

uncertainties simulated by FAVOR 

(blue line with X symbols) with the uncertainties 

in the experimental embrittlement shift database 

used by Eason to construct the model 

9.2.1.2.5 Chemical Composition 

Re-Sampling for Welds 

In welds, a gradient of properties is expected to 

exist through the thickness of the RPV because 

of through-wall changes in copper content. 

These copper content changes arise from the fact 

that, given the large volume of weld metal 

needed to fill an RPV weld, manufacturers often 

needed to use weld wire from multiple weld 

wire spools to completely fill the groove. Lack 

of control of the process used to copper plate the 

weld wires (a step taken for corrosion control) 

resulted in wide variability in copper coating 

thickness from spool to spool (variability that is 

manifested in measurable variations in Cu 

content through the RPV wall thickness). These 

copper variations produce variations in 

sensitivity to irradiation embrittlement, and 

consequent variations in resistance to fracture 

though the vessel wall. 

FAVOR adopts a weld composition gradient 

model wherein the Cu content is re-sampled in a 

through-wall cracking calculation every time the 

crack passes the 1⁄4 thickness, the 1⁄2 thickness, 

and the 3⁄4 thickness locations in the vessel wall. 

A four-weld layer model was developed based 

on considerations of the volume of weld metal 

needed to fill an RPV weld. To assess the effect 

of this model on TWCF, a sensitivity study was 

performed wherein the Cu resampling in 

FAVOR was turned off. Again, the sensitivity 

study included analysis of Beaver Valley and 

Palisades at two different embrittlement levels. 

The results of this study show that turning off 

the FAVOR 4-weld layer model increase the 

estimated TWCF by a small amount (factor of 

2.5 on average). 

9.2.1.2.6 Crack Face Pressure 

As part of the peer review, Dr. Schultz noted 

that FAVOR had inappropriately not accounted 

for the effects of crack face pressure loading 

(see Appendix B, Reviewer Comment #23). 

FAVOR Ver. 04.1 (which was used to generate 

all of the results reported in Chapter 8) now 

accounts for the effects of crack face pressure. 

The effect of including crack-face pressure on 

non-SO-1 transients is a negligible (a 0% to 6% 

increase in CPTWC) because pressure does not 

contribute significantly to the failure probability 

of these transients. For SO-1 transients, larger 

increases (25% to 75%) in the CPTWC are seen. 

The effect of including crack face pressure in an 

integrated analysis of PTS risk (all transients) is, 

however, small. An analysis of Beaver Valley at 

60 EFPY showed that including crack face pressure 

increased the estimated TWCF by only 6%. 
9-13 

9.2.1.2.7 Upper Shelf Toughness 

Model 

In FAVOR Version 03.1, upper shelf fracture 

toughness values (JIc, J-R) were estimated 

through correlations with Charpy V-notch 

energy. These empirical relationships had very 

low correlation coefficients and high scatter, 

reflecting the different underlying physical 

processes that control Charpy energy and 

fracture toughness on the upper shelf. 

Comments from the peer review group (see 

Comment #40, Appendix B) questioned the 

appropriateness of this approach. After 

reviewing the existing FAVOR model and other 

available alternatives, the staff adopted a new 

upper shelf model and implemented it in 

FAVOR Version 04.1 to address this concern. 

This new model does not rely on Charpy 

correlations in any way, and features an explicit 

treatment of the uncertainty in upper shelf 

toughness (both the ductile initiation toughness 

as measured by JIc and the resistance to further 

crack extension as measured by J-R). 

Additionally, the new model links transition 

toughness and upper shelf toughness properties, 

a relationship motivated by trends in fracture 

toughness data and physical considerations, and 

a feature the FAVOR Version 03.1 models did 

not have. This upper shelf model is based on 

work recently completed by EPRI [EricksonKirk 

04]. Details of the FAVOR implementation of 

this new model can be found in [EricksonKirkPFM] and [Williams]. 

The new upper shelf model does not change the 

TWCF values in any substantive way. On 

average, the TWCF values estimated using the 

new model are ~5% lower than the values 

estimated using the correlative approaches used 

in FAVOR 03.1. However, the linkage between 

transition toughness and upper shelf toughness 

properties in the new model has eliminated 

FAVOR predictions of physically implausible 

results (e.g., predicting that flaws in a particular 

axial weld (say Axial Weld A) of the RPV 

beltline contribute more to the TWCF than do 

flaws in another axial weld (say Axial Weld B) 

even though the toughness of Axial Weld A 

exceeds that of Axial Weld B). 

9.2.2 Sensitivity Studies Performed to 

Assess the Applicability of the 

Results in Chapter 8 to PWRs in 

General 

As detailed in [EricksonKirk-SS], the following 

sensitivity studies were performed to assess the 

applicability of the TWCF results presented in 

Chapter 8 to PWRs in general: 

• method for simulating increased levels of 

embrittlement 

• assessment of the applicability of these 

results to forged vessels 

• effect of vessel thickness 

The results of these sensitivities are summarized 

in the following sections. 

9.2.2.1 Simulating Increased Levels of 

Embrittlement 

Use of more realistic models and input values 

than were used in the calculations that provide 

the technical basis for the current PTS Rule 

produces a considerable reduction in the 

estimated values of TWCF. As detailed in Table 

8.4, at 60 EFPY (an operational lifetime beyond 

that anticipated after a single license extension), 

the TWCF values estimates for the three study 

plants lie between 10-11 and 10-8 events/year. 

However, the through-wall cracking frequency 

limit recommended in Chapter 10 as being 

consistent with Regulatory Guide 1.174 is 10-6

events/year. Consequently, to develop a 

reference temperature based screening limit 

(see Chapter 11), it was necessary to somehow 

artificially increase the level of embrittlement of 

the vessels and, thereby, the estimated TWCF 

values so that they would approach the 10-6

events/year limit. In the baseline calculations 

reported in Chapter 8, embrittlement was 

artificially increased by increasing EFPY 

(increasing time) and extrapolating fluence in 

linear proportion to time. An alternative 

procedure for artificially increasing 

embrittlement would be to allow the temporal 

and irradiation exposure parameters to remain 

within realistic ranges and, instead, increase the 

unirradiated transition temperature (the RTNDT(u)) 
9-14 

of the beltline materials. To determine what 

effect these two procedures have on estimated 

TWCF values, we performed a sensitivity study 

using the Beaver Valley and Palisades plants. 

In this sensitivity study, the 32 EFPY analyses 

reported in Table 8.4 were treated as a baseline 

above which embrittlement was increased. 

Increases in embrittlement achieved by 

increasing EFPY/time are also reported in Table 

8.4. Each EFPY/time increase in this table can 

be quantified as an increase in the reference 

temperature by subtracting from the reference 

temperature associated with a particular 

EFPY/time increment the reference temperature 

associated with 32 EFPY. In this sensitivity 

study, we compared the TWCF increases 

produced by these EFPY/time-driven reference 

temperature increases with TWCF increases 

driven by simply increasing the RTNDT(u) of the 

beltline materials by some fixed increment. 

Figure 9.7 shows the result of this analysis, 

which demonstrates that the EFPY/time method 

of artificially increasing embrittlement results in 

TWCF estimates that exceed those produced by 

the alternative method of increasing RTNDT(u). 

It must be emphasized that both of these 

procedures (as well as any other alternative 

procedures) extrapolate outside of the empirical 

bounds of the database used to establish the 

embrittlement shift model. We selected the 

EFPY/time extrapolation method over the 

RTNDT(u) extrapolation method because the 

embrittlement shift model includes explicitly 

both time and irradiation exposure variables. 

During the development of this model, the 

known physical bases for time/exposure trends 

were explicitly considered, and this knowledge 

was incorporated into the functional form of the 

model [Eason]. Thus, there is some reason to 

expect that time and irradiation exposure 

variables will extrapolate better than the fracture 

toughness before irradiation begins (as 

quantified by RTNDT(u)), which was not 

considered in the development of the 

embrittlement shift model. 

0

100

200

300

0 50 100

Increase in Reference Temperature 

from 32 EFPY Analysis [o

F]

Ratio of TWCF to 32 EFPY Analy

s

TWCF Ratio, Beaver, EFPY Increase

TWCF Ratio, Palisades, EFPY Increase

TWCF Ratio, Beaver, RTNDT(u) Increase

TWCF Ratio, Palisades, RTNDT(u) Increase

Figure 9.7. Effect of different methods 

to artificially increase embrittlement 

on the predicted TWCF values 

9.2.2.2 Applicability to Forged Vessels 

All three of our study plants are plate vessels. 

However, 21 of the operating PWRs have 

beltline regions made of ring-forgings. As such, 

these vessels have no axial welds. The lack of 

the large axially oriented axial flaws from such 

vessels indicates that they should, in general, 

have much lower values of TWCF than a 

comparable plate vessel of equivalent 

embrittlement. However, forgings have a 

population of embedded flaws that is particular 

in density and size to their method of 

manufacture. Additionally, under certain 

conditions forgings are subject to subclad 

cracking associated with the deposition of the 

austenitic stainless steel cladding layer. Thus, to 

investigate the applicability of the results 

reported in Chapter 8 to forged vessels, we 

performed a number of analyses on vessels using 

properties (RTNDT(u), Cu, Ni, P) and flaw 

populations appropriate to forgings. 
9-15 

Appendix G details the technical basis for the 

distributions of flaws used in these sensitivity 

studies. The distribution of embedded forging 

flaws is based on destructive examination of an 

RPV forging [Schuster 02]. These flaws are 

similar in both size and in density to plate flaws. 

The distribution of subclad cracks is based on a 

review of the literature on subclad flaws, in 

particular that appearing in a summary article 

[Dhooge 78]. Subclad cracks occur as dense 

arrays of shallow cracks extending into the 

vessel wall from the clad to basemetal interface 

to depths limited by the heat affected zone 

(~0.08-in. (~2mm)). These cracks are oriented 

normal to the direction of welding for clad 

deposition, producing axially oriented cracks in 

the vessel beltline. They are clustered where the 

passes of strip clad contact each other. Subclad 

flaws are much more likely to occur in particular 

grades of pressure vessel steels that have 

chemical compositions that enhance the 

likelihood of cracking. Forging grades such as 

A508 are more susceptible than plate materials 

such as A533. High levels of heat input during 

the cladding process also enhance the likelihood 

of subclad cracking. 

9.2.2.2.1 Embedded Forging Flaw 

Sensitivity Study 

This sensitivity study was constructed as 

follows: 

(1) Two sets of forging properties were 

selected: those of the Sequoyah 1 and Watts 

Bar 1 RPVs [RVID2]. These properties 

were selected because they are among the 

most irradiation-sensitive of all the forging 

materials in RVID. 

(2) Two hypothetical models of forged vessels 

were constructed based on our existing 

models of the Beaver Valley and Palisades 

vessels. In each case, the hypothetical 

forged vessels were constructed by 

removing the axial welds and combining 

these regions with the surrounding plates to 

make “forgings.” These “forgings” were 

assigned the properties from Step 1. 

(3) A FAVOR analysis of each vessel/forging 

combination from Steps 1 and 2 was 

analyzed at two embrittlement levels: 

32 EFPY and Ext-B. Thus, a total of 23

(or 8) FAVOR analyses were performed 

(2 material property definitions x 2 vessel 

definitions x 2 embrittlement levels). 

On average, the TWCF of the “forging” vessels 

was only 3% of the plate welded vessels; at most, 

it was 15%. These reductions are consistent 

with those expected when the large axial weld 

flaws are removed from the analysis. 

9.2.2.2.2 Subclad Crack Sensitivity 

Study 

This sensitivity study was constructed as 

follows: 

(1) One set of forging properties was selected: 

that of the Sequoyah 1 RPV [RVID2]. 

(2) One hypothetical model of a forged vessel 

was constructed based on our existing model 

of the Beaver Valley vessel. The 

hypothetical forged vessel was constructed 

by removing the axial welds and combining 

these regions with the surrounding plates to 

make a “forging.” This “forging” was 

assigned the properties from Step 1. 

(3) A FAVOR analysis of each vessel/forging 

combination from Steps 1 and 2 was 

analyzed at three embrittlement levels: 

32 EFPY, 60 EFPY, and Ext-B. Thus, 

a total of 3 FAVOR analyses were 

performed (1 material property definition x 

1 vessel definition x 3 embrittlement levels). 

At 32 and 60 EFPY the TWCF of the “forging” 

vessels was ~0.2% and 18% of the plate welded 

vessels. However, at the much higher 

embrittlement level represented by the Ext-B 

condition the “forging” vessels had TWCF 

values 10 times higher than that characteristic of 

plate welded vessels at an equivalent level of 

embrittlement. While these very high 

embrittlement levels are unlikely to be 

approached in the foreseeable future, these 

results indicate that a more detailed assessment 

of vessel failure probabilities associated with 

subclad cracks would be warranted should a 
9-16 

subclad cracking prone forging ever in future be 

subjected to very high embrittlement levels. 

9.2.2.3 Effect of RPV Wall Thickness 

on TWCF 

In Section 8.5.2.4.1, we noted in the FAVOR 

results for primary side pipe breaks a potential 

effect of vessel wall thickness on the conditional 

probability of through-wall cracking. This affect 

can be expected for the following reasons: 

• The magnitude of thermal stress scales 

in proportion to the thickness, with thicker 

vessels generating higher levels of thermal 

stress. Figure 9.8 shows the effect of this 

increased thermal stress on the applied 

driving force to fracture associated with a 

large-diameter pipe break. This effect will 

tend to increase the probability of throughwall cracking for thicker vessels. 

• Because thicker vessels will have a larger 

volume of plate material and a larger weld 

fusion line area, they will also have a larger 

number of flaws. This effect will also tend 

to increase the probability of through-wall 

cracking for thicker vessels. 

• There is more distance in a thicker vessel 

over which an initiated crack can arrest, 

thereby not failing the vessel. Also, thicker 

vessels would tend to have more weld layers 

with different Cu contents. This effect will 

tend to reduce the probability of throughwall cracking for thicker vessels. 

To investigate the effect of these first two 

factors (the third could not be investigated 

without modifying the structure of the FAVOR 

code), we increased the thickness of the Beaver 

Valley vessel from 7.875-in. (20-cm) (its actual 

thickness) in 5 increments up to 11-in. (27.9-cm) 

(characteristic of the thickest PWRs in service, 

see Figure 9.9). For each of these 5 thicker 

versions of Beaver Valley, we used FAVOR to 

estimate the CPTWC of the following four 

transients (all of which are dominant 

contributors to the TWCF of Beaver Valley): 

• BV9: 16-in. diameter hot leg break 

• BV56: 4-in. diameter surge line break 

• BV126: stuck-open safety relief valve that 

recloses after 100 minutes resulting in 

repressurization of the primary system 

• BV102: main steam line break 

Figure 9.10 shows that increasing the vessel wall 

thickness increases the CPTWC for all four 

transients. Recalling that these CPTWC values 

would be weighted by their bin frequencies (and 

those of other transients) to obtain a TWCF 

estimate, these results suggest that through a 

wall thickness of 9.5-in. (24.13-cm) (thicker 

than all but three of the in-service PWRs), the 

integrated effect of wall thickness on TWCF 

should be modest (factor of ~3 increase at most) 

relative to our analyses (see Chapter 8) of one 

7.875-in. (20-cm) thick vessel and two 8.5-in. 

(21.6-cm) thick vessels. For vessels of greater 

wall thicknesses, a plant-specific analysis is 

warranted to properly capture all aspects of 

increased vessel wall thickness on TWCF. 

However, given that the three plants of 11-in. 

(27.9-cm) and greater thickness are Palo Verde 

Units 1, 2, and 3, and these vessels have very 

low embrittlement projected at either EOL or 

EOLE, the practical need for such plant-specific 

analysis is mitigated. It can also be noted that 

using the TWCF results from Chapter 8 will 

overestimate the TWCF of the seven thinner 

operating PWRs (7-in. (17.78-cm) thick or less). 
9-17 

Beaver Valley transient 9 

transient time (minutes) 

0 50 100 150 200 250 300

applied KI (ksi in1/2) 

0

10

20

30

40

50

60

70

80

base (t = 8.036") 

v3 (t = 9.156")

v5 (t = 11.156") 

Figure 9.8. Effect of vessel wall thickness on the 

variation of applied-KI vs. time for a 16-in. 

(40.64-cm) diameter hot leg break in Beaver 

Valley. The flaw has the following dimensions: 

L=0.35-in., 2a=0.50-in., 2c=1.5-in. 

(L=8.89-mm, 2a=12.7-mm, 2c=38.1-mm) 

0

5

10

15

20

25

30

6.57.07.58.08.59.09.5

10.010.511.011.5

Vessel Wall Thickness [in]

Number of PWR

s

Figure 9.9. Distribution of RPV wall thicknesses 

for PWRs currently in service [RVID2] 

0

10

20

30

40

50

7 8 9 10 11 12

Vessel Wall Thickness [in]

TWCF / TWCF for 7-7/8-in. Thi

c

Beaver Valley Vessel at 60 EF

P

BV9 - 16" Hot Leg Break

BV56 - 4" Surge Line Break

BV102 - MSLB

BV126 - Stuck open SRV, re-closes after 100 minutes

Figure 9.10. Effect of vessel wall thickness 

on the TWCF of various transients in Beaver Valley 

(all analyses at 60 EFPY) 

9.2.3 Summary and Conclusions 

This section summarized sensitivity studies on 

our PFM model (and on PFM-related variables) 

performed with two aims in mind: 

• To provide confidence in the robustness of 

our PFM model we assessed the effect of 

credible model and input perturbations on 

TWCF estimates: 

o flaw distribution (size and density of 

simulated flaws) 

o residual stresses assumed to exist in the 

RPV wall 

o embrittlement shift model: model used 

and treatment of uncertainties 

o re-sampling of chemical composition 

variables at the 1⁄4T, 1⁄2T, and 3⁄4T 

locations for welds 

o crack face pressure 

o upper shelf toughness model 
9-18 

• To provide confidence that the results of our 

calculations for three specific plants can be 

generalized to apply to all PWRs, we 

performed sensitivity studies to assess the 

influence of factors not fully considered in 

our baseline TWCF estimates (see Chapter 8): 

o method for simulating increased levels 

of embrittlement 

o assessment of the applicability of these 

results to forged vessels 

o effect of vessel thickness 

In the former category, all effects were 

negligible or small. The small effects included 

our adoption of an embrittlement shift model 

different from that in ASTM E900-02 (which 

increases TWCF by ~3x) and our model that 

accounts for distinctly different Cu contents in 

different weld layers (which reduces TWCF by 

~ 2.5x relative to the assumption that the mean 

value of Cu does not vary through the vessel 

thickness). Neither of these effects is significant 

enough to warrant a change to our baseline 

model, or to recommend a caution regarding its 

robustness. 

Sensitivity studies in the latter category suggest 

the following minor cautions regarding the 

applicability of the results in Chapter 8 to PWRs 

in general: 

• In general, the TWCF of forged PWRs can 

be assessed using the Chapter 8 results by 

ignoring the TWCF contribution of axial 

welds. However, should changes in future 

operating conditions result in a forged vessel 

being subjected to very high levels of 

embrittlement, a plant-specific analysis to 

assess the effect of subclad flaws on TWCF 

would be warranted. 

• For PWRs with thicknesses of 7.5 to 9.5-in. 

(19.05 to 24.13-cm), the TWCF results in 

Chapter 8 are realistic. The Chapter 8 

results overestimate the TWCF of the seven 

thinner vessels (wall thicknesses below 7-in. 

(17.78-cm)) and underestimate the TWCF of 

Palo Verde Units 1, 2, and 3, all of which 

have wall thicknesses above 11-in. (27.94-cm). 

However, these vessels have very low 

embrittlement projected at either EOL or 

EOLE, suggesting little practical effect of 

this underestimation. 

9.3 Plant-to-Plant Differences 

in Design/Operational 

Characteristics that Impact 

PTS Transient Severity 

This section describes an effort in which we 

examined the plant design and operational 

characteristics of five additional highembrittlement plants. Our aim was to identify 

whether the design and operational features that 

are the key contributors to PTS risk 

(see Section 8.6) vary significantly enough in 

the larger population of PWRs to question the 

generality of our results. Full details of this 

work are reported elsewhere [Whitehead-Gen]. 

In this activity, we focused on several plants 

beyond the three for which we have conducted 

detailed plant-specific analyses to assess PTS 

risk. To identify which additional plants to 

study, Table 9.5 was constructed early in 2002. 

At the time, we understood from our plantspecific analyses of Oconee that circumferential 

welds did not contribute significantly to 

through-wall cracking. Therefore, we calculated 

a reference temperature metric for each plant 

equal to the sum of the un-irradiated RTNDT plus 

the embrittlement shift after 40 years of 

operation [Eason] calculated for the most 

irradiation-sensitive region in the beltline 

(i.e., most irradiation-sensitive axial weld, plate, 

or forging; circumferential welds were 

excluded). This metric, shown as a column in 

Table 9.5, provided an approximate ranking of 

the PTS sensitivity of the plants based on 

information we had available at the time. Since 

the goal of this activity was to determine 

whether the design and operational features that 

we have identified as being the key contributors 

to PTS risk (see Section 8.6) vary significantly 

enough in the larger population of PWRs to 

question the generality of our findings from 

Chapter 8, we felt it important to select the most 

embrittled plants from the list. In the end, we 

selected the following five plants: 
9-19 

• Salem 1 (W-41) [comparable to Beaver 

Valley (W-32

)] 

• TMI 1 (B&W3

) [comparable to Oconee] 

• Ft. Calhoun (CE4

) [comparable to Palisades] 

• Diablo Canyon 1 (W-4) [comparable to 

Beaver Valley] 

• Sequoyah 1 (W-4) [comparable to Beaver 

Valley] 

Following identification of the study plants, we 

conducted the following three activities: 

• A questionnaire was developed to elicit 

PTS-relevant information about the 

additional PWRs. 

• Responses to the questionnaire were 

examined to determine whether results from 

the detailed analyses were generically 

applicable to the additional PWRs. 

• Conclusions were generated as to the 

generic applicability of the detailed results. 

We compared potentially important design and 

operational features (as related to PTS) of these 

five PWRs to the same features from the three 

plants on which we have performed detailed 

analyses to determine whether these features are 

similar or different. Based on these comparisons, 

we made judgments regarding the appropriateness 

of treating the results presented in Chapter 8 

as being representative of PWRs in general. 

Section 9.3.1 details the questionnaire we 

developed and sent to the five plants, while 

Section 9.3.2 details our analysis of the results 

we obtained. Combined observations and 

overall conclusions are provided in Section 9.3.3. 

 

1

 W-4 denotes a Westinghouse 4-loop design. 

2

 W-3 denotes a Westinghouse 3-loop design. 

3

 B&W denotes Babcock and Wilcox. 

4

 CE denotes Combustion Engineering. 

9.3.1 Generalization Questionnaire 

Based on the insights obtained during an 

examination of the results from the three plantspecific studies, the analysts identified five 

general event scenarios for which plant design 

and operational features should be obtained. 

Plant design and operational features were 

examined to identify those that play a role in 

determining the importance of these five 

overcooling scenarios. 

Table 9.6 identifies the scenarios and their 

corresponding plant design and operational 

features. Once the scenarios and the design and 

operational features were identified, a questionnaire 

was constructed. Collection of the information 

via this questionnaire was facilitated by an 

industry representative working under the auspices 

of the Electric Power Research Institute (EPRI). 

9.3.2 Analysis of Collected Information 

Our analysis of the plant design and operational 

information collected via the questionnaire 

entails both PRA/HRA and TH information. 

Judgmental analysis of the comparable design 

and operational information between Oconee, 

Beaver Valley, and Palisades and the 

generalization plants (i.e., Ft. Calhoun, TMI, 

Diablo Canyon, Sequoyah, and Salem) was 

performed to determine if there are any 

differences that would be expected to have a 

significant impact on any conclusions that would 

be reached by the activity if it were to be 

performed in detail (i.e., to the same level of 

rigor as was done in the plant-specific analyses). 

The following subsections summarize the results 

of the PRA/HRA (9.3.2.1) and TH judgmental 

analyses (9.3.2.2) 
9-20 

9.3.2.1 PRA/HRA Judgmental 

Analyses 

For secondary breaches, the following 

observations were made: 

• For generalization issue (GI) 1‡‡‡‡‡, each of 

the generalization plants is similar to or 

better than their corresponding detailed 

plant. Thus, for GI 1, we conclude that there 

would be no significant adverse differences 

between the generalization plants and their 

corresponding detailed plant. 

• For GI 2, each of the generalization plants is 

similar to their corresponding detailed plant. 

Thus, for GI 2, we conclude that there would 

be no significant adverse differences 

between the generalization plants and their 

corresponding detailed plant. 

• For GI 3, each of the generalization plants is 

similar to their corresponding detailed plant 

with one possible exception. For Salem, 

it appears that early isolation opportunities 

exist; however, exactly when these occur 

is not clear. Nonetheless, since Salem’s 

procedures are based on Westinghouse 

Owners Group (WOG) Emergency 

Response Guidelines, it is expected that 

Salem is similar to its corresponding 

detailed analyzed plant, Beaver Valley. 

Thus, for GI 3, we conclude that there would 

be no significant adverse differences 

between the generalization plants and their 

corresponding detailed plant. 

 

‡‡‡‡‡ GI # refers to the number assigned to each 

generic issue. For example, GI 1 refers to 

number of MSIVs and GI 26 refers to emergency 

operating procedure (EOP) criteria for initiation 

of feed–and-bleed. 
9-21 

Table 9.5. Plant list for generalization study 

Tolerance 

to a PTS 

Challenge 

Plant Name NSSS Vendor Most 

Embrittled 

Material 

RTNDT(u) + 

Irradiation 

Shift at 40 

years [o

F] 

Vessel Manufacturer 

1 Salem 1 Westinghouse Plate 204 Combustion Engineering 

2 Beaver Valley 1 Westinghouse Plate 194 Combustion Engineering 

3 TMI-1 Babcock & Wilcox Axial Weld 186 Babcock & Wilcox 

4 Fort Calhoun Combustion Engineering Axial Weld 181 Combustion Engineering 

5 Palisades Combustion Engineering Axial Weld 179 Combustion Engineering 

6 Calvert Cliffs 1 Combustion Engineering Axial Weld 178 Combustion Engineering 

7 Diablo Canyon 1 Westinghouse Axial Weld 171 Combustion Engineering 

8 Diablo Canyon 2 Westinghouse Plate 170 Combustion Engineering 

9 Sequoyah 1 Westinghouse Forging 167 Rotterdam Dockyard 

10 Watts Bar 1 Westinghouse Forging 164 Rotterdam Dockyard 

11 St. Lucie 1 Combustion Engineering Axial Weld 164 Combustion Engineering 

12 Surry 1 Westinghouse Axial Weld 163 Babcock & Wilcox 

13 Indian Point 2 Westinghouse Plate 162 Combustion Engineering 

14 Ginna Westinghouse Forging 161 Babcock & Wilcox 

15 Point Beach 1 Westinghouse Axial Weld 159 Babcock & Wilcox 

16 Farley 2 Westinghouse Plate 158 Combustion Engineering 

17 Mcguire 1 Westinghouse Axial Weld 158 Combustion Engineering 

18 Oconee 1 Babcock & Wilcox Axial Weld 157 Babcock & Wilcox 

19 North Anna 2 Westinghouse Forging 155 Rotterdam Dockyard 

20 Shearon Harris Westinghouse Plate 153 Chicago Bridge & Iron 

21 North Anna 1 Westinghouse Forging 153 Rotterdam Dockyard 

22 Cook 2 Westinghouse Plate 152 Chicago Bridge & Iron 

23 Salem 2 Westinghouse Axial Weld 148 Combustion Engineering 

24 Crystal River 3 Babcock & Wilcox Axial Weld 141 Babcock & Wilcox 

25 Calvert Cliffs 2 Combustion Engineering Plate 139 Combustion Engineering 

26 Robinson 2 Westinghouse Plate 138 Combustion Engineering 

27 Cook 1 Westinghouse Axial Weld 138 Combustion Engineering 

28 Farley 2 Westinghouse Plate 133 Combustion Engineering 

29 Farley 1 Westinghouse Plate 133 Combustion Engineering 

The estimated tolerance to a PTS challenge increases as the number in the next column increases (i.e., plants with the lowest 

ranking have the most embrittled materials). 

30 Arkansas Nuclear 1 Babcock & Wilcox Axial Weld 129 Babcock & Wilcox 

Notes: 

Plants analyzed in the PTS reevaluation effort. 

Plants compared in the Generalization activity. 
9-22 

Table 9.6 Important PTS scenarios and corresponding plant design and operational features 

 Scenario Types 

 Secondary Breach Secondary Overfeed LOCA Related PORV and SRV 

Related 

Feed and Bleed Related 

 Number of MSIVs (1) Information on the 

feed (MFW and 

AFW or emergency 

feedwater (EFW)) 

capabilities to the 

steam generators 

including inventory 

of water available to 

continue MFW or 

AFW/EFW (8) 

Allowable range of safety

injection water 

temperatures (11) 

Number and sizes of 

PORVs and SRVs, 

whether each plant 

operates with PORV 

block valves normally 

shut, and if there are any 

auto-operation features of 

the PORVs (20) 

Number of AFW/EFW 

pumps/flow paths versus 

minimum success criteria for 

adequate feed to the steam 

generators (hints to reliability 

of AFW/EFW and, hence, 

probability for going to feedand-bleed) (25) 

 Isolation capability with 

regards to other paths (2) 

Information on 

normal steam 

generator inventory 

(9) 

Information to estimate 

recirculation water 

temperature (12) 

Instrumentation available 

(e.g., acoustic monitors, 

differential pressure, etc.) 

to identify open PORVs 

or SRVs and to notice if 

they have reclosed (21) 

Emergency operating 

procedure (EOP) criteria for 

initiation of feed-and-bleed 

(26) 

 Identification of 

procedures, steps, and 

location of steps within 

procedures that ensure 

likelihood of early 

identification and isolation 

of faulted steam generators 

(3) 

Information on 

possible feed 

temperatures for all 

feed sources 

(especially how cold 

they could be) (10) 

Safety injection/ 

accumulators water 

source size (i.e., 

inventory) (13) 

Procedures for addressing 

LOCAs resulting from 

stuck-open PORVs or 

SRVs (22) 

Number of PORVs opened 

out of total available (or even 

SRVs if pumps can open 

SRVs) when in feed-andbleed mode (27) 

 Operator training or 

procedural allowances that 

support early isolation of 

steam generators (4) 

Safety injection flow rate 

versus LOCA break size 

(14) 

Procedures for addressing 

the sudden reclosure of 

such valves, including 

safety injection (SI) 

throttling/termination 

guidance (23) 

Number of HPI pumps used 

in feed-and-bleed and is 

actual flow rate equivalent to 

number of pumps (28) 

 Location and size of 

steamline flow restrictors 

(5) 

 Charging, high-pressure 

injection (HPI), and lowpressure injection (LPI) 

shutoff heads (15) 

Operating characteristics 

of the charging system 

when pressurizer level 

goes back high (e.g., stop, 

keep running) (24) 

Auxiliary feedwater (AFW) 

and main feedwater (MFW) 

control during steamline 

break (or similar) (6) 

 Actuation requirements 

for containment spray 

and flow rate once 

running (16) 

 

Key Assumptions 

Relative to MSLB Analysis Determination of whether 

turbine-driven AFW pump 

(auto) isolates in MSLB (7) 

Impact on HPI, LPI, and 

charging when sump 

switchover occurs (which 

pumps on vs. off) (17) 

 

 Any significant changes 

in flow rates going from 

injection to recirculation 

(18) 

 

Generalization Issues (Number) Accumulator (e.g., safety 

injection tank (SIT), core 

flood tank (CFT)) 

discharge pressure (19) 

 
9-23 

• For GI 4, each of the generalization plants is 

similar to their corresponding detailed plant 

with one possible exception. For Salem, 

it appears that training supports early action, 

even though it is unclear exactly when 

the actions would occur. Since Salem’s 

procedures are based on Westinghouse 

Owners Group (WOG) Emergency 

Response Guidelines, it is expected that 

Salem is similar to its corresponding 

detailed analyzed plant, Beaver Valley. 

Thus, for GI 4, we conclude that there would 

be no significant adverse differences 

between the generalization plants and their 

corresponding detailed plant. 

• GI 5 is not a PRA/HRA issue. This issue 

is examined in section 9.3.2.2. 

• For GI 6, each of the generalization plants is 

similar to or as good as their corresponding 

detailed plant. Thus, for GI 6, we conclude 

that there would be no significant adverse 

differences between the generalization 

plants and their corresponding detailed 

plant. 

• For GI 7, each of the generalization plants is 

similar to their corresponding detailed plant 

with one exception. For TMI the turbinedriven AFW pump is not automatically 

isolated while it is automatically isolated for 

the corresponding detailed analyzed plant, 

Oconee. Thus, for GI 7, this could increase 

the importance of a faulted steam generator 

for the Babcock & Wilcox (B&W) 

generalization plant. 

From the observations provided above, only GI 7 

has the potential for a significant adverse 

difference between the generalization plants and 

their corresponding detailed plant — and that 

only for the B&W generalization plant 

(i.e., TMI). However, when observations for 

GI 3 and GI 4 are considered in combination, 

we expect the importance of the GI 7 difference 

to be minimal, since operators would be 

expected to isolate the feed flow. Thus, we 

conclude that for secondary breaches, no 

significant adverse differences exist. 

For secondary overfeed, the GIs are not 

PRA/HRA issues. These issues are examined in 

section 9.3.2.2. 

For LOCA-related, the GIs are not PRA/HRA 

issues. These issues are examined in the in 

section 9.3.2.2. 

For PORV- and SRV-related, the following 

observations are made:

• For GI 20, generic data were used to estimate 

the probabilities associated with the sticking 

open and subsequent closure of either 

PORVs or SRVs [Poloski 99]. No 

significant differences are expected for 

Westinghouse and B&W plants. For the 

Combusting Engineering (CE) 

generalization plant, Fort Calhoun, we might 

expect a higher estimated probability of 

having a stuck-open valve. This expectation 

comes from the fact that Fort Calhoun 

experienced one of the two stuck-open valve 

events that were used to estimate the generic 

probability of a stuck-open valve (1.6E-3). 

If we approximate the probability by using 

one event in the 12 years covered by 

[Poloski 99] (the most conservative 

interpretation of the data), we get 

approximately 0.08. Using this approximate 

value for Fort Calhoun, the probability 

associated with stuck-open valves would 

increase by about a factor of 50. This ignores 

the fact that there may be appropriate 

reasons to combine both generic PWR 

experience and the Fort Calhoun plantspecific experience (such as through a 

Bayesian analysis) or to obtain other 

information to arrive at a more realistic 

estimate of a stuck-open valve event at Fort 

Calhoun. 

In an effort to determine a more realistic 

estimate, additional information was 

obtained with the help from staff at Fort 

Calhoun Station about the SRV opening 

event that actually happened in 1992, 

subsequent analyses of the root cause, and 

the corrective actions. This additional 

information [LER 92-023, LER 92-028, and 

NRC-IR] including phone conversations 

with plant staff, revealed that the causes of 
9-24 

the actual event are well-understood, and 

actions have been taken that should make 

Fort Calhoun no more susceptible to SRV 

demand events than other PWRs. 

In particular, the event was caused by both 

a SRV setpoint drift as a result of movement 

of an adjusting nut during valve vibrations 

that resulted in a lower setpoint for valve 

opening, and determination that setpoint 

calibration of the SRVs at an outside 

laboratory was not being done under 

laboratory conditions (particularly 

temperature conditions) that sufficiently 

approximated actual plant installation 

conditions closely enough. This latter 

situation was unknowingly contributing to 

the SRV setpoint being lower than what was 

specified. 

The SRVs at Fort Calhoun are manufactured 

by Crosby (one of the manufacturers used in 

other plants), so Fort Calhoun is not unique 

from this perspective. The specific 

corrective actions included adding a torque 

setting for the adjusting nut that did not exist 

in the procedures, adding a locking nut that 

prevents inadvertent movement of the 

adjusting nut, and changes in the laboratory 

setup and procedures during valve 

calibration that now allow for sufficient 

approximation of actual installation 

conditions. Additionally, Fort Calhoun, like 

other plants, has lowered the plant’s highpressurizer pressure trip setpoint, making it 

less likely to cause an SRV demand. 

Considering the use of a valve manufacturer 

not uncommon among PWRs, changes in 

the plant’s high-pressure setpoint to be like 

other PWRs, the specific “fixes” for the 

identified Fort Calhoun SRV problems, and 

a history of no subsequent SRV events or 

significant problems at Fort Calhoun since 

1992, we conclude that no evidence exists to 

suggest that Fort Calhoun is any more 

susceptible to SRV events than other PWRs. 

Hence, our best estimate of Fort Calhoun’s 

frequency of stuck-open SRV events 

looking to the future, is that Fort Calhoun 

can be treated as among the “generic” 

population of PWRs, and the generic value 

used for such events in our PTS models can 

be used for Fort Calhoun. Hence, there is no 

identifiable frequency difference to be 

considered in this generalization study. 

Thus, for GI 20, we conclude that there 

would be no significant adverse differences 

between the generalization plants and their 

corresponding detailed plant. 

• For GI 21, except for possibly Salem, all 

plants have multiple indications to know 

when pressurizer PORV/SRVs are open 

and/or reclose. Thus, it would be 

appropriate to postulate that for Salem, there 

might be some increase in the human error 

probability (HEP) associated with the failure 

to throttle because operators have less direct 

indication of stuck-open valves (e.g., no 

acoustic monitors) and, thus, less indication 

of valve reclosure than for Beaver Valley 

(the corresponding detailed plant). Without 

a detailed analysis of the specifics associated 

with stuck-open valves that reclose at 

Salem, it is difficult to estimate the amount 

of increase in the throttling HEP. 

Nonetheless, given the fact that there are 

indications available at Salem (although 

they are neither as redundant nor as direct 

as for other plants), we expect the HEP for 

failure to throttle should not increase by 

more than a factor of 5 (at most). Thus, 

for GI 21, we conclude that Salem is the 

only generalization plant that might have a 

significant adverse difference compared to 

the corresponding detailed plant. 

• For GI 22, it appears that procedural 

guidance is sufficiently similar among all 

plants. From this similarity, we do not 

expect significant differences in operator 

response or large delays in attempting to 

isolate paths (e.g., >15–20 minutes). Thus, 

for GI 22, we conclude that there would be 

no significant adverse differences between 

the generalization plants and their 

corresponding detailed plant. 

• For GI 23, all plants have throttling 

guidance and specific steps; particularly 

once a transition to the appropriate 

procedure occurs. For the very rapid rise in 

RCS pressure and subcooling that would 

occur with an unexpected/sudden reclosure 
9-25 

of PORVs or SRVs, it would seem that there 

is likely to be some delay in responding to 

the very quick transition from a saturated 

RCS to a filled RCS (as we have seen for the 

analyzed plants). Thus, for GI 23, we 

conclude that there would be no significant 

adverse differences between the 

generalization plants and their 

corresponding detailed plant. 

• For GI 24, all plants require (or appear to 

require) manual action to control charging 

flow. Thus, for GI 24, we conclude that 

there would be no significant adverse 

differences between the generalization 

plants and their corresponding detailed 

plant. 

From the observations provided above, one 

potential difference has been found between the 

detailed analysis plants and the generalization 

plants. For Salem, the frequency could increase 

by at most a factor of 5 (GI 21). 

For feed-and-bleed-related, the following 

observations are made: 

• For GI 25, all plants appear to have a similar 

“over-capacity” of feed than what is needed 

for sufficient heat removal. Hence, losing 

all feedwater and having to go to feed-andbleed would seem similarly “unlikely.” 

To test this, information in Table D-5 

of NUREG/CR-5500, Vol. 1 [Poloski 98] 

was examined. From this examination, we 

found that for B&W plants, the 

generalization plant (TMI) has an 

AFW/EFW unavailability that is a factor of 

1.2 higher than the detailed plant (Oconee). 

For the Westinghouse plants, the 

unavailability is either lower for the 

generalization plants (Diablo Canyon and 

Salem) or higher by a factor of 1.1 

(for Sequoyah) compared to the detailed 

plant (Beaver Valley). For the CE plants, 

the unavailability for the generalization 

plant (Ft. Calhoun) is a factor of 26 higher 

than the detailed analysis plant (Palisades). 

However, this does not include credit for the 

diesel-driven AFW pump at the 

generalization plant. If we conservatively 

assign a 0.1 probability of failure to the 

diesel-driven pump, this difference becomes 

a factor of 3. Thus, for GI 25, we conclude 

that only the CE generalization plant would 

have a frequency that is somewhat higher 

than its detailed analysis plant. 

• For GI 26, all plants have specific criteria 

that direct the operators to go to feed-andbleed. While there are some differences in 

the specifics, it is unlikely that such 

specifics would substantially affect the 

operators’ response. Thus, for GI 26, we 

conclude that there would be no significant 

adverse differences between the 

generalization plants and their 

corresponding detailed plant. 

• GI 27 is not a PRA/HRA issue. This issue is 

examined in in section 9.3.2.2. 

• GI 28 is not a PRA/HRA issue. This issue is 

examined in section 9.3.2.2. 

From the observations provided above, one 

potential difference has been found between the 

detailed analysis plants and the generalization 

plants. For Fort Calhoun, the frequency could 

increase by about a factor of 3 (GI 25). 

9.3.2.2 TH Judgmental Analyses 

9.3.2.2.1 Introduction 

To facilitate the performance of the individual 

judgmental TH analyses, the five general 

scenarios identified in Table 9.6 of Section 9.3.1 

were recategorized into four basic groups based 

on (1) more global examination of the dominant 

types of scenarios in more detail and the lessdominant scenarios, (2) the TH characteristics of 

the scenarios in the group, and (3) the systems 

that determine the downcomer fluid temperature 

behavior. These groups are described in the 

following subsections. 
9-26 

9.3.2.2.1.1 Group 1: Large-Diameter 

Pipe Breaks 

Group 1 consists of LOCAs with a break 

diameter of 8-in. (20.32-cm) or greater. 

This group of LOCAs results in rapid system 

cooldown and complete system depressurization. 

The operator trips the reactor coolant pumps in 

these transients because of loss of primary 

system subcooling. The high- and low-pressure 

injection systems are running at or near pump 

runout conditions within several minutes of 

initiation. The safety injection tanks also 

discharge within several minutes. With the 

combined flow of the injection systems and 

safety injection tank discharge, the downcomer 

is filled with subcooled water after the initial 

blowdown for the duration of the transient§§§§§. 

The downcomer fluid temperature is principally 

determined by the flow from the high- and lowpressure injection systems, the safety injection 

tank discharge, and the initial temperature of the 

water used in the injection systems. 

9.3.2.2.1.2 Group 2: Small- to 

Medium-Diameter Pipe Breaks 

Group 2 consists of LOCAs with a break 

diameter of 2.0 to 5.7-in. (5.08 to 14.37-cm). 

This group of LOCAs results in slower 

cooldown and depressurization than the Group 1 

transients. For this break diameter range, the 

balance between break flow and ECCS injection 

flow governs the primary system cooldown and 

depressurization rate. The operator trips the 

reactor coolant pumps in these transients 

because of loss of primary system subcooling, 

although there is some trip time variation for 

different break sizes. Safety injection tank 

discharge and initiation of low-pressure injection 

occur later in the sequence, relative to Group 1 

transients. In cases where the break diameters 

are small, low-pressure injection flow may not 

be initiated at all. Also, the safety injection 

tanks may not totally discharge, again depending 

on the break size. In this range of break sizes, 

the system pressure limits the rate of high- and 

 

§§§§§ The term “transient” is used in its generic 

sense to represent the occurrence of a set of 

events that lead to a specific outcome 

low-pressure injection system injection to the 

reactor system. The downcomer fluid conditions 

are principally determined by the break 

diameter, the flow from the high- and lowpressure injection systems, the safety injection 

tank discharge, and the initial temperature of the 

water used in these systems. The break location 

plays a role in the downcomer fluid conditions. 

In the case of a cold leg break, some of the 

ECCS goes directly out the break instead of into 

the downcomer, resulting in warmer downcomer 

fluid temperatures over an equivalent-sized hot 

leg break. Note that the use of feed-and-bleed 

can be considered to “fit” within this group, 

since this involves one or more open pressurizer 

valves (hence, like a LOCA) with successful 

safety injection. Since feed-and-bleed can be 

controlled by the operator, it cannot be worse 

than an equivalent-sized break. 

9.3.2.2.1.3 Group 3: Stuck-Open 

Valves in the Primary 

System that Reclose 

Group 3 consists of transients involving stuckopen primary side SRVs that reclose. This 

group of transients results in cooldown and 

depressurization characteristics of a LOCA with 

a diameter at the low end of the Group 2 range. 

Once the valve recloses, the system heats up as a 

result of the loss of primary system coolant flow 

out the valve, and repressurizes as a result of 

charging or high-pressure injection flow. The 

operator trips the reactor coolant pumps in these 

transients because of loss of primary system 

subcooling, although there may be some time 

separation when individual pumps are tripped 

depending on the trip criteria used. In Group 3 

transients, low-pressure injection flow is not 

initiated. Safety injection tanks do not 

generally totally discharge because the system 

remains at relatively high pressure, compared to 

Groups 1 and 2. The high-pressure injection 

system is not operating near pump runout 

conditions, especially once the valve recloses. 

In this range of break sizes, the break flow limits 

the rate of high-pressure injection system 

injection to the reactor system. 
9-27 

9.3.2.2.1.4 Group 4: Main Steam Line 

Breaks and Other 

Secondary Side Failures 

Group 4 consists of main steam line breaks and 

other secondary side failures (e.g., valve 

openings, overfeed). This group of transients 

results in overcooling of the primary system 

through the steam generator loop affected by the 

failure of the steam line or other secondary fault. 

The response of these events is determined by 

numerous factors, including break location and 

operator actions. If the operator isolates the 

affected steam generator within a reasonable 

time, the primary system cooldown stops. The 

secondary side pressure equalizes with the 

containment pressure (slightly above 

atmospheric), and the secondary side fluid is 

near saturation temperature (somewhat 

subcooled as a result of adverse containment 

conditions). On the primary side, the operator 

does not trip the reactor coolant pumps, as 

subcooling is not lost; however, if the break is 

inside containment, the reactor coolant pumps 

are manually tripped as a result of adverse 

containment conditions. High-pressure injection 

starts but does not operate at runout conditions, 

as the primary system pressure remains high. 

Low-pressure injection initiation and safety 

injection tank discharge do not occur. The 

downcomer fluid conditions generally remain 

subcooled throughout the transient. 

Included in Group 4 are transients involving 

stuck-open secondary side SRVs and overfeeds. 

Like the main steam line break, this group of 

transients results in overcooling of the primary 

system through the steam generator loop 

affected by the stuck-open valve or overfeed. 

The cooldown rate is much slower because the 

flow through the valve is much lower than the 

flow through the failed steam line, and the 

consequences of any overfeed are not 

significant, particularly if isolated by the time 

the SG(s) are full. The operator does not trip the 

reactor coolant pumps, as subcooling is not lost. 

High-pressure injection starts but does not 

operate at runout conditions, as the primary 

system pressure remains high. Low-pressure 

injection initiation and safety injection tank 

discharge are not likely to occur. The 

downcomer fluid conditions generally remain 

subcooled throughout the transient. 

9.3.2.2.2 Analysis 

The approach used for the plant TH generalization 

is to compare key design features in conjunction 

with the RELAP5 TH results for the Oconee, 

Beaver Valley, and Palisades plants against the 

comparable designs in the generalization plants 

to determine whether there are any differences 

that would have a significant impact on the 

downcomer fluid temperature prediction. 

System pressure is considered in those transients 

where repressurization occurs. Further 

information and data on the four groups of TH 

sequences is presented in [Whitehead-Gen]. 

9.3.2.2.2.1 Group 1: Large Diameter 

Pipe Breaks 

Group 1 sequences result in the most rapid 

cooldown and depressurization of any of the 

dominant sequences analyzed for the Oconee, 

Beaver Valley, and Palisades plants. S ystem 

cooldown and depressurization is essentially 

complete by about 150 seconds for 16-in. 

(40.64-cm) diameter LOCAs. For 8-in. 

(20.32-cm) LOCAs, the time for system 

depressurization to occur is longer because the 

break area is a factor of 4 lower than in the case 

of a 16-in. (40.64-cm) break. For the 8-in. 

(20.32-cm) break, the system depressurizes to 

1.38 MPa [200 psia] in about 300 seconds for 

the Beaver Valley and Palisades plants. For 

Oconee, the system depressurizes to under 

1.38 MPa [200 psia] in about 600 seconds. 

Similar downcomer temperature characteristics 

are expected in the generalization plants, 

factoring in the plants’ power level, primary 

system volume and ECCS design differences. 

For the CE designs, the comparable plants are 

Fort Calhoun and Palisades. Some differences 

are found in the injection system capacities and 

safety injection tank water volume as a result of 

the difference in power level between these 

plants, although differences in the reactor vessel 

volume may also be a factor as a key function of 
9-28 

the safety injection tanks is to refill the reactor 

vessel after blowdown. In any event, the safety 

injection tanks are designed to refill the system 

in large-break LOCAs. 

In the case of B&W plants, the Oconee and TMI 

plants are comparable. These plants have about 

the same power level (2,568 MWt for Oconee 

compared to 2,530 MWt for TMI). The ECCS 

flow and safety injection tank volumes are 

comparable, which is not surprising, given that 

these plants operate at about the same power 

level. 

The comparable Westinghouse plants are Beaver 

Valley, Diablo Canyon, Sequoyah, and Salem. 

These plants have significant basic design 

differences, including the core power level and 

number of loops in the plant. The core power 

level in Beaver Valley is 2,652 MWt compared 

to 3,338 MWt for Diablo Canyon (Unit 1) and 

3,411 MWt for the Salem and Sequoyah plants. 

Beaver Valley is a 3-loop design, while Diablo 

Canyon, Salem, and Sequoyah are 4-loop 

designs. As a result, the system volume for 

Beaver Valley is less than the 4-loop plants7

. 

The Beaver Valley plant has three safety 

injection tanks (one for each loop), compared to 

four injection tanks for the other plants. As 

noted earlier, reactor vessel volume is a factor 

since a key function of the tanks is to refill the 

vessel after blowdown. Because of the higher 

power levels, ECC injection flow is higher in the 

comparison plants compared to Beaver Valley. 

The initial water temperature in the high- and 

low-pressure injection system and safety 

injection tanks is a factor in the cooldown rate 

and in the final downcomer fluid temperature. 

A review of the data obtained from the 

generalization plants show that the temperatures 

used in the plant analyses for Oconee, Beaver 

Valley, and Palisades is in the range of injection 

temperatures used in all plants. All the plants 

operate with injection temperatures within a 

range set in the plant technical specifications, 

 

7

 The plant design factors in the power level when 

selecting ECCS injection and safety injection tank 

capacities. 

which is represented by the temperatures used in 

the analysis. 

In summary, no differences in the plant system 

designs have been found that will cause 

significant differences in the downcomer fluid 

temperature from a thermal-hydraulic 

perspective. It is possible that there will be 

temperature variations attributable to the power 

level (i.e., MWt), although breaks in the range of 

8 to 16-in. (20.32 to 40.64-cm) are sufficiently 

large that the water injected into the system as a 

result of combined high- and low-pressure 

injection and safety injection tank discharge 

largely governs the downcomer fluid temperature. 

Also, the conditional probability of vessel failure 

is at a maximum in this break size diameter 

range, as discussed in Sections 8.5.2.4.1 and 

9.1.2.1of this report. 

9.3.2.2.2.2 Group 2: Small- to MediumDiameter Pipe Breaks 

The Group 2 sequences result in a slower 

cooldown and depressurization rate compared to 

the Group 1 dominant sequences for the Oconee, 

Beaver Valley, and Palisades plants. No general 

behavior pattern emerges in downcomer 

temperature for this mix of transients compared 

to the Group 1 transients. This lack of a general 

pattern is attributable to variations in such 

factors as break location, assumed injection 

temperature, and initial reactor power level. 

In addition, different operator actions, pump 

shutoff heads, and trip setpoints are also factors. 

Although the downcomer temperature results are 

highly variable among the plant types, 

generalization among plants by a given vendor 

can still be made. In the range of break sizes 

from 2.0 to 5.7-in. (5.08 to 14.37-cm) from hot 

full-power conditions, the rate of injection is 

limited by the size of the break, particularly as 

the break sizes becomes smaller. As a result, 

variations in reactor power level have more of 

an impact on downcomer temperature 

predictions compared to Group 1. Safety 

injection tank discharge and low-pressure 

injection flow initiation occur later, if at all. 
9-29 

The tendency of the injection flow to be limited 

by the break flow in Group 2 transients also 

limits the amount of energy that can be 

discharged through the break. Higher-power 

systems have a larger system volume with more 

steel mass and more water in the steam 

generators on the secondary side. Consequently, 

for a given break size, the higher-power systems 

should result in a slower cooldown and 

depressurization rate and, hence, somewhat 

warmer downcomer temperatures, particularly 

during depressurization, given comparable ECC 

injection rates. In general, the cooldown rate 

should be slower for the Salem, Sequoyah, and 

Diablo Canyon plants (compared to Beaver 

Valley), as these plants operate at higher reactor 

power relative to Beaver Valley. Conversely, a 

reactor system that operates at lower power 

could have a faster cooldown rate, which is the 

situation between the Palisades and Fort 

Calhoun plants. However, the capacity of the 

high- and low-pressure injection systems is 

smaller and generally scaled to the core power. 

Comparing Palisades and Fort Calhoun, for 

example, the high-pressure injection system 

pump at Palisades has about twice the flow 

capacity as at Fort Calhoun, so these plants 

should have comparable depressurization and 

cooldown rates. Once the system has 

depressurized and reached an equilibrium 

pressure, the downcomer temperature becomes 

comparable among the plants and is principally 

governed by the injection water temperature. 

For hot zero power conditions, downcomer 

temperature behavior should be less sensitive to 

the power level, simply because the power level 

is low. For the analyzed plants, the assumed 

power level is 0.2% of rated core power (about 

5 MWth) for hot zero power operation. If 

analyses were performed for the generalization 

plants, the models could be initialized to the 

same power level. In this case, the difference 

among plants of similar design would be small. 

An issue that needs to be considered for the 

thermal-hydraulic generalization is the 

switchover of the ECCS injection suction from 

the refueling water storage tank (or equivalent) 

to the containment sump. The increase in 

downcomer fluid temperature later in the 

transient is attributable to this switchover at a 

point in time after system cooldown and 

depressurization has occurred, so the 

downcomer temperature is governed by the 

injection temperature. Many times, however, 

vessel failure is predicted to occur before

switchover of ECCS suction. As a result, ECCS 

suction switchover to the containment sump is 

generally unimportant to the vessel failure 

prediction. 

In summary, break flow and energy released 

through the break govern the rate of cooldown 

and depressurization in the reactor system. For 

hot full-power cases, the cooldown and 

depressurization rates are expected to be slower 

for reactor systems that operate at higher powers 

and faster for systems that operate at lower 

powers. However, since the flow capacity of the 

high-pressure injection pumps at Fort Calhoun is 

about one-half that of Palisades, all 

generalization plants should have 

depressurization and cooldown rates that are 

comparable to their corresponding detailed 

analysis plant. The difference in cooldown and 

depressurization rates should have less of an 

impact on downcomer temperature if the 

transient begins from hot zero power operation. 

It should be noted that the feed-and-bleed LOCA 

scenarios have a thermal-hydraulic behavior that 

is similar to the small LOCA described above. 

9.3.2.2.2.3 Group 3: Stuck-Open 

Valves in the Primary 

System 

Transients involving stuck-open primary side 

SRVs that reclose have cooldown and 

depressurization characteristics of a LOCA with 

a diameter at the low end of the Group 2 range. 

A key difference, however, is the reclosure of 

the stuck-open valve after significant cooldown 

and depressurization has occurred. Once the 

valve recloses, rapid system repressurization 

occurs as a result of continued operation of the 

high-pressure injection system or charging 

system. The rate of repressurization depends on 

the flow characteristics of the high-pressure 
9-30 

injection or charging pumps. The operator 

action to control system pressure by controlling 

the high-pressure injection system pumps is 

important to determining system response in this 

group of transients. 

The system cooldown and depressurization rates 

are governed by the capacity of the PORVs or 

SRVs, power level, system volume, and ECCS 

injection temperatures/rates. For the B&W 

design, the Oconee PORV and SRV capacities 

are slightly larger than the TMI capacities, so the 

cooldown and depressurization rates would be 

slightly faster for Oconee. For the 

Westinghouse designs, the capacity of the 

Beaver Valley PORV is higher than Sequoyah 

and Salem, even though the reactor power for 

both Salem and Sequoyah is more than 

750 MWth higher. The cooldown and 

depressurization rates for Salem and Sequoyah 

would be slower, and the downcomer fluid 

temperature would remain higher throughout the 

transient if the PORV fails. The results are 

similar, comparing the relief valve capacity for 

these plants, as Beaver Valley has a higher relief 

capacity than Sequoyah or Salem. 

Compared to Beaver Valley, the Diablo Canyon 

PORV has a 25% higher flow capacity. 

However, the reactor power is also about 25% 

higher, so the cooldown and depressurization 

rates would be about the same for both plants if 

the PORV fails. In the case of the SRVs, 

Beaver Valley has a higher capacity valve than 

Diablo Canyon, so the cooldown and 

depressurization rates for Diablo Canyon should 

be slower than for Beaver Valley. 

For the CE designs, Fort Calhoun has a higher 

SRV capacity per valve than Palisades, even 

though its core power is lower. As a result, the 

cooldown and depressurization rates for Fort 

Calhoun are higher than for Palisades, given 

failure of a single valve. Palisades has large 

PORVs, but operates with closed block valves 

that prevent the function of pressure relief 

through these valves, so no comparison is made 

using PORV capacity for these plants. 

As in the case of the Group 2 LOCAs, 

downcomer temperature behavior should be less 

sensitive to the power level for hot zero power 

conditions, simply because the power level is 

low for the reasons cited at the end of the Group 2 

discussion. 

In contrast to the Group 2 transients, late stage 

repressurization and operator actions to control 

the subcooling and system pressure must be 

factored into the evaluation. In LOCAs, the 

system pressure is low and does not play a 

significant role in the prediction of vessel 

failure. However, in the case of a stuck-open 

primary relief valve that subsequently recloses, 

the primary repressurizes (without operator 

intervention), and the resulting pressure rise can 

drive cracks through the vessel wall. The pump 

head of the high-pressure injection system is 

also a factor in determining the primary 

pressure. The Oconee, Beaver Valley, Diablo 

Canyon, and TMI plants have high-head pumps 

that can repressurize the system to the setpoint 

of the PORV or pressurizer SRV. The Palisades, 

Fort Calhoun, Sequoyah, and Salem plants have 

low-head pumps that can repressurize the system 

to the range of 8.9 to 10.3 MPa (1,290 to 1,500 psia). 

However, the charging systems of these plants 

can also repressurize the system, albeit at a 

slower rate. Primary system reheating after the 

valve recloses as a result of decay heat also 

contributes to system repressurization. For hot 

zero power cases, the system can also 

repressurize after the valve recluses, although 

throttling of the high-pressure injection system 

allows the system to eventually depressurize. 

Operators are trained to control system pressure 

and subcooling by controlling high-pressure 

injection flow and to reestablish normal charging 

and letdown flow (see Table 9.7, GI 23). The 

criteria used to establish when the operator starts 

high-pressure injection system throttling and 

continues to throttle varies significantly from 

plant-to-plant. It is not possible to generalize 

system response to the variety of possible 

throttling strategies without further analysis. 

In summary, the system cooldown and 

depressurization rates are higher for Oconee 

(B&W) and Beaver Valley (W-3) than for the 

generalization plants from the same NSSS 

vendor (i.e., the generalization plants are 
9-31 

warmer). However, Fort Calhoun (CE) has 

higher system cooldown and depressurization 

rates than its corresponding detailed analysis 

plant, Palisades. The impact of high-pressure 

injection system throttling strategies among the 

plants is discussed in Section 9.3.2.1. 

9.3.2.2.2.4 Group 4: Main Steam Line 

Breaks and Other 

Secondary Side Failures 

Group 4 transients includes large steam line 

breaks and stuck-open secondary side valves, 

as well as consideration of overfeeds such as the 

unexpected opening of the feed regulating 

valves. The secondary breaches can vary from 

double-ended guillotine breaks of the main 

steam line to a single stuck-open turbine bypass 

valve. There are many factors that influence the 

thermal-hydraulic response of the reactor system 

during such events. Key factors are operator 

actions, the location of the break, and steam line 

flow restrictors. If the operator can isolate the 

affected steam generator in a reasonable amount 

of time, primary system cooldown is stopped 

and there may not be a primary system 

overcooling problem. In all plants, the operator 

is instructed to isolate the affected steam 

generator, and training and procedures support 

early operator actions (see more on this above 

under the PRA/HRA discussion). In order for 

main steam line breaks and other secondary 

faults to become a PTS problem, feedwater must 

be continued to the affected steam generator. 

Break location is another factor in system 

response during a main steam line break 

transient. Plant response is different depending 

on whether the break is inside or outside 

containment because of effects on reactor trip, 

containment spray actuation, safety injection and 

reactor coolant pump trips, and other adverse 

condition issues. If the break/stuck valve is 

downstream of the MSIV, the valves should 

close and the primary system cooldown is 

stopped. While the MSIV closure setpoints vary 

from plant-to-plant, they all close relatively 

early in the transient. Note that some B&W 

plants (such as Oconee) do not have MSIVs, so 

the break location is less important. If the break 

occurs inside containment, the operators should 

trip the RCPs in response to adverse 

containment conditions. In general, RCP trip 

makes conditions worse as the downcomer fluid 

is not as well-mixed as when the pumps are 

running so lower downcomer fluid temperatures 

may result. The flow restrictors (if available) 

are in place to limit the break flow during steam 

line breaks and determine the cooldown rate. 

Note that the B&W plants (Oconee and TMI) do 

not have flow restrictors, and the break flow is 

determined by the flow area of the steam line. 

Starting with the B&W plants designs (Oconee 

and TMI) some comparisons and observations 

are made. Both plants use the once-through 

steam generator design and have comparable 

power levels (2,568 MWt for Oconee and 

2,533 MWt for TMI). The steam generator 

water mass in the Oconee plant is estimated 

between 35,000 to 40,000 lbm (15,875 to 

18,143 kg), while TMI is estimated between 

42,000 and 45,000 lbm (19,050 and 20,411 kg). 

Neither plant has flow restrictors, so the steam 

line break flow is limited by steam line size 

(34-in. (86.4-cm) for Oconee, and 24-in. 

(61.0-cm) for TMI). Since the steam line flow 

area is smaller in TMI, the break flow is 

expected to be less than at Oconee, thus leading 

to a slower primary side cooldown. In addition, 

neither the Oconee nor TMI plants have MSIVs, 

so the break location is relatively unimportant. 

Both plants have main feedwater automatically 

isolated after an MSLB, so main feedwater 

temperature and flow rate are unimportant. 

On the primary system side, the high-pressure 

injection system has a major effect on 

downcomer fluid temperature during a main 

steam line break transient. The two B&W plants 

have similar high-pressure injection systems. 

Based on an overall general comparison, the 

Oconee and TMI plants are expected to have 

similar thermal-hydraulic responses to an MSLB 

transient. Given that TMI has smaller-diameter 

steam lines, the average downcomer fluid 

temperature is expected to be slightly warmer 

than at Oconee. 
9-32 

Next, comparisons are made between the two 

CE plants: Palisades and Ft. Calhoun. Both 

plants utilize vertical U-tube steam generators. 

These two plants have significantly different 

power levels (2,530 MWt for Palisades and 

1,500 MWt for Ft. Calhoun). Consequently, 

Ft. Calhoun has smaller steam generators. 

The normal full power water mass in the steam 

generator for Palisades is 142,138 lbm 

(64,472 kg), compared to 82,000 lbm (37,194 kg) 

for Ft. Calhoun. Both plants have flow 

restrictors at the steam generator outlets with a 

flow area of approximately 2.0 ft2

 (0.18 m2). 

In Palisades, the MFW is typically isolated by 

the operator; however, MFW is runback 

automatically if the operator does not take 

control in time. In Ft. Calhoun, MFW is isolated 

automatically during an MSLB. Auxiliary 

feedwater temperature can vary from 294 to 311 

K (70 to 100°F). The Palisades analysis uses a 

nominal temperature of 305 K (90°F). In the 

Palisades plant, a control system limits the total 

AFW flow to the affected steam generator. In 

other plants, this type of control system is not 

used, so total AFW flow to a single steam 

generator is possible. 

The high-pressure injection pumps at Palisades 

have a shutoff head of 8.9 MPa (1,291.7 psia), 

while Ft. Calhoun pumps are slightly higher at 

9.6 MPa (1,390 psia). However, both plants 

have charging pumps capable of pressurizing the 

primary system to above the PORV setpoint. 

Note that Palisades normally operates with the 

PORV block valves closed. The flow capacity 

of the Palisades HPI pumps is about twice that 

of the Ft. Calhoun pumps. The Ft. Calhoun 

plant probably has a smaller primary side fluid 

volume than Palisades, consistent with the 

difference in power level. 

Based on an overall general comparison, the 

Palisades and Ft. Calhoun plants are expected to 

have similar thermal-hydraulic responses to an 

MSLB transient. 

Finally, comparisons are made between the 

Westinghouse-designed plants, Beaver Valley 

(3-loop), Diablo Canyon (4-loop), Sequoyah 

(4-loop), and Salem (4-loop). All plants utilize 

vertical U-tube steam generators. The power 

levels vary from 2,652 MWt for Beaver Valley 

to 3,411 MWt for Sequoyah and Salem. Note 

that the power levels are larger on the 4-loop 

plants than on the 3-loop Beaver Valley plant. 

The steam generator mass varies from 

100,000 lbm (45,360 kg) for Salem to 

115,000 lbm (52,160 kg) for Diablo Canyon. 

All plants use a flow restrictor at the steam 

generator outlet. For the 4-loop plants, the flow 

area is 1.4 ft2

 (0.13 m2), but is much larger 

(4.7 ft2

 (0.44 m2)) on the 3-loop Beaver Valley 

plant. Based on its larger flow restrictor, Beaver 

Valley is expected to have a much faster 

cooldown rate than the other Westinghouse 

plants. 

The main feedwater temperature for the 

Westinghouse plants is typically around 497 K 

(435°F), and decreases to 311 K (100°F) after a 

reactor trip. In all four plants, main feedwater 

should automatically trip on a main steam line 

break. Auxiliary feedwater temperature varies 

from 275 to 322 K (35 to 120°F) among the four 

plants. The Beaver Valley analysis uses a 

temperature of 295 K (72°F). In all four plants, 

the AFW is capable of maintaining steam 

generator level even during an MSLB. 

The four plants have somewhat different highpressure injection systems. At Beaver Valley, 

the charging and high-pressure injection systems 

use the same pumps. These pumps have a 

shutoff head greater than 18 MPa (2,600 psia) 

and are capable of pressurizing the primary 

system to above the PORV setpoint. The other 

Westinghouse plants use high-head charging 

pumps but intermediate-pressure HPI pumps. 

These intermediate-pressure pumps have a 

shutoff head of approximately 10.3 MPa 

(1,500 psia). The minimum HPI temperature 

varies from 275 to 289 K (35 to 60°F) among 

the four plants. In the Beaver Valley analysis, 

283 K (50°F) was used for HPI temperature. 

Based on an overall general comparison, the 

four Westinghouse plants are expected to have 

similar thermal-hydraulic responses to an MSLB 

transient. 
9-33 

Stuck-open valves on the secondary side are 

equated to smaller steam line breaks. Transients 

with stuck-open secondary side (turbine bypass, 

atmospheric dump, and safety relief) valves are 

less severe thermal-hydraulically than the larger 

steam line breaks discussed above. For all 

plants evaluated, all secondary side valves can 

be isolated with the exception of the SRVs. 

In summary, the generalization plants should be 

warmer (or about the same) when compared to 

the plants analyzed in detail. 

The simple overfeeds are worth a brief mention. 

In these events, an unexpected overfeed of one 

or more SGs occurs. If such an overfeed 

condition is allowed to continue for many tens 

of minutes, the secondary temperature will 

ultimately drive toward the main condenser 

water temperature (~311 K (100EF)) following a 

plant trip and likely isolation of warming (i.e., 

steam addition) of the feedwater. This causes 

depressurization and cooldown of the primary 

system. However, as discussed in the above 

comparable PRA/HRA section, the likelihood of 

a continuing overfeed, which would involve 

failure of automatic high SG level trips backed 

by operator action to either close feed valves or 

shutdown pumps as necessary, makes such an 

event very unlikely. Further, the plant-specific 

plant analyses show that the PTS challenge, if 

the feed is not controlled even until the SGs are 

completely full, is not significant. For these 

reasons, simple overfeed scenarios are not 

important and, hence, not discussed any further. 

9.3.3 Combined Observations and 

Overall Conclusion 

Group 1 (Large-Diameter Primary Side 

Pipe Breaks): No differences were found that 

would cause significant changes in either the 

progression or frequencies of the PTS 

scenarios. From the TH perspective, no 

differences in the plant system designs were 

found that would cause significant changes in 

the downcomer fluid temperature. While 

some temperature variations could be expected 

because of the initial power level, breaks in 

this range are sufficiently large that the water 

injected into the system due to combined highand low-pressure injection and safety injection 

tank discharge should largely govern the 

downcomer fluid temperature. Thus, we 

expect that the generalization plants can be 

bounded (or represented) by the detailed 

analysis plants. 

Group 2 (Small- to Medium-Diameter 

Primary Side Pipe Breaks): No differences 

were found that would cause significant 

changes in either the progression or frequency 

of the pipe break LOCAs. For the feed-andbleed LOCAs, the only identified difference 

affected the frequency for the CE 

generalization plant (i.e., Fort Calhoun). The 

frequency for these types of scenarios could be 

higher by a factor of ~3; however, this 

increase would not prevent the generalization 

plants from being bounded (or represented) by 

the detailed analysis plants. All generalization 

plants should have depressurization and 

cooldown rates associated with pipe break and 

feed-and-bleed transients that are comparable 

to their corresponding detailed analysis plant. 

Thus, we expect that the generalization plants 

can be bounded (or represented) by the 

detailed analysis plants. 

Group 3 (Stuck-Open Valves on the 

Primary Side that May Later Reclose): 

The progression of accident scenarios should 

be the same across all plants. However, the 

frequencies associated with these scenarios 

could increase by at most a factor of 5 for one 

of the Westinghouse plants (i.e., Salem). The 

importance of this factor of 5 increase at 

Salem was approximated by increasing the 

failure probability assigned to the operator 

fails to throttle basic event in the Beaver 

Valley model and requantifying the Beaver 

Valley results. The total point estimate for 

Beaver Valley increased by a factor of 1.02; 

thus, we conclude that this difference is 

unimportant. 

Only Fort Calhoun is expected to have a 

downcomer temperature that is cooler than its 

corresponding detailed analysis plant 

(Palisades). The downcomer temperature for 

the other generalization plants is actually 
9-34 

expected to be somewhat warmer. Given the 

expected Fort Calhoun results, a surrogate 

analysis was performed. This analysis used 

the Palisades TH model, adjusting the model 

to account for the differences in thermal power 

to primary system volume and size of the 

relief valve opening(s). Results from the 

analysis indicated that Fort Calhoun would 

have a lower downcomer temperature, as 

expected. The results from the surrogate TH 

calculation were then analyzed using FAVOR 

and the Palisades embrittlement map. Results 

from the FAVOR calculation indicated an 

increase in conditional probability of throughwall cracking. While this resulted in much 

higher TWCFs for Fort Calhoun than for 

Palisades for the same type of sequence, the 

TWCFs were still small in an absolute sense 

(low E-08/yr or lower range). These values 

are comparable to but not higher than the 

highest TWCFs estimated for all types of 

sequences (LOCAs, SRV openings, MSLBs, 

etc.), which are also in the E-08/yr range. 

Thus, the TWCF of Fort Calhoun can be 

bounded by Palisades. 

Group 4 (Main Steam Line Breaks and 

Secondary Side Breaks, in General): 

No differences were found that would cause 

significant differences in either the 

progression or frequency of the PTS scenarios. 

The downcomer temperature for the 

generalization plants should be about the same 

(Westinghouse and CE) or warmer (B&W). 

Thus, we expect that the generalizations plants 

can be bounded (or represented) by the 

detailed analysis plants. 

These combined observations support the overall 

conclusion that the TWCF estimates produced 

for the detailed analysis plants are sufficient to 

characterize (or bound) the TWCF estimates for 

the five generalization plants and, thus, 

by inference, PWRs in general. 

9.4 Consideration of External Events 

9.4.1 Introduction 

In examining the potential for a revised PTS 

screening limit, it is important to also consider 

the potential risk from external events. External 

events are those in which spatial interactions 

may be important to the propagation of the 

accident sequence, and these can contribute to 

the PTS risk. External events include such 

scenarios as those involving fires, floods, high 

winds and tornados, and seismic events, among 

others. As an example, a fire could start in an 

electrical cabinet causing the spurious opening 

of one or more secondary relief valves such as 

turbine bypass (steam dump) valves, which 

could induce a serious overcooling and a 

potential PTS concern depending on subsequent 

plant equipment and operator responses. Since 

external events can affect multiple plant 

equipment and operator actions as well, they 

could be important to PTS. 

Because (1) the specific effects of external 

events are very plant-specific (e.g., into which 

rooms the water from an internal flood 

propagates and, thus, what equipment is 

affected), and (2) since these analyses can be 

resource-intensive, requiring the gathering of 

significant spatial information about each plant, 

it was not practical to perform plant-specific 

external event PTS analyses. Instead, 

conservative analyses were performed with the 

goal of bounding the potential PTS TWCFs 

from external events. This is in contrast to the 

internal event PTS analyses results, which are 

generally “best-estimate” analyses meant to 

determine a realistic assessment of PTS TWCFs 

attributable to scenarios initiated by such events 

as turbine trips, loss of feedwater, etc. (i.e., 

internal events). In contrast, the contribution 

from external events was assessed by using 

conservative assumptions to bound the PTS 

TWCFs from external events and, hopefully, 

demonstrates that the bounding TWCFs from 

external events are at least no higher than the 

highest best-estimate internal events TWCFs. 

Such a result would provide reasonable 

assurance that the total external event-caused 
9-35 

PTS TWCF is no worse than the total internal 

event-caused PTS TWCF (which is as high as 

the low E-8/yr range at 60 EFPY based on the 

three detailed plant analyses). 

As a result, the numerical results from the 

external events analyses (described in detail in 

[Kolaczkowski-Ext] and which contains the 

references to the other documents cited here) 

should not be taken as best-estimate or realistic 

values; they are intended to provide bounding 

TWCF estimates for the pertinent external event 

scenarios. Also note that in following this 

approach, no particular plant was taken as a 

representative model for the analysis (with the 

exception of earthquake hazard, where H.B. 

Robinson and Diablo Canyon were used as 

surrogates). Therefore, because these results are 

intended to bound the worst situation that might 

arise at virtually any plant, they may be 

extremely conservative for many plants. The 

degree of conservatism cannot be determined 

without performing plant-specific analyses. 

9.4.2 Approach 

A multi-faceted approach was used to gain 

insight as to the potential contribution of 

external events to the PTS TWCFs. This 

approach included the following: 

(1) A review was performed of the late 2001 – 

early 2002 version of the Calvert Cliffs PRA 

model, with cooperation from the utility, 

which includes not only core damage 

scenarios, but also PTS scenarios. The 

model includes contributions from both 

internal and external events for both core 

damage frequencies and PTS TWCFs and 

can offer insight into the potential 

importance of external events. 

(2) As further evidence of the potential 

importance of external events, a review of 

licensee event reports (LERs) was 

performed of actual overcooling events in 

U.S. plant operating experience covering a 

recent approximately twenty year period. 

(3) Further, a review was conducted of a 

sampling of (just two) individual plant 

examinations for external events (IPEEE) 

submittals, one for Salem and one for Ginna, 

to determine what insights could be gained 

from those studies that might be applicable 

to PTS. 

(4) With all of the above as background, it was 

nonetheless decided that additional 

analytical analyses were necessary to be able 

to bound the potential TWCFs from external 

event overcooling scenarios. 

9.4.3 Findings Based on the Reviews 

The late 2001 – early 2002 version of the 

Calvert Cliffs PRA suggests that the TWCFs as 

a result of PTS caused by external events are 

low compared to that caused by internal events 

(i.e., less than 10%). The PRA shows fire as the 

external event of greatest concern. While this is 

an indicator of the potential relative contributions, 

it is only one plant’s result and the finding is 

subject to some modifications that would need to 

be made to the model in order to be more 

comparable to the three analyses conducted as 

part of this work. For instance, the Calvert 

Cliffs model needs modifications in the areas of 

the sequences being modeled, and some human 

failure probabilities may need to be reconsidered 

during certain external events. Additionally, the 

latest CPTWC information from this study needs 

to be reflected in any update of the Calvert Cliffs 

PRA. Hence, while encouraging, the relative 

importance of external events to the PTS 

TWCFs cannot be generically determined based 

on this one input alone. 

The LER review of events occurring in a recent 

20-year period identified a total of 128 PTSrelevant (i.e., cooldown) events. Of these, only 

three events could be potentially categorized as 

involving an external event, although only one 

(a switchgear fire) was clearly an external event 

(LER No. 26989002). This evidence suggests 

that external events will be involved in no more 

than approximately 2% of all PTS occurrences. 

While this is a valuable insight in that it suggests 

that experience shows that cooldowns are more 

likely to be caused by internal events rather than 

external events, it still does not address the 

potential TWCFs from external events even if 

they do occur less frequently. This is because 
9-36 

external events could still lead to more serious 

scenarios with higher CPTWC values, thereby 

resulting in potentially higher TWCFs. 

The two IPEEEs were originally conducted to 

determine core damage frequencies as a result of 

undercooling (rather than overcooling events); 

hence, there were very limited insights from 

these reports applicable to PTS. Nonetheless, 

during the review of the IPEEEs, one general 

type of interaction between external events and 

effects of interest to PTS was noted to be 

included in both studies. This was a fireinduced opening of one or more pressurizer 

PORVs — a possible serious overcooling event. 

This indicates that any estimation of the external 

event contribution to PTS needs to include 

consideration of spurious actions such as that 

described as a result of fire scenarios. However, 

no other meaningful insights were gained from 

reviewing the two IPEEEs that would be 

applicable to this PTS work. 

9.4.4 Additional Analyses 

9.4.4.1 Overview 

The above reviews provided some insights with 

regard to how important external events may be 

to PTS. However, the set of insights was 

incomplete. As a result, additional analytical 

analyses were performed. These additional 

analyses involved comparisons of the following 

factors: 

(1) TWCF results from the internal events 

analyses for the three plants 

(2) conservatively estimated corresponding 

external event TWCF results 

This comparative analysis was structured based 

on the following broad types of overcooling 

scenarios analyzed in this PTS work: 

• Category 1: Loss-of-Coolant Accidents 

(LOCAs). These are scenarios that involve 

primary system breaches (such as pipe 

breaks and open pressurizer valves) but 

without any secondary anomalies or faults. 

• Category 2: Secondary Anomalies or Faults. 

These are scenarios that involve such events 

as stuck-open secondary valves, main steam 

line breaks, and steam generator overfeeds 

but without any primary system anomalies 

or faults. 

• Category 3: Coexisting LOCA - Secondary 

Faults. These are scenarios that involve 

both primary system breaches and secondary 

faults at the same time. 

As required, the analyses further divided these 

broad categories of scenarios into more specific 

types of scenarios. Table 9.7 summarizes all 

types of scenarios for which TWCF comparisons 

were made. These were examined for both fullpower and hot zero power conditions. For each 

type of scenario, conservative judgments were 

made with regard to the type of external event 

that could directly contribute to the cause of 

such a scenario. In addition, conservative 

estimates were made with regard to the 

applicable external event frequencies, plant 

equipment responses, and operator effects. With 

regard to operator actions, little or no credit was 

given in these analyses in response to the 

external event-induced PTS challenges; this 

further contributed to the conservative 

estimations of external event TWCFs, thereby 

making them artificially more important. 

Finally, the resulting TWCFs from both internal 

event contributions and the conservatively 

assessed external event contributions were 

compared. The following is provided as just one 

example of such a comparison. 

9.4.4.2 A Representative Comparison 

Category 1 - LOCAs; Scenario Type #3: In this 

scenario, a small LOCA (with an equivalent 

diameter of ~1.5 to 3-in. (~3.8 to 7.6-cm)) 

occurs as a result of a pipe break, and everything 

else functions as designed. (Other small 

LOCAs, such as those caused by an open 

PORV, are a different scenario type that is 

analyzed elsewhere.) By this, we mean that HPI 

operates (so cold water enters the vessel 

downcomer region) and the system likely 

continues to provide full flow, since throttling 

criteria are not likely to be met for most breaks 
9-37 

in this size range during the time period of 

interest to PTS when large temperature gradients 

occur across the vessel wall. It is assumed the 

operator does shut down the RCPs as 

procedurally required (this is worse for PTS 

since there is less mixing of the primary 

coolant), and there are no secondary anomalies 

or other operator errors that induce secondary 

complications. 

Table 9.8 summarizes the major inputs and 

resulting TWCFs from such a scenario caused 

by a random small-break LOCA (i.e., an internal 

event initiator) based on results from the three 

plant analyses. 

Table 9.7. Scenarios covered under the external event analyses 

Overall Scenario Category Scenario Types 

Large LOCA pipe break 

Medium LOCA pipe break 

Small LOCA pipe break 

Scenario with single stuck-open pressurizer PORV 

Scenario with single stuck-open pressurizer SRV 

Scenario with two stuck-open pressurizer PORVs 

Scenario with two stuck-open pressurizer SRVs 

Scenario with two stuck-open pressurizer PORVs that reclose 

Scenario with one or two stuck-open pressurizer SRVs that reclose 

Total loss of secondary heat sink with subsequent use of feed-andbleed 

Category 1: LOCAs 

Small LOCA, or PORV or SRV opening, with initial loss of primary 

system injection 

Steam generator(s) overfeeds 

Uncontrolled secondary depressurization to feed steam generator(s) 

with condensate 

Two or fewer valves open upstream of MSIVs 

Turbine bypass (steam dump) valves open downstream of MSIVs 

Large steamline break upstream of MSIVs 

Category 2: Secondary Anomalies 

or Faults 

Large steamline break downstream of MSIVs 

Category 3: Coexisting LOCA - 

Secondary Faults 

Consideration of combinations of above 

Table 9.8. Small-break LOCA internal event results 

Scenario Internal Event 

Frequency (yr-1) 

CPTWC at 60 EFPY Internal Event TWCF 

(yr-1) 

Small LOCA 

at Full Power 

Up to 1E-3 Up to 1E-5 Up to 2E-9* 

Small LOCA 

at Hot Zero Power 

Up to 2E-5 <1E-4 

(conservative estimate) 

<2E-9 

* Highest CPTWC does not necessarily correspond to the highest frequency shown, so one cannot simply 

multiply the highest frequency in the table with the highest CPTWC shown in the table. 

Consideration was given to how external events 

might directly induce a small pipe break LOCA. 

Seismic, flooding, fire, high wind/tornado, and 

other (e.g., aircraft crash) external events were 

considered. In large part because of the nature 

of the primary coolant system and containment 

designs, and their relative location to the rest of 

the plant (e.g., a fire in the auxiliary building 
9-38 

should not be able to induce a pipe break in the 

primary coolant housed inside the containment), 

we concluded that only a seismic event might be 

able to induce a small pipe break LOCA. Hence 

an analysis of a seismic-induced small pipe 

break LOCA was conducted. 

Possible Seismic-Small Loca Scenario: 

For the small LOCA case, a 0.3g high 

confidence of low probability of failure 

(HCLPF) is assumed to be representative of the 

seismic strength of the primary piping and other 

components for which failure as a result of a 

seismic event could result in a small LOCA. 

This corresponds to the review-level earthquake 

(RLE) peak ground acceleration for most plants 

in the IPEEE program. Most (if not all) IPEEEs 

concluded that primary piping and components 

have higher seismic strengths than that 

corresponding to a 0.3g HCLPF; thus, use of the 

0.3g HCLPF in this analysis is conservative. 

It is further assumed that both $R and $u (which 

define the uncertainty in the HCLPF) are 0.3 

(typical), giving a median fragility of about 0.5g. 

Using the H.B. Robinson site as a surrogate for 

Eastern plants, because it has the largest hazard 

of any Eastern PWR, this corresponds to a mean 

accidence frequency of 1.6E-4/yr. An analysis 

was performed using the SAPHIRE computer 

code to convolve the above fragility information 

with the revised Lawrence Livermore National 

Laboratory (LLNL) hazard curve for H.B. 

Robinson, resulting in a mean seismic-induced 

small pipe break LOCA frequency estimated to 

be 1.1E-4/yr. 

As an additional sensitivity, the hazard curve for 

Diablo Canyon was also used as representative 

of a high-seismicity site. A corresponding 

HCLPF for a small pipe break LOCA at such a 

site was assumed to be 0.5g, because of the more 

rugged plant design (higher RLE). Maintaining 

$R and $u of 0.3, and convolving this fragility 

information for a small pipe break LOCA with 

the mean hazard curve from the Diablo Canyon 

IPEEE submittal results in a mean seismicinduced small pipe break LOCA frequency of 

5.0E-4/yr******. 

Using a value of 0.02 (i.e., 2%) as the fraction of 

the year the plant is at HZP conditions, as done 

in the internal events analysis, yields 1E-5/yr as 

the highest estimated frequency (5.0E-4/yr from 

above x 0.02 = 1E-5/yr) of a seismic event 

causing a small pipe break LOCA while the 

plant is at HZP conditions. 

By using the frequencies conservatively 

estimated above, and the same maximum 

CPTWC from the internal events analyses of the 

three plants (the CPTWC will be the same 

whether the event is caused by an internal event 

initiator or a seismic event), the corresponding 

seismically induced small pipe break LOCA 

TWCFs are as shown in Table 9.9. 

Note that the conservative external event 

contributions to the TWCFs for this type of 

accident are either less than or not significantly 

greater than the internal event TWCFs. 

9.4.5 Overall Findings 

In spite of the conservative nature of the external 

event analyses, no external event scenarios were 

found where the TWCFs significantly exceed 

that of the worst internal event scenarios 

(contributions from LOCA-type and SRV openreclose-type accidents) as discussed in detail in 

the companion report [Kolaczkowski-Ext]. 

From that report, and as reiterated in this 

summary section, the highest total best-estimate 

TWCF across all internal event scenarios for the 

three plants analyzed at 60 EFPY is 

approximately 2E-8/yr and is used as part of the 

basis for proposing revised PTS Rule criteria. 

The comparable bounding total TWCF across all 

external event scenarios is also approximately 

2E-8/yr. Therefore, given the bounding nature 

of the external event analyses, there is 

 

****** The hazard curve in the Diablo Canyon 

IPEEE is given in terms of peak spectral 

acceleration in the range of 3.5–8Hz. This was 

converted to a zero-period peak ground 

acceleration by dividing the accelerations by a 

factor of 2. 
9-39 

considerable assurance that the external event 

contribution to overall TWCF as a result of PTS 

is at least no greater than the highest bestestimate contribution from internal events. In 

fact, given the conservative probabilities and 

dependencies assumed in the external event 

analyses, with the addition of little or no credit 

for any operator actions for the external event 

scenarios, it is more likely that the “realistic” 

external event contribution to overall TWCF is 

much less than the highest internal event 

contribution. It is, therefore, our view that the 

contribution of external initiating events to the 

overall TWCF attributable to PTS is enveloped 

by the internal event results. Hence, for general 

purposes, it is recommended that the overall 

PTS TWCF can be estimated by neglecting the 

potential contribution from external events. 

To the extent it may be necessary or desirable, 

individual plants could provide a detailed 

external events PTS analysis to ensure that the 

plant staff understands the specific contributions 

to PTS TWCF from external events. 

Table 9.9. Small-break LOCA TWCF comparison 

Scenario Internal Event 

Frequency (yr-1) 

CPTWC 

at 60 EFPY 

Internal Event 

TWCF (yr-1) 

Bounding 

External Event 

Frequency 

(yr-1) 

Bounding 

External Event 

TWCF 

(yr-1) 

Small LOCA 

at Full Power 

Up to 1E-3 Up to 1E-5 Up to 2E-9 5E-4 5E-9 

Small LOCA 

at Hot Zero 

Power 

Up to 2E-5 <1E-4 

(conservative 

estimate) 

<2E-9 1E-5 <1E-9 

9.5 Summary of Generalization 

Studies 

In this chapter, we examined the applicability of 

the TWCF estimates presented in Chapter 8 

for Oconee Unit 1, Beaver Valley Unit 1, and 

Palisades to PWRs in general. The information 

presented focused on the following topics: 

• Sensitivity studies performed on the TH and 

PFM models to engender confidence in both 

the robustness of the results presented in 

Chapter 8 and their applicability to PWRs 

in general. 

• An examination of the plant design and 

operational characteristics of five additional 

plants to determine whether the design and 

operational features that are the key 

contributors to PTS risk vary significantly 

enough in the general plant population to 

question the generality of our results. 

• An examination of the effects of external 

events (e.g., fires, floods, earthquakes) to 

PTS risk. 

Except for a few situations that are not expected 

to occur, none of these analyses revealed any 

reason to question the applicability of the results 

presented in Chapter 8 to the general population 

of operating PWRs in the United States. The 

information developed in these analyses is 

summarized as follows: 

TH Sensitivity Studies 

• Changes to the RELAP heat transfer 

coefficient model to account for low-flow 

situations where mixed convection heat 

transfer may be occurring in the 

downcomer were made based on the 

Petukhov-Gnielinski heat transfer 

correlation. This change in the heat 

transfer coefficient increases the CPTWC 

by a factor ~3 (averaged across all 

transients analyzed) compared to using the 

default heat transfer correlations in 

RELAP5/MOD3.3 Version ei. There is 

some variability from the average CPF 

factor, depending upon the transient being 

considered. 
9-40 

PFM Sensitivity Studies 

• An examination of the effects of all 

postulated credible perturbations to our 

PFM model revealed no effects significant 

enough to warrant a change to our baseline 

model, or to recommend a caution 

regarding its robustness. 

• In general, the TWCF of forged PWRs 

can be assessed using the Chapter 8 results 

(for plate welded PWRs) by ignoring the 

TWCF contribution of axial welds. 

However, should changes in future 

operating conditions result in a forged 

vessel being subjected to very high levels 

of embrittlement (far beyond any currently 

anticipated at EOL or EOLE) a plantspecific analysis to assess the effect of 

subclad flaws on TWCF would be 

warranted. 

• For PWRs with vessel thicknesses of 7.5 to 

9 .5-in. (19.05 to 24.13-cm), the TWCF 

results in Chapter 8 are realistic. The 

Chapter 8 results overestimate the TWCF 

of the seven thinner vessels (with wall 

thicknesses below 7-in. (17.78-cm)) and 

underestimate the TWCF of Palo Verde 

Units 1, 2, and 3, all of which have wall 

thicknesses above 11-in (27.94-cm). 

However, these vessels have very low 

embrittlement projected at either EOL or 

EOLE, suggesting little practical effect of 

this underestimation. 

Plant Design and Operational Characteristics 

• Large-Diameter Primary Side Pipe Breaks: 

No differences were found that would 

cause significant changes in either the 

progression or frequencies of the PTS 

scenarios. Additionally, no differences in 

the plant system designs were found that 

would cause significant changes in the 

downcomer fluid temperature. 

• Small- to Medium-Diameter Primary Side 

Pipe Breaks: No differences were found 

that would cause significant changes in 

either the progression or frequency of the 

pipe break LOCAs. For the feed-and-bleed 

LOCAs, the only difference that was found 

affected the frequency for the CE 

generalization plant (i.e., Fort Calhoun). 

The frequency for these types of scenarios 

could be higher by a factor of ~3; however, 

this increase would not prevent the 

generalization plants from being bounded 

(or represented) by the detailed analysis 

plants. 

• Stuck-Open Valves on the Primary Side 

that May Later Reclose: The progression 

of the accident scenarios should be the 

same across all plants. While, the 

frequency associated with this type of 

scenarios could increase at some 

Westinghouse plants, the integrated effect 

of this increase was determined to be small. 

Fort Calhoun is expected to have a 

downcomer temperature that is cooler than 

its corresponding detailed analysis plant 

(Palisades) because of the smaller size of 

the plant. The downcomer temperature for 

the other generalization plants is actually 

expected to be somewhat warmer. PFM 

calculations performed to quantify the 

effect of the colder temperatures in 

Ft. Calhoun determined that while the 

conditional through-wall cracking 

probabilities would increase (as expected), 

the increase was not so substantial as to 

prevent the Palisades plant analysis from 

upper-bounding the Ft. Calhoun plant 

analysis. Thus, the colder downcomer 

temperature for smaller plants was not 

viewed as impeding the applicability of the 

TWCF values in Chapter 8 to PWRs 

in general. 

• Main Steam Line and other Secondary Side 

Breaks: No differences were found that 

would cause significant differences in 

either the progression or frequency of the 

PTS scenarios. 

• Summary: These observations support the 

conclusion that the Chapter 8 TWCF 

estimates produced can be used to 

characterize (or bound) the TWCF of 

PWRs in general. 
9-41 

External Events 

• No external event scenarios were found 

where the TWCFs significantly exceed that 

of the worst internal event scenarios 

(contributions from LOCA-type and SRV 

open-reclose-type accidents). Given the 

bounding nature of the external event 

analyses, there is considerable assurance 

that the external event contribution to 

overall TWCF as a result of PTS does not 

exceed than the highest best-estimate 

contribution from internal events. Given 

the conservative probabilities and 

dependencies assumed in the external event 

analyses, with the addition of little or no 

credit for any operator actions for the 

external event scenarios, it is more likely 

that the “realistic” external event 

contribution to overall TWCF is much less 

than the highest internal event contribution. 

Therefore, the contribution of external 

initiating events to the overall TWCF 

attributable to PTS can be considered 

negligible. 
10-1

10 Risk-Informed Reactor Vessel Failure Frequency 

Acceptance Criteria 

10.1 Introduction 

As discussed in Chapter 2, the current PTS Rule 

establishes a series of steps that PWR licensees 

must perform. The initial step involves a 

deterministic evaluation of the RPV’s RTPTS for 

welds and plate materials (RTNDT evaluated at 

EOL). If the computed RTPTS values exceed the 

screening limit established in 10 CFR 50.61, 

licensees are directed to accomplish reasonably 

practicable neutron flux reduction to avoid 

exceeding the screening limit during the RPV’s 

licensed life. Plants for which the computed 

RTPTS values still exceed the screening limit, 

even with neutron flux reduction, are required, 

at least 3 years before exceeding the criteria, 

to submit a plant-specific safety analysis 

demonstrating that the risk associated with PTS 

events is acceptably low. Regulatory Guide 

1.154 [RG 1.154], describes one acceptable 

method for performing such safety analyses. 

Two key aspects of the PTS safety analysis 

approach described in RG 1.154 are the 

estimation of RPV TWCF and comparison of the 

estimated TWCF with an acceptance criterion of 

5 x 10-6 per reactor year (ry). Neither RG 1.154 

nor Enclosure A to SECY-82-465 [SECY-82-

465] provides a detailed discussion regarding 

this specific value, although Enclosure A to 

SECY-82-465 does argue that an even higher 

TWCF value (i.e., 1 x 10-5/ry) is consistent with 

the then-proposed Safety Goal Policy guidelines 

on “core melt frequency” and the desire that the 

core melt frequency ascribable to “one sequence” 

(such as PTS) should be a small fraction of the 

overall core melt frequency. Based on the 

assessed likelihood of potential PTS challenges, 

predicted TH response of the plant, and 

predicted behavior of the RPV, the RTNDT

screening limits recommended by the staff 

in 1982 and subsequently incorporated in 

10 CFR 50.61 were determined to be consistent 

with a TWCF of around 5 x 10-6/ry. 

The NRC has established a considerable amount 

of guidance on the use of risk information in 

regulation since it issued SECY-82-465 and 

published the original PTS Rule. In light of this 

more recent guidance, and as part of the PTS 

technical basis reevaluation project, the staff has 

identified and assessed options for a riskinformed criterion for the reactor vessel failure 

frequency (RVFF) associated with PTS 

(currently specified in RG 1.154 in terms of 

TWCF). The assessment includes a scoping 

study of the issue of containment performance 

during PTS accidents, which has implications 

for the specification of the acceptance criterion. 

The resulting conclusions and their bases are 

provided in this chapter. 

10.2 Current Guidance on RiskInformed Regulation 

Key documents published since the issuance of 

the original PTS Rule include the Commission’s 

Safety Goal Policy Statement (issued in 1986); 

a June 1990 Staff Requirements Memorandum 

(SRM) [NRC 90]; and RG 1.174 [RG 1.174], 

as well as the associated revision of Chapter 19 

of NUREG-0800, “Standard Review Plan for the 

Review of Safety Analysis Reports for Nuclear 

Power Plants (LWR Edition)” (SRP) [NRC 98b]. 

The Safety Goal Policy Statement [NRC FR 86] 

defines qualitative goals and quantitative health 

objectives (QHOs) for the acceptable risk of 

nuclear power plant operations. The QHOs 

address the prompt fatality risk to individuals, 

and the cancer fatality risk to society. For both 

the individual and societal risks, the QHOs are 

defined to ensure that the public health and 

safety risk arising from nuclear power plant 
10-2

operations is a very small fraction (0.1% or less) 

of the total risk to the public. 

The June 1990 SRM [NRC 90] discusses 

subsequent Commission decisions with respect 

to the policy statement. Of particular interest, 

the SRM establishes a subsidiary core damage 

frequency (CDF) goal of 1x10-4/ry. At the time 

it was developed, this subsidiary goal, as well as 

the qualitative safety goals and QHOs, was 

intended for use in generic agency decisions 

such as rulemakings. It was not aimed at plantspecific applications. 

RG 1.174 [RG 1.174] and SRP Chapter 19 

[NRC 98b] describe a risk-informed process by 

which licensee-proposed license amendments 

that act to change regulatory requirements can 

be submitted, reviewed, and, if appropriate, 

approved. Toward that end, RG 1.174 fulfills 

the following purposes: 

• Describe a set of general principles for this 

process. 

• Extend the policies established in the Safety 

Goal Policy Statement, by providing a large 

early release frequency (LERF) subsidiary 

objective and making use of the QHOs in 

plant-specific decision-making. 

• Provide a set of probabilistic guidelines 

defining acceptable changes in CDF and 

LERF associated with proposed reductions 

in regulatory requirements. 

RG 1.174 applies to voluntary changes to a 

plant’s licensing basis. However, it provides a 

general template for improving consistency in 

regulatory decisions in areas in which the results 

of risk analyses are used to help justify 

regulatory action. The principles of integrated, 

risk-informed decision-making (involving 

consideration of risk information, defense-indepth, safety margins, and uncertainties) 

discussed in that RG apply broadly to riskinformed regulatory activities. RG 1.174 

provides acceptance guidelines for changes in 

CDF and LERF. These guidelines were 

developed to provide assurance that proposed 

increases in CDF and LERF are small and 

consistent with the intent of the Safety Goal 

Policy Statement. If the baseline risk can be 

shown to be acceptable (as indicated by a total 

mean CDF of less than 1 x 10-4/ry and a total 

mean LERF less than 1 x 10-5/ry), applications 

for plant changes leading to small increases in 

mean CDF (up to 1 x 10-5/ry) and mean LERF 

(up to 1 x 10-6/ry) will be considered for 

regulatory approval. 

The relationship between the RG 1.174 LERF 

criterion and the QHOs is discussed in Appendix A 

to NUREG/CR-6595 [Pratt 99]. In particular, 

that appendix argues that, for certain large early 

releases (involving the release of 2.5% to 3% of 

the reactor’s iodine and/or tellurium inventory 

within 4 hours of accident initiation), a LERF of 

1 x 10-5/ry roughly corresponds to the prompt 

fatality QHO (currently around 5 x 10-7/yr). 

The calculations supporting NUREG/CR-6094 

[Hanson 94] and SECY-93-138 [SECY-93-138] 

are cited as the basis for these conclusions. 

The staff’s current activities on Option 3 for 

risk-informing 10 CFR Part 50, as described in 

SECY-00-0198 [SECY-00-0198], takes 

advantage of the groundwork laid by RG 1.174. 

The Option 3 framework being developed 

employs the total mean CDF and mean LERF 

guidelines mentioned above (1 x 10-4/ry and 

1 x 10-5/ry, respectively). The framework also 

provides guidelines to limit the CDF and LERF 

associated with any single accident type from 

being a large fraction of the plant’s total CDF 

and LERF. 

10.3 Containment Performance 

During PTS Accidents 

As discussed in Section 10.1, the current TWCF 

criterion of 5 x 10-6/ry provided in RG 1.154 

was established to ensure that the risk associated 

with PTS is a small fraction of the acceptable 

level of risk established by the Safety Goals and 

is consistent with the philosophy of distributing 

risk among accident types. However, the 

relationship between this criterion and the CDF 

and LERF guidelines established in RG 1.174 

and those proposed in the draft Option 3 

framework is not clear because there is currently 

an incomplete understanding regarding the 
10-3

progression of an accident following a 

postulated PTS-induced RPV failure. 

10.3.1 Previous Research Results 

Several previous research efforts have addressed 

potential PTS-induced RPV failure modes and 

their effects on core cooling and containment 

integrity. In the late 1970s and 1980s, largescale experiments, in which prototypic RPVs 

were subjected to pressure and temperature 

transients characteristic of PTS loadings, were 

conducted as part of the NRC-sponsored Heavy 

Steel Section Technology (HSST) research 

program. These experiments demonstrated three 

potential outcomes of a PTS event (depending 

on the particulars of the transient, material 

embrittlement, etc.): 

• No cracks initiate, and the vessel remains 

intact. 

• A crack initiates, propagates to some depth 

into the entire vessel wall, and stops. The 

vessel remains intact with little additional 

deformation. 

• A crack initiates and propagates entirely 

through the vessel wall. In addition to large 

openings in the reactor vessel, this outcome 

involves significant additional deformation 

of the vessel. 

In the context of RPVs, the third outcome 

presents a potentially significant challenge to 

core cooling and containment integrity. 

In the mid-1980s, following the promulgation 

of the initial versions of 10 CFR 50.61 and 

RG 1.154, the NRC sponsored a number of 

studies on the risk associated with PTS. One 

such study, documented in NUREG/CR-4483 

[Simonen 86], evaluated the current state of 

knowledge regarding post-vessel failure accident 

progression. The study considered such issues 

as the axial and azimuthal extent of crack 

propagation, depressurization of the reactor 

coolant system, RPV vertical movement 

resulting from postulated full circumferential 

breaks of the vessel wall, and the possibility of 

missiles generated during the RPV failure. 

From the perspective of an RVFF acceptance 

criterion, NUREG/CR-4483 offers two key 

findings: 

(1) The possibility of axial cracks propagating 

into embrittled circumferential welds and 

then propagating along these welds cannot 

be neglected. 

(2) The effects of PTS-induced missiles 

(including the RPV in extreme cases) are 

likely to be contained within the concrete 

barriers surrounding the RPV. 

In 2001, the NRC sponsored a study of the 

potential structural consequences of PTS events. 

This study [Theofanous 2001] assumed the 

instantaneous opening of a very large axially 

oriented hole (4-m x 0.4-m, ~2,480-in.2

) in the 

RPV as a postulated result of PTS. Under these 

conditions, and given the relatively low energy 

of the fluid, the impulse on the RPV and piping 

resulting from the blowdown was predicted to be 

within the bounds of a design-basis safeshutdown earthquake (SSE). However, the 

study did not model either the effects of internal 

structures (fuel supports, fuel assemblies, etc.) 

on the blowdown loads, or the possible effects of 

blowdown on the internal structures themselves. 

The study also explored a simplified crack 

opening model that predicts a small hole 

(~110-in2

 (0.07-m2)) resulting from a postulated 

157.48-in. (4-m) long axial crack, rather than the 

very large hole (~2,480-in2

 (1.6-m2)) assumed in 

the analysis of blowdown loads. The study 

found that ECCS injection would not be 

challenged by a crack (and predicted hole area) 

of this size. However, the study did not address 

either the possibility of more extensive axial 

crack propagation, or the possibility of 

circumferential cracks that could challenge the 

ECCS. The staff’s evaluation, summarized in 

Section 10.3.2, addresses these issues. 

On July 18, 2002, the Advisory Committee on 

Reactor Safeguards (ACRS) wrote a letter on the 

issue of PTS acceptance criteria [Apostolakis 

02]. The letter noted that the LERF criterion 

provided in RG 1.174 is not a proper starting 

point for PTS considerations, since the “...source 

terms used to develop the current goal do not 
10-4

reflect the air-oxidation phenomena that would 

be a likely outcome of a PTS event.” 

The concern with air-oxidation events is 

associated with potential scenarios where fuel 

cooling has been lost and the fuel rods are 

exposed to air (as opposed to steam). Should 

such a situation arise, some portion of the 

reactor fuel will eventually be oxidized in an air 

environment. Based upon currently available 

information, this oxidation is expected to result 

in release fractions for key fission products 

(ruthenium being of primary concern) that may 

be significantly (e.g., a factor of 20) larger than 

those associated with fuel oxidation in steam 

environments, and these larger release fractions 

could lead to a larger number of prompt fatalities 

than predicted for non-PTS risk-significant 

scenarios. 

10.3.2 Post-RPV Failure Scenarios 

Scoping Study 

In order to support the assessment of options for 

an RVFF acceptance criterion (see Section 10.4 

for a description of the options considered), the 

staff conducted a limited scoping study of PTSinduced post-RPV failure scenarios. The 

specific aim of the study was to develop an 

initial qualitative assessment of the potential 

impact (both positive and negative) of the 

unique characteristics of such scenarios on the 

likelihood of severe source terms, especially 

source terms beyond those typically assessed for 

non-PTS-associated risk-significant scenarios. 

The study involved the structured identification 

of technical issues underlying the assessment of 

the margins to core damage and large early 

release following potentially significant PTSinduced RPV failure scenarios (dominant 

scenarios for the pilot plants addressed by the 

PTS reevaluation project are discussed in 

Chapter 8 of this report), and the collection and 

evaluation of currently available information 

relevant to these issues. Of particular interest 

was the identification of PTS-unique physical 

mechanisms that could lead to dependent 

failures of accident mitigation features. 

To better inform the evaluation, a small number 

of limited-scope TH and structural calculations 

were performed. 

The scoping study focused on differences 

between post-PTS-induced RPV failure accident 

progression and accident progression associated 

with non-PTS core damage events. Thus, in 

addition to the previously mentioned airoxidation issue, the scoping study addressed 

issues associated with the development and 

characteristics of the postulated opening in the 

RPV, the resulting blowdown forces, the effect 

on key structural components (e.g., the RPV, 

containment penetrations), and the potential for 

damaging missiles. Table 10.1 lists and briefly 

describes the issues addressed. 

To support the identification and semiquantitative analysis of the issues, an accident 

progression event tree (APET) was developed. 

This tree, shown in Figure 10.1, identifies 

potentially important phenomena and possible 

scenarios following PTS-induced RPV 

failure.†††††† 

In general, the APET explicitly addresses the 

issues listed in Table 10.1. Two notable 

exceptions are the issues of missiles and early 

overpressure. Regarding missiles, activities 

performed as part of the scoping study indicate 

that the possibility of a PTS-induced RPV 

failure leading to energetic missiles that could 

affect important top events in the APET (i.e., 

those associated with containment isolation, 

sprays, and ECCS) is sufficiently remote to 

allow exclusion of this issue from the APET. 

Missile generation attributable to a PTS event 

would result in an object being directed laterally 

into the reactor vessel cavity wall by the 

blowdown forces associated with the breach in 

the RPV. For a missile to affect the containment 

spray systems, ECCS systems or containment 

penetrations, it would have to traverse a tortuous 

 

†††††† Note that the APET includes branches for 

issues whose uncertainties are more epistemic 

in character (e.g., the blowdown forces 

associated with a given break size), as well as 

branches associated with issues for which the 

uncertainties are more aleatory in character 

(e.g., the availability of ECCS). 
10-5

path through tight clearances of the RPV cavity 

(between the reactor vessel and the concrete of 

the cavity wall). It would then have to hit an 

extremely small target (either ECCS piping, 

containment penetration or containment spray 

piping). The missile’s energy would be 

dissipated through its multiple contacts with the 

RPV cavity wall, as well as the distance it 

traveled. 

Table 10.1. Post-RPV-failure technical issues 

Dominant PTS scenarios This issue concerns the relative likelihood and characteristics of the scenarios 

predicted to contribute most to PTS-induced RPV failure. The characteristics of the 

PTS scenario (e.g., pressure, temperature, timing) directly affect the issues of crack 

propagation, blowdown forces, and ECCS status (see below). 

Relative contribution of 

axial and circumferential 

welds 

This issue concerns the relative frequencies of PTS-induced RPV failures attributable 

to flaws in axial welds vs. flaws in circumferential welds. The orientation of the 

crack affects crack propagation and the characteristics of the resulting hole. 

Crack propagation, 

hole size, hole location 

This issue concerns the characteristics of the crack and the resulting hole in the RPV 

(including the rate of opening and the shape of the hole). This issue directly affects 

the issues of blowdown forces, fuel coolability, and fuel environment (see below). 

Blowdown forces This issue concerns the pressure differential driving fluid out of the RPV and the 

associated forces on the RPV, its internals, and connected piping. This issue directly 

affects the issues of containment isolation, missiles, ECCS status, core status, and fuel 

dispersal (see below). 

Containment isolation Early failure of containment isolation (e.g., by the failure of containment 

penetrations) is a contributing factor to the occurrence of a large early release. 

Missiles This issue concerns the possibility of a PTS-induced RPV failure leading to energetic 

missiles that could affect accident progression. This issue directly affects the issues 

of ECCS status and containment spray status (see below). 

ECCS status 

(injection, recirculation) 

This issue concerns the reliability of ECCS (given that ECCS was working prior to 

RPV failure). Potential contributors to ECCS failure include random hardware 

failure, failure to switch over properly to recirculation, failure of ECCS piping, and 

containment sump clogging. 

Containment spray status Early failure of containment spray is a contributing factor to the occurrence of a large 

early release. This issue concerns the reliability of containment spray (given that 

ECCS was working prior to RPV failure). Potential contributors to failure include 

random hardware failure, failure of piping (attributable to missiles), and containment 

sump clogging. 

Core status (intact, 

distorted, disrupted) 

This issue concerns whether the fuel geometry is distorted or severely disrupted as a 

result of the blowdown forces associated with a PTS-induced RPV failure. 

Fuel dispersal This issue concerns the location of fuel, should it be dispersed from the core as a 

consequence of a PTS-induced RPV failure. 

Fuel coolability This issue concerns fuel coolability, given its location and the core status. 

RPV water level This issue concerns the availability of water to cool the fuel (even if the ECCS is not 

working). It is affected by a number of factors, including the characteristics of the 

RPV cavity and the inventory of water available. 

Fuel environment 

(steam, air) 

This issue concerns the possibility of large-scale air oxidation of fuel. It is strongly 

dependent on the development of the accident scenario. 

Early overpressure This issue concerns the possibility of early containment failure attributable to 

(1) overpressures resulting from PTS-induced RPV failure events, and 

(2) overpressure caused by other mechanisms (e.g., hydrogen combustion). 
10-6

Figure 10.1. Post-RPV failure accident progression tree 

S e qu enc eEa rlyC o re D a magePo ssible ?L arg e Early R e le asePo ssible ?

PTSEventC rackOrie ntatio nC rackExten sio nHoleSizeBlowdownForce sC on ta in mentI solat ed?C on ta in mentSpraysW orking?FuelLo cationEC CSC on tinu esTo R u n?Ca vity Fl oo de dTo To p o f Fue l?

~ Design

Basis

Arrested a t

Circumferen tial Weld

Beyo nd

 C ircumferential Welds

Init iates

Circumfe rential

Crack

Axial

La rge

(~100-10 00 in )2

>> D esig n

Basis

1

2

3

4

5

6

7

8

9

10

11

12

13-24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57 -128

129-172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

Y

Y*

Y

Y

Y*

Y

Y

Y

Y*

Y

Y*

Y

Y*

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y*

Y*

Y

Y*

Y*

Y*

Y*

Y

Y

 

Y

Y*

 

Y

 

 

Y*

 

Y

Y*

Y*

Y

Y

See Sequ ences 1-12

RPV

Cavity

Complete

Arrested

 

Y 

Y 

Y 

Y 

Y 

Y 

Y 

Y 

Y

Y

Y

Y

Y

Y

Y

Y

See Sequ ences 129-200

See Sequ ences 13-56

Circumferential

Small

(~0-10 in )2

Yes

No

“Y” = yes

“Y*” = yes, but reduced magnitude

“ “ = no

Very Large

(>>1000 in )2

RPV

Cavity

RPV

Cavity

RPV

Cavity

Therefore, there is little chance that the missile 

would possess the energy to damage the ECCS, 

containment spray system, or any containment 

penetrations. Additional activities regarding 

missiles included a review of NUREG/CR-4483 

[Simonen 86] in light of currently available 

information on missile generation and 

penetration potential, a review of the reactor 

cavity designs of the plants considered in this 

study, and limited calculations to estimate 

plastic strains associated with a postulated, 

instantaneous large (~4 m x 0.3 m, 1,728 in.2

) 

hole in the side of a representative RPV. 
10-7

To address scenarios involving early 

overpressure, limited-scope RELAP5 

calculations (performed for a representative 

plant) were performed. These calculations 

indicate that the initial containment pressure rise 

associated with a range of PTS-induced RPV 

failures should be small, relative to the 

containment design pressure. PTS-initiated 

scenarios involving large amounts of hydrogen 

generation are possible (e.g., see Scenario 56 in 

the APET), but are not likely to lead to failure of 

either large, dry containments or ice condenser 

containments. The former are capable of 

withstanding the overpressure associated with a 

severe accident hydrogen burn, and the principal 

failure mode of the hydrogen igniters for the 

latter is a loss of station power, which is not a 

concern for PTS scenarios. (Loss of power is, 

of course, an issue for core overheating 

scenarios typically addressed by PRAs, in which 

possible RPV failures occur after core damage.) 

Figure 10.1 identifies scenarios that have the 

potential to lead to source terms significantly 

worse than those associated with risksignificant, non-PTS related accident scenarios. 

Scenarios that are judged to have a possibility of 

leading to an early (e.g., less than 4 hours after 

RPV failure) release with a severe source term 

(i.e., a source term associated with large-scale 

air-oxidation of fuel) are highlighted in red. 

Scenarios that are judged to have a possibility of 

leading to an early release with a containmentspray-scrubbed, air-oxidation source term are 

highlighted in yellow. 

Table 10.2 summarizes the key characteristics 

associated with each of the highlighted 

scenarios. The common characteristics of these 

scenarios are also shared with risk-significant 

non-PTS scenarios: they require the loss of fuel 

cooling (either from ECCS or from water in the 

reactor cavity), the loss of containment isolation, 

and, in the case of the most severe scenarios, 

the loss of containment spray. Table 10.2 also 

provides a summary assessment of the 

conditional likelihood of each scenario, 

given the occurrence of a PTS event. 

The discussion in Table 10.2 identifies two 

classes of plants, including (1) those for which it 

is expected that, following a PTS-initiated RPV 

failure, the reactor cavity will be flooded above 

the top of the active fuel, and (2) all other plants. 

For the first class, it is believed that, for all 

scenarios identified by the APET, the 

conditional probability of PTS-induced fuel 

damage and subsequent large early release is 

extremely small (i.e., less than 0.001). 

For the second class of plants, the most 

important APET postulated scenarios appear 

to be Scenarios 96, 100, 118, and 125. These 

scenarios all involve the following factors: 

• an initial crack in an axial weld that 

propagates to the circumferential weld, 

and then initiates a circumferential crack 

• blowdown forces above those anticipated 

for design-basis events 

• the possibility of containment penetration 

failures as a result of RPV movement 

• the possibility of ECCS failure attributable 

to RPV movement 

Table 10.3 identifies the key differences 

between the four scenarios and their assessed 

likelihoods. A likelihood rating of “extremely 

small” corresponds to a conditional probability 

less than 0.001, while a rating of “very small” 

corresponds to a conditional probability less 

than 0.01, and a rating of “small” corresponds to 

a conditional probability less than 0.1. 
10-8

Table 10.2. Potentially risk-significant post-RPV failure accident progression scenarios 

Scena

rio 

Characteristics 

Potential 

Consequential 

Failuresb

Independent 

Failuresc Conditional Probability Ratingd,e

36 - Axial crack that extends beyond circumferential weld 

- Medium-to-large (~100-1,000 in2

) hole in RPV 

- Blowdown forces within design basis 

- Failed containment isolation 

- Operating containment spray 

- Loss of fuel cooling 

- Containment 

Isolation 

- ECCS 

Extremely small 

40 - Axial crack that extends beyond circumferential weld 

- Medium-to-large (~100-1000 in2

) hole in RPV 

- Blowdown forces within design basis 

- Failed containment isolation 

- Failed containment spray 

- Loss of fuel cooling 

 - Containment 

Isolation 

- Containment 

Spray 

- ECCS 

Extremely small 

52 - Axial crack that extends beyond circumferential weld 

- Medium-to-large (~100-1000 in2

) hole in RPV 

- Blowdown forces greater than design basis 

- Failed containment isolation 

- Operating containment spray 

- Loss of fuel cooling 

- Containment 

Penetration 

- ECCS piping 

- Extremely small for 

plants where cavity 

flooding above the top 

of the fuel is expected 

- May be very small for 

other plants, depending 

on effect of blowdown 

forces 

56 - Axial crack that extends beyond circumferential weld 

- Medium-to-large (~100-1000 in2

) hole in RPV 

- Blowdown forces greater than design basis 

- Failed containment isolation 

- Failed containment spray 

- Loss of fuel cooling 

- Containment 

Penetration 

- ECCS piping 

- Containment 

Spray 

Extremely small 

80 - Axial crack that initiates a circumferential crack that 

arrests after limited propagation 

- Medium-to-large (~100-1000 in2) hole in RPV 

- Blowdown forces within design basis 

- Failed containment isolation 

- Operating containment spray 

- Loss of fuel cooling 

 - Containment 

Isolation 

- ECCS 

Extremely small 

 84 - Axial crack that initiates a circumferential crack that 

arrests after limited propagation 

- Medium-to-large (~100-1000 in2

) hole in RPV 

- Blowdown forces within design basis 

- Failed containment isolation 

- Failed containment spray 

- Loss of fuel cooling 

 - Containment 

Isolation 

- Containment 

Spray 

- ECCS 

Extremely small 

96 - Axial crack that initiates a circumferential crack that 

arrests after limited propagation 

- Medium-to-large (~100-1000 in2) hole in RPV 

- Blowdown forces greater than design basis 

- Failed containment isolation 

- Operating containment spray 

- Loss of fuel cooling 

- Containment 

Penetration 

- ECCS piping 

- Extremely small for 

plants where cavity 

flooding above the top 

of the fuel is expected 

- May be small to very 

small for other plants, 

depending on effect of 

blowdown forces 

100 - Axial crack that initiates a circumferential crack that 

arrests after limited propagation 

- Medium-to-large (~100-1000 in2) hole in RPV 

- Blowdown forces greater than design basis 

- Failed containment isolation 

- Failed containment spray 

- Loss of fuel cooling 

- Containment 

Penetration 

- ECCS piping 

- Containment 

Spray 

- Extremely small for 

plants where cavity 

flooding above the top 

of the fuel is expected 

- May be very small to 

extremely small for 

other plants, depending 

on effect of blowdown 
10-9

Scena

rio 

Characteristics 

Potential 

Consequential 

Failuresb

Independent 

Failuresc Conditional Probability Ratingd,e

forces 

118 - Axial crack that initiates a circumferential crack that 

subsequently progresses around the entire RPV 

- Very large (>>1000 in2

) hole 

- Blowdown forces greater than design basis 

- Failed containment isolation 

- Operating containment spray 

- Majority of fuel retained in RPV 

- Loss of fuel cooling 

- Containment 

Penetration 

- ECCS piping 

- Extremely small for 

plants where cavity 

flooding above the top 

of the fuel is expected 

- May be small to very 

small for other plants, 

depending on effect of 

blowdown forces 

 121 - Axial crack that initiates a circumferential crack that 

subsequently progresses around the entire RPV 

- Very large (>>1000 in2) hole 

- Blowdown forces greater than design basis 

- Failed containment isolation 

- Operating containment spray 

- Majority of fuel dispersed into reactor cavity 

- Loss of fuel cooling 

- Containment 

Penetration 

- ECCS piping 

- Extremely small for 

plants where cavity 

flooding above the top 

of the fuel is expected 

- May be very small to 

extremely small for 

other plants, depending 

on effect of blowdown 

forces 

125 - Axial crack that initiates a circumferential crack that 

subsequently progresses around the entire RPV 

- Very large (>>1000 in2

) hole 

- Blowdown forces greater than design basis 

- Failed containment isolation 

- Failed containment spray 

- Majority of fuel retained in RPV 

- Loss of fuel cooling 

- Containment 

Penetration 

- ECCS piping 

- Containment 

Spray 

- Extremely small for 

plants where cavity 

flooding above the top 

of the fuel is expected 

- May be very small to 

extremely small for 

other plants, depending 

on effect of blowdown 

forces 

128 - Axial crack that initiates a circumferential crack that 

subsequently progresses around the entire RPV 

- Very large (>>1000 in2) hole 

- Blowdown forces greater than design basis 

- Failed containment isolation 

- Failed containment spray 

- Majority of fuel dispersed into reactor cavity 

- Loss of fuel cooling 

- Containment 

Penetration 

- ECCS piping 

- Containment 

Spray 

Extremely small 

152 - Circumferential crack that arrests 

- Medium-to-large (~100-1000 in2

) hole in RPV 

- Blowdown forces within design basis 

- Failed containment isolation 

- Operating containment spray 

- Loss of fuel cooling 

 - Containment 

Isolation 

- ECCS 

Extremely small 

156 - Circumferential crack that arrests 

- Medium-to-large (~100-1000 in2

) hole in RPV 

- Blowdown forces within design basis 

- Failed containment isolation 

- Failed containment spray 

- Loss of fuel cooling 

- Containment 

Isolation 

- Containment 

Spray 

- ECCS 

Extremely small 

168 - Circumferential crack that arrests 

- Medium-to-large (~100-1000 in2

) hole in RPV 

- Blowdown forces greater than design basis 

- Failed containment isolation 

- Operating containment spray 

- Loss of fuel cooling 

- Containment 

Penetration 

- ECCS piping 

- Extremely small for 

plants where cavity 

flooding above the top 

of the fuel is expected 

- May be very small to 

extremely small for 

other plants, depending 

on effect of blowdown 

forces 

172 - Circumferential crack that arrests 

- Medium-to-large (~100-1000 in2

) hole in RPV 

- Blowdown forces greater than design basis 

- Containment 

Penetration 

- ECCS piping 

- Containment 

Spray 

Extremely small 
10-10

Scena

rio 

Characteristics 

Potential 

Consequential 

Failuresb

Independent 

Failuresc Conditional Probability Ratingd,e

- Failed containment isolation 

- Failed containment spray 

- Loss of fuel cooling 

190 - Circumferential crack that progresses around the 

entire RPV 

- Very large (>>1000 in2

) hole 

- Blowdown forces greater than design basis 

- Failed containment isolation 

- Operating containment spray 

- Majority of fuel retained in RPV 

- Loss of fuel cooling 

- Containment 

Penetration 

- ECCS piping 

- Extremely small for 

plants where cavity 

flooding above the top 

of the fuel is expected 

- May be very small to 

extremely small for 

other plants, depending 

on effect of blowdown 

forces 

193 - Axial crack that initiates a circumferential crack that 

subsequently progresses around the entire RPV 

- Very large (>>1000 in2) hole 

- Blowdown forces greater than design basis 

- Failed containment isolation 

- Operating containment spray 

- Majority of fuel dispersed into reactor cavity 

- Loss of fuel cooling 

- Containment 

Penetration 

- ECCS piping 

 Extremely small 

197 - Axial crack that initiates a circumferential crack that 

subsequently progresses around the entire RPV 

- Very large (>>1000 in2) hole 

- Blowdown forces greater than design basis 

- Failed containment isolation 

- Failed containment spray 

- Majority of fuel retained in RPV 

- Loss of fuel cooling 

- Containment 

Penetration 

- ECCS piping 

- Containment 

Spray 

Extremely small 

200 - Axial crack that initiates a circumferential crack that 

subsequently progresses around the entire RPV 

- Very large (>>1000 in2

) hole 

- Blowdown forces greater than design basis 

- Failed containment isolation 

- Failed containment spray 

- Majority of fuel dispersed into reactor cavity 

- Loss of fuel cooling 

- Containment 

Penetration 

- ECCS piping 

- Containment 

Spray 

Extremely small 
10-11

Table 10.3. Key APET scenarios 

Scenario 

Circumferential Crack Arrested? Containment Spray Status 

Likelihood Rating 

96 Yes Operating Very small to small 

100 Yes Failed Extremely small to 

very small 

118 No Operating Very small to small 

125 No Failed Extremely small to 

very small 

The ratings are based largely on the following 

considerations: 

• Containment spray operation is not expected 

to be adversely affected by the occurrence of 

a PTS event. In fact, its reliability may be 

higher than for non-PTS risk-significant 

scenarios, since support system availability 

is not generally a concern for PTS 

scenarios.‡‡‡‡‡‡

• As shown in Chapter 8, PTS scenarios 

generally involve situations where the RCS 

is at relatively low temperature. 

Consequently, the stored energy in the RCS 

is relatively low, and there is little driving 

force to directly cause the damage 

postulated in the scenarios. 

• An initial assessment of the RPV 

deformation associated with a 

(conservatively assumed) instantaneous hole 

opening in the RPV indicates that substantial 

deformations will not occur and, therefore, 

the movement of the pipes connected to the 

RPV will be limited by the gap between the 

RPV and the cavity wall. 

• Since reactor vessel movement attributable 

to blowdown forces is limited, damage of 

ECCS piping, containment spray or 

containment penetrations is not expected. 

The limited vessel movement would be 

 

‡‡‡‡‡‡ This assessment is based on an assumption 

that any potential recirculation sump clogging 

issues, as identified under GSI-191, are 

addressed. 

compensated for by the pipe ductility, long 

runs of piping with many bends, and the 

hanger and support systems. 

Table 10.3 is based upon currently available 

information. Resolution of the following key 

uncertainties could affect the assessment: 

• the likelihood that an axial crack will indeed 

initiate a propagating circumferential crack 

• the potential effect of “external events” 

(e.g., earthquakes) and other environmental 

hazards (e.g., internal fires) on PTS-induced 

LERF that were not addressed in the scoping 

study 

10.4 Acceptance Criteria Options 

The staff has developed two sets of options for 

PTS-associated RVFF acceptance guidelines. 

The first set of options concerns the specific 

definition of RPV failure to be used. The 

second concerns possible quantitative 

acceptance limits for that metric. Note that any 

potential changes to the RTNDT screening limits 

discussed in Chapter 11 may affect RVFF, but 

are not likely to affect the conditional 

probability of core damage (given a PTSinduced RPV failure) or the conditional 

probability of large, early release (given a PTSinduced core damage event). Thus, they will 

likely have little effect on the level of defensein-depth against PTS challenges already 

provided by the current rule. 

The following two options were considered for 

defining RPV failure: 

(1) RPV failure occurs when a PTS-induced 

crack penetrates the RPV wall (i.e., RVFF = 

TWCF). 

(2) RPV failure occurs when a PTS event 

initiates a crack in the RPV wall (i.e., RVFF 

= Vessel Crack Initiation Frequency, or 

VCIF). 

The first option uses the current definition of 

RPV failure. The second reflects the position 

adopted by non-U.S. regulatory bodies. 
10-12

In developing the possible quantitative 

acceptance limits for RVFF (denoted by 

RVFF*), the staff considered the following four 

options: 

A. RVFF* = 5 x 10-6/ry 

B. RVFF* = 1 x 10-5/ry 

C. RVFF* = 1 x 10-6/ry 

D. RVFF* << 1 x 10-6/ry 

Option A is suggested by the current value in 

RG 1.154. Option B is suggested by current 

guidelines on CDF provided by RG 1.174 and 

the Option 3 framework for risk-informing 

10 CFR Part 50. Option C is suggested by 

current guidelines on LERF provided by 

RG 1.174 and the Option 3 framework for 

risk-informing 10 CFR Part 50. Option D is 

suggested by the possibility of significantly 

worse consequences for PTS events (as opposed 

to other risk-significant scenarios), as discussed 

by the July 2002 letter from ACRS [Bonaca 02]. 

10.5 Conclusions 

The staff’s analysis has led to the following 

conclusions regarding the establishment of 

a criterion for RVFF: 

(1) The analysis supports a definition of RVFF 

as being equivalent to TWCF (i.e., for PTS 

considerations, RPV “failure” can be 

defined as an occurrence of a through-wall 

crack). This conclusion is based on the 

following two factors: 

(a) TWCF is a more direct measure than 

VCIF of the likelihood of events with 

potentially significant public health 

consequences. This is desirable from a 

risk-informed decision-making 

perspective. 

(b) The uncertainties associated with the 

prediction of a through-wall crack 

(under PTS conditions) are only slightly 

larger than those associated with the 

prediction of crack initiation (also under 

PTS conditions). For example, at the 

10 CFR 50.61 RTPTS screening limit, the 

separation between the 50th and 95th

percentiles in the distribution of VCIF

ranges from 0.8 to 1.8 orders of 

magnitude, while the separation between 

the 50th and 95th percentiles in the 

distribution of TWCF ranges from 0.9 

to 2.6 orders of magnitude. This slight 

increase in uncertainty is a natural and 

expected consequence of a cleavage 

failure mechanism and does not reflect a 

state of knowledge limitation regarding 

crack arrest. (See [EricksonKirk-PFM] 

for details of the crack arrest model.) 

(2) The analysis supports an acceptance 

criterion for RVFF, RVFF*, of 1x10-6/ry. 

This is based on the following observations: 

(a) The conditional probability of an 

unscrubbed, large early release with a 

large air-oxidation source term (given a 

PTS-induced RPV failure) appears to be 

very small (i.e., less than 0.01). It is 

particularly small for plants where water 

in the reactor cavity (following a PTSinduced RPV failure) will cover the fuel. 

For plants with larger cavities, the low 

probability of the scenario is largely 

attributable to the independence and 

reliability of containment sprays. 

(b) The assessment underlying the above 

observation does not account for 

potential dependencies associated with 

PTS-events initiated by “external events” 

(e.g., earthquakes) or internal fires. 

(c) For plants with cavities such that fuel 

cooling is not assured following a PTSinduced RPV failure, the APET (Figure 

10.1) identifies the most probable 

scenarios where limited fuel damage 

might occur, even if ECCS operates as 

designed. 

Observation (a), taken in isolation, supports 

the use of an RVFF* based on 

considerations of core damage consistent 

with those proposed in current activities for 

risk-informing 10 CFR Part 50 [SECY-00-

0198]. However, Observation (b) identifies 

a potentially significant uncertainty 

regarding the margin between PTS-induced 

RPV failure and large early release, and 

Observation (c) raises a potential concern 
10-13

regarding defense-in-depth. Therefore, 

RG 1.174 guidelines on CDF supporting 

a value for RVFF* of 1x10-5 events/year 

may not have sufficient justification, 

whereas the scoping study developed for 

RG 1.174 guidelines on LERF is more 

defensible given currently available 

information. This rationale supports our 

recommended value of 1x10-6 events/year 

for RVFF*, which is consistent with the 

RG 1.174 guidelines on LERF. 

When assessing the acceptability of the 

PTS-associated risk at a given plant, the 

mean value of the plant’s PTS-induced 

RVFF (i.e., the mean TWCF) should be 

compared with RVFF*. This conclusion 

is based on how other NRC risk-informed 

decisions use risk information 

(e.g., see RG 1.174). 

(3) Should additional work be performed to 

address the key post-RPV failure accident 

progression uncertainties identified in this 

study, the following issues are of principal 

importance: 

(a) the likelihood that a PTS-induced axial 

crack will, upon reaching a 

circumferential weld, turn and progress 

along the circumferential weld 

(b) the likelihood of PTS-induced 

containment isolation failure (especially 

failures associated with failure of 

containment penetrations) and ECCS 

failure (especially ECCS piping failures) 

(c) the magnitude of potential source terms 

and consequences associated with PTS 

events 

(d) substantiation of conditional probability 

values in Table 10.2 and Table 10.3 

(e) the impact of external events on PTSinduced LERF. 

It is anticipated that state-of-knowledge 

improvements in any of these areas will 

strengthen this study’s conclusions 

regarding the margin between a PTSinduced RPV failure and consequent large 

early releases. Although not quantified, 

several aspects of our analysis performed to 

support an RVFF* value 1x10-6 events/year 

have a known conservative bias. The 

following is a summary of a few of these 

areas identified earlier in this chapter: 

• Given the relatively low energy of the 

fluid following a postulated PTS event, 

the impulse on the RPV and piping 

resulting from a blowdown was 

predicted to be within the bounds of a 

design-basis SSE. The limited vessel 

movement from a blowdown forces 

would be compensated for by the pipe 

ductility, long runs of piping with many 

bends, and the hanger and support 

systems. For these reasons, damage of 

ECCS piping or containment 

penetrations is not expected. 

• Missile generation attributable to a 

postulated PTS event would result in an 

object being directed laterally into the 

reactor vessel cavity wall by the 

blowdown forces associated with the 

breach in the reactor vessel. For a 

missile to affect the containment spray 

system or containment penetrations, it 

would have to traverse a tortuous path 

through tight clearances of the reactor 

vessel cavity. The missile’s energy 

would be dissipated by multiple contacts 

with the reactor cavity wall, as well as 

the distance it travels, and it would have 

to hit an extremely small target to render 

the containment spray system 

inoperable. 

• Through-wall crack frequency is 

assumed to equal core damage, which is 

assumed to equal a release. The 

through-wall cracks may cover a wide 

spectrum of sizes, from very large to 

very small. Very small cracks would 

result in only minor leakage that would 

not significantly challenge the reactor 

safety systems. 

 
11-1

11 Reference Temperature (RT)-Based 

PTS Screening Criteria 

11.1 Introduction 

In Chapter 8, we presented our baseline 

estimates of the variation of TWCF in the three 

study plants over a range of embrittlement 

levels. These estimates demonstrated that the 

challenge to the structural integrity of the RPV 

posed by the dominant transient classes (i.e., 

large-diameter primary side pipe breaks, stuckopen primary side valves that later reclose, and 

breaks of the main steam line) is approximately 

equal (at equivalent levels of embrittlement) 

across the three plants. We also identified why 

the structural integrity challenges posed by these 

dominant transients are not expected to vary 

from plant-to-plant, and are not expected to be 

influenced by factors that may differ between 

the three study plants and the general population 

of PWRs (see Sections 8.5.2.4.5, 8.5.3.4.3, and 

8.5.4.4.2, respectively). This finding was further 

reinforced in Section 9.3, which included a 

survey of five additional plants having high 

levels of embrittlement. This survey assessed 

the factors in these plants that could influence 

either the severity of the transients or the 

frequency of their occurrence, with the aim of 

identifying the potential for situations in the 

general PWR population having greater severity 

and/or frequency than in the three study plants. 

The survey’s outcome supported the view 

presented in Chapter 8. In the great majority of 

cases, the severity and frequency of transients in 

the general PWR population is no greater, and is 

often less, than in the three study plants. A few 

situations were identified where greater 

severities or frequencies did occur, but never 

both. Thus, the effect of these situations not 

being considered in the baseline TWCF results 

presented in Chapter 8 can be regarded as 

negligible. 

Overall, the evidence presented in both Chapter 8 

and Chapter 9 supports the use of the TWCF 

values presented in Table 8.5, together with the 

reactor vessel failure frequency acceptance 

criterion of 1x10-6 events per year proposed in 

Chapter 10 to develop a materials-based 

screening limit applicable to PWRs in general. 

In this chapter, we propose such a limit, making 

use of the reference temperature (RT) metrics 

also found in Table 8.5. As illustrated in Figure 

8-4, an RT establishes a material’s resistance to 

fracture, the variability in this resistance, and 

how this resistance varies with temperature. 

Since RT values can be estimated from 

information on vessel materials available in the 

RVID database [RVID2], as well as surveillance 

programs conducted in accordance with 

Appendix H to 10 CFR Part 50, they provide a 

means to estimate the fracture resistance of 

vessel materials and how this resistance 

diminishes with increased neutron irradiation. 

The remainder of the chapter is organized as 

follows: 

• Section 11.2 addresses RT metrics. We 

review the discussion of Section 8.4.1, 

which concerns the characteristics an RT

metric needs so that it can be expected to 

correlate/predict the probability of vessel 

failure. This section also includes a critique 

of how well the RT metric currently used in 

10 CFR 50.61, RTPTS, meets these 

characteristics. 

• In Section 11.3, we develop relationships 

between the RTAW, RTPL, and RTCW metrics 

(see Table 8.5) and TWCF. 

• Section 11.4 includes our proposed PTS 

screening criteria derived from the 

relationship developed in Section 11.3. We 

discuss the applicability of these screening 

criteria to PWRs in general, and we assess 
11-2

the proximity of currently operating PWRs 

to this proposal at both end of license 

(40 years of operation) and end of license 

extension (60 years of operation). 

11.2 Reference Temperature (RT) 

Metrics 

As discussed in Section 8.4.1, in order to 

correlate and/or predict a RPV’s resistance to 

fracture, we need some measure of the fracture 

resistance of the materials in the vessel at the 

location of the flaws in the vessel. RT values 

characterize fracture resistance, as illustrated in 

Figure 8-4. In Section 8.4.1, we proposed three 

RT metrics (RTAW, RTPL, and RTCW), each of 

which is associated with a different flaw 

population (flaws on the axial weld fusion lines, 

flaws in plates, and flaws on the circumferential 

weld fusion lines, respectively). These three RT

metrics were defined as follows (see Eq. 8-1, Eq. 

8-2, and Eq. 8-3 for mathematical definitions): 

• The axial weld reference temperature 

RTAW characterizes the RPV’s resistance to 

fracture initiating from flaws found along 

the axial weld fusion lines. It corresponds to 

the maximum RTNDT of the plate/weld that 

lies to either side of each weld fusion lines, 

and is weighted to account for differences in 

weld fusion line length (and, therefore, the 

number of simulated flaws). 

• The plate reference temperature RTPL

characterizes the RPV’s resistance to 

fracture initiating from flaws found in plates 

that are not associated with welds. 

It corresponds to the maximum RTNDT

occurring in each plate, and is weighted to 

account for differences in plate volumes 

(and, therefore, the number of simulated 

flaws). 

• The circumferential weld reference 

temperature RTCW characterizes the RPV’s 

resistance to fracture initiating from flaws 

found along the circumferential weld fusion 

lines. It corresponds to the maximum RTNDT

of the plate/weld that lies to either side of 

each weld fusion lines, and is weighted to 

account for differences in weld fusion 

line length (and, therefore, the number of 

simulated flaws). 

We proposed these three different RTs in 

recognition of the fact that the probability of 

vessel fracture initiating from these three 

different flaw populations varies considerably 

as a result of the following known factors. 

• Different regions of the vessel have flaw 

populations that differ in size (weld flaws 

are considerably larger than plate flaws), 

density (weld flaws are more numerous than 

plate flaws), and orientation (axial and 

circumferential welds have flaws of 

corresponding orientations, whereas 

plate flaws may be either axial or 

circumferential). The driving force to 

fracture depends on both flaw size and 

flaw orientation, so different vessel regions 

experience different fracture driving forces. 

• The degree of irradiation damage suffered 

by the material at the flaw tips varies with 

location in the vessel because of differences 

in chemistry and fluence. 

These differences indicate that it is impossible 

for a single RT to accurately represent the RPV’s 

resistance to fracture in the general case. 

Indeed, this is precisely the liability associated 

with the 10 CFR 50.61 RT value RTPTS. 

10 CFR 50.61 defines RTPTS as the maximum 

RTNDT of any region in the vessel (a region is an 

axial weld, a circumferential weld, a plate, or a 

forging) evaluated at the peak fluence occurring 

in that region. Consequently, the RTPTS value 

currently assigned to a vessel may only 

coincidentally correspond to the toughness 

properties of the material region responsible for 

the bulk of the TWCF, as illustrated by the 

following examples: 

• Out of 71 operating PWRs, 14 have their 

RTPTS values established based on 

circumferential weld properties [RVID2]. 

However, our results show that the 

probability of a vessel failing as a 

consequence of a crack in a circumferential 

weld is extremely remote because of the 

lack of through-wall fracture driving force 

associated with circumferentially oriented 
11-3

cracks. For these 14 vessels, the RTPTS value 

is unrelated to any material that has any 

significant chance of causing vessel failure. 

• Out of 71 operating PWRs, 32 have their 

RTPTS values established based on plate 

properties [RVID2]. Certainly, plate 

properties influence vessel failure 

probability; however, the 10 CFR 50.61 

practice of evaluating RTPTS at the peak 

fluence occurring in the plate is likely to 

estimate a toughness value that cannot be 

associated with any large flaws because the 

location of the peak fluence may not 

correspond to an axial weld fusion line. 

While the RTPTS value for these 32 vessels is 

related to a material that contributes 

significantly to the vessel failure probability, 

it is likely that RTPTS has been overestimated 

(perhaps significantly so) because the 

fluence assumed in the RTPTS calculation 

does not correspond to the fluence at a likely 

flaw location. 

• Out of 71 operating PWRs, 10 have their 

RTPTS values established based on forgings 

[RVID2]. Forged vessels do not have axial 

welds, and consequently do not have the 

large flaws associated with axial weld fusion 

lines that account for a large portion of the 

TWCF. As discussed in Section 9.2 of this 

report and in [EricksonKirk-SS], flaws in 

forgings arise either as a consequence of the 

forging process itself or as “subclad” defects 

associated with the stainless steel cladding. 

Forging flaws are approximately equivalent 

to plate flaws in terms of both size and 

density, while subclad flaws occur as dense 

arrays of axially oriented flaws with a depth 

of ≈0.08-in. (≈2mm). Our sensitivity studies 

show that at an equivalent level of 

embrittlement, a forged vessel will have a 

through-wall cracking frequency that is 

at most ~15% that of an equivalent plate 

vessel (with axial welds). Thus, while 

forgings do contribute to the risk of vessel 

failure, the RTPTS value for a forging-limited 

plant could considerably exceed the 

10 CFR 50.61 screening criteria and still 

have a TWCF value below that of a plate 

vessel. 

• Out of 71 operating PWRs, 15 have their 

RTPTS values established based on axial weld 

properties [RVID2]. It is only for these 

vessels where the RTPTS value is clearly 

associated with a material region that 

contributes significantly to the vessel failure 

probability, and is evaluated at a fluence that 

is clearly associated with a potential location 

of large flaws. 

11.3 Relationship between RT

Metrics and TWCF 

11.3.1 Weighted RT Values 

The information in Table 8.5 provides the 

percent contribution to the total TWCF 

attributable to axial weld flaws, circumferential 

weld flaws, and plate flaws. We use this 

information in Table 11.1 to determine the 

TWCF attributable to each flaw population. 

Figure 11-1 shows the relationships between 

the weighted RT metrics RTAW, RTPL, and RTCW

(described in Section 8.4.1 and quantified by Eq. 

8-1, Eq. 8-2, and Eq. 8-3) and the TWCF values 

presented in Table 11.1. At a fixed reference 

temperature, the TWCF increases ≈50-fold 

between circumferential weld flaws and plate 

flaws, and ≈100-fold between plate flaws and 

axial weld flaws, reflecting the differences in 

fracture driving force caused by the different 

flaw sizes and orientations associated with the 

three flaw populations. The close agreement 

between TWCF values for different plants 

shown in Figure 11-1 is attributable to two 

factors: 

• the similarity in both the frequency of, and 

the structural integrity challenge posed by, 

the most aggressive transients (i.e., largediameter primary side pipe breaks, stuckopen primary side valves that later reclose, 

and breaks of the main steam line), as 

discussed in Section 8.5 

• the fact that the weighted RT metrics 

appropriately reflect the toughness of the 

vessel at the location of postulated flaws 

The fits shown in Figure 11-1 can be combined 

to estimate the TWCF of other PWRs, 

as follows: 
11-4

Eq. 11-1 TWCFTOTAL TWCFAXIAL−WELD PL TWCFPLATE + TWCFCIRC−WELD = +α ⋅

where 

{ 0585.0exp10x4 ( 69.459 )} 26 ⋅= +⋅ − TWCFAXIAL−WELD RTAW (see Eq. 8-1 for RTAW) 

= 7.1 α PL , { 064.0exp10x4 ( 69.459 )} 29 +⋅⋅= − TWCFPLATE RTPL (see Eq. 8-2 for RTPL)

{ 051.0exp10x3 ( 69.459 )} 27 +⋅⋅= − TWCFCIRC−WELD RTCW (see Eq. 8-3 for RTCW) 
11-5

Table 11.1. Contributions of different flaw populations to the TWCF values estimated by FAVOR Version 04.1 

Weighted Reference 

Temperatures [oF] 

Maximum Reference 

Temperatures [oF] % TWCF Due to Flaws in Mean TWCF, events/yr. EFPY 

RTAW RTCW RTPL RTMAX

-AW

RTMAX

-CW

RTMAX

-PL

Axial 

Welds 

Circ 

Welds Plates Total Axial Welds Circ Welds 

Oconee Unit 1 

32 134 136 72 152 175 79 100.00% 0.00% 0.00% 2.30E-11 2.30E-11 0.00E+00 60 149 156 83 171 193 89 99.90% 0.10% 0.00% 6.47E-11 6.46E-11 6.47E-14 

Ext-Oa 200 207 134 232 251 136 99.83% 0.16% 0.00% 1.30E-09 1.30E-09 2.08E-12 Ext-Ob 227 229 164 263 281 170 99.81% 0.11% 0.08% 1.16E-08 1.16E-08 1.28E-11 

Beaver Valley Unit 1 

32 171 243 217 192 243 243 68.44% 0.33% 31.23% 8.89E-10 6.08E-10 2.93E-12 60 188 272 244 210 272 272 39.19% 0.72% 60.09% 4.84E-09 1.90E-09 3.48E-11 

Ext-Ba 203 301 273 225 301 301 15.69% 1.74% 82.55% 2.02E-08 3.17E-09 3.51E-10 Ext-Bb 226 354 324 250 354 354 9.21% 6.18% 84.62% 3.00E-07 2.76E-08 1.85E-08 

Palisades 

32 210 201 165 212 201 189 99.95% 0.05% 0.00% 4.90E-09 4.90E-09 2.45E-12 60 227 215 181 230 215 205 99.97% 0.04% 0.00% 1.55E-08 1.55E-08 6.20E-12 

Ext-Pa 271 259 231 277 259 259 99.91% 0.02% 0.08% 1.88E-07 1.88E-07 3.76E-11 Ext-Pb 324 335 293 333 335 335 98.62% 0.01% 1.37% 1.26E-06 1.24E-06 1.26E-10 

 Note: See Eq. 8-1, Eq. 8-2, and Eq. 8-3 for reference temperature definitions. 
11-6

In Eq. 11-1, the RT values are expressed in °F; 

the formula converts Fahrenheit to Rankine to 

prevent the introduction of negative numbers to 

the exponential terms. The TWCF attributable 

to plate flaws is multiplied by a factor of 1.7 to 

prevent a systematic underestimation of the 

TWCF results for Beaver Valley. Averaged 

across all embrittlement levels analyzed, Eq. 

11-1 overpredicts the Oconee, Beaver Valley, and 

Palisades results by 65%, 1%, and 25%, 

respectively. Figure 11-3 compares the FAVOR 

04.1 TWCF estimates with the predictions of Eq. 

11-1, showing good agreement overall. 

11.3.2 Maximum RT Values 

The TWCF estimation formula (Eq. 11-1) 

developed in the preceding Section is based on 

weighted RT values; it provides a means to 

estimate with reasonable accuracy how TWCF 

changes with embrittlement level. However, 

information from construction drawings 

regarding the dimensions and placement of the 

welds, plates, and forgings in the beltline region 

is needed to estimate the weighted reference 

temperatures (RTAW, RTCW, and RTPL) used in Eq. 

11-1, in addition to information available in the 

RVID database concerning chemical 

composition, fluence, and the RTNDT before 

irradiation [RVID2]. While this additional 

information is readily available to licensees, and 

indeed has been docketed with the NRC, not 

having this information available in one place 

for all PWRs makes it difficult to estimate 

TWCF using Eq. 11-1 for the operating fleet. 

Conversely, the maximum reference 

temperatures RTMAX-AW, RTMAX-CW, and RTMAX-PL

that are used to estimate the weighted reference 

temperatures (RTAW, RTCW, and RTPL, 

respectively) can be evaluated based only on 

information in RVID. Consequently, in Figure 

11-2, we examine the relationships between 

these maximum reference temperatures and the 

TWCF values presented in Table 11.1 for each 

of the three flaw populations. The uncertainty in 

the correlations of TWCF with maximum RT

values exceeds slightly the uncertainty in the 

correlations of TWCF with weighted RT values 

(compare Figure 11-2 to Figure 11-1). 

Nonetheless, the relationships in Figure 11-2 do 

provide a basis for estimating TWCF when only 

the information in RVID is available. The fits 

shown in Figure 11-2 can be combined to 

estimate the TWCF of other PWRs, as follows: 

Eq. 11-2 TWCFTOTAL AW TWCFAXIAL−WELD PL TWCFPLATE + TWCFCIRC−WELD = α ⋅ +α ⋅

where 

= 6.1 α AW , { 0605.0exp10x3 ( 69.459 )} 27 ⋅= ⋅ − + − TWCFAXIAL−WELD RT AWMAX 

= 7.1 α PL , { 0543.0exp10x9 ( 69.459 )} 27 ⋅= ⋅ − + − TWCFPLATE RT PLMAX

{ 0561.0exp10x4 ( 69.459 )} 29 ⋅= ⋅ − + − TWCFCIRC−WELD RT CWMAX

(see Eq. 8-1, Eq. 8-2, and Eq. 8-3 for the definitions of RTMAX-AW, RTMAX-PL, and RTMAX-CW, 

respectively) 

In Eq. 11-2, the RT values are again expressed in 

°F; the formula converts Fahrenheit to Rankine 

to prevent the introduction of negative numbers 

to the exponential terms. The TWCF 

attributable to axial weld flaws and to plate 

flaws are multiplied by factors of 1.6 and 1.7, 

respectively, to prevent a systematic 

underestimation of the TWCF results of 

Palisades and of Beaver Valley, respectively. 

Averaged across all embrittlement levels 

analyzed, Eq. 11-2 overpredicts the Oconee, 

Beaver Valley, and Palisades results by 278%, 

1%, and 2%,respectively. Figure 11-4 compares 

the FAVOR 04.1 TWCF estimates with the 

predictions of Eq. 11-2. As expected, based on 

the lower correlation coefficients of the TWCF 

vs. maximum RT relationships shown in Figure 

11-2, the estimation accuracy of Eq. 11-2 is not 

quite as good as that of Eq. 11-1. 
11-7

11.4 Proposed RT-Based Screening 

Limits 

A RT-based screening limit can be established 

by setting the total TWCF in either Eq. 11-1 or 

Eq. 11-2 equal to the reactor vessel failure 

frequency acceptance criterion of 1x10-6 events 

per year proposed in Chapter 10. In the 

following two subsections we propose two RTbased screening limits: first in Section 11.4.1 

for plate vessels (which have axial welds), and 

second in Section 11.4.2 for forged vessels 

(which do not have axial welds). In both 

sections, we compare our proposed screening 

limits to the RT values for currently operating 

PWRs at both EOL and EOLE. This section 

concludes with a discussion of the need for 

margins when using these screening limits to 

assess operating PWRs (see Section 11.4.3). 

11.4.1 Plate Vessels 

Plate vessels are made up of axial welds, plates, 

and circumferential welds, so in principal flaws 

in all of these regions will contribute to the 

through-wall cracking frequency. However, as 

revealed by our results (see Table 8.5) and as 

reflected in Eq. 11-1 and Eq. 11-2, the 

contribution of flaws in circumferential welds to 

TWCF is negligible relative to that of flaws in 

axial welds and in plates. A RT-based screening 

limit for PTS can therefore be derived from Eq. 

11-1 by the following procedure: 

(1) Set RTCW to a fixed value. 

(2) Set TWCFTOTAL to the 1x10-6 value proposed 

in Chapter 10. 

(3) Solve the equation to establish (RTAW, RTPL) 

pairs that satisfy equality. 
11-8

y = 4E-26e0.0585x

R2 = 0.9655

1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-05

550 600 650 700 750 800 850

Weighted RT AW [oR]

TWCF Due to Axial Weld flaws

OconeeBeaverPalisadesAllExpon. (All)

y = 4E-29e0.064x

R2 = 0.9544

1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-05

550 600 650 700 750 800 850

Weighted RTPL [oR]

TWCF Due to Plate Flaw

OconeeBeaverPalisadesAllExpon. (All)

Figure 11-1. Correlation of through-wall cracking frequencies with weighted reference temperature metrics 

for the three study plants (°R = °F + 459.69) 

y = 3E-27e0.051x

R2 = 0.8804

1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-05

550 600 650 

Weighte

TWCF Due to Circ Weld Flaw
11-9

y = 3E-27e0.0605x

R2 = 0.9194

1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-05

550 600 650 700 750 800 850

Max. RT AW [oR]

TWCF Due to Axial Weld flaws

OconeeBeaverPalisadesAllExpon. (All)

y = 9E-27e0.0543x

R2 = 0.9257

1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-05

550 600 650 700 750 800 850

Max. RTPL [oR]

TWCF Due to Plate Flaw

OconeeBeaverPalisadesAllExpon. (All)

Figure 11-2. Correlation of through-wall cracking frequencies with maximum reference temperature metrics 

for the three study plants (°R = °F + 459.69)

y = 4E-29e0.0561x

R2 = 0.7971

1.E-141.E-131.E-121.E-111.E-101.E-091.E-081.E-071.E-061.E-05

550 600 650 

Max. 

TWCF Due to Circ Weld Flaw
11-10

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-111.E-101.E-091.E-081.E-071.E-061.E-05

FAVOR Values of TWCF

Fit Values of TWC

F

Oconee

Beaver

Palisades

1:1

Figure 11-3. Comparison of FAVOR 04.1 TWCF 

estimates with TWCF values estimated using 

weighted RT values (Eq. 11-1) 

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-111.E-101.E-091.E-081.E-071.E-061.E-05

FAVOR Values of TWCF

Fit Values of TWC

F

Oconee

Beaver

Palisades

1:1

Figure 11-4. Comparison of FAVOR 04.1 TWCF 

estimates with TWCF values estimated using 

maximum RT values (Eq. 11-2) 

As graphically illustrated in Figure 11-5, this 

procedure establishes a locus of (RTAW, RTPL) 

pairs. In the region of the graph between the 

locus and the origin, the TWCF is below the 

1x10-6 acceptance criterion, so these 

combinations of RTAW and RTPL would be 

considered acceptable and require no further 

analysis. In the region of the graph outside of 

the locus, the TWCF is above the 1x10-6

acceptance criterion, indicating the need for 

additional analysis or other measures to justify 

continued plant operation. Figure 11-5 also 

indicates the effects of the RTCW value (left-hand 

graph) and the TWCFTOTAL value (right-hand 

graph) on the position of the RTAW vs. RTPL

locus. As previously mentioned, the RTCW value 

has little effect on the location of the 1x10-6

locus for any RTCW value that is likely to occur 

within the foreseeable future. 

Figure 11-6 provides loci of (RTMAX-AW, RTMAX-PL) 

similar to those shown in Figure 11-5, but based 

instead on Eq. 11-2 (that is, on maximum RT

values rather than on weighted RT values). 

These loci are used to assess the condition of 

currently operating PWRs relative to RT-based 

screening limits derived from the results of this 

investigation because maximum RT values can 

be estimated using only the information 

available in the RVID database [RVID2]. We 

assess the condition of operating PWRs at EOL 

(40 years, or 32 EFPY) and EOLE (60 years of 

operation, or 48 EFPY). The ID fluence at 

EOLE was assumed to be 1.5 times the value 

reported in RVID at EOL. This assumption 

implies that no changes in core loading will be 

made during the period of license extension. 

Were any licensee to change their core loading 

(e.g., remove their halfnium suppression to 

increase power), these changes would be 

reflected in both calculated fluence values and in 

the results of the surveillance programs 

conducted under Appendix H to 10 CFR Part 50, 

and so could easily be accounted for by 

recalculating the various RT metrics based on 

these different input values. 

The results of these calculations are reported in 

Appendix D and are compared to the proposed 

screening limit for plate vessels in Figure 11-7. 

At EOL, at least 70°F (21°C) and up to 290°F 

(143°C) separate operating PWRs from the 

proposed screening limit; these values reduce by 

between 10 and 20°F (5.5 to 11°C) at EOLE. 

The wide separation of operating plants at EOL 

from these proposed screening limits contrasts 

sharply with the current regulatory situation (see 

Figure 1.1), where some operating plants lie 

within less than a single degree Fahrenheit of the 
11-11

10 CFR 50.61 RTPTS screening limits. This 

increase in estimated “distance” from a RT

screening limit occurs as a direct consequence of 

the more accurate models used throughout this 

investigation. Figure 11-8 points out that these 

improvements can, equivalently, be quantified in 

terms of a reduction in the estimated annual 

frequency of through-wall cracking associated 

with operating PWRs. As shown in the figure, 

even at EOLE no currently operating plant is 

projected to exceed a annual TWCF of 1x10-7

(again, most plants have projected TWCFs far 

below this value, see Figure 11-8). 

11.4.2 Forged Vessels 

Forged vessels are comprised of forgings and 

circumferential welds; they contain no axial 

welds and so there can be no contribution to 

TWCF from the RTMAX-AW term in Eq. 11-2. 

While we have not performed a detailed analysis 

of a forged vessel, the sensitivity studies on 

forging flaw distributions reported in Section 9.2 

of this report and in [EricksonKirk-SS] support 

the use of the RTMAX-PL term (evaluated using 

forging properties) in Eq. 11-2 to estimate the 

contribution of TWCF of forgings. 

150

200

250

300

350

400

150 200 250 300

RTAW [oF]

RTPL [oF]

RTCW < 200oF, TWCF Limit = 1E-06

RTCW < 400oF, TWCF Limit = 1E-06

RTCW < 425oF, TWCF Limit = 1E-06

RTCW < 450oF, TWCF Limit = 1E-06

TWCF < 1x10-6

Acceptable

TWCF > 1x10-6

Additional Analysis 

or Actions Required

0

50

100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350

RTAW [oF]

RTPL [oF]

1E-8

1E-6

1E-7

1E-5

5E-6

Figure 11-5. Weighted RT-based screening criterion for plate vessels based on Eq. 11-1 

(Left: Effect of RTCW value for a fixed TWCFTOTAL value of 1x10-6; 

Right: Effect of TWCFTOTAL for a fixed RTCW value of 300°F (149°C)) 
11-12

0

50

100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350

RTMAX-AW [oF]

RTMAX-PL [oF]

1E-8

1E-6

1E-7

1E-5

5E-6

Figure 11-6. Maximum RT-based screening criterion for plate vessels based on Eq. 11-2 

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300

RTMAX-AW [oF]

RTMAX-PL [oF]

Plate 

PWRs 

at EOL

1E-8

1E-7

5E-7 1E-6

Plate 

PWRs 

at EOLE

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300

RTMAX-AW [oF]

RTMAX-PL [oF]

1E-8

1E-7

5E-7 1E-6

Figure 11-7. Comparison of the maximum RT-based screening limit for plate vessels based on Eq. 11-2

with assessment points for all operating PWRs at EOL (32 EFPY, 40 operating years) (left) 

and EOLE (48 EFPY, 60 operating years) (right) (Plant RT values estimated from information in [RVID2]. 

RTMAX-CW is 300°F (149°C) for both graphs, exceeding the calculated RTMAX-CW value for any plant at EOL or EOLE.) 
11-13

at EOL (32 EFPY)

0

5

10

15

20

E-15 to E-14

E-14 to E-13

E-13 to E-12

E-12 to E-11

E-11

to E-10

E-10 to E-9

E-9 to E-8

E-8 to E-7

E-7 to E-6

TWCF

Number of PWRs

Plate

Vessels

Forged

Vessels

 

at EOLE (48 EFPY)

0

5

10

15

20

E-15 to E-14

E-14 to E-13

E-13 to E-12

E-12 to E-11

E-11

to E-10

E-10 to E-9

E-9 to E-8

E-8 to E-7

E-7 to E-6

TWCF

Number of PWRs

Plate

Vessels

Forged

Vessels

Figure 11-8. TWCF values for operating PWRs estimated using Eq. 11-1 at EOL (left) and EOLE (right) 

(Values for individual plants are reported in Appendix D.) 
11-14

Figure 11-9 provides the locus of (RTMAX-CW, 

RTMAX-PL) pairs that can be used to assess the 

compliance of forged vessels with the reactor 

vessel failure frequency limit of 1x10-6

events/year proposed in Chapter 10. Figure 11-9 

is interpreted in the same way as the proposed 

screening limit for plate vessels (Figure 11-6). 

 

Figure 11-10 compares this proposed screening 

limit with the RTMAX-CW and RTMAX-PL values for 

currently operating forged vessels at EOL and at 

EOLE (see Appendix D for plant-specific values 

of RTMAX-CW and RTMAX-PL). These results 

demonstrate that no forged plant is anywhere 

close to screening limits based on a reactor 

vessel failure frequency limit of 1x10-6

events/year (see also Figure 11-8, which 

expresses these results in terms of frequency, 

rather than in terms or reference temperature). 

0

50

100

150

200

250

300

350

400

450

-50 50 150 250 350 450 550

RTMAX-CW [oF]

Forging: RTMAX-PL [oF]

1E-8

1E-6 5E-7

1E-7

1E-5

5E-6

 

Figure 11-9. Maximum RT-based screening 

criterion for forged vessels based on Eq. 11-1, 

illustrating the effect of TWCFTOTAL

Forged 

PWRs 

at EOL

0

50

100

150

200

250

300

350

-50 50 150 250 350 450

RTMAX-CW [

o

F]

Forging: RTMAX-PL [oF]

1E-8

1E-7

5E-7 1E-6

Forged 

PWRs 

at EOLE

0

50

100

150

200

250

300

350

-50 50 150 250 350 450

RTMAX-CW [

o

F]

Forging: RTMAX-PL [oF]

1E-8

1E-7

5E-7 1E-6

Figure 11-10. Comparison of maximum RT-based screening limit for forged vessels based on Eq. 11-2

with operating PWRs at EOL (32 EFPY, 40 operating years) (left) and EOLE (48 EFPY, 60 operating years) (right) 

(Plant RT values estimated from information in [RVID2]. RTMAX-PL is estimated based on forging properties.) 

11.4.3 Need for Margin 

Aside from relying on different RT metrics, the 

PTS screening limits proposed in Figure 11-6 

and Figure 11-9 differs from the 10 CFR 50.61 

RTPTS screening limit by the absence of a 

“margin term.” Use of a margin term is 

appropriate to account (at least approximately) 

for factors that occur in application that were not 

considered in the analyses upon which these 

proposed screening limits are based. For example, 

the 10 CFR 50.61 margin term (see Eq. 2-4) 

accounts for uncertainty in copper, in nickel, and 

in initial RTNDT. However, as summarized in 

Chapter 7 and discussed in detail by 

[EricksonKirk-PFM], our model explicitly 

considers uncertainty in all of these variables, 

and represents these uncertainties as being larger 
11-15

(a conservative representation) than would be 

appropriate in any plant-specific application of 

the proposed screening limit. Consequently, 

use of the 10 CFR 50.61 margin term with the 

screening limits proposed in Figure 11-6 and 

Figure 11-9 would be inappropriate. 

In general, the following additional reasons 

suggest that use of any margin term with the 

proposed screening limits is inappropriate: 

(1) The TWCF values used to establish the 

screening limit represent 90th percentile 

values or greater (see Figure 8-3). 

(2) Chapter 8 and Chapter 9 demonstrate that 

the results from our three plant-specific 

analyses apply to PWRs in general. 

(3) Certain aspects of our modeling cannot be 

reasonably represented as “best estimates.” 

On balance, there is a conservative bias to 

these non-best estimate aspects of our 

analysis, as discussed in the following 

section. 

11.4.4 Non-Best Estimate Aspects 

of the Model 

Throughout this project, every effort has been 

made to perform a “best estimate” analysis. 

Nonetheless, comparison of the analytical 

models upon which the screening limits 

proposed in Sections 11.4.1 and 11.4.2, with the 

actual situation being assessed, reveals that 

certain features of that situation have not been 

represented as realistically as possible. These 

parts of the model may be judged as providing 

either a conservative representation (i.e., tending 

to increase the estimated TWCF) or a 

nonconservative representation (i.e., tending to 

decrease the estimated TWCF) relative to the 

actual situation in service. Table 11.2 

summarizes these conservatisms and 

nonconservatisms, which are discussed in 

greater detail in Section 11.4.4.1 and 

Section 11.4.4.2, respectively. This discussion 

does not include factors that our models do not 

accurately represent when these inaccuracies 

have been demonstrated not to significantly 

influence the TWCF results. This information 

demonstrates that, on balance, more 

conservatisms than nonconservatisms remain in 

the model, suggesting the appropriateness of 

applying the proposed screening limits 

(see Figure 11-6 and Figure 11-9) without 

an additional margin term. 

11.4.4.1 Residual Conservatisms 

In the reactor vessel failure frequency limit 

• The reactor vessel failure frequency limit of 

1x10-6 events/year was established based on 

the assumption that through-wall cracking of 

the RPV will produce a large early release in 

all circumstances. As discussed in Chapter 10, 

through-wall cracking of the RPV is likely 

to lead to core damage, but large early 

release is unlikely because of reactor safety 

systems and the multiple barriers that block 

radioactive release to the environment 

(e.g., containment). Current guidelines on 

core damage frequency provided by 

RG 1.174 and the Option 3 framework 

for risk-informing 10 CFR Part 50 suggest 

a reactor vessel failure frequency limit of 

1x10-5 events/year [RG1.174]. As illustrated 

in Figure 11-6 and Figure 11-9 changing 

from a 1x10-6 to a 1x10-5 limit would 

increase all of the proposed RT limits 

by ≈40°F (22°C) 
11-16

Table 11.2. Non-best estimate aspects of the models used to develop the RT-based screening limits for PTS 

shown in Figure 11-5 and Figure 11-9 

Situation in Service Potential Conservatism in the Analytical Model 

The model assumes that all failures produce a large early release; 

however, in the APET (Ch. 10), most sequences lead only to core 

damage. 

An initiated axial crack is assumed to instantly propagate to infinite length. 

In reality, the crack length will be finite and limited to the length of a single 

shell course because the cracks will most likely arrest when they 

encounter higher toughness materials in either the adjacent 

circumferential welds or plates. 

If the vessel fails, what happens next? 

An initiated circumferential crack is assumed to instantly propagate 360o

around the vessel ID. In reality, the crack length is limited because the 

azimuthal fluence variation places strips of tougher material in the path of 

the extending crack. 

How the many possible PTS initiators 

are binned, and how TH transient are 

selected to represent each bin to the 

PFM analysis. 

When uncertainty of how to bin existed, consistently conservative 

decisions were made 

The minimum temperature of main steam line break inside containment is 

modeled as ~50o

F (28°C) colder than it can be because containment Characterization of secondary side pressurizes as a result of the steam escaping from the break. failures Stuck-open valves on the secondary side are conservatively modeled in 

Palisades. 

Through-wall attenuation of neutron 

damage 

Attenuation is assumed to be less-significant than measured in 

experiments. 

Model of material unirradiated 

toughness and chemical composition 

variability. 

The statistical distributions sampled produce more uncertainty than could 

ever occur in a specific weld, plate, or forging. 

Correction for systematic conservative 

bias in RTNDT

Model corrects for mean bias, but over represents uncertainty in RTNDT. 

Embrittlement shift model Model used produces systematically higher TWCF than that estimated by 

the embrittlement shift model adopted by ASTM. 

All defects found were assumed to be planar. 

Flaw model Systematically conservative judgments were made when developing 

the flaw distribution model. 

Interdependency of between initiation 

toughness and arrest toughness. 

Model employed allows all initiated flaws a chance to propagate into the 

vessel. 

Extrapolation of irradiation damage Most conservative approach taken (increasing time, vs. increasing 

unirradiated RTNDT). 

Situation in Service Potential Non-Conservatism in the Analytical Model 

If the vessel fails, what 

happens next? The potential for air oxidation has been ignored. 

External PTS initiators 

The potential for external events (e.g., fires, earthquakes) initiating PTS transients has 

been ignored. A conservative bounding analysis (see Section 9.4) estimates the effect 

of external events to be at most a factor of 2 increase in TWCF, but the likely increase 

is expected to be much less than 2x. 

Through-wall chemistry 

layering 

Model assumes that the mean level of copper can change four times through the vessel 

wall thickness. If copper layering is not present, the TWCF would increase. 
11-17

In the PRA model 

• In the PRA binning process, when there was 

uncertainty regarding what bin to place a 

particular scenario in, the scenario was 

intentionally binned in a conservative 

manner. Thus, the loading severity has a 

tendency toward being overestimated. 

In the thermal-hydraulics model 

• The temperature of water held in the safety 

injection accumulators was assumed to be 

60°F (15.6°C). These accumulators are 

inside containment and (so) exist at 

temperatures of 80–90°F (26.7–32.2°C) 

in the winter and above 110°F (43.3°C) 

in the summer. Again, this conservative 

estimate of injection water temperature 

increases the magnitude of the thermal 

stresses that occur during of pipe breaks 

and reduces the fracture resistance of the 

vessel steel. 

• When a main steam line breaks inside of 

containment the release of steam from the 

break pressurizes the containment structure 

to ~50psi (335 kPa). Consequently, the 

minimum temperature for MSLBs is 

bounded by the boiling point of water at 

~50psi (335 kPa), or ~260°F (126.7°C). 

However, our models of secondary side 

breaks do not account for pressurization of 

containment, so the minimum temperature 

calculated by RELAP for these transients is 

212°F (100°C), or approximately 50°F 

(28°C) too cold. This conservative estimate 

of the minimum temperature associated with 

an MSLB increases the magnitude of the 

thermal stresses that occur during pipe 

breaks and reduces the fracture resistance of 

the vessel steel. 

In the fracture model 

• Once a circumferential crack initiates, it is 

assumed to instantly propagate 360° around 

the vessel wall. However, full 

circumferential propagation is highly 

unlikely because of the azimuthal variation 

in fluence, which causes alternating regions 

of more embrittled and less embrittled 

material to exist circumferentially around 

the vessel wall. Thus, our model tends to 

overestimate the extent of cracking initiated 

from circumferentially oriented defects 

because it ignores this natural crack arrest 

mechanism. 

• Once an axial flaw initiates, it is assumed to 

instantly become infinitely long. In reality, 

it only propagates to the length of an axial 

shell course (~8 to 12–ft (~2.4 to 3.7-m)), 

at which point, it encounters tougher material 

and arrests. Even though a shell course is 

very long, flaws of finite length tend to 

arrest more readily than do flaws of infinite 

length because of systematic differences in 

the through-wall variation of crack driving 

force. Because of this approximation, our 

model tends to overestimate the likelihood 

of through-wall cracking. 

• As detailed in Section 4.2.3.1.3 of 

[EricksonKirk-PFM] and in [English 02], 

the adopted FAVOR model of how fluence 

attenuates through the RPV wall is 

conservative relative to experimental data. 

• As detailed in Section 4.2.2.2 of 

[EricksonKirk-SS] and in Appendix D 

to [EricksonKirk-PFM], the statistical 

distributions of Cu, Ni, P, and RTNDT

sampled by FAVOR overestimate the degree 

of uncertainty in these variables relative to 

what can actually exist in any particular 

weld, plate, or forging. 

• While the FAVOR model corrects (on 

average) for the systematic conservative bias 

in RTNDT, the model overestimates the 

uncertainty associated with the fracture 

toughness transition temperature metric. 

• As detailed in Section 9.2.1.2.3, the 

embrittlement shift model adopted by 

FAVOR systematically overestimates the 

TWCF relative to the embrittlement shift 

model currently recommended by the 

ASTM (an international consensus body). 

In the flaw model 

• In the experimental data upon which the 

flaw distribution is based, all detected 

defects were modeled as being crack-like 

and, therefore, potentially deleterious to the 
11-18

fracture integrity of the vessel. However, 

many of these defects are actually 

volumetric rather than planar, making them 

either benign or, at a minimum, much less of 

a challenge to the fracture integrity of the 

vessel. Thus, the model we have adopted 

overestimates the seriousness of the defect 

population in RPV materials, which leads to 

overly pessissimistic assessments of the 

fracture resistance of the vessel. 

• FAVOR incorporates an interdependence 

between initiation and arrest fracture 

toughness values premised on physical 

arguments (see Sections 5.3.1.1 and 5.3.1.2 

of [EricksonKirk-PFM]). While the staff 

believes these models are appropriate, this 

view is not universally held (see reviewer 

comment 40D in Appendix B). The 

alternative model, with no interdependence 

between initiation and arrest fracture 

toughness values, would reduce the 

estimated values of TWCF. 

• As detailed in Section 9.2.2.1, we have 

simulated levels of irradiation damage 

beyond those occurring over currently 

anticipated lifetimes using the most 

conservative available techniques. 

11.4.4.2 Residual Non-Conservatisms 

In the reactor vessel failure frequency limit 

• Air oxidation. The LERF criterion provided 

in RG 1.174, which was used to establish the 

1x10-6/ry TWCF limit, assumes source terms 

that do not reflect scenarios where fuel 

cooling has been lost, exposing the fuel rods 

to air (rather than steam). Should such a 

situation arise, some portion of the reactor 

fuel would eventually be oxidized in an air 

environment, which would result in release 

fractions for key fission products (ruthenium 

being of primary concern) that may be 

significantly (e.g., a factor of 20) larger than 

those associated with fuel oxidation in steam 

environments. These larger release fractions 

could lead to larger numbers of prompt 

fatalities than predicted for non-PTS risksignificant scenarios. Nonetheless, the 

APET developed in Chapter 10 

demonstrates that the number of scenarios 

where air oxidation is possible is extremely 

small, certainly far smaller than the number 

of scenarios where only core damage (not 

LERF) is the only plausible outcome. Thus, 

the nonconservatism introduced by not 

explicitly considering the potential for air 

oxidation is more than compensated for by 

the conservatism of establishing a TWCF 

limit based on LERF when many accident 

sequences can only plausibly result in core 

damage. 

In the PRA model 

• External initiating events. As detailed in 

Section 9.4, our analysis hast not considered 

the potential for a PTS transient to be started 

by an initiating event external to the plant 

(e.g., fire, earthquake). The bounding 

analyses reported in Section 9.4 demonstrate 

that this would increase the TWCF values 

reported herein by at most a factor of 2. 

However, the bounding nature of our 

external events analysis suggests strongly 

that the actual effect of ignoring the 

contribution of external initiating events 

would be much smaller than 2x. 

In the fracture model 

• Through-wall chemistry layering. 

As detailed in Section 9.2.1.2.5, FAVOR 

models the existence of a gradient of 

properties through the thickness of the RPV 

because of through-wall changes in copper 

content. These copper content changes arise 

from the fact that, given the large volume of 

weld metal needed to fill an RPV weld, 

manufacturers often need to use weld wire 

from multiple weld wire spools (having 

different amounts of copper coating) to 

completely fill the groove. The model 

adopted in FAVOR resamples the mean 

copper content of the weld at the 1⁄4T, 1⁄2T, 

and 3⁄4T locations through the thickness. 

This resampling increases the probability of 

crack arrest because it allows the simulation 

of less irradiation-sensitive materials, which 

could arrest the running crack before it fails 

the vessel. If these weld layers did not occur 

in a real vessel, the TWCF would increase 
11-19

relative to those reported herein by a small 

factor (~2.5 based on the limited sensitivity 

studies performed). 
12-1

12 Summary of Findings and Considerations 

for Rulemaking

The investigation documented by this report 

reevaluates the technical basis of the PTS Rule 

and its associated screening criteria. Our 

approach considers the factors that influence the 

risk of vessel failure during a PTS event, while 

accounting for uncertainties as an integrated part 

of a quantitative PRA. Two central features of 

our approach are a focus on the use of realistic 

input values and models (wherever possible), 

and an explicit treatment of uncertainties (to the 

greatest extent practicable). Thus, our approach 

differs markedly from that employed in 

developing 10 CFR 50.61, in which many 

aspects of the analysis included intentional and 

unquantified conservatisms, and uncertainties 

were implicitly treated by incorporating them 

into the models. 

In this chapter, we summarize the results of our 

findings in the following four areas: 

• baseline analysis of the likelihood of PTSinduced RPV failure at three plants (Oconee 1, 

Beaver Valley, and Palisades), as presented 

in Chapter 8 

• examination of the applicability of the 

results from Chapter 8 to PWRs in general, 

as presented in Chapter 9 

• assessment of a annual per plant limit on 

through-wall cracking frequency that is 

consistent with current NRC guidelines on 

risk-informed regulation, as presented in 

Chapter 10 

• use of information from Chapters 8, 9, and 

10 to develop a reference temperature (RT)-

based PTS screening criteria, as presented in 

Chapter 11 

This chapter concludes with a short discussion 

of considerations for rulemaking and possible 

regulatory implications of this work beyond 

those associated with 10 CFR 50.61. 

12.1 Plant-Specific Baseline Analysis 

of the PTS Risk at Oconee Unit 1, 

Beaver Valley Unit 1, and Palisades 

Chapter 8 provided the results of plant-specific 

analyses of Oconee Unit 1, Beaver Valley Unit 1, 

and Palisades. In the following list, which 

summarizes the information presented in 

Chapter 8, the conclusions are shown in bold 

italics, while supporting information is shown in 

regular type: 

• The degree of PTS challenge for currently 

anticipated lifetimes and operating

conditions is low. 

o Even at the end of license extension 

(60 operational years, or 48 EFPY at an 

80% capacity factor), the mean estimated 

through-wall cracking frequency (TWCF) 

does not exceed 2x10-8/year for the 

plants analyzed. Considering that the 

Beaver Valley and Palisades RPVs are 

constructed from some of the most 

irradiation-sensitive materials in 

commercial reactor service today, these 

results suggest that, provided that 

operating practices do not change 

dramatically in the future, the operating 

reactor fleet is in little danger of 

exceeding either the limit on TWCF of 

5x10-6/yr expressed by Regulatory 

Guide 1.154 [RG 1.154] or the 1x10-6/yr 

value recommended in Chapter 10, even 

after license extension. 

• Mean TWCF values are in fact upper 

bounds. 

o Because of the skewness characteristic 

of the TWCF distributions that arise as a 

result of the physical processes 

responsible for steel fracture, mean 

TWCF values correspond to the 90th
12-2

percentile (or higher) of the TWCF

distribution. Thus, the mean TWCF values 

we report in this chapter are appropriately 

regarded as upper bounds to the 

uncertainty distribution on TWCF. 

• Axial flaws, and the toughness properties 

that can be associated with such flaws, 

control nearly all of the TWCF. 

o Axial flaws are much more likely to 

propagate through-wall than 

circumferential flaws because the 

applied driving force to fracture 

increases continuously with increasing 

crack depth for an axial flaw. 

Conversely, circumferentially oriented 

flaws experience a driving force peak 

mid-wall, providing a natural crack 

arrest mechanism. It should be noted 

that crack initiation from 

circumferentially oriented flaws is 

likely; it is only their through-wall 

propagation that is much less likely 

(relative to axially oriented flaws). 

o It is, therefore, the toughness properties 

that can be associated with axial flaws 

that control nearly all of the TWCF. 

These include the toughness properties 

of plates and axial welds at the flaw 

locations. Conversely, the toughness 

properties of both circumferential welds 

and forgings have little effect on TWCF 

because these can be associated only 

with circumferentially oriented flaws. 

• Transients involving primary side faults 

are the dominant contributors to TWCF. 

Transients involving secondary side faults 

play a much smaller role. 

o The severity of a transient is controlled 

by a combination of three factors: 

 the initial cooling rate, which 

controls the thermal stress in the 

RPV wall 

 the minimum temperature of the 

transient, which controls the 

resistance of the vessel to fracture 

 the pressure retained in the primary 

system, which controls the pressure 

stress in the RPV wall 

o The significance of a transient (i.e., how 

much it contributes to PTS risk) depends 

on these three factors and on the 

likelihood of the transient occurring. 

o Our analysis considered transients in the 

following classes: 

 primary side pipe breaks 

 stuck-open valves on the primary side 

 main steam line breaks 

 stuck-open valves on the secondary side 

 feed-and-bleed 

 steam generator tube rupture 

 mixed primary and secondary initiators 

o Table 12.1 summarizes our results for 

these transient classes in terms of both 

transient severity indicators and the 

likelihood of the transient occurring. 

The color-coding of table entries 

indicates the contribution (or not) 

of these factors to the TWCF of the 

different classes of transients. 

This summary indicates that the riskdominant transients (medium- and largediameter primary side pipe breaks, and 

stuck-open primary side valves that later 

reclose) all have multiple factors that, 

in combination, result in their significant 

contribution to TWCF. 

 For medium- to large-diameter 

primary side pipe breaks, the fast to 

moderate cooling rates and the low 

downcomer temperatures (generated 

by the rapid depressurization and 

emergency injection of lowtemperature makeup water directly 

to the primary) combine to produce 

a high-severity transient. Despite 

the moderate to low likelihood of 

transient occurrence, the severity of 

these transients (if they occur) 

makes them significant contributors 

to the total TWCF. 

 For stuck-open primary side valves 

that later reclose, the repressurization 

associated with valve reclosure 
12-3

coupled with low temperatures in 

the primary combine to produce a 

high-severity transient. This 

coupled with a high likelihood of 

transient occurrence makes stuckopen primary side valves that later 

reclose significant contributors to 

the total TWCF. 

Table 12.1. Factors contributing the severity and risk dominance of various transient classes. 

Transient Severity 

Transient Class Cooling 

Rate 

Minimum 

Temperature Pressure 

Transient 

Likelihood 

TWCF 

Contribution 

Large Diameter Fast Low Low Low Large 

Medium Diameter Moderate Low Low Moderate Large 

Primary 

Side Pipe 

Breaks Small Diameter Slow High Moderate High ~0 

Primary Valve Recloses Slow Moderate High High Large 

Stuck-Open 

Valves 

Valve Remains 

Open Slow Moderate Low High ~0 

Main Steam Line Break Fast Moderate High High Small 

Stuck-Open Valve(s), Secondary 

Side Moderate High High High ~0 

Feed-and-Bleed Slow Low Low Low ~0 

Steam Generator Tube Rupture Slow High Moderate Low ~0 

Mixed Primary & Secondary 

Initiators Slow Mixed Very Low ~0 

Color Key Enhances TWCF Contribution Intermediate Diminishes TWCF 

Contribution 
12-4

 The small or negligible contribution 

of all secondary side transients 

(MSLBs, stuck-open secondary 

valves) results directly from the lack 

of low temperatures in the primary 

system. For these transients, the 

minimum temperature of the 

primary for times of relevance is 

controlled by the boiling point of 

water in the secondary (212°F (100°C) 

or above). At these temperatures, 

the fracture toughness of the RPV 

steel is sufficiently high to resist 

vessel failure in most cases. 

• Credits for operator action, while included 

in our analysis, do not influence these 

findings in any significant way. Operator 

action credits can dramatically influence the 

risk-significance of individual transients. 

Appropriate credits for operator action, 

therefore, need to be included as part of a 

“best estimate” analysis because there is no 

way to establish a priori if a particular 

transient will make a large contribution to 

the total risk. Nonetheless, the results of our 

analyses demonstrate that the overall effect

of these operator action credits on the total 

TWCF for a plant is small, for the following 

reasons:

o Medium- and Large-Diameter Primary 

Side Pipe Breaks: No operator actions 

are modeled for any break diameter 

because, for these events, the safety 

injection systems do not fully refill 

the upper regions of the RCS. 

Consequently, operators would never 

take action to shut off the pumps. 

o Stuck-Open Primary Side Valves that 

May Later Reclose: Reasonable and 

appropriate credit for operator actions 

(throttling of HPI) has been included in 

the PRA model. However, the influence 

of these credits on the estimated values 

of vessel failure probability attributable 

to SO-1 transients is small because the 

operator actions credited only prevent 

repressurization when SO-1 transients 

initiate from HZP conditions and when 

the operators act promptly (within 

1 minute) to throttle HPI. Complete 

removal of operator action credits from 

the model increases the total risk 

associated with SO-1 transients only 

slightly. 

o Main Steam Line Breaks: For the 

overwhelming majority of MSLB 

transients, vessel failure is predicted to 

occur between 10 and 15 minutes after 

transient initiation because it is within 

this timeframe that the thermal stresses 

associated with the rapid cooldown 

reach their maximum. Thus, all of the 

long-time effects (isolation of feedwater 

flow, timing of HSSI control) that can 

be influenced by operator actions have 

no effect on vessel failure probability 

because these factors influence the 

progression of the transient after failure 

has occurred (if it occurs). Only factors 

affecting the initial cooling rate (i.e., 

plant power level at transient initiation, 

break location inside or outside of 

containment) can influence the CPTWC 

values. These factors are not influenced 

in any way by operator actions. 

• Because the severity of the most significant 

transients in the dominant transient classes 

are controlled by factors that are common 

to PWRs in general, the TWCF results 

presented in this chapter can be used with 

confidence to develop revised PTS 

screening criteria that apply to the entire 

fleet of operating PWRs. 

o Medium- and Large-Diameter Primary 

Side Pipe Breaks: For these break 

diameters, the fluid in the primary cools 

faster than can the wall of the RPV. 

In this situation, only the thermal 

conductivity of the steel and the 

thickness of the RPV wall control the 

thermal stresses and, thus, the severity 

of the fracture challenge. Perturbations 

to the fluid cooldown rate controlled by 

break diameter, break location, and 

season of the year do not play a role. 

Thermal conductivity is a physical 

property, so it is very consistent for all 
12-5

RPV steels, and the thicknesses of the 

three RPVs analyzed are typical of 

PWRs. Consequently, the TWCF 

contribution of medium- to largediameter primary side pipe breaks is 

expected to be consistent from plant-toplant and can be well-represented for all 

PWRs by the analyses reported herein. 

o Stuck-Open Primary Side Valves that 

May Later Reclose: A major 

contributor to the risk-significance of 

SO-1 transients is the return to full 

system pressure once the valve recloses. 

The operating and safety relief valve 

pressures of all PWRs are similar. 

Additionally, as previously noted, 

operator action credits affect the total 

risk associated with this transient class 

only slightly. 

o Main Steam Line Breaks: Since MSLBs 

fail early (within 10–15 minutes after 

transient initiation), only factors 

affecting the initial cooling rate can 

have any influence on CPTWC values. 

These factors include the plant power 

level at event initiation and the location 

of the break (inside or outside of 

containment). These factors are not 

influenced in any way by operator 

actions. 

12.2 Applicability of these Plant 

Specific Results to Estimating the PTS 

Risk at PWRs in General 

In Chapter 9, we examined the applicability of 

the TWCF estimates presented in Chapter 8 for 

Oconee Unit 1, Beaver Valley Unit 1, and 

Palisades to PWRs in general. The information 

presented focused on the following topics: 

• Sensitivity studies performed on the TH and 

PFM models to engender confidence in both 

the robustness of the results presented in 

Chapter 8 and their applicability to PWRs 

in general. 

• An examination of the plant design and 

operational characteristics of five additional 

plants to determine whether the design and 

operational features that are the key 

contributors to PTS risk vary significantly 

enough in the general plant population to 

question the generality of our results. 

• An examination of the effects of external 

events (e.g., fires, floods, earthquakes) to 

PTS risk. 

Except for a few situations that are not expected 

to occur, none of these analyses revealed any 

reason to question the applicability of the results 

presented in Chapter 8 to the general population 

of operating PWRs in the United States. The 

information developed in these analyses is 

summarized as follows: 

TH Sensitivity Studies 

• Changes to the RELAP heat transfer 

coefficient model to account for low-flow 

situations where mixed convection heat 

transfer may be occurring in the 

downcomer were made based on the 

Petukhov-Gnielinski heat transfer 

correlation. This change in the heat 

transfer coefficient increases the CPTWC 

by a factor ~3 (averaged across all 

transients analyzed) compared to using the 

default heat transfer correlations in 

RELAP5/MOD3.3 Version ei. There is 

some variability from the average CPF 

factor, depending upon the transient being 

considered. 
12-6

PFM Sensitivity Studies 

• An examination of the effects of all 

postulated credible perturbations to our 

PFM model revealed no effects significant 

enough to warrant a change to our baseline 

model, or to recommend a caution 

regarding its robustness. 

• In general, the TWCF of forged PWRs 

can be assessed using the Chapter 8 results 

(for plate welded PWRs) by ignoring the 

TWCF contribution of axial welds. 

However, should changes in future 

operating conditions result in a forged 

vessel being subjected to very high levels 

of embrittlement (far beyond any currently 

anticipated at EOL or EOLE) a plantspecific analysis to assess the effect of 

subclad flaws on TWCF would be 

warranted. 

• For PWRs with vessel thicknesses of 7.5 to 

9 .5-in. (19.05 to 24.13-cm), the TWCF 

results in Chapter 8 are realistic. The 

Chapter 8 results overestimate the TWCF 

of the seven thinner vessels (with wall 

thicknesses below 7-in. (17.78-cm)) and 

underestimate the TWCF of Palo Verde 

Units 1, 2, and 3, all of which have wall 

thicknesses above 11-in (27.94-cm). 

However, these vessels have very low 

embrittlement projected at either EOL or 

EOLE, suggesting little practical effect of 

this underestimation. 

Plant Design and Operational Characteristics 

• Large-Diameter Primary Side Pipe Breaks: 

No differences were found that would 

cause significant changes in either the 

progression or frequencies of the PTS 

scenarios. Additionally, no differences in 

the plant system designs were found that 

would cause significant changes in the 

downcomer fluid temperature. 

• Small- to Medium-Diameter Primary Side 

Pipe Breaks: No differences were found 

that would cause significant changes in 

either the progression or frequency of the 

pipe break LOCAs. For the feed-and-bleed 

LOCAs, the only difference that was found 

affected the frequency for the CE 

generalization plant (i.e., Fort Calhoun). 

The frequency for these types of scenarios 

could be higher by a factor of ~3; however, 

this increase would not prevent the 

generalization plants from being bounded 

(or represented) by the detailed analysis 

plants. 

• Stuck-Open Valves on the Primary Side 

that May Later Reclose: The progression 

of the accident scenarios should be the 

same across all plants. While, the 

frequency associated with this type of 

scenarios could increase at some 

Westinghouse plants, the integrated effect 

of this increase was determined to be small. 

Fort Calhoun is expected to have a 

downcomer temperature that is cooler than 

its corresponding detailed analysis plant 

(Palisades) because of the smaller size of 

the plant. The downcomer temperature for 

the other generalization plants is actually 

expected to be somewhat warmer. PFM 

calculations performed to quantify the 

effect of the colder temperatures in 

Ft. Calhoun determined that while the 

conditional through-wall cracking 

probabilities would increase (as expected), 

the increase was not so substantial as to 

prevent the Palisades plant analysis from 

upper-bounding the Ft. Calhoun plant 

analysis. Thus, the colder downcomer 

temperature for smaller plants was not 

viewed as impeding the applicability of the 

TWCF values in Chapter 8 to PWRs 

in general. 

• Main Steam Line and other Secondary Side 

Breaks: No differences were found that 

would cause significant differences in 

either the progression or frequency of the 

PTS scenarios. 

• Summary: These observations support the 

conclusion that the Chapter 8 TWCF 

estimates produced can be used to 

characterize (or bound) the TWCF of 

PWRs in general. 
12-7

External Events 

• No external event scenarios were found 

where the TWCFs significantly exceed that 

of the worst internal event scenarios 

(contributions from LOCA-type and SRV 

open-reclose-type accidents). Given the 

bounding nature of the external event 

analyses, there is considerable assurance 

that the external event contribution to 

overall TWCF as a result of PTS does not 

exceed than the highest best-estimate 

contribution from internal events. Given 

the conservative probabilities and 

dependencies assumed in the external event 

analyses, with the addition of little or no 

credit for any operator actions for the 

external event scenarios, it is more likely 

that the “realistic” external event 

contribution to overall TWCF is much less 

than the highest internal event contribution. 

Therefore, the contribution of external 

initiating events to the overall TWCF 

attributable to PTS can be considered 

negligible. 

12.3 An Anual Per-Plant Limit on 

Through-Wall Cracking Frequency 

Consistent with Current Regulatory 

Guidance on Risk-Informed 

Regulation 

The analysis presented in Chapter 10 produced 

the following conclusions regarding the 

establishment of an annual per-plant limit on 

through-wall cracking frequency (i.e., a criterion 

for RVFF): 

(1) The analysis supports a definition of RVFF 

as being equivalent to TWCF (i.e., for PTS 

considerations, RPV “failure” can be 

defined as an occurrence of a through-wall 

crack). This conclusion is based on the 

following two factors: 

(a) TWCF is a more direct measure than 

VCIF of the likelihood of events with 

potentially significant public health 

consequences. This is desirable from a 

risk-informed decision-making 

perspective. 

(b) The uncertainties associated with the 

prediction of a through-wall crack 

(under PTS conditions) are only slightly 

larger than those associated with the 

prediction of crack initiation (also under 

PTS conditions). For example, at the 

10 CFR 50.61 RTPTS screening limit, the 

separation between the 50th and 95th

percentiles in the distribution of VCIF

ranges from 0.8 to 1.8 orders of 

magnitude, while the separation between 

the 50th and 95th percentiles in the 

distribution of TWCF ranges from 0.9 

to 2.6 orders of magnitude. This slight 

increase in uncertainty is a natural and 

expected consequence of a cleavage 

failure mechanism and does not reflect a 

state of knowledge limitation regarding 

crack arrest. (See [EricksonKirk-PFM] 

for details of the crack arrest model.) 

(2) The analysis supports an acceptance 

criterion for RVFF, RVFF*, of 1x10-6/ry. 

This is based on the following observations: 

(a) The conditional probability of an 

unscrubbed, large early release with a 

large air-oxidation source term (given a 

PTS-induced RPV failure) appears to be 

very small (i.e., less than 0.01). It is 

particularly small for plants where water 

in the reactor cavity (following a PTSinduced RPV failure) will cover the fuel. 

For plants with larger cavities, the low 

probability of the scenario is largely 

attributable to the independence and 

reliability of containment sprays. 

(b) The assessment underlying the above 

observation does not account for 

potential dependencies associated with 

PTS-events initiated by “external events” 

(e.g., earthquakes) or internal fires. 

(c) For plants with cavities such that fuel 

cooling is not assured following a PTSinduced RPV failure, the APET (Figure 

10.1) identifies the most probable 

scenarios where limited fuel damage 

might occur, even if ECCS operates as 

designed. 
12-8

Observation (a), taken in isolation, supports 

the use of an RVFF* based on 

considerations of core damage consistent 

with those proposed in current activities for 

risk-informing 10 CFR Part 50 [SECY-00-

0198]. However, Observation (b) identifies 

a potentially significant uncertainty 

regarding the margin between PTS-induced 

RPV failure and large early release, and 

Observation (c) raises a potential concern 

regarding defense-in-depth. Therefore, 

RG 1.174 guidelines on CDF supporting 

a value for RVFF* of 1x10-5 events/year 

may not have sufficient justification, 

whereas the scoping study developed for 

RG 1.174 guidelines on LERF is more 

defensible given currently available 

information. This rationale supports our 

recommended value of 1x10-6 events/year 

for RVFF*, which is consistent with the 

RG 1.174 guidelines on LERF. 

When assessing the acceptability of the 

PTS-associated risk at a given plant, the 

mean value of the plant’s PTS-induced 

RVFF (i.e., the mean TWCF) should be 

compared with RVFF*. This conclusion 

is based on how other NRC risk-informed 

decisions use risk information 

(e.g., see RG 1.174). 

(3) Should additional work be performed to 

address the key post-RPV failure accident 

progression uncertainties identified in this 

study, the following issues are of principal 

importance: 

(a) the likelihood that a PTS-induced axial 

crack will, upon reaching a 

circumferential weld, turn and progress 

along the circumferential weld 

(b) the likelihood of PTS-induced 

containment isolation failure (especially 

failures associated with failure of 

containment penetrations) and ECCS 

failure (especially ECCS piping failures) 

(c) the magnitude of potential source terms 

and consequences associated with PTS 

events 

(d) substantiation of conditional probability 

values in Table 10.2 and Table 10.3 

(e) the impact of external events on PTSinduced LERF 

It is anticipated that state-of-knowledge 

improvements in any of these areas will 

strengthen this study’s conclusions 

regarding the margin between a PTSinduced RPV failure and consequent large 

early releases. Although not quantified, 

several aspects of our analysis performed to 

support an RVFF* value 1x10-6 events/year 

have a known conservative bias. The 

following is a summary of a few of these 

areas identified earlier in this chapter: 

• Given the relatively low energy of the 

fluid following a postulated PTS event, 

the impulse on the RPV and piping 

resulting from a blowdown was 

predicted to be within the bounds of a 

design-basis SSE. The limited vessel 

movement from a blowdown forces 

would be compensated for by the pipe 

ductility, long runs of piping with many 

bends, and the hanger and support 

systems. For these reasons, damage of 

ECCS piping or containment 

penetrations is not expected. 

• Missile generation attributable to a 

postulated PTS event would result in an 

object being directed laterally into the 

reactor vessel cavity wall by the 

blowdown forces associated with the 

breach in the reactor vessel. For a 

missile to affect the containment spray 

system or containment penetrations, it 

would have to traverse a tortuous path 

through tight clearances of the reactor 

vessel cavity. The missile’s energy 

would be dissipated by multiple contacts 

with the reactor cavity wall, as well as 

the distance it travels, and it would have 

to hit an extremely small target to render 

the containment spray system 

inoperable. 

• Through-wall crack frequency is 

assumed to equal core damage, which is 

assumed to equal a release. The 

through-wall cracks may cover a wide 

spectrum of sizes, from very large to 

very small. Very small cracks would 
12-9

result in only minor leakage that would 

not significantly challenge the reactor 

safety systems. 

12.4 A Reference Temperature 

Based PTS Screening Criteria 

In Chapter 11, we proposed the use of different 

reference temperatures (RT) metrics to 

characterize the resistance of an RPV to fracture 

initiating from different flaws at different 

locations in the vessel: 

• To characterize the contribution of flaws in 

axial welds to vessel fracture probability, 

we have proposed two reference temperature 

metrics: RTAW and RTAW-MAX. RTAW-MAX can 

be estimated for any plant based solely on 

the information contained in the NRC’s 

RVID database [RVID], while estimation of 

RTAW requires information from plant 

drawings concerning the dimensions and 

placement of axial welds in the beltline 

region of the RPV. 

• To characterize the contribution of flaws in 

plates to vessel fracture probability, we 

have proposed two reference temperature 

metrics: RTPL and RTPL--MAX. RTPL-MAX can 

be estimated for any plant based solely on 

the information contained in the NRC’s 

RVID database [RVID], while estimation of 

RTPL requires information from plant 

drawings concerning the dimensions and 

placement of plates in the beltline region of 

the RPV. 

• To characterize the contribution of flaws in 

circumferential welds to vessel fracture 

probability we have proposed two reference 

temperature metrics: RTCW and RTCW-MAX. 

RTCW-MAX can be estimated for any plant 

based solely on the information contained in 

the NRC’s RVID database [RVID], while 

estimation of RTCW requires information 

from plant drawings concerning the 

dimensions and placement of circumferential 

welds in the beltline region of the RPV. 

These different RT values were proposed in 

recognition of the fact that the probability of 

vessel fracture starting from different flaw 

populations varies considerably as a result of 

factors that are both understood and predictable: 

• Different regions of the vessel have flaw 

populations that differ in size (weld flaws 

are considerably larger than plate flaws) 

and orientation (axial and circumferential 

welds have flaws of corresponding 

orientations, whereas plate flaws may be 

either axial or circumferential). The driving 

force to fracture depends on both flaw size 

and flaw orientation, so different vessel 

regions experience different fracture driving 

forces. 

• The degree of irradiation damage suffered 

by the material at the flaw tips varies with 

location in the vessel as a result of 

differences in chemistry and fluence. 

Correlations between these RT-metrics and the 

TWCF attributable to axial weld flaws, plate 

flaws, and circumferential weld flaws showed 

little plant-to-plant variability as a result of the 

general similarity of PTS challenge between 

plants detailed in Chapters 8 and 9 and 

summarized in Sections 12.2 and 12.3. The 

following two relationships were developed 

based on these correlations: 
12-10

TWCF estimated from weighted RT metrics 

TWCFTOTAL TWCFAXIAL−WELD PL TWCFPLATE + TWCFCIRC−WELD = +α ⋅

where 

{ 0585.0exp10x4 ( 69.459 )} 26 ⋅= +⋅ − TWCFAXIAL−WELD RTAW (see Eq. 8-1 for RTAW) 

= 7.1 α PL , { 064.0exp10x4 ( 69.459 )} 29 +⋅⋅= − TWCFPLATE RTPL (see Eq. 8-2 for RTPL)

{ 051.0exp10x3 ( 69.459 )} 27 +⋅⋅= − TWCFCIRC−WELD RTCW (see Eq. 8-3 for RTCW) 

TWCF estimated from maximum RT metrics 

TWCFTOTAL AW TWCFAXIAL−WELD PL TWCFPLATE + TWCFCIRC−WELD α ⋅= +α ⋅

where 

= 6.1 α PL , { 0605.0exp10x3 ( 69.459 )} 27 ⋅= ⋅ − + − TWCFAXIAL−WELD RT AWMAX 

= 7.1 α PL , { 0543.0exp10x9 ( 69.459 )} 27 ⋅= ⋅ − + − TWCFPLATE RT PLMAX

{ 0561.0exp10x4 ( 69.459 )} 29 ⋅= ⋅ − + − TWCFCIRC−WELD RT CWMAX

(see Eq. 8-1, Eq. 8-2, and Eq. 8-3 for the definitions of RTMAX-AW, RTMAX-PL, and RTMAX-CW, 

respectively) 

In these relationships, all temperatures are in °F. 

RT-based screening limits were established by 

setting the total TWCF in these equations equal 

to the reactor vessel failure frequency 

acceptance criterion of 1x10-6 events per year 

proposed in Chapter 10. Two different RTbased screening limits were developed from 

each of the above relationships: one for plate 

welded vessels based on axial weld and plate 

properties (the contribution of circumferential 

welds at realistic embrittlement levels is so small 

that it can be neglected), and one for forged 

vessels based on circumferential weld and plate 

properties (there are no axial welds in these 

vessels so their contribution to TWCF is, by 

definition, zero). Figure 12-1 provides graphical 

representations of these screening criteria along 

with an assessment of all operating PWRs 

relative to limits based on the maximum RT

embrittlement metrics§§§§§§. In these figures, 

 

§§§§§§ Maximum RT embrittlement metrics are used in 

these comparisons because these metrics can be 

estimated based only on the information in 

RVID. In principal PTS limits based on 

weighted RT embrittlement metrics should 

provide a somewhat more accurate estimate of 

plant risk. 

the region of the graph between the red locus 

and the origin has TWCF values below the 1x10-6

acceptance criterion, so these combinations of 

reference temperatures would be considered 

acceptable and require no further analysis. In 

the region of the graph outside of the red locus, 

the TWCF is above the 1x10-6 acceptance 

criterion, indicating the need for additional 

analysis or other measures to justify continued 

plant operation. 

To compare the condition of currently operating 

PWRs with this proposed screening limit, we 

used the information in the RVID database 

[RVID2] to estimate values of RTMAX-AW, RTMAX-PL, 

and RTMAX-CW for each operating PWR. At EOL, 

at least 70°F (21°C) and up to 290°F (143°C) 

separate operating PWRs from the proposed 

screening limit; these values reduce by between 

10 and 20°F (5.5 to 11°C) at EOLE. Even at 

EOLE, no plate-welded PWR is projected to 

exceed an annual TWCF of 1x10-7 (again, most 

plants have projected TWCFs far below this 

value, see Figure 11-8). Additionally, no forged 

plant is anywhere close to the limit of 1x10-6

events per year at either EOL or EOLE. This 

separation of operating plants from the proposed 
12-11

screening limits can be compared with the 

current situation where the most embrittled 

plants are within 1°F of the 10 CFR 50.61 

screening limit. As noted in Sections 9.2.2.2 

and 9.2.2.3, these RT-based screening limits 

apply to PWRs in general subject to the 

following three provisos: 

• When assessing a forged vessel where the 

forging has a very high reference 

temperature (RTPL above 225°F (107°C)) 

and the forging is believed to be susceptible 

to subclad cracking, a plant-specific analysis 

of the TWCF produced by the subclad 

cracks should be performed. However, no 

forging is projected to reach this level of 

embrittlement, even at EOLE. 

• When assessing an RPV having a wall 

thickness of 7-in. (18-cm) or less (7 vessels), 

the proposed RT limits are conservative. 

• When assessing an RPV having a wall 

thickness of 11-in. (28-cm) or greater, the 

proposed RT limits may be nonconservative. 

For the three plants meeting this criterion, 

either the RT limits would need to be 

reduced or known conservatisms in the 

current analysis would have to be removed to 

demonstrate compliance with the TWCF 

limit of 1x10-6 event/year. 

Aside from relying on different RT metrics than 

10 CFR 50.61, the proposed revision to the PTS 

screening limit differs from that used currently 

in the absence of a “margin term.” Use of a 

margin term is appropriate to account (at least 

approximately) for factors that occur in 

application that were not considered in the 

analysis upon which the screening limit is based. 

For example, the 10 CFR 50.61 margin term 

accounts for uncertainty in copper, in nickel, and 

in initial RTNDT. However, our model considers 

explicitly uncertainty in all of these variables, 

and represents these uncertainties as being larger 

(a conservative representation) than would be 

appropriate in any plant-specific application of 

the proposed screening limit. Consequently, use 

of the 10 CFR 50.61 margin term with the new 

screening limits is inappropriate. In general, the 

following additional reasons suggest that use of 

any margin term with the proposed screening 

limits is inappropriate: 

(1) The TWCF values used to establish the 

screening limit represent 90th percentile 

values or greater (see Figure 8-3). 

(2) Chapter 8 and Chapter 9 demonstrate that 

the results from our three plant-specific 

analyses apply to PWRs in general. 

(3) Certain aspects of our modeling cannot be 

reasonably represented as “best estimates.” 

On balance, there is a conservative bias to 

these non-best estimate aspects of our 

analysis. Residual conservatisms and 

nonconservatisms in our model are as 

follows: 

Conservatisms

(a) The assumption that all vessel failures 

lead to LERF, when in fact many would 

lead only to core damage. 

(b) The assumption that once initiated all 

circumferential cracks instantly 

propagate 360° around the vessel ID. 

In reality, crack length is limited 

because the azimuthal fluence variation 

places strips of tougher material in the 

path of the extending crack. 

(c) The assumption that once initiated, 

an axial crack will instantly propagate to 

infinite length. In reality, crack length 

is finite and limited to the length of a 

single shell course because axial cracks 

most likely arrest when they encounter 

higher toughness materials in either the 

adjacent circumferential welds or plates. 

(d) The systematically conservative 

judgments made when placing potential 

PTS initiators into bins. 

(e) The systematic underestimation of the 

minimum temperature associated with 

secondary side breaks (MSLBs) because 

the pressurization of containment 

(attributable to steam escaping from the 

break) is not modeled. 

(f) The attenuation of neutron damage by 

steel in the vessel wall is assumed to be 

less than that measured in experiments. 
12-12

(g) The distributions used to represent the 

statistical uncertainty in unirradiated 

transition temperature and chemical 

composition variables contain more 

uncertainty than could ever occur 

in a given weld, plate, or forging. 

(h) The systematic modeling overestimation 

in the uncertainty in used to correct for 

the mean bias in the RTNDT index 

temperature. 

(i) The production of systematically higher 

TWCF values by the model used to 

estimate the increase in RTNDT index 

temperature caused by irradiation 

damage (compared to those estimated by 

the model adopted by ASTM). 

(j) The flaw model assumption that all 

defects are planar (when many are 

actually volumetric), as well as the use 

of systematically conservative 

judgments when developing the flaw 

model (in the absence of definitive 

evidence). 

(k) Use of the most conservative available 

extrapolation schemes when the effects 

of irradiation damage were extrapolated 

forward in time. 

Nonconservatisms

(a) The fact that the small potential for air 

oxidation has been ignored. 

(b) The fact that the small possibility of 

external events (e.g., fire) initiating PTS 

has been ignored. 

(c) The assumption that the mean level of 

copper can change four times through 

the vessel wall thickness, consistent 

with measurements made on thicksection RPV welds. (If copper layering 

is not present, the TWCF would actually 

increase slightly.) 

0

50

100

150

200

250

300

350

0 50 100 150 200 250 300

RTMAX-AW [oF]

RTMAX-PL [oF]

Plate 

PWRs 

at EOL

1E-8

1E-7

5E-7 1E-6

Forged 

PWRs 

at EOL

0

50

100

150

200

250

300

350

-50 50 150 250 350 450

RTMAX-CW [

o

F]

Forging: RTMAX-PL [oF]

1E-8

1E-7

5E-7 1E-6

Figure 12-1. Comparison of RT-based screening limit (curves) with assessment points for operating PWRs 

at EOL in plate vessels (left) and forged vessels (right) 
12-13

12.5 Considerations for Rulemaking 

The calculations reported herein demonstrate 

that PTS events are associated with an extremely 

small risk of vessel failure, suggesting the 

existence of considerable safety margin in the 

current PTS Rule. The magnitude of this margin 

appears to justify consideration of rulemaking. 

Should rulemaking proceed, it appears feasible 

to use improved (i.e., more risk-informed) 

metrics to represent RPV embrittlement. The 

metrics proposed herein reflect the principal 

contributors to PTS-induced RPV failure. 

A numeric value can be established for an 

RT-based screening limit based on the 

information provided herein, as well as 

considerations of risk in current NRC guidance 

and other non-PTS-related risk-informed 

regulatory activities. 

While numerous factors should be addressed in 

any revision of 10 CFR 50.61, our research 

shows that a significant increase in the PTS 

screening limit can be justified. Such a change 

could be implemented without imposing 

on licensees either new material testing 

requirements or new inspection programs. 
13-14 

13 References 

13.1 Citations Summarized by this Report 

The following three sections provide the citations that are summarized by this report (see also Figure 4-1). 

Taken together, these documents provide complete documentation of the NRC’s PTS reevaluation project. 

When these reports are cited in the text, the citations appear in italicized boldface to distinguish them 

from the related literature citations. 

13.1.1 Probabilistic Risk Assessment 

Kolaczkowski-Oco Kolaczkowski, A.M., et al., “Oconee Pressurized Thermal Shock (PTS) 

Probabilistic Risk Assessment (PRA),” 9-28-2004, available in the NRC’s 

Agencywide Documents Access and Management System (ADAMS) under 

Accession #ML042880452. 

Kolaczkowski-Ext Kolaczkowski, A. et al., “Estimate of External Events Contribution to 

Pressurized Thermal Shock (PTS) Risk,” Letter Report, 10-1-2004, available 

in ADAMS under Accession #ML042880476. 

Siu 99 Sui, N., “Uncertainty Analysis and Pressurized Thermal Shock: An Opinion,” 

U.S. Nuclear Regulatory Commission, 1999, available in ADAMS under 

Accession #ML992710066. 

Whitehead-PRA Whitehead, D.L. and A.M. Kolaczkowski, “PRA Procedures and Uncertainty 

for PTS Analysis,” NUREG/CR-6859, U.S. Nuclear Regulatory 

Commission, 12-31-2004. 

Whitehead-BV Whitehead, D.L., et al., “Beaver Valley Pressurized Thermal Shock (PTS) 

Probabilistic Risk Assessment (PRA),” 9-28-2004, available in ADAMS 

under Accession #ML042880454. 

Whitehead-Gen Whitehead, D.W., et al., “Generalization of Plant-Specific Pressurized 

Thermal Shock (PTS) Risk Results to Additional Plants,” 10-14-2004, 

available in ADAMS under Accession #ML042880482. 

Whitehead-Pal Whitehead, D.L., et al., “Palisades Pressurized Thermal Shock (PTS) 

Probabilistic Risk Assessment (PRA),” 10-6-2004, available in ADAMS 

under Accession #ML042880473. 

13.1.2 Thermal-Hydraulics 

Arcieri-Base Arcieri, W.C., R.M. Beaton, C.D. Fletcher, and D.E. Bessette, “RELAP5 

Thermal-Hydraulic Analysis to Support PTS Evaluations for the Oconee-1, 

Beaver Valley-1, and Pallisades Nuclear Power Plants,” NUREG/CR-6858, 

U.S. Nuclear Regulatory Commission, 9-30-2004. 
13-15 

Arcieri-SS Arcieri, W.C., et al., “RELAP5/MOD3.2.2Gamma Results for Palisades 1D 

Downcomer Sensitivity Study,” August 31, 2004, available in ADAMS 

under Accession #ML061170401.

Bessette Bessette, D.E., “Thermal-Hydraulic Evaluations of Pressurized Thermal 

Shock,” NUREG-1809, U.S. Nuclear Regulatory Commission, 5-30-2005.

Chang Chang, Y.H., K. Almenas, A. Mosleh, and M. Pour-Gol, “Thermal-Hydraulic 

Uncertainty Analysis in Pressurized Thermal Shock Risk Assessment: 

Methodology and Implementation on Oconee-1, Beaver Valley, and 

Palisades Nuclear Power Plants,” NUREG/CR-6899, U.S. Nuclear 

Regulatory Commission.

Fletcher Fletcher, C.D., D.A. Prelewicz, and W.C., Arcieri, “RELAP5/MOD3.2.2γ

Assessment for Pressurized Thermal Shock Applications,” NUREG/CR-6857, 

U.S. Nuclear Regulatory Commission, 9-30-2004.

Junge “PTS Consistency Effort,” Staff Letter Report to file, 10-1-2004, available in 

ADAMS under Accession #ML042880480. 

Reyes-APEX Reyes, J.N., et al., “Final Report for the OSU APEX-CE Integral Test 

Facility,” NUREG/CR-6856, U.S. Nuclear Regulatory Commission, 12-16-

2004.

Reyes-Scale Reyes, J.N., et al., “Scaling Analysis for the OSU APEX-CE Integral Test 

Facility,” NUREG/CR-6731, U.S. Nuclear Regulatory Commission, 11-30-

2004.

13.1.3 Probabilistic Fracture Mechanics 

Dickson-Base Dickson, T.L., and S. Yin, “Electronic Archival of the Results of Pressurized 

Thermal Shock Analyses for Beaver Valley, Oconee, and Palisades Reactor 

Pressure Vessels Generated with the 04.1 Version of FAVOR,” 

ORNL/NRC/LTR-04/18, 10-15-2004, available in ADAMS under Accession 

#ML042960391 

Dickson-UG Dickson, T.L., and P.T.Williams, “Fracture Analysis of Vessels Oak Ridge, 

FAVOR v04.1, Computer Code: User’s Guide,” NUREG/CR-6855, U.S. 

Nuclear Regulatory Commission, 10-21-2004. 

EricksonKirk-PFM EricksonKirk, M.T., “Probabilistic Fracture Mechanics: Models, Parameters, 

and Uncertainty Treatment Used in FAVOR Version 04.1,” NUREG-1807, 

U.S. Nuclear Regulatory Commission, 1-26-2005. 

EricksonKirk-SS EricksonKirk, M.T., et al., “Sensitivity Studies of the Probabilistic Fracture 

Mechanics Model Used in FAVOR Version 03.1,” NUREG-1808, U.S. 

Nuclear Regulatory Commission, 11-30-2004. 

Kirk 12-02 EricksonKirk, M.T., “Technical Basis for Revision of the Pressurized 

Thermal Shock (PTS) Screening Limit in the PTS Rule (10 CFR 50.61),” 

December 2002, available in ADAMS under Accession #ML030090626. 
13-16 

Malik Malik, S.N.M., “FAVOR Code Versions 2.4 and 3.1: Verification and 

Validation Summary Report,” NUREG-1795, U.S. Nuclear Regulatory 

Commission, 10-31-2004. 

Simonen F.A. Simonen, S.R. Doctor, G.J. Schuster, and P.G. Heasler, “A Generalized 

Procedure for Generating Flaw Related Inputs for the FAVOR Code,” 

NUREG/CR-6817, Rev. 1, U.S. Nuclear Regulatory Commission, 

October 2003, available in ADAMS under Accession #ML051790410. 

Williams Williams, P.T., and T.L. Dickson, “Fracture Analysis of Vessels Oak Ridge, 

FAVOR v04.1: Computer Code: Theory and Implementation of Algorithms, 

Methods, and Correlations,” NUREG/CR-6854, U.S. Nuclear Regulatory 

Commission, 10-21-2004. 

13.2 Literature Citations 

10 CFR 50.61 Title 10, Section 50.61, of the Code of Federal Regulations, “Fracture 

Toughness Requirements for Protection Against Pressurized Thermal Shock 

Events,” promulgated June 26, 1984. 

10 CFR Part 50 App. H. Appendix H to Title 10, Part 50, of the Code of Federal Regulations, 

“Reactor Vessel Material Surveillance Program Requirements.” 

ASME NB2331 ASME NB-2331, 1998 ASME Boiler and Pressure Vessel Code, Rules for 

Construction of Nuclear Power Plants, Division 1, Subsection NB, Class 1 

Components, American Society of Mechanical Engineers. 

ASTM E23 ASTM E23, “Standard Test Methods for Notched Bar Impact Testing of 

Metallic Materials,” American Society for Testing and Materials, 1998. 

ASTM E185 ASTM E185-94, “Standard Practice for Conducting Surveillance Tests for 

Light-Water Cooled Nuclear Power Reactor Vessels,” American Society for 

Testing and Materials, 1998. 

ASTM E208 ASTM E208, “Standard Test Method for Conducting Drop-Weight Test to 

Determine Nil-Ductility Transition Temperature of Ferritic Steels,” 

American Society for Testing and Materials, 1998. 

ASTM E399 ASTM E399, “Test Method for Plane-Strain Fracture Toughness Testing of 

Metallic Materials,” American Society for Testing and Materials, 1998. 

ASTM E900 ASTM E900-02, “Standard Guide for Predicting Radiation-Induced 

Transition Temperature Shift in Reactor Vessel Materials, E706 (IIF),” 

American Society for Testing and Materials, 2002. 

ASTM E1221 ASTM E1221-96, “Standard Test Method for Plane-Strain Crack-Arrest 

Fracture Toughness, KIa, of Ferritic Steels,” American Society for Testing 

and Materials, 1996. 

ASTM E1921 ASTM E1921-02, “Test Method for Determination of Reference 

Temperature, To, for Ferritic Steels in the Transition Range,” American 

Society for Testing and Materials, 2002. 

Apostolakis 02 Apostakolis, G.E.., Chairman, Advisory Committee on Reactor Safeguards 

(ACRS), U.S. Nuclear Regulatory Commission, “Risk Metrics and Criteria 
13-17 

for Reevaluating the Technical Basis of the Pressurized Thermal Shock 

Rule,” ADAMS ML0220406120, July 18, 2002. 

Bass 04 Bass, B.R., et al., “Experimental Program for Investigating the Influence of 

Cladding Defects on Burst Pressure,” ORNL/NRC/LTR-04/13, NRC Adams 

Number ML042660206, 2004. 

Bonaca 03 Bonaca, M.V., Chairman, Advisory Committee on Reactor Safeguards 

(ACRS), U.S. Nuclear Regulatory Commission, “Pressurized Thermal Shock 

(PTS) Reevaluation Project: Technical Bases for Potential Revision to PTS 

Screening Criteria,” February 21, 2003. 

Brothers 63 Brothers, A.J., and S. Yukawa, “The Effect of Warm Prestressing on Notch 

Fracture Strength,” Journal of Basic Engineering, March 1963, p. 97. 

Charpy Charpy, M.G., “Note sur l'Essai des Metaux à la Flexion par Choc de 

Barreaux Entailles,” Soc. Ing. Francais, June 1901, p. 848. 

Cheverton 85a Cheverton, R.D., et al., “Pressure Vessel Fracture Studies Pertaining to the 

PWR Thermal-Shock Issue: Experiments TSE-5, TSE-5A, and TSE-6,” 

NUREG/CR-4249 (ORNL-6163), Oak Ridge National Laboratory, June 

1985. 

Cheverton 85b Cheverton, R.D., et al., Pressure Vessel Fracture Studies Pertaining to the 

PWR Thermal-Shock Issue: Experiment TSE-7,” NUREG/CR-4303 

(ORNL-6177), Oak Ridge National Laboratory, August 1985. 

Chopra 06 Chopra, O.K., et al., “Crack Growth Rates of Irradiated Austenitic Stainless 

Steel Weld Heat Affected Zone in BWR Environments,” NUREG/CR-6891, 

U.S. Nuclear Regulatory Commission, January 2006. 

Congleton 85 Congleton, J., T. Shoji, and R.N. Parkins, “The Stress Corrosion Cracking of 

Reactor Pressure Vessel Steel in High-Temperature Water” Corrosion 

Science, Vol. 25, No. 8/9: 1985. 

CSAU Boyack, B., et al., “Quantifying Reactor Safety Margins – Application of 

Code Scaling, Applicability, and Uncertainty Evaluation Methodology to a 

Large-Break Loss of Coolant Accident,” NUREG/CR-5249, U.S. Nuclear 

Regulatory Commission, December 1989. 

Dhooge 78 A. Dhooge, R.E. Dolby, J. Sebille, R. Steinmetz, and A.G. Vinckier, 

“A Review of Work Related to Reheat Cracking in Nuclear Reactor Pressure 

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BIBLIOGRAPHIC DATA SHEET

(See instructions on the reverse)

NRC FORM 335

(9-2004)

NRCMD 3.7

U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT NUMBER

 (Assigned by NRC, Add Vol., Supp., Rev.,

 and Addendum Numbers, if any.)

NUREG-1806, Vol.1

3. DATE REPORT PUBLISHED

MONTH

August

YEAR

2007

4. FIN OR GRANT NUMBER

2. TITLE AND SUBTITLE

Technical Basis for Revision of the Pressurized Thermal Shock (PTS) Screening Limit in the

PTS Rule (10 CFR 50.61): Summary Report

5. AUTHOR(S)

Mark EricksonKirk, Mike Junge, William Arcieri, B. Richard Bass, Robert Beaton, David

Bessette, T.H.(James) Chang, Terry Dickson, C. Don Fletcher, Alan Kolaczkowski, Shah Malik,

Todd Mintz, Claud Pugh, Fredric Simonen, Nathan Siu, Donnie Whitehead, Paul Williams, Roy

Woods, Sean Yin

6. TYPE OF REPORT

Technical

7. PERIOD COVERED (Inclusive Dates)

6-99 to 6-06

8. PERFORMING ORGANIZATION - NAME AND ADDRESS (If NRC, provide Division, Office or Region, U.S. Nuclear Regulatory Commission, and mailing address; if contractor,

Division of Fuel, Engineering, and Radiological Research

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, 

Division of Fuel, Engineering, and Radiological Research

provide name and mailing address.)

and mailing address.)

10. SUPPLEMENTARY NOTES

M. EricksonKirk, NRC Project Manager

11. ABSTRACT (200 words or less)

During plant operation, the walls of reactor pressure vessels (RPVs) are exposed to neutron radiation, resulting in localized

embrittlement of the vessel steel and weld materials in the core area. If an embrittled RPV had a flaw of critical size and certain

severe system transients were to occur, the flaw could very rapidly propagate through the vessel, resulting in a through-wall

crack and challenging the integrity of the RPV. The severe transients of concern, known as pressurized thermal shock (PTS),

are characterized by a rapid cooling of the internal RPV surface in combination with repressurization of the RPV. Advancements

in our understanding and knowledge of materials behavior, our ability to realistically model plant systems and operational

characteristics, and our ability to better evaluate PTS transients to estimate loads on vessel walls led the NRC to realize that the

earlier analysis, conducted in the course of developing the PTS Rule in the 1980s, contained significant conservatisms.

This report summarizes 21 supporting documents that describe the procedures used and results obtained in the probabilistic risk

assessment, thermal hydraulic, and probabilistic fracture mechanics studies conducted in support of this investigation. 

Recommendations on toughness-based screening criteria for PTS are provided.

12. KEY WORDS/DESCRIPTORS (List words or phrases that will assist researchers in locating the report.)

pressurized thermal shock, probabilistic fracture mechanics, nuclear reactor pressure vessel

pressurized water reactor 14. SECURITY CLASSIFICATION

13. AVAILABILITY STATEMENT

unlimited

(This Page)

unclassified

(This Report)

unclassified

15. NUMBER OF PAGES

16. PRICE

NRC FORM 335 (9-2004) PRINTED ON RECYCLED PAPER

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001