ML24162A131
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| Issue date: | 06/24/2024 |
| From: | Matthew Homiack, Nellis C NRC/RES/DE |
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| Christopher Nellis 3014155973 | |
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| NRR-2021-008 TLR-RES/DE/REB?2024-08 | |
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Technical Letter Report TLR-RES/DE/REB2024-08 Probabilistic Fracture Mechanics Analysis of French Stress Corrosion Cracking Operating Experience Applied to the US Fleet using the Extremely Low Probability of Rupture Code Date:
June 04, 2024 Prepared in response to Task 6 in User Need Request NRR-2021-008, by:
Christopher Nellis U.S. Nuclear Regulatory Commission Matthew Homiack U.S. Nuclear Regulatory Commission Division of Engineering Office of Nuclear Regulatory Research U.S. Nuclear Regulatory Commission Washington, DC 20555-0001
ii DISCLAIMER This report was prepared as an account of work sponsored by an agency of the U.S. Government.
Neither the U.S. Government nor any agency thereof, nor any employee, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for any third party's use, or the results of such use, of any information, apparatus, product, or process disclosed in this publication, or represents that its use by such third party complies with applicable law.
iii This report does not contain or imply legally binding requirements. Nor does this report establish or modify any regulatory guidance or positions of the U.S. Nuclear Regulatory Commission and is not binding on the Commission.
iv EXECUTIVE
SUMMARY
Unexpected stress corrosion cracking (SCC) was found during routine inspections of the emergency core cooling systems in some French pressurized water reactors (PWRs). More rigorous inspections performed afterwards from the French authorities revealed more instances of cracking. Though this phenomenon has not been observed in the United States (US), the Nuclear Regulatory Commission (NRC) staff initiated an effort to evaluate the risks to the US PWR fleet. The NRC staff initiated an analysis following the process in NRC Office of Nuclear Reactor Regulation (NRR) Office Instruction LIC504, Revision 5, Integrated Risk-Informed Decision-Making Process for Emergent Issues, that quantifies risk for emergent issues to plant safety and makes recommendations for possible NRC actions to mitigate the risk, if required. As part of that effort, NRC staff in the Office of Nuclear Regulatory Research performed probabilistic fracture mechanics analyses on a representative piping system using the Extremely Low Probability of Rupture (xLPR) code. The results of these analyses are presented and discussed in this technical letter report.
A piping system was modeled to be representative of PWR systems thought to be susceptible to the SCC cracking found in the French PWR fleet. The geometry and material details came from an US Westinghouse four-loop PWR and applicable information from databases packed with the xLPR code. This baseline analysis incorporated several conservative assumptions. Chiefly, a crack was assumed to have existed from the onset of plant operation rather than initiating during service through a SCC mechanism. Also, because weld residual stress (WRS) is expected to have played a role in the French operating experience (OE), four scenarios were run with varying WRS profiles. A polynomial WRS profile was selected because it produced more through-wall cracks (TWCs) and ruptures. Results from the scenario with the most instances of small-break (SB) loss of coolant accident (LOCA) were used in the probabilistic risk assessment (PRA) conducted for NRRs LIC504 process. The baseline scenario results had very few SB LOCAs, and when leak rate detection was activated with a 0.063 kg/s (1.0 gpm) threshold, the most conservative SB LOCA initiating event frequency was 3.0x10-4 per calendar year (CY) at the plant-level after 80 CYs. No instances of medium-break (MB) and large-break (LB) LOCA were recorded in any of the 100,000 realizations by either the leak rate or crack opening area (COA) thresholds. There were also no surface crack ruptures (i.e., break-before-leak events).
The prevalence of long, shallow flaws found in the French piping systems prompted a sensitivity study on the crack aspect ratio. While LOCA probabilities did increase with larger aspect ratios, the increase was not drastic and was roughly within the same order of magnitude. For instance, a five-fold increase in the average baseline initial crack aspect ratio would only roughly double the SB LOCA probability. Only when the initial crack aspect ratio had an exceedingly large value, so that the crack length spanned half the inner circumference, did instances of MB and LB LOCA occur. The xLPR code was also used to simulate the effect of ultrasonic testing (UT) every 10 years in reducing the likelihood of LOCAs. If the 10-year inspections start at 8 CY, then the likelihood of SB LOCA was reduced by an order of magnitude after 40 CY. If the 10-year inspections start at 2 CY, then the likelihood of SB LOCA was reduced by an additional order of
v magnitude. These results underscore the importance of performance monitoring in early crack detection.
The probabilistic fracture mechanics (PFM) analyses found the probability of LOCA from the SCC found in the French PWR fleet was low in comparable US PWR piping systems without inspections. Sensitivity studies regarding the initial crack aspect ratio found a weak influence on the LOCA probabilities. Finally, the study found starting 10-year inspections early reduced the LOCA probabilities by an order of magnitude compared to later inspection start times.
The results of this study were used successfully for a LIC504 analysis to risk-inform an emergent possible safety issue for regulators. This effort marks the first regulatory application where the xLPR code has been used to develop initiating event frequencies as inputs for a PRA. Knowledge and experience gained from prior PFM analyses were leveraged to shorten the time for input set development and the computational time of the code. The success of this effort highlights the role of the xLPR code in providing insights to support risk-informed decision-making for performance and integrity of reactor piping systems.
vi ACKNOWLEDGMENTS The authors would like to thank Drs. Daivd Rudland and Robert Tregoning for their valuable experience and insights. This study benefited from their knowledge of the French operating experience and probabilistic fracture mechanics.
vii TABLE OF CONTENTS Executive Summary......................................................................................................................iv AcknowledgMENTS......................................................................................................................vi Table of Contents.........................................................................................................................vii List of Tables...............................................................................................................................viii List of Figures...............................................................................................................................ix Acronyms.......................................................................................................................................x 1
Introduction............................................................................................................................1 1.1 Background.....................................................................................................................1 1.2 The xLPR Code..............................................................................................................3 1.3 Objectives of this Study..................................................................................................3 2
Analysis Approach.................................................................................................................4 2.1 Piping System Description..............................................................................................4 2.2 Project Team...................................................................................................................4 2.3 Quantities of Interest.......................................................................................................4 2.3.1 LOCA Probabilities..................................................................................................4 2.3.2 Conditional LOCA Initiating Event Frequencies.......................................................5 2.4 xLPR Simulation Procedure............................................................................................6 2.5 Computational Platforms and Simulation Execution Strategy.........................................6 3
Analyses.................................................................................................................................8 3.1 Scope..............................................................................................................................8 3.2 Baseline Analysis............................................................................................................9 3.3 Aspect Ratio Sensitivity Study......................................................................................13 3.4 Impact of Inspections with Long Flaws.........................................................................14 4
Analysis Assumptions..........................................................................................................16 5
Summary and Conclusions..................................................................................................18
viii LIST OF TABLES Table 2.1 LOCA Thresholds used in the xLPR Code Simulations................................................5 Table 3.1 Summary of xLPR Analyses by Key Simulation Inputs.................................................8 Table 3.2 Conditional LOCA Initiating Event Frequency Estimates based on xLPR Simulation Results for 20 SIS Welds Subject to Stress Corrosion Cracking................................................13
ix LIST OF FIGURES Figure 3.1 WRS Profiles..............................................................................................................10 Figure 3.2 Probability of LOCA at or above SB LOCA for Each WRS Profile.............................11 Figure 3.3 Probability of LOCA at or above SB LOCA by leak rate and COA models................12 Figure 3.4 Probability of LOCA at or above SBLOCA by Aspect Ratio.......................................13 Figure 3.5 Relative Risk Reduction of LOCA at and above SB LOCA Threshold with Inspections
....................................................................................................................................................15
x ACRONYMS ASME American Society of Mechanical Engineers CSN Spanish Nuclear Safety Council CY Calendar Year COA Crack Opening Area ECCS Emergency Core Cooling System EDF
Électricité de France EPRI Electric Power Research Institute GDC General Design Criteria ID Inside Diameter IGSCC Intergranular Stress Corrosion Cracking ISI Inservice Inspection LB Large-Break LOCA Loss of Coolant Accident MB Medium-Break NDE Nondestructive Examination OE Operating Experience PRA Probabilistic Risk Assessment PWR Pressurized Water Reactor PWROG Pressurized Water Reactor Owners Group PWSCC Primary-Water Stress Corrosion Cracking QoI Quantity of Interest SB Small-Break SIS Safety Injection System SCC Stress Corrosion Cracking TWC Through-Wall Crack UT Ultrasonic Testing WRS Weld Residual Stress xLPR Extremely Low Probability of Rupture
1 1
INTRODUCTION
1.1 Background
During a typical inservice inspection (ISI) on October 21, 2021, at Civaux Unit 1 (a 4-loop, 1450 MW pressurized water reactor (PWR)) in France, Électricité de France (EDF) found circumferential cracking at several locations near an elbow in the emergency core cooling system (ECCS). The maximum depth of the cracking was 5.6 mm (0.22 inch) and, in one case, extended all the way around the inside circumference of the pipe. EDF also found similar cracking at Civaux Unit 2 and Chooz Unit 2. On November 13, 2021, it was reported that cracking, less severe than the others, was found in EDF's Penly Unit 1 (a 4 loop, 1300 MW PWR) during a routine inspection in the safety injection system (SIS) piping near the cold leg. The SIS piping is about 300 mm (12 inches) in diameter with a 30-mm (1.2-inch) wall thickness. These lines are typically stagnant, but some circulation occurs in these sections of the SIS due to the proximity of the piping to both the hot and cold leg reactor coolant piping. The locations of the flaws were in a non-isolable section of the piping system that is susceptible to thermal fatigue. In most cases, the cracks were long, but very shallow. The maximum depth was about 5.6 mm (0.22 inch). Through destructive examination, EDF determined that the root cause of the cracking was intergranular stress corrosion cracking (IGSCC) caused by stresses associated with thermal stratification. Weld residual stress (WRS) may have also played a role in the cracking. Most of the cracking occurred in reactors designed by Westinghouse and modified by Framatome.
Because of these indications, inspections were expanded to all the ECCS and residual heat removal (RHR) systems in operating French PWRs. Because of the expanded inspections, over 400 welds were inspected either by destructive testing or by updated NDE procedures that were better suited for both detection and sizing of cracks caused by IGSCC. From this expanded inspection program, over 100 flaws* were found at a variety of locations in the RHR and ECCS piping. In most cases, the cracks were long, but very shallow. The maximum depth was about 6.5 mm (0.26 inch), and the average depth was around 1.5 mm (0.06 inch). In addition to the shallow flaws, EDF also found an 85 % deep,152 mm (6-inch)-long circumferential crack in a non-isolable location in the SIS piping of Penly Unit 1 near the hot leg at a location where the thermal stratification loads found in the other locations was not expected. Even though it was believed that this cracking was due to pre-service weld repairs, and the piping was forced into place during fit-up (i.e., highly restrained), which induces stresses at this location, the size and location of this flaw raises questions about the safety impact.
In response to this international operating experience (OE), the Electric Power Research Institute (EPRI) and the Pressurized Water Reactor Owners Group (PWROG) created a focus group to study the issue, understand its applicability to the US fleet, and make any needed
- Per ASN, most of the flaws were found at locations of high thermal stratification loads, but some were found at locations of weld repairs.
2 recommendations. The focus group had two goals: (1) develop a safety assessment to determine the potential safety impact of the OE on the US industry, and (2) develop an applicability assessment for the US fleet. The PWROG has drafted PWROG23007NP, Revision 0, Safety Assessment of Recent Atypical Stress Corrosion Cracking Operating Experience in Non-Isolable Stainless Steel Branch Piping[1]. This report concludes that the observed, atypical IGSCC OE does not represent a significant safety concern for the PWROG members based on the likelihood and consequences of such flaws. However, an IGSCC-specific volumetric inspection method is recommended to address this OE. The PWROG applicability assessment is still underway and is expected to be soon.
As an example of the international response to the French OE, the Spanish Nuclear Safety Council (CSN) asked its licensees to analyze the OE and send their conclusions to the CSN. The Spanish licensees reported that the OE had been reviewed and specific inspections at the areas of interest had been conducted. The nondestructive examination (NDE) techniques used were qualified per the Spanish CEX-120, NDE-ISI Qualification Methodology [2] approved by the CSN and based on the European Network for Inspection Qualification for the detection and length-sizing of flaws in austenitic stainless steel pipes caused by IGSCC and thermal fatigue. The Spanish licensees used a criterion for selection that included similar size, location, and function as the locations that were degraded in the French plants. They also included some areas with weld repairs. Inspections were conducted at six plants in 49 areas, and no reportable defects were found. In addition, there has been similar inspections and results from plants in the United Kingdom, Belgium, the Netherlands, and Switzerland.
To address this issue for the US fleet, the NRC staff performed a quantitative risk-informed analysis in accordance with Office of Nuclear Reactor Regulation (NRR) Office Instruction LIC-504, Revision 5, Integrated Risk-Informed Decision-Making Process for Emergent Issues
[3]. The purpose of the LIC504 process is to present risk-informed options to disposition emergent safety issues and document the bases of those decisions. Under the process, the NRC staff first determines if immediate action is needed and, if not, a few options are considered that could resolve the issue and the risks associated with each option are analyzed.
The process does not determine which option to take, but it does make a recommendation based on the results of the analyses.
The final report on the LIC504 analyses on the implications of the French operating experience with SCC was published in September 2023 [4]. The NRC staff used the Extremely Low Probability of Rupture (xLPR) computer code to perform probabilistic fracture mechanics (PFM) simulations to inform a probabilistic risk assessment (PRA) of the potential additional risks incurred by this degradation mechanism. It was found that the increase in risk for the US PWR fleet from SCC in these weld types was very low and acceptable even if no NRC action was taken. It was recommended that the NRC staff continue to monitor industry actions in response to the SCC issue, including any changes in their inspections procedures. The present technical letter report provides details on the PFM analyses that were performed for that work.
3 1.2 The xLPR Code The xLPR code was codeveloped by the NRC and EPRI to perform PFM studies on nuclear piping systems that are subject to degradation mechanisms such as fatigue and stress corrosion cracking. For each realization, the xLPR code can track crack growth from initiation to rupture using a suite of deterministic state-ofpractice models. The code can also model methods of crack detection such as leak detection and periodic ultrasonic tests (UTs). A full accounting of the xLPR codes capabilities is given in NUREG-2247, Extremely Low Probability of Rupture Version 2 Probabilistic Fracture Mechanics Code [5].
1.3 Objectives of this Study To support the NRC Office of Nuclear Reactor Regulations LIC504 evaluation, the primary objectives of the PFM analyses were threefold:
1.
Use the xLPR code to generate numerical LOCA initiating event annual frequency estimates with uncertainties for welds in a PWR piping system representative of the ECCS systems found in the US PWR fleet that may be susceptible to cracking like found in the French PWR fleet.
2.
Use the LOCA probabilities to develop an annual piping system LOCA initiating event frequencies for use as an input to a PRA.
3.
Conduct sensitivity studies on the impact of different initial crack size characteristics and UT schedules.
To the support these objectives, several quantities of interest (QoIs) produced by the xLPR code were considered as follows:
LOCA Probability with Leak Rate Detection - This QoI estimates the probability of a LOCA occurring after a given period of plant operation conditional on leak rate detection.
Small-break (SB), medium-break (MB), and large-break (LB) LOCAs were all considered for both the leak rate and crack opening area LOCA threshold definitions.
LOCA Probability with Leak Rate Detection and InService Inspection (ISI) - This QoI estimates the probability of a LOCA occurring after a given period of plant operation conditional on leak rate detection and ISI. SB, MB, and LB LOCAs were all considered for both the leak rate and crack opening area LOCA threshold definitions.
Probability of surface crack rupture - This QoI estimates the probability of a break-before-leak occurring after a given period of plant operation.
4 2
ANALYSIS APPROACH 2.1 Piping System Description The piping systems of interest in this study are the SISs in PWRs in the non-isolable region between the hot leg and the first containment isolation valve. The cracks found by EDF were typically between the cold leg and the first containment isolation valve; however, the large crack found in Penly Unit 1 was between the hot leg and the first containment isolation valve. A representative butt-weld in such a piping system was analyzed using the xLPR code based on details from Byron Station, Units 1 and 2, and Braidwood Stations, Units 1 and 2 [6]. The piping material is 316 stainless steel with an outside diameter of 273.05 mm (10.75 inches) and a wall thickness of 25.4 mm (1 inch).
2.2 Project Team The LIC504 evaluation was planned and conducted as a joint effort between NRR and the Office of Nuclear Regulatory Research (RES). The PFM analyses using the xLPR code were conducted by the RES staff with the results and conclusions reviewed by the NRR staff.
2.3 Quantities of Interest 2.3.1 LOCA Probabilities When the rate of water leaking from a cracked pipe exceeds a certain threshold, the reactors ability to cool itself degrades. For distinguishing when a LOCA has occurred, the xLPR code supports two definitions of a LOCA. The first definition is directly determined from the leak rate caused by the through-wall crack. The second definition characterizes a LOCA by the crack opening area corresponding to an equivalent piping break size that would result in a LOCA.
Because the leak rate calculations are based on the crack opening area, the main difference between the two definitions is that the first uses the leak rate model, whereas the second does not. This study used the LOCA by leak rate definition both because it is based on the more realistic leak rate model calculations that consider the thermodynamics of the pipe break, and as a conservative approach because it led to higher LOCA frequencies.
Table 2.1 shows the LOCA thresholds used in the xLPR code simulations. The LOCA category distinctions between SB, MB, and LB LOCAs were drawn from Table 3.2 in NUREG-1829, Estimating Loss-of-Coolant Accident (LOCA) Frequencies Through the Elicitation Process [7].
The equivalent nominal pipe break sizes corresponding to the crack opening areas for SB, MB, and LB LOCAs in Table 2.1 are 12.7, 38, and 76 mm (0.5, 1.5, and 3-inches) in diameter, respectively.
5 Table 2.1 LOCA Thresholds used in the xLPR Code Simulations SBLOCA MBLOCA LBLOCA Leak Rate Definition lpm (gpm) 378.5 (100) 5,678 (1,500) 18,927 (5,000)
Crack Opening Area Definition mm2 (in2) 94 (0.146) 1,408 (2.183) 4,695 (7.278) 2.3.2 Conditional LOCA Initiating Event Frequencies 2.3.2.1 Estimates with Recorded Failures The xLPR code will give the mean LOCA probabilities,, for a single weld in the form of the number of failures (i.e., undesirable events) at a given time divided by the total number of realizations. The failure probability is converted to an annual frequency by dividing by the elapsed time in CY as detailed in TLR-RES/DE/REB-2021-09, Probabilistic Leak-Before-Break Evaluation of Westinghouse Four-Loop Pressurized-Water Reactor Primary Coolant Loop Piping using the Extremely Low Probability of Rupture Code [8], Section 4. The initiating event frequency,, for this mechanism at the plant-level can then be determined by multiplying the annual frequency by the total number of welds,, in the piping system that may be subject to the degradation mechanism as shown in Equation 1. Confidence intervals,, for 100(1-
) percent confidence can be constructed from the standard error of the binomial proportion,,
as show in Equation 2, where /2 is the standard score. This report used 95 % confidence intervals.
=
x
Equation 1
=
/2 x x
Equation 2 2.3.2.2 Estimates with No Recorded Failures When a Monte Carlo simulation does not record any instances of failure, the probability of failure is not zero. NUREG/CR-7278, Technical Basis for the use of Probabilistic Fracture Mechanics in Regulatory Applications [9], Section 4.3.6.4, describes a method of estimating the mean probability based on the sample size within desired confidence bounds and is briefly defined in Equation 3.
6
= 1 1
Equation 3 Here, is the number of realizations, and is the estimated one-sided confidence interval below which there is a 100(1- )% confidence that the true probability is below that threshold.
2.4 xLPR Simulation Procedure The xLPR code was run from the epistemic loop for enough realizations to detect failure events occurring at an annual frequency as low as 106/yr. Some of the analyses differed in the simulated length of time based on the computational needs; however, all analyses conformed to this requirement.
All cases were run with the xLPR code in 10 batches of 10,000 realizations rather than a single batch of 100,000 realizations due to computational memory limitations of the xLPR model in GoldSim for large simulations. A 1-month time step was used; however, the simulation results were only saved at 20-year intervals up to 80 CY or at 5-year intervals up to 40 CY. Each batch initiated xLPRs random number generator with a distinct random seed to ensure that all realizations had a unique sample of the probabilistic parameters. A table of the random seeds per replicate for each case is provided in Appendix A10. Results from the 10 batches were compiled and statistical information on the QoIs was extracted.
2.5 Computational Platforms and Simulation Execution Strategy All the analyses were executed on the computational platforms below.
xLPR Version 2.2 Random-access Memory 32.0 GB Central Processing Unit Intel Xeon Platinum 8259CL
@2.5GHz CPUs 16 Operating System Windows Server 2016
7 GoldSim License GoldSim with Distributed Processing Plus module GoldSim Version 12.1
8 3
ANALYSES 3.1 Scope The scope of the xLPR analyses consisted of nine scenarios modeled by xLPR, which are summarized in Table 3.1. Scenarios 1 through 4 modeled different WRS profiles that varied in magnitude and functional form. After comparing the results from these four scenarios, Scenario 2 was selected as the baseline scenario whose results would be used in the PRA described in the NRR LIC504 report [4]. All subsequent sensitivity analyses (i.e., Scenarios 5 through 9) used the same WRS profile as the baseline scenario. Scenarios 5 through 7 evaluated the effects of different crack aspect ratios on the QoIs in comparison to those from the baseline scenario. Lastly, Scenarios 8 and 9 modeled potential long, shallow flaws and incorporated different ISI schedules ISI to gauge their effects on reducing LOCA and rupture probabilities.
Table 3.1 Summary of xLPR Analyses by Key Simulation Inputs Scenario No.
WRS Profile Mean Aspect Ratio (2c/a)
Leak Detection Capability ISI Schedule Operating Time 1
Linear, 276 MPa (40 ksi) at inside diameter (ID) 3.2:1 0.063 kg/s (1.0 gpm)
None 80 CY 2
Polynomial, 276 MPa (40 ksi) at ID 3.2:1 0.063 kg/s (1.0 gpm)
None 80 CY 3
Linear, 207 MPa (30 ksi) at ID 3.2:1 0.063 kg/s (1.0 gpm)
None 80 CY 4
Polynomial, 207 MPa (30 ksi) at ID 3.2:1 0.063 kg/s (1.0 gpm)
None 80 CY 5
Polynomial, 276 MPa (40 ksi) at ID 4:1 0.063 kg/s (1.0 gpm)
None 80 CY 6
Polynomial, 276 MPa (40 ksi) at ID 10:1 0.063 kg/s (1.0 gpm)
None 80 CY 7
Polynomial, 276 MPa (40 ksi) at ID 20:1 0.063 kg/s (1.0 gpm)
None 80 CY 8
Polynomial, 276 MPa (40 ksi) at ID 233:1 0.063 kg/s (1.0 gpm) 0.1/year beginning at 2 years 40 CY 9
Polynomial, 276 MPa (40 ksi) at ID 233:1 0.063 kg/s (1.0 gpm) 0.1/year beginning at 8 years 40 CY
9 3.2 Baseline Analysis The input set for the baseline analysis was modified from the input set for Case 1, Scenario 3 described in the xLPR Inputs Group Report [10]. The full list of modifications is recorded in APPENDIX A.
Leak and rupture events are particularly sensitive to the WRS that remains in a weld from the joining process. The WRS profile for all analyses in this study was selected based on American Society of Mechanical Engineers (ASME) recommendations for stainless steel welds [11]. An ASME task group collected empirical data of axial WRS profiles in stainless steel pipes of various sizes and developed suggested equations based on pipe diameter, wall thickness, and stress at the inner surface,. The recommended axial WRS profiles,, based on pipe wall thickness,, and crack depth,, are as follows:
() =
(1 2(
)), < 1.
(1 6.91
+ 8.69
2 0.48
3 2.03
4
), 1 Equation 4 The ASME task group noted that the 1-inch wall thickness threshold was not meant to be a precise interval, so there is some uncertainty as to which profile to select for pipes at or near this thickness, like the ones in the system being modeled in this study. The value for was defined as 206.8 MPa (30 ksi) or 275.79 MPa (40 ksi), which is reflective of measurements for a 10-in diameter pipe from the same ASME task group [11]. To determine which WRS profile to use, four initial cases were run with the same the input set except for the WRS profile. Four combinations of functional form (i.e., linear or polynomial) or magnitude of stress at the inner diameter,, for the WRS profile are plotted in Figure 3.1.
10 Figure 3.1 WRS Profiles The polynomial WRS profile had more instances of rupture and would therefore be a more conservative selection. To reflect the uncertainty in the WRS profile, the WRS values at each depth are sampled from a normal distribution where the means are calculated from Equation 4 with a standard deviation of 57.9 MPa. This value bounds recommendations from the xLPR WRS subgroup [12] for axial WRS profiles.
The baseline analysis simulated 100,000 realizations of a crack in a representative system of SIS piping under operating conditions for a total of 80 CY. While the xLPR code can probabilistically model crack initiation, there is no validated model for IGSCC initiation for stainless steels in a PWR environment. Instead, a single circumferential flaw was assumed to exist at the onset of plant operation. The initial flaw length and depth were probabilistically sampled from distributions representative of PWSCC (another form of IGSCC in PWRs). Based on the mean values of 4.8 mm (0.19 inch) for the full flaw length 2, and 1.5 mm (0.06 inch) for the flaw depth, the aspect ratio, 2/, for the baseline analysis was 3.2:1.
Industry and regulators have not developed a consensus around a specific mathematical model for IGSCC growth rates in stainless steels in PWR environments. Instead, the analysis used a probabilistic crack growth model for PWSCC. PWSCC has been observed internationally in nickel-based alloy components and has been the subject of numerous investigations [13]. It is therefore expected to be a more aggressive degradation mechanism than IGSCC in a stainless steel pipe. While the simulated stainless steel pipe experiences the crack growth characteristics
-400
-300
-200
-100 0
100 200 300 400 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Scenario 1 Scenario 2 Scenario 3 Scenario 4 Weld Residual Stress (MPa)
Relative Through-Thickness Depth
11 of PWSCC seen in nickel-based alloy piping materials, the general material properties such as strength and toughness were representative of 316 stainless steel.
Figure 3.2 shows the probability of SB LOCA over time for each of the four WRS profiles seen in Figure 3.1. There were no instances of SB LOCA with 0.063 kg/s (1.0 gpm) leak rate detection and a linear WRS profile, while the scenarios with a polynomial WRS profile saw a few instances of SB LOCA. To promote conservatism in the analysis, Scenario 2, which had the highest SB LOCA probability after 80 CY, was selected to be the baseline scenario whose results would inform the PRA.
Figure 3.2 Probability of LOCA at or above SB LOCA for Each WRS Profile A typical PWR might have as many as 15 welds in the non-isolable SIS piping connected to the cold leg and 5 welds in the non-isolable SIS piping connected to the hot leg. Thus, there are 20 welds in a single piping loop, meaning a typical 4-loop PWR could have as many of 80 such welds. EDF inspected 400 such welds in their PWR fleet and found cracking to some degree in 25 % of the welds. Based on these results, the present analysis assumes that a quarter of the welds of this type in the SIS piping of a US PWR will also have flaws present. Thus, the conditional LOCA initiating event frequencies are estimated with Equation 1 assuming =
- 20. Table 3.2 shows the conditional LOCA frequencies defined by the leak rate definition in Table 2.1 when leak rate detection is enabled at 0.063 kg/s (1.0 gpm) converted to annual frequencies. The LOCA values from the xLPR code were lower by nearly an order of magnitude when the threshold for LOCA was defined in terms of COA as seen in Figure 3.3. When a non-
12 zero LOCA probability is recorded, the frequencies are estimated with 95 % confidence intervals using the standard error of the LOCA probability results.
Figure 3.3 Probability of LOCA at or above SB LOCA by leak rate and COA models Despite there being no instances of MB or LB LOCAs in all 100,000 realizations, the MB and LB LOCA frequencies cannot be assumed to be zero. Instead, an upper bound probability, where there is a 95 % confidence the true probability is below, is calculated from the sample size using the methods described in Section 2.3.2.2 and converted into a conditional initiating event frequency.
13 Table 3.2 Conditional LOCA Initiating Event Frequency Estimates based on xLPR Simulation Results for 20 SIS Welds Subject to Stress Corrosion Cracking Mean
>= SBLOCAlLD (1/CY)
Mean
>= MBLOCAlLD (1/CY)
Mean
>= LBLOCAlLD (1/CY) 20 CY 1.7 x 10-4
+/- 3.1 x 10-4
< 3.0 x 10-5
< 3.0 x 10-5 40 CY 2.7 x 10-4
+/- 2.6 x 10-4
< 1.5 x 10-5
< 1.5 x 10-5 60 CY 3.0 x 10-4
+/- 2.3 x 10-4
< 1.0 x 10-5
< 1.0 x 10-5 80 CY 3.0 x 10-4
+/- 2.0 x 10-4
< 7.5 x 10-6
< 7.5 x 10-6 3.3 Aspect Ratio Sensitivity Study Since the flaws found in the French PWRs were generally long but with shallow depths, the impact of varying the aspect ratio of the initial flaw was considered as a sensitivity study. The initial flaw depth distribution with the 1.5 mm (0.06 inch) average crack depth was kept while the initial flaw length was set to the sampled depth value multiplied by the intended aspect ratio.
The same xLPR simulation procedure of 10 batches of 10,000 realizations was run for aspect ratios of 3.2:1 (the baseline), 4:1, 10:1, and 20:1. Figure 3.4 shows the probability of SB LOCA by leak rate over time for the four aspect ratios. Even when the aspect ratio of the initial crack is 20:1, or approximately 5 times greater than the baseline aspect ratio, the probability of SBLOCA after 80 CY only roughly doubles.
Figure 3.4 Probability of LOCA at or above SBLOCA by Aspect Ratio
14 3.4 Impact of Inspections with Long Flaws An additional sensitivity study was conducted on a much longer assumed flaw that extends across 180-degrees of the inner pipe circumference. For this study, the length of the flaw was adjusted from the baseline analysis; however, the flaw depth was sampled from the same distribution as in the baseline analysis. A weld with such a long flaw at the onset of service would be substantially more likely to fail. Indeed, the subsequent xLPR analyses calculated the probability of LOCA at or above the SB LOCA lower threshold with leak rate detection but without UTs at approximately 86 % after only 40 years. The probability of a LOCA meeting MB LOCA leak rate criterion was 55 % with leak rate detection enabled at 40 years, though there were no instances of LB LOCA. However, the formation of such a long flaw undetected is highly unlikely. Such a flaw would likely form from the coalescence of multiple smaller flaws, and the probability of multiple flaws occurring in the same weld in a manner susceptible to coalesce with each other is several orders of magnitude lower than the formation of a single flaw [14]. These sensitivity analyses would not be used further in the PRA to quantify risks to the US fleet because PRA uses a best estimate approach. Rather, this long flaw case provides insights into the impact of additional inspections on aging management efforts as might be implemented if the NRC staff ultimately adopts Option 1 from the NRR LIC504 report [4] is pursued.
Two cases were run with UTs modeled on a 10-year interval. One case began the UTs at the 2 CY mark, so the UTs occurred at 12, 22, 32, etc. CYs. The other case began the UTs at the 8 CY mark, so the UTs occurred at 18, 28, 38, etc. CYs. With more realizations proceeding to rupture, more computational time and memory was required for these calculations. For efficiency, the plant operating time was reduced to 40 CY. The detectable event frequency still
15 falls under 106/ expectation. The NRC staff ran the xLPR code in 10 replicates of 10,000 realizations.
The UT detection and sizing model parameters were treated probabilistically based on the recommendations in EPRI MRP-262, Revision 3 [15], for the pressurizer surge line nozzle dissimilar metal weld configuration, which has a comparable geometry to the SIS stainless steel welds. See APPENDIX A for the precise values of the ISI parameters.
Figure 3.5 shows the relative reduction in the probability of SBLOCA from the 180-degree crack due to periodic UTs. By the 40 CY mark, the risk of SBLOCA declines nearly a full order of magnitude when the inspections begin at 8 CY. When UT inspections began at the 2 CY mark, the decline in risk more pronounced by another order of magnitude reduction. Both cases see SB LOCAs risks continually reduce with each subsequent inspection, although the magnitude of risk reduction declines with each interval before converging by the 40 CY mark. These results should not be interpreted as seeing diminishing returns on inspections, rather, they are more reflection on the presence of the flaw at initial plant operation. In an actual PWR, flaws could initiate at any time, and thus the need for ongoing UTs.
Figure 3.5 Relative Risk Reduction of LOCA at and above SB LOCA Threshold with Inspections
16 4
ANALYSIS ASSUMPTIONS Biases in the PFM analysis make the results upper bound estimates overall and thus conservative approximations. The PFM models retain the biases presented in the report on sources and treatment of uncertainties in the xLPR code [16]. The following assumptions contribute additional biases, which have been loosely ranked by magnitude from highest to lowest impact based on the NRC staffs engineering judgment:
The simulation included a pre-existing flaw of engineering scale size. This assumption is conservative for one weld because it ignores the incubation time required for crack initiation. As stated earlier, past work [14] suggests that the probability of PWSCC initiation at 40 years is approximately 1x10-3.
The method in which the component-level results were aggregated to estimate the plant-level initiating event frequencies is conservative because it assumes that all 20 susceptible welds have a pre-existing flaw at the same time.
The crack growth rates were bounded by assuming PWSCC growth rates with a lower-bound hydrogen water chemistry concertation of 25 cc/kg. This assumption is conservative because it leads to faster crack growth rates than would be expected in a stainless steel weld subject to stress corrosion cracking.
The SIS piping operates at either hot or cold leg temperatures depending on where it connects to the reactor coolant system; however, the xLPR code simulation used only a hot leg operating temperature, and the results were assumed to bound SIS components operating at cold leg temperatures. This approach is conservative because the crack growth rates are higher at higher operating temperatures.
A 100 percent plant capacity factor (e.g., 80 effective full power years) was assumed. This assumption is conservative because, due to outages, plants cannot practically achieve such a capacity.
Periodic, ultrasonic inspections were not modeled in the baseline analyses. Such inspections may detect cracks if they are performed on welds that are susceptible to stress corrosion cracking.
The normal operating loads represent elastically-calculated, design-basis values. This approach is a conservative because it over-estimates the actual applied loading.
The leak rate detection capability was assumed to be 3.8 lpm (1 gpm). Plant leakage detection systems can reliably detect lower leak rates and much more quickly than the 1-month time step used in the xLPR code simulation.
Seismic effects were not modeled in the analysis because they have been demonstrated in both NUREG-1903, Seismic Considerations for the Transition Break Size [17] and TLR-RES/DE/REB-2021-14R1, Probabilistic Leak-Before-Break Evaluations of Pressurized-Water Reactor Piping Systems using the Extremely Low Probability of Rupture Code [13] to generally have a small impact on large-bore piping rupture probabilities because of the flaw tolerance of the stainless steel piping. For instance, large flaws (greater than 30 % of wall thickness) subjected to rare, large-loading seismic events (less than 1x10-5 probability of exceedance) could be required to induce rupture.
17 While its difficult to qualify the level of bias in these analyses, the above points demonstrate that the level of bias can lead to LOCA frequency estimates that are conservative by several orders of magnitude. All other uncertainties were modeled explicitly in the xLPR code.
18 5
SUMMARY
AND CONCLUSIONS This study had three primary objectives:
1.
Use the xLPR code to generate numerical LOCA probabilities with uncertainties for welds in a representative US PWR ECCS that may be susceptible to cracking like EDF found in the French PWR fleet.
2.
Use the LOCA probabilities to develop an annual plant failure frequency for use in a PRA.
3.
Conduct sensitivity studies on the impact of crack size characteristics (i.e., aspect ratio) and ISI schedules.
For the xLPR analyses, inputs were developed for a representative stainless steel weld in a US PWR ECCS that could be susceptible to SCC. The geometry and material details came from an US Westinghouse four-loop PWR and applicable information from databases packed with the xLPR code. The baseline analysis incorporated several conservative assumptions. Chiefly, a crack was assumed to have existed from the onset of plant operation rather than initiating during service through an SCC mechanism. Also, because WRS is expected to have played a role in the French OE, four scenarios were run with varying WRS profiles. A polynomial WRS profile was selected because it produced more TWCs and ruptures. Results from the scenario with the most instances of leakage exceeding the SB LOCA lower threshold were used in the PRA conducted for NRRs LIC504 process. The baseline scenario results had very few SB LOCAs, and when leak rate detection was activated with a 0.063 kg/s (1.0 gpm) threshold, the most conservative SB LOCA initiating event frequency was 3.0 x 10-4 per CY at the plant-level after 80 CY. No instances of MB and LB LOCA were recorded in any of the 100,000 realizations by either the leak rate or COA thresholds. There were also no surface crack ruptures (i.e.,
break-before-leak events).
The prevalence of long, shallow flaws found in the French piping systems prompted a sensitivity study on the crack aspect ratio. While LOCA probabilities did increase with larger aspect ratios, the increase was not drastic and was roughly within the same order of magnitude. For instance, a five-fold increase in the average baseline initial crack aspect ratio would only roughly double the SB LOCA probability. Only when the initial crack aspect ratio had an exceedingly large value, so that the crack length spanned half the inner circumference, did instances of MB and LB LOCA occur. The xLPR code was also used to simulate the effect of UTs every 10 years in reducing the likelihood of LOCAs. If the 10-year inspections start at 8 CY, then the likelihood of SB LOCA was reduced by an order of magnitude after 40 CY. If the 10-year inspections start at 2 CY, then the likelihood of SB LOCA was reduced by an additional order of magnitude. This result underscores the importance of performance monitoring in early crack detection.
The PFM analyses found the probability of LOCA from the SCC found in the French PWR fleet was low in comparable US PWR piping systems without inspections. Sensitivity studies regarding the initial crack aspect ratio found a weak influence on the LOCA probabilities. Finally,
19 the study found starting 10-year inspections early reduced the LOCA probabilities by an order of magnitude compared to later inspection start times.
The results of this study were used successfully for a LIC504 analysis to risk-inform an emergent issue for regulators. This effort marks the first regulatory application where the xLPR code has been used to develop initiating event frequencies as inputs for a PRA. Knowledge and experience gained from prior PFM analyses were leveraged to shorten the time for input set development and the computational time of the code. The success of this effort highlights the role of the xLPR code in providing insights to support risk-informed decision-making for performance and integrity of reactor piping systems.
References
[1] PWROG-23007-NP, Revision 0, Safety Assessment of Recent Atypical Stress Corrosion Cracking Operating Experience in Non-Isolable Stainless Steel Branch Piping., Framatome Doc. No. 51-9357850-000, Apr. 2023.
[2] UNESA CEX-120, Qualification Methodology of NDE systems used in the In-service Inspection of Spanish NPPs, Apr. 2003.
[3] NRR Office Instruction LIC-504, Revision 5, Integrated Risk-Informed Decision-Making Process for Emergent Issues, Rockville, Maryland, Mar. 09, 2020. [Online]. Available:
ADAMS Accession No. ML19253D401
[4] NRC, Risk-informed Assessment of French Stress Corrosion Cracking Operational Experience Relative to US Fleet, Rockville, Maryland, Sep. 2023. [Online]. Available:
ADAMS Accession No. ML23236A080
[5] NRC NUREG-2247, Extremely Low Probability of Rupture Version 2 Probabilistic Fracture Mechanics Code, Aug. 2021. [Online]. Available: ADAMS Accession No. ML21225A736
[6] Sargent and Lundy, SL-4518, Leak-Before-Break Evaluation for Stainless Steel Piping Byron and Braidwood Nuclear Power Stations Units 1 and 2, May 12, 1989. [Online].
Available: ADAMS Accession No. ML20247L175
[7] R. Tregoning, L. Abramson, and P. Scott, Estimating Loss-of-Coolant Accident (LOCA)
Frequencies Through Expert Elicitation Process, Vol. 1, Rockville, Maryland, 2008.
[Online]. Available: ADAMS Accession No. ML080630013
[8] NRC,Technical Letter Report TLR-RES/DE/REB-2021-09, Probabilistic Leak-Before-Break Evaluation of Westinghouse Four-Loop Pressurized-Water Reactor Primary Coolant Loop Piping using the Extremely Low Probability of Rupture Code, Rockville, Maryland, 2021.
[Online]. Available: ADAMS Accession No. ML21217A088
[9] NRC NUREG/CR-7278, Technical Basis for the use of Probabilistic Fracture Mechanics in Regulatory Applications, Rockville, Maryland, 2022. [Online]. Available: ADAMS Accession No. ML22014A406
[10]M. Homiack, xLPR Group Report -- Inputs Group, Version 1.0, Dec. 19, 2017. [Online].
Available: ADAMS Accession No. ML19337B876
[11]A. C.Section XI Task Group for Piping Flaw Evaluation, Evaluation of Flaws in Austenitic Steel Piping, J. Press. Vessel Technol., vol. 108, no. 3, pp. 352-366, Aug. 1986, doi:
10.1115/1.3264797.
[12]F. W. Brust, xLPR Models Subgroup ReportWelding Residual Stresses, Version 1.0, Oct. 05, 2016. [Online]. Available: ADAMS Accession No. ML16341B049
[13]NRC, Technical Letter Report TLR-RES/DE/REB-2021-14-R1, Probabilistic Leak-Before-Break Evaluations of Pressurized-Water Reactor Piping Systems using the Extremely Low
20 Probability of Rupture Code, Apr. 2022. [Online]. Available: ADAMS Accession No. ML22088A006
[14]D. L. Rudland, Predicting Pipe Rupture Frequencies Using xLPR, in PVP2020, Volume 1:
Codes and Standards, Aug. 2020. doi: 10.1115/PVP2020-21080.
[15]EPRI, Materials Reliability Program: Development of Probability of Detection Curves for Ultrasonic Examination of Dissimilar Metal Welds (MRP-262, Revision 3): Typical PWR Leak-Before-Break Line Locations, Palo Alto, CA, 2017. [Online]. Available: EPRI Report No: 3002010988
[16]M. Erickson, xLPR Technical ReportSources and Treatment of Uncertainties, Version 2.0, Nov. 16, 2020. [Online]. Available: ADAMS Accession No. ML19337C165
[17]NRC NUREG-1903, Seismic Considerations for the Transition Break Size, Rockville, Maryland, 2008. [Online]. Available: ADAMS Accession No. ML080880140
[18]EPRI Materials Reliability Program Letter 2021-015, Transmittal of Applicability Assessment Guidance for Probability of Detection Curves, 2021. [Online]. Available:
ADAMS Accession No. ML21266A006
A-1 APPENDIX A Analysis Inputs A1 Scenario 2 The input set for Scenario 2, which served as the baseline scenario in this study, was developed by modifying the input set for Case 1, Scenario 3 as described in the xLPR Inputs Group Report
[10]. The specific modifications are described in the following table.
Global ID Name Value/
Distribution Parameters Units Basis 0001 Plant Operation Time 960 months (mon)
Equivalent to 80 EFPY, which accounts for a subsequent license renewal term 0003 Crack Orientation 1
Only circumferential cracks are modeled, because the cracks found in the French PWRs were circumferentially oriented 0203 DM/SM weld indicator 1
The pipe base and weld materials are all stainless steel (i.e., a similar metal weld).
0402 Period End Time (Op Period #1) 961 mon Set to model one operating period 0405 Period End Time (Op Period #2) 962 mon Set to model one operating period 0403 Input Type Choice (Op Period #1) 2 Input stress instead of loads to avoid the Known Error, Error in the operating load calculations described in the xLPR V2.2 User Manual 0501 Crack Initiation Type Choice 0
Preexisting flaw assumed 0808-0808.10 Inspection Months 1-10 (Pre-Mitigation) 961 mon Disable inspections because they were not modeled in this scenario
A-2 Global ID Name Value/
Distribution Parameters Units Basis 0902 max time between 2 check - single SC - CC 1
mon 0904 max time between 2 check - single TWC - CC 1
mon 0906 max time between 2 check - multi SC - CC 1
mon 0908 max time between 2 check - single SC - AC 1
mon 0910 max time between 2 check - single TWC - AC 1
mon Set to enable stability checks in every time step 1001 Effective Full Power Years (EFPY) 960 mon Assumes a 100 % plant capacity factor 1101 Pipe Outer Diameter 0.273050 meters (m)
Outside diameter for representative Westinghouse four-loop PWR 10-inch safety injection system piping from SL-4518 [6],
Table 4-2 (10.75 inches converted to m) 1102 Pipe Wall Thickness 0.0254 m
Pipe wall thickness for representative Westinghouse four-loop PWR 10-inch safety injection system piping from SL-4518 [6],
Table 4-2 (1.0 inches converted to m) 1209 Number of Flaws (Circ) 1 Assumed a single, preexisting flaw 1210 Initial Flaw Full-Length (Circ)
Lognormal (1, 4.8E3, 2.226) m 1211 Multiplier Starting Full-Length (Circ) 1 1212 Initial Flaw Depth (Circ)
Lognormal (1, 1.5E3, 1.419) m Flaw of engineering scale size caused by PWSCC.
These flaw size parameters are consistent with the recommendations for PWSCC-initiated flaws as described in the xLPR Inputs Group Report [10]
for Case 1, Scenario 3.
A-3 Global ID Name Value/
Distribution Parameters Units Basis 1213 Multiplier Starting Depth (Circ) 1 3002 Unmitigated H2 Level 25 Cc/kg Conservative lower bound hydrogen concentration for PWSCC growth model as documented in TLR-RES-DE-REB-2021-14R1 [13],
Section B1 3101 Operating Pressure 16.07858032 MPa Highest pressure for representative Westinghouse four-loop PWR 10-inch safety injection system piping from SL-4518 [6], Table 4-2 (2332 psia converted to MPa).
3102 Operating Temperature 291.666667 C
Highest temperature for representative Westinghouse four-loop PWR 10-inch safety injection system piping from SL-4518 [6],
Table 4-2 (557 °F a converted to °C).
4001-4004 Earthquake Probability 0
1/yr 4002 Earthquake Total Membrane 0
MPa 4003 Earthquake Inertial Bending 0
MPa 4004 Earthquake Anchor Bending 0
MPa No earthquakes modeled consistent with analysis assumptions described in Section 4 4101-4108 Operating loads for period 1 0
Various Not used because input by stresses specified in Global ID 0403 Mean Std.
Dev.
Pre-mitigation axial WRS 275.790 2908 57.9 MPa ASME recommendations
[11] for stainless steel welds greater than or equal to 1-inch in
A-4 Global ID Name Value/
Distribution Parameters Units Basis 203.386 5371 57.9 138.581 061 57.9 81.2714 3261 57.9 31.3208 2466 57.9 11.4419 8758 57.9 47.2226 263 57.9 76.2611 1112 57.9 98.8318 5912 57.9 115.243 6848 57.9 125.839 8002 57.9 130.997 8147 57.9 131.129 7351 57.9 126.681 9658 57.9 118.135 3085 57.9 thickness and using an ID surface stress of 275.79 MPa (40 ksi), which is reflective of measurements for a 10-inch diameter pipe from the same ASME recommendations.
A-5 Global ID Name Value/
Distribution Parameters Units Basis 106.004 9625 57.9 90.8405 2436 57.9 73.2259 8823 57.9 53.7797 4565 57.9 33.1545 8563 57.9 12.0376 9461 57.9 8.84934 3514 57.9 28.7505 474 57.9 46.8755 3826 57.9 62.3995 3986 57.9 74.4633 7851 57.9 4121 Membrane Stress (DW) 0.225094216647 584 MPa 4122 Maximum Bending Stress (DW) 0.710682219629 296 MPa 4123 Membrane Stress (Thermal) 3.601507466361 34 MPa 4124 Bending Stress (Thermal) 99.44324172328 8
MPa Deterministic stress values calculated from the load and geometry information in SL-4518 [6], Table 4-2, for representative Westinghouse four-loop PWR 10-inch safety injection system piping.
A-6 Global ID Name Value/
Distribution Parameters Units Basis
- 2101, 2301, 2501 Yield Strength, Sigy Lognormal (0,197,53.86)
Min: 102 Max: 355 MPa
- 2102, 2302, 2502 Ultimate Strength, Sigu Lognormal (0,440,66.5)
Min: 273 Max: 617 MPa
- 2105, 2305, 2505 Elastic Modulus, E Normal (176600, 26500)
Min: 150110 Max: 203090 MPa
- 2106, 2306, 2506 Material Init J-Resistance, Jic Normal (1182, 612)
Min: 175 Max: 2605 N/mm
- 2107, 2307, 2507 Material Init J-Resist Coef, C Normal (335.1, 113)
Min: 117 Max: 615.9 N/mm
- 2108, 2308, 2508 Material Init J-Resist Exponent, m Normal (0.728, 0.155)
Min: 0.2 Max: 1.0 Correl.
2101-
- 2102, Correl.
2301-
- 2302, Correl.
2501-2502 Correlation between Yield Strength, Sigy and Ultimate Strength, Sigu General material property inputs for 316 stainless steel from the xLPR Inputs Group Report [10],
Appendix C, Section 4.3.
Per SL-4518 [6],
Table 4-2, the material corresponding with the highest temperature and highest operating pressure location for representative Westinghouse four-loop PWR 10-inch safety injection system piping is SA376 TP316 (i.e., a specific grade of 316 stainless steel).
A-7 Global ID Name Value/
Distribution Parameters Units Basis Correl.
2106-
- 2107, Correl.
2306-
- 2307, Correl.
2506-2507 Correlation between Material Init J-Resistance, Jic and Material Init J-Resist Coef, C A2 Scenario 1 The input set for Scenario 1 was developed based on the input set for Scenario 2 with the modifications described in the following table.
Global ID Name Value/
Distribution Parameters Units Basis Mean Std.
Dev.
275.790 3
57.9 253.727 1
57.9 231.663 8
57.9 209.600 6
57.9 187.537 4
57.9 165.474 2
57.9 143.411 57.9 121.347 7
57.9 Pre-mitigation axial WRS 99.2845 57.9 MPa ASME recommendations
[11] for stainless steel welds less than 1-inch in thickness and using an ID surface stress of 275.79 MPa (40 ksi), which is reflective of measurements for a 10-inch diameter pipe from the same ASME recommendations.
A-8 Global ID Name Value/
Distribution Parameters Units Basis 77.2212 8
57.9 55.1580 6
57.9 33.0948 3
57.9 11.0316 1
57.9
-11.0316 57.9
-33.0948 57.9
-55.1581 57.9
-77.2213 57.9
-99.2845 57.9
-121.348 57.9
-143.411 57.9
-165.474 57.9
-187.537 57.9
-209.601 57.9
-231.664 57.9
-253.727 57.9
-275.79 57.9 A3 Scenario 3 The input set for Scenario 3 was developed based on the input set for Scenario 2 with the modifications described in the following table.
Global ID Name Value/
Distribution Parameters Units Basis Mean Std.
Dev.
Pre-mitigation axial WRS 206.842 7
57.9 MPa ASME recommendations
[11] for stainless steel welds less than 1-inch in thickness and using an ID
A-9 Global ID Name Value/
Distribution Parameters Units Basis 190.295 3
57.9 173.747 9
57.9 157.200 5
57.9 140.653 57.9 124.105 6
57.9 107.558 2
57.9 91.0108 57.9 74.4633 8
57.9 57.9159 6
57.9 41.3685 4
57.9 24.8211 3
57.9 8.27370 9
57.9
-8.27371 57.9
-24.8211 57.9
-41.3685 57.9
-57.916 57.9
-74.4634 57.9
-91.0108 57.9
-107.558 57.9
-124.106 57.9
-140.653 57.9
-157.2 57.9
-173.748 57.9 surface stress of 207 MPa (30 ksi), which is reflective of measurements for a 10-inch diameter pipe from the same ASME recommendations.
A-10 Global ID Name Value/
Distribution Parameters Units Basis
-190.295 57.9
-206.843 57.9 A4 Scenario 4 The input set for Scenario 4 was developed based on the input set for Scenario 2 with the modifications described in the following table.
Global ID Name Value/
Distribution Parameters Units Basis Mean Std.
Dev.
206.842 72 57.9 152.539 9
57.9 103.935 8
57.9 60.9535 74 57.9 23.4906 18 57.9 8.58149 1
57.9 35.4169 7
57.9 57.1958 3
57.9 Pre-mitigation axial WRS 74.1238 9
57.9 MPa ASME recommendations
[11] for stainless steel welds great than or equal to 1-inch in thickness and using an ID surface stress of 207 MPa (30 ksi), which is reflective of measurements for a 10-inch diameter pipe from the same ASME recommendations.
A-11 Global ID Name Value/
Distribution Parameters Units Basis 86.4327 6
57.9 94.3798 5
57.9 98.2483 6
57.9
-98.3473 57.9 95.0114 7
57.9 88.6014 8
57.9 79.5037 2
57.9 68.1303 9
57.9 54.9194 9
57.9 40.3348 1
57.9 24.8659 4
57.9 9.02827 1
57.9 6.63700 76 57.9 21.5629 11 57.9
A-12 Global ID Name Value/
Distribution Parameters Units Basis 35.1566 54 57.9 46.7996 55 57.9 55.8475 34 57.9 A5 Scenario 5 The input set for Scenario 5 was the same Scenario 2; however, the logic in the xLPR computational core was modified so that the aspect ratios of the initial cracks were the same in every realization. To affect this modification, the formula for selector element Init_HL_selector_cc was changed such that the initial crack half-length would depend solely on the initial crack depth, Init_depth_cc_init_flaw, multiplied by a constant half the value of the desired aspect ratio, which for this scenario was 4:1. Specifically, the revised formula was as follows: 0.5*4*Init_depth_cc_init_flaw*Pipe_Thickness/Max_iHL_cc.
A6 Scenario 6 The input set for Scenario 6 was the same Scenario 2; however, the logic in the xLPR computational core was modified so that the aspect ratios of the initial cracks were the same in every realization. The same approach was taken as for Scenario 5, except that the aspect ratio was 10:1 in this scenario. The revised formula for selector element Init_HL_selector_cc was as follows: 0.5*10*Init_depth_cc_init_flaw*Pipe_Thickness/Max_iHL_cc.
A7 Scenario 7 The input set for Scenario 7 was the same as Scenario 2; however, the logic in the xLPR computational core was modified so that the aspect ratios of the initial cracks were the same in every realization. The same approach was taken as for Scenario 5, except that the aspect ratio was 20:1 in this scenario. The revised formula for selector element Init_HL_selector_cc was as follows: 0.5*20*Init_depth_cc_init_flaw*Pipe_Thickness/Max_iHL_cc.
A8 Scenario 8 The input set for Scenario 8 was developed based on the input set for Scenario 2 with the modifications described in the following table.
Global ID Name Value/
Units Basis
A-13 Distribution Parameters 0001 Plant Operation Time 480 mon Equivalent to 40 EFPY, which covers four inspection internals 0808 Inspection Month 1 (Pre-Mitigation) 24 mon 0808.2 Inspection Month 2 (Pre-Mitigation) 144 mon 0808.3 Inspection Month 3 (Pre-Mitigation) 264 mon 0808.4 Inspection Month 4 (Pre-Mitigation) 384 mon 0808.5 Inspection Month 5 (Pre-Mitigation) 504 mon 0808.6 Inspection Month 6 (Pre-Mitigation) 624 mon 0808.7 Inspection Month 7 (Pre-Mitigation) 744 mon 0808.8 Inspection Month 8 (Pre-Mitigation) 864 mon 0808.9 Inspection Month 9 (Pre-Mitigation) 984 mon 0808.10 Inspection Month 10 (Pre-Mitigation) 1104 mon Inspections every 10 years beginning at 2 CY 1001 Effective Full Power Years (EFPY) 480 mon Assumes a 100 % plant capacity factor 1210 Initial Flaw Full-Length (Circ) 0.3491 m
Length of 180 of the ID circumference 5101 Log reg intercept param, beta_ 0 (circ)
Normal (2.71, 0.21) 5102 Log reg slope param, beta_1 (circ)
Normal (0.31, 0.45)
Based on the guidance in EPRI Materials Reliability Program Letter 2021-015
[18], the UT detection and sizing model parameters were treated
A-14 5103 Log reg intercept param, beta_ 0 (axial)
Normal
(-0.8, 0.38) 5104 Log reg slope param, beta_1 (axial)
Normal (8.3, 1.45) 5105 Depth-sizing bias term, a (circ)
Normal (0.034, 0.006) 5106 Depth-sizing slope term, b (circ)
Normal (0.955, 0.013) 5107 Depth-sizing bias term, a (axial)
Normal (0.041, 0.011) 5108 Depth-sizing slope term, b (axial)
Normal (0.88, 0.029) 5109 Sigma_depth (circ.)
0.072 5110 Sigma_depth (axial) 0.078 probabilistically based on the recommendations in EPRI MRP-262, Revision 3 [15], for the pressurizer surge line nozzle dissimilar metal weld configuration, which has a comparable geometry to the representative Westinghouse four-loop PWR 10-inch safety injection system piping welds. The recommendations are also for detecting SCC.
A9 Scenario 9 The input set for Scenario 9 was developed based on the input set for Scenario 8 with the modifications described in the following table.
Global ID Name Value/
Distribution Parameters Units Basis 0808 Inspection Month 1 (Pre-Mitigation) 96 mon 0808.2 Inspection Month 2 (Pre-Mitigation) 216 mon 0808.3 Inspection Month 3 (Pre-Mitigation) 336 mon 0808.4 Inspection Month 4 (Pre-Mitigation) 456 mon Inspections every 10 years beginning at 8 CY
A-15 0808.5 Inspection Month 5 (Pre-Mitigation) 576 mon 0808.6 Inspection Month 6 (Pre-Mitigation) 696 mon 0808.7 Inspection Month 7 (Pre-Mitigation) 816 mon 0808.8 Inspection Month 8 (Pre-Mitigation) 936 mon 0808.9 Inspection Month 9 (Pre-Mitigation) 1056 mon 0808.10 Inspection Month 10 (Pre-Mitigation) 1176 mon A10 Epistemic Random Seeds per Replicate per Scenario Replicate No.
Scenario 1
2 3
4 5
6 7
8 9
10 1
75822 84 85235 08 49814 810 565769 97 62464 159 632746 84 609219 59 8211367 4
821136 74 955256 94 2
4 96 232 391 446 556 908 974 1124 2737 3
75822 84 85235 08 49814 810 565769 97 62464 159 632746 84 609219 59 8211367 4
821136 74 955256 94 4
4 96 232 391 446 556 908 974 1124 2737 5
195 231 392 445 555 615 909 974 1124 2737 6
87 95 231 392 445 555 909 974 1124 2737 7
87 95 231 392 445 555 909 974 1124 2737 8
75822 84 85235 08 49814 810 565769 97 62464 159 632746 84 609219 59 8211367 4
821136 74 955256 94
A-16 9
75822 84 85235 08 49814 810 565769 97 62464 159 632746 84 609219 59 8211367 4
821136 74 955256 94
ML24162A129; ML24162A131 OFFICE RES/DE/REB RES/DE/CIB RES/DE NAME CNellis RIyengar MSampson JMcKirgan for DATE Jun 18, 2024 Jun 21, 2024 Jun 24, 2024