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Proceedings of the ASME 2012 Pressure Vessels & Piping Conference
July 15-19, 2012, Toronto, Ontario, CANADA
Initial Development of the Extremely Low Probability of Rupture (xLPR)
Version 2.0 Code
D. Rudland*†
US Nuclear Regulatory Commission
Office of Nuclear Regulatory Research
Mail Stop: CSB-5CA24
Washington, DC 20555-0001
NRC Standard Review Plan (SRP) 3.6.3 describes LeakBefore-Break (LBB) assessment procedures that can be used to
assess compliance with the 10CFR50 Appendix A, GDC-4
requirement that primary system pressure piping exhibit an
extremely low probability of rupture. SRP 3.6.3 does not allow
for assessment of piping systems with active degradation
mechanisms, such as Primary Water Stress Corrosion Cracking
(PWSCC) which is currently occurring in systems that have
been granted LBB approvals.
Along with a series of existing qualitative steps to assure safety
in LBB-approved lines experiencing PWSCC, NRC staff,
working cooperatively with the Electric Power Research
Institute through a memorandum of understanding, is
developing a new, modular based, comprehensive piping
system assessment methodology to directly assess compliance
with the regulations. This project, called eXtremely Low
Probability of Rupture (xLPR), will model the effects and
uncertainties of relevant active degradation mechanisms and the
associated mitigation activities. The resulting analytical tool
will be comprehensive with respect to known and significant
materials challenges (PWSCC, etc.), vetted with respect to the
technical bases of models and inputs, flexible enough to permit
analysis of a variety of in-service situations and adaptable such
as to accommodate evolving and improving knowledge.
A multi-year project has begun that has been focused on the
development of a viable method and approach to address the
effects of PWSCC as well as define the requirements necessary
for such a modular-based assessment tool. As reported in a
previous paper, the first version of this code was developed as
part of a pilot study, which leveraged existing fracture
Corresponding author,
The views expressed herein are those of the author and do not represent
an official position of the USNRC
C. Harrington
Electric Power Research Institute
Dallas, Texas, USA
mechanics based models and software coupled to both a
commercial and open source code framework to determine the
framework and architecture requirements appropriate for
building a modular-based code with this complexity. The pilot
study focused on PWSCC in pressurizer surge nozzles, and was
meant to demonstrate the feasibility of this code and approach
and not to determine the absolute values of the probability of
This paper examines the plans for the xLPR Version 2.0 model
which will broaden the scope of xLPR to all LBB-approved
primary piping in pressurized water reactors (PWR), using an
incremental approach that incorporates the design requirements
and lessons learned from previous iterations. After a review of
the Version 1.0 final results, this paper will document the plans
for Version 2.0 including the revised management structure, the
technical scope, and the progress in the code development
effort to date.
10 CFR Part 50, Appendix A, General Design Criteria (GDC) 4
states, in part, that the dynamic effects associated with
postulated reactor coolant system pipe ruptures may be
excluded from the design basis when analyses reviewed and
approved by the NRC demonstrate that the probability of fluid
system piping rupture is extremely low under conditions
consistent with the design basis. Licensees have typically
demonstrated compliance with this probabilistic criterion
through deterministic and highly conservative analyses [1].
Given recent advances in probabilistic methodologies, the NRC
staff and industry believe that performing a probabilistic
analysis of primary system piping that fully addresses and
quantifies uncertainties and can be used to directly assess
compliance with GDC 4 is more appropriate. The NRC and
EPRI expect that a robust probabilistic software tool, developed
cooperatively, will facilitate meeting this goal, and result in
improvement in licensing, regulatory decision-making and
design, and will be mutually beneficial. Based on the
terminology of GDC 4, this effort is titled eXtremely Low
Copyright © 2012 by ASME
This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government’s contributions.
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Probability of Rupture (xLPR). Development of the xLPR
methodology and the corresponding software tool will involve
many challenging technical decisions, modeling judgments, and
sensitivity analyses.
Models, Inputs, and Acceptance) coordinated by an overarching
Project Integration Board (PIB). Each task group and the PIB
consisted of equivalent NRC and industry representatives. The
role of the PIB was to provide overall guidance, coordinate the
work, and make programmatic decisions on an as-required
basis. The PIB was comprised of twelve members, two from
each of the task groups and two management and two at large
members. However, no one was identified in a leadership role
and no process for the PIB to provide guidance or review and
approve task group recommendations was ever developed. In
addition, the schedule set forth for the pilot study was relatively
short, and to adhere to that schedule, the task groups
necessarily made decisions without consulting the PIB.
However, even without the input of the PIB, the project team
successfully completed the pilot study and produced results that
demonstrated the feasibility of the approach. This achievement
was due to the leadership of the technical tasks groups.
However, it was clear that the organizational structure needed
to be revised.
The development of a sophisticated probabilistic software tool
that meets quality assurance (QA) and technical requirements is
a daunting task. The management structure, the probabilistic
framework, and data handling are just a few of the issues that
need to be addressed early in the software development effort.
In order to meet this need, a pilot study was conducted to
demonstrate the feasibility of the proposed NRC-industry
cooperative development process and determine the appropriate
probabilistic framework for calculating the probability of
rupture for a pressurizer surge nozzle dissimilar metal weld.
The pilot study provided relative, order-of-magnitude estimates
of piping rupture probabilities; such analysis identified areas
requiring more focused attention in the long-term study.
Using the lessons learned from the pilot study, a more detailed
long term study has begun to generalize the analysis procedures
to all primary system piping, focusing on piping systems
already approved for LBB. Version 2.0 of the xLPR code
employs the same basic organizational, management, and NRCindustry cooperative structure as the pilot study. However,
technical and programmatic lessons learned from the pilot
study will be incorporated into this version of the code.
Through the efforts documented in the xLPR Version 1 report
[3], the project team successfully demonstrated that it is
feasible to develop a modular-based computer code for
determination of primary piping rupture probabilities. In fact,
the team developed two computational frameworks using a
common set of deterministic modules and similar input and
output modules. The program team conducted a set of analyses
using each framework that demonstrated the ability to calculate
the probability of rupture under operating conditions taking into
account PWSCC growth rates, in-service inspections and leak
detection limits. In addition, the problem uncertainties were
quantified and propagated throughout the problem such that a
distribution of rupture probabilities was generated for each pilot
study problem. The project team concluded that importance
sampling is required for low rupture probability calculations
and that uncertainty classification and quantification is not
trivial and needs involvement by all team members during the
development of the xLPR code.
An example of the results
generated in the pilot study is shown in Figure 1. For this case,
a pressurizer surge nozzle with a short safe end was considered.
This paper specifically examines the plans and status for the
xLPR Version 2.0 model, which will be applicable to LBB
approved piping. After a review of the Version 1.0 final
results, this paper documents the plans for Version 2.0
including the revised management structure, the technical
scope, and the progress in the code development effort to date.
The xLPR Pilot Study [2] was the culmination of the initial
development of a sophisticated, thorough and quality-assured
probabilistic failure assessment software tool. The Pilot Study
program team developed and exercised the initial version of
this code on a limited scope problem to assess the structure and
feasibility of the management and technical approach. The
main goal of the Pilot Study was three-fold:
• Assess the proposed management structure’s ability to
support cooperative and efficient code development and
• Assess the feasibility of developing a modular-based
probabilistic fracture mechanics computer code that can
calculate the probability of rupture for a reactor coolant
nozzle weld while properly accounting for the problem
uncertainties; and
• Determine the appropriate probabilistic framework for
constructing the modular-based probabilistic fracture
mechanics code.
As shown in this figure, the mitigation at 20 years reduced the
rupture probability at 60 years by two orders of magnitude,
while the leak detection and inspection reduced the rupture
probabilities by about three orders of magnitude.
combined effect caused a reduction of six orders of magnitude
on the rupture probability at 60 years.
The management structure developed within the pilot study
consisted of four topical technical task groups (Computational,
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parties [5]. The xLPR Version 2.0 development project is led
by the Code Development group, and supported by the Code
Review and Acceptance groups.
The leadership of each group consists of two individuals (Lead
and Co-lead), one designated by NRC and the other by
industry. The remaining participants of each group are
similarly representative of both organizations.
Figure 1 Mean probability of rupture for safe end
sensitivity case with mitigation, leak detection
(LD) and inspection (ISI)
Within the xLPR pilot study, the project team successfully
implemented two unique framework codes to investigate the
advantages and disadvantages of two approaches: 1) use of
available commercial software, and 2) use of open source code.
The project team used the commercial software, GoldSim, to
investigate the commercial software approach for the xLPR
Model, and used the open source code, SIAM-PFM, to
demonstrate the open source approach.
Within these
frameworks, the project team implemented essentially the same
program flow and deterministic modules through a detailed
configuration management program.
After completing a
verification process, the program team exercised each code
through a set of pilot study problems and compared the results
[3]. Even though some slight differences between the results
were documented, the project team found that the comparison
between results was favorable and differences were
Figure 2 xLPR Version 2.0 Organizational Structure
Although significant rigor and control were used in the
implementation of the framework codes in the xLPR pilot
study, a structured and traceable Quality Assurance program
was not in place. In the spring of 2011, a QA expert panel was
assembled, consisting of industry experts and key leadership
from the pilot study to ensure that Version 2.0 would be
structured to meet nuclear industry standards. The results of
that expert panel meeting were accepted as the scope and
framework of the xLPR Version 2.0 QA Program for the
developmental phase (pre-release) of the product.
The xLPR Version 2.0 QA Program is based on 10 CFR Part 50
Appendix B, Quality Assurance Criteria for Nuclear Power
Plants and Fuel Reprocessing Plants. In addition, NRC
Regulatory Guide 1.28, Revision 4,
Quality Assurance
Program Criteria (Design and Construction) is referenced as a
basis and it in turn endorses the use of ASME NQA-1-2008
with the ASME NQA-1a-2009 Addenda, Quality Assurance
Requirements for Nuclear Facility Applications, as an adequate
basis for complying with the requirements of 10 CFR Part 50
Appendix B.
An independent contractor conducted a comparison of each
framework code [4] and concluded that each framework has its
own set of strengths and limitations, so that neither code has a
distinct advantage. However, after conducting a cost analysis,
and factoring in the long term prospects of the software, the
xLPR project team recommended that the future versions of
xLPR be developed using the GoldSim commercial software as
the computational framework.
Based on the lessons learned from the xLPR Version 1.0 pilot
study, the project organizational structure was revised to allow
more efficient and effective project coordination,
communication and management, see Figure 2. As with the
pilot study, this effort is being undertaken as a cooperative
effort between industry (represented by EPRI’s Materials
Reliability Program (MRP)) and the NRC Office of Nuclear
Regulatory Research through a Memorandum of Understanding
(MOU) that defines and guides the interactions between the two
NQA-1-2008 and the NQA-1a-2009 Addenda were thoroughly
reviewed and evaluated by the expert panel to determine the
applicable requirements for this software-based initiative.
These requirements are captured in the xLPR Version 2.0 QA
Program documents, which consist of the xLPR Software
Project Management Plan, that incorporates the applicable
NQA-1 requirements not specific to software, but necessary to
manage the project; and the xLPR Software Quality Assurance
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Plan that incorporates the applicable NQA-1 requirements that
are specific to developing software, including the phased
lifecycle activities. In addition, the global processes of
Configuration Management and Problem Reporting and
Corrective Action are addressed in the xLPR Configuration
Management Plan.
framework complexity (e.g., improve transparency). This work
involves checking the flow of information, i.e. that inputs and
outputs of upstream modules are appropriate in their range and
distribution for the downstream modules. It also includes a
robust design to insure that inputs used multiple times do not
artificially increase (or decrease) the uncertainty. An extension
of the user and data input interface will be studied to allow a
user greater flexibility in parameterizing the analysis and
adjusting uncertain distributions without making the interface
too complex. Consideration will be given to enhancing the use
of Excel spreadsheets or moving into databases for better
flexibility and traceability of inputs to performed runs.
Since the xLPR Version 2.0 scope is currently limited to the
developmental phase (pre-release) of the product, the
requirements for operational and maintenance activities
following code release for use are still being evaluated,
including the applicability of 10 CFR Part 21 and the ongoing
processes for permanent records management, user interface
and product release and tracking.
The combined enhancement focuses on improvements in the
accuracy, computational efficiency, modularity, and flexibility
of the framework to permit analysis of a variety of in-service
situations as well as adaptability to accommodate evolving and
improving knowledge.
Life cycle development will follow the Spiral Model [6],
depicting layers of refinement from inception through
elaboration, construction, transition and release. It entails an
iterative approach which allows increased understanding of the
problem through successive refinements. Each iteration ends
with an executable release of the code.
Loads: The objective of the loads module is to account for all
piping system loads that are used in the stress calculations
within the code. Version 1.0 accounted for design and
operational loads, including normal thermal, deadweight, Safe
Shutdown Earthquake (SSE), and normal thermal stratification
loads. Piping system loads as a result of weld residual stress
(WRS) were defined in a separate model and combined with
the piping system loads to calculate stress intensity factors.
Version 1.0 only considered PWSCC degradation, so thermal
transient behavior was not addressed. A major update to
Version 2.0 is the inclusion of fatigue in addition to PWSCC as
a mechanism for initiation and crack growth; therefore thermal
transient data will be required in order to provide fatigue usage
factor estimates.
Implementation of the xLPR QA requirements adopts the IEEE
Software Engineering Standards at a level appropriate for, and
applicable to, the scope of the project in order to promote
conformance to best industry practices and ensure consistency
of deliverables throughout the project life cycle
While the purpose of Version 1.0 of the xLPR code was
principally to show the feasibility of the approach, the next
generation of the code will place greater emphasis on
computational capabilities and efficiencies. Version 2.0
computational objectives focus on evaluation and development
of advanced computational algorithms, software features, and
framework design to address specific needs identified during
the xLPR pilot study effort.
Sampling techniques will be improved and complemented with
optimization methods, as the analyses of Version 1.0 results
showed the importance of adding more sophisticated
techniques: many Monte Carlo samples or parameter-specific
importance sampling were required to correctly estimate
extremely low probability occurrences. Version 2.0
developments include an investigation of computational
optimization (performance) methods and more adaptive
sampling algorithms. Consequently, the parameter uncertainty
and sensitivity analysis tools for analyzing the corresponding
results will be updated in order to further understand the
uncertainty that controls the problem. Specific enhancements to
evaluate non-linear and non-monotonic relationships will be
Weld Residual Stress: Within the Version 1.0 code, throughthickness WRS distributions calculated from finite element
simulations are approximated as 3rd order polynomials,
compatible with the stress intensity factor solutions used.
Uncertainty in the through-thickness WRS distribution is
modeled by the uncertainty in the inner diameter stress, the
outer diameter stress, and the point at which the stress switches
from tension to compression for a given polynomial WRS
representation. Not all WRS profiles are well described by this
procedure. Version 2.0 is updating to a piecewise WRS profile
representation defined by 20 points through thickness. This
approach is able to capture all features present in a WRS
profile, allowing for improved representation of uncertainty at
each point through thickness or the sampling of discrete WRS
profiles. Currently a WRS sampling scheme is being developed
for Version 2.0 based on the WRS datasets collected as part of
the NRC/EPRI WRS program [7,8] and stress intensity factor
solutions for piece-wise stress distributions.
Framework software and design enhancements will be
evaluated to address ease of linking modules to the framework,
improvements to the user interface, and to reduce overall
Initiation Module: Within the Version 1.0 code, the pipe cross
section of interest was divided into a collection of segments of
a given length for PWSCC initiation modeling. This approach
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Version 1.0 code. A modification to the MRP-115 equation
was developed in the MRP-263 study adding the dependence
on dissolved hydrogen concentration.
allows correlation of time to initiation as a function of
stress/temperature to an area of a given size where
stress/temperature/environment is assumed constant. Two
direct initiation models, where initiation time is a function of
stress/temperature, and a Weibull model with parameters fit to
crack initiation/service data were used. Probabilities of rupture
calculated were nominally the same for the three initiation
models, as each model was fit to the same crack initiation data.
The crack growth model that is being considered for Version
2.0 is an extension to the Version 1.0 model. In addition to
circumferential cracks, the model will include axial crack
growth, with-in weld variability [14], and crack initiation and
crack growth correlation factors.
As part of the Version 2.0 effort, the initiation framework from
Version 1.0 was reviewed by an expert panel. The expert panel
concluded that the initiation models used in Version 1.0 are
sufficient for the Version 2.0 effort. Recommendations were
made regarding the fitting of PWSCC initiation models to
service data, the possibility of accounting for surface plasticity
on initiation and including a threshold stress for initiation.
Finally as noted in the loads module, an appropriate fatigue
(initiation and growth) model will be included in Version 2.0.
In addition to the PWSCC growth model, scoping studies are
being conducted to determine the appropriate fatigue model for
inclusion in the Version 2.0 code.
Inspection: The ISI module in Version 1.0 calculates the
probability of non-detection of circumferential flaws of specific
sizes and at specific times during a simulation. The source of
inspection reliability information used in the inspection models
is the database of ultrasonic procedure and personnel
Demonstration Initiative (PDI) program administered by EPRI
Stress Intensity Factors: Within the Version 1.0 code, stress
intensity factor solutions for part-through circumferential semielliptical surface cracks (SC) [9] and straight-fronted throughwall circumferential cracks (TWC) [10] were included. These
solutions assumed the stress through thickness was represented
by a polynomial distribution. The part-through solutions
consider through-wall stress distributions described by a fourth
order polynomial. These stresses vary only through the
thickness. Local stress intensity factors for the deepest point
and surface point are provided. For through-wall cracks,
tension, through-thickness, and global bending stresses are
Version 2.0 will implement Probability Of Detection (POD)
and sizing models for LBB weld locations other than the
pressurizer surge nozzle considered in Version 1.0. A technical
basis for the treatment of both axial and small flaws requires
development. Specifically it is unclear if the POD model for
circumferential flaws holds for axial flaws or if the linear
extrapolation used to model small flaws (~less than 10%
through-wall) in Version 1.0 is a reasonable approximation of
POD as the flaw depth approaches zero. Finally Version 1.0
allows the user to input an inspection schedule. If Version 2.0
allows for inspections that are conditional on an event, changes
to the xLPR structure are required.
Version 2.0 uses a stress intensity factor solution that allows a
piecewise through thickness WRS representation, the Universal
Weight Function Method (UWFM) [11]. This update to the
stress intensity factor solution represents a change to the xLPR
framework and development work on integrating the UWFM
into xLPR has begun. Finite element fracture mechanics
calculations to bench mark the UWFM work, as well as to
investigate the sensitivity of circumferential through wall
cracks to weld residual stresses are being conducted.
Crack Stability:
Within the Version 1.0 code, the stability of part-through cracks
is based on net-section collapse for tension and bending loading
[16], and the stability of through-wall cracks is based on tearing
instability that employs an elastic-plastic formulation for
evaluation of the applied J-integral that is based on a reduced
thickness analogy to estimate the compliance of cracked
elastic-plastic tubes subject to tension and bending [17].
Crack Growth:
For the pilot study, circumferential PWSCC of DM butt welds
was the only subcritical cracking mechanism that was
considered. The PWSCC crack growth model incorporated
into the xLPR Version 1.0 code was developed from Alloy
82/182 dissimilar metal (DM) weld laboratory experimental
data used to measure the growth rate of PWSCC. The
collective experimental data has been gathered and analyzed by
EPRI in MRP-115 [12].
The PWSCC growth model
developed in that effort included a temperature corrected crack
growth rate with uncertainty in the rate both from a within weld
and weld-to-weld perspective, although the “within weld
feature” was not implemented in the pilot study. The effects of
dissolved hydrogen on the MRP-115 crack growth rate were
detailed in MRP-263 [13] and implemented into the xLPR
For Version 2.0, the solutions listed above will be included
with the following additions:
• Axial surface and through-wall crack stability.
Available solutions in the Ductile Fracture Handbook
[18] and API 579-1/ASME-FFS-1 [19] will be
reviewed to determine the most suitable formulation
for xLPR Version 2.0.
• Effects of different strength base metals on DM weld
fracture behavior. It is known [ 20] that the fracture
behavior of a SC or a TWC in a DMW is not governed
exclusively by either the properties of the stainless
steel safe end or the properties of the low alloy steel
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nozzle, because all three materials (stainless, alloy
steel, and weld) participate in the fracture process.
The appropriate factors to use in combining these
materials properties within the fracture analyses will
be developed in the xLPR effort.
matrix of leak rates for an extensive range of possible solutions.
An interpolation routine will be necessary to solve for cases
that fall between the values available from the matrix. The
extensive range that must be accounted for includes ranges for
pipe geometry, material properties, thermodynamic conditions,
crack opening parameters and crack morphology parameters.
In addition, scoping studies will be conducted that will
investigate the need for and/or development of elastic-plastic
fracture solutions for surface cracked piping that properly
accounts for crack-tip constraint and piping system constraints.
Mitigation: The mitigation framework for Version 1.0 only
considered Mechanical Stress Improvement Process (MSIP) as
a proof of concept. Not all aspects of the MSIP process were
modeled in Version 1.0 and the uncertainties, both with regard
to effectiveness and WRS profile, require quantification in
Version 2.0. The Version 2.0 framework will account for other
mitigation methods, such as weld overlay repairs, changes to
water chemistry (H, Zn), and changes to surface stress as a
result of peening. These mitigation techniques will affect the
crack initiation and crack growth behavior as dictated by the
mitigation method. While the Version 2.0 framework will
provide a range of mitigation options, regulatory approval for
the mitigation applied is required and inclusion of a mitigation
method in Version 2.0 does not imply regulatory approval.
Transition from part-through to through-wall cracks is handled
by determining the through-wall crack length where the
cracked area is equal to the part-through wall crack area at
through-wall penetration. Once a through-wall crack becomes
unstable, a double-ended break is considered to occur.
Crack Opening Displacement:
Calculation of crack opening displacement (COD) is essential
in the prediction of leakage through cracks. There is a range of
COD prediction performance as documented in [21], where the
GE/EPRI method is suggested to be the most accurate method
for calculating COD. The basis for the recommendation in [21]
was presented in [22], where the details of a comparison of a
variety of COD analysis methods with finite element
calculations are presented. The conclusion was that the
GE/EPRI method is the best choice for COD calculation over
the range of interest.
Based on these results and
recommendation, the decision was made to use the GE/EPRI
COD analysis in xLPR Version 1.0. While implementing this
process, errors were found in the combined tension and bending
solutions described in [22]. The work conducted within the
xLPR program [3] and which is currently coded in Version 1.0,
corrected the errors in the proceeding publication. Version 2.0
will update the GE/EPRI COD analysis using contemporary
finite element analyses (3D elements versus shell elements) and
over a wider range of combined loading conditions (tension +
bending) than were applied in GE/EPRI. Axial COD solutions
will also be included, and benchmarking of closed form elastic
axial COD solutions against finite element calculations is
The Inputs Task Group for xLPR Version 2.0 is responsible for
identifying and collecting data and their associated distributions
to quantify the various input parameters required to assess
primary system piping safety. These input parameters include
initial flaw distributions, thermal and mechanical steady-state
and transient loads, residual stresses, piping geometry and weld
fabrication methods, environments, and material properties.
The Inputs Task Group is also responsible for establishing an
input database for supplying the input data to Version 2.0. The
Inputs Task Group is also working closely with the Models and
Computational Task Groups to quantify uncertainties by
providing plant design, fabrication and/or operating data that
may be used to define the variability and uncertainty of the
For the xLPR Version 2.0 project, the Inputs Task Group will
obtain all relevant data for one reactor coolant loop from a fourloop Westinghouse pressurized water reactor (PWR) plant and
one reactor coolant loop from a Babcock & Wilcox (B&W)
PWR plant. Based on availability of data and project resources,
additional data may be obtained for selected locations in a
Combustion Engineering (CE) PWR plant. At this time,
assessment of boiling water reactors (BWRs) is not included in
the xLPR Version 2.0 project scope.
Leak Rates:
For Version 1.0, leak rates for straight-fronted through-wall
cracks are evaluated based on the SQUIRT software [23],
which, in turn, is based on the Henry-Fauske two-phase flow
model. Pressure drops due to entrance effects, friction, phase
change (liquid to gas), and bends and protrusions are
The schedule for the Version 2.0 xLPR project is shown in
Figure 3. The schedule is driven by the regulatory need to have
a computational tool that can be used to assess compliance with
the ongoing regulations pertaining to LBB. The NRC has taken
the position that, in the short term, those plants that have been
approved for LBB, but have RCS primary piping systems that
are currently undergoing active material degradation, remain
For Version 2.0, a survey of the leak rate software (including
the Version 1.0 SQUIRT module) will be conducted to
determine the most appropriate and efficient algorithm for
calculating the leak rate. Since the calculation of leak rate can
be an expensive calculation from a run-time standpoint, the
option of creating a leak-rate rate look-up table is being
considered. The table look-up will consist of generating a
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compliant with the regulation [24] through their updated
inspection [25, 26] and mitigation programs. However, in the
long term, a computational code is needed to directly assess this
compliance. It is the goal of the NRC that this version of the
xLPR code be operational by the end of 2013.
The initial development of the Version 2.0 xLPR code is an
ongoing group effort that spans a variety of experts across
many fields of expertise from the U.S. NRC, EPRI, and their
contractors. The ongoing success of this program emphasizes
the dedication of the xLPR team, the strength of its leadership,
and the support from both the NRC and EPRI. There are many
people to thank, including members from the computational,
models, inputs and acceptance groups, as well as the Program
Integration Board. Every person on this team provided
valuable contributions, and their efforts were sincerely
Computational Group
Patrick Mattie – Sandia National Laboratories
David Harris – Structural Integrity Associates
Cedric Sallaberry – Sandia National Laboratories
Don Kalinich – Sandia National Laboratories
Jon Helton – Sandia National Laboratories
Robert Kurth – Emc2
Dilip Dedhia – Structural Integrity Associates
Anitha Gubbi – Structural Integrity Associates
Cliff Lange – Structural Integrity Associates
Hilda Klasky – Oak Ridge National Laboratory
Paul Williams – Oak Ridge National Laboratory
Scott Sanborn – PNNL
Figure 3 Overall xLPR Version 2.0 Development Schedule
This paper provides a summary of the plans for the
development of Version 2.0 of the xLPR computer code.
Following the success of the xLPR pilot study, Version 2.0
development is aimed at a comprehensive probabilistic
computer code that can be used to assess compliance with the
regulations pertaining to LBB. The project is being conducted
cooperatively between the US NRC Office of Nuclear
Regulatory Research and EPRI through an ongoing
Memorandum of Understanding.
Models Group
Marjorie Erickson – PEAI
Matthew Kerr – U.S. NRC
David Rudland – U.S. NRC
Howard Rathbun – U.S. NRC
Gary Stevens – U.S. NRC
Carol Nove – U.S. NRC
Mark Kirk – U.S. NRC
John Broussard – Dominion Engineering
Glenn White – Dominion Engineering
Chuck Marks – Dominion Engineering
Do-Jun Shim – Emc2
Elizabeth Kurth – Emc2
Bud Brust – Emc2
Sean Yin – Oak Ridge National Laboratory
Richard Bass – Oak Ridge National Laboratory
Cliff Lange – Structural Integrity Associates
Dave Harris – Structural Integrity Associates
Steven Xu – Kinetrics
Doug Scarth – Kinetrics
Russ Cipolla – Aptech
Mike Hill – UC Davis
Steve Fyfitch – AREVA NP Inc.
Ashok Nana – AREVA NP Inc.
Rick Olson – Battelle
Andrew Cox – Battelle
Lee Fredette – Battelle
Bruce Young – Battelle
Craig Harrington – EPRI
As with the pilot study, for the Version 2.0 code development
effort, experts were engaged to determine the appropriate
models and inputs needed to determine the probability of
rupture for piping systems approved for LBB. Using the
project-specific quality assurance program, these experts will
compile, code, and verify the modules needed for the stated
purpose. These modules include loads (with weld residual
stress), crack initiation, crack growth, crack stability, crack
opening displacement, leakage, inspection, and mitigation. In
addition, these self-contained modules will be incorporated into
a computational framework that utilizes the commercial
software GoldSim. The framework will control the time flow
of the analyses, while linking the modules and properly
accounting for and propagating the problem uncertainty.
The regulatory need for this software is based on the
assessment of piping systems that have been previously
approved for LBB that are experiencing active degradation. It
is the goal of the NRC that this version of the xLPR code be
operational by the end of 2013.
Copyright © 2012 by ASME
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Jean Smith – EPRI
Patrick Heasler – PNNL
Bruce Bishop – Westinghouse
Mark Dennis - EPRI
George Connolly - EPRI
Inputs Group
Guy DeBoo – Exelon
Gary Stevens – U.S. NRC
Craig Harrington – EPRI
Ashok Nana – AREVA NP Inc.
Nathan Palm – Westinghouse
Program Integration Board
Denny Weakland - Ironwood Consulting
Bruce Bishop – Westinghouse
Rob Tregoning – U.S. NRC
Bob Hardies – U.S. NRC
Ted Sullivan – PNNL
Report of the U.S. Nuclear Regulatory Commission Piping
Review Committee, Evaluation of Potential for Pipe Break,
NUREG-1061, Volume 3, November 1984, ML093170485
Rudland, D., and Harrington C., Extremely Low
Probability of Rupture (xLPR) Version 1.0 Code – Pilot
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the ASME 2011 Pressure Vessels & Piping Conference,
PVP2011, July 17-21, 2011, Baltimore, Maryland, USA.
Rudland, D., “xLPR Version 1.0 report, Technical Basis
and Pilot Study Problem Results.” NRC Letter Report,
xLPR Computational Group, ML110660292, 2011.
Pensado, O., et al., “Assessment of Capabilities of
Extremely Low Probability of Rupture (xLPR) Software –
GoldSim and SIAM Version 1.0,” Center for Nuclear
Waste Regulatory Analyses, 2011, San Antonio, Texas.
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Sheron, B. and Modeen, D., “Addendum To Memorandum
of Understanding Between U.S. Nuclear Regulatory
Commission and Electric Power Research Institute On
Cooperative Nuclear Safety Research - Extremely Low
Probability Of Rupture (xLPR)”, October 2009
Boehm, B., 1988, "A Spiral Model of Software
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Program International Round Robin Program and
Findings,” PVP2011-57642, Proceedings of the ASME
2011 Pressure Vessels & Piping Conference, PVP2011,
July 17-21, 2011, Baltimore, Maryland, USA.
Fredette, L, Broussard, J., Kerr, M., and Rathbun, H.,
“NRC/EPRI Welding Residual Stress Validation Program Phase III Details and Findings,” PVP2011-57645,
Proceedings of the ASME 2011 Pressure Vessels & Piping
Conference, PVP2011, July 17-21, 2011, Baltimore,
Maryland, USA.
Anderson, T.L., Thorwald, G., Revelle, D.A., and Lanaud,
C., “Stress Intensity Solutions for Surface Cracks and
Buried Cracks in Cylinders, Spheres, and Flat Plates,”
Structural Reliability Technology final report to The
Materials Property Council, Inc., March 14, 2000.
Anderson, T.L., “Stress Intensity and Crack Opening Area
Solutions for Through-wall Cracks in Cylinders, and
Spheres,” Structural Reliability Technology final report to
The Materials Property Council, Inc., January 29, 2003.
Xu, S., Scarth, D., and Cipolla, R., “Technical Basis for
Proposed Weight Function Method for Calculation of
Stress Intensity Factor for Surface Flaws in ASME Section
XI Appendix A,” PVP2011-57911, Proceedings of the
ASME 2011 Pressure Vessels & Piping Conference,
PVP2011, July 17-21, 2011, Baltimore, Maryland, USA.
G.A. White, N.S., Nordmann, J. Hinkling, and C.D.
Harrington, “Development of Crack Growth Rate
Disposition Curves for Primary Water Stress Corrosion
Cracking (PWSCC) of Alloy 82, 182 and 132 weldments,”
TMS (The Minerals, Metals and Materials Society),
Proceedings of the 12th International Conference on
Environmental Degradation of Nuclear Power Systems –
Water Reactors, (2005)
Materials Reliability Program: Technical Bases for the
Chemical Mitigation of Primary Water Stress Corrosion
Cracking in Pressurized Water Reactors (MRP-263), EPRI,
Palo Alto, CA: 2009. 1019082. [Proprietary]
Models and Inputs Selected for Use in the xLPR Pilot
Study, EPRI, Palo Alto, CA. 2010, 1022528
Materials Reliability Program: Development of Probability
of Detection Curves for Ultrasonic Examination of
Dissimilar Metal Welds (MRP-262, Revision 1), 1020451,
EPRI, Palo Alto, CA: 2009.
Rahman, S.; "Net-Section-Collapse Analysis of
Circumferentially Cracked Cylinders - Part II: Idealized
Cracks and Closed-Form Equations"; Engineering Fracture
Mechanics; Vol. 61; 1998; pp. 213-230.
Gilles, P., and Brust, F. W., “Approximate Methods for
Fracture Analysis of Tubular Members Subjected to
Combined Tension and Bending Loads,” Proceedings of
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Zahoor, A., Ductile Fracture Handbook, EPRI Report NP6301-D, V3 1989.
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July 27-31, 2008, Chicago, IL, USA.
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21 Scott, P., Olson, R. and Wilkowski, G.; “Development of
Technical basis for Leak-Before-Break Evaluation
Procedures”; NUREG/CR-6765, May 2002.
22 Rudland, D., Wang, Y., and Wilkowski, G.; “Comparison
of Crack-Opening Displacement Predictions for LBB
Applications”; International Journal of Pressure Vessels
and Piping; Vol 79; 2002: pp. 209-217.
23 “User’s Guide for SQUIRT (Windows Version 1.1),”
Battelle Memorial Institute, March 2003.
24 “Regulatory Approach for Primary Water Stress Corrosion
Cracking Of Dissimilar Metal Butt Welds In Pressurized
Water Reactor Primary Coolant System Piping,” NRC
Regulatory Issue Summary 2008-25, October 22, 2008,
25 Materials Reliability Program: Primary System Piping Butt
Weld Inspection and Evaluation Guidelines (MRP-139)
EPRI, Palo Alto, CA: 2005.
26 Code Case N770-1, “Alternative Examination
Requirements and Acceptance Standards for Class 1 PWR
[Pressurized-Water Reactor] Piping and Vessel Nozzle
Butt Welds Fabricated with UNS N06082 or UNS W86182
Weld Filler Material with or without Application of Listed
Mitigation Activities.” Cases of ASME Boiler and Pressure
Vessel Code, American Society of Mechanical Engineers,
New York, December 2009.
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