Preclosure Criticality Analysis Process Report Rev 04, ICN 00

TDR-EBS-NU-000004

October 2004


EXECUTIVE SUMMARY
This report describes a process for performing preclosure criticality analyses for a repository at 
Yucca Mountain, Nevada. These analyses will be performed from the time of receipt of fissile 
material until permanent closure of the repository (preclosure period). The process describes 
how criticality safety analyses will be performed for various configurations of waste in or out of 
waste packages that could occur during preclosure as a result of normal operations or event 
sequences. The criticality safety analysis considers those event sequences resulting in 
unanticipated moderation, loss of neutron absorber, geometric changes, or administrative errors 
in waste form placement (loading) of the waste package. The report proposes a criticality 
analyses process for preclosure to allow a consistent transition from preclosure to postclosure, 
thereby possibly reducing potential cost increases and delays in licensing of Yucca Mountain. 
The proposed approach provides the advantage of using a parallel regulatory framework for 
evaluation of preclosure and postclosure performance and is consistent with the U.S. Nuclear 
Regulatory Commission’s approach of supporting risk-informed, performance-based regulation 
for fuel cycle facilities, Yucca Mountain Review Plan, Final Reporta, and 10 CFR Part 63b. The 
criticality-related criteria for ensuring subcriticality are also described as well as which guidance 
documents will be utilized. Preclosure operations and facilities have significant similarities to 
existing facilities and operations currently regulated by the U.S. Nuclear Regulatory 
Commission; therefore, the design approach for preclosure criticality safety will be dictated by 
existing regulatory requirements while using a risk-informed approach with burnup credit for in-
package operations. 



1. INTRODUCTION
1.1 BACKGROUND 
This report presents a process for analyzing the potential for criticality during the Yucca 
Mountain repository preclosure period. This approach can be used to demonstrate compliance 
with U.S. Nuclear Regulatory Commission (NRC) criticality requirements for handling, storage, 
and disposal of fissionable material and to support the resolution of Key Technical Issue 
agreement PRE 7.01 (Reamer 2001, Attachment 1, p. 2). Application of the approach will 
address applicable NRC design criteria and will also provide input to the preclosure safety 
analysis that will determine if the repository will meet its overall performance objectives for the 
repository operations relative to criticality through permanent closure. 
This report is written consistent with Yucca Mountain Review Plan, Final Report (NRC 2003), 
Standard Review Plan for the Review of a License Application for a Fuel Cycle Facility 
(NRC 2002a, Section 5) issued by the NRC’s Office of Nuclear Material Safety and Safeguards, 
and 10 CFR Part 63, Disposal of High-Level Radioactive Wastes in a Geologic Repository at 
Yucca Mountain, Nevada. Each of these documents provides a basis for risk-informed 
compliance demonstrations. While NUREG-1520 (NRC 2002a, Section 5) is not directly 
applicable to a facility for handling spent nuclear fuel (SNF), the risk-informed approach to 
criticality analysis in NUREG-1520 (NRC 2002a, Section 5) provides insight into the NRC’s 
approach to risk-informed criticality analysis. 
This report provides a single analysis process for determining the criticality potential or effective 
neutron multiplication factor (keff) of a configuration during preclosure operations. The process 
can be applied to design calculations and preclosure safety analyses. The difference between the 
two types of evaluations is the source of the configurations to be evaluated. Specific 
deterministically selected design configurations (e.g., fully moderated, most reactive fuel state) 
are used for design calculations. For the preclosure safety analysis, the probabilities of event 
sequences are estimated (e.g., Categorization of Event Sequences for License Application [BSC 
2004e, Section 7]). For those event sequences that could lead to potentially critical 
configurations, the probability of reaching such a configuration will be evaluated. If the overall 
probability of reaching a potentially critical configuration is above the probability threshold, a 
criticality evaluation of that configuration will be performed. 
The proposed approach for out-of-package operations will use the most reactive fuel state (i.e., a 
fresh fuel assumption with no burnup credit for nonbreeder reactor fuel, or the calculated most 
reactive state for breeder reactor fuel). The in-package operations will include credit for burnup 
similar to the postclosure methodology in Disposal Criticality Analysis Methodology Topical 
Report (YMP 2003). This approach is consistent with 10 CFR Part 63, NRC 2003, and NRC 
2002a, Section 5. 
Further, this methodology will provide a consistent transition from preclosure to postclosure 
analyses by using the same general approach, for in-package operations, submitted to the NRC in 
Disposal Criticality Analysis Methodology Topical Report (YMP 2003), which is intended for 
postclosure, and uses a risk-informed approach. The proposed approach will provide margin-to-

criticality for the preclosure time period. Margin-to-criticality is the sum of biases and 
uncertainties, administrative margins, and reactivity due to use of bounding models and 
parameters. For the cases described in this report, bounding models and parameters are those 
that describe a more reactive state than the actual state. 
For commercial SNF (CSNF), the primary difference between traditional licensing of fuel cycle 
facilities away from a reactor and the approach proposed here is the absence of burnup credit in 
the traditional approach. However, burnup credit is allowed for commercial spent nuclear fuel 
pools at commercial reactor sites (NRC 1998), storage, and transportation systems (NRC 2002b), 
which sets a precedent for obtaining burnup credit. Section 3.2.2 shows the similarities and 
differences between the proposed approach for obtaining burnup credit for preclosure and the 
approach used for spent nuclear fuel pools at reactor sites. 
1.2 OBJECTIVE 
The objective of this report is to present the approach for performing preclosure criticality 
analyses for waste packages and repository facilities for the time period beginning with waste 
form receipt at the surface facility until permanent closure of the subsurface facility. This report 
may be referenced for work supporting the license application. In addition, it is to provide a 
single reference for the proposed preclosure criticality analysis methodology and to present that 
methodology for review. The information presented in this report is not design information that 
can be used to support procurement, fabrication, or construction. 
1.3 SCOPE 
The scope of this report is to document the approach for performing preclosure criticality safety 
analyses. The approach will be used to perform criticality safety analyses for various 
configurations of waste forms, including but not limited to CSNF, defense high-level radioactive 
waste (e.g., Savannah River Site glass), and U.S. Department of Energy (DOE) SNF that could 
occur during preclosure as a result of normal operations and event sequences. Because of the 
characteristics of naval SNF, the Naval Nuclear Propulsion Program will apply a separate 
methodology to the preclosure analysis for naval fuel. The focus is on safety requirements and 
the methodology applied to all processes starting with the receipt of transportation casks in the 
Transportation Cask Receipt/Return Facility and includes everything through the final loading of 
waste packages for closure and emplacement in the subsurface, and their residence in the 
subsurface up to the time of permanent closure of the repository. 
The preclosure criticality analysis process is a derivative of the criticality analysis methodology 
presented in Disposal Criticality Analysis Methodology Topical Report (YMP 2003) and its 
supporting documents, especially Criticality Model (BSC 2004c) and Isotopic Model Report for 
Commercial SNF Burnup Credit (BSC 2004d). This ensures commonality in the calculational 
approaches. The essential differences in the methodology from the topical report and the process 
presented in this report are 1) the source of the configurations to be analyzed, 2) the time period 
over which events and processes are considered, and 3) the application (i.e., safety analysis 
versus waste isolation analysis). 

The proposed preclosure criticality analysis process is also applicable to scenarios involving the 
surface facility and fuel handling operations. It is used to evaluate an eigenvalue (i.e., the 
effective neutron multiplication factor, keff). The process describes only how the criticality 
calculations are performed for a given scenario. Construction of the scenarios to be evaluated is 
outside the scope of the process. This report has been written to consider many possible features 
of the process in order to provide flexibility to the user. Note that the user will apply the 
methodology appropriate to the process under analysis. 
The means to prevent and control criticality must be addressed as part of the preclosure safety 
analysis (10 CFR 63.112[e][6]). The purpose of the preclosure safety analysis is to identify 
initiating events, their potential event sequences, and their consequences, as well as structures, 
systems, and components (SSCs); and personnel activities that are important to safety. The 
identification of preclosure event sequences relating to criticality and the description of the 
process for the necessary criticality analyses are discussed in more detail in Section 3.1. 
The methods and guidance for developing and documenting the preclosure safety analysis are 
presented by Preclosure Safety Analysis Guide (BSC 2003b) in which Section 11 specifically 
discusses criticality and refers to this report for the process description. Section 11.1 
(BSC 2003b) notes three criticality safety analysis components. First, hazards analyses identify 
potential failures of SSCs designed to prevent or control the occurrence of a criticality. Next, an 
event sequence frequency analysis provides the means to evaluate the likelihood of such 
occurrences and to demonstrate whether or not they are credible. Last, if applicable, neutronics 
analyses provide design bases to prevent or control criticality, and to verify sub-criticality is 
maintained during the occurrence of Category 1 or 2 event sequences (10 CFR 63.2). 
1.4 QUALITY ASSURANCE 
The development of this report has been subject to DOE Office of Civilian Radioactive Waste 
Management Quality Assurance Requirements and Description (DOE 2004) controls, as 
specified in Technical Work Plan for: Criticality Department Work Packages ACRM01 and 
NSN002 (BSC 2004a, Section 8). Electronic management of data was accomplished in 
accordance with the controls specified in the Technical Work Plan for: Risk and Criticality 
Department Work Packages ACRM01 and NSN002 (BSC 2004a, Section 8). 
The work that is to be performed to support the license application using this information will be 
performed in accordance with the then current versions of NRC regulations and Quality 
Assurance Requirements and Description (DOE 2004). 
1.5 USE OF COMPUTER SOFTWARE 
No computer software subject to Quality Assurance Requirements and Description (DOE 2004) 
was used in the development of this report. Graphical figures are presented for illustrative 
purposes only, and no computations were performed for this report. 

INTENTIONALLY LEFT BLANK

2. PROCESS
Operation of a repository involves a number of distinct but interrelated waste form activities and 
functions; the major ones include receiving, handling, and packaging. 
There are five basic waste form handling operations that may affect preclosure criticality safety: 
1. 
Operations in the carrier/cask handling system 
2. 
Operations in the assembly transfer system 
3. 
Operations in the canister transfer system 
4. 
Operations in the waste package handling system 
5. 
Emplacement of waste packages 
It should be noted that the surface facilities are not finalized, but the major functions for 
criticality analyses are expected to remain the same. Therefore, any reference to a particular 
building designation or system is only conceptual. 
2.1 REQUIREMENTS 
The regulatory requirements for criticality safety for the Yucca Mountain project are described in 
10 CFR Part 63. The only citation in this regulation that specifically addresses criticality safety 
is: 
Requirements for preclosure safety analysis of the geologic repository operations 
area; The preclosure safety analysis of the geologic repository operations area 
must include an analysis of the performance of the structures, systems, and 
components to identify those that are important to safety. This analysis identifies 
and describes the controls that are relied on to limit or prevent potential event 
sequences or mitigate their consequences. This analysis also identifies measures 
taken to ensure the availability of safety systems. The analysis required in this 
paragraph must include, but not necessarily be limited to, consideration of means 
to prevent and control criticality (10 CFR 63.112 [e][6]). 
Project requirements relating to criticality safety are described in Project Requirements 
Document (Canori and Leitner 2003) and Project Functional and Operational Requirements 
(Curry 2004). These requirements are not detailed here, but this report’s applications refer to 
appropriate preclosure project requirements. 
2.2 CRITICALITY CONTROL CRITERIA AND GUIDANCE 
Since the regulatory requirements of 10 CFR 63.112 [e][6] are not detailed, it is useful to 
describe the general design criteria, NRC guidance, analysis methods and computer codes, 
events, operations, and other considerations that will be used to guide the design approach for 
criticality analyses. This section focuses on the guidance that will be used to implement the 
requirements of 10 CFR 63.112[e][6]. 

2.2.1 General Design Criteria 
The general guidance used for waste form storage and handling is to confirm that analyses used 
to identify SSCs important to safety, safety controls, and measures to ensure the availability of 
the safety systems include adequate consideration of means to prevent or control criticality, such 
as complying with American National Standards Institute (ANSI)/American Nuclear Society 
(ANS) nuclear criticality safety standard documents listed in Regulatory Guide 3.71 (1998). The 
standards applicable to nuclear criticality safety are listed in Section 2.2.3. The term “waste 
form” will be applied to the canistered or uncanistered form (e.g., commercial fuel assembly). 
According to Appendix A of 10 CFR Part 50, General Design Criterion 62, the primary design 
criterion for prevention of criticality in fuel storage and handling is as follows: 
Criticality in the fuel storage and handling system shall be prevented by physical 
systems or processes, preferably by use of geometrically safe configurations. 
This criterion has been used in recent license applications for multiregion spent nuclear fuel 
storage racks, checkerboard-loading patterns for spent nuclear fuel storage, credit for burnup, 
and credit for nonremovable poison inserts (Kopp 1998). It applies to the waste forms in the 
scope of this report. 
Additional project design criteria applicable to criticality safety will also be met. 
2.2.2 NRC Guidance 
Guidance from the NRC pertaining to nuclear criticality safety analysis is contained in several 
technical documents issued by the NRC or under NRC direction. They include Regulatory 
Guides, Interim Staff Guidance documents, as well as those issued by the NRC directly (NUREG 
series) or by their contractors (NUREG/CR series). Those applicable to the preclosure criticality 
analysis process are listed in Table 1. 

Table 1. NRC Guidance Document Applicability 
Guidance Document Applicability Description 
Regulatory Guide 3.60 (1987), Design of Out-of-package Supports issues regarding criticality safety for 
an Independent Spent Fuel Storage fuel staging area and surface aging facility. 
Installation (Dry Storage) 
Regulatory Guide 3.71 (1998), Nuclear Out-of-package Acceptance and exceptions to the ANSI/ANS 
Criticality Safety Standards for Fuels and and in-package standards in Section 2.2.3 are noted. 
Material Facilities 
ISG-1, Revision 1 (NRC 2002c), Out-of-package Includes a definition of damaged fuel and 
Damaged Fuel and in-package describes requirements for nuclear criticality 
safety analysis of damaged fuel. 
ISG-8, Revision 2 (NRC 2002b), Burnup In-package This guidance includes information regarding 
Credit in the Criticality Safety Analyses of the use of burnup credit. 
PWR Spent Fuel in Transport and Storage 
Casks 
ISG-11, Revision 2 (NRC 2002d), Out-of-package Describes the potential reconfiguration of fuel 
Cladding Considerations for the and in-package during storage operations as related to creep 
Transportation and Storage of Spent Fuel and temperature effects. 
ISG-15 (NRC 2001), Materials Evaluation Out-of-package This guidance includes information regarding 
and in-package the use of neutron absorbing/poison materials 
for criticality control. 
NRC Letter (Kopp 1998), “Guidance on Out-of-package Although directed at nuclear power plants, 
the Regulatory Requirements for Criticality and in-package this guidance is useful to the Yucca Mountain 
Analysis of Fuel Storage at Light-Water Project because it includes several 
Reactor Power Plants” clarifications and documents the current NRC 
positions regarding the storage of SNF. 
NUREG-1536 (NRC 1997), Standard 
Review Plan for Dry Cask Storage 
Systems (Section 6) 
Out-of-package 
and in-package 
This guidance includes information regarding 
criticality design and analysis related to spent 
nuclear fuel handling, packaging, transfer, 
and storage procedures for normal, off-
normal, and accident conditions as pertaining 
to 10 CFR Part 72. 
NUREG-1567 (NRC 2000, Sections Out-of-package This guidance includes information regarding 
4.4.3.5, 4.5.3.5, and 8), Standard Review stored materials remaining subcritical under 
Plan for Spent Fuel Dry Storage Facilities normal, off-normal, and accident conditions 
during all operations, transfers, and storage 
at the site as pertaining to 10 CFR Part 72. 
NUREG-1804 (NRC 2003), Yucca Out-of-package This guidance is the review plan for the 
Mountain Review Plan, Final Report and in-package Yucca Mountain project and pertains to 
(Various sections) 10 CFR Part 63. 
NUREG/CR-6361 (Lichtenwalter et al. Out-of-package This guidance includes information regarding 
1997), Criticality Benchmark Guide for and in-package benchmark experiment selection process and 
Light-Water-Reactor Fuel in methods for calculating critical limits. 
Transportation and Storage Packages 
NUREG-1520 (NRC 2002a, Section 5), Out-of-package This guidance includes information regarding 
Standard Review Plan for the Review of a and in-package nuclear criticality safety to support safe 
License Application (LA) for a Fuel Cycle operation of the facility, as required by 
Facility 10 CFR Part 70. 

Although not directly applicable to the Yucca Mountain Project, 10 CFR Part 72 provides a more 
detailed list of regulations relating to criticality safety, which will be used for general guidance. 
The portion that specifically addresses criticality safety, which provides guidance for out-of-
package operations, is noted in 10 CFR 72.124, which states: 
(a) 
Design for criticality safety. Spent fuel handling, packaging, transfer, and 
storage systems must be designed to be maintained subcritical and to ensure that, 
before a nuclear criticality accident is possible, at least two unlikely, independent, 
and concurrent or sequential changes have occurred in the conditions essential to 
nuclear criticality safety. The design of handling, packaging, transfer, and storage 
systems must include margins of safety for the nuclear criticality parameters that 
are commensurate with the uncertainties in the data and methods used in 
calculations and demonstrate safety for the handling, packaging, transfer and 
storage conditions and in the nature of the immediate environment under accident 
conditions. 
(b) 
Methods of criticality control. When practicable, the design of an ISFSI 
[independent spent fuel storage installation] or MRS [monitored retrievable 
storage] must be based on favorable geometry, permanently fixed neutron 
absorbing materials (poisons), or both. Where solid neutron absorbing materials 
are used, the design must provide for positive means of verifying their continued 
efficacy. For dry spent fuel storage systems, the continued efficacy may be 
confirmed by a demonstration or analysis before use, showing that a significant 
degradation of the neutron absorbing materials cannot occur over the life of the 
facility. 
Out-of-package criticality analysis includes the evaluation of processes starting with the receipt 
of transportation casks and includes everything up to the loading of waste packages for closure 
and emplacement in the subsurface. In-package criticality analysis includes the evaluation of 
processes starting with the loading of waste packages for closure and emplacement and 
continuing until the time of permanent closure. 
The guidance provided in NUREG-1520 (NRC 2002a, Section 5), for criticality safety analysis, 
provides insight into the NRC’s approach to risk-informed regulation of spent nuclear fuel 
handling and storage facilities. Criticality control in the carrier/cask handling system is largely 
provided by transportation casks designed and licensed in accordance with requirements in 
10 CFR Part 71, Packaging and Transportation of Radioactive Material, and by spent nuclear 
fuel loading procedures implemented at the transportation cask’s point of origin. 
The guidance from Guidance on the Regulatory Requirements for Criticality Analysis of Fuel 
Storage at Light-Water Reactor Power Plants (Kopp 1998) was intended for commercial spent 
nuclear fuel; however, it is being applied for waste forms listed in this report, unless indicated 
differently. This guidance comes from the NRC Reactor Systems Branch and is used in assuring 
criticality safety in the storage of new and spent nuclear fuel at light-water reactor power 
stations. 

The following guidance from Kopp (1998) is applicable to CSNF (pressurized water reactor 
[PWR] and boiling water reactor [BWR] spent nuclear fuel). 
Preclosure criticality analyses will use a bounding model and parameters, which will result in a 
more reactive state than the actual or real state. Sensitivity studies will be performed to ensure 
that a bounding representation is used. The determination of the effective neutron multiplication 
factor (keff) for CSNF will consider the following: 
A. Fuel rod parameters, including: 
1. 
Fuel pellet diameter 
2. 
Cladding material and inner and outer diameters 
3. 
Fuel rod pellet or stack density and initial fissile enrichment of each fuel rod in 
the assembly (a bounding enrichment is acceptable) 
4. 
Active fuel height. 
B. Fuel assembly parameters, including: 
1. 
Assembly length and planar dimensions 
2. 
Fuel rod pitch 
3. 
Total number of fuel rods in the assembly 
4. 
Locations in the fuel assembly lattice that are empty or contain nonfuel material 
(e.g., guide tubes, burnable poison rods) 
5. 
Integral neutron absorber (burnable poison) content of various fuel rods and 
locations in fuel assembly. This is typically proprietary information and may not 
be available. For out-of-package operations no credit will be taken for the 
presence of integral absorbers. For in-package operations, no credit will be taken 
for residual integral absorbers in the fuel. 
6. 
Structural materials (e.g., grids) that are an integral part of the fuel assembly. 
Similar considerations on geometry and material concentrations will be used for the other waste 
forms (e.g., DOE SNF), both in-package and out-of-package, in the scope of this report. These 
considerations will also focus on the geometry and material concentrations of the waste forms. 
For CSNF, the criticality safety analyses will use a bounding approach for the treatment of axial 
and planar variations of fuel assembly characteristics, such as fuel enrichment and integral 
neutron absorber if present (e.g., gadolinia (Gd2O3) in certain fuel rods of BWR and PWR 
assemblies or integral fuel burnable absorber coatings in certain fuel rods of PWR assemblies, or 
gadolinia in plutonium). The latter characteristics should only be required if it is intended to take 
credit for the presence of these materials; however, they may be required if burnup credit is taken 

for in-package operations. The bounding approach used for axial variations will be to use the 
maximum initial enrichment at each axial level, and planar variations will be bounded by not 
taking credit for integral neutron absorbers. When burnup credit is taken, the spent nuclear fuel 
isotope concentrations will be generated using the isotopic model (BSC 2004d), which will 
provide conservative spent nuclear fuel isotope concentrations with respect to criticality safety 
applications. For waste forms other than CSNF, credit for integral absorbers can be used if there 
are no mechanisms that remove the absorber during preclosure. 
Whenever reactivity equivalencing (i.e., burnup credit or credit for imbedded burnable 
absorbers) is employed, or if a correlation with the reactivity of commercial fuel assemblies in 
standard core geometry is used, the equivalent reactivities must be evaluated in the waste 
package configuration (out-of-package operations will not use reactivity equivalencing). 
Sufficient margin will be incorporated into the calculated keff values to account for the reactivity 
effects of the following: 
• 
Nonuniform enrichment variation (this will be handled by using the maximum 
enrichment over the whole assembly length) 
• 
Uncertainty in the calculation of keff (bias and uncertainty determined from benchmark 
calculations) 
• 
Uncertainty in average enrichment (this will be handled by using the maximum 
enrichment over the whole assembly length). 
If criticality safety relies on administrative controls, these controls will be explicitly identified 
and implemented in operating procedures and/or technical specification limits. 
2.2.3 Standards 
Several standards have been identified by the NRC in Regulatory Guide 3.71 (1998) as being 
applicable to nuclear criticality safety. These have also been cited in various NUREG 
documents relating to nuclear criticality safety, including NUREG-1520, -1567, and -1804 (NRC 
2002a, Section 5; NRC 2000, Sections 4.4.3.5, 4.5.3.5, and 8; and NRC 2003) and are as follows: 
• 
ANSI/ANS-8.1-1983. Nuclear Criticality Safety in Operations with Fissionable 
Materials Outside Reactors. 
• 
ANSI/ANS-8.3-1997. Criticality Accident Alarm System. 
• 
ANSI/ANS-8.5-1996. Use of Borosilicate-Glass Raschig Rings as Neutron Absorber in 
Solutions of Fissile Material. 
• 
ANSI/ANS-8.7-1998. 1999. American National Standard for Nuclear Criticality Safety 
in the Storage of Fissile Materials. 
• 
ANSI/ANS-8.10-1983. Criteria for Nuclear Criticality Safety Controls in Operations 
with Shielding and Confinement. 

• 
ANSI/ANS-8.12-1987. American National Standard for Nuclear Criticality Control 
and Safety of Plutonium-Uranium Fuel Mixtures Outside Reactors. 
• 
ANSI/ANS-8.15-1981. Nuclear Criticality Control of Special Actinide Elements. 
• 
ANSI/ANS-8.17-1984. Criticality Safety Criteria for the Handling, Storage, and 
Transportation of LWR Fuel Outside Reactors. 
• 
ANSI/ANS-8.19-1996. American National Standard, Administrative Practices for 
Nuclear Criticality Safety. 
• 
ANSI/ANS-8.21-1995. American National Standard for the Use of Fixed Neutron 
Absorbers in Nuclear Facilities Outside Reactors. 
• 
ANSI/ANS-8.22-1997. American National Standard for Nuclear Criticality Safety 
Based on Limiting and Controlling Moderators. 
The following provides a listing of exceptions to parts of the recommended standard documents 
and guidance from Regulatory Guide 3.71 (1998): 
1. Exceptions are taken with portions of the recommended ANSI/ANS-8 nuclear 
criticality safety standards that are being used. 
a. 
The double contingency principle is not applied since it is expanded on and 
subsumed in the risk-informed, performance-based approach from 10 CFR Part 
63. The double contingency approach typically evaluates event sequences until at 
least two unlikely, independent, and concurrent changes in process conditions are 
required before a criticality accident is possible. The risk-informed approach uses 
Probabilistic Risk Assessment to calculate probabilities of events with potential 
public health consequences and the magnitudes of these potential health 
consequences, so that an entire event sequence is evaluated from initiation to 
conclusion, including event sequences which may have been otherwise terminated 
by a double contingency approach. 
b. 
Use of single parameter limits for aqueous solutions, aqueous mixtures, metallic 
units, and oxides of fissile material described that are not scheduled for disposal 
at the repository. 
c. 
Use of multiparameter control for systems of fissile material described that are not 
scheduled for disposal at the repository. 
2. 
An exception is being made to the requirement in Regulatory Guide 3.71 (1998) that 
criticality alarm systems be present in each area where special nuclear material is 
handled, used, or stored. Criticality accident alarm systems will not be used in 
repository facilities provided an adequate demonstration is made to show that the dose 
consequence to personnel locations is less than 0.12 gray/12 rads (ANSI/ANS-8.3-
1997, Section 3.3) or, the probability of criticality is beyond a Category 2 event 
sequence. 

3. 
Additional physical measurements of burnup are not performed for CSNF assemblies. 
The burnup values used for burnup credit purposes will be based on reactor records 
and process knowledge, with allowance made for uncertainty in the burnup values 
from the records. The records are more accurate than the physical measurements 
performed outside a reactor. Physical measurements of burnup will not be performed 
for the other waste forms either since a fresh fuel assumption with no burnup credit is 
used for nonbreeder reactor fuel, and calculated most reactive state, is used for breeder 
reactor fuel. 
2.2.4 Criticality Analysis Methods and Computer Codes 
The MCNP (Briesmeister 1997) computer code will be used for the criticality analyses. The 
Monte Carlo computational method is discussed in the Criticality Model (BSC 2004c, Section 
6.1) and briefly summarized in Section 3.3 of this report. As noted below, the analysis method 
embodied in this code will be benchmarked by comparison with experiments. However, if 
further confirmation is needed, Kopp (1998, p. 3) recommends the primary method of analysis 
be verified by a second, independent method of analysis. According to Kopp (1998, p. 3) 
acceptable computer codes include, but are not necessarily limited to, the following: 
• 
CASMO–A multigroup transport theory code in two dimensions 
• 
NITAWL-KENO5a–A multigroup transport theory code in three dimensions, using the 
Monte Carlo technique 
• 
PHOENIX-P or DOT–A multigroup transport theory code in two dimensions, using 
discrete ordinate 
• 
MONK6B–A multigroup transport theory code in three dimensions, using the Monte 
Carlo technique. 
These codes are not currently used on the Yucca Mountain Project, and would have to be 
qualified if used in the future. 
The proposed analysis methods and neutron cross-section data will be benchmarked by 
comparison with critical experiments. This qualifies the application and the computer 
environment. The critical experiments used for benchmarking will include, to the extent 
possible, configurations having neutronic and geometric characteristics similar to those of the 
proposed system. As it is released, the latest version of International Handbook of Evaluated 
Criticality Safety Benchmark Experiments (NEA 2001) will be the primary benchmark 
experiment reference. Commercial reactor critical (CRC) systems will also be used in 
benchmarking for in-package operations. A comparison with methods of analysis of similar 
sophistication (e.g., transport theory) may be used to augment or extend the range of applicable 
critical experiment data. 
The benchmarking analysis will establish both a bias (defined as the mean difference between 
experimental and calculated values) and uncertainty of the mean with a one-sided tolerance 

factor for 95 percent probability at the 95 percent confidence level (Kopp 1998, pp. 3 and 4). 
The maximum keff shall be evaluated from the following expression: 
keff = k (calc) + .k (uncert) + .k (burnup) (Eq. 1) 
where 
k (calc) = calculated nominal value of keff 
.k (uncert) = manufacturing and calculational bias and uncertainties 
.k (burnup) = correction for the effect of the axial distribution in burnup when credit 
for burnup is taken (Note: provisions for the uncertainty in the average 
burnup of a fuel assembly must also be made in the loading criteria) 
Use of the last term, .k (burnup), is not applicable to out-of-package applications and may be 
obviated for in-package applications by use of the design constraints for postclosure criticality 
analysis (YMP 2003). The uncertainty associated with a SNF assembly’s assigned burnup value 
is accounted for by adjusting the minimum required burnup, as a function of enrichment, upward 
by the uncertainty associated with the assigned assembly average burnup values. 
A bias that would reduce the calculated value of keff will not be applied to ensure calculations 
will always be conservative. Uncertainties should be determined for the system to account for 
tolerances in the mechanical and material specifications. An acceptable method for determining 
the maximum reactivity may be either: (1) a worst-case combination with mechanical and 
material conditions set to maximize keff, or (2) a sensitivity study of the reactivity effects of 
tolerance variations. 
If used, a sensitivity study should include all possible significant variations (tolerances) in the 
material and mechanical specifications of the storage racks and waste packages including fuel 
assembly bowing and crud build-up on the rods. The results may be combined statistically, 
provided they are independent variables. 
Classification of SNF and high-level waste from commercial and DOE sources will be 
performed in order to economize in the number of criticality cases that must be considered. This 
is accomplished by reducing the many different types of SNF and high-level radioactive waste to 
as few as possible bounding types. From these classifications, a reduced set of groupings will be 
defined according to those that result in greatest reactivity conditions based on parametric 
studies. 
2.2.5 Initiating Events and Event Sequences 
Criticality safety analyses will consider event sequences related to criticality. An analysis of the 
performance of the SSCs to identify those that are important to safety will be performed. This 
analysis will identify and describe the controls that are relied on to limit or prevent potential 
event sequences or mitigate their consequences. This analysis will consider means to prevent 
and control criticality, and to identify measures taken to ensure safety systems availability. 

2.2.6 In-Package Operations 
Dry waste forms are transferred into waste packages and then into the repository. However, 
moderator may be introduced into the system under abnormal situations, such as flooding or the 
introduction of foam, water mist (e.g., a result of fire fighting operations), or oil (e.g., hydraulic 
fluids). Optimum moderation is the level at which peak reactivity occurs. Because, in the case 
of foam or mist, the peak reactivity may occur at less than full-density water (1.0 g/cm3), 
sensitivity studies will be conducted to determine the optimum moderation condition and its 
associated keff. Therefore, criticality safety analyses must address one of two conditions that 
should be incorporated into facility technical specifications. The second condition needs to be 
incorporated only in the event a waste package is determined to be overmoderated. The two 
conditions follow: 
• 
With the waste package loaded with waste of the maximum permissible reactivity and 
flooded with pure water, the maximum keff shall be no greater than 0.95 (Kopp 1998, 
p. 5), including mechanical and calculational uncertainties, with a 95-percent probability 
at a 95-percent confidence level. 
• 
With the waste package loaded with waste of the maximum permissible reactivity and 
flooded with moderator at the (low) density corresponding to optimum moderation, the 
maximum keff shall be no greater than 0.98 (Kopp 1998, p. 5), including mechanical and 
calculational uncertainties, with a 95-percent probability at a 95-percent confidence 
level. 
An evaluation need not be performed for the waste package flooded with low-density or 
full-density water if it can be clearly demonstrated that design features prevent such flooding 
(Kopp 1998, p. 5). 
The waste package may be designed with lattice controls (e.g., large lattice spacing or 
mechanically blocked lattice positions) sufficient to maintain a low reactivity under the accident 
condition of flooding. In the evaluation of the waste package, waste form and system 
characteristics upon which subcriticality depends will be explicitly identified (e.g., the presence 
of steel plates or other structures). The waste package should be designed to contain the most 
reactive waste form to be stored without taking credit for any nonfixed neutron absorber. 
2.2.7 Out-of-Package Operations 
Spent nuclear fuel assemblies may be stored in dry storage racks with off-normal assemblies 
being stored in a pool if necessary. For each storage configuration the following processes will 
be used in performing the out-of-package criticality calculations: 
1. 
Design of facilities will be based on most reactive fuel assemblies. 
2. 
The effective neutron multiplication factor (keff), including all biases and uncertainties 
at a 95-percent confidence level, will not exceed 0.95 under all credible normal, off-
normal, and accident conditions (NRC 2000, Section 8.4.1.1). The latter two 
conditions are inclusive of Category 1 and 2 event sequences as defined in 

10 CFR 63.2. If bias is positive for any variable, a value of 0.0 will be assigned for 
that variable in the overall determination. 
3. 
Criticality modeling will use conservative assumptions leading to maximum reactivity 
for all dimensional variables including: 
A. Pitch for fuel assemblies and canisters 
B. Manufacturing tolerances for assemblies, canisters, storage racks, etc. 
4. Criticality modeling will use conservative assumptions regarding materials in fuel 
including but not limited to: 
A. No burnable poisons will be accounted for in fuel. 
B. No credit will be taken for 234U or 236U in fuel. 
C. No credit will be taken for fission product or transuranic absorbers in fuel. 
D. Most reactive fuel stack density will be assumed. 
5. 
For fixed neutron absorbers used for criticality control such as grid plates or inserts, no 
more than 75 percent (NRC 2000, Section 8.4.1.1) credit of the neutron absorber 
content is used for preclosure criticality analyses, unless standard acceptance tests 
verify that the presence and uniformity of the neutron absorber are more effective. 
6. 
The design of storage racks in the pool located in the remediation facility will be based 
on excluding soluble boron for criticality control. 
7. 
Consideration will be given to extensions of important data variables such as quantity 
and density of moderator. For any moderator present (e.g., water, foam, oil), 
appropriate ranges of quantity and density will be examined. This will ensure 
optimum moderation conditions will be considered. 
8. 
Consideration will be given to potential reflectors during transfer and placement. 
2.2.8 Additional Considerations 
Although not strictly part of the process of calculating keff, the following additional 
considerations may apply to determination of design configurations or event sequences. The first 
four items apply to in-package or out-of-package operations. The last two items apply to in-
package operations. 
1. 
The analysis must consider the effect on criticality of natural events (e.g., earthquakes) or 
incidents (e.g., dropped assembly) that may deform or change the relative position of the 
storage configuration or the waste package. 

2. 
Normally, credit may only be taken for neutron absorbers that are an integral 
(nonremovable) part of the system. Credit for added absorber (rods, plates, or other 
configurations) will be considered on a case-by-case basis, provided it can be clearly 
demonstrated that design features prevent the absorbers from being removed, either 
inadvertently or intentionally without unusual effort, such as the necessity for special 
equipment maintained under administrative control. 
3. 
Consolidated fuel assemblies usually result in low values of reactivity (undermoderated 
lattice, which results in less effective neutron thermalization). Nevertheless, criticality 
calculations, using an explicit geometric description (usually triangular pitch) or as near 
an explicit description as possible, should be performed to assure a keff less than 0.95. 
This option may be applied for off-nominal assembly types. 
4. 
Evaluation of fabrication errors for canister, waste packages, and storage racks. 
5. 
Misloading of waste form in the waste package must be considered. Normally, a 
misloading error involving more than a single unit need not be considered unless there 
are circumstances that make multiloading errors credible. 
6. 
Although the surface facilities are not in the final design phase, it is expected that waste 
packages, once loaded, will be kept in separate handling lines such that package-to-
package interaction is unlikely. Once the waste package is sealed, the introduction of 
moderator into the package is not probable; therefore, even if packages were placed next 
to each other, the spacing between assemblies within the packages provides sufficient 
neutronic decoupling. Nevertheless, sensitivity calculations should be performed to 
demonstrate that waste packages will not interact with each other, from a neutronics 
standpoint. 

3. CRITICALITY ANALYSIS
Criticality evaluations are performed for configurations from event sequences or design 
configurations over the range of parameters established based on pertinent characteristics (e.g., 
geometric arrangement). In-package and out-of-package configurations that may have the 
potential for criticality are considered. 
An overview of the preclosure criticality analysis process is presented in Figure 1. This process 
is described in Sections 3.1 through 3.5, as outlined below. 
Section 3.1 describes the identification of event sequences and design configurations requiring 
criticality evaluations. This includes establishment of the range of parameters for the event 
sequences and design configurations, specifically the materials of the waste package and waste 
form, the geometry of the waste package and waste form, and the neutron energy spectrum 
affecting fissionable materials. 
Section 3.2 discusses waste form characteristics, i.e., isotopic concentrations, including use of 
burnup credit for in-package evaluations of commercial spent nuclear fuel (CSNF). 
Section 3.3 summarizes the calculation of keff using the Criticality Model (BSC 2004c). 
Section 3.4 describes validation, including determination and application of an upper subcritical 
limit (USL). The USL is an upper limit placed on keff to ensure subcriticality with allowances 
made for the bias and uncertainty in the calculation model, as well as an arbitrary administrative 
criticality safety margin. Determination of the USL includes (1) selection of appropriate 
benchmark experiments, (2) establishment of the range of applicability of those experiments, (3) 
establishment of a lower-bound tolerance limit, and, if necessary, (4) establishment of any 
penalties for extending the range of applicability. 
Section 3.5 discusses the USL criterion. 
Finally, Section 3.6 discusses the application of the preclosure criticality analysis process. 

Event 
Sequence or 
Design 
Configuration 
Evaluated 
Establish ROP for 
Benchmark 
Experiment Select experiments Event Sequence or
Design Configuration
Waste form 
Database 
characteristics 
Perform criticality analysis over 
Evaluate 
Establish ROA the range of parameter values for 
additional 
(k
experiments of experiments event sequence or design
configuration
eff and spectral parameters)
Yes 
Are there other 
Does ROA 
Spectral 
parameters 
Isotopic 
No
experiments? 
include ROP? 
Model 
(if using 
burnup credit) 
No Yes 
k
eff 
Establish
additional
Establish USL .kISO 
margin 
(.k
EROA) 
.km 
Satisfy Yes Is keff < USL? 
No 
Does Not Satisfy 
NOTES: .kEROA = penalty for extending the range of applicability 
.kISO = penalty for isotopic composition bias and uncertainty for burnup credit 
.km = an arbitrary margin ensuring subcriticality for preclosure 
Figure 1. Preclosure Criticality Analysis Process Overview 
3.1 IDENTIFICATION OF CRITICALITY EVENT SEQUENCES AND DESIGN 
CONFIGURATIONS 
Criticality event sequences are a series of actions, occurrences, or both within the repository 
operations area that could potentially lead to a criticality event. An event sequence may include 

one or more initiating events and any associated number of combinations of system component 
failures, including those produced by operating personnel action or inaction. Those event 
sequences expected to occur one or more times before permanent closure of the repository are 
referred to as Category-1 event sequences. Those with at least one chance in 10,000 of occurring 
before permanent closure are referred to as Category-2 (10 CFR 63.2). 
Criticality safety standards require the keff of the system being evaluated be maintained below 
unity (1.0), after allowance for bias and uncertainty in the method of calculation and any 
administrative margin imposed during all Category-1 and Category-2 event sequences. Hazards 
considered incredible (i.e., that could initiate neither a Category-1 or Category-2 event sequence) 
would be identified, but will not require evaluation in the preclosure safety analysis. 
The event sequences to be considered as part of the criticality safety analysis are identified as 
part of preclosure safety analysis. Event sequences must be determined through review of the 
facility design. Reviews to identify and categorize such events have been previously identified 
in Categorization of Event Sequences for License Application (BSC 2004e, Section 7). 
However, the list of event sequences provided in this categorization is not specific to criticality 
safety. For the criticality safety portion of the preclosure safety analysis, otherwise benign 
events must also be considered. These include events that may result in unanticipated 
moderation (e.g., activation of sprinkler systems, introduction of hydrogenous fluids from failed 
hydraulic cylinders or oil systems), formation of unanticipated geometries (e.g., drop events), or 
administrative errors in waste form placement (e.g., misloads [BSC 2003a]). 
Design configurations are identified during the design process for the surface facilities and the 
waste packages. Criticality evaluations of these configurations, e.g., spacing of CSNF 
assemblies in storage racks or determination of absorber plate materials for a waste package, are 
performed as part of the design process. 
Given an event sequence from a hazards analysis or a design configuration to be evaluated, the 
appropriate range of parameters representing the material composition and geometry is 
determined. Specifically, there are three fundamental areas (Lichtenwalter et al. 1997, p. 179) to 
be considered: (1) materials of the waste package and waste form, especially fissionable 
materials, (2) geometry of the waste package and waste forms, and (3) the inherent neutron 
energy spectrum affecting fissionable materials. For example, these could include the range of 
initial enrichments of the CSNF, the thickness of absorber plates in a waste package, the 
spacings of assemblies in a storage rack, and neutronic parameters such as the H/X ratio and the 
neutron spectrum. 
3.2 WASTE FORM CHARACTERISTICS 
The approach for modeling isotopic concentrations from the waste forms applicable to preclosure 
is described by a two-step process (BSC 2004d). First, the initial isotopic concentrations of the 
waste form at the time of emplacement in the repository are established. Second, the changes in 
isotopic concentrations resulting from isotopic decay are calculated. 
For each waste form type, design values for fissionable isotopic concentrations or technical 
specification limits for fissile isotope concentrations will be used in establishing the initial 

isotopic content of the waste form. When fissile isotope production during reactor operations 
leads to a higher reactivity (e.g., breeder fuel), adjustments will be made to the design values to 
account for the increase in fissile isotopic content. For in-package operations, the isotopic 
concentrations will then be adjusted to account for isotopic decay until the time of the potential 
criticality or a time that provides more conservative isotopic concentrations. This modeling 
approach for these waste forms must be confirmed to be conservative with respect to criticality. 
3.2.1 Fresh or Most-Reactive Fuel 
Out-of-package evaluations for all waste forms and in-package evaluations for DOE SNF and 
high-level waste will use the most reactive fuel state (i.e., fresh fuel assumption with no burnup 
credit for nonbreeder reactor fuel, or calculated most reactive state for breeder reactor fuel). The 
in-package operations will include credit for burnup for CSNF similar to the postclosure 
methodology (YMP 2003). 
3.2.2 Isotopic Model for CSNF Burnup Credit 
For CSNF, the reduced reactivity associated with the net depletion of fissile isotopes and the 
creation of neutron-absorbing isotopes during the period since the fuel was first inserted into a 
commercial reactor can reduce the criticality potential of CSNF configurations. This period 
includes the irradiation time of the fuel in a reactor, the downtime between irradiation cycles, 
and the cooling time since the fuel was removed from the reactor. Taking credit for the reduced 
reactivity associated with this change in fuel material composition is known as burnup credit. 
This credit is taken only for in-package evaluations for CSNF. The isotopic model (BSC 2004d) 
determines the concentrations of the isotopes that are present in the CSNF and subsequently used 
in the in-package criticality evaluations. 
Typically, an assembly’s reported burnup values are averages, which underestimate burnup at the 
center of the assembly and overestimate burnup at the top and the bottom. As fuel is burned in a 
reactor, the fuel burnup distributes axially and fuel reactivity decreases. To adequately use 
burnup credit, axial effects must be understood. This requires that an estimate of the reactivity 
effects of the axial burnup distribution relative to uniform distribution must be determined and 
appropriately applied to the results. This is discussed in Section 3.2.3. Alternatively, the explicit 
axial distribution can be modeled in the keff calculation, which removes the need for application 
of an axial burnup penalty. 
Radiochemical assay data can be used in conjunction with CRC data to validate the isotopic 
model (BSC 2004d). The CRC data addresses the integral contribution of isotopic 
concentrations to criticality. Radiochemical assay data provide measured concentrations for 
individual isotopes. Conservative calculations of isotopic concentrations are ensured by 
choosing bounding parameters for the fuel irradiation. A comparison of the keff for nominal 
parameter values and bounding values are performed to determine the magnitude of 
conservatism caused by the use of bounding values. 
The following discussion compares licensing approaches for obtaining burnup credit for CSNF 
in commercial reactor spent nuclear fuel pools and for a waste package during preclosure at 

Yucca Mountain. The purpose of this comparison is to demonstrate the similarities between 
NRC accepted industry practices and the project approach. 
The basis for the statements on the proposed approach for the waste package is Disposal 
Criticality Analysis Methodology Topical Report (YMP 2003). The basis for the statements on 
licensing practices used for burnup credit at spent nuclear fuel pools are provided in “Guidance 
on the Regulatory Requirements for Criticality Analysis of Fuel Storage at Light-Water Reactor 
Power Plants” (Kopp 1998) and Rochester Gas and Electric Corporation, Docket No. 50-244, 
R.E. Ginna Nuclear Power Plant, Amendment to Facility Operating License (NRC 1998). 
Spent nuclear fuel pools at reactor sites and preclosure conditions for a waste package are similar 
since (1) both involve the movement and storage of CSNF in a secured facility with no proximity 
to the public, and (2) both have multiple protective barriers against criticality or its consequences 
(e.g., geometric spacing, soluble or fixed absorbers, shielding). Consequently, the NRC can 
consider reductions in administrative margin-to-criticality for reactor sites (Kopp 1998, 4(b) p. 5, 
2(a) p. 6). 
Other similarities are as follows: 
• 
Isotopic Calculations-Both use isotopic compositions from computer codes using the 
same basic equations. Calculations for pools and waste packages can both use one- or 
two-dimensional geometry. 
• 
Criticality Calculations-Both use industry-accepted computer codes. The NRC has 
accepted the codes when used for spent nuclear fuel pools. 
• 
Modeling of Axial Burnup Effects-Both use bounding axial shapes obtained from 
reactor experience. 
• 
Loading Curves-The approach for the waste package (see the example in Appendix A) 
is identical to that for a spent nuclear fuel pool. 
• 
Bias and Uncertainties-Both use a statistical approach defined in standards and 
regulatory guides. 
• 
Validation of Criticality Calculations-Both use laboratory critical experiments (LCE). 
For the waste package, CRCs are used directly. The spent nuclear fuel pools use their 
commercial reactor experience indirectly; that is, the NRC recognizes licensees have 
reactor experience with their methods for determining burnup and isotopic content for 
reactivity calculations (NRC 1998, p.1 and Section 2.1.1). 
• 
Risk Analysis- This is not necessarily related to burnup credit, although it could be 
(e.g., frequency of misloads based on loading restriction related to minimum burnup). 
For spent nuclear fuel pools, the current practice is to use the double-contingency 
principle, except the frequency of events is not necessarily determined. For the waste 
package, the proposed approach is to classify event sequences and show criticality is the 
result of an incredible event. 

The method to predict CSNF compositions for preclosure begins by calculating the isotopic 
concentrations of fissile and neutron-absorbing isotopes to be used for criticality evaluations. 
These calculations are based on conservative model input parameters, fuel-assembly burnup 
data, and fuel-assembly design data. 
The criticality analysis model that will be applied for waste packages containing CSNF uses a 
subset of the isotopes present in the CSNF, which is consistent with the postclosure methodology 
(YMP 2003). The process for establishing the isotopes to be included is based on the nuclear, 
physical, and chemical properties. Nuclear properties considered are isotope cross-sections and 
half-lives (as applicable); physical properties are concentration (amount present in the SNF) and 
state (solid, liquid, or gas); and chemical properties are isotope volatility and solubility. Time 
effects (during disposal) and relative importance of isotopes for criticality (combination of cross-
sections and concentrations) are considered in this selection process. None of the isotopes with 
significant positive reactivity effects (fissionable isotopes) are removed from consideration, only 
nonfissionable absorbers are removed. Thus, the selection process is conservative. 
This process results in selecting 14 actinides and 15 fission products (referred to as “principal 
isotopes” and listed in Table 2) as the SNF isotopes to be used for burnup credit (YMP 2003, 
Section 3.5.2.1.1). 
Table 2. Principal Isotopes for CSNF Burnup Credit 
95Mo 145Nd 151Eu 236U 241Pu 
99Tc 147Sm 153Eu 238U 242Pu 
101Ru 149Sm 155Gd 237Np 241Am 
103Rh 150Sm 233U 238Pu 242mAm 
109Ag 151Sm 234U 239Pu 243Am 
143Nd 152Sm 235U 240Pu 
3.2.3 Requirements for Confirmation of Conservatism 
For preclosure criticality analyses, two aspects of the isotopic model (BSC 2004d) for CSNF 
must be addressed. First, values for the initial isotopic concentrations must be conservative with 
respect to their contribution towards criticality. Second, changes to the initial isotopic 
concentration values as a function of time must also be conservative with respect to their 
contribution towards criticality. Proposed requirements addressing these aspects are presented in 
this section. Confirmation of the conservatism in the isotopic model used for burnup credit for 
CSNF will be demonstrated in analyses that will support licensing activities. 
• 
Reactor operating histories and conditions must be selected together with axial burnup 
profiles such that the isotopic concentrations used to represent CSNF assemblies in 
preclosure criticality analyses shall produce values for keff that are conservative in 
comparison to any other expected combination of reactor history, conditions, or profiles. 
This will ensure initial isotopic concentrations (i.e., at time of discharge from the 
reactor) are conservative with respect to criticality. Alternatively, additional margin 
may be added to account for uncertainties, including axial effects, in isotopic 
concentrations. 

• 
Values for the isotopic concentrations representing CSNF must produce conservative 
values for keff for all preclosure time periods for which criticality analyses are 
performed. This ensures changes to the initial isotopic concentration values as a function 
of time will also be conservative with respect to criticality. 
The first requirement addresses axial burnup effects. The quantities and distributions of the 
isotopics are governed by the local neutron spectrum, which depends upon the reactor operating 
history. Local neutron spectra effects are modeled for the burnup calculations by including local 
power density, moderator density, and fuel temperatures, as well as soluble boron concentrations 
for the burnup period of interest. However, for preclosure criticality analyses, detailed modeling 
of reactor operating histories and conditions is not practical. Therefore, bounding values will be 
chosen for parameters representing reactor operating histories and conditions. As for postclosure 
analysis (YMP 2003, Section 3.5.2.1.3), axial profile effects will be accounted for by using either 
conservative isotopic concentrations, or conservative profiles, or both. Analyses will be 
performed using the isotopic model (BSC 2004d), and the sufficiency of the fuel assembly 
database used in satisfying the first requirement will be demonstrated. Alternatively, additional 
margin may be added to account for uncertainties, including axial effects, in isotopic 
concentrations. 
The second requirement addresses changes to the initial isotopic concentration values, as a 
function of time, for preclosure. Uncertainties in keff resulting from uncertainties in the half-life 
and branching fractions can be established as a function of enrichment, burnup, and decay time. 
Satisfying the second requirement will necessitate repeatedly applying the method for treating 
uncertainties in isotopic decay to a range of sets of initial isotopic concentrations to determine 
the largest values for uncertainty in keff. 
These requirements are provided to ensure assumptions used in modeling fuel depletion (and 
decay) are conservative with respect to criticality. 
3.3 EFFECTIVE NEUTRON MULTIPLICATION FACTOR (keff) CALCULATION 
The Criticality Model (BSC 2004c) will be used for evaluating the criticality potential of 
configurations of fissionable materials at Yucca Mountain. The criticality evaluations for 
preclosure will be performed using the Monte Carlo simulation method (implemented by MCNP) 
for solving the neutron transport equation (BSC 2004c, Section 6.1). MCNP is a general purpose 
Monte Carlo N-Particle code that can be used for neutron, photon, electron, or coupled neutron– 
photon–electron transport including the capability to calculate eigenvalues for various systems. 
The code treats an arbitrary three-dimensional configuration of materials in geometric cells 
bounded by first- and second-degree surfaces and fourth-degree elliptical tori (Briesmeister 
1997, p. ix). 
The Monte Carlo method is based on following a number of individual neutrons through their 
transport, including interactions such as scattering, fission and absorption, and leakage. The 
probability distributions governing these events are statistically sampled to describe the total 
phenomenon. The cross-sections for the various neutron interactions dictate the reaction 
required for the criticality calculation at each interaction site. The fission process is regarded as 
the birth event that separates generations of neutrons. A generation is the lifetime of a neutron 

from birth by fission, to loss by escape, parasitic capture, or absorption leading to fission. The 
average behavior of a sample set of neutrons is used to estimate the average behavior of the 
system with regard to the number of neutrons in successive generations (i.e., keff). 
The Monte Carlo method allows explicit geometrical modeling of material configurations. 
Using appropriate material cross-section data in the criticality calculation is essential to obtaining 
credible results. The accuracy of the Monte Carlo method for criticality calculations is limited 
only by the accuracy of the material cross-section data, a correct explicit modeling of the 
geometry, and the duration of the computation. The accuracy of the method and cross-section 
data is established by evaluating critical experiments. Nuclear cross-section data are available 
from several source evaluations (data libraries). The choice of specific cross-section data will be 
evaluated during criticality model validation and documented in the analyses that will support 
licensing activities. 
3.4 VALIDATION 
Validation is the process of determining the applicability of a computational method and 
establishing the bias of the method by using benchmarks appropriate for the intended evaluation 
of operations. This section presents a description of this process for calculating the criticality 
potential of a waste form. 
During the process of validation, criticality experiments are selected from three types of 
experimental data—laboratory critical experiments, CRCs, and radiochemical assays. It should 
be noted that out-of-package operations model validation will use only laboratory critical 
experiments, and not the isotopic model. 
Laboratory critical experiments are used to benchmark the Criticality Model (BSC 2004c) (as 
part of the validation) for a range of fissionable materials, enrichments of fissile isotopes, 
moderator materials, absorber materials, and configurations. CRCs are used to benchmark the 
Criticality Model (BSC 2004c) for intact initial configurations of CSNF. 
3.4.1 Upper Subcritical Limit Determination 
An essential element of the Criticality Model (BSC 2004c) used for calculating keff for a waste 
form configuration is the determination of the critical limit (CL). The CL is derived from the 
bias and uncertainties associated with the criticality code and modeling process. The CL for a 
waste form configuration is a limiting value of keff at which a configuration is considered 
potentially critical. An upper subcritical limit (USL) is an upper limit placed on keff to ensure 
subcriticality with allowances made for the bias and uncertainty in the calculation model as well 
as an administrative criticality safety margin. The administrative criticality safety margin is the 
difference between a CL and a USL, illustrated as follows: 
CL = 1 – sum of bias and uncertainties 
USL = CL – administrative margin 
The CL is characterized by statistical tolerance limits that account for biases and uncertainties 
associated with the criticality code trending process, and any uncertainties due to extrapolation 

outside the range of experimental data, or limitations in the geometrical or material 
representations used in the computational method. 
A CL is associated with a specific type of waste form configuration. The CL is characterized by 
a representative set of benchmark criticality experiments. This set of criticality experiments also 
prescribes the basic range of applicability of the results. 
To establish a CL requires: (1) selection of benchmark experiments; (2) establishment of the 
range of applicability of the benchmark experiments (identification of physical and spectral 
parameters that characterize the benchmark experiments); (3) establishment of a lower-bound 
tolerance limit; and, if necessary, (4) establishment of the penalties for extending the range of 
applicability. 
3.4.1.1 Selection of Critical Experiments 
Applications must discuss and justify the critical experiments (LCEs and CRCs) used in the 
validation, which includes establishment of the USL. For commercial fuel, these experiments 
will be chosen from a database that simulates low-enriched, light water, reactor-fuel arrays in 
configurations similar to those used in storage, handling, and waste package configurations. This 
will include both UO2 and mixed-oxide fuel compositions. The experiments for CSNF should 
contain uranium-enrichments from about 2.0 to 5.0 wt% 235U and plutonium-enrichments from 
2 to 6 wt% 239Pu. For defense high-level radioactive waste glass or DOE SNF, experiments that 
simulate their criticality characteristics will be chosen. If the database used does not cover the 
total range of parameters for the storage, handling, or waste package configurations, then those 
methods required for extending the range of applicability provided in Section 3.4.1.4 will be 
used. 
3.4.1.2 Range of Applicability 
The following discussion is taken from Disposal Criticality Analysis Methodology Topical 
Report (YMP 2003, Section 3.5.3.2.2) and also applies to preclosure criticality safety. 
In ANSI/ANS-8.1-1983 (p. 1), the term “area of applicability” means “the limiting ranges of 
material compositions, geometric arrangements, neutron energy spectra and other relevant 
parameters (such as heterogeneity, leakage, interaction, absorption, etc.) within which the bias of 
a calculational method is established.” The term “area of applicability” and range of 
applicability are used interchangeably here. 
Bias is a measure of the systematic differences between the results of a calculational method and 
experimental data. Uncertainty is a measure of the random error associated with the difference 
between the calculated and measured result. When evaluating biases and uncertainties and 
choosing parameters (or areas) for which a bias would exhibit a trend, there are three 
fundamental areas (Lichtenwalter et al. 1997, p. 179) that should be considered: 
1. 
Materials of the waste package and the waste form, especially the fissionable materials 
2. 
The geometry of the waste package and waste forms 
3. 
The inherent neutron energy spectrum affecting the fissionable materials. 

There are substantial variations within each of these categories that require further 
considerations. These are discussed in Lichtenwalter et al. (1997, p. 180). Quantifying the 
various categories of parameters is complicated and generally requires approaches that use 
benchmark experiments that are characterized by a limited set of physical and computed neutron 
parameters that are then compared with the neutronic parameters of a waste package. 
In the general practice of characterizing biases and trends in biases, one would first look at those 
fundamental parameters that might create a bias. That is, what are the main parameters that 
could be in error and have the most significant effect on the accuracy of the calculation? 
Important areas for evaluating criticality are the geometry of the configuration, the concentration 
of important materials (reflecting materials, moderating materials, fissionable materials, and 
significant neutron absorbing materials), and the nuclear cross sections that characterize the 
nuclear reaction rates that will occur in a system containing fissionable and absorbing materials. 
Quite often, it is not simple to characterize the trends in a bias for some of the fundamental 
parameters chosen. In most cases, other parameters, called proxy parameters, will exhibit 
statistically definable trends. Generally, these proxy parameters reflect the effects of a 
combination of fundamental parameters; therefore, a proxy parameter is one that acts in the place 
of one or more fundamental parameters. 
It is desirable that the range of the fundamental parameters of the benchmark critical experiments 
(range of applicability) and the range of the fundamental parameters of the system (range of 
parameters) evaluated be identical. This is not practical usually, and for those parameters that do 
not show a bias, it is acceptable to use critical benchmark experiments that cover most, but not 
all, of the range of parameters of the system under evaluation. In these situations, expert 
judgment may be used to determine if there is a reasonable assurance that the two are sufficiently 
close. 
3.4.1.3 Development of Lower-Bound Tolerance Limit Function 
The application of statistical methods to biases and uncertainties of keff values is determined by 
trending criticality code results for a set of benchmark critical experiments that will be the basis 
of establishing lower-bound tolerance limits for a waste form. This process involves obtaining 
data on various neutronic parameters that are associated with the set of critical experiments used 
to model the code-calculated values for keff. These data, with the calculated values of keff, are the 
basis of the calculation of the lower-bound tolerance limit function. 
Since the determination of lower-bound tolerance limit functions for a waste form is data 
dependent, the set of benchmark critical experiments must be carefully selected to cover the 
range of parameters expected in the repository. Data quantity, diversity, and quality are 
important considerations to ensure appropriate range of applicability coverage for a waste form. 
The lower-bound tolerance limit function for a waste form results from the process shown in 
Figure 2. The data set and the resulting keff values produced by the criticality code must be 
confirmed as appropriate and valid for the waste form. This is fundamental to the development 
of the lower-bound tolerance limit function. The objective of this process is to produce 
lower-bound tolerance limits that are statistically meaningful and practical in application. 

The purpose of the lower-bound tolerance limit function is to translate the benchmarked keff 
values from the criticality code to a design parameter for a waste form–waste package 
combination. This design parameter is used in criteria for determining criticality potential. To 
meet this purpose, it is necessary to account for criticality code calculation differences from the 
true value of the effective neutron multiplication factor of 1.0. This latter value is an 
assumption, as explained above. The lower-bound tolerance limit definition addresses biases and 
uncertainties that cause the calculation results to deviate from the true value of keff for a critical 
experiment, as reflected over an appropriate set of critical experiments. 
Figure 2 displays two general statistical methods for establishing lower-bound tolerance limit 
functions: (1) regression-based methods reflecting criticality code results over a set of critical 
experiments that can be trended, and (2) random sample based methods that apply when trending 
is not an appropriate explanation of criticality code calculations. The regression approach 
addresses the calculated values of keff as a trend of spectral or physical parameters or both. That 
is, regression methods are applied to the set of keff values to identify trending with such 
parameters. The trends show the results of systematic errors or bias inherent in the calculational 
method used to estimate criticality. In some cases, a data set may be valid, but might not cover 
the full range of parameters used to characterize the waste form. The area (or areas) of 
applicability of a calculational method may be extended beyond the range of the experimental 
conditions of the data set over which the bias is established by making use of correlated trends in 
the bias (see Section 3.4.1.4). 
If no trend is identified, a single value may be established for a lower-bound tolerance limit that 
provides the desired statistical properties associated with the definition of this quantity. The data 
are treated as a random sample of data (criticality code values of keff) from the waste form 
population of interest and straightforward statistical techniques are applied to develop the 
lower-bound tolerance limit. For purposes of differentiation, this technique will be described as 
“nontrending.” The normal-distribution tolerance limit method and the distribution-free 
tolerance limit method, described below, are “nontrending” methods. 

iOutput ki) 
ion fikeffion(s) 
siwiiion 
eff data 
iit 
Normal? 
Yes No 
No 
Yes 
Define set of validation experiments to 
be processed by Monte Carlo code 
encompassng desired range of 
applicability 
eff values, spectral 
parameters, physcal parameters 
(enrichment, burnup, etc.
Perform regressts of 
on predictor variables to 
identify the trending 
parameter 
Is regressgnificant? 
Select predictor 
th conservatve 
correlatExamine kset for normalty 
Use LUTB method to 
establish lower bound 
tolerance limit 
Use NDTL method to 
establish lower bound 
tolerance limit 
Use DFTL method to 
establish lower bound 
tolerance limApply lower bound 
tolerance limit 
Note: LUTB Lower Uniform Tolerance Band 
NDTL Normal Distribution Tolerance Limit 
DFTL Distribution Free Tolerance Limit 
Figure 2. Process for Calculating Lower-Bound Tolerance Limits 
The regression or “trending” methods (YMP 2003, Section 3.5.3.2.7) use statistical tolerance 
values based on linear regression techniques to establish a lower-bound tolerance limit function. 
Trending in this context is linear regression of keff on the predictor variable(s). Statistical 
significance of trending is determined by the test of the hypothesis in which the regression model 
mean square error is zero. Here the predictor variable(s) may be a parameter such as burnup, or 

a parameter that indicates the distribution of neutrons within the system, such as the average 
energy of a neutron that causes either fission or absorption. Where multiple candidates are found 
for trending purposes, each regression model will be applied and the conservative model will be 
used to determine the value of the lower-bound tolerance limit. The lower uniform tolerance 
band method, described below, trends a single parameter against keff. Multiple regression 
methods that trend multiple parameters against keff may also be used to establish the lower-bound 
tolerance limit function. In either single or multiple situations, the regression trend that produces 
the lowest lower-bound tolerance limit is defined to be the more conservative regression. 
In nontrending situations, standard statistical tolerance limit methods, which characterize a 
proportion of a population with a confidence coefficient, are used to establish the single-valued 
lower-bound tolerance limit function that applies for the range of applicability of the set of 
critical experiments. There are two standard tolerance limit methods described, each specific to 
the result of examination of the hypothesis of normality of keff values of the benchmark set of 
critical experiments. Disposal Criticality Analysis Methodology Report (YMP 2003, Section 
3.5.3.2.8) addresses situations in which the distribution of the keff values for the set of benchmark 
critical experiments can be treated as coming from a normal probability distribution. This 
technique is the normal distribution tolerance limit. Section 3.5.3.2.9 of Disposal Criticality 
Analysis Methodology Report (YMP 2003) describes the distribution free tolerance limit method. 
The distribution free tolerance limit method applies when trending is not appropriate and data for 
benchmark critical experiments do not pass the test for normality. In this situation, there is no 
assumption about the form of the underlying probability model. Assumptions about the 
randomness of the process and the data as representing a random sample from the population of 
interest, however, are necessary. 
In all calculations of lower-bound tolerance limit functions, the concept described as the “no 
positive bias” (Lichtenwalter et al. 1997, p. 160) rule must be accommodated. This rule excludes 
benefits for raising the lower-bound tolerance limit for cases in which the best estimate of the 
bias trend would result in a lower-bound tolerance limit greater than 1.0. The treatment of this 
element is discussed below in the context of each method used to establish the basic lower-bound 
tolerance limit function. 
The lower-bound tolerance limit function is defined as: 
f(x) = kC(x) -.kC(x) (Eq. 2) 
where 
x = parameter vector used for trending 
kC (x) = the value obtained from a regression of the calculated keff of benchmark 
critical experiments or the mean value of keff for the data set if there is no 
trend 
.kC (x) = the uncertainty of kC based on the statistical scatter of the keff values of the 
benchmark critical experiments, accounting for the confidence limit, the 
proportion of the population covered, and the size of the data set. 
The statistical description of the scatter quantifies the variation of the data set about the expected 
value and the contribution of the variability of the calculation of the keff values for the 
benchmark critical experiments. 

Based on a given set of critical experiments, the lower-bound tolerance limit is estimated as a 
function (f[x]) of a parameter(s). Because .kC (x) and kC (x) can vary with this parameter, the 
lower-bound tolerance limit function is typically expressed as a function of this parameter vector, 
within an appropriate range of applicability derived from the parameter bounds, and other 
characteristics that define the set of critical experiments. 
The calculational bias, ß, is defined as: 
ß = kC - 1 (Eq. 3) 
and thus the uncertainty in the bias is identical to the uncertainty in kC (i.e., .kC = .ß). This 
makes the bias negative if kC is less than 1 and positive if kC is greater than 1. 
To prevent taking credit for a positive bias, the lower-bound tolerance limit is further reduced by 
a positive bias adjustment. The positive bias adjustment sets kC equal to 1.0 when kC 
exceeds 1.0. 
Various sections of Disposal Criticality Analysis Methodology Report (YMP 2003) discuss the 
various methods for estimating a lower-bound tolerance limit function. Section 3.5.3.2.7 of the 
report presents the regression method for trending keff versus a parameter vector and Sections 
3.5.3.2.8 and 3.5.3.2.9 detail the other two methods to be used if statistically significant trends 
cannot be identified via regression methods for a set of benchmark experiments. 
An MCNP bias will be evaluated and determined for out-of-package and in-package operations 
using a selected set of critical experiments from the laboratory critical experiment database as 
well as CRCs from the CRC database. Of particular interest will be trends versus neutron 
spectral parameters and any of the control parameters that will be used for criticality control. A 
brief description of the critical experiments used for the determination of any biases and a 
validation of the trend or trends discovered will also be provided. Out-of-package operations 
will only use fresh fuel critical experiments for determining bias values. 
3.4.1.4 Extension of the Range of Applicability 
Where data are not available, it is prudent to use appropriate bounding models or assign 
additional penalties. In these cases, there may be an extension of the range of applicability to 
cover the range of parameters of the system. 
The means used to extend the range of applicability will depend on a number of factors. These 
include, but are not necessarily limited to: (1) the nature of the critical experiments used to 
determine the range of applicability and trends with biases, (2) the particular waste form 
involved, and (3) the availability of other proven computer codes or methods used to evaluate the 
situation. 
ANSI/ANS-8.1-1983 (p. 18) Appendix C, Section C4 will be used for the extension of the range 
of applicability: 
The area (or areas) of applicability of a calculational method may be extended 
beyond the range of experimental conditions over which the bias is established by 

making use of correlated trends in the bias. Where the extension is large, the 
method should be: 
A. Subjected to a study of the bias and potentially compensating biases 
associated with individual changes in materials, geometries or neutron 
spectra. This will allow changes, which can affect the extension to be 
independently validated. In practice, this can be accomplished in a 
stepwise approach; that is, benchmarking for the validation should be 
chosen (where possible) such that the selected experiments differ from 
previous experiments by the addition of one new parameter so the effect of 
only the new parameter, on the bias can be observed. 
B. Supplemented by alternative calculational methods to provide an 
independent estimate of the bias (or biases) in the extended area (or areas) 
of applicability. 
If a range of applicability is extended, where there is a trend in the data, without the use of 
additional experiments, additional penalty will be added to the criteria used to determine if a 
system has potential for criticality. The same techniques described above for extending the 
range of applicability when there are trends may be used to determine the additional penalty: 
(1) expert judgment (an evaluation by someone skilled, by training and experience, in criticality 
analysis), (2) sensitivity analysis, (3) statistical evaluation of the importance of these parameters, 
or (4) comparison with other credible methods (code-to-code comparisons). 
For situations where a bias (trend) is not established, there are two options for extending the 
range of applicability. If the extension of the range of applicability is small and the performance 
of the criticality code for these parameter ranges is also understood, it would be appropriate to 
use the established lower bound tolerance limit and an appropriate penalty to calculate the 
critical limit. If the extension is not small, then more data, covering the range of applicability, 
will be necessary. When more data are obtained, the process illustrated in Figure 1 must be 
applied to the new data set. This applies when the range of applicability for fundamental 
parameters (material concentrations, geometry, or nuclear cross-sections) does not cover the 
range of parameters of the waste package configuration and no trend is exhibited. 
3.4.2 Upper Subcritical Limit Application 
Geometric modeling and inputs for computing the keff for a critical experiment with a criticality 
code often induce bias in the resulting keff value. Bias is a measure of the systematic differences 
between the results of a calculational method and experimental data. Uncertainty is a measure of 
the random error associated with the difference between the calculated and measured result. 
These keff values deviate from the expected result (keff equal to 1) of benchmark sets of critical 
experiments. The experimental value of keff for some benchmarks may not be unity (some are 
extrapolations to critical); however, this value is used for purposes of calculating errors. 

The critical limit (CL) is represented in equation form as (based on ANSI/ANS-8.17-1984, 
Section 5): 
CL(x) = f(x) – .kEROA -.kISO -.km (Eq. 4) 
where 
x = a neutronic parameter used for trending 
f(x) = the lower-bound tolerance limit function accounting for biases and 
uncertainties that cause the calculation results to deviate from the true value of 
keff for a critical experiment, as reflected over an appropriate set of critical 
experiments 
.kEROA = penalty for extending the range of applicability 
.kISO = penalty for isotopic composition bias and uncertainty 
.km = an arbitrary margin ensuring subcriticality for preclosure analyses, turning the 
CL function into an USL function 
Based on a given set of critical experiments, the USL is estimated as a function of a trending 
parameter for the experiments. Because CL(x) can vary with this parameter, the USL is 
expressed as a function of this parameter within an appropriate range of applicability derived 
from the parameter bounds. 
For the preclosure period, USLs will be determined as prediction limits, at the user-specified 
confidence level, using the techniques described in Disposal Criticality Analysis Methodology 
Topical Report (YMP 2003, Section 3.5.3.2). 
Part of the range of applicability of a benchmark data set is based on the range of parameter 
variation in the benchmark experiments that are used for estimating the USL. The other part is 
based on the range of fundamental parameters of the benchmark experiments. Lichtenwalter et 
al. (1997, p. 163) define three classes of fundamental characteristics from which a fundamental 
parameter may be defined. The three characteristics are (1) materials of construction (including 
fissionable materials), (2) the geometry of construction, and (3) the inherent neutron energy 
spectrum affecting the fissionable material(s). 
Once fundamental parameters and a set of critical experiments have been established, calculated 
values of keff are trended against a number of these parameters to determine the parameter that 
provides the best fit to the data from the benchmark critical experiments. This parameter may be 
used for extending the range of applicability to the waste form. 
The repository will contain various types of waste forms, the majority of which will be CSNF, 
comprised of two waste forms: PWR and BWR SNF. Each waste form will be analyzed 
separately for criticality potential and characterized with a set of benchmark critical experiments 
that span the characteristics of the particular waste form. This includes analyzing potential 
critical configurations during the receiving, packaging, and emplacing operations. Analyses for 
each of these operations may require different sets of benchmark critical experiments since the 
neutronic parameters may change between operations. For example, the geometric structure of 
potential critical configurations will be different during the receiving operation (i.e., during 

handling of the waste form) than during the emplacing operation (intact waste package); 
therefore, this difference must be accommodated in the benchmark data set. 
For CSNF in-package operations, CRC data are being used as benchmark data to estimate USLs 
for a limited range. For all CSNF out-of-package operations, including damaged fuel operations, 
a fresh fuel assumption will be used which restricts the benchmark data set for determining 
subcritical limits to fresh fuel laboratory critical experiments. 
3.5 UPPER SUBCRITICAL LIMIT CRITERION 
For preclosure, a USL criterion is used for comparison to predicted keff values to determine a 
configuration’s criticality potential. The USL is an upper limit placed on keff to ensure 
subcriticality, with allowances made for the bias and uncertainty in the calculation model, as well 
as an administrative criticality safety margin. A predicted keff greater than or equal to the USL 
indicates a configuration in violation of the administrative safety limit. A predicted keff less than 
the USL indicates that the configuration has no criticality potential. 
A USL is estimated such that a calculated keff on or below this limit is subcritical, and a system is 
considered acceptably subcritical if a calculated keff plus calculation uncertainties and margin lies 
at, or below, this limit. In equation notation, the USL criterion is defined as: 
kS + .kS = USL (Eq. 5) 
where 
kS = calculated keff for the system 
.kS = an allowance for: 
(a) statistical or convergence uncertainties, or both in the computation of ks 
(b) material and fabrication tolerances, and 
(c) uncertainties due to the geometric or material representations used in the 
computational method [Note: allowance for items (b) and (c) can be obviated 
by using bounding representations] 
USL = the value characterized by statistical tolerance limits that account for biases and 
uncertainties associated with the criticality code trending process, any 
uncertainties due to extrapolation outside the range of experimental data, or 
limitations in the geometrical or material representations used in the 
computational method, and an administrative margin-to-criticality that can 
reduce the CL(x) (current practices suggest a value of 0.05 [Kopp 1998, p. 4]) 
3.6 APPLICATION 
A description of the base input parameters for all of the criticality analyses including a general 
design arrangement of the areas to be evaluated will be provided in each analysis. Also, the 
evaluation of reactivity effects due to manufacturing tolerance for the waste package and 
components as well as uncertainties related to storage of a waste package prior to loading will be 
provided. Other structural and thermal-hydraulic effects will also be addressed. 

Each configuration used in these analyses will provide a calculated keff based upon nominal 
dimensions. Adjustments will be made to the calculated keff to contain the maximum keff (kmax). 
The maximum multiplication factor kmax will be a sum of the calculated keff from the criticality 
software (e.g., MCNP) calculation plus biases and uncertainties that result from a number of 
other conditions, e.g., the manufacturing tolerances, structural and thermal-hydraulic effects 
mentioned earlier. 
Any computer codes used to provide code-to-code verification will be described, critical 
experiments used to provide the verification will be discussed, and the results documented. 
3.6.1 Loading Restrictions for Commercial Spent Nuclear Fuel 
A single-parameter regression analysis will be performed, using the initial enrichment and 
burnup, for all potential CSNF assemblies in the repository to determine loading restrictions, or 
curves, for in-package operations. In these analyses, calculations will be made to determine 
acceptable enrichment and burnup pairs that can be loaded into a waste package. There may be 
different waste packages for different classes of enrichment–burnup pairs. Acceptable pairs are 
those combinations that yield a keff less than the USL. Design and statistical uncertainty will be 
added to the keff calculated before comparing to the USL. 
Having established a series of acceptable values for keff for these configurations, a regression 
analysis will be performed. The burnup, in terms of either MWd/MTU or GWd/MTU, will be 
formulated as a function of the nominal enrichment. Uncertainty in burnup values will also be 
incorporated into these regressions. A more detailed explanation of a process to determine 
loading curve restrictions is given below in this section. An example of a loading curve is 
presented in Appendix A. 
A loading curve is prepared for loading fuel assemblies in the waste package in a manner similar 
to that used for spent nuclear fuel pools that are approved for burnup credit. The process for 
developing the loading curves for CSNF involves the following steps: 
1. 
CSNF isotopic concentration data is generated for a range of enrichment and burnup 
pairs using the isotopic model (BSC 2004d). 
2. 
Waste package configurations to evaluate for preclosure and postclosure are 
determined. 
3. 
Administrative limits for the configurations, the upper subcritical limit for the 
preclosure configuration, and the critical limit for the postclosure configurations are 
determined, as described in the Criticality Model (BSC 2004c). These limits include 
the bias and uncertainties. The difference between the administrative limits is that the 
upper subcritical limit includes an administrative margin (i.e., 5 percent). 
4. 
For each initial enrichment, burnup is varied, and the keff and corresponding s 
(uncertainty) of the configuration with the different burnups is calculated. 
5. 
A curve of keff plus 2s (collectively referred to as keff) versus burnup is generated from 
the results for each configuration and initial enrichment. Figure A-1 in Appendix A 

shows an example of a calculated required minimum burnup used to generate a 
loading curve. Those data points where keff exceeds the administrative limit (above the 
line) do not have enough burnup to be critically safe. Data points on or below the 
administrative limit are acceptable. The intersection of the calculated keff -versusburnup 
curve and the administrative limit line defines the required minimum burnup 
for the selected initial enrichment value (See Figure A-1 in Appendix A). 
6. 
The burnup values at the intersection of the calculated keff-versus-burnup curve for the 
different initial enrichments are plotted against the initial enrichment values on a 
single curve to generate the loading curve for each particular waste package (e.g., 
Figure A-2 in Appendix A). 
7. 
The burnup values are then adjusted to account for the uncertainty in the reported 
burnup values. The adjustment is a percentage in burnup that gives a 95/95 confidence 
and probability level. 
8. 
A polynomial equation is then fit to the adjusted burnup values and plotted on an 
initial enrichment-versus-burnup curve to generate the criticality loading curve for the 
specific waste package configuration and range of fuel types covered. The area above 
the curve includes the acceptable SNF because the burnup in this area exceeds the 
required minimum burnup. The area below the curve defines unacceptable SNF, 
which cannot be loaded into the particular waste package (see Figure A-2 in Appendix 
A). All CSNF assemblies can be accommodated in some waste package using some 
combination of additional criticality control and/or loading schemes. 
3.6.2 Out-of-Package Criticality Safety 
Criticality safety calculations for out-of-package operations will focus on the following: 
• 
Safe Design for Storage Racks-The design of storage racks will include the use of fixed 
burnable neutron absorbers (poisons), as required, to ensure subcriticality for Category-1 
and Category-2 event sequences. Wet and dry storage rack conditions will be considered 
as part of the evaluation and will include partial flooding as well as varying moderator 
density in order to include all credible conditions. The most reactive fuel assemblies and 
canister conditions will be used in the calculations along with the processes described in 
Section 2.2.7. 
• 
Safe Design in Handling-Event sequences involving mishandling SNF will be evaluated 
including placement outside of storage racks, misplacement inside storage racks, and 
dropping of SNF when it is handled. Additionally, the possible reconfiguration of SNF 
will be considered as a result of dropping. 
• 
Fixed Neutron Absorber Burnup-Evaluation of fixed neutron absorbers for storage 
rack design is required to ensure sufficient neutron absorbers will remain over the life of 
the facility. Limited fixed neutron absorber credit of 75 percent will be used in the 
design of fixed neutron absorbers as specified in NUREG-1567 (NRC 2000, Section 
8.4.1.1), unless comprehensive fabrication acceptance tests capable of verifying the 

presence and uniformity of the neutron absorber are implemented. To ensure 
subcriticality over the life of the facility, the regulatory requirement of 10 CFR Part 
72.124(b) “…Where solid neutron absorbing materials are used, the design must provide 
for positive means of verifying their continued efficacy…” will be implemented by using 
the maximum credible neutron flux for a given configuration in depletion calculations of 
fixed neutron absorbers. 
Using the above criteria, the process for criticality design calculations for CSNF in the surface 
facility (BSC 2004b) can be summarized as follows. The most reactive PWR and BWR fuel 
assemblies will be identified by calculation of keff for fully moderated single assemblies 
containing fresh fuel. For storage rack design, calculations will be performed to confirm that the 
same assembly designs remain the most reactive in the presence of fixed absorbers. Using the 
most reactive fuel assemblies, assembly spacing for storage rack design will be determined by 
computing keff as a function of assembly pitch for different average (uniform) fuel enrichments, 
and comparing the computed values of keff to the USL determined by the process described in 
Section 3.4.1. Calculations of keff will be performed for racks with and without fixed neutron 
absorber to evaluate absorber effectiveness. In addition, calculations will be performed for a 
range of uniform moderator densities covering the range from dry to fully moderated conditions, 
as well as for partial flooding, to ensure that optimum moderation has been considered. 
The process for criticality safety analyses in the surface facility can be summarized as follows. 
Using Category 1 and Category 2 event sequences identified as part of the preclosure safety 
analysis, as described in Section 3.1, criticality safety analyses will be performed for the 
identified event sequences. The analyses for some kinds of event sequences (e.g., those related 
to transportation casks) may simply note that compliance with existing regulations (e.g., 
10 CFR Parts 50, 71, and 72) provides sufficient assurance of criticality safety. Where necessary 
(e.g., reconfiguration of fuel pins or relocation of assemblies due to drops or collisions), 
additional calculations of keff will be performed to demonstrate that subcriticality is maintained. 

4. CONCLUSIONS
The process for analyzing the potential for criticality during the preclosure period will be 
dictated by existing regulatory requirements. The proposed process is based on the fact that 
planned preclosure operations and facilities have significant similarities to existing facilities and 
operations currently regulated by the NRC. The major difference is the use of a risk-informed 
approach with burnup credit for in-package operations. 
The probability of success for this proposed licensing strategy is increased, since there exist both 
precedents of regulation (10 CFR Part 63; NRC 2002a, Section 5) and commercial precedents for 
allowing burnup credit at sites similar to Yucca Mountain during preclosure. While NUREG1520 
(NRC 2002a, Section 5) is not directly applicable to a facility for handling spent nuclear 
fuel, the risk-informed approach to criticality analysis in NUREG-1520 (NRC 2002a, Section 5) 
provides insight into the NRC’s approach to risk-informed criticality analysis. 
The types of event sequences which must be considered during the criticality safety analysis are 
those events which result in unanticipated moderation, loss of neutron absorber, geometric 
changes in the critical system, or administrative errors in waste form placement (loading) of the 
waste package. The specific events to be considered must be based on the review of the system’s 
design, as discussed in Section 3.1. 

INTENTIONALLY LEFT BLANK

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APPENDIX A - LOADING OF A WASTE PACKAGE 
A. INTRODUCTION 
This appendix provides an example calculation of loading restrictions (loading curve), taken 
from 21-PWR Waste Package with Absorber Plates Loading Curve Evaluation (BSC 2004f). 
A.1 LOADING CURVES FOR A WASTE PACKAGE 
The purpose of this example loading curve calculation was to determine the required minimum 
burnup as a function of initial PWR assembly enrichment that permits loading of fuel into a 
21-PWR waste package. The results are intended to provide an example of how PWR SNF 
assemblies whose actual burnup exceeds the required minimum burnup may be loaded into a 
21-PWR waste package with a borated steel criticality control basket design. 
An example of a determination of a minimum required burnup for a specific enrichment is 
shown in Figure A-1, which was adapted from Figure 13 of 21-PWR Waste Package with 
Absorber Plates Loading Curve Evaluation (BSC 2004f). In the example shown, the initial 
enrichment is 4.0 wt% 235U. The calculated keff values include a two-s allowance for 
computational uncertainty. The required minimum burnup for this example is 29.5 GWd/MTU, 
determined from the intersection of the line representing the USL and the curve of the calculated 
keff values. 
A loading curve using burnup credit depicts the relationship between the initial enrichment of a 
fuel assembly and the required minimum average burnup needed to suppress the reactivity of that 
fuel assembly sufficiently to allow it to be safely loaded into the waste package. Any assembly 
with burnup that exceeds the required minimum burnup, given the initial enrichment of the fuel 
assembly, may be placed in the waste package. The points for the loading curve are determined 
by taking the required minimum burnup from curves like that in Figure A-1 for a range of 
enrichments sufficient to cover the fuel inventory of interest. 
The example loading curves in Figure A-2 show the required minimum burnup for fuel with 
initial 235U enrichments from 2.0 to 5.0 wt%, adapted from Figure 34 of 21-PWR Waste Package 
with Absorber Plates Loading Curve Evaluation (BSC 2004f). When these burnups are plotted 
against the enrichments, the resulting curve determines the loading restrictions for a waste 
package. The solid blue curve is the preclosure loading curve without consideration of burnup 
uncertainty. The solid red curve is a quintic polynomial that was fit to the preclosure loading 
curve including a 5-percent adjustment for burnup uncertainty. That is, the minimum burnup 
required for a given initial enrichment has been increased by 5 percent to account for uncertainty 
associated with assembly burnup records. The squares in the legend indicate number groupings 
of assemblies at a particular burnup and enrichment (e.g., 100-199 indicates that there are 100 to 
199 assemblies at a listed burnup and enrichment) for a 10-year-old youngest fuel first arrival 
scenario for 63,000 MTU of CSNF, taken from Attachment III of Waste Packages and Source 
Terms for the Commercial 1999 Design Basis Waste Streams (CRWMS M&O 2000). The area 
to the left of the curve in Figure A-2 shows acceptable enrichment–burnup pairs for SNF 
assemblies that can be loaded. The area to the right defines unacceptable assemblies for loading 
in the applicable waste package. These will need to be accommodated for by using some 
combination of additional criticality control and/or loading scheme. 

1 
keff+2s 
Mi/) 
s 
0.8 
0.85 
0.9 
0.95 
1.05 
1.1 
n. Burnup (GWdMTU1 Node = 29.062 
Calculated keff + 2
0 5 101520253035404550 
Burnup (GWd/MTU) 
iniimi)Admstrative Lt (USL
Figure A-1. Required Minimum Burnup for 4.0 wt% Enriched PWR SNF 
y5432R2 = 1 
0 
10 
20 
30 
40 
50 
60 
70 
80 
()
lial 
Ale 
= 0.451x - 8.7061x + 66.281x - 249.22x + 475.35x - 358.38 
BurnupGWd/MTU1-99 
100-199 
200-299 
300+ 
Base LC 
Fitted Poynom 
cceptable 
Unacceptab
0123 456 
Initial Enrichment (Wt% U-235) 
NOTE: The fitted polynomial represents the loading curve based on a five percent burnup uncertainty of the 
bounding curve (Base LC) 
Figure A-2. Loading Restrictions for Waste Package