Clad Degradation  Summary and Abstraction Rev 00, ICN 00

ANL-WIS-MD-000007

April 2000

1. PURPOSE 
The purpose of this analysis is to develop the summary cladding degradation abstraction that is 
consistent with and used in the Total System Performance Assessment - Site Recommendation 
(TSPA-SR). This analysis is to describe the postulated condition of commercial Zircaloy clad 
fuel after it is placed in the Yucca Mountain Project (YMP) site (post-closure) as a function of 
time. Most commercial nuclear fuel is encased in Zircaloy cladding. This analysis is developed 
to describe cladding degradation from the expected failure modes. These include failure before 
receipt at YMP (reactor operation impacts including incipient failures; during spent fuel storage 
in pool and dry storage; and impacts due to transportation) and degradation in the repository 
(cladding creep, seismic failures, localized corrosion and cladding unzipping). This AMR does 
not address potential damage to assemblies that might occur at the YMP surface facilities. In 
accordance with AP-2.13Q, Technical Product Development Planning, a work plan (CRWMS 
M&O 1999a) was developed, issued, and utilized in the preparation of this document. 
There are constraints, caveats and limitations to this analysis. This cladding degradation analysis 
is based on commercial Pressurized Water Reactor (PWR) fuel with Zircaloy cladding but is 
applicable to Boiling Water Reactor (BWR) fuel. Fuel reliability from reactor operation is 
determined for both PWRs and BWRs. This analysis is also limited to fuel exposed to normal 
operation and anticipated operational occurrences (i.e. events which are anticipated to occur 
within a reactor lifetime), and is not applicable to fuel that has been exposed to severe accidents. 
Fuel burnup projections have been limited to the current commercial reactor licensing 
environment with restrictions on fuel enrichment, oxide coating thickness, and rod plenum 
pressures. Ranges and uncertainties have been defined. The information provided in this 
analysis will be used in evaluating the post-closure performance of the Monitored Geologic 
Repository (MGR) in relation to waste form degradation. 
2. QUALITY ASSURANCE 
The Quality Assurance program applies to the development of this analysis documentation. The 
Performance Assessment Operations responsible manager has evaluated the technical document 
development activity in accordance with QAP-2-0, Conduct of Activities. The QAP-2-0 activity 
evaluation, Conduct of Performance Assessment (CRWMS M&O 1999b), has determined that 
the preparation and review of this technical document is subject to Quality Assurance 
Requirements and Description DOE/RW-0333P (DOE 2000) requirements. Note that the 
activity evaluation (CRWMS M&O 1999b) remains in effect even though QAP-2-0 has been 
superseded by AP-2.16Q, Activity Evaluation. This AMR was prepared in accordance with AP- 
3.10Q, Analyses and Models. Preparation of this analysis did not require the classification of 
items in accordance with QAP-2-3, Classification of Permanent Items. This activity is not a 
field activity. Therefore, an evaluation in accordance with NLP-2-0, Determination of 
Importance Evaluations was not required.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 7 April 2000 
3. COMPUTER SOFTWARE USAGE 
Microsoft Excel for Windows Version 4.0 was used in the analysis to develop a software routine. 
Excel is a commercially available software, and one macro was used. The software routine was 
run on a Dell Pentium personal computer (CPU number 111920) with a Windows 95 operating 
system. The software routine, including the one macro, is documented in Attachments I and II of 
this AMR in accordance with AP-SI.1Q, Software Management, Section 5.1.1. The software 
routine is contained in file AMR-F0155-V1.xls and the version number is one (1) as implied in 
the file name. This file is contained in Data Tracking Number (DTN: 
MO00004SPACLD07.043). 
There were no models used in support of this analysis activity. 
This AMR was documented using only commercially available software (Microsoft Word 97- 
SR2) for word processing, which is exempt from qualification requirements in accordance with 
AP-SI.1Q, Software Management. There were no additional applications (routines or macros) 
developed for documentation using this commercial software. 
SigmaPlot, Scientific Graphic Software, Version 2.0, Jandel Corporation is used to plot data 
from the analysis. No calculations are performed with this software. 
4. INPUTS 
4.1 DATA AND PARAMETERS 
This AMR summarizes several other AMRs and generates the cladding degradation abstraction 
that is to be used in the TSPA-SR. Much of the data used in this AMR and the cited AMRs is 
from published literature for Pressurized Water Reactor (PWR) fuel performance and the 
respective reference is cited where the data is used. These data are appropriate for describing 
commercial nuclear fuel since they are published descriptions of commercial fuels. The 
following AMRs or calculations supply input (with Data Tracking Numbers (DTNs) noted) to 
this AMR: 
a) Initial Cladding Condition (CRWMS M&O 2000a). 
Contains discussion and analysis of cladding condition as received at YMP. 
Data supplied in DTN: MO0001SPAICC48.037. 
1) Complementary Cumulative Distribution Function (CCDF) for rods perforated before 
receipt at Yucca Mountain Project (YMP) (Table 14), used in Section 6.1. 
2) Rod stress distribution (Output table represented by Figure 26) file = Rod-Initial- 
C.xls, Sheet = Crack, Cells = K15 through M2014, used in Section 6.2.2. 
3) Dry storage and shipping temperature history: file = Rod-Initial-C.xls, Sheet = 
Creep, Cells B25 through C39, used in Section 6.2.1.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 8 April 2000 
b) CSNF Waste Form Degradation: Summary Abstraction (CRWMS M&O 2000d). 
Intrinsic dissolution rate equation for basic and acidic conditions (Equation 16, 18, page 82) and 
Figure 12 of this AMR showing the intrinsic dissolution equation. Gap inventories for cesium 
and iodine as a function of fission gas release fraction. Roughness factors are taken from this 
reference. 
c) Clad Degradation  Wet Unzipping (CRWMS M&O 2000e). 
Equations for cladding wet unzipping (Equation 29) as a function of intrinsic dissolution rate. 
Distribution of ratio of unzipping speeds to intrinsic dissolution speeds. Molar volumes of 
metaschoepite and UO2. 
d) Thermal History of Cladding in a 21-PWR SNF WP Loaded with Average Fuel, 
(CRWMS M&O 2000f). 
Design information ACC: MOL.20000216.0105. 
Radial temperature distribution across the waste package (WP) and change in temperature in WP 
as a function of time. Peak internal WP temperatures from Table 6-2 are used in Section 6.2.1 for 
establishing uncertainties. 
e) Thermal Evaluation of Breached 21-PWR Waste Packages (CRWMS M&O 1999e). 
Design information ACC: MOL.20000120.0447. 
Peak internal WP temperature profile from Table 6-7 used for establishing uncertainties. Used in 
Section 6.2.1. 
f) In-Drift Thermodynamic Environment and Percolation Flux (CRWMS M&O 2000h). 
Data Used for this AMR: DTN: SN0001T0872799.006. 
Bin 4 average temperatures used in Section 6.2.1. 
Bin 4 peak temperatures used to define waste package surface temperature uncertainties in 
Section 6.2.1. 
g) Comparison of Creep Correlations. Input Transmittal PA-WP-0048.Ta. (CRWMS 
M&O, 2000j). 
Design information used in this AMR: ACC: MOL.20000223.0002. 
Uncertainty range of 80% for creep strain from Attachment Item 1, on the 503 item data table. 
Used in Section 6.2.2. 
h) Stainless Steel in Waste Packages for TSPA-SR.(CRWMS M&O 2000k). 
Data used from this AMR: DTN: SN0001T0810599.008. 
WP fraction with stainless steel cladding and fraction of stainless steel in them. Used in Section 
6.7.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 9 April 2000 
i) Breakage of Commercial Spent Nuclear Fuel Cladding by Mechanical Loading, 
(CRWMS M&O 1999d). 
Design information used from ACC: MOL.19991213.0237. 
Frequency of seismic event that damages all cladding determined to be 1.1x10-6 events/year. 
This frequency is used in Section 6.4.1. 
Outside sources of data include: 
j) "Fracture Behavior and Microstructural Characteristics of Irradiated Zircaloy Cladding." 
Special Technical Publication, (Chung et al. 1987, Table 1 and 2, p. 780, 781). 
Data used: DTN: MO9912SPASFC01.032. 
Reported failure strain measurements used to develop CCDF for creep failure criterion. Used in 
Section 6.2.3. 
k) Results from NNWSI Series 1 Spent Fuel Leach Tests. (Wilson, C.N. 1985, Tables 3 and 
12) TIC: 210347. 
Data used in DTN: MO0003SPATCR30.039. 
Measurements of releases of technetium reported in cited tables used in Section 6.5.2 to predict 
fast release fraction for fuel. 
l) Results from Cycles 1 and 2 of NNWSI Series 2 Spent Fuel Dissolution Tests. (Wilson, 
C.N. 1987, Tables 13, A.3, A.4, A.7, and A.8). TIC: 202294 
Data used in DTN: MO0003SPATCR22.038. 
Measurements of releases of technetium reported in cited tables used in Section 6.5.2 to predict 
fast release fraction for fuel. 
m) Results From NNWSI Series 3: Spent Fuel Dissolution Tests.(Wilson, C.N. 1990, Tables 
3.8, A.5, and A.6). TIC: 200816. ACC: NNA.19900329.0142. 
Data used in DTN: MO0003SPATCR70.040. 
Measurements of releases of technetium reported in cited tables used in Section 6.5.2 to predict 
fast release fraction for fuel. 
n) Report of the Committee to Review the Use of J-13 Well Water in Nevada Nuclear Waste 
Storage Investigations (Harrar et al. 1990). ACC: NNA.19910131.0274. 
Data used in DTN: LL980711104242.054. 
Content of fluorides in J-13 water used to calculate fluoride corrosion rate from flow through 
geometry in Section 6.3. Alkalinity is used to calculate UO2 dissolution rate in Section 6.5.2. 
o) CRC Handbook of Chemistry and Physics (Lide 1995). 
Accepted data from handbook in TIC: 216194.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 10 April 2000 
The molar masses of H (1.00794 g/mol), C (12.011 g/mol) and O (15.9994 g/mol) taken from the 
inside cover are used to calculate fluoride corrosion rates in Section 6.5.2. Density of UO2, 
fluorine, and zirconium, taken from page 4-94 through 4-98, used in 6.3 and 6.5.2. 
p) Modeling of Zirconium Stress-Corrosion Cracking: Texture Effects and Dry Storage 
Spent Fuel Behavior (Tasooji et al. 1984, p. 600, their Figure 3) TIC: 223247. 
Data used from DTN: MO0003SPASSC24.041. 
Reference Figure 3 shows stress threshold of 180 MPa is needed to fail cladding from stress 
corrosion cracking. This is used in Section 6.2.3 as a failure threshold. 
4.2 CRITERIA 
The U.S. Nuclear Regulatory Commissions (NRCs) Total System Performance Assessment and 
Integration (TSPAI) Issue Resolution Status Report (IRSR) (NRC 1998) establishes generic 
technical acceptance criteria considered by the NRC staff to be essential to a defensible, 
transparent, and comprehensive assessment methodology for the repository system. These 
regulatory acceptance criteria address four fundamental elements of the DOE TSPA analysis for 
the Yucca Mountain site, namely: 
Data and analysis shall address their justification (The AMR shall focus on sufficiency of data to 
support the conceptual basis of the process analysis and abstractions) 
1. The AMR shall address the data uncertainty and verification (focusing on technical 
basis for bounding assumptions and statistical representations of uncertainties and 
parameter variabilities) 
2. Analysis uncertainty shall be addressed (focusing on alternative conceptual analysis 
consistent with available site data) 
3. Analysis verification shall be addressed (focusing on testing of analysis abstractions 
using detailed process-level analysis and empirical observations) 
4. Integration shall be addressed (focusing on appropriate and consistent coupling of 
analysis abstractions). 
Relevant to the topic of this AMR, elements (1) through (4) of the acceptance criteria are 
addressed herein. Element (5) of the acceptance criteria, which strictly applies to the completed 
synthesis of process-level analysis and abstractions, will be addressed separately in the Total 
System Performance Assessment-Site Recommendation (TSPA-SR). 
In addition, a second NRC IRSR Key Technical Issue: Container Life and Source Term (NRC 
1999) establishes generic technical acceptance criteria used by the NRC staff for the waste form, 
with the cladding degradation abstraction being part of this Key Technical Issue (KTI). Section 
7 describes how this AMR addresses the IRSR issues.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 11 April 2000 
4.3 CODES AND STANDARDS 
American Society for Testing and Materials (ASTM) Standard C1174-97-Standard Practice for 
the Long-Term Behavior of Materials, Including Waste Forms, Used in Engineered Barrier 
Systems (EBS) for Geologic Disposal of High-Level Radioactive Waste (ASTM 1997) is used to 
support the degradation analysis development methodology, categorize the analysis developed 
with respect to its usage for long-term TSPA, and relate the information/data used to develop the 
analysis to the requirements of the standard. 
This AMR was prepared to conform with the above NRC TSPAI acceptance criteria, as well as 
the DOE interim guidance (Dyer 1999) which requires the use of specified Subparts/Sections of 
the proposed NRC high-level waste rule, 10 Code of Federal Register (CFR) Part 63 (64 FR 
8640). Subparts of this proposed rule that are particularly applicable to data include Subpart B, 
Section 15 (Site Characterization) and Subpart E, Section 114 (Requirements for Performance 
Assessment). Subparts applicable to analysis are outlined in Subpart E, Sections 114 
(Requirements for Performance Assessment) and 115 (Characteristics of the Reference 
Biosphere and Critical Group). 
5. ASSUMPTIONS 
5.1 CLADDING CONDITION AS RECEIVED 
The assumptions from CRWMS M&O 2000a apply and are summarized below. 
5.1.1 The Waste Packages (WP) will be loaded with spent fuel in the order of discharge of 
the fuel from the various reactors as a function of calendar years. This generates some 
variability in the fraction of rods failed within a WP. This loading sequence tends to 
place fuel with higher cladding failure rates into the same WP or consecutively loaded 
WPs and produces larger variations in rod failure fractions than would be expected if 
thermal blending were employed. This is a credible and reasonable assumption based 
on the fuel that current owners would be expected to ship first. (Section 6.1) 
5.1.2 Each failed Pressurized Water Reactor (PWR) fuel assembly has an average of 221 rods 
and has an average of 2.2 failed fuel rods. The basis for the average of 2.2 failed fuel 
rods per failed assembly is described in the Initial Cladding Condition AMR (CRWMS 
M&O 2000a). This failure value applies for the early years of nuclear reactor power 
operations in the US (the 1960s and 1970s) and the number of failed rods per failed 
assembly has decreased to be closer to one (1) today. It is reasonably bounding to 
apply this failure rate for all time since it increases the fuel available for unzippping. 
(Section 6.1) 
5.1.3 All rods are exposed to the conditions of dry storage at the design temperature of the 
Castor Mark V (CRWMS M&O 2000a) cask. Best estimate dry storage temperatures 
were not available at the time of this AMR, therefore the design temperature of the

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 12 April 2000 
Castor Mark V cask with 55 MWd/kgU burnup fuel was selected to be reasonably 
bounding since actual temperatures are lower than design temperatures. (Section 6.2.1) 
5.1.4 All rods are exposed to the temperature conditions in a shipping cask for three weeks at 
350C. This is a reasonable upper limit as 350C is the peak design basis temperature 
for all rods during shipment. Most rods will actually be exposed to lower temperatures 
for a shorter time frame during shipment. (Section 6.2.1) 
5.1.5 The uncertainty value for the rod failure data is four (4). This is based on a square pitch 
array of fuel rods in the fuel assembly. The rods more likely to have damage are these 
rods near the damaged rod. There are four rods near the damaged rod in a square pitch. 
This is bounding when compared to operating experience which shows reliability 
improves with time in reactor (little incipient failures). (Section 6.1) 
5.1.6 BWR cladding degrades in a similar manner as the base case PWR fuel. This is 
reasonably bounding since, in comparison to PWR fuel, the BWR cladding is thicker, 
the BWR fuel typically is discharged with lower burnups and stresses, and each BWR 
fuel assembly is enclosed in a flow channel for additional protection. (Section 6.1) 
5.1.7 It is assumed that no further cladding degradation occurs at the YMP surface facilities. 
This is accomplished by appropriate operating and administrative procedures. 
Sufficient care will be exercised in these facilities such that damaging the cladding 
which would lead to radionuclide contamination, higher operating expenses, and 
greater radiation risk to employees, does not occur. (Section 7) 
5.2 CREEP AND SCC FAILURE 
5.2.1 Creep is analyzed using Murtys correlation. Both Murtys correlation and Matsuos 
correlation (Matsuo 1987, p. 23) fit the available data almost equally well. Murtys 
correlation was selected because it explicitly considers Coble Creep, a type of creep 
that could be important at lower stresses and temperatures. The uncertainty in the creep 
correlation is 0.80, the maximum error range for Murtys correlation. The uncertainty 
is assumed to be uniformly distributed with the calculation of creep for all the rods and 
varies in the range of 80%. (Section 6.2.2) 
5.2.2 The creep failure distribution is determined by a series of tests by Chung et al. (1987). 
Chung et al. (1987) did a series of 20 burst tests with irradiated cladding and in 18 of 
these tests measured an average strain at failure of 3.3% with a range of 0.4% to 11.7%. 
They also did scanning electron microscope inspection of the failures. The inspection 
identified over half the failures as occurring at cracks. Four of the tests were on BWR 
fuel which showed a lower failure strain. The use of this failure criterion accounts for 
both crack damage and possibly weaker cladding types (i.e. BWR fuel). (Section 6.2.3) 
5.2.3 Any rod with a stress greater than 180 MPa is assumed to fail from Stress Corrosion 
Cracking (SCC). This is based on both experiments and analysis presented by Tasooji 
et al. (1984, p. 600, their Figure 3). In this AMR, sufficient iodine is assumed to exist

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 13 April 2000 
such that SCC occurs at the stress threshold of 180 MPa. This is a bounding 
assumption. (Section 6.2.2) 
5.3 LOCALIZED CORROSION 
5.3.1 It is assumed that corrosion of the cladding is limited by the supply of fluoride. The 
rationale for this assumption is that little information is available on the rate of 
consumption of fluoride in a waste package. In the absence of information, a bounding 
approach is needed. Since the assumption is an upper limit, no confirmation is 
necessary. (Section 6.3) 
5.3.2 Fluoride attack is assumed to completely degrade the cladding on a 10 mm length of 
one fuel rod before degradation begins on another rod. This length represents a 
reasonable drip width. The rationale for this assumption is that little information is 
available on how corrosion is distributed within a waste package. This assumption is 
reasonably bounding because each rod breaches as soon as enough fluoride is available; 
there is no delay in breaching one rod because fluoride is being diverted to start the 
degradation of another. Since the assumption is a reasonable bound, no confirmation is 
necessary. (Section 6.3) 
5.3.3 It is assumed that all fuel rods are subject to fluoride corrosion. The rationale for this 
assumption is that little information is available on how water flows within a waste 
package. This assumption is a reasonable bound because each rod is exposed to water 
and therefore subject to fluoride corrosion. Under many exposure conditions, some of 
the fuel rods would be out of the flow path. In those cases, only the fuel rods in the 
flow path would be subject to fluoride corrosion. Since the assumption is an upper 
limit, no confirmation is necessary. (Section 6.3) 
5.3.4 In determining the amount of fluoride that is necessary to breach a fuel rod, it is 
assumed that fluoride removes all the cladding from a 10-mm length of the fuel rod. 
The rationale for this assumption is that this width is comparable to the width of typical 
water drop splat sizes and water flow paths. However, the actual wetted width would 
be wider because the rough, porous products of corrosion on the surface of fuel rods 
would tend to wick water and promote wider flow paths. Since this assumption is a 
reasonable bound, it does not require verification. (Section 6.3) 
5.4 OTHER FAILURE MECHANISMS 
5.4.1 Seismic analysis showed that rods would fail from a very severe earthquake (a once per 
million years event) and that most of the rods would fail. Therefore, in the TSPA-SR, 
the seismic event is assumed to have a frequency of 1.1x10-6 /yr and it is assumed that 
all the cladding is failed at the rod center and available for clad unzipping when a 
seismic event occurs. Failing all the rods is an upper limit and failing the rods in the 
center minimizes the release time for unzipping. (Section 6.4.1)

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 14 April 2000 
5.5 FAST RELEASE OF RADIONUCLIDES 
5.5.1 It is assumed that the absolute rate of fast release of radionuclides from a breached fuel 
rod is proportional to the length of the rod. Results for short rod segments are used to 
predict the performance of full-length rods, and the same fractional release rate is used 
for both. The rationale for this assumption is that, over the time necessary to plug the 
cracks in a fuel rod, the characteristic distance for aqueous diffusion is comparable to 
the active length of a fuel rod (Section 6.5.2). The assumption could be inaccurate if 
transport limitations result in smaller release rates, and in that case the assumption 
would be reasonably bounding. Since this assumption is both realistic and a reasonable 
bound, it does not require verification. (Section 6.5) 
5.5.2 It is assumed that, during the fast release phase, the fuel reacts with water to form 
metaschoepite. This assumption is consistent with a similar assumption for the 
unzipping phase. Reaction products with a large volume increase would tend to 
produce small fast release fractions (because cracks would plug quickly) and fast 
unzipping, whereas reaction products with a small volume increase would tend to 
produce larger fast release fractions and slower unzipping. However, the fast release 
fraction is small, so it is reasonably bounding to favor fast unzipping. Since the 
assumption is reasonably bounding, no confirmation is necessary. (Section 6.5) 
5.6 CLADDING UNZIPPING AND FUEL DISSOLUTION 
5.6.1 It is assumed that, during the unzipping phase, the fuel reacts with water to form 
metaschoepite. Oxidation and hydration of uranium dioxide can result in a variety of 
mineral species. Of these, metaschoepite is the one that entails the largest change in 
volume, and larger volume increases correspond to faster degradation. Other uranium 
minerals (such as sodium boltwoodite) can also be formed from uranium dioxide, but 
these require a supply of a solute (such as sodium), so the rate of formation will be 
limited by the supply of solute. Therefore, the rationale for this assumption is that 
conversion to metaschoepite provides the largest plausible volume increase. Since the 
assumption is reasonably bounding, no confirmation is necessary. (Section 6.6) 
5.6.2 It is assumed that the rate of reaction of the uranium dioxide with water is controlled by 
the intrinsic dissolution rate of UO2. The rationale for this assumption is that this is the 
fastest rate at which reaction can advance into a uranium dioxide pellet surface. If the 
products of reaction of UO2 limit the transport of water to the uranium dioxide surface, 
the reaction will necessarily be slower. Since this assumption is reasonably bounding, 
no confirmation is necessary. (Section 6.6) 
5.6.3 It is assumed that all cladding breaches occur at the center of the active fuel length. 
The rationale for this assumption is that this location provides the fastest unzipping of a 
fuel rod. If the breach is at the center of the active fuel length, propagation of the 
breach by a distance of half the active fuel length (toward each end) will result in 
complete unzipping of the active fuel length of the rod. If the breach is at some other 
location, the required propagation distance will be larger for one end. Since this 
assumption is reasonably bounding, no confirmation is necessary. (Section 6.6)

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 15 April 2000 
5.7 STAINLESS STEEL CLADDING 
5.7.1 The stainless steel (SS) clad fuel is loaded into WPs as it is received at the YMP 
facilities. This is used to define the number of WPs containing SS cladding and the 
fraction of SS cladding in these WPs. The basis of this assumption is that it simplifies 
surface facility operations. This assumption is not critical since the product of WPs 
containing SS cladding and fraction of SS in each WP is constant (i.e. there is a fixed 
amount of SS cladding). (Section 6.7) 
6. ANALYSIS 
Earlier studies (Ahn et al. 1999, Henningson 1998, Rothman 1984, Pescatore et al. 1990, 
Manaktala, 1993) have evaluated cladding degradation under repository conditions. Others 
(Cunningham et al. 1987, Peehs 1998, Einziger and Kohli 1984) evaluated fuel performance 
under dry storage conditions, which are similar to early repository conditions. As part of the 
Environmental Protection Agencys development of environmental standards, S. Cohen & 
Associates (1999) did a detailed study of cladding degradation, both before reception at a 
repository and in the repository. Sanders et al. (1992) reviewed the condition of cladding after 
reactor operation and reviewed the potential of damage from external mechanical loading. 
Experiments (Wilson 1985, 1987, 1990) also measured the releases from damaged cladding. The 
Yucca Mountain Project (YMP) 1998 Total System Performance Assessment Viability 
Assessment (TSPA-VA) included cladding degradation as part of the fuel degradation analysis. 
TSPA-1995, a previous analysis of repository performance, neglected the presence of cladding, 
as did most earlier performance assessments (PAs). In doing so, all the fuel in the Waste 
Package (WP) was considered available for dissolution at the speed of the intrinsic fuel 
dissolution rate. For some radionuclides, solubility limits were reached which controlled the rate 
of those radionuclides leaving the WP. In the Total System Performance Assessment Site 
Recommendation (TSPA-SR), the cladding is considered an integral part of the waste form. 
The cladding degradation abstraction summarizes numerous studies of cladding degradation and 
is incorporated into the TSPA-SR computer analysis as an abstraction. The abstraction consists 
of two phases, cladding perforation and cladding unzipping. Cladding perforation is the 
formation of small cracks or holes in the cladding from various sources ranging from failures 
during reactor operation to cladding creep rupture during repository storage. Perforation permits 
the fuel inside the cladding to begin to react with moisture or air and potentially leads to the 
cladding unzipping phase. In the unzipping phase, the cladding is torn open by the formation of 
secondary mineral phases on the UO2 fuel, and the radionuclides are available for release. The 
various components of the abstraction are discussed below. 
The numbers reported in this section are given to three (3) figures to assist in making the 
numbers more traceable. This analysis is considered accurate to only the first significant figure, 
that is, accurate to approximately 80% to 90%. The remaining figures are only reported for 
traceability.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 16 April 2000 
6.1 CLADDING CONDITION AS RECEIVED 
The Initial Cladding Condition AMR (CRWMS M&O 2000a) describes the condition of the 
commercial nuclear fuel as it is expected to be received at the YMP site. This analysis generates 
the initial boundary condition for the subsequent analysis of degradation of the cladding in the 
repository. It also evaluates the fraction of fuel rods that are perforated before emplacement in 
the repository and are immediately available for cladding unzipping when the WP fails. 
A distribution for the fraction of cladding within a WP that failed as a result of reactor operation 
was developed from the fraction of rods failed as a function of calendar years by assuming that 
the fuel assemblies are loaded into WPs in their order of discharge from the reactors. This is the 
Complementary Cumulative Distribution Function (CCDF) shown in Table 1. This loading 
sequence tends to place fuel with high failure rates (BWR fuel in 1970 and also in 1973-1976, 
and PWR fuel in 1972, 1983, and 1989) into the same or consecutive WPs and produces larger 
variations in rod failure fractions than would be expected if thermal blending were employed. A 
factor of four uncertainty was applied to represent the uncertainty in rod failure data. Rod failure 
from dry storage (0.045% of rods failed per WP) and transportation (vibration and impact, at 
0.01% of rods failed per WP) were also included (CRWMS M&O 2000a, Section 7). Failure 
from creep during dry storage and transportation is included with the creep analysis presented in 
Section 6.2 of this AMR. Table 1 gives the distribution of rods that have failed cladding at 
emplacement in the repository. This table is the same as Table 14 of CRWMS M&O 2000a and 
is given in the Excel file: fuel-rel.xls, cells G112 through J134 of DTN: 
MO0001SPAICC48.037. In the TSPA-SR, the WPs are grouped into 5 bins, each representing 
approximately 1500 CSNF WPs. Table 1 represents the distribution of individual WPs and 
cannot be applied to the individual bins because of the limited number of WPs represented by the 
distribution tail. For example, the very far point of the distribution is represented by the BWR 
fuel discharged in 1970 with 4.5% of the rods failed. That year, only 29 assemblies were 
discharged, about 70% of a single BWR WP containing 44 assemblies. In sampling for a bin or 
group of 1500 WPs, it would be incorrect to represent the whole group by an individual WP that 
exists in such small numbers. For the TSPA-SR abstraction of bins or groups, the bins are 
represented by the 98% to 5% range of the CCDF in Table 1 with the median representing the 
best estimate. A triangular distribution was assigned. In summary, the initial failure percentage 
for the rods in a WP in the TSPA-SR for the five bins or groups of WPs is represented by: 
Minimum = 0.0155% 
Best Estimate = 0.0948% 
Maximum = 1.285% 
and the probabilistic distribution is triangular. These percentages of fuel rods undergo cladding 
unzipping and fuel dissolution when the WP fails. 
As received at YMP, the cladding of rods that are not perforated also has an internal pressure 
resulting from reactor operation and therefore will be stressed. The creep strain calculations in 
this AMR use the stress distribution developed in the Initial Cladding Condition AMR (CRWMS 
M&O 2000a, file = Rod-Initial-C.xls, Sheet = Crack, Cells = K15 through M2014). The 
cladding analysis is based on the Westinghouse 17 x 17 fuel design. This design represents over 
30% of the PWR fuel discharged to date and is also the thinnest Zircaloy cladding design. The 
BWR cladding degrades in a similar manner. This is reasonably bounding since BWR cladding

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 17 April 2000 
is thicker, is discharged with lower burnups and stresses, and is enclosed in flow channels for 
additional protection. Starting with a distribution of PWR fuel burnups that are anticipated for 
storage at YMP, distributions for various cladding properties were developed, culminating with 
the room temperature stress distribution represented by Figure 1. 
Table 1. CCDF of Rod Perforation for As-Received Fuel 
CCDF Lower 
Uncertainty. 
Best Estimate 
% Failure 
Upper 
Uncertainty 
1.000 0.0138 0.0550 0.220 
0.999 0.0146 0.0585 0.234 
0.985 0.0155 0.0622 0.249 
0.856 0.0179 0.0717 0.287 
0.655 0.0212 0.0849 0.340 
0.582 0.0224 0.0895 0.358 
0.506 0.0237 0.0948 0.379 
0.271 0.0284 0.1136 0.454 
0.1966 0.0361 0.1445 0.578 
0.1084 0.0507 0.2028 0.811 
0.0970 0.0522 0.2089 0.836 
0.0766 0.0741 0.2965 1.186 
0.0640 0.0746 0.2983 1.193 
0.0503 0.0803 0.3213 1.285 
0.0373 0.1248 0.4990 1.996 
0.0323 0.247 0.9875 3.95 
0.0221 0.289 1.1568 4.63 
0.0196 0.450 1.7985 7.19 
0.0190 0.509 2.035 8.14 
0.0115 0.694 2.776 11.10 
0.0036 0.763 3.051 12.20 
0.0002 1.321 5.286 21.14 
0.0000 1.321 5.286 21.14 
DTN: MO0001SPAICC48.037 
6.2 CREEP STRAIN AND SCC FAILURE 
The current repository design utilizes backfill, which affects the temperatures. A statistical 
distribution of rod properties has been developed so that creep failure is included in the analysis. 
All the rods are assumed to be exposed to a temperature history that includes 20 years of dry 
storage, three weeks of transportation and then a temperature profile for storage in the repository. 
Rods at six zones across the WP are evaluated, and Murtys creep strain correlation is used. The 
failure strain criterion is a distribution based on eighteen tests of irradiated cladding. The peak 
surface temperature of the WP is varied and the fraction of rods failed is calculated. The 
following sections discuss the analysis in more detail.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 18 April 2000 
6.2.1 Temperature History 
The rods are exposed to a temperature history that includes 20 years of dry storage starting at 
350C and then decreasing during dry storage plus an additional three weeks of transportation at 
350C (CRWMS M&O 2000a, Section 6.10.1, cladding initial condition data, file = Rod-Initial- 
C.xls, Sheet = Creep, Cells B25 through C39). Best estimate dry storage temperatures were 
not available at the time of this analysis and the peak (center rod) temperature history for the 
Castor V package with 55 MWd/kgU fuel (Peehs 1998, Figure 13a) was used in this analysis. 
These temperatures were given for the first ten years and have been extrapolated to 20 years. In 
addition, a three-week period of temperatures at 350C has been added to represent design bases 
shipping temperatures. It is reasonably bounding to use the peak design bases temperatures for 
all rods since most will actually see lower temperatures. 
For storage in the WP, the temperature distribution across the WP was obtained from CRWMS 
M&O 2000f. These temperatures are reproduced in AMR-F0155-V1.xls, Sheet TempC2, 
Cells = D5 through U44. This temperature distribution varies both radially across the WP and 
with time. Figure 2 shows the location of the different temperature nodes. The WP internals 
were divided into 6 zones, which are also shown in Figure 2. An estimate of the fraction of each 
assembly in each zone is made by visual inspection of Figure 2. Table 2 gives the fraction of 
rods in each zone and the temperature nodes used to calculate the zone temperature. The 
temperature of the WP surface was obtained from CRWMS M&O 2000h. Temperatures for 5 
bins, grouped by water ingression, were supplied in CRWMS M&O 2000h and are shown here 
as Figure 3. The bin numbers are assigned by increasing water ingression rate with Bin 4 
representing 20 to 60 mm/year water ingression. This AMR uses Bin 4 with water ingression in 
the range of 20 to 60 mm/yr. Bin 4 has one of the widest temperature peaks and therefore could 
produce the most creep but, more importantly, it also represents over 53% of the WPs. Figure 4 
shows the WP surface temperature, temperature increase across the WP, and center rod 
temperature. Figure 5 shows the total center rod temperature profile used for the creep analysis. 
This profile (reading from left to right) shows dry storage for 20 years starting at 350C, three 
(3) weeks of shipping at 350C, preclosure with forced ventilation for 50 years, and then the 
postclosure temperature profile. This profile extends for 1000 years although only 200 years are 
shown on the figure. All rods undergo identical dry storage and shipping conditions. The creep 
analysis of the different phases of the life cycle of the rods must be integrated so that the creep 
components from the various stages (dry storage, shipping) are added. Creep failures during dry 
storage are combined with the creep failures during shipping because the damage is cumulative.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 19 April 2000 
Table 2. Fuel Rod Zones in a WP 
Zone Assemblies Fraction of Rods 
Temperature 
Nodes 
Temperature (oC) 
Scaling Factor 
1 0.4 0.019 1 1.000 
2 0.6 0.029 Avg, 1 & 2 0.933 
3 2.4 0.114 Avg, 5 & 6 0.888 
4 4.4 0.210 Avg, 6 & 7 0.820 
5 7.0 0.333 Avg, 9 & 10 0.661 
6 6.2 0.295 Avg,10 & 11 0.446 
Sum 21 1.0 N/A N/A 
DTN: MO00004SPACLD07.043 
Temperature uncertainties are also included in the creep strain analysis. The difference between 
the maximum WP surface temperature for Bin 4 and the average WP surface temperature is 
22.1C (CRWMS M&O 2000h) (see Figure 7 of this AMR). The uncertainty in WP internal 
temperature was 19.5C (at peak times), which is the difference in peak temperature between a 
helium filled WP (CRWMS M&O 2000f, p. 29) and an air/water vapor filled WP (CRWMS 
M&O 1999e, p. 38). These differences sum to 41.6oC and represent an uncertainty of 13.5% 
above the peak temperature for the average WP of 308C. The uncertainty is uniformly 
distributed with a range of " 13.5%. The uncertainty in the WP internal power was neglected 
because of the small predicted uncertainty (CRWMS M&O 1999c, Item 1, p.1/1) 
The creep analysis is performed for 12,000 fuel rods. The initial room temperature stress as 
received at YMP for each of 2000 rods is determined from the CCDF in Figure 1. A rod with 
each of these 2000 initial stresses is then placed into each of the six WP zones (totaling 2000 
rods/zone x 6 zones = 12,000 rods) and is exposed during repository storage to the temperature 
profile predicted for that particular zone (with uncertainty included). The temperature scaling 
factors to calculate the temperature of a rod in each zone are given in Column 5 of Table 2. The 
temperature of the center rod is multiplied by this factor to calculate the rod temperature for each 
zone. The uncertainty is then applied for each rod in each zone. The temperature uncertainty is 
uniformly distributed over a range of " 13.5%. 
The center rod in an average WP peaks at 308oC at 53 years, three years after closure. At this 
time, the outer rods peak at 291oC and the WP surface temperature is 277oC. After an additional 
50 years, the center rod has cooled to 226oC and the outer rod is 215oC. The hottest center rod 
will peak at 350oC (13.5% above 308oC) while the hottest outer rod will peak at 314oC (see 
Attachment II, Table II-10a). 
In generating the failure probability distribution for stress and SCC, the WP peak surface 
temperature is treated in this analysis as an independent variable and failures are predicted for 
various WP peak surface temperatures. In the TSPA-SR for each realization, the WP peak 
temperature will be established and then creep and SCC rod failure fractions will be looked up 
on a table.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 20 April 2000 
6.2.2 Creep Strain and SCC Correlation 
CRWMS M&O 2000j compares the creep predictions using six (6) different creep correlations to 
the results from five (5) different experiments (Tables 3 and 4). The tables give the relative 
error, that is the absolute value of the difference between the calculated and measured values 
divided by the measured values [Abs((Calculated-Measured)/Measured)]. Using relative error as 
a measurement, the smaller numbers represent the better fit. The five (5) different experiments 
were for unirradiated material, with the temperature range: 250C < TC < 385C, and the stress 
range: 55 MPa < Stress < 120 MPa. There were a total of 503 reported strain measurements, 
many of which were obtained at intermediate times in the analysis and 95 of which were at end 
points (last measured strain). Table 3 compares the equations for all the data points, including 
the intermediate and end points. Both Murtys correlation and Matsuos correlation fit the data 
approximately equally well. Murtys correlation was selected because it explicitly considers 
Coble creep, a type of creep that could be important at lower stresses and temperatures and that 
might not have been observed in the ranges of these experiments. Table 4 compares the fit at the 
end points (last measured strain) for each of the 95 analyses. This prediction is more important 
for this AMR because failure is predicted for the larger creep strains, for which the end points of 
the analyses should be more representative. It is important to note that the experimental ranges, 
250C < ToC < 385C and 55 MPa < Stress (MPa) < 120 MPa are close to the upper end of 
repository conditions shortly after closure. Some of these tests also ran for 10,000 hours (1.1 
years) (CRWMS M&O 2000j, p.II-1). Again, Murtys correlation gives one of the better fits and 
will be used for creep failure calculations. For Murtys correlation, the uncertainty in the creep 
correlation for all 503 data points ranges from 0.283 to 0.727 and with a weighted average of 
0.557 (Table 3). The uncertainty used in the creep correlation is 0.80 (0.727 rounded upward) 
uniformly distributed with the calculated creep for each of the 12,000 rods and varies in the 
range of +/- 80% of the calculated value. 
Table 3. Comparison of Relative Error of Creep Correlations for All Data Points * 
Creep Correlations 
Ref.2 
Total Data 
Points1 Matsuo Murty Mayuzumi Limback Spilker Peehs 
Spilker, T2 192 0.758 0.727 0.648 0.560 0.344 0.726 
Spilker, T3 240 0.340 0.482 0.901 1.779 2.256 0.546 
Matsuo 21 0.135 0.392 0.640 0.557 1.994 0.521 
Mayuzumi 31 0.282 0.283 0.121 0.477 1.291 0.579 
Limback 19 0.334 0.417 0.142 0.145 1.354 0.596 
Weighted 
Average 
N/A 0.487 0.557 0.717 1.121 1.431 0.606 
NOTE: *Values are: Absolute Value [ (Calculated-Measured)/Measured ] 
1Total number of points : 503 
2Tests: unirradiated material, over the range 250T (C) 385 and 55 Stress (Mpa)  120 
(MOL.20000223.0002)

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 21 April 2000 
Table 4. Comparison of Relative Error of Creep Correlations for Experimental End Points * 
Creep Correlations 
Ref.2 
Total Data 
Points1 Matsuo Murty Mayuzumi Limback Spilker Peehs 
Spilker, T2 32 0.780 0.669 0.603 0.581 0.166 0.773 
Spilker, T3 40 0.294 0.339 0.834 2.533 1.871 0.674 
Matsuo 15 0.092 0.823 2.886 0.931 3.042 0.296 
Mayuzumi 4 0.338 0.133 0.148 0.993 1.099 0.624 
Limback 4 0.411 0.340 0.134 0.147 0.980 0.680 
Weighted 
Average N/A 0.432 0.518 1.022 1.457 1.232 0.634 
NOTE: *Values are: Absolute Value [ (Calculated-Measured)/Measured ] 
1Total number of points : 95 
2Tests: unirradiated material, over the range 250T (C) 385 and 55 Stress (Mpa)  120 
(MOL.20000223.0002) 
The Murty correlation is described in Henningson (1998, Section 4, pp. 51 to 61) and the 
recommended equations (Henningson 1998, p. 57) are reproduced below. Hoop creep 
characteristics of Zircaloy tubing were collected at temperatures between 316C and 427C and 
at stress levels in the range of 55 MPa to 235 MPa. Three different sets of experimental data 
were used by Murty in generating the equations. The equations combine a high-stress creep 
mechanism of glide creep with a low-stress creep mechanism of Coble creep: 
3 / 31200 6 )] 807 [sinh( 10 97 . 4 
E T
E 
e x T 
Glide 
s e - = & (Eq. 6.2-1) 
T 
e T 
Coble 
s e / 21000 83 . 8 - = & (Eq. 6.2-2) 
Glide creep strain: 
t 
t 
t 
de 
de 
de 
gli 
gli 
gli glide 
T 
T 
e k e 
e ke 
e e 
& 
& 
& 
+ 
+ = (Eq. 6.2-3) 
Coble creep strain: 
t Coble Coble e e & = (Eq. 6.2-4) 
Total creep: 
Coble glide e e e + = 
(Eq. 6.2-5)

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 22 April 2000 
Various parameters and constants include: 
eT = 0.008, 
k = 10 
E = (1.148x105  59.9T) x106, Youngs Module, Pa (T in K) (Eq. 6.2-6) 
T = temperature (K) 
s = stress (Pa) 
t = time (hours) 
The above equations calculate the creep for a specific time at a constant temperature. To 
calculate creep strain for a rod exposed to the temperature history shown in Figure 5, the 
temperature history is divided into finite intervals and a time hardened technique recommended 
by Murty (Henningson 1998, p. 57, equation 15) and given below is used: 
e (ti) = e(Ti-1, ti-1) + [ e(Ti, ti) - e (Ti, ti-1)] (Eq. 6.2-7) 
Where the subscript i-1 represents the previous time step and the subscript i represents the 
current time step. This is necessary because the creep rate for a constant temperature starts out 
very fast (primary creep) and then decreases to a slower secondary creep rate. If Equations 6.2-2 
through 6.2-6 were applied separately to each time step, the primary creep would never saturate 
and the total creep would be over-predicted and also would be dependent on the number of time 
steps (number of times that the primary creep calculation was started). The actual analytical 
method and the software routine are discussed in Attachment II. 
This creep correlation is for unirradiated cladding. Its use for irradiated cladding is reasonably 
bounding. Peehs (1998, Figure 10) compares the creep for irradiated and unirradiated cladding 
and shows that the creep for irradiated cladding is about half (1/2) that of unirradiated cladding. 
The analysis presented in this section is based on an empirical creep equation developed by 
Murty. Many of the alternative equations are discussed by Pescatore and Cowgill (1994, pp. 47- 
86). One equation discussed is the Diffusion Controlled Cavity Growth (DCCG). Pescatore and 
Cowgill (1994, p. 83-85) concludes that the DCCG has not been validated against cavity data 
and voids or cavities are very infrequently seen in irradiated Zircaloy. He recommends (p. 85) a 
methodology similar to the approach used here. Commercial power plant dry storage license 
applicants were once required by the NRC to use the DCCG method to evaluate dry storage 
designs. The current NRC Interim Staff Guidance (ISG) - 11 (NRC 2000) recognizes the 
controversy with this conceptual method and permits commercial power plant license applicants 
to use other creep equations and methods in their license application. The use of Murtys 
correlation is consistent with this ISG. 
For SCC failures, no detailed analysis of iodine concentrations or crack velocities is used. The 
maximum rod stress is compared with a threshold SCC stress and failure is predicted if the rod 
stress exceeds the threshold stress.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 23 April 2000 
6.2.3 Creep and SCC Failure Criterion 
To estimate the percent of the rods that will fail from creep, a creep failure criterion must be 
established. For this, data from Chung et al. (1987, pp. 780-781) will be used. Chung et al. 
(1987) conducted a series of 20 slow pressure burst tests and mandrel tests with irradiated 
cladding. Four tests were on BWR Zircaloy 2 cladding with a burnup of 22 MWd/kgU and the 
remaining tests were on PWR Zircaloy 4 cladding with a burnup of 28 MWd/kgU. For 18 tests, 
they reported strains at failure which averaged 3.3% with a range of 0.4% to 11.7%. They also 
conducted scanning electron microscope inspection of the failures and found evidence that, in 11 
of the tests, the failures occurred at cracks formed in the cladding. The use of these results for a 
failure criterion addresses the potential for lower failure strains from pre-existing internal cracks 
and the situation that failure might not be a pure material creep. Figure 6 gives the CCDF for the 
creep failure criterion. This CCDF is sampled for each of the 12,000 rods analyzed (2,000 
rods/zone x 6 zones). The lower 4 creep failures in the CCDF are for BWR fuel and are applied 
in the PWR rod analysis. This failure criterion does not address potential changes in the failure 
strain criterion with strain rate. The strain rates in Chungs gas pressurization experiment are 
such that the tests extended for periods of 1 to 312 hours with an average of 152 hours. The 
mandrel test durations were in the range of 0.3 to 691.8 hours with an average of 236 hours. 
While these strain rates are faster than expected in repository conditions, they are not rapid burst 
tests. The creep tests summarized in CRWMS M&O 2000j (p. II-1) extend up to 10,000 hours 
(approximately 1.14 year) and show creep strains, without failure, in excess of the failure 
criterion being used in this AMR. 
There is corroborating evidence for using this creep failure criterion which is summarized in 
Section 6.10.1 of CRWMS M&O 2000a (Initial Cladding Condition AMR). 
For most rods, the stresses during dry storage are too low to produce Stress Corrosion Cracking 
(SCC). Tasooji et al. (1984, p. 600, their Figure 3) show that stresses need to be above 180 MPa 
for SCC to occur. In this analysis, sufficient iodine exists and a rod with a peak stress greater 
than or equal to 180 MPa fails from SCC. 
6.2.4 Creep and SCC Failure Results 
Figure 1 gives the CCDF for the hoop stress (at room temperature of 27EC) in the rods expected 
to be received at YMP. A sampling of 2000 rods with stresses that are defined by this 
distribution was used for the stress variation. A rod (total of 12,000 rods analyzed, 6 x 2000) 
with each of these 2000 stresses was placed in each of the six (6) zones shown in Figure 2 and 
described in Table 2. This rod represents the fraction of the total WP inventory in the zones as 
given in Table 2, Column 3. Each rod is exposed first to a temperature profile represented by 
Figure 5 (for dry storage and shipping) and then to the repository temperature history normalized 
by the WP radial scaling factor corresponding to the particular zone as given in Table 2, 
Column 5. A uniform temperature uncertainty of " 13.5% is included. The creep strain is then 
calculated for the rod using the equations in Section 6.2.2 (including a uniform uncertainty of " 
80%). This strain is compared to a random sampling of the creep failure strain criteria CCDF in 
Figure 6. The peak stress is also compared to a SCC stress threshold of 180 MPa. If the rod 
creep strain exceeds the creep failure strain criterion, or the SCC stress threshold is met, the 
fraction of the rods in that radial zone of the WP has become perforated and that fraction of a rod

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 24 April 2000 
is available for cladding unzipping. This procedure is repeated for 12,000 rods in a software 
routine and the fraction of the WP inventory perforated is calculated. The details of this analysis 
are described in Attachment II and the software routine AMR-F0155-V1.xls has been submitted 
as DTN: MO00004SPACLD07.043. 
The above analysis has not been directly incorporated into the TSPA-SR but an abstraction has 
been included. For this abstraction, the independent variable is the peak WP surface 
temperature. The above analysis was performed for peak WP surface temperatures that vary 
from 177C to 412C. The WP temperature history as shown in Figure 4 is linearly shifted 
upward or downward by the difference between the base case and new peak WP surface 
temperature. Figure 7 shows the WP temperature for the peak, average and minimum WP in 
group 4 (CRWMS M&O 2000h). The peak temperatures are approximately a constant shift 
above the average temperatures. The minimum temperature falls off more quickly than the 
average. Analyzing the minimum temperature WPs as a constant temperature difference below 
the average WP temperature is reasonably bounding because it increases the amount of time at 
an elevated temperature. The change in temperature radially across the WP is then added to the 
scaled WP surface temperature. The temperature uncertainty is established to cover the 
maximum temperatures. 
Table 5 gives the fraction of rods failed in a WP (failed from creep) as a function of peak WP 
surface temperature. This table is imported into the TSPA-SR and the TSPA-SR interpolates the 
fraction of rods failed in a realization after establishing the peak WP surface temperature for that 
realization. Figure 8 is a graphical representation of this table. The plateau of the fraction of 
rods perforated from creep at the lower WP peak surface temperatures represents the rods that 
were failed in dry storage and shipping. These rods can only fail once and therefore cannot fail 
again in the repository. Rods that have not failed have undergone some creep during dry storage 
and shipping and start to accumulate additional creep from that point. Figure 8 shows that above 
a peak WP surface temperature of about 300C, the best estimate fraction of rods perforated from 
creep increases dramatically. This is because the creep correlation has an Arrhenius temperature 
dependency and the activation energy is reached at that point. The upper limit curve represents 
the fraction of rods failed from creep if the failure criterion were 0.4% creep, the minimum value 
in the creep failure strain criterion CCDF. The lower limit curve represents the fraction of rods 
failed from creep if the maximum creep failure strain criterion of 11.7% were applied. The best 
estimate value represents a random sampling of the creep failure strain criterion CCDF. In the 
TSPA-SR, a triangular distribution is used between the upper limit, best estimate and lower limit 
to incorporate uncertainties. 
SCC requires a susceptible material, an aggressive chemical environment, and high stress levels. 
Iodine induced SCC requires an iodine concentration in the fuel-cladding gap greater than 5x10-6 
g/cm2 (Cunningham et al. 1987, p. A.5). Below this threshold of free iodine concentration, 
Zircaloy cracking due to SCC has not been observed. In actual fuel rods, free iodine 
concentrations are expected to be negligible. For this analysis the amount of iodine was 
considered to be present in sufficient quantities for SCC. The times at high stress and the times 
of elevated temperatures were sufficiently long such that, once cracking started, there was 
sufficient time to propagate through the cladding (crack velocities were not considered). A rod 
with a stress above 180 MPa fails by SCC. This threshold was reported by Tasooji et al. (1984, 
p.600, their Figure 3). Few rods have such high stresses and the same rods that fail from SCC

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 25 April 2000 
are also prone to fail from creep. If the calculations were not combined, double counting of the 
failed rods would be possible. The inclusion of SCC increases the mean failure from creep alone 
from 2.0% to 2.4% for dry storage and transportation (left side of Figure 8). For higher 
repository temperatures, the difference disappears. 
Table 5. Fraction of Rods Perforated From Creep as a Function of Peak WP Surface Temperature 
WP Peak 
Temperature, oC Upper Limit Best Estimate Lower Limit 
#177 0.1942 0.0244 0.0105 
227 0.1949 0.0244 0.0105 
252 0.2057 0.0258 0.0105 
262 0.2156 0.0267 0.0105 
277 0.2479 0.0339 0.0106 
292 0.3264 0.0604 0.0120 
297 0.3628 0.0783 0.0133 
302 0.4080 0.0987 0.0173 
312 0.5052 0.1622 0.0370 
327 0.6379 0.3019 0.1067 
352 0.8227 0.5567 0.3424 
377 0.9553 0.7789 0.5920 
402 0.9970 0.9302 0.7986 
$412 0.9985 0.9658 0.8720 
(DTN: MO00004SPACLD07.043) 
6.3 LOCALIZED CORROSION 
Corrosion of zirconium has been observed in fluoride-containing environments. Since fluoride is 
present in Yucca Mountain groundwater, fluoride corrosion may occur in waste packages. Two 
scenarios for fluoride corrosion may be considered. In the first (water filled WP scenario), the 
waste package is full of water, and fluoride ions are transported to the cladding by aqueous 
diffusion. In the second (flow-through scenario), water enters the waste package through one or 
more breaches on the upper surface of the waste package and drips out through a breach on the 
bottom. These two scenarios represent extremes of the rate of drainage. 
The flow-through scenario is the more severe of the two. In this scenario, fluoride can be rapidly 
transported through the waste package by advection, whereas in the water filled WP scenario it is 
transported by diffusion, which is a comparatively slow mechanism. In the flow-through 
scenario, advective flow is directed downward by gravity, so fluoride attack can be localized on 
a relatively small area of cladding (and even on a small area of an individual fuel rod). In 
contrast, diffusion does not have a preferred direction, so in the water filled WP scenario the 
fluoride can be transported to a large volume of the waste package. Spreading the fluoride over a 
larger area of cladding (i.e. a larger area on an individual rod or area on more than one fuel rod) 
means that more fluoride will be consumed in breaching each fuel rod. Since the flow-through 
scenario is more severe, the water filled WP scenario will not be considered further.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 26 April 2000 
A bounding approach has been used to describe the flow-through scenario. At least three sources 
of conservatism have been identified. First, it might be expected that the corrosion of zirconium 
is sufficiently slow, and the flow of groundwater through the waste package is sufficiently fast, 
that some fluoride will simply flow through the waste package without reacting. Credit has not 
been taken for this loss of fluoride. Instead, corrosion of the cladding is limited by the supply of 
fluoride. 
A second source of conservatism is that fluoride attack is assumed to degrade one fuel rod before 
degradation begins on another rod. This is reasonably bounding because each rod breaches as 
soon as enough fluoride is available to corrode a 10-mm length of cladding; there is no delay in 
breaching one rod because fluoride is being diverted to start degrading another. Credit has not 
been taken for simultaneous attack of more than one fuel rod. Instead, all the available fluoride 
goes to and reacts with a single fuel rod. When that patch on a fuel rod is completely degraded 
(corroded through), the fluoride starts to attack another fuel rod. 
Finally, there is conservatism in that it is assumed that all fuel rods are subject to fluoride 
corrosion. Such an exposure might result if the water entered through numerous breaches or 
through a cracked circumferential weld over the top half of the waste package. In that case, drips 
could be distributed over all of the fuel rods. Under many other exposure conditions, however, 
some of the fuel rods would be out of the flow path. In those cases, only the fuel rods in the flow 
path would be subject to fluoride corrosion. 
In determining the amount of fluoride that is necessary to breach a fuel rod, fluoride removes all 
the cladding from a 10-mm length of the fuel rod by reacting to form ZrF4. The as-manufactured 
thickness of the cladding may be used because, although some of the zirconium may be oxidized, 
the zirconium atoms remain in the products of corrosion. 
The volume of zirconium VZr that must react to breach all of the fuel rods may be calculated with 
the formula 
) ( ) ) 2 ( ( 
4 
2 2 w d w mL w d d mL VZr - = - - = p p 
(Eq. 6.3-1) 
where m is the number of fuel rods, L is the length that is subject to corrosion, d is the outside 
diameter of the cladding, and w is the wall thickness of the cladding. For this calculation, the 
most common waste package type (21 PWR) and the most common fuel assembly type 
(W1717WL) are used. Since W1717WL is a 17  17 assembly and the waste package contains 
21 assemblies, the number of positions is m = 172  21 = 6069. Since the control rod guide tubes 
and instrument tubes are similar in geometry to fuel rod cladding, all rod positions are counted, 
rather than just the number of fuel rods. 
In a volume of water Vw with a fluoride concentration of cF, the number of moles of fluoride is 
VwcF / mF, where mF is the molar mass of fluorine. In forming ZrF4, n = 4 moles of fluoride are 
required for each mole of zirconium. Therefore, the volume of zirconium VZr that can be reacted 
with this volume of water is

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 27 April 2000 
n m 
v c V 
V 
F 
Zr F w 
Zr = (Eq. 6.3-2) 
where vZr is the molar volume of zirconium. By combining Equations 6.3-1 and 6.3-2 , one finds 
that 
) ( w d w mL 
v c 
n m 
V 
Zr F
F 
w - = p (Eq. 6.3-3) 
In Equation 6.3-3, mF = 19.0 g/mol (Lide 1995, inside front cover), cF = 2.18 mg/L = 2.18 g/m3 
(Harrar et al. 1990, Table 4.1), n = 4, m = 6069, L = 10 mm, w = 0.5715 mm, and d = 9.50 mm 
(CRWMS M&O 2000a, Table 2). The molar volume of zirconium is vZr = mZr / rZr, where mZr = 
91.2 g/mol (Lide 1995, inside front cover) is the molar mass of zirconium and rZr = 6520 kg/m3 
(Lide 1995, p. 4-98) is the density of zirconium. Evaluation of Equation 6.3-3 yields Vw = 2424 
m3. The result is that the fraction of fuel rods failed by fluoride corrosion starts at zero when the 
waste package is breached. After breach, the fraction failed is proportional to the volume of 
water that has entered the package, reaching one when 2424 m3 of water has entered the waste 
package. An alternative description is that the fraction of fuel rods that fail in a given year is the 
volume of water that enters the waste package during that year divided by 2424 m3. This volume 
(2424 m3) is equivalent to filling and emptying the waste package hundreds of times. Upper and 
lower limits are 10 times and 1/10 the best estimate rate to represent the uncertainties in this 
model and a log uniform distribution is selected between the maximum and minimum values. 
This analysis makes the rod failure fraction linearly dependent on the water ingression rate (% 
failed = 0.0413 * m3 water in WP). The water ingression into the WP increases with time as 
additional patches on the WP fail or open. Rod failure rate also depends on the location of the 
WP group because of different drip rates in different repository regions. Figure 9 is an example; 
with 50 liters/year of J13 water (2.2 ppm fluorides) entering the WP, 20% of the rods would fail 
by fluoride corrosion in 10,000 years. 
6.4 OTHER FAILURE MECHANISMS 
6.4.1 Mechanical Damage 
Seismic analysis (CRWMS M&O 1999d) shows that most of the rods in the WPs would fail 
from a very severe earthquake (a once per million years event) but no rods would fail for less 
severe and moderate frequency seismic events. This is consistent with studies (Witte et al. 1989, 
p. 194) of rod damage during transportation accidents that concluded that 63 g accelerations are 
needed to fail the rods in the shipping container (or WP). This also indicates that rock drops 
onto an intact WP will not cause rod failure. Therefore, the seismic failures have been included 
in the analysis as a disruptive event. 
The analysis of seismic events is included in the TSPA-SR. Based on the analysis (CRWMS 
M&O 1999d), seismic events with a frequency of 1.1x10-6 events/year would break most of the

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 28 April 2000 
fuel. Such events are sampled, and, when such an event occurs, all cladding is failed and to be 
available for unzipping. 
CRWMS M&O 1999d (Section 6.2) also considered the effect of a rubble bed consisting of 
rocks from a drift collapse on bare fuel rods (no WP or possible drip shield protection). The 
analysis showed that the bare fuel assemblies would fail under the static loading of the rocks. 
This effect was not included in the cladding degradation abstraction because it does not occur 
until after the WP no longer affords any protection. The first patches (about 100 cm by 100 cm) 
penetrate the WP in 50,000 to 60,000 years, and a significant number of patches (about 100 
patches) are open in about 350,000 years. With the potential for rubble bed damage not occuring 
until well after the 10,000 years considered for the TSPA-SR, rubble bed damage to the cladding 
was neglected. 
6.4.2 DHC and FEP Issues 
Delayed hydride cracking (DHC) of existing cracks is analyzed (CRWMS M&O 2000a, Section 
6.10.2) using the distribution of stresses shown in Figure 1. Stress intensity factors are 
calculated to have a mean of 0.47 MPa-m0.5 (range 0.002 to 2.7 MPa-m0.5), which is below the 
threshold stress intensity factors that are in the range of 5 to 12 MPa-m0.5. Therefore, crack 
propagation by DHC is not expected. These stress intensities are also below those needed to 
produce embrittlement failures (KI < KIC). Failure of the cladding by hydride reorientation is 
unlikely and has not been included in the abstraction for the TSPA-SR analysis. Stresses and 
temperatures are too low for reorientation to occur. Even if the material did reorient, it will 
maintain sufficient strength such that failure would not be expected. 
Various AMRs have ruled out many cladding failure modes. CRWMS M&O 2000b outlines the 
Features, Events, and Processes (FEPs) that have been excluded from this analysis. CRWMS 
M&O 2000c describes the various corrosion mechanisms that are not expected to fail the 
cladding, considering the expected in-package chemistry predicted in CRWMS M&O 2000i. 
CRWMS M&O 2000l describes the various hydride mechanisms that are not expected to fail the 
cladding. This Summary and Abstraction AMR only addresses the cladding failure mechanisms 
that are expected to contribute to radionuclide release from CSNF. 
6.5 FAST RELEASE OF RADIONUCLIDES 
The release of radionuclides from the fuel rod occurs in three stages, (1) release of true gap 
inventory, (2) fast release from initial UO2/water reaction and (3) wet unzipping (tearing of the 
cladding). Sections 6.1 through 6.4 discuss the potential of failing (perforating) the cladding. 
This section addresses the release of radionuclides through the initial cladding failure. 
Section 6.6 analyzes the tearing open (unzipping) of the cladding and the release of radionuclides 
from the bulk fuel matrix. 
6.5.1 Fast Release Abstraction 
The true gap inventory (iodine, cesium, and noble gasses) is released in proportion to the fission 
gas release fractions (CRWMS M&O 2000d, p. 82). The release of iodine is the same fraction as 
the noble fission gas release fraction of 4.2% (CRWMS M&O 2000a, Table 12). Cesium gap 
inventory is 1/3 of the fission gas release fraction or 1.4%.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 29 April 2000 
The fast release refers to the radionuclides that are released with the initial fuel dissolution 
before the cladding starts to unzip. Wilson (1985, 1987, 1990) reports releases of various 
radionuclides from fuel rod samples. The samples included intact and defected fuel rod sections 
and bare fuel. Wilson exposed the samples to water and measured the amounts of various 
radionuclides that were released during the exposure period. The first measurements were made 
in about 200 days. The samples were again exposed, and the measurements were repeated after 
an additional exposure of similar length. The fast release from the uranium pellet through slits 
and holes in the cladding is estimated by calculating the release rate from Wilsons eight 
experiments and extrapolating this release rate until the larger gaps are closed by secondary 
phases (approximately 50 years). Figure 11 presents a uniform distribution of fast release 
fraction between 0 and 0.4% (mean and median value = 0.2%) which is used in the TSPA-SR 
abstraction. This linear fit is reasonably bounding, over-predicting the fast release fraction for 
the lower Cumulative Distribution Function (CDF, equivalent to 1-CCDF) samplings. The 
cesium and iodine true gap inventories are added to this fuel matrix fast release fraction. 
6.5.2 Fast Release Analysis 
The purpose of this section is to estimate the fast release inventory. The current conceptual 
analysis of release from a breached fuel rod considers that the radionuclide inventory may be 
divided into three parts: a true gap inventory, a fast release inventory, and a delayed release 
inventory. 
The true gap inventory is the portion of the few elements (e.g., Cs, I and noble gasses) that 
segregate to the gap during reactor operation. In the TSPA-SR treatment, this inventory is 
immediately released upon cladding and WP failure. 
The fast release inventory results from the process of plugging the cracks and gaps in the fuel 
rod. A substantial length of the fuel rod may be wetted, and uranium dioxide in the wetted 
length will be converted to a hydroxide (e.g., metaschoepite). As a result, the volume of solid 
material increases. When the cracks and gaps are fully plugged with reaction products, the 
conversion process slows to insignificant rates. However, alteration of uranium dioxide will 
make other radionuclides available for release. In the TSPA-SR treatment, the fast release 
inventory should be made available for release during the first time step. In total system 
performance assessment, the true gap and fast release inventories are made available for release 
during the first time step. 
The delayed release inventory is the remainder of the inventory in the fuel rod. This is released 
during cladding unzipping. 
CRWMS M&O 2000e (Section 7) predicts a fast release inventory of 2.8% to 5.5%. This value 
is reasonably bounding because it is based on complete plugging occurring over the entire active 
length of the fuel rod and that all radionuclides other than uranium are released. A less 
conservative treatment can be developed on the basis of data for 99Tc release as measured by 
Wilson (1985, 1987, 1990). Wilsons experiments included intact and defected fuel rod sections 
and bare fuel. Only the results for defected fuel rods were considered. Results for bare fuel are 
not relevant because it has no protection by cladding; results for intact fuel rods are not relevant

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 30 April 2000 
because the fuel is not exposed. In Wilsons experiments, the cladding of the defected samples 
had either one slit or two holes. 
To estimate the fast release fraction, Wilsons results were analyzed by an approach that is 
shown schematically in Figure 10. The period from time 0 to time t1 corresponds to Wilsons 
first exposure cycle. During this period, 99Tc is released at rate R1, which is the measured 
release rate for this cycle. The period from time t1 to time t2 corresponds to the second exposure 
cycle, and during this period 99Tc is released at rate R2, which is the measured release rate for the 
second cycle. The rate of release during the second cycle of testing was often smaller than that 
during the first cycle. At later times, the release rate decreases linearly from a rate of R2 at time 
t2 to a rate of zero at time tpl, which is the time for complete plugging of the cracks by 
metaschoepite. Narrow cracks will plug quickly because they can be filled with a small amount 
of metaschoepite, but wide cracks will take longer to plug because they require a larger amount 
of metaschoepite. The gradual decrease in release rate thus corresponds to progressive plugging 
of cracks of different widths. In all cases, the release rate is expressed as a fraction of the total 
inventory, so it has the units of reciprocal time (e.g, yr-1) and is not expressed as an amount of 
material per unit time (e.g., mol/yr). The analysis described above was repeated for each of 
Wilsons fuel rod samples, and the fast release fraction F was calculated as 
] 2 / ) ( [ ) ( 2 2 1 2 2 1 1 t t R t t R t R F pl - + - + = Eq. 6.5-1 
where the variables are as defined above. A cumulative distribution function is determined in the 
following paragraphs based on the values of F from the eight (8) tests by Wilson (1985, 1987, 
1990). 
The fast release fractions were calculated on the basis of measurements of 99Tc. Of the releases 
tabulated by Wilson (1985, Tables 7 through 13, total measured release divided by 10-5 
inventory for slit defect and holes defect), 99Tc has the second-largest release as a fraction of 
inventory. The only radionuclide with a larger release fraction is 137Cs. However, 137Cs would 
be expected to have a substantial true gap inventory, so its measured releases would be larger 
than the fast release inventory. 
Of the variables used in Equation 6.5-1, all but tpl can be obtained from the data tabulated in 
Table 6. The value of tpl may be estimated from photomicrographs of the fuel. Wilson (1990, 
p. 2.7, Figure 2.3) provided a photomicrograph of a cross section of one of his fuel samples. The 
widest crack of interest is the middle section of the nearly diametral crack. A few cracks appear 
even wider. However, their irregular shapes and variable widths indicate that these are not 
unusually wide cracks but rather cracks that appear wide because there is a small dihedral angle 
between the crack and the plane of the cross section. The middle section of the nearly diametral 
crack in the photomicrograph (Wilson 1990, p. 2.7, Figure 2.3) has a width of about 0.8 mm in 
the print provided in the document. Since the magnification in the print is 14.5, the actual crack 
width w is about w = 55 mm. 
CRWMS M&O (2000d, Equation 16) gives the following equation for the forward reaction rate 
of spent fuel in alkaline water:

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 31 April 2000 
2 3 10 32 . 0 12 . 0 
1085 
69 . 4 log pO pCO 
T 
Dr  -  - - = Eq. 6.5-2 
where Dr is the reaction rate in mg/m2 day, pCO3 is the negative of the common logarithm of the 
total carbonate concentration in mol/L, and pO2 is the negative of the common logarithm of the 
oxygen partial pressure. 
For exposure of spent fuel in a repository, it is reasonable to approximate the environment by 
J-13 water in equilibrium with air at 25 C. This is the same water chemistry as is used in 
calculating the unzipping speed. The bicarbonate concentration of J-13 water is 128.9 mg/L 
(Harrar et al. 1990, Table 4.1). Using the molar masses of H (1.00794 g/mol), C (12.011 g/mol) 
and O (15.9994 g/mol) (Lide 1995, inside front cover), one finds that the concentration of 
carbonate is 0.1289 g/L / (1.00794 g/mol + 12.011 g/mol + 315.9994 g/mol) = 2.1110-3 mol/L, 
and thus pCO3 = -log10(2.1110-3) = 2.68. In a standard atmosphere, the fraction of O2 is 0.2095 
(Weast and Astle 1980, p. F-208), so pO2 = -log10(0.2095) = 0.679. By applying 
Equation 6.5-2, one obtains Dr = 3.26 mg/m2 day. The density r of UO2 is r = 10970 kg/m3 
(Lide 1995, p. 4-94). By dividing Dr by r, one finds that Dr / r = 0.297 nm/day. 
Wet oxidation of the fuel produces metaschoepite. The molar volume of metaschoepite 
(UO32H2O) is vms = 64.5 cm3/mol; that of UO2 is vUO2 = 24.6 cm3/mol (CRWMS M&O 2000e, 
Table 4). Therefore, oxidation of a layer of UO2 yields a layer of metaschoepite that is (vms / 
vUO2) times as thick as the original layer. Since the original UO2 is consumed, the surface moves 
by ((vms / vUO2) - 1) times the thickness of the original layer. 
The reaction rates predicted by Equation 6.5-2 are for a microscopically smooth surface. In 
contrast, the surfaces of cracks will be rough, so the exposed surface area will be larger, and the 
oxidation rate will be higher. The ratio R of the actual surface area to the apparent surface area is 
estimated as R = 3 (CRWMS M&O 2000d, p. 82). 
By combining the results above, one obtains the plugging time tpl as 
RDr v v 
w 
t 
UO ms 
pl ) 1 / ( 2 2 - 
= r 
Eq. 6.5-3 
The factor of 2 is present because oxidation occurs on both sides of the crack. Using the values 
above, one finds that tpl = 1.9104 day (about 50 years). 
The data from Table 6 are put into the notation of this section as follows. The values for first 
cycle 99Tc release (10-5 of sample inventory) are R1t1. The values for second cycle 99Tc release 
(10-5 of sample inventory) are R2(t2 - t1). The first cycle time (days) and second cycle time 
(days) are t1 and t2 - t1, respectively. From these values, R2 and t2 can be calculated. Using the 
data in Table 6, the results in Table 7 are obtained. 
Using the approach described above, the fast release fraction was calculated for each of Wilsons 
eight samples. The results were plotted as an experimental Cumulative Distribution Function 
(CDF) in Figure 11.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 32 April 2000 
The CDF for the fast release fraction is generally expected to overestimate the actual fast release 
fraction for two reasons. First, Wilsons tests are for short samples rather than full-length fuel 
rods. In full-length rods, transport limitations may reduce the fraction released. Transport 
limitations are discussed in more detail below. Second, some preferential release of 99Tc is 
expected. Wilson (1985, p. 36) states, It is likely that 99Tc partitions to the grain boundaries in 
the hotter central portions of the fuel. As grain boundary attack (which is clearly visible in 
Figure 3 of Wilson 1985) progresses in these regions, enhanced 99Tc release would then be 
observed. For these reasons, it is expected that the recommended CDF gives a reasonably 
bounding estimate of the fast release fraction. 
In determining the fast release fraction, the CDF is determined from experiments on short rod 
sections. For total system performance assessment, the same CDF applies to full-length rods. 
This treatment is clearly reasonably bounding, but it may be thought to be overly conservative. 
To determine whether it is overly conservative, it is helpful to compare the fuel rod length to the 
characteristic diffusion distance, 2(Dt)1/2 where D is the diffusion coefficient and t is the time 
allowed for diffusion. For strong electrolytes dissolved in water at 25 C, diffusion coefficients 
are typically on the order of 10-9 m2/s (Weast and Astle 1980, p. F-62). The diffusion time may 
be approximated by the plugging time tpl = 1.9104 day = 1.65109 s. The diffusion distance is 
then 2(Dt)1/2 = 2.6 m. Since this distance is comparable to the active length of a fuel rod, it is 
reasonable to expect that, if the entire length of the fuel rod is saturated, the entire length will 
contribute to radionuclide releases. Additional conservatism will result if only part of the rod is 
saturated. However, information on rod saturation is not available, so credit cannot be taken for 
partial saturation.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 33 April 2000 
Table 6. Inputs on 99Tc Releases 
First Cycle 99Tc Release Second Cycle 99Tc Release 
Sample Source (nCi) (10- 5 of Inv.) (nCi) (10- 5 of Inv.) Locationd 
First Cycle 
Time (days) 
Second Cycle 
Time (days) Locationd 
H-6-12 Wilson (1985) 28.2+5.4b 12.133.6/50.8c 15.8+1.4b 12.117.2/50.8c Table 12 252 128 Table 3 
J-8-24 Wilson (1985) 4.5+1.4b 6.75.9/27.7c 18.0+3.8b 6.721.8/27.7c Table 12 244 128 Table 3 
C5C-E Wilson (1987) 25 2.8 18.5 2.1 Table 13 223 202 Table A.3 
I9-19 Wilson (1987) 73 15.3 32 6.6 Table 13 181 195 Table A.7 
C5C-C Wilson (1987) -- 0.5a -- 0.5a Table 13 223 202 Table A.4 
I9-12 Wilson (1987) -- 0.5a -- 0.5a Table 13 181 195 Table A.8 
C5B-D Wilson (1990) 12.7 1.4 -- 0.5a Table 3.8 174 181 Table A.5 
C5B-B Wilson (1990) 18.9 2.2 -- 0.5a Table 3.8 174 181 Table A.6 
Sample Defect Type Locationd 
H-6-12 Slit Table 3 
J-8-24 Holes Table 3 
C5C-E Slit Table 1 
I9-19 Slit Table 1 
C5C-C Holes Table 1 
I9-12 Holes Table 1 
C5B-D Slit Table 2.1 
C5B-B Holes Table 2.1 
NOTES: Inv. = Sample inventory. 
-- = Not reported. 
a Release was below detection limit. The value used here (510-6) is half of the detection limit (10-5) (Wilson (1985, p. 35). 
b Total was not reported. 
c Expression is (release for both cycles divided by 10-5 of inventory)(release for cycle 1 in nCi)/(release for both cycles in nCi) 
d. Location refers to the Table in the Reference Source identified in the second column of this Table 6. 
DTN: MO0003SPATCR30.039, MO0003SPATCR22.038, MO0003SPATCR70.040.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 34 April 2000 
Table 7. Fast Release Fractions for Defected Samples 
Sample Fast Release Fraction 
H-6-12 0.00311 
J-8-24 0.00392 
C5C-E 0.00102 
I9-19 0.00338 
C5C-C 0.00024 
I9-12 0.00025 
C5B-D 0.00028 
C5B-B 0.00029 
DTN: MO00004SPACLD07.043 
6.6 CLADDING UNZIPPING AND FUEL DISSOLUTION 
Under wet conditions, the fuel matrix reacts with moisture at the intrinsic fuel matrix dissolution 
rate and precipitates locally as metaschoepite. This secondary phase isolates most of the fuel 
from the moisture but the fuel in the split cladding region continues to react with moisture, thus 
increasing in volume and forcing the split further along the cladding. Such alteration results in 
significant volume expansion, and the cladding breach will eventually propagate from its original 
location to the ends of the fueled length. Propagation of a cladding breach is termed unzipping 
which is used interchangeably with splitting. 
As discussed in CRWMS M&O 2000e (Section 6.8), the reaction front is cone shaped and 
propagates along the rod at a rate that is related to the intrinsic fuel matrix dissolution rate (see 
Section 6.6.1 of this AMR). However, since fuel rods are long and thin, the conical reaction 
front can be approximated by a planar front that propagates at some multiple of the intrinsic fuel 
matrix dissolution rate. 
To determine the inventory of radionuclides that is available for release from the entire 
repository, it is necessary to have a means for predicting the fraction of breached waste 
packages, the fraction of fuel rods with cladding breaches, and the speed of propagation of a 
cladding split. This section provides a mathematical framework for describing these processes in 
a way that is computationally efficient. The approach is intended for use in total system 
performance assessments. 
The various subsections have different emphases. Section 6.6.1 summarizes the abstraction for 
fuel rod unzipping. That abstraction uses the intrinsic dissolution rate, so Section 6.6.2 restates 
the equations for dissolution rate that were developed in CRWMS M&O 2000d. The general 
formalism for unzipping described in Section 6.6.3 is intentionally abstract and general. It is 
applicable to essentially any combination of waste package and waste form analysis. In 
Section 6.6.4, the treatment is made more specific. It is applied to a particula r analysis of fuel 
rod unzipping, and simplifications to the general formalism are discussed. In Section 6.6.5, the 
specific treatment of Section 6.6.4 is summarized for many waste packages. Finally, in

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 35 April 2000 
Section 6.6.6, the results of Section 6.6.5 are simplified for a system with only one waste 
package. This form is useful in implementing a performance assessment. 
6.6.1 Wet Unzipping Abstraction 
Fuel rods with perforated cladding are expected to remain intact until the WP breaches and 
permits air and moisture to enter. While the humidity is low, dry unzipping could occur. Since 
the WP is expected to remain intact for at least 200 years, the fuel temperatures will be too low 
for dry unzipping (fuel conversion to U3O8) to occur. Wet unzipping of failed rods is analyzed to 
start when the WP breaches. Rods that fail after WP breach immediately start to unzip. The fuel 
matrix is dissolved at the intrinsic dissolution rate that is evaluated for the current temperature 
and in-package chemistry. The dissolved UO2 precipitates locally as metaschoepite. This 
secondary phase isolates most of the fuel from the moisture and increases in volume compared to 
UO2. In time, the cladding in the reaction region is torn as the reaction continues. This reaction 
region is cone shaped and the cone angle is based on experimental observations in dry unzipping 
and theoretical analyses. 
The unzipping propagates along the rod at a rate that is proportional to the intrinsic dissolution 
rate. The ratio of unzipping speed to intrinsic dissolution rate is given by a triangular 
distribution. The distribution has a minimum of 1, a mode of 40, and a maximum of 240 
(CRWMS M&O 2000e, Section 7). It is assumed that the perforation is at the middle of the 
fueled length of the rod. This maximizes the release rate. The unzipping time or velocity is also 
a function of local chemistry and pH. In TSPA-SR, the unzipping velocity and fraction of fuel 
exposed are evaluated at each time step because of the evolution of in-package chemistry and 
temperature. Section 6.6.6 gives equations for determining the rate at which fuel is exposed as a 
result of unzipping. These equations take into account the effect of having fuel rods fail at 
different times. 
6.6.2 Intrinsic Dissolution Abstraction 
The intrinsic dissolution rate is used in the unzipping calculations to determine the reaction rate 
velocity. The intrinsic dissolution equation is to be applied at each TSPA-SR simulation time 
step and is to be based on the local chemical conditions. At some times the pH could be basic 
and at other times it could be acidic (CRWMS M&O 2000i). The abstraction is therefore 
divided into regions of pH greater than and less than a neutral pH (pH = 7). CRWMS M&O 
2000d (p. 82) develops the intrinsic dissolution equations that are recommended for TSPA-SR. 
For basic conditions (pH > 7), 
Log10 Dr = a0 + a1 / Tk + a2  PCO3 + a3  PO2 (Eq. 6.6-1) 
where a0 = 4.69, a1 = -1085, a2 = -0.12, and a3 = -0.32. 
For acid conditions (pH < 7), 
Log10 Dr = a0 + a1 / Tk + a3  PO2 + a4  pH (Eq. 6.6-2) 
where a0 = 7.13, a1 = -1085, a3 = -0.32, and a4 = -0.41.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 36 April 2000 
Equations 6.6-1 and 6.6-2 may be combined in the following form: 
Log10(Dr) = a0 + a1/Tk + a2  PCO3 + a3  PO2 + a4  pH (Eq. 6.6-3) 
where Tk = absolute temperature (K) 
PCO3 = -Log10 (molar concentration of CO3--) 
PO2 = -Log10 (partial pressure in atmospheres of O2) 
Dr = intrinsic dissolution rate = mg /m2d. 
The coefficients for these equations are summarized in Table 8. This function is used in the 
TSPA-SR. The uncertainty in the intrinsic dissolution rate is applied to the coefficient a0. The 
value of a0 is uniformly distributed by + or  1.0. This is equivalent to a log uniform distribution 
of the intrinsic dissolution rate by a multiple of ten (10). CRWMS M&O 2000d recommended 
an uncertainty of 1.5 orders of magnitude. An inspection of the test results shown in CRWMS 
M&O 2000d (Table 1) suggests a much smaller range. Three tests under identical conditions 
(Runs 1,2 3) varied by only 18% from the mean. There is also an independent uncertainty of a 
factor of six (6) associated with the unzipping velocity in the use of the intrinsic dissolution rate. 
Figure 12 (CRWMS M&O 2000d, p. 55) shows the dependency of the intrinsic dissolution on 
temperature and pH for a constant O2 and CO3
-- content. In the TSPA-SR, each of the variables 
could vary with time. 
Table 8. Intrinsic Dissolution Equation and Terms 
a0 a1 a2 a3 a4 
pH>7 4.69 -1085 -0.12 -0.32 0 
pH<7 7.13 -1085 0 -0.32 -0.41 
CRWMS M&O 2000d, p. 55 
Both the intrinsic dissolution tests and the equations given above are based on tests for individual 
grains of UO2. The unzipping analyzed in TSPA-SR occurs on the pellet surface and the rate in 
mg/m2 d is converted to a reaction rate velocity of cm/yr. A grain boundary penetration factor of 
six (6) from CRWMS M&O 2000e (Section 7) is applied to the intrinsic dissolution rate to 
account for water penetration into grain boundaries. Figure 13 is an example of unzipping times 
as a function of temperature for a constant chemistry of approximate J-13 water, and Figure 14 
shows the dependency on pH at a fixed temperature of 35 C. In the TSPA-SR, both in-package 
chemistry and temperature are changing with time and the unzipping velocity is evaluated within 
the TSPA-SR analysis itself. 
6.6.3 General Formalism for Wet Unzipping 
Each fuel rod can be classified as either intact, unzipping, or exhausted. Intact is used broadly 
to denote those rods whose fuel is protected from alteration, thus the intact fraction includes all 
rods in intact waste packages and all rods with intact cladding in breached waste packages. 
Unzipping denotes rods that are in the process of alteration, that is those rods that are in 
breached waste packages and have breached cladding but are not yet fully unzipped.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 37 April 2000 
Exhausted refers to those rods that were breached so long ago that they are fully unzipped, that 
is the split has propagated all the way to the ends of the fueled region of the rod. 
For convenience, the time of emplacement will be taken as time = zero and time since 
emplacement will simply be called time. The waste package and waste form analysis must 
provide the following three functions. Let W(t) be the fraction of waste packages breached at 
some time t. For a particular waste package that breached at time tw, let fb(t, tw) be the fraction of 
fuel rods that are breached at time t. Breached fuel rods are those that are either unzipping or 
exhausted, so fb(t, tw) = 0 for t < tw. Let v(t) be the unzipping speed for a breached fuel rod in a 
breached waste package at time t. The method described here applies only for t  0. 
To describe the instantaneous state of unzipping for the entire group of waste packages, define 
fi(t), fu(t), and fe(t) which are the fractions of the fuel rods that are intact, unzipping, and 
exhausted, respectively, at time t. These functions are not applied to individual waste packages; 
rather, they describe all the rods in the entire group of waste packages. Note that the unzipping 
fraction includes rods with a variety of split lengths, from very short to nearly the entire fueled 
length. No distinction among these rods is made on the basis of split length. None of the 
functions fi(t), fu(t), and fe(t) is specified in advance; they are all derived from W(t), fb(t, tw), and 
v(t). Note, however, that fi(t) + fu(t) + fe(t) = 1 for any time t, so only two of fi(t), fu(t), and fe(t) 
are independent. 
The first of these functions to be derived is fi(t). Initially: 
) 0 , 0 ( ) 0 ( 1 ) 0 ( b i f W f - = (Eq. 6.6-4) 
Equation 6.6-4 follows because, out of the entire set of rods, the fraction that is breached rods in 
breached waste packages at the time of emplacement is W(0)fb(0, 0); all other rods are intact in 
the sense defined above. At later times, there may be additional breached waste packages and 
breached rods. The fraction that remains intact at time t will be: 
 - - = t 
b b i d t f 
d 
dW 
t f W t f 
0 
) , ( 
) ( 
) 0 , ( ) 0 ( 1 ) ( t t 
t
t 
(Eq. 6.6-5) 
Equation 6.6-5 is justified as follows. The first term (1) corresponds to the entire set of rods. 
The second term corresponds to those rods that are in defective waste packages (i.e., the WPs 
have failed at the time of emplacement) and the rods either are breached at emplacement or 
breach after emplacement but before time t. The third term corresponds to rods in the waste 
packages that breach after emplacement. During a given infinitesimal time interval from t to t + 
dt, the fraction of waste packages that breach is (dW(t) / dt) dt. At some later time t, the 
fraction of breached rods in these packages is fb(t, t). The integral takes into account all waste 
package failure times up to time t. 
The amount of fuel altered could be determined by solving a partial differential equation for the 
distribution of split lengths as a function of time, but this approach is computationally costly. A 
more efficient approach is derived here. Figure 15 is a schematic plot of the alteration rate as a 
function of time for two individual fuel rods in a breached waste package. For the time scales of 
interest in performance assessment, the radionuclide inventory can be divided into two parts: the

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 38 April 2000 
gap inventory and the fuel matrix inventory. The alteration of both parts is shown schematically 
in Figure 15. The cladding of rod A breaches at time t0A. There is a pulse of alteration at this 
time; the pulse corresponds to the gap inventory. The fuel matrix inventory takes much longer to 
alter; fuel matrix alteration begins at time t0A and continues until time t1A, when the fuel rod is 
fully unzipped (exhausted) and the fuel matrix is fully altered. The fuel matrix alteration rate is 
time-dependent because the conditions (e.g., temperature and water chemistry) inside the waste 
package are time-dependent. The alteration of the fuel in rod B is similar, but the cladding of rod 
B breaches later, at time t0B. Since the fuel matrix alteration rate is decreasing with increasing 
time, alteration of the entire inventory in rod B takes longer, and the rod is not exhausted until 
time t1B. The alteration rate for an entire waste package will be a superposition of the alteration 
rates for each rod. 
Let Fg(t) be the fraction of the total gap inventory (for the entire group of waste packages) that 
has been altered at time t. The gap inventory is altered immediately if the waste package and 
fuel cladding are both breached, and thus the altered fraction can be written as follows 
) ( 1 ) ( t f t F i g - = (Eq. 6.6-6) 
The following approach can be used to determine the fraction of the fuel matrix inventory that 
has been altered. Before significant numbers of waste packages begin to breach, the heat output 
of the packages will have become fairly small, so the temperatures and in-package chemical 
environment will be fairly uniform. Therefore, it is a reasonable approximation to use a single 
unzipping speed for all the fuel rods in the entire group of WPs. In light of that approximation, 
define the function h(t) as: 
 = 
t 
d v t h 
0 
) ( ) ( t t (Eq. 6.6-7) 
where v(t) is the speed of unzipping at time t. Note that h(0) = 0 because the interval of 
integration will have zero length. The function h is referred to as the propagation distance. As 
an alternative to Equation 6.6-7, changes in h(t) may be expressed in differential form: 
) ( ) ( t v t h 
dt 
d = (Eq. 6.6-8) 
For simplicity, the initial cladding damage always occurs at the center of the fueled region. The 
split will then propagate to both ends of the fueled length. This gives the fastest alteration rate: 
If the split starts at the center, the rod is exhausted when each end of the split has propagated by 
a distance of L / 2, where L is the length of the fueled region. In contrast, if the split starts 
somewhere besides the center, the split must propagate farther in one direction, and thus for a 
longer time, before the rod is exhausted. 
The time for unzipping of fuel rods A and B is shown schematically in Figure 16, where the 
propagation distance h is plotted as a function of time. For the purposes of this illustration, it is 
assumed that rod A is failed at the time of emplacement and is in a waste package that is 
breached at emplacement. (This will presumably be an extremely rare occurrence.) In this case 
t0A = 0. As can be seen from Figure 16, rod A starts unzipping at time t0A, when h = 0, and is

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 39 April 2000 
exhausted at time t1A, when h = L / 2. This is readily understandable in light of the definition of 
h(t) in Equation 6.6-7. The situation for rod B is slightly more complicated. The fuel in rod B is 
not exposed for alteration until time t0B; this is the time when both the waste package and 
cladding are breached. At this time, rod A is already partially unzipped. As is shown in Figure 
16 for rod A, h(t0B) = c. Both rods then unzip at the same rate, since there is a single unzipping 
speed for all rods. At time t, the distance that the split has propagated from the center of rod A is 
h(t) (for t0A  t  t1A), but the distance that the split has propagated from the center of rod B is 
h(t) - c (for t0B  t  t1B). Thus, rod B is exhausted when h reaches L / 2 + c. 
The discussion above also sheds additional light on the nature of h. In an actual rod, splitting 
initiates at some time, the split propagates until it reaches the ends of the fueled region, and 
splitting stops. In contrast, h(t) increases without limit. Thus, h(t) is the propagation distance for 
an infinitely long rod that starts splitting at the time of emplacement. 
The invariance of the unzipping speed has an important implication: It is not necessary to track 
the propagation of splits in individual rods or even the state of individual waste packages. The 
fraction of matrix alteration can be deduced from fi(t) and v(t) alone, as is shown below. 
The first step in determining the fraction of matrix alteration is to define a function h-1, which is 
the inverse function of h, that is: 
t t h h = - )) ( ( 1 for t  0 (Eq. 6.6-9) 
The physical meaning of h-1 is straightforward. Given a time t  0, h(t) is the distance that the 
split has propagated at that time. Given a propagation distance x  0, h-1(x) is the time at which 
that propagation distance is reached. 
Consider a time t that is sufficiently large that some rods are exhausted. The exhausted rods 
became exhausted by breaching at some earlier time and having the split propagate by a distance 
of L / 2 to the ends of the fueled region. At the time t in question, the propagation distance is 
h(t). The rods that are exhausted at time t are therefore exactly those that were breached (either 
exhausted or unzipping at the earlier time) when the propagation distance was h(t) - L / 2. But a 
propagation distance of h(t) - L / 2 corresponds to a time of h-1(h(t) - L / 2). Therefore: 
) 2 / ( for 0 
) 2 / ( for )) 2 / ) ( ( ( 1 ) ( 
1 
1 1 
L h t 
L h t L t h h f t f i e 
- 
- - 
< = 
 - - = 
(Eq. 6.6-10) 
because 1 - fi is the fraction of breached rods. For times earlier than h-1(L / 2), there are no 
exhausted rods because there has not been enough time for any split to propagate by a distance of 
L / 2. 
Given the fraction of intact rods and the fraction of exhausted rods, the fraction of unzipping 
rods follows: 
) ( ) ( 1 ) ( t f t f t f e i u - - = (Eq. 6.6-11)

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 40 April 2000 
Let Fm(t) be the fraction of the total fuel matrix inventory that has been altered at time t. At the 
time of emplacement (t = 0), Fm(0) = 0. At later times, some of the fuel may be altered. Let n be 
the total number of fuel rods in all the waste packages and let A be the cross-sectional area of one 
fuel rod. The total volume of fuel is ALn. In each unzipping rod, the rate at which fuel is being 
altered is 2Av(t). But there are nfu(t) unzipping rods, so: 
) ( ) ( 
2 ) ( ) ( 2 ) ( 
t f t v 
L ALn 
t nf t Av 
dt 
t dF 
u 
u m = = (Eq. 6.6-12) 
Since Fm(0) = 0, integration of Equation 6.6-12 yields: 
 = t 
u m d f v 
L 
t F 
0 
) ( ) ( 
2 
) ( t t t (Eq. 6.6-13) 
6.6.4 Application to a Specific Analysis of Unzipping 
The general formalism presented in Equations 6.6-4 through 6.6-13 is quite general, but it is still 
computationally costly to implement. In particular, Equation 6.6-5 requires evaluation of an 
integral whenever a value of fi(t) is needed. To simplify the implementation, this section applies 
the general formalism to a particular analysis for unzipping. 
In place of the general function fb(t, tw) for the fraction of fuel rods that are breached, define a 
new function fb(t - tw) where t is the time since emplacement and tw is the time of waste package 
breach. This function can be used in the general formalism above by replacing Equations 6.6-4 
and 6.6-5 above with the following equations: 
) 0 ( ) 0 ( 1 ) 0 ( b i f W f - = (Eq. 6.6-14) 
 - - - = t 
b b i d t f 
d 
dW 
t f W t f 
0 
) ( 
) ( 
) ( ) 0 ( 1 ) ( t t 
t
t 
for t  0 (Eq. 6.6-15) 
Even with this simplification, Equation 6.6-15 includes a convolution integral, and a complete 
evaluation of the integral is necessary whenever fi(t) is needed. However, the form of fb that has 
been proposed for performance assessment is particularly simple: 
1 
0 
1 
0 
1 0 
1 
for 1 
1 
0 for 
0 for 0 ) ( 
a 
a 
z 
a 
a 
z z a a 
z z fb 
- > = 
- 
  + = 
< = 
(Eq. 6.6-16) 
As in the general formulation, fuel rods in an intact waste package are not considered to be 
breached, regardless of the condition of the cladding. In Equation 6.6-16, a0 and a1 are 
positive constants; a0 is the fraction of fuel rods that are breached when the waste package 
breaches. Rods that breach by short-term processes (such as creep rupture) may be included in

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 41 April 2000 
this set because these processes will be essentially complete before significant numbers of waste 
packages breach. The constant a1 gives the rate of change of the fraction of breached rods after 
the waste package is breached. This constant describes processes such as localized corrosion of 
the cladding. The fraction of breached rods cannot exceed 1. In general, the values of a0 and a1 
will reflect the abstraction of the cladding degradation analysis, and their values will vary from 
one realization to the next. Note that fb(z) is continuous at z = (1 - a0) / a1, but it is discontinuous 
at z = 0 because all the rods that were perforated earlier are suddenly considered as breached. 
However, fb(z) is generally not of interest for z < 0, so the discontinuity will not cause difficulty. 
The form of Equation 6.6-16 allows for further simplification of Equation 6.6-15, but it requires 
separate consideration of the different time intervals listed in Equation 6.6-16. For 0  t  (1 - 
a0) / a1: 
 
 
 
  
 
+ - = 
+ - - - = 
+ - + - - = 
+ + - - = 
- + - - = 
t 
b 
t 
b b 
t 
b 
t t 
b 
t 
b i 
d 
d 
dW 
a t W t f 
d 
d 
dW 
a W t W t f t f W 
d 
d 
dW 
a W t W t a a t f W 
d 
d 
dW 
a d 
d 
dW 
t a a t f W 
d t a a 
d 
dW 
t f W t f 
0 1 
0 1 
0 1 1 0 
0 0 1 1 0 
0 1 0 
) ( 
) ( ) ( 1 
) ( 
)] 0 ( ) ( )[ ( ) ( ) 0 ( 1 
) ( 
)] 0 ( ) ( )[ ( ) ( ) 0 ( 1 
) ( ) ( 
) ( ) ( ) 0 ( 1 
)] ( [ 
) ( 
) ( ) 0 ( 1 ) ( 
t t 
t
t 
t t 
t
t 
t t 
t
t 
t t 
t
t 
t 
t
t 
t t 
t
t 
(Eq. 6.6-17) 
Equation 6.6-17 can then be differentiated with respect to time: 
) ( 
) ( 
) ( 
) ( 
) ( ) ( 
) ( 
) ( 
) ( ) ( 
) ( 
) ( 
1 0 
1 1 1 0 
1 
t W a 
dt 
t dW 
a 
dt 
t dW 
t a t W a 
dt 
t dW 
t a 
dt 
t dW 
a 
t 
dt 
t dW 
a t W 
dt 
t df 
dt 
t dW 
t f 
dt
t df b 
b 
i 
- - = 
+ - - - = 
+ - - = 
(Eq. 6.6-18) 
Equation 6.6-18 applies for all t such that for 0  t  (1 - a0) / a1. 
For convenience, define: 
1 
0 1 
a 
a 
tc 
- = (Eq. 6.6-19) 
From Equations 6.6-15 and 6.6-16 it follows that, for t = 99Tc + tx, where tx > 0:

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 42 April 2000 
 
  
  
  
+ - + - - = 
+ + - - - - = 
- + - - - = 
- - - - - = 
t 
t x x 
t 
t 
t 
t x 
t 
t 
t 
t 
t b 
t 
b b i 
x 
x x 
x 
x 
x 
x 
d 
d 
dW 
a t W t W t a a t W 
d 
d 
dW 
a d 
d 
dW 
t a a W t W W 
d t a a 
d 
dW 
d 
d 
dW 
W 
d t f 
d 
dW 
d t f 
d 
dW 
t f W t f 
t t 
t
t 
t t 
t
t t 
t
t 
t t 
t
t t 
t
t 
t t 
t
t t t 
t
t 
) ( 
)] ( ) ( )[ ( ) ( 1 
) ( ) ( 
) ( )] 0 ( ) ( [ ) 0 ( 1 
)) ( ( 
) ( ) ( 
) 0 ( 1 
) ( 
) ( 
) ( 
) ( 
) ( ) 0 ( 1 ) ( 
1 1 0 
1 1 0 
1 0 0 
0 
(Eq. 6.6-20) 
In writing Equation 6.6-20, the interval of integration from Equation 6.6-15 has been divided in 
two. These intervals reflect the differing forms of fb in different regions. 
By differentiating Equation 6.6-20, one obtains: 
) ( ) ( 
) ( 
) ( ) ( 
) ( 
) 1 ( 
) ( 
) ( ) ( 
) ( ) ( 
) ( 
) ( 
) ( 
) ( 
) ( ) ( 
1 1 0 
1 1 1 1 0 0 
1 1 
1 1 1 0 1 0 
x 
x 
x 
x 
x 
x 
x 
x x i 
t W a t W a 
dt 
t dW 
a 
t W a t W a 
dt
t dW 
t a t a a 
dt 
t dW 
a 
dt
t dW 
t a 
dt 
t dW 
t a 
t W a t W a 
dt
t dW 
t a a 
dt 
t dW 
t a a 
dt
t dW 
dt
t df 
+ - - = 
+ - - - + + - = 
- + 
+ - + + + - - = 
(Eq. 6.6-21) 
In carrying out the differentiation, it is important to recognize that tx is a function of t; tx = t - tc. 
To obtain the last line of Equation 6.6-21, note that a1tx = a1(t - tc) = a1t - (1 - a0), so a0 + a1t - 1 - 
a1tx = 0. Equation 6.6-21 applies for t > tc. 
6.6.5 Unzipping Abstraction Summary for Many Waste Packages 
This section summarizes the results of Sections 6.6.3 and 6.6.4 in a concise form for guidance in 
implementing a performance assessment. First, the inputs and outputs are defined. Next, the 
initial state of degradation is expressed in terms of the inputs. Finally, the method for 
determining changes in state of degradation is given. 
Definition of Inputs and Outputs-The following inputs are required: 
t Time since emplacement. 
L Fueled length of rod.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 43 April 2000 
W(t) Fraction of waste packages breached at time t. W(t) will be provided by a 
analysis of waste package degradation and will vary from one realization to the 
next. 
v(t) Unzipping speed at time t. v(t) will be provided by a analysis of fuel rod 
unzipping and will vary from one realization to the next. 
fb(t - tw) Fraction of breached fuel rods at time t for a particular waste package that 
breached at time tw. The function is defined by the following equation: 
1 
0 
1 
0 
1 0 
1 
for 1 
1 
0 for 
0 for 0 ) ( 
a 
a 
z 
a 
a 
z z a a 
z z fb 
- > = 
- 
  + = 
< = 
(Eq. 6.6-22) 
The constant a0 is the fraction of fuel rods that are breached when the waste 
package breaches. Rods that breach by short-term processes (such as creep 
rupture) may be included in this set because these processes will be essentially 
complete before significant numbers of waste packages breach. The constant a1 
gives the rate of change of the fraction of breached rods after the waste package 
is breached. This constant describes processes such as localized corrosion of the 
cladding. The values of a0 and a1 will reflect the cladding degradation analysis, 
and their values will vary from one realization to the next. 
The following outputs are produced: 
h(t) Split propagation distance at time t. 
fi(t) Fraction of intact fuel rods at time t. fi(t) is an average over all the rods in the 
entire group of waste packages. Intact means rods whose fuel is protected 
from alteration, thus the intact fraction includes all rods in intact waste packages 
and all rods with intact cladding in breached waste packages. 
fu(t) Fraction of unzipping fuel rods at time t. fu(t) is an average over all the rods in 
the entire group of waste packages. No distinction among these rods is made on 
the basis of split length. 
fe(t) Fraction of exhausted (fully unzipped) fuel rods at time t. fe(t) is an average over 
all the rods in the entire group of waste packages. 
Fg(t) Fraction of fuel gap inventory altered at time t. 
Fm(t) Fraction of fuel matrix inventory altered at time t.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 44 April 2000 
Initial State of Degradation-The initial state of degradation (t = 0) is given by the following 
equations: 
0 ) 0 ( = h (Eq. 6.6-23) 
) 0 ( ) 0 ( 1 ) 0 ( b i f W f - = (Eq. 6.6-24) 
) 0 ( ) 0 ( ) 0 ( b u f W f = (Eq. 6.6-25) 
0 ) 0 ( = e f (Eq. 6.6-26) 
) 0 ( ) 0 ( ) 0 ( b g f W F = (Eq. 6.6-27) 
0 ) 0 ( = m F (Eq. 6.6-28) 
Changes in State of Degradation-Changes in the state of degradation are calculated by the 
following method. First, values of h and fi are calculated at a new value of time by integrating 
the following rates of change: 
) ( ) ( t v t h 
dt 
d = (Eq. 6.6-29) 
1 
0 
1 
0 
1 1 0 
1 
0 
1 0 
1 
for 
1 
) ( 
) ( 
1 
0 for ) ( 
) ( 
) ( 
a 
a 
t 
a
a 
t W a t W a 
dt 
t dW 
a 
a
a 
t t W a 
dt 
t dW 
a t f 
dt 
d 
i 
- >   
 
  
 - - + - - = 
-   - - = 
(Eq. 6.6-30) 
Values of h and fi must be accumulated so that previous values can be looked up later. After h 
and fi have been calculated for a new value of time, fe, fu, and Fg are calculated at that time: 
) 2 / ( for 0 
) 2 / ( for )) 2 / ) ( ( ( 1 ) ( 
1 
1 1 
L h t 
L h t L t h h f t f i e 
- 
- - 
< = 
 - - = 
(Eq. 6.6-31) 
) ( ) ( 1 ) ( t f t f t f e i u - - = (Eq. 6.6-32) 
) ( 1 ) ( t f t F i g - = (Eq. 6.6-33) 
In applying Equation 6.6-31, h-1 is the inverse function of h, that is: 
t t h h = - )) ( ( 1 for t  0 (Eq. 6.6-34) 
The last step is to calculate changes in Fm by integrating the following rate of change:

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 45 April 2000 
) ( ) ( 
2 ) ( 
t f t v 
L dt 
t dF 
u 
m = (Eq. 6.6-35) 
6.6.6 Unzipping Abstraction Summary for One Waste Package 
The definitions and equations in Section 6.6.5 apply with the following exceptions: 
Definition of Inputs and Outputs-The following input is changed: 
tw Time of waste package breach. 
W(t) This function is repla ced by a Heaviside step function at t = tw, i.e., F(t-tw). For 
simplicity, W(t) does not appear in the equations. Instead, its value (1 for times 
of interest) is used directly. 
Initial State of Degradation-Since fuel alteration does not occur in an intact waste package, the 
initial state of degradation is defined at t = tw rather than t = 0: 
0 ) ( = w t h (Eq. 6.6-36) 
) 0 ( 1 ) ( b w i f t f - = (Eq. 6.6-37) 
) 0 ( ) ( b w u f t f = (Eq. 6.6-38) 
0 ) ( = w e t f (Eq. 6.6-39) 
) 0 ( ) ( b w g f t F = (Eq. 6.6-40) 
0 ) ( = w m t F (Eq. 6.6-41) 
Changes in State of Degradation-Equations 6.6-30 and 6.6-34 are replaced by the following 
equations: 
) ( 1 ) ( w b i t t f t f - - = (Eq. 6.6-42) 
w t t t t h h  = - for )) ( ( 1 (Eq. 6.6-43) 
6.7 STAINLESS STEEL CLADDING 
As discussed in CRWMS M&O 2000a, about 1.1% of the commercial fuel was clad with 
Stainless Steel (SS) cladding material. This material was used in the early core designs and is no 
longer used. CRWMS M&O 2000k analyzed the expected inventory of SS clad fuel and 
concluded that 3.49% of the CSNF WPs would contain SS clad fuel and the average percent of 
fuel in these WPs with SS cladding is 29.9%. This analysis is based on loading the fuel at the

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 46 April 2000 
repository as it is expected to be delivered. In TSPA-SR, the SS cladding will be assumed to be 
perforated when the WP fails and to be immediately available for unzipping. It was also 
discussed in Section 6.1 of CRWMS M&O 2000a that failed rods from reconstituted assemblies 
were loaded into assembly size cans for pool storage and later disposal. These cans will be 
analyzed as SS clad and will be available for unzipping as soon as the WP fails (no credit for the 
can itself). This group was analyzed to be 10% of the SS assemblies or about 200 cans. This 
raised the fraction of stainless steel assemblies from 29.9% to 32.9%. This is summarized in 
Attachment I, Rows 109 and 110. 
7. CONCLUSIONS 
The purpose of this AMR is to develop the summary cladding degradation abstraction that is 
consistent with and used in the TSPA-SR. This summary is also submitted to the Waste Form 
PMR. The methodology developed for this AMR is consistent with ASTM Standard C1174-97 
(ASTM 1997). Earlier TSPAs analyzed the waste form as bare UO2 which was available for 
dissolution at the intrinsic dissolution rate. Water in the WP quickly became saturated with 
many of the radionuclides, limiting their release rate. In TSPA-VA cladding was analyzed as 
part of the waste form and limited the amount of fuel available at any time to dissolve. The 
major components of cladding failure were failure in reactor operation, mechanical failure from 
rocks and general corrosion of patches. The current analysis considers rod perforations from 
failure from reactor operation, creep and stress corrosion cracking (SCC) failures, localized 
corrosion from fluorides, and seismic events as mechanisms for perforating the cladding. All 
stainless steel cladding is assumed perforated. The second phase of the analysis is the release of 
radionuclides through the fast release and unzipping of the cladding from the reaction of water 
and UO2. The unzipping starts in the middle of the cladding and progress toward each end. This 
unzipping is driven by the intrinsic dissolution rate, which is dependent on the local temperature 
and chemistry. The following is a summary of the components used in TSPA-SR. Attachment I 
is a table of the numerical values. This information is also given in DTN: 
MO00004SPACLD07.043. 
Cladding Condition as Received 
The groups of WPs represented in the TSPA-SR have an initial percent of rods failed defined by: 
Lower limit = 0.0155 % 
Median = 0.0948 % 
Upper limit = 1.285 % 
This failure rate is based on historical data on reactor operation and includes an uncertainty 
factor of 4. It also includes failure from dry storage, handling, and transportation. This 
percentage of rods is available for radionuclide release through fast release and unzipping when 
the WP fails. This information is summarized in Attachment I, Rows 6 and 7.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 47 April 2000 
Creep Strain and SCC Failure 
Creep is analyzed using Murtys creep correlation. Also, a rod with a maximum stress exceeding 
180 MPa is assume to fail by Stress Corrosion Cracking (SCC). The resulting rod failure 
distribution is displayed in Figure 8 and given in Rows 40 through 55 of Attachment I. In 
TSPA-SR, for each realization, the peak WP surface temperature is established and a triangular 
distribution of the rod fraction is interpolated from the table given in Attachment I, Rows 40 
through 55. As an example, for the average WP, the peak WP surface temperature is 277oC. 
The center rod peak temperature is 308oC and the rod failure distribution is: 
Lower limit = 1.06 % 
Mean = 3.39 % 
Upper limit = 24.8 % 
Almost all of these failures were calculated to occur in the highest stressed rods during dry 
storage and shipping during which time temperatures of 350oC were calculated. When WP peak 
surface temperatures reach 300oC which is not expected in the repository, rod failures in the 
repository start to become more significant. 
The percent of failed rods from creep strain and SCC is summed with the failures from as 
received and is available to release radionuclides through fast release and unzipping when the 
WP fails. 
Localized Corrosion 
In the localized corrosion analysis, all the J13 water is concentrated on a 10 mm length of a 
single rod. All of the fluoride reacts with the 10 mm length of cladding of this single rod until 
the cladding fails from fluoride corrosion. Corrosion then starts on another rod. This analysis 
makes the rod failure fraction linearly dependent on the water ingression rate (% failed = 0.0413 
* m3 water in WP). The water ingression into the WP increases with time as additional patches 
on the WP fail or open. Rod failure rate also depends on the location of the WP group because 
of different drip rates in different repository regions. As an example, with 50 liters/year of J13 
water entering the WP (2.2 ppm fluoride), 20% of the rods would fail by fluoride corrosion in 
10,000 years. This information is summarized in Attachment I, Rows 57 through 59. 
Mechanical (Seismic ) Failures 
A very severe seismic event which occurs with a frequency of 1.1x10-6 events/year fails all of the 
cladding and all the rods are available for fast release and unzipping when the WP fails. This is 
included in the TSPA-SR base case and sampled every time step. This information is 
summarized in Attachment I, Rows 115 through 117. 
Stainless Steel Cladding 
The abstraction places the Stainless Steel (SS) cladding into WPs as it arrives at YMP. This 
results in 3.49% of the WPs contain SS cladding. These WPs contain 32.9% SS cladding which 
is failed and available for fast release and unzipping when the WP fails. In the TSPA-SR, WPs 
containing SS cladding are considered a different fuel type group with a high initial cladding

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 48 April 2000 
failure percent (32.9%). This information is summarized in Attachment I, Rows 109 through 
111. 
Fast Release Fraction 
When the WP fails or when the rod fails after WP failure, some of the radionuclides are 
immediately released. This includes the inventory of radionuclides in the gap between the fuel 
pellet and cladding, including that which is initially released from the early UO2 interaction with 
the water. The gap release of iodine equals the fission gas release of 4.2% and cesium is one 
third this value or 1.4%. The fast release fraction for other radionuclides including additional 
cesium and iodine is an average of 0.2% (range 0 to 0.4%, uniformly distributed) from the UO2 
dissolution. This information is summarized in Attachment I, Rows 62 through 65. 
Cladding Unzipping and Fuel Dissolution 
The initial cladding damage occurs at the center of the fuel rod and the split (unzipping) will then 
propagate to both ends of the active fuel length. The unzipping velocity is 40 (range 1 to 240, 
triangle distribution) times the intrinsic dissolution velocity. The intrinsic dissolution velocity is 
a function of the temperature and chemistry inside the WP. This relationship is given in Rows 
69 to 92 of Attachment I and is included in the TSPA-SR. An example calculation with a WP 
with J13 type water chemistry at 40oC, predicts 20% unzipping of failed rods in 10,000 years. 
In summary, the cladding degradation is analyzed in TSPA-SR in two stages: Cladding failure 
and cladding fast release and unzipping. The cladding degradation abstraction depends on the 
WP temperature, internal chemistry, WP surface perforation rate, and location (amount of water 
dripping on the WP). Uncertainties have been established for the important parameters and the 
results vary for each TSPA-SR realization. Typically, 2.54% of the cladding is failed from 
previous reactor operations and creep or SCC failures. Little additional creep or SCC failures 
occur under design repository conditions but creep failures could become important for a high 
temperature repository design. Localized corrosion depends on the water ingression rate which 
depends on the number of patches open or failed on the WP surface and the location of the WP 
in the repository. For a water ingression rate of 50 liters/year of J13 water into a WP, 20% of the 
rods in that WP fail from localized corrosion in 10,000 years. Most WPs are located in regions 
of little or no water ingression and do not undergo localized failure. When the WP fails, there is 
a fast release of radionuclides from the failed cladding gap. Then an average additional 20% is 
released from cladding unzipping in the next 10,000 years after WP failure from cladding 
unzipping, depending on local chemistry. With the ranges and uncertainties included in the 
abstraction, this analysis is valid for its intended use, analyzing cladding degradation in the 
TSPA-SR . This analysis and the TSPA-SR abstraction do not address the potential for 
damaging the cladding at the surface facilities at YMP. The cladding degradation analysis 
considers the WP peak surface temperature as an independent variable, and the results are usable 
for a repository design with or without backfill. The models are sensitive to thermal loading and 
would have to be modified if the WP thermal loading were significantly changed. 
Alternative Conceptual Analysis: The analysis by S. Cohen & Associates (1999, p. 7-1 to 7-4) is 
considered an alternative conceptual analysis and qualitatively agrees with this AMR. The 
earlier YMP TSPAs performed in 1993 and 1995 did not consider cladding, and as such are an

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 49 April 2000 
alternative conceptual analysis that is extremely conservative because it permits all fuel to 
dissolve at the intrinsic dissolution rate. A solubility limit (an indirect way of considering 
secondary phases) is used to limit the release rate of the fuel. European site TSPAs also did not 
consider cladding. The European sites were both saturated and reducing environments where the 
UO2 dissolution rates were so slow that cladding degradation was not considered. 
The following table contains a listing of specific technical issues addressed in Revision 2 of the 
NRC IRSR, for Container Life and Source Term (IRSR-CLST) (NRC 1999, pp. 56-59) and the 
status of their resolution. 
Table 9. Resolution of IRSR-CLST Issues 
Technical Issue Resolution Status 
Evaluate the processes of pitting corrosion and 
Stress Corrosion Cracking in the presence of 
oxidizing chloride solutions. Evaluate the effects on 
cladding integrity within the WC. 
Pitting is addressed in CRWMS M&O 2000c 
SCC is addressed in this AMR 
Localized corrosion by Fluoride is addressed in this 
AMR 
Evaluate and assess creep rupture models and the 
validity of extrapolation to lower temperatures. 
Resolve issues relating to the DCCG model of 
creep. 
Creep Rupture addressed in CRWMS M&O 2000a 
and this AMR 
Further qualify the DHC analysis with the use of a 
crack-size distribution in the cladding. 
Assess hydrogen embrittlement in the cladding as a 
function of cladding temperature and assess the 
possibility of hydride reorientation. 
DHC is quantified in CRWMS M&O 2000a, and 
CRWMS M&O 2000l 
Hydride embrittlement is addressed in CRWMS 
M&O 2000b 
Hydride reorientation is addressed in CRWMS M&O 
2000l 
Develop models for clad splitting for repository 
storage temperatures in dry air and aqueous 
environments. 
Clad dry splitting is addressed in CRWMS M&O 
2000b 
Wet splitting is addressed in CRWMS M&O 2000e 
and this AMR 
Assess the possibility of cladding mechanical failure 
during rock fall and seismic events using a fracture 
mechanics model. 
Addressed in CRWMS M&O 1999d and this AMR 
Evaluate the damage introduced during reactor 
operation and deterioration during transportation and 
dry storage that may affect the behavior under 
disposal conditions. 
Addressed in CRWMS M&O 2000a and this AMR 
DTN: MO00004SPACLD07.043 
Some of the input data listed in Section 4 have been labeled to be verified (TBV) in the DIRS 
database. These reactor fuel parameters from the open literature have been submitted to the 
DOE for approval as accepted data. When acceptance is received, the TBVs will be removed 
from these parameters. 
This document may be affected by technical product input information that requires 
confirmation. Any changes to the document that may occur as a result of completing the 
confirmation activities will be reflected in subsequent revisions. The status of the input 
information quality may be confirmed by review of the Document Input Reference System 
database.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 50 April 2000 
8. SOURCES OF INPUT 
8.1 REFERENCES CITED 
Ahn, T.M.; Cragnolino, G.A.; Chan, K.S.; and Sridhar, N. 1999. "Scientific Bases for Cladding 
Credit as a Barrier to Radionuclide Release at the Proposed Yucca Mountain Repository." 
Scientific Basis for Nuclear Waste Management XXII, Symposium held November 30-December 
4, 1998, Boston, Massachusetts, U.S.A. Wronkiewicz, D.J. and Lee, J.H., eds. 556, 525-533. 
Warrendale, Pennsylvania: Materials Research Society. TIC: 246426. 
Chung, H.M.; Yaggee, F.L.; and Kassner, T.F. 1987. "Fracture Behavior and Microstructural 
Characteristics of Irradiated Zircaloy Cladding." Zirconium in the Nuclear Industry, Seventh 
International Symposium Sponsored by ASTM Committee B-10 on Reactive and Refractory 
Metals, Strasbourg, France, 24-27 June 1985. Adamson, R.B. and Van Swam, L.F.P., eds. Pages 
775-801. Philadelphia, Pennsylvania: American Society for Testing and Materials. TIC: 238255. 
CRWMS M&O 1999a. Cladding Degradation - Abstraction and Summary Analysis Results for 
Input to TSPA Analyses. TDP-WIS-MD-000005 REV 00. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.19990902.0471. 
CRWMS M&O 1999b. Conduct of Performance Assessment. Activity Evaluation, September 30, 
1999. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.19991028.0092. 
CRWMS M&O 1999c. Thermal Loading Histogram for 21-PWR (Pressurized Water Reactor) 
Absorber Plate Waste Packages. Input Transmittal PA-WP-99366.T. Las Vegas, Nevada: 
CRWMS M&O. ACC: MOL.19991115.0138. 
CRWMS M&O 1999d. Breakage of Commercial Spent Fuel Cladding by Mechanical Loading. 
CAL-EBS-MD-000001 REV 00. Las Vegas, Nevada: CRWMS M&O. ACC: 
MOL.19991213.0237. 
CRWMS M&O 1999e. Thermal Evaluation of Breached 21-PWR Waste Packages. CAL-UDCME-
000002 REV 00. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.20000120.0447. 
CRWMS M&O 2000a. Initial Cladding Condition. ANL-EBS-MD-000048 REV 00. Las Vegas, 
Nevada: CRWMS M&O. Submit to RPC. URN-0246. 
CRWMS M&O 2000b. Clad Degradation - FEPs Screening Arguments. Input Transmittal 
00138.T. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.20000317.0475. 
CRWMS M&O 2000c. Clad Degradation - Local Corrosion of Zirconium and Its Alloys Under 
Repository Conditions. ANL-EBS-MD-000012 REV 00. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.2000405.0479.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 51 April 2000 
CRWMS M&O 2000d. CSNF Waste Form Degradation: Summary Abstraction. ANL-EBS-MD- 
000015 REV 00. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.20000121.0161. 
CRWMS M&O 2000e. Clad Degradation - Wet Unzipping: Release Rates from Breached 
Cladding and Potential Unzipping Velocity. ANL-EBS-MD-000014 REV 00. Las Vegas, 
Nevada: CRWMS M&O. Submit to RPC. URN-0247. 
CRWMS M&O 2000f. Thermal History of Cladding in a 21 PWR SNF WP Loaded with Average 
Fuel. CAL-UDC-ME-000001 REV 00. Las Vegas, Nevada: CRWMS M&O. ACC: 
MOL.20000216.0105. 
CRWMS M&O 2000g. Reference Deleted. 
CRWMS M&O 2000h. Abstraction of Near Field Environment Drift Thermodynamic 
Environment and Percolation Flux. ANL-EBS-HS-000003 REV 00. Las Vegas, Nevada: 
CRWMS M&O. Submit to RPC. URN-0039. 
CRWMS M&O 2000i. In-Package Chemistry Abstraction. ANL-EBS-MD-000037 REV 00. Las 
Vegas, Nevada: CRWMS M&O. Submit to RPC. URN-0245. 
CRWMS M&O 2000j. Comparison of Creep Correlations. Input Transmittal PA-WP-00048.Ta. 
Las Vegas, Nevada: CRWMS M&O. ACC: MOL.20000223.0002. 
CRWMS M&O 2000k. Stainless Steel in Waste Packages for TSPA-SR. CAL-WAS-MD- 
000010. Las Vegas, Nevada: CRWMS M&O. Submit to RPC. URN-0252. 
CRWMS M&O 2000l. Hydride-Related Degradation of SNF Cladding Under Repository 
Conditions. ANL-EBS-MD-000011 REV 00. Las Vegas, Nevada: CRWMS M&O. ACC: 
MOL.20000319.0048. 
Cunningham, M.E.; Simonen, E.P.; Allemann, R.T.; Levy, I.S.; Gilbert, E.R.; and Hazelton, R.F. 
1987. Control of Degradation of Spent LWR Fuel During Dry Storage in an Inert Atmosphere. 
PNL-6364. Richland, Washington: Pacific Northwest Laboratory. TIC: 210249. 
Dyer, J.R. 1999. "Revised Interim Guidance Pending Issuance of New U.S. Nuclear Regulatory 
Commission (NRC) Regulations (Revision 01, July 22, 1999), for Yucca Mountain, Nevada." 
Letter from Dr. J.R. Dyer (DOE/YMSCO) to Dr. D.R. Wilkins (CRWMS M&O), September 3, 
1999, OL&RC:SB-1714, with enclosure, "Interim Guidance Pending Issuance of New NRC 
Regulations for Yucca Mountain (Revision 01)." ACC: MOL.19990910.0079. 
Einziger, R.E. and Kohli, R. 1984. "Low-Temperature Rupture Behavior of Zircaloy-Clad 
Pressurized Water Reactor Spent Fuel Rods Under Dry Storage Conditions." Nuclear 
Technology, 67, (1), 107-123. Hinsdale, Illinois: American Nuclear Society. TIC: 216868.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 52 April 2000 
Harrar, J.E.; Carley, J.F.; Isherwood, W.F.; and Raber, E. 1990. Report of the Committee to 
Review the Use of J-13 Well Water in Nevada Nuclear Waste Storage Investigations. UCID- 
21867. Livermore, California: Lawrence Livermore National Laboratory. ACC: 
NNA.19910131.0274. 
Henningson, P.J. 1998. Cladding Integrity Under Long Term Disposal. 51-1267509-00. 
Lynchburg, Virginia: Framatome Technologies. ACC: MOL.19990310.0103. 
Lide, D.R., ed. 1995. CRC Handbook of Chemistry and Physics. 76th Edition. Boca Raton, 
Florida: CRC Press. TIC: 216194. 
Manaktala, H.K. 1993. Characteristics of Spent Nuclear Fuel and Cladding Relevant to High- 
Level Waste Source Term. CNWRA 93-006. NRC-02-88-005. San Antonio, Texas: Center for 
Nuclear Waste Regulatory Analyses. TIC: 208034. 
Matsuo, Y. 1987. "Thermal Creep of Zircaloy-4 Cladding Under Internal Pressure." Journal of 
Nuclear Science and Technology, 24, (2), 111-119. Tokyo, Japan: Atomic Energy Society of 
Japan. TIC: 237137. 
NRC (U.S. Nuclear Regulatory Commission) 2000. Interim Staff Guidance-11  Storage of 
High Burnup Spent Fuel. Washington, D.C.: U.S. Nuclear Regulatory Commission. TIC: 
247227. 
Peehs, M. 1998. Assessment of Dry Storage Performance of Spent LWR Fuel Assemblies with 
Increasing Burn-Up. Erlangen, Germany: Bereich Energieerzeugung. TIC: 245171. 
Pescatore, C. and Cowgill, M. 1994. Temperature Limit Determination for the Inert Dry Storage 
of Spent Nuclear Fuel. EPRI TR-103949. Palo Alto, California: Electric Power Research 
Institute. TIC: 102933. 
Pescatore, C.; Cowgill, M.G.; and Sullivan, T.M. 1990. Zircaloy Cladding Performance under 
Spent Fuel Disposal Conditions Progress Report May 1 - October 31, 1989. BNL 52235. Upton, 
New York: Brookhaven National Laboratory. ACC: NNA.19900710.0055. 
Rothman, A.J. 1984. Potential Corrosion and Degradation Mechanisms of Zircaloy Cladding on 
Spent Nuclear Fuel in a Tuff Repository. UCID-20172. Livermore, California: Lawrence 
Livermore National Laboratory. ACC: NNA.19870903.0039. 
S. Cohen & Associates 1999. Effectiveness of Fuel Rod Cladding as an Engineered Barrier in 
the Yucca Mountain Repository. McLean, Virginia: S. Cohen & Associates. TIC: 246541. 
Sanders, T.L.; Seager, K.D.; Rashid, Y.R.; Barrett, P.R.; Malinauskas, A.P.; Einziger, R.E.; 
Jordan, H.; Duffey, T.A.; Sutherland, S.H.; and Reardon, P.C. 1992. A Method for Determining 
the Spent-Fuel Contribution to Transport Cask Containment Requirements. SAND90-2406. 
Albuquerque, New Mexico: Sandia National Laboratories. TIC: 232162.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 53 April 2000 
Tasooji, A.; Einziger, R.E.; and Miller, A.K. 1984. "Modeling of Zircaloy Stress-Corrosion 
Cracking: Texture Effects and Dry Storage Spent Fuel Behavior." Zirconium in the Nuclear 
Industry, Sixth International Symposium, Vancouver, British Columbia, June 28- July 1, 1982. 
Franklin, D.G. and Adamson, R.B., eds. ASTM STP 824, 595-626. Philadelphia, Pennsylvania: 
American Society for Testing and Materials. TIC: 241417. 
Weast, R.C. and Astle, M.J., eds. 1980. CRC Handbook of Chemistry and Physics. 61st Edition. 
Boca Raton, Florida: CRC Press. TIC: 242182. 
Wilson, C.N. 1985. Results from NNWSI Series 1 Spent Fuel Leach Tests. HEDL-TME-84-30. 
Richland, Washington: Hanford Engineering Development Laboratory. TIC: 210347. 
Wilson, C.N. 1987. Results from Cycles 1 and 2 of NNWSI Series 2 Spent Fuel Dissolution Tests. 
HEDL-TME-85-22. Richland, Washington: Hanford Engineering Development Laboratory. TIC: 
202294. 
Wilson, C.N. 1990. Results from NNWSI Series 3 Spent Fuel Dissolution Tests. PNL-7170. 
Richland, Washington: Pacific Northwest Laboratory. ACC: NNA.19900329.0142. 
Witte, M.C.; Chun, R.C.; and Schwartz, M.W. 1989. "Dynamic Impact Effects on Spent Fuel 
Assemblies." 9th International Symposium on the Packaging and Transportation of Radioactive 
Materials, Washington, D.C., June 11-16, 1989. 1, 186-194. Oak Ridge, Tennessee: Oak Ridge 
National Laboratory. TIC: 240741. 
8.2 CODES, STANDARDS, REGULATIONS AND PROCEDURES 
64 FR 8640. Disposal of High-Level Radioactive Wastes in a Proposed Geologic Repository at 
Yucca Mountain, Nevada. Proposed rule 10 CFR 63. Readily Available. 
AP-2.13Q, Rev. 0, ICN 0. Technical Product Development Planning. Washington, D.C.: U.S. 
Department of Energy, Office of Civilian Radioactive Waste Management. ACC: 
MOL.19990701.0617. 
AP-2.16Q, Rev. 0, ICN 0. Activity Evaluation. Washington, D.C.: U.S. Department of Energy, 
Office of Civilian Radioactive Waste Management. ACC: MOL.20000207.0716. 
AP-3.10Q, Rev. 2, ICN 0. Analyses and Models. Washington, D.C.: U.S. Department of Energy, 
Office of Civilian Radioactive Waste Management. ACC: MOL.20000217.0246. 
AP-SI.1Q, Rev. 2 ICN 4. Software Management. Washington, DC: U.S. Department of Energy, 
Office of Civilian Radioactive Waste Management. ACC: MOL.20000223.0508 
ASTM C 1174-97. 1997. Standard Practice for Prediction of the Long-Term Behavior of 
Materials, Including Waste Forms, Used in Engineered Barrier Systems (EBS) for Geological 
Disposal of High-Level Radioactive Waste. West Conshohocken, Pennsylvania: American 
Society for Testing and Materials. TIC: 246015.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 54 April 2000 
DOE (U.S. Department of Energy) 2000. Quality Assurance Requirements and Description. 
DOE/RW-0333P, Rev. 9. Washington, D.C.: U.S. Department of Energy, Office of Civilian 
Radioactive Waste Management. ACC: MOL.19991028.0012. 
NLP-2-0, Rev. 5. Determination of Importance Evaluations. Las Vegas, Nevada: CRWMS 
M&O. ACC: MOL.19981116.0120. 
NRC (U.S. Nuclear Regulatory Commission) 1998. Issue Resolution Status Report Key 
Technical Issue: Total System Performance Assessment and Integration. Rev. 1. Washington, 
D.C.: U.S. Nuclear Regulatory Commission. ACC: MOL.19990105.0083. 
NRC (U.S. Nuclear Regulatory Commission) 1999. Issue Resolution Status Report Key 
Technical Issue: Container Life and Source Term. Rev. 2. Washington, D.C.: U.S. Nuclear 
Regulatory Commission. TIC: 245538. 
QAP-2-0, Rev. 5. Conduct of Activities. Las Vegas, Nevada: CRWMS M&O. ACC: 
MOL.19980826.0209. 
QAP-2-3, Rev. 10. Classification of Permanent Items. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.19990316.0006. 
8.3 SOURCE DATA 
LL980711104242.054. Report of the Committee to Review the Use of J-13 Well Water in 
Nevada Nuclear Waste Storage Investigations. Submittal date: 08/05/1998. 
MO0001SPAICC48.037. Initial Cladding Condition for CSNF. Submittal date: 01/27/2000. 
Submit to RPC. URN-0248. 
MO0003SPASSC24.041. SCC Stress Threshold. Submittal date: 03/09/2000. Submit to RPC. 
URN-0251. 
MO0003SPATCR22.038. Release from Wilson Series 2 Tests. Submittal date: 03/09/2000. 
MO0003SPATCR30.039. TC Release From Wilson Series 1 Tests. Submittal date: 03/09/2000. 
Submit to RPC. URN-0249. 
MO0003SPATCR70.040. TC Release From Wilson Series 3 Tests. Submittal date: 03/09/2000. 
Submit to RPC. URN-0250. 
MO9912SPASFC01.032. Strain Failure Criteria. Submittal date: 12/15/99. 
SN0001T0810599.008. Stainless Steel in Waste Packages for TSPA-SR (Total System 
Performance Assessment-Site Recommendation). Submittal date: 01/18/2000. 
SN0001T0872799.006. In-Drift Thermodynamic Environment and Percolation Flux. Submittal 
date: 01/27/2000.

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 55 April 2000 
Figure 1. CCDF for Rod Stress as Received (Room Temperature) 
(DTN: MO00001SPAIC48.037) 
Figure 2. Nodal Locations and Zones for the 21 Assembly PWR Waste Package 
(DTN: MO00004SPACLD07.043) 
Temperature = 27oC 
Time = 100 years
stress2.spw 
Hoop Stress, MPa 
20 40 60 80 100 120 140 160 
Percent of Rods with Stress Exceeding X Stress 
0.1
1 
10 
100

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 56 April 2000 
Figure 3. Maximum Temperature Distribution of the 5 Bins of WPs 
(DTN: SN0001T0872799.006) 
Figure 4. Temperature Histories for WP Surface and Center Rod 
(DTN: MO00004SPACLD07.043) 
Time, Years 
100 1000 Temperature, oC 
0 
50 
100 
150 
200 
250 
300 
350 
Center Rod Temperature 
WP Surface 
Delta T, WP to Center 
Tem12-13.swp 
0 
25 
50 
75 
100 
125 
150 
175 
200 
225 
250 
275 
300 
325 
1 10 100 1000 10000 100000 1000000 
Time (years) 
Temperature (C) 
T max bin0-3 
T max bin10-20 
T max bin20-60 
T max bin3-10 
T max bin -60

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 57 April 2000 
Figure 5. Center Rod Temperature History for Creep and SCC Analysis 
(DTN: MO00004SPACLD07.043) 
Figure 6. CCDF for Creep Strain Failure Criterion 
(DTN: MO00004SPACLD07.043) 
Failure Strain 
0 2 4 6 8 10 12 14 
Probability that Failure Strain > X 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
Time, Years 
0.1 1 10 100 
Center Rod Temperature, oC 
0 
50 
100 
150 
200 
250 
300 
350 
400 
temp12b13.spw 
Dry Storage Shipping 
Preclosure 
Postclosure

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 58 April 2000 
Figure 7. Minimum, Maximum, and Average Temperatures for Bin 4 
(DTN: SN0001T0872799.006) 
Figure 8. Creep Failure Fraction as a Function of Peak WP Surface Temperature 
(DTN: MO00004SPACLD07.043) 
Time, years 
100 1000 
WP surface Temperature, oC 
50 
100 
150 
200 
250 
300 Z4-temp.spw 
Peak 
Min 
Avg. 
CREEP-Mu.spw Creep-Mu.spw 
Peak WP Surface Temperature,oC 
260 280 300 320 340 360 380 400 
Fraction of Rods with Creep Failure 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
Upper Limit 
Best Estimate 
Lower Limit 
Creep-Mu.spw

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 59 April 2000 
Figure 9. Example of Localized Corrosion with a Constant Water Ingression into WP 
(DTN: MO00004SPACLD07.043) 
Figure 10. Radionuclide Release Rate Over Time for Fast Release 
(DTN: MO00004SPACLD07.043) 
fluor6a 
Maximum 
Best Estimate 
Linear 
Model LNT Calculation 
fluor6a.spw 
Time from WP Failure, Years 
0 10000 20000 30000 40000 50000 
Fraction of Rods Failed in WP 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
Maximum 
Minimum 
Best Estimate 
fluor9.spw 
Water Ingress into WP = 50 liters/yr 
Cycle 1 
Cycle 2 
Release Rate 
Time 
0 tpl t2 t1 
R1 
R2

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 60 April 2000 
Figure 11. CDF for Fast Radionuclide Release Fraction from Fuel Matrix 
(DTN: MO00004SPACLD07.043) 
NOTE: Abstracted analysis evaluated at 10-3 atm. CO2 and 0.2 atm. O2 
Figure 12. Abstracted Intrinsic Dissolution Analysis 
(DTN: MOL.20000121.0161) 
0.000 0.001 0.002 0.003 0.004 0.005 
Fast Release Fraction 
0.0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
1.0 
CDF 
From Measurement 
Recommended 
1 
10 
100 
1000 
3 4 5 6 7 8 9 10 
pH 
DR [mg/(m2*d)] 
25C 
90C 
50C

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 61 April 2000 
Figure 13. Unzipping Times vs. Temperature in WP 
(DTN: MO00004SPACLD07.043) 
Figure 14. Unzipping Times vs. pH in Waste Package 
(DTN: MO00004SPACLD07.043) 
WP Temperature, oC 
20 30 40 50 60 70 80 90 100 110 
Time to Unzip Rod, Years 
10000 
20000 
30000 
40000 
50000 
60000 
70000 
unzip4.spw 
O2 = 0.2 atm. 
CO3 = 0.001 M 
pH = 8 
WP pH 
3 4 5 6 7 8 9 10 11 
Time to Unzip Rod, Years 
0 
10000 
20000 
30000 
40000 
50000 
60000 
unzip5.spw 
O2 = 0.2 atm. 
CO3 = 0.001 M 
Tc = 350C

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 62 April 2000 
Figure 15. UO2 Alteration Rate as a Function of Time for Two Fuel Rods (Schematic) 
(DTN: MO00004SPACLD07.043) 
Figure 16. Propagation Distance and Unzipping of Two Fuel Rods (Schematic) 
(DTN: MO00004SPACLD07.043) 
Time 
Alteration Rate 
0 t0A t0B t1A t1B 
Rod A 
Rod B 
Time 
Propagation Distance h 
t1B t0B 
0 
t1A t0A 
0 
L/2+c 
L/2
c 
Time interval 
for unzipping 
of rod A
Time interval for unzipping of rod B 
h interval 
for unzipping 
of rod A 
h interval 
for unzipping 
of rod B

Clad Degradation  Summary and Abstraction 
ANL-WIS-MD-000007 REV 00 63 April 2000 
9. ATTACHMENTS 
The attachments are listed as follows: 
Attachment Title Pages 
I Summary of Cladding Degradation Abstraction used in TSPA 2 
II Description of Software Routine: AMR-F0155 V1.xls 21

ANL-WIS-MD-000007 REV 00 I-1 April, 2000 
Attachment I 
Summary of Cladding Degradation Abstraction Used in TSPA 
1
2
3
4
5
6
7
89
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
A B C D E F G H 
file = AMR-F0155-V1.xls 
Sheet = Summary, p. 1 Total Cladding Abstraction 
6.1) Cladding Condition as Received (to be added to creep failures) 
For the 5 groups of WPs (approx. 1500 WPs / group) 
Lower Limit= 0.0155 % 
Median= 0.0948 % 
Uppper lim= 1.2853 % 
Distribution is triangular 
error factor = 4 
CCDF Lower Unc. 
% failure, best 
estimate Upper Unc 
1.0000 0.0138 0.0550 0.2200 % 
0.9987 0.0146 0.0585 0.2341 % 
0.9849 0.0155 0.0622 0.2486 % 
0.8561 0.0179 0.0717 0.2869 % 
0.6555 0.0212 0.0849 0.3397 % 
0.5819 0.0224 0.0895 0.3582 % 
0.5058 0.0237 0.0948 0.3793 % 
0.2709 0.0284 0.1136 0.4545 % 
0.1966 0.0361 0.1445 0.5780 % 
0.1084 0.0507 0.2028 0.8111 % 
0.0970 0.0522 0.2089 0.8357 % 
0.0766 0.0741 0.2965 1.1859 % 
0.0640 0.0746 0.2983 1.1930 % 
0.0503 0.0803 0.3213 1.2853 % 
0.0373 0.1248 0.4990 1.9962 % 
0.0323 0.2469 0.9875 3.9499 % 
0.0221 0.2892 1.1568 4.6274 % 
0.0196 0.4496 1.7985 7.1941 % 
0.0190 0.5088 2.0352 8.1408 % 
0.0115 0.6939 2.7757 11.1029 % 
0.0036 0.7626 3.0505 12.2022 % 
0.0002 1.3214 5.2856 21.1424 % 
0.0000 1.3214 5.2856 21.1424 % 
6.2) Creep&SCC Model, % Perforated rods at time=0 
Table gives percents of pins considered perforated at time t=0 
use triangular distribution between low, best, high 
WP Peak TC Upper Limit Best Estimate Lower limit 
<=177 19.4157 2.4400 1.0500 % 
177 19.4157 2.4400 1.0500 % 
227 19.4862 2.4414 1.0500 % 
252 20.5719 2.5762 1.0500 % 
262 21.5552 2.6686 1.0500 % 
277 24.7919 3.3914 1.0605 %, temp is nominal avg. WP temperature. 
292 32.6414 6.0357 1.2024 % 
297 36.2786 7.8276 1.3286 % 
302 40.7986 9.8676 1.7319 % 
312 50.5172 16.2162 3.6976 % 
327 63.7876 30.1857 10.6743 % 
352 82.2672 55.6748 34.2400 % 
377 95.5310 77.8867 59.1972 % 
402 99.6990 93.0167 79.8619 % 
>=412 99.8519 96.5757 87.1962 % 
6.3) Localized Corrosion Uncertainty distribution log uniform between max and min 
equation : fraction = M^3 water / 2.42E3M^3, max=10*fraction, min = fract/10 
test case, 50 l/yr, 10,000 yrs, 1 L = 1E-3 m^3 
Fraction failed= 0.20661157

ANL-WIS-MD-000007 REV 00 I-2 April, 2000 
60 
61 
62 
63 
64 
65 
66 
67 
68 
69 
70 
71 
72 
73 
74 
75 
76 
77 
78 
79 
80 
81 
82 
83 
84 
85 
86 
87 
88 
89 
90 
91 
92 
93 
94 
95 
96 
97 
98 
99 
100 
101 
102 
103 
104 
105 
106 
107 
108 
109 
110 
111 
112 
113 
114 
115 
116 
117 
A B C D E F G H 
file = AMR-F0155-V1.xls 
6.5 Fast Release Fraction, % Sheet = Summary. P.2 
Gap release Iodine (I) 4.20% 
Gap release Cesium (Cs) 1.40% 
Fast release 
all 
radionuclides= 0 - 0.4% uniform distribution 
Includes additional I, Cs 
6.6.1) Unzipping Velocity 
Perf =rods available for unzipping,sum(localized corrosion (2), creep (3), Initial failures(4)) 
Vz = rod unzip velocity 
Vz = A * Vin Active fuel length = 366 cm 
A = Unzip model parameter, triangle fit from lower, best estimate, upper 
Possible range, Amin =1, Abest =40, Amax=240 
Vin = Intrinsic dissolution Velocity 
Vin = Dis rate (item 1) * 2.190E-05 cm/yr / (mg/m2-d) 
Fuel exposed and disolved= Vz* Perf, check perf <=1.0 
density, uo2 10 gm/cc (includes 10% porosity) 
grain area/macro area= 6 area-micro/area-macro 
intrinsic, macro 0.000219 gm/cm2-yr 
cm/yr / ( mg/m^2-d), conversion of dissolution 0.0000219 cm/yr / (mg/m2-d) 
to velocity 
6.6.2) Abstraction of Intrinsic Dissolution Rate 
log10(rate) = a0 + a1/Tk + a2* PCO3 + a3* PO2 + a4 * pH 
Term= a0 a1 a2 a3 a4 
pH>7 4.69 -1085 -0.12 -0.32 0 
pH< =7 7.13 -1085 0 -0.32 -0.41 
Example calc. Tc PCo3 PO2 pH 
dis Rate log10(dis rt) 
Acidic 
solution 
Basic 
solution Tc PCo3 PO2 pH 
6.066 0.783 0.6769 0.7829 50 2.7 0.7 7 
14.224 1.153 1.0470 1.1530 90 2.7 0.7 7 
73.624 1.867 1.8670 1.1530 90 2.7 0.7 5 
325.638 2.513 2.5127 0.9787 70 2.7 0.7 3 
units: dis rate= mg/m2-d, m2 is microscopic (grains) 
Tc = temperature, centigrade, WP wall Tk = Temp, Kelvin 
PCO3 = CO3 activity = -log10(molar CO3) 
PO2 = O2 activity = -log10(partial pressure O2) 
pH = standard, 
Uncertainty in dissolution a0 +- 1.0, uniformly distributed 
This equation is used in the unzipping abstraction 
6.7 Stainless Steel Clad Commercial Reactor Fuel 
% of WPs containing SS cladding = 3.49 
% of fuel in these WPs with SS cladding = 32.89 
Assumption, all SS cladding is perforated, available for unzipping 
6.4.1 Seismic Failures 
Frequency = 1.1E-6/yr 
All cladding failed (perforated) 
All cladding available for unzipping

ANL-WIS-MD-000007 REV 00 II - 1 April 2000 
Attachment II 
Description of Software Routine: AMR-F0155-V1.xls 
The statistical analysis of the rod creep is performed in the software routine AMRF0155-
V1.xls (V1 represents Version 1) which is included in the DTN file: d$$. 
Microsoft Excel for Windows Version 4.0 was used for the analysis and the analysis is 
documented in this AMR as a software routine. The analysis was performed on a Dell 
Pentium personal computer (CPU number 111920) with a WINDOWS 95 operating 
system. One macro is used and is listed, tested and documented in this attachment. This 
attachment describes the various sheets that compose this software routine, including a 
listing of the top rows of each sheet of the file, and correlates the various equations 
presented in the text of this report to the software routine. 
The software routine contains 9 sheets and one macro, many of which are linked. Each 
sheet addresses a specific aspect of cladding condition. Table II-1 summarizes the 
different sheets. 
Table II-1. Description of Sheets in AMR-F0155-V1.xls 
Sheet Title Subject Supports Sheet Uses Sheet 
Creep-Lim Creep Failure Limit Samples Fail-Calc Rand # 
Creep-Rod Creep strain for single rod Creep-WP Temp-C 
Creep-WP Calculates creep across WP Fail-Calc Macro: Creep1, Creep-Rod 
Fail-Calc Collects statistics on creep failure Final Creep Results Creep-WP, Creep-Lim 
Macro: 
Creep1 
Calls Creep-Rod from Creep-WP Creep-WP Creep-Rod 
Rand # Table of random numbers All distributions None 
Summary Summary of output passed to 
TSPA 
Listed as 
Attachment I 
All 
Temp-C Temperature across WP Creep-Rod Temp-C2 
Temp-C2 Initial rod and WP temperature 
histories 
Temp-C None 
Unzip Time to unzip rod Figures 13,14 None 
The Sheet Summary is listed as Attachment I and is not repeated in this attachment. 
The first 30 to 40 rows of the other sheets are included (in alphabetical order) in this 
attachment (Table II-5 to II-12). Many of the sheets have 2000 statistical samples and 
only the first few rows are included. A brief description of each sheet follows including 
the testing and test results. 
This analysis is based on observed fuel performance for PWR fuel with Zircaloy cladding 
and therefore there are constraints, caveats and limitations to this analysis. This analysis 
is only applicable to U.S. commercial PWR and BWR fuel with Zircaloy cladding. It is 
also limited to fuel exposed to normal operation and anticipated operational occurrences 
(AOOs) and not for fuel that has been exposed to severe accidents. Fuel burnup 
projections have been limited to the current commercial power licensing environment

ANL-WIS-MD-000007 REV 00 II - 2 April 2000 
with restrictions on fuel enrichment, oxide coating thickness and rod plenum pressures. 
The ranges of applicability are: 
1. Temperature: 27oC to 420oC. The upper temperature limit is the highest 
temperatures of Matsuos experiments. This is also the approximate temperature of 
the inside surface of the cladding during normal operation in a PWR (340oC to 370oC, 
(Pescatore et al. 1990, Table 3, p. 7)). The lower limit is not important since the 
cladding degradation rates become negligible at these temperatures. 
2. Stress: 0 to 314 MPa. The lower limit is not important because low stress does not 
cause damage. The upper limit is the upper limit of Murtys test data for which the 
creep equation was derived. 
3. Burnup: 2 to 80 MWd/kgU, the approximate range of experiments reported in this 
AMR. 
The analysis itself addresses the uncertainties of the various parameters. Uncertainty 
ranges are defined for each parameter based on experimental observations reported in the 
literature. These uncertainties are statistically combined in the sampling routine. The 
range for each parameter is defined and justified in the body of this AMR. 
The following sections describe how the analysis is performed and the analytical 
sequence used. 
Sheet Fail-Calc 
The Sheet Fail- Calc (for failure calculation) is the main driver for the calculation of 
creep failures in the WP (see Table II-8 for the first 2 of 6 zones). The user inputs the 
shift in the WP surface temperature into Cell D22 and starts the macro: Creep1. The 
creep calculations are then calculated for the specific WP temperature history. The user 
must copy the results for this WP temperature (Cells E22 through H22) into the table of 
results shown in Cells E3 through H18. This table is used to generate Figure 8 and is 
reproduced in the Summary Sheet, Rows 37 to 55. 
The user also specifies the strain uncertainty (Cell B22, usually 0.8). Calculated strain is 
uniformly distributed by a multiplication factor of 0.2 to 1.8. This factor was developed 
in CRWMS M&O 2000m. The upper and lower creep failure criteria are also specified 
in Cells B23 and B24. These are the maximum and minimum creep failures measured by 
Chung et al. (1987, pp. 780,781). 
The rod stress (room temperature) is given in Cells C29 through C2028. These are 
generated in CRWMS M&O 2000a and have been ordered by decreasing stress so that 
trends can be observed. Column B gives the sample or case number so that specific 
characteristics of a sample can be determined. One rod, at the stress specified in Column 
C, is placed in each of the 6 zones of the WP and the creep is calculated in the Sheet 
Creep-WP. Table II-2 identifies the columns used for calculating the various failure 
indices for the six zones. Row 26 identifies the zones. For each zone, the resulting creep

ANL-WIS-MD-000007 REV 00 II - 3 April 2000 
strain is calculated in the Sheet: Creep-WP and is given in the first column of Fail- 
Calc for the specific zone. A creep strain (in percent) greater than 100 means that creep 
failure is expected for that rod. Creep strain of 99 means that the rod was identified as 
having a peak stress over 180 MPa and failure is expected for that rod by SCC. As the 
stresses decrease (i.e. at the higher row numbers in Fail-Calc), the strains decrease. 
The random sampled failure criterion is given in the second column for each zone of 
Fail- Calc. This criterion is generated in the Sheet: Creep-Lim and will be discussed 
later. 
The next three columns contain a rod failure index, either zero (0, i.e. the rod did not 
fail) or one (1, i.e. the rod failed). The creep strain uncertainty is calculated in these cells. 
The first column is the resulting comparison for the upper limit, using 0.4% creep as the 
failure criterion. The next column uses the full CCDF for the failure criterion and 
compares the creep (Column D for Zone 1) to the failure criterion (Column E for Zone 
1). The third column is the resulting comparison for the lower failure limit, using 11.7% 
creep as the failure criterion. 
Table II-2. Column Assignments in Sheet Fail-Calc for Rod Creep Failure 
Calculations 
Zone Creep Strain 
Column 
Creep Failure 
Criteria Column 
Upper Limit 
Failure Index 
CCDF Failure Index Lower Limit Failure 
Index 
1 D E F G H 
2 I J K L M 
3 N O P Q R 
4 S T U V W 
5 X Y Z AA AB 
6 AC AD AE AF AG 
The final statistics for rod failure from creep are performed in rows 22 to 25. The 
fraction of the 2000 samplings failed in each zone using the three failure criteria is 
calculated in Row 25 and is the sum of the index column divided by 2000. Row 24 is the 
fraction of rods in the WP that are located in each zone. This is calculated in Table 2 and 
shown in Figure 2. Row 23 is the product of Rows 24 and 25 and represents the fraction 
of rods in the WP that are located in a zone and have failed. Row 22 (Cells F22, G22, 
H22) sums the zones in Row 23 for the three failure criteria and gives the fraction of rods 
in the WP that have failed using the three failure criteria. These results are copied into 
the table in Cells E3 through H18 and are used to generate Figure 8. 
Tests: The stress and case number (Columns C and B, starting in Row 29) are imported 
from CRWMS M&O 2000a and are tested by visual inspection using the case number. 
For Zone 1, the resultant creep values are listed in Column D. This can be tracked back 
to Creep-WP. Failure criteria are given in Column E and can be tracked back to 
Creep-Lim, Col. C. Col. F compares the creep, multiplied by an uncertainty, to the 
upper limit failure criteria (Cell B23). The creep uncertainty factor is 0.8 (Cell B22) and 
a uniform distribution of uncertainty is used as shown below: 
Creep = Creep(Col. D)*[(1-uncertainty) + 2 * uncertainty* rand()] (Eq. II-1)

ANL-WIS-MD-000007 REV 00 II - 4 April 2000 
Creep = Creep(Col. D)*[0.2 + 1.6* rand()] (Eq. II-2) 
Where rand() = a random number from Sheet Rand #, Col. J 
This calculation can be tested by hand calculations (at lower stresses where creep is near 
the failure criterion). Column F assigns a zero or one, depending on whether the creep 
exceeds the creep limit. This is tested by inspecting down the 2000 samples of 
decreasing stress (all 2000 samples are not actually shown in Table II-8). This 
calculation is repeated in Columns G, H (Zone 1), K, L, M (Zone 2), P, Q, R (Zone 3), U, 
V, W (Zone 4), Z, AA, AB (Zone 5), AE, AF, AG (Zone 6). The summing of the 
statistics is tested with visual inspection. 
Sheet Fail-Calc used Sheets Creep-Lim and CreepWP. A description of these 
sheets follows. 
Sheet Creep-Lim 
This sheet contains 6000 samplings of creep failure criteria. Rows 3 through 20 give the 
18 creep strains reported by Chung et al. (1987, pages 780, 781). These are repeated in 
Rows 20 and 21 where the linear interpolation on the CCDF is performed. The samples 
are given in Rows 25 through 6024. Column D is a random number taken from Sheet: 
Rand #. The random number is interpolated in Columns E through U and the resulting 
strain failure criterion is presented in Column C. Table II-3 shows the assignment of 
random failure criteria to zones. Table II-5 shows the top rows of this sheet. 
Table II-3. Assignment of Creep Failure Criteria to Zones 
Zone Starting Location Ending Location 
1 C25 C2024 
2 C1025 C3024 
3 C2025 C4024 
4 C2500 C4499 
5 C30250 C5024 
6 C4025 C6024 
Test: Only part of the interpolation table is shown in Table II-5. Using Row 27 as a test, 
the random number 0.602 is taken from Rand #, Cell C7. The interpolation is done 
with Cells K20 through L21 and can be tested: 
Creep Lim (C27) = 1.4 + (2.4-1.4)*(0.647-0.602) / (0.647-0.588) 
= 1.4 + 0.762 = 2.16

ANL-WIS-MD-000007 REV 00 II - 5 April 2000 
Sheet Creep-WP 
In this sheet, the rod temperature coefficients are calculated for the 12,000 rods sampled 
across the WP (2000 stress samples, located in each of 6 zones). The temperature 
uncertainty (13.5%) is specified in Cell E3 and represents an uncertainty of 41.6oC from 
the combined WP surface temperature uncertainty (22.1oC) and the uncertainty in 
temperature across the WP (19.5oC). The temperature uncertainty is calculated in Sheet 
TempC2 Cell N55. The 2000 stress samples are repeated in Column C. The zone 
numbers are given in Row 5. For each zone, the first column is the temperature shaping 
coefficient and the second column is the resulting creep from the Sheet Creep-Rod. 
The macro Creep1 is used to couple Sheets Creep-WP to Creep-Rod and will be 
described below. The temperature shaping coefficient represents the product of the 
uniformly distributed temperature uncertainty (Cell E3) and the WP radial temperature 
shaping term. The WP radial temperature shaping term is calculated in Sheet TempC, 
Cells F7 to K7 and will be described in that sheet description. The radial temperature 
shaping term adjusts the WP center rod temperature downward for the outer zones. The 
rod stress (Column C) and temperature shaping coefficient (example: Column D for Zone 
1) are input for the rod creep calculation (Sheet Creep-Rod) and the resulting creep 
(example: Column E for Zone 1) is stored in this sheet. The macro Creep1 couples the 
Creep-WP Sheet and the Creep-Rod Sheet. Table II-7 shows the top rows (Zone 1 
and 2) of Sheet Creep-WP. 
Test: This sheet imports the stress (Column C) from Fail-Calc Column C. The only 
calculation done here is the calculation of the temperature shaping coefficient (Column D 
for Zone 1). Using Cell D7 as a test calculation, the temperature uncertainty (Cell E3) is 
uniformly distributed using an equation similar to Equation II-1 and Rand # Cell A5 
(0.232 value). The shaping coefficient for Zone 1 is in TempC, Cell F7 and is one (1, 
i.e. center zone). The test calculation for Cell D7 is: 
Temp. Adj = Shape coef * Uncertainty 
= 1.0 * [ (1.0- 0.135) + 2* 0.135*0.232] 
= 0.928 (Cell D7) 
This calculation is repeated for each stress sample and each zone (Cols. D, F, H, J, L, N). 
Macro: Creep1 
A macro is used to couple the Creep-WP Sheet and the Creep-Rod Sheet. As 
described above, Creep-WP generates the temperature shaping term and contains the 
stress for 12,000 rods located across the WP. The Sheet Creep-Rod calculates the 
amount of creep for a single rod using these two inputs: Stress and temperature shaping 
factor. Creep-Rod produces a single output number of creep strain for the one rod 
analyzed. The details of Creep-Rod are described below. The macro Creep1 copies 
the two inputs from Creep-WP to Creep-Rod and then writes the resulting answer 
(creep strain) from Creep-Rod to Creep-WP for the 12,000 rods being analyzed. The 
actual listing of the macro is given below in numbered lines printed in italics.

ANL-WIS-MD-000007 REV 00 II - 6 April 2000 
First line is the Macro title: 
1) Sub Creep1() 
This next line steps down the 2000 lines of stress samples 
2) For i = 0 To 1999 
Zone 1 
This next line copies the temperature shaping term from Sheet Creep-WP, Row I+7, 
Column 4 (Column D) to Sheet Creep-Rod, Location B3. 
3) Sheets("Creep-Rod").Range("B3").Value = Sheets("Creep-WP").Cells(i + 7, 4).Value 
This next line copies the stress value from Creep-WP, Row i+7 Column 3 (Column C) 
to Sheet Creep-Rod, Cell B4. 
4) Sheets("Creep-Rod").Range("B4").Value = Sheets("Creep-WP").Cells(i + 7, 3).Value 
The next line shifts the resulting calculated strain from Creep-Rod Cell B5 to Creep- 
WP, row i+7, Column 5 (Column E). 
5) Sheets("Creep-WP").Cells(i + 7, 5).Value = Sheets("Creep-Rod").Range("B5").Value 
For the next 5 WP radial zones the temperature shaping index is copied to Creep-Rod 
and the resulting creep strain is written into Creep-WP. The same value of stress is 
used in all zones as was used for Zone 1 above. 
Zone 2 
6) Sheets("Creep-Rod").Range("B3").Value = Sheets("Creep-WP").Cells(i + 7, 6).Value 
7) Sheets("Creep-WP").Cells(i + 7, 7).Value = Sheets("Creep-Rod").Range("B5").Value 
Zone 3 
8) Sheets("Creep-Rod").Range("B3").Value = Sheets("creep-WP").Cells(i + 7, 8).Value 
9) Sheets("Creep-WP").Cells(i + 7, 9).Value = Sheets("Creep-Rod").Range("B5").Value 
Zone 4 
10) Sheets("Creep-Rod").Range("B3").Value = Sheets("Creep-WP").Cells(i + 7, 10).Value 
11) Sheets("Creep-WP").Cells( i + 7, 11).Value = Sheets("Creep-Rod").Range("B5").Value 
Zone 5 
12) Sheets("Creep-Rod").Range("B3").Value = Sheets("Creep-WP").Cells(i + 7, 12).Value 
13) Sheets("Creep-WP").Cells( i + 7, 13).Value = Sheets("Creep-Rod").Range("B5").Value 
Zone 6 
14) Sheets("Creep-Rod").Range("B3").Value = Sheets("Creep-WP").Cells(i + 7, 14).Value 
15) Sheets("Creep-WP").Cells( i + 7, 15).Value = Sheets("Creep-Rod").Range("B5").Value 
Bottom of the i Do Loop. 
16) Next i 
Alarm to announce problem is complete 
17) Beep 
18) Beep 
19) Beep 
20) Beep 
21) End Sub 
Test: The macro can be tested the following ways: 
A) After running the macro, Creep-Rod contains the last rod analyzed, 2000 stress 
sample, zone 6. This can be visually compared with the value stored in Creep-WP. 
The cells to compare are given in Table II-4.

ANL-WIS-MD-000007 REV 00 II - 7 April 2000 
Table II-4. Comparison of Cells after Macro Run 
Value Creep-Rod Creep-WP 
Temperature Index B3 N2006 
Stress B4 C2006 
Strain B5 O2006 
B) The value of temperature index and stress for any rod in Creep-WP can manually 
be copied into Cells B3 and B4 of Creep-Rod and the resulting strain can be compared 
with that in Creep-WP. 
C) While having the top of the Sheet Creep-Rod on the computer screen, the macro 
can be run. The macro may be confirmed to step down the rod sample stresses since they 
are ordered by decreasing stress. 
D) First run the macro with very high WP temperatures (Fail- Calc Cell D22 = 135oC). 
This will fail most rods and the failure indices in Fail- Calc will be 1. While showing 
the indices for the middle of the stress samples (about Row 1000) on the computer 
monitor, the macro can be run again with Fail- Calc Cell D22 = -100oC (very cold WP). 
This will produce very few rod failures and the macro may be confirmed to sweep down 
Sheet Fail- Calc changing the failure indices. 
Sheet CreepRod 
This sheet calculates the creep strain for a single rod given the initial room temperature 
stress and temperature index. As described above, this sheet is used 12,000 times to 
calculate the creep for all the rods listed in  Creep-WP. Table II-6a and b list this sheet. 
The actual calculations are performed in Rows 10 through 67. The room temperature 
stress is specified as an input in Cell B4 and the temperature index is specified in Cell B3. 
The resulting strain is shown in Cell B5. The details of the creep analysis are as follows: 
For Rows 8 through 64 
Column Description 
A Time in years, at YMP 
B Time, years, starting with dry storage 
C Gives the cladding temperatures, oC, at that time. The temperature history of the 
rod being analyzed is of the center rod, multiplied by the scaling factor to reduce 
the temperature for other zones and multiplied by the uncertainty factor. 
D Gives the cladding temperatures, Kelvin, at that time. 
E Stress, adjusted for the temperature at time using ideal gas law for the fission gas 
in the gas plenum, MPa 
F Time in hours 
G Total running sum of creep strain (Eq. 6.2-7, below) 
H Total (Glide +Coble) creep for temperature i and time i(Eq. 6.2-5, below) 
I Glide creep for temperature and time i (Eq. 6.2-3, below)

ANL-WIS-MD-000007 REV 00 II - 8 April 2000 
J Coble creep for temperature i and time i (Eq. 6.2-4, below) 
K Total (Glide +Coble) creep for temperature i but time i-1 (Eq. 6.2-5, below) 
L Glide creep for temperature i but time i-1 (Eq. 6.2-3, below) 
M Coble creep for temperature i but time i-1 (Eq. 6.2-4, below) 
N Youngs module, E (Eq. 6.2-6, below) 
O Temperature coefficient for Arrhenius term (Temperature term Eq. 6.2-1, below) 
P Coble creep rate (fraction/yr) for temperature at time i (Eq. 6.2-2, below) 
P Glide creep rate (fraction/yr) for temperature at time i (Eq. 6.2-1, below) 
The creep correlation developed by Murty (Henningson, 1998, p. 57, eqs. 9b, 11, 12, and 
15) was used and is repeated below from Section 6.2: 
3 / 31200 6 )] 807 [sinh( 10 97 . 4 
E T
E 
e x T 
Glide 
s e - = & (Eq. 6.2-1) 
T 
e T 
Coble 
s e / 21000 83 . 8 - = & (Eq. 6.2-2) 
Glide creep strain: 
t 
t 
t 
de 
de 
de 
gli 
gli 
gli glide 
T 
T 
e k e 
e ke e e 
& 
& 
& 
+ 
+ = (Eq. 6.2-3) 
Coble creep strain: t Coble Coble e e & = (Eq. 6.2-4) 
Total creep: Coble glide e e e + = (Eq. 6.2-5) 
Various parameters and constants include: 
eT = 0.008, 
k= 10 
E = (1.148x105  59.9T) x106, Pa (T in K) (Eq. 6.2-6) 
T= temperature (K) 
s= stress (Pa) 
t= time (hours) 
Integration over thermal transient: e (ti)=e(Ti-1, ti-1) + [ e(Ti, ti) - e (Ti, ti-1)] (Eq. 6.2-7) 
The Sheet Creep-Rod uses a rod temperature history in Cells C10 through C64 that is 
developed in two different places for two different time intervals. The rod temperatures 
for dry storage and transportation are developed in CRWMS M&O 2000a. The 
temperatures in the repository are developed in Sheets TempC and TempC2, which 
are discussed next. 
Test: In Row 71 of the Sheet Creep-Rod is a test case. This case is presented in 
CRWMS M&O 2000m and is an analysis of three experiments reported by Matsuo. The 
test conditions are: time duration = 960 hours, temperature = 360C, stress = 118 MPa (at

ANL-WIS-MD-000007 REV 00 II - 9 April 2000 
360oC). The measured strains (three tests) were 0.33, 0.40, and 0.44%. The reference, 
CRWMS M&O 2000m, reports a calculated creep of 0.517%, the same result as shown in 
Cell G71. This demonstrated that the equations were programmed correctly. Visual 
inspection and hand calculations were also performed. The summing of the creep strains 
(Column G) is tested with a hand calculation of the first few points. 
Sheet TempC2 
Cells A5 through B39 (Table II-11a) contain the WP surface temperature history from 
CRWMS M&O 2000h. Cells D5 through T44 give the WP internal temperatures from 
CRWMS M&O 2000f, Table 6-2, p. 29. Cells U5 to U44 give the temperature difference 
between the WP surface and center rod. Rows 46 through 91 interpolate in time the WP 
surface temperatures and internal temperature difference so that temperatures are 
available at the same times and can be added. The results of the interpolation are listed in 
Cells G46 through I90. These are copied to Sheet TempC, Cells A8 through F51. 
The temperature uncertainty is also calculated in Cells L46 through N55. The difference 
between the WP surface maximum temperature and average temperature (at the time of 
maximum temperature) for the WP is 22.1oC (CRWMS M&O 2000h). The uncertainty 
in temperature across the WP is the difference in peak center rod temperatures for a WP 
with helium fill (325.8oC, CRWMS M&O 2000f, Table 6-2, page 29) and the peak 
temperature with air and water in the WP (345.3oC, CRWMS M&O 2000g, Table 6-2, 
p.29) or 19.5oC. These two uncertainties are added and the total uncertainty is calculated 
to be 13.5% in Cell N55. 
Tests: Rows 7 through 44 are a repeat of input temperatures and times and are tested by 
inspection. Column U (not shown in Table II-11a) is the difference between Columns F 
and T and is verified by hand calculation. The interpolation of WP temperatures is in 
Cells C46 through C91 and the interpolation of temperature difference across the WP is 
in Cells F7 through F90. Both are tested by visual inspection and hand calculations. 
Sheet TempC 
Sheet TempC2 calculated the WP surface temperature history and the WP internal 
temperature difference history. These are imported into Cells A8 through F51 of Sheet 
TempC. Sheet TempC (see Table II-10a, b) develops the temperature history for the 
rods that are located in the five non-center zones. The ratio of the temperature in any 
zone divided by the center rod temperature is the temperature shaping factor. 
The temperature in the various zones is calculated in Cells A57 through F72. Column A 
gives the location for the temperatures as shown in Figure 2 and supplied by CRWMS 
M&O 2000f, Table 6-2, p. 29). Column B gives the temperature at the time that the 
temperatures peak for the 15 locations across the WP (Row 19 of Sheet TempC2). The 
time for the peak temperature is used because the greatest cladding creep occurs at the 
peak temperature. Column C gives the points that are averaged to give the rod 
temperatures in the various zones (see Table 2 and Figure 2). The results are in Column

ANL-WIS-MD-000007 REV 00 II - 10 April 2000 
D and temperature differences between locations 1-6 and the surface (i.e. location 15) are 
in Column E. The reduction factor (temperature difference in each zone/temperature 
difference for center zone) is given in Column F and copied to Cells F6 to K6. 
The temperature distribution, both in time and radial location, is given in Cells F8 
through K51. These are calculated by adding the product of the zone temperature index 
(Cells F6 through K6) and center rod temperature difference (Column E) to the WP 
surface temperature (Column B + Cell B55 for WP temperature shift). The gross 
temperature index is then calculated and given in Cells F7 through K7. This is used in 
Fail-Calc to calculate the temperature for each rod. Cells F5 through K5 give the 
fraction of rods from the WP in each zone. This is the fraction that is given in Table 2 
and also used in Fail- Calc. 
Test: This sheet averages the temperatures for the 6 zones. Testing is by visual 
inspection and hand calculations. 
Sheet Rand # (Random Number Sheet) 
This sheet contains 2000 rows of random numbers that were fixed after they were 
generated (see Table II-9). This has the same effect as using a fixed seed in a random 
number generator and is needed if the user is to get the same answer each time he 
accesses the spreadsheet. Row 4 identifies which calculation uses each column. Column 
P contains the sample number, which is available for tracking the results for any specific 
sample. 
Test: This sheet is tested by inspection. As a test, the calculated mean and median for 
Cells A5 through O2004 are: 
Test mean = 0.4992 
Test median = 0.4989 
These values are very close to the theoretical value of 0.5. 
Sheet Unzip 
This sheet calculated the time to unzip the cladding as a function of temperature (Rows 9 
to 25) used for Figure 13 and pH (Rows 27 to 40) used for Figure 14. The intrinsic 
dissolution equation is given in Rows 4 to 7. For the temperature and chemical 
conditions given in Columns E through J, the dissolution rate is calculated in Column A. 
The unzipping velocity is calculated in Column K and the time to unzip a rod is 
calculated in Column L. 
Test: This is tested by hand calculations. In addition, the calculations can be compared 
with the dissolution test calculation in Sheet Summary, by applying the same chemical 
and temperature conditions.

ANL-WIS-MD-000007 REV 00 II - 11 April 2000 
Table II-5. Listing of Top Rows of Sheet: Creep-Lim 
123456
789
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
A B C D E F G H I J K L M N O P Q R 
creep limit file = AMR-F0155-V1.xls 
ccdf strain % Sheet = Creep-Lim 
1 0.4 
0.941177 0.8 
0.882354 1 This CCDF used for Fig. 6 
0.823531 1.1 
0.764708 1.2 
0.705885 1.3 
0.647062 1.4 
0.588239 2.4 
0.529416 2.4 
0.470593 2.5 
0.41177 3.3 
0.352947 3.6 
0.294124 4.7 
0.235301 4.7 
0.176478 4.7 
0.117655 6 
0.058832 6 
0 11.7 CCDF 1 0.941177 0.882354 0.823531 0.764708 0.705885 0.647062 0.588239 0.529416 0.470593 0.41177 0.352947 0.294124 0.235301 
Mean 3.288889 F. Strain 0.40 0.80 1 1.1 1.2 1.3 1.4 2.40 2.40 2.50 3.30 3.60 4.70 4.7 
Median 2.45 
Fail Strain 
rand, 
f.Strain 
0.95 0.898514 0.00 0.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 
4.70 0.202301 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 4.70 
2.16 0.60249 0.00 0.00 0.00 0.00 0.00 0.00 2.16 0.00 0.00 0.00 0.00 0.00 0.00 0.00 
0.65 0.962604 0.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 
2.58 0.464965 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.58 0.00 0.00 0.00 0.00 
1.04 0.860576 0.00 0.00 1.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 
2.40 0.562003 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2.40 0.00 0.00 0.00 0.00 0.00 0.00 
0.79 0.942233 0.79 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 
4.70 0.204424 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 4.70 
0.83 0.931116 0.00 0.83 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

ANL-WIS-MD-000007 REV 00 II - 12 April 2000 
Table II-6a. Listing of Top Rows of Sheet: Creep-Rod (Col. A-J) 
123 
4
56789
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 
61 
62 
63 
64 
65 
66 
67 
68 
69 
70 
A B C D E F G H I J 
Calculation of creep for a given stress and temperature profile file = AMR-F0155-V1.xls 
Checks for SCC Sheet = Creep-Rd 
TC Unc 0.9101584 Input 
Room TC 
stress 15.601665 Input 
Resultant 
strain 1.45E-02 Output 
Columns B,C (with WP temperature shift = 0) used for Figure 5 
YMP time total Time T,C Temperature Stress Time, hrs Total strain % % % 
Yrs C K Mpa hrs run sum e(Ti,ti) e-glide e-coble 
0 350 
0.50 330 613.2 31.89 4.38E+03 9.36E-03 9.36E-03 9.09E-03 2.69E-04 
1.0 322 595.2 30.95 8.76E+03 1.12E-02 3.77E-03 3.58E-03 1.91E-04 
2.0 310 583.2 30.33 1.75E+04 1.25E-02 2.48E-03 2.29E-03 1.85E-04 
3.0 295 568.2 29.55 2.63E+04 1.28E-02 8.83E-04 7.76E-04 1.07E-04 
4.0 285 558.2 29.03 3.50E+04 1.29E-02 4.41E-04 3.67E-04 7.35E-05 
6.0 270 543.2 28.25 5.26E+04 1.29E-02 1.48E-04 1.09E-04 3.90E-05 
8.0 260 533.2 27.73 7.01E+04 1.29E-02 7.20E-05 4.68E-05 2.52E-05 
10.0 252 525.2 27.31 8.76E+04 1.30E-02 4.02E-05 2.30E-05 1.73E-05 
20.000 240 513.2 26.69 1.75E+05 1.30E-02 2.43E-05 1.07E-05 1.36E-05 
20.010 350 623.2 32.41 1.75E+05 1.31E-02 4.97E-01 4.78E-01 1.86E-02 
20.068 350 623.2 32.41 1.76E+05 1.40E-02 4.98E-01 4.79E-01 1.87E-02 
0 20.07 57 330.3 17.18 1.76E+05 1.40E-02 1.98E-15 8.26E-21 1.98E-15 
50 70.07 110 382.8 19.91 6.14E+05 1.40E-02 4.21E-11 1.75E-14 4.21E-11 
50.2 70.27 192 464.7 24.17 6.16E+05 1.40E-02 7.18E-07 5.04E-08 6.68E-07 
50.4 70.47 206 479.1 24.91 6.17E+05 1.40E-02 3.02E-06 4.13E-07 2.60E-06 
50.6 70.67 221 493.9 25.69 6.19E+05 1.40E-02 1.30E-05 3.20E-06 9.76E-06 
50.8 70.87 236 508.8 26.46 6.21E+05 1.40E-02 5.59E-05 2.20E-05 3.39E-05 
51 71.07 251 523.7 27.23 6.23E+05 1.40E-02 2.46E-04 1.37E-04 1.10E-04 
52 72.07 271 544.2 28.30 6.31E+05 1.40E-02 1.98E-03 1.47E-03 5.07E-04 
53 73.07 280 553.6 28.79 6.40E+05 1.41E-02 5.11E-03 4.12E-03 9.86E-04 
55 75.07 278 551.0 28.66 6.58E+05 1.42E-02 4.06E-03 3.21E-03 8.49E-04 
57 77.07 276 548.7 28.54 6.75E+05 1.43E-02 3.31E-03 2.57E-03 7.43E-04 
59 79.07 273 546.5 28.42 6.93E+05 1.43E-02 2.73E-03 2.07E-03 6.53E-04 
60 80.07 272 545.5 28.37 7.01E+05 1.44E-02 2.48E-03 1.87E-03 6.13E-04 
70 90.07 262 535.0 27.83 7.89E+05 1.45E-02 9.81E-04 6.54E-04 3.26E-04 
80 100.07 238 511.3 26.59 8.77E+05 1.45E-02 1.01E-04 4.25E-05 5.85E-05 
90 110.07 222 495.1 25.75 9.64E+05 1.45E-02 2.26E-05 5.82E-06 1.68E-05 
100 120.07 206 479.0 24.91 1.05E+06 1.45E-02 5.10E-06 6.97E-07 4.41E-06 
110 130.07 193 466.2 24.24 1.14E+06 1.45E-02 1.55E-06 1.17E-07 1.43E-06 
120 140.07 182 455.1 23.67 1.23E+06 1.45E-02 5.37E-07 2.31E-08 5.14E-07 
130 150.07 172 445.3 23.16 1.31E+06 1.45E-02 2.05E-07 5.18E-09 2.00E-07 
140 160.07 164 437.3 22.74 1.40E+06 1.45E-02 9.08E-08 1.45E-09 8.94E-08 
150 170.07 159 432.3 22.48 1.49E+06 1.45E-02 5.52E-08 6.56E-10 5.46E-08 
160 180.07 155 427.8 22.25 1.58E+06 1.45E-02 3.50E-08 3.16E-10 3.47E-08 
180 200.07 146 419.4 21.81 1.75E+06 1.45E-02 1.46E-08 7.79E-11 1.45E-08 
205 225.07 141 414.2 21.54 1.97E+06 1.45E-02 8.67E-09 3.30E-11 8.63E-09 
232 252.07 136 409.3 21.29 2.21E+06 1.45E-02 5.33E-09 1.48E-11 5.32E-09 
250 270.07 134 406.7 21.15 2.37E+06 1.45E-02 4.07E-09 9.42E-12 4.07E-09 
265 285.07 132 404.7 21.05 2.50E+06 1.45E-02 3.34E-09 6.76E-12 3.34E-09 
310 330.07 127 400.0 20.80 2.89E+06 1.45E-02 2.11E-09 3.09E-12 2.11E-09 
350 370.07 123 396.6 20.63 3.24E+06 1.45E-02 1.50E-09 1.72E-12 1.50E-09 
365 385.07 122 395.4 20.56 3.37E+06 1.45E-02 1.33E-09 1.40E-12 1.33E-09 
450 470.07 116 389.3 20.25 4.12E+06 1.45E-02 7.10E-10 4.81E-13 7.10E-10 
480 500.07 114 387.3 20.14 4.38E+06 1.45E-02 5.68E-10 3.30E-13 5.67E-10 
550 570.07 110 383.3 19.93 4.99E+06 1.45E-02 3.68E-10 1.58E-13 3.67E-10 
615 635.07 107 379.7 19.75 5.56E+06 1.45E-02 2.46E-10 8.08E-14 2.46E-10 
650 670.07 105 378.2 19.67 5.87E+06 1.45E-02 2.06E-10 6.00E-14 2.06E-10 
695 715.07 103 376.2 19.56 6.26E+06 1.45E-02 1.63E-10 4.05E-14 1.63E-10 
750 770.07 101 374.1 19.45 6.75E+06 1.45E-02 1.29E-10 2.71E-14 1.29E-10 
790 810.07 99 372.6 19.38 7.10E+06 1.45E-02 1.08E-10 2.02E-14 1.08E-10 
850 870.07 97 370.6 19.27 7.62E+06 1.45E-02 8.58E-11 1.36E-14 8.58E-11 
900 920.07 96 369.0 19.19 8.06E+06 1.45E-02 7.12E-11 9.96E-15 7.12E-11 
950 970.07 95 367.7 19.12 8.50E+06 1.45E-02 6.17E-11 7.77E-15 6.16E-11 
1000 1020.07 93 366.5 19.06 8.94E+06 1.45E-02 5.32E-11 6.03E-15 5.32E-11 
SCC flag 0 % 32.41 Limited Strain= 1.45E-02 
Test Problem eq. 11 eq.12 
YMP time total Time T,C Temperature Stress Time, hrs Total strain % % % 
Yrs C K Mpa hrs run sum e(Ti,ti) e-glide e-coble 
0.11 360 633.2 118.00 9.60E+02 0.517 5.17E-01 5.16E-01 6.23E-04 
Test problem answer = 0.517

ANL-WIS-MD-000007 REV 00 II - 13 April 2000 
Table II-6b. Listing of Top Rows of Sheet: Creep-Rod (Col. J-Q) 
123 
4
56789
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 
61 
62 
63 
64 
65 
66 
67 
68 
69 
70 
J K L M N O P Q 
file = AMR-F0155-V1.xls 
Sheet = Creep-Rd 
% fraction fraction 
% Creep tot,t(i-1) t(i-1) t(i-1) fraction fraction 
e-coble e(Ti,ti-1) e-glide e-coble E Tp Coe Ec Es-gl 
2.69E-04 na na na 7.81E+10 7.96E-23 6.13E-10 1.90E-09 
1.91E-04 1.89E-03 1.79E-05 9.53E-07 7.92E+10 1.71E-23 2.18E-10 3.73E-10 
1.85E-04 1.24E-03 1.15E-05 9.23E-07 7.99E+10 5.81E-24 1.05E-10 1.19E-10 
1.07E-04 5.89E-04 5.17E-06 7.13E-07 8.08E+10 1.41E-24 4.07E-11 2.69E-11 
7.35E-05 3.31E-04 2.75E-06 5.52E-07 8.14E+10 5.29E-25 2.10E-11 9.53E-12 
3.90E-05 9.85E-05 7.25E-07 2.60E-07 8.23E+10 1.13E-25 7.43E-12 1.88E-12 
2.52E-05 5.40E-05 3.51E-07 1.89E-07 8.29E+10 3.85E-26 3.60E-12 6.07E-13 
1.73E-05 3.22E-05 1.84E-07 1.38E-07 8.33E+10 1.58E-26 1.97E-12 2.38E-13 
1.36E-05 1.21E-05 5.36E-08 6.79E-08 8.41E+10 3.93E-27 7.75E-13 5.56E-14 
1.86E-02 4.97E-01 4.78E-03 1.86E-04 7.75E+10 1.80E-22 1.06E-09 4.53E-09 
1.87E-02 4.97E-01 4.78E-03 1.86E-04 7.75E+10 1.80E-22 1.06E-09 4.53E-09 
1.98E-15 1.98E-15 8.26E-23 1.98E-17 9.50E+10 9.52E-42 1.13E-22 4.27E-29 
4.21E-11 1.21E-11 5.01E-17 1.21E-13 9.19E+10 4.00E-36 6.86E-19 2.59E-23 
6.68E-07 7.16E-07 5.03E-10 6.66E-09 8.70E+10 6.92E-30 1.08E-14 7.44E-17 
2.60E-06 3.01E-06 4.12E-09 2.60E-08 8.61E+10 5.21E-29 4.22E-14 6.09E-16 
9.76E-06 1.29E-05 3.19E-08 9.74E-08 8.52E+10 3.69E-28 1.58E-13 4.70E-15 
3.39E-05 5.58E-05 2.20E-07 3.38E-07 8.43E+10 2.34E-27 5.46E-13 3.23E-14 
1.10E-04 2.45E-04 1.36E-06 1.09E-06 8.34E+10 1.33E-26 1.76E-12 1.99E-13 
5.07E-04 1.95E-03 1.45E-05 5.00E-06 8.22E+10 1.27E-25 8.03E-12 2.12E-12 
9.86E-04 5.04E-03 4.06E-05 9.73E-06 8.16E+10 3.34E-25 1.54E-11 5.88E-12 
8.49E-04 3.95E-03 3.13E-05 8.26E-06 8.18E+10 2.57E-25 1.29E-11 4.46E-12 
7.43E-04 3.23E-03 2.50E-05 7.23E-06 8.19E+10 2.03E-25 1.10E-11 3.47E-12 
6.53E-04 2.66E-03 2.02E-05 6.36E-06 8.21E+10 1.61E-25 9.42E-12 2.73E-12 
6.13E-04 2.45E-03 1.85E-05 6.06E-06 8.21E+10 1.44E-25 8.75E-12 2.43E-12 
3.26E-04 8.72E-04 5.82E-06 2.90E-06 8.28E+10 4.73E-26 4.14E-12 7.54E-13 
5.85E-05 9.10E-05 3.83E-07 5.27E-07 8.42E+10 3.15E-27 6.68E-13 4.41E-14 
1.68E-05 2.06E-05 5.29E-08 1.53E-07 8.51E+10 4.29E-28 1.74E-13 5.48E-15 
4.41E-06 4.68E-06 6.39E-09 4.04E-08 8.61E+10 5.16E-29 4.19E-14 6.02E-16 
1.43E-06 1.43E-06 1.08E-09 1.32E-08 8.69E+10 8.60E-30 1.25E-14 9.33E-17 
5.14E-07 4.99E-07 2.15E-10 4.77E-09 8.75E+10 1.68E-30 4.19E-15 1.71E-17 
2.00E-07 1.91E-07 4.83E-11 1.86E-09 8.81E+10 3.73E-31 1.52E-15 3.58E-18 
8.94E-08 8.52E-08 1.36E-11 8.38E-10 8.86E+10 1.03E-31 6.37E-16 9.39E-19 
5.46E-08 5.20E-08 6.17E-12 5.14E-10 8.89E+10 4.51E-32 3.66E-16 4.00E-19 
3.47E-08 3.30E-08 2.98E-12 3.27E-10 8.92E+10 2.11E-32 2.20E-16 1.82E-19 
1.45E-08 1.31E-08 7.01E-13 1.30E-10 8.97E+10 4.93E-33 8.26E-17 4.04E-20 
8.63E-09 7.70E-09 2.94E-13 7.68E-11 9.00E+10 1.92E-33 4.38E-17 1.52E-20 
5.32E-09 4.76E-09 1.32E-13 4.75E-11 9.03E+10 7.91E-34 2.41E-17 6.08E-21 
4.07E-09 3.80E-09 8.79E-14 3.79E-11 9.04E+10 4.79E-34 1.72E-17 3.62E-21 
3.34E-09 3.17E-09 6.40E-14 3.16E-11 9.06E+10 3.29E-34 1.34E-17 2.46E-21 
2.11E-09 1.83E-09 2.67E-14 1.82E-11 9.08E+10 1.34E-34 7.30E-18 9.73E-22 
1.50E-09 1.34E-09 1.54E-14 1.34E-11 9.10E+10 6.82E-35 4.63E-18 4.84E-22 
1.33E-09 1.28E-09 1.34E-14 1.27E-11 9.11E+10 5.35E-35 3.93E-18 3.76E-22 
7.10E-10 5.82E-10 3.94E-15 5.81E-12 9.15E+10 1.57E-35 1.72E-18 1.06E-22 
5.67E-10 5.34E-10 3.10E-15 5.33E-12 9.16E+10 1.03E-35 1.29E-18 6.85E-23 
3.67E-10 3.22E-10 1.39E-15 3.22E-12 9.18E+10 4.44E-36 7.36E-19 2.88E-23 
2.46E-10 2.21E-10 7.25E-16 2.21E-12 9.21E+10 2.08E-36 4.42E-19 1.32E-23 
2.06E-10 1.95E-10 5.68E-16 1.95E-12 9.21E+10 1.48E-36 3.51E-19 9.29E-24 
1.63E-10 1.53E-10 3.80E-16 1.53E-12 9.23E+10 9.50E-37 2.61E-19 5.88E-24 
1.29E-10 1.20E-10 2.52E-16 1.20E-12 9.24E+10 5.97E-37 1.91E-19 3.65E-24 
1.08E-10 1.03E-10 1.92E-16 1.03E-12 9.25E+10 4.29E-37 1.53E-19 2.59E-24 
8.58E-11 7.99E-11 1.27E-16 7.99E-13 9.26E+10 2.73E-37 1.13E-19 1.63E-24 
7.12E-11 6.73E-11 9.42E-17 6.73E-13 9.27E+10 1.90E-37 8.83E-20 1.12E-24 
6.16E-11 5.85E-11 7.37E-17 5.85E-13 9.28E+10 1.42E-37 7.25E-20 8.31E-25 
5.32E-11 5.06E-11 5.73E-17 5.05E-13 9.28E+10 1.06E-37 5.95E-20 6.13E-25 
eq.12 Pa coble-rt 9b glide,lft 9b 
% t(i-1) t(i-1) t(i-1) fraction fraction 
e-coble e(Ti,ti-1) e-glide e-coble E Tp Coe Ec Es-gl 
6.23E-04 na na na 7.69E+10 3.97E-22 6.48E-09 9.47E-07

ANL-WIS-MD-000007 REV 00 II - 14 April 2000 
Table II-7. Listing of Top Rows of Sheer: Creep-WP 
1
2
34
5
67
89
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
A B C D E F G H I J K L M N O 
file = AMR-F0155-V1.xls 
Sheet = creep-WP 
Temp 
range 0.135006637 
figure 1 from cdf&stress 
Zone1 Zone1 Zone2 Zone2 Zone 3 Zone 3 Zone 4 Zone 4 Zone 5 Zone 5 Zone 6 Zone 6 
CDF 
Case 
Number 
Stress, 
Mpa 
Temperat 
ure adj. Creep 
Temperature 
adj. Creep 
Temperat 
ure adj. Creep 
Temperat 
ure adj. Creep 
Temperat 
ure adj. Creep 
Temperat 
ure adj. Creep 
100.00 278 146.34 0.928 99.000 0.998 99.000 0.992 99.000 1.004 99.000 0.933 99.000 1.015 99.000 
99.95 1814 137.15 0.935 99.000 0.863 99.000 0.877 99.000 1.109 100.000 0.962 99.000 1.028 99.000 
99.90 1653 131.40 1.030 99.000 0.929 99.000 0.998 99.000 1.036 99.000 1.048 99.000 1.072 99.000 
99.85 1282 122.57 1.112 100.000 1.112 100.000 0.967 99.000 1.108 100.000 1.072 99.000 0.985 99.000 
99.80 837 108.37 0.947 99.000 1.029 99.000 0.921 99.000 0.964 99.000 1.071 99.000 0.998 99.000 
99.75 730 105.69 1.029 99.000 1.108 99.000 1.058 99.000 0.921 99.000 0.863 99.000 0.853 99.000 
99.70 1368 105.12 1.007 99.000 1.032 99.000 0.962 99.000 0.906 99.000 1.074 99.000 1.003 99.000 
99.65 51 98.11 1.085 99.000 1.095 99.000 0.884 99.000 1.103 99.000 1.022 99.000 1.069 99.000 
99.60 1660 96.79 0.907 99.000 1.089 99.000 0.916 99.000 1.101 99.000 1.064 99.000 0.952 99.000 
99.55 484 94.99 1.010 99.000 1.046 99.000 1.100 99.000 1.080 99.000 1.026 99.000 0.973 99.000 
99.50 242 94.75 0.868 99.000 0.920 99.000 0.938 99.000 0.960 99.000 0.929 99.000 1.041 99.000 
99.45 1675 93.75 0.939 99.000 0.961 99.000 1.088 99.000 0.855 99.000 1.050 99.000 0.987 99.000 
99.40 346 92.04 0.912 99.000 0.935 99.000 0.935 99.000 1.021 99.000 1.057 99.000 0.878 99.000 
99.35 756 91.45 0.988 99.000 1.090 99.000 1.027 99.000 1.064 99.000 0.872 99.000 0.935 99.000 
99.30 994 89.98 0.936 99.000 1.121 99.000 0.958 99.000 1.034 99.000 1.077 99.000 0.834 99.000 
99.25 881 89.81 0.893 99.000 0.971 99.000 0.896 99.000 0.951 99.000 1.029 99.000 0.895 99.000 
99.20 860 87.96 1.006 99.000 1.066 99.000 0.943 99.000 0.951 99.000 0.910 99.000 1.054 99.000 
99.15 1000 87.70 0.874 99.000 1.078 99.000 0.874 99.000 0.960 99.000 1.005 99.000 1.037 99.000 
99.10 1848 87.17 1.103 99.000 0.899 99.000 1.068 99.000 1.075 99.000 0.940 99.000 0.819 99.000 
99.05 1270 87.08 1.104 99.000 0.897 99.000 1.082 99.000 1.012 99.000 1.082 99.000 0.914 99.000 
99.00 1418 87.07 0.879 99.000 1.022 99.000 1.110 99.000 1.056 99.000 0.851 99.000 0.976 99.000 
98.95 1274 85.20 0.919 2.083 1.066 4.503 0.877 2.049 0.868 2.043 0.856 2.036 0.843 2.030 
98.90 769 84.03 0.926 2.007 0.897 1.982 1.098 7.642 1.095 7.306 0.933 2.014 1.004 2.306 
98.85 1289 83.59 1.032 2.716 0.986 2.132 0.955 2.018 0.988 2.142 0.969 2.054 0.900 1.956 
98.80 1696 83.39 0.972 2.050 0.927 1.965 0.910 1.950 1.090 6.282 1.046 3.110 0.890 1.935 
98.75 1502 83.14 0.994 2.144 1.026 2.550 1.103 8.085 1.110 9.561 1.028 2.584 0.985 2.089 
98.70 1851 82.22 1.078 4.691 1.043 2.852 0.923 1.886 1.008 2.202 0.870 1.846 0.944 1.909 
98.65 1051 82.15 1.014 2.266 1.083 5.153 0.943 1.904 0.890 1.855 0.861 1.837 0.881 1.849 
98.60 258 80.42 1.044 2.666 1.009 2.069 1.031 2.365 1.024 2.243 0.861 1.732 1.061 3.266 
98.55 1129 78.05 0.911 1.633 0.938 1.657 1.059 2.849 0.855 1.598 1.079 3.826 0.910 1.633 
98.50 905 77.80 0.997 1.793 0.940 1.646 0.859 1.587 1.102 5.834 1.068 3.182 0.850 1.583 
98.45 655 77.70 1.127 10.227 1.060 2.832 1.083 4.087 1.097 5.296 0.892 1.601 1.050 2.523 
98.40 1065 77.59 0.989 1.742 1.012 1.884 0.892 1.595 0.904 1.604 0.939 1.633 0.975 1.693 
98.35 1723 77.39 1.078 3.679 0.957 1.644 0.943 1.626 0.868 1.569 0.924 1.609 0.948 1.632

ANL-WIS-MD-000007 REV 00 II - 15 April 2000 
Table II-8. Listing of top Rows of Sheet: Fail- Calc 
12 
3456789
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
A B C D E F G H I J K L M 
file = AMR-F0155-V1.xls 
sheet = fail calc Creep and SSC, table used for Figure 8 Creep only 
Shift 
WP Peak 
TC 
Upper 
Limit 
Mean fail 
fra. Lower limit Upper Limit 
Mean fail 
fra. 
Lower 
limit 
-150 127 0.1942 0.0244 0.0105 
-100 177 0.1942 0.0244 0.0105 0.19415714 0.019552 0.001381 
-50 227 0.1949 0.0244 0.0105 
-25 252 0.2057 0.0258 0.0105 
-15 262 0.2156 0.0267 0.0105 
0 277 0.2479 0.0339 0.0106 
15 292 0.3264 0.0604 0.0120 
20 297 0.3628 0.0783 0.0133 
25 302 0.4080 0.0987 0.0173 
35 312 0.5052 0.1622 0.0370 
50 327 0.6379 0.3019 0.1067 
75 352 0.8227 0.5567 0.3424 
100 377 0.9553 0.7789 0.5920 
125 402 0.9970 0.9302 0.7986 
135 412 0.9985 0.9658 0.8720 
Above Table used for Fig. 8 
Strain 
Uncertanty 0.8 Summary 0 277 0.2479 0.0339 0.0106 
Upper fail 
index 0.4 Product 0.0053 0.0009 0.0002 0.0079 0.0014 0.0003 
lower fail 
index 11.7 Weight 0.0191 0.0191 0.0191 0.0286 0.0286 0.0286 
Fail Fract. 0.2790 0.0450 0.0105 0.2755 0.0495 0.0105 
Zone1 Zone1 Zone1 Zone1 Zone1 Zone2 Zone2 Zone2 Zone2 Zone2 
Case 
Number Stress Creep Fail criteria 
Upper Fail 
index 
Mean fail 
index lower fail index Creep 
Fail 
criteria 
Upper Fail 
index 
Mean fail 
index 
lower fail 
index 
CCDF 
Case 
Number Mpa 
100.00 278 146.34 99.00 0.95 1 1 1 99.00 8.97 1 1 1 
99.95 1814 137.15 99.00 4.70 1 1 1 99.00 4.70 1 1 1 
99.90 1653 131.40 99.00 2.16 1 1 1 99.00 4.70 1 1 1 
99.85 1282 122.57 100.00 0.65 1 1 1 100.00 2.02 1 1 1 
99.80 837 108.37 99.00 2.58 1 1 1 99.00 5.25 1 1 1 
99.75 730 105.69 99.00 1.04 1 1 1 99.00 1.80 1 1 1 
99.70 1368 105.12 99.00 2.40 1 1 1 99.00 1.10 1 1 1 
99.65 51 98.11 99.00 0.79 1 1 1 99.00 9.44 1 1 1 
99.60 1660 96.79 99.00 4.70 1 1 1 99.00 6.00 1 1 1 
99.55 484 94.99 99.00 0.83 1 1 1 99.00 0.90 1 1 1 
99.50 242 94.75 99.00 2.41 1 1 1 99.00 2.43 1 1 1 
99.45 1675 93.75 99.00 1.01 1 1 1 99.00 4.37 1 1 1

ANL-WIS-MD-000007 REV 00 II - 16 April 2000 
Table II-9. Listing of Top Rows of Sheet: Rand # 
1
23 
45
67
89
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
A B C D E F G H I J K L M N O P 
This sheet contains columns of random numbers used for the Fuel Rod Characteristics analysis. file = AMR-F0155-V1.xls 
Each column is used for the calculation noted at the column title. Sheet = Rand # Test mean= 0.499266 
Test median= 0.498918 
Temp C 
Zone 1 
Temp C 
Zone 2 C Fail 1 C fail 2 C fail3 
Temp C 
Zone 3 
Temp C 
Zone 4 
Temp C 
Zone 5 
Temp C 
Zone 6 
Creep 
Zone 1 
Creep 
Zone 2 
Creep 
Zone 3 
Creep 
Zone 4 
Creep 
Zone 5 
Creep 
Zone 6 
sample 
Numb. 
0.232125157 0.516956 0.898514 0.341278 0.252533 0.511765 0.5829651 0.372403 0.774887 0.907806 0.565085 0.78631 0.291068 0.008969 0.304836 278 
0.260801258 0.013344 0.202301 0.325831 0.527147 0.080065 0.9805385 0.483736 0.827744 0.082132 0.156488 0.477543 0.877331 0.632386 0.522495 1814 
0.611550437 0.260707 0.60249 0.961042 0.184783 0.532937 0.7045435 0.814733 0.997821 0.538518 0.795879 0.497769 0.025485 0.024826 0.676389 1653 
0.916302715 0.942135 0.962604 0.856405 0.362758 0.417997 0.9748709 0.904772 0.658456 0.001064 0.642174 0.045457 0.446272 0.929563 0.921059 1282 
0.303152686 0.633244 0.464965 0.313843 0.050209 0.245376 0.4313241 0.902375 0.707738 0.37262 0.800444 0.416413 0.337563 0.113341 0.489146 837 
0.608346534 0.928968 0.860576 0.868715 0.571496 0.758004 0.2687656 0.10529 0.141523 0.801439 0.531167 0.694463 0.556408 0.709841 0.083036 730 
0.525643003 0.645791 0.562003 0.642536 0.809432 0.398187 0.2128283 0.911822 0.729427 0.674119 0.837233 0.223768 0.974851 0.740532 0.542972 1368 
0.814069086 0.878078 0.942233 0.120734 0.667336 0.108182 0.9557985 0.715991 0.985694 0.714568 0.147389 0.527129 0.468213 0.583775 0.009915 51 
0.154437886 0.855915 0.204424 0.209041 0.862437 0.228251 0.9494977 0.875037 0.527814 0.589483 0.100436 0.041125 0.281319 0.57724 0.142589 1660 
0.537888612 0.697416 0.931116 0.541668 0.418117 0.918156 0.87147 0.731154 0.609767 0.678485 0.347365 0.242657 0.302111 0.639761 0.817272 484 
0.012881751 0.224804 0.523471 0.558834 0.174458 0.311268 0.4175848 0.359659 0.877115 0.840512 0.939072 0.99203 0.449321 0.419228 0.568701 242 
0.272310328 0.380314 0.877117 0.088857 0.152823 0.872308 0.0213482 0.821689 0.667509 0.167748 0.327253 0.377774 0.527356 0.827036 0.011365 1675 
0.173095511 0.282452 0.385406 0.57389 0.332895 0.299575 0.6460735 0.849652 0.239043 0.217598 0.393851 0.968861 0.46561 0.171292 0.892369 346 
0.455396338 0.860426 0.220105 0.270136 0.729667 0.643266 0.8090247 0.141085 0.461249 0.173429 0.471333 0.048189 0.146099 0.960079 0.823007 756 
0.262097141 0.974244 0.411747 0.358742 0.282369 0.384184 0.6968916 0.923988 0.064526 0.499425 0.370053 0.268013 0.293764 0.908877 0.852225 994 
0.104180317 0.415629 0.817962 0.885715 0.273157 0.154268 0.3817272 0.741897 0.304504 0.662366 0.1651 0.38071 0.782422 0.280987 0.363107 881 
0.523601867 0.770218 0.7902 0.472109 0.191046 0.330107 0.3839852 0.285223 0.928834 0.207384 0.519091 0.060718 0.954674 0.223067 0.586194 860 
0.03158437 0.814461 0.486774 0.96999 0.683511 0.071018 0.4166439 0.650973 0.863908 0.266536 0.415849 0.027207 0.887569 0.091811 0.03196 1000 
0.882318223 0.148933 0.428463 0.786398 0.801301 0.79784 0.8507878 0.400024 0.005518 0.866388 0.354817 0.844226 0.268876 0.111094 0.183474 1848 
0.884378554 0.140584 0.059966 0.288652 0.727938 0.848031 0.6145644 0.944955 0.379771 0.264858 0.288673 0.696882 0.932439 0.348612 0.036161 1270 
0.051703482 0.605217 0.459057 0.59192 0.056347 0.954266 0.7790187 0.058199 0.623037 0.076714 0.431409 0.285329 0.597299 0.555278 0.952178 1418 
0.201558558 0.772629 0.859033 0.338219 0.679984 0.080997 0.0693279 0.078083 0.102318 0.861205 0.600412 0.254087 0.481931 0.413529 0.658711 1274 
0.226445835 0.141331 0.059152 0.853156 0.680851 0.907389 0.9279805 0.372846 0.731816 0.9021 0.847846 0.523331 0.754028 0.690311 0.415791 769 
0.617316359 0.474331 0.226888 0.000613 0.242927 0.373387 0.5228757 0.510876 0.326576 0.405368 0.553833 0.134339 0.720795 0.381479 0.501697 1289 
0.39518612 0.25315 0.135734 0.505745 0.398258 0.205293 0.9070353 0.806201 0.285979 0.700445 0.742133 0.162156 0.067707 0.198539 0.138376 1696 
0.476381941 0.622672 0.753326 0.573011 0.439503 0.925896 0.9826611 0.737173 0.657319 0.276697 0.57785 0.746092 0.642148 0.838553 0.891215 1502 
0.788442292 0.684409 0.262751 0.63772 0.094331 0.253119 0.5999432 0.129762 0.496581 0.377893 0.674795 0.605688 0.578291 0.742935 0.903628 1851 
0.553292172 0.835082 0.720968 0.003514 0.768129 0.329453 0.1537642 0.098457 0.251898 0.404138 0.031788 0.852339 0.692154 0.854748 0.815359 1051 
0.662464615 0.56007 0.257341 0.857962 0.114005 0.657153 0.6566995 0.09525 0.954779 0.318068 0.343866 0.524909 0.427381 0.192976 0.212502 258 
0.168922185 0.294365 0.197952 0.122797 0.274607 0.762047 0.0203188 0.931454 0.3647 0.390098 0.178208 0.207206 0.779757 0.029485 0.826781 1129

ANL-WIS-MD-000007 REV 00 II - 17 April 2000 
Table II-10a. Listing of Top Rows of Sheet: TempC 
1234
5
6
7
89
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
A B C D E F G H I J K L 
file = AMR-F0155-V1.xls 
Sheet = TmpC (Temperature, C) 
Temperature Calculations Components of below table shown on Fig. 2, Table 2 
radal zone 1 2 3 4 5 6 sum 
Fraction 1.91E-02 2.86E-02 0.11429 2.10E-01 0.33333 0.29524 1.0000 
average 
TC Adj 
(inWP). 1 9.334E-01 0.887987 0.819805 0.660714 0.446429 
TC adj 
(gross) 1 0.99334703 0.988804 0.981988 0.966086 0.944667 
YMPTime 
WP Wall 
TC 
inside WO 
Delta TC 
Zone1, 
Center rod 
TC Z 2 Z 3 Z 4 Z 5 Z 6 
0 24.61 38.20 62.81 60.27 58.53 55.93 49.85 41.66 
50 82.26 38.20 120.46 117.92 116.18 113.58 107.50 99.31 
50.2 176.54 33.90 210.44 208.18 206.64 204.33 198.93 191.67 
50.4 193.16 33.10 226.26 224.06 222.55 220.30 215.03 207.94 
50.6 209.79 32.80 242.59 240.40 238.91 236.67 231.46 224.43 
50.8 226.41 32.50 258.91 256.75 255.27 253.05 247.88 240.92 
51 243.03 32.20 275.23 273.09 271.63 269.43 264.31 257.41 
52 266.46 31.40 297.86 295.77 294.34 292.20 287.20 280.47 
53 277.33 30.80 308.13 306.08 304.68 302.58 297.68 291.08 
55 275.61 29.70 305.31 303.33 301.98 299.95 295.23 288.86 
57 273.88 28.90 302.78 300.85 299.54 297.57 292.97 286.78 
59 272.15 28.20 300.35 298.47 297.19 295.27 290.78 284.74 
60 271.29 27.90 299.19 297.33 296.06 294.16 289.72 283.74 
70 262.65 25.10 287.75 286.08 284.94 283.23 279.23 273.86 
80 238.65 23.00 261.65 260.12 259.07 257.50 253.84 248.92 
90 222.46 21.40 243.86 242.44 241.47 240.01 236.60 232.02 
100 206.28 19.90 226.18 224.85 223.95 222.59 219.43 215.16 
110 193.19 18.90 212.09 210.83 209.97 208.68 205.68 201.63 
120 181.91 18.00 199.91 198.71 197.89 196.67 193.80 189.95 
130 172.06 17.10 189.16 188.02 187.24 186.07 183.35 179.69 
140 164.01 16.30 180.31 179.23 178.48 177.37 174.78 171.29 
150 159.43 15.40 174.83 173.81 173.11 172.06 169.61 166.31 
160 154.86 15.03 169.89 168.89 168.20 167.18 164.79 161.57 
180 146.41 14.29 160.70 159.75 159.10 158.13 155.86 152.79 
205 141.57 13.37 154.94 154.05 153.44 152.53 150.40 147.54 
232 137.27 12.37 149.63 148.81 148.25 147.41 145.44 142.79 
250 134.99 11.70 146.69 145.91 145.38 144.58 142.72 140.22 
265 133.10 11.43 144.53 143.77 143.25 142.47 140.65 138.20 
310 128.79 10.62 139.41 138.70 138.22 137.49 135.80 133.53 
350 125.73 9.90 135.63 134.97 134.52 133.84 132.27 130.15 
365 124.58 9.71 134.29 133.64 133.20 132.54 130.99 128.91 
450 119.04 8.60 127.64 127.07 126.68 126.09 124.72 122.88 
480 117.09 8.30 125.39 124.84 124.46 123.89 122.57 120.79 
550 113.40 7.60 121.00 120.49 120.15 119.63 118.42 116.79 
615 109.97 7.15 117.12 116.64 116.32 115.83 114.69 113.16 
650 108.49 6.90 115.39 114.93 114.62 114.15 113.05 111.57 
695 106.59 6.59 113.17 112.73 112.43 111.98 110.94 109.53 
750 104.68 6.20 110.88 110.46 110.18 109.76 108.77 107.44 
790 103.29 5.96 109.25 108.85 108.58 108.17 107.22 105.95 
850 101.45 5.60 107.05 106.67 106.42 106.04 105.15 103.95 
900 99.91 5.40 105.31 104.95 104.71 104.34 103.48 102.32 
950 98.71 5.20 103.91 103.57 103.33 102.98 102.15 101.04 
1000 97.52 5.00 102.52 102.18 101.96 101.61 100.82 99.75 
Columns A,B E F used if Fig. 4

ANL-WIS-MD-000007 REV 00 II - 18 April 2000 
Table II-10b. Listing of Rows 53 to 72 of Sheet: TempC 
53 
54 
55 
56 
57 
58 
59 
60 
61 
62 
63 
64 
65 
66 
67 
68 
69 
70 
71 
72 
A B C D E F G H I J K L 
file = AMR-F0155-V1.xls 
Sheet = TmpC (Temperature, C) 
WP wall 
shift TC 0.00E+00 (defined fail calc sheet) 
Calculation of shaping factors for temperatures across WP 
Location 
Temperatu 
re 
points 
averaged Zone TC 
delta TC 
from 
surface 
reduction 
factor 
1 313.4 1 313.4 30.8 1 
2 309.3 1&2 311.35 28.75 0.9334416 
3 308.8 5&6 309.95 27.35 0.887987 
4 308.8 6&7 307.85 25.25 0.8198052 
5 309 9&10 302.95 20.35 0.6607143 
6 310.9 10&11 296.35 13.75 0.4464286 
7 304.8 
8 304.3 
9 304.1 
10 301.8 
11 290.9 
12 289.8 
13 283.4 
14 282.9 
15 282.6

ANL-WIS-MD-000007 REV 00 II - 19 April 2000 
Table II-11a. Listing of Top Rows of Sheet: TempC2 
12 
3
4
56789
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
A B C D E F G H I J K L M N O P Q 
file = AMR-F0155-V1.xls sheet = TempC2 
Takes input temperatures for WP and interior and aligns them up to the same time steps 
Average Waste 
Package Surface 
Temp (C) 
RIP_Tavg_csnf_ 
dsps_bc_bin20- 
60_mean Radial Temperature Distribution for EDA II (Axial Peaking Factor of 1.102) 
Time(yr) 
Bin 
Weight= 
0.528528 
Time, Yr T,C 1 2 3 4 5 6 7 8 9 10 11 12 
0.0 24.6 50 4374.9 147.5 139.8 139.1 139.1 139.5 145.0 135.3 134.8 134.5 135.1 119.8 118.6 
1.0 78.7 50.1 4369.5 236.9 231.5 230.9 231.0 231.2 234.4 226.9 226.5 226.2 224.9 212.5 211.4 
2.0 87.2 50.2 4364.2 263.0 258.0 257.4 257.4 257.7 260.4 253.2 252.8 252.5 250.7 238.4 237.3 
5.0 95.0 50.3 4359.0 273.0 268.1 267.5 267.6 267.8 270.4 263.4 262.9 262.6 260.8 248.8 247.6 
30.0 90.6 50.4 4353.5 278.8 274.0 273.5 273.5 273.7 276.2 269.3 268.9 268.6 266.7 254.7 253.6 
40.0 85.7 50.5 4348.3 282.9 278.1 277.6 277.6 277.9 280.3 273.4 273.0 272.7 270.7 258.9 257.8 
50.0 82.3 50.6 4342.8 286.0 281.3 280.8 280.8 281.0 283.4 276.6 276.2 275.9 273.9 262.1 261.0 
50.2 176.5 50.7 4337.6 288.7 284.0 283.5 283.5 283.8 286.1 279.4 278.9 278.6 276.5 264.9 263.8 
51.0 243.0 50.8 4332.3 291.0 286.4 285.9 285.9 286.1 288.4 281.8 281.3 281.0 278.9 267.3 266.2 
52.0 266.5 50.9 4327.1 293.0 288.5 288.0 288.0 288.2 290.4 283.8 283.4 283.1 281.0 269.4 268.3 
53.0 277.3 51 4321.6 294.8 290.3 289.8 289.8 290.0 292.2 285.7 285.2 284.9 282.8 271.3 270.2 
70.0 262.7 52 4269.1 306.3 302.0 301.5 301.5 301.7 303.7 297.4 297.0 296.7 294.4 283.3 282.2 
80.0 238.6 53 4217.0 313.4 309.3 308.8 308.8 309.0 310.9 304.8 304.3 304.1 301.8 290.9 289.8 
100.0 206.3 54 4165.8 317.9 313.9 313.4 313.4 313.6 315.4 309.4 309.0 308.7 306.4 295.7 294.7 
110.0 193.2 55 4115.0 321.2 317.3 316.8 316.8 317.0 318.8 312.9 312.5 312.2 309.9 299.4 298.3 
120.0 181.9 56 4064.8 323.4 319.6 319.1 319.1 319.3 321.0 315.2 314.8 314.5 312.2 301.9 300.9 
130.0 172.1 57 4015.4 324.8 321.0 320.5 320.5 320.7 322.4 316.7 316.3 316.0 313.7 303.5 302.5 
140.0 164.0 58 3966.5 325.7 322.0 321.5 321.5 321.7 323.4 317.7 317.3 317.1 314.8 304.8 303.8 
160.0 154.9 59 3918.2 325.8 322.1 321.6 321.7 321.9 323.5 317.9 317.5 317.3 315.0 305.1 304.1 
180.0 146.4 60 3881.0 325.4 321.7 321.3 321.3 321.5 323.1 317.6 317.2 316.9 314.7 304.9 303.9 
205.0 141.6 70 3670.6 320.5 317.2 316.7 316.8 316.9 318.4 313.4 313.1 312.8 310.9 302.0 301.1 
232.0 137.3 80 3481.2 309.7 306.6 306.2 306.2 306.4 307.8 303.2 302.9 302.6 300.9 292.8 292.0 
265.0 133.1 90 3308.6 298.4 295.4 295.1 295.1 295.2 296.7 292.3 292.0 291.8 290.3 282.7 282.0 
310.0 128.8 100 3152.7 287.9 285.1 284.7 284.7 284.9 286.3 282.2 281.9 281.7 280.4 273.3 272.6 
365.0 124.6 110 2511.0 281.8 279.1 278.8 278.8 278.9 280.3 276.4 276.1 275.9 274.7 268.0 267.3 
420.0 120.8 120 2369.0 275.9 273.3 273.0 273.0 273.1 274.5 270.7 270.5 270.3 269.2 262.8 262.2 
480.0 117.1 130 2235.0 269.4 266.9 266.6 266.6 266.7 268.0 264.4 264.2 264.0 263.0 256.9 256.3 
545.0 113.4 140 2108.6 262.3 259.8 259.5 259.5 259.7 261.0 257.5 257.3 257.2 256.3 250.4 249.8 
615.0 110.0 150 1989.3 254.7 252.4 252.1 252.1 252.2 253.5 250.2 250.0 249.9 249.0 243.4 242.9 
695.0 106.6 250 1448.6 222.7 220.8 220.6 220.6 220.7 221.8 219.2 219.0 218.9 218.5 214.2 213.8 
790.0 103.3 350 1306.2 206.3 204.6 204.5 204.5 204.5 205.6 203.3 203.2 203.1 202.8 199.1 198.8 
900.0 99.9 450 1193.2 194.9 193.4 193.3 193.3 193.4 194.3 192.3 192.2 192.1 191.9 188.7 188.4 
1030.0 96.8 550 1101.5 185.5 184.1 184.0 184.0 184.1 184.9 183.1 183.0 183.0 182.8 180.0 179.7 
650 1025.9 178.1 176.8 176.7 176.7 176.8 177.6 175.9 175.9 175.8 175.7 173.1 172.9 
750 957.6 171.5 170.4 170.2 170.3 170.3 171.0 169.6 169.5 169.4 169.3 167.0 166.8 
850 895.4 165.9 164.8 164.8 164.8 164.8 165.5 164.1 164.0 164.0 163.9 161.8 161.6 
950 586.1 161.2 160.2 160.2 160.2 160.2 160.8 159.6 159.5 159.5 159.4 157.5 157.3 
1050 539.9 157.5 156.6 156.5 156.5 156.6 157.2 156.0 155.9 155.9 155.9 154.0 153.9 
Time (years) 
WP Heat 
(W) Node

ANL-WIS-MD-000007 REV 00 II - 20 April 2000 
Table II-11b. Listing of Rows 45 to 92 of Sheet: TempC2 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 
61 
62 
63 
64 
65 
66 
67 
68 
69 
70 
71 
72 
73 
74 
75 
76 
77 
78 
79 
80 
81 
82 
83 
84 
85 
86 
87 
88 
89 
90 
91 
92 
A B C D E F G H I J K L M N O 
file = AMR-F0155-V1.xls sheet = TempC2 
Time(yr) 
Bin 
Weight= 
0.528528 
Tc, 
Interpolate 
Time, WP 
internals 
Internal 
del TC 
Internal 
Delta Tc, 
Interpolat 
ed WP Temp 
Dellt Tc 
internal 
Center 
Rod 
Temperat 
ure Uncertainties 
Time, Yr T,C, WP T,C,WP time, yr Tc Tc Tc Tc Tc 
0.0 24.6 0 38.2 24.6 38.2 62.8 WP surface 
50.0 82.3 50 38.2 82.3 38.2 120.5 Max -avg 22.1 deg C 
50.2 176.5 50.2 33.9 176.5 33.9 210.4 
50.4 193.1605 50.4 33.1 193.2 33.1 226.3 unceert interior 19.5 
50.6 209.785 50.6 32.8 209.8 32.8 242.6 air vs He 
50.8 226.4095 50.8 32.5 226.4 32.5 258.9 Sum 41.6 
51.0 243.0 51 32.2 243.0 32.2 275.2 
52.0 266.5 52 31.4 266.5 31.4 297.9 fraction uncert 0.135007 
53.0 277.3 277.333 53 30.8 277.3 30.8 308.1 
55 275.605706 55 29.7 275.6 29.7 305.3 
57 273.878412 57 28.9 273.9 28.9 302.8 
59 272.151118 59 28.2 272.2 28.2 300.4 
60 271.287471 60 27.9 271.3 27.9 299.2 
70.0 262.7 70 25.1 262.7 25.1 287.8 
80.0 238.6 80 23 238.6 23 261.6 
90 222.463 90 21.4 222.5 21.4 243.9 
100.0 206.3 100 19.9 206.3 19.9 226.2 
110.0 193.2 110 18.9 193.2 18.9 212.1 
120.0 181.9 120 18 181.9 18 199.9 
130.0 172.1 130 17.1 172.1 17.1 189.2 
140.0 164.0 140 16.3 164.0 16.3 180.3 
150 159.4335 150 15.4 159.4 15.4 174.8 
160.0 154.9 160.0 15.03 154.9 15.03 169.9 
180.0 146.4 180.0 14.29 146.4 14.29 160.7 
205.0 141.6 205.0 13.365 141.6 13.365 154.9 
232.0 137.3 232.0 12.366 137.3 12.366 149.6 
250 134.992364 250 11.7 135.0 11.7 146.7 
265.0 133.1 265.0 11.43 133.1 11.43 144.5 
310.0 128.8 310.0 10.62 128.8 10.62 139.4 
350 125.728091 350 9.9 125.7 9.9 135.6 
365.0 124.6 365.0 9.705 124.6 9.705 134.3 
450.0 119.042696 450 8.6 119.0 8.6 127.6 
480.0 117.1 480.0 8.3 117.1 8.3 125.4 
550.0 113.397704 550 7.6 113.4 7.6 121.0 
615.0 110.0 615.0 7.145 110.0 7.145 117.1 
650.0 108.490063 650 6.9 108.5 6.9 115.4 
695.0 106.6 695.0 6.585 106.6 6.585 113.2 
750.0 104.675474 750 6.2 104.7 6.2 110.9 
790.0 103.3 790.0 5.96 103.3 5.96 109.2 
850.0 101.446073 850 5.6 101.4 5.6 107.0 
900.0 99.9 900.0 5.4 99.9 5.4 105.3 
950.0 98.7139538 950 5.2 98.7 5.2 103.9 
1000.0 97.5151077 1000 5 97.5 5 102.5 
1030.0 96.8 1050 4.8

ANL-WIS-MD-000007 REV 00 II - 21 April 2000 
Table II-12. Listing of Top Rows of Sheet: Unzip 
12345678 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
A B C D E F G H I J K L 
file = AMR-F0155-V1.xls 
Sheet = Unzip 
velocity conversion = 0.0000219 cm/yr /(mg/m2-d) Fuel length 366 cm 
log10(rate) = a0 + a1/Tk + a2* PCO3 + a3* PO2 + a4 * pH 
Term= a0 a1 a2 a3 a4 
Basic pH>7 4.69 -1085 -0.12 -0.32 0 E10 to E25 and L10 to L25 
Acidic pH< =7 7.13 -1085 0 -0.32 -0.41 used in Figure 13 
Example calculation Tc PCo3 PO2 pH 
dis Rate 
log10(dis 
rt) 
Acidic 
solution 
Basic 
solution Tc PCo3 PO2 pH M-CO3 Atm. O2 
Velocity, 
cm/yr yrs to unzip 
15.757 1.197 0.7175 1.1975 100 3 0.69897 8 0.001 0.2 1.38E-02 1.33E+04 
14.387 1.158 0.6780 1.1580 95 3 0.69897 8 0.001 0.2 1.26E-02 1.45E+04 
13.102 1.117 0.6373 1.1173 90 3 0.69897 8 0.001 0.2 1.15E-02 1.59E+04 
11.902 1.076 0.5956 1.0756 85 3 0.69897 8 0.001 0.2 1.04E-02 1.76E+04 
10.781 1.033 0.5527 1.0327 80 3 0.69897 8 0.001 0.2 9.44E-03 1.94E+04 
9.739 0.989 0.5085 0.9885 75 3 0.69897 8 0.001 0.2 8.53E-03 2.15E+04 
8.771 0.943 0.4631 0.9431 70 3 0.69897 8 0.001 0.2 7.68E-03 2.38E+04 
7.875 0.896 0.4163 0.8963 65 3 0.69897 8 0.001 0.2 6.90E-03 2.65E+04 
7.048 0.848 0.3681 0.8481 60 3 0.69897 8 0.001 0.2 6.17E-03 2.96E+04 
6.286 0.798 0.3184 0.7984 55 3 0.69897 8 0.001 0.2 5.51E-03 3.32E+04 
5.587 0.747 0.2672 0.7472 50 3 0.69897 8 0.001 0.2 4.89E-03 3.74E+04 
4.947 0.694 0.2144 0.6944 45 3 0.69897 8 0.001 0.2 4.33E-03 4.22E+04 
4.364 0.640 0.1599 0.6399 40 3 0.69897 8 0.001 0.2 3.82E-03 4.79E+04 
3.834 0.584 0.1036 0.5836 35 3 0.69897 8 0.001 0.2 3.36E-03 5.45E+04 
3.353 0.525 0.0455 0.5255 30 3 0.69897 8 0.001 0.2 2.94E-03 6.23E+04 
3.834 0.584 0.1036 0.5836 35 3 0.69897 8 0.001 0.2 3.36E-03 5.45E+04 
Variation in pH H27 to H40 and L27 to L40 used for Figure 14 
55.412 1.744 1.7436 0.5836 35 3 0.69897 4 0.001 0.2 4.85E-02 3.77E+03 
34.562 1.539 1.5386 0.5836 35 3 0.69897 4.5 0.001 0.2 3.03E-02 6.04E+03 
21.558 1.334 1.3336 0.5836 35 3 0.69897 5 0.001 0.2 1.89E-02 9.69E+03 
13.446 1.129 1.1286 0.5836 35 3 0.69897 5.5 0.001 0.2 1.18E-02 1.55E+04 
8.387 0.924 0.9236 0.5836 35 3 0.69897 6 0.001 0.2 7.35E-03 2.49E+04 
5.231 0.719 0.7186 0.5836 35 3 0.69897 6.5 0.001 0.2 4.58E-03 3.99E+04 
3.834 0.584 0.5136 0.5836 35 3 0.69897 7 0.001 0.2 3.36E-03 5.45E+04 
3.834 0.584 0.3086 0.5836 35 3 0.69897 7.5 0.001 0.2 3.36E-03 5.45E+04 
3.834 0.584 0.1036 0.5836 35 3 0.69897 8 0.001 0.2 3.36E-03 5.45E+04 
3.834 0.584 -0.1014 0.5836 35 3 0.69897 8.5 0.001 0.2 3.36E-03 5.45E+04 
3.834 0.584 -0.3064 0.5836 35 3 0.69897 9 0.001 0.2 3.36E-03 5.45E+04 
3.834 0.584 -0.5114 0.5836 35 3 0.69897 9.5 0.001 0.2 3.36E-03 5.45E+04 
3.834 0.584 -0.7164 0.5836 35 3 0.69897 10 0.001 0.2 3.36E-03 5.45E+04 
3.834 0.584 -0.9214 0.5836 35 3 0.69897 10.5 0.001 0.2 3.36E-03 5.45E+04