NUREG/CR-6672, Vols. 1,2

SAND2000-0234

Reexamination of Spent

Fuel Shipment Risk

Estimates

Volume I: Main Report

Manuscript Completed: February 2000

Date Published: March 2000

Prepared by

J. L. Sprung, D. J. Ammerman, N. L. Breivik, R. J. Dukart, F. L. Kanipe,

J. A. Koski, G. S. Mills, K. S. Neuhauser, H. D. Radloff, R. F. Weiner, H. R. Yoshimura

Sandia National Laboratories

Albuquerque, NM 87185-0718

Prepared for

Spent Fuel Project Office

Office of Nuclear Material Safety and Safeguards

U.S. Nuclear Regulatory Commission

Washington, DC 20555

NRC Job Code J5160
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ABSTRACT

The risks associated with the transport of spent nuclear fuel by truck and rail are reexamined and

compared to results published in NUREG-0170 and the Modal Study. The reexamination

considers transport by truck and rail in four generic Type B spent fuel casks. Cask and spent fuel

response to collision impacts and fires are evaluated by performing three-dimensional finite

element and one-dimensional heat transport calculations. Accident release fractions are

developed by critical review of literature data. Accident severity fractions are developed from

Modal Study truck and rail accident event trees, modified to reflect the frequency of occurrence

of hard and soft rock wayside route surfaces as determined by analysis of geographic data.

Incident-free population doses and the population dose risks associated with the accidents that

might occur during transport are calculated using the RADTRAN 5 transportation risk code. The

calculated incident-free doses are compared to those published in NUREG-0170. The calculated

accident dose risks are compared to dose risks calculated using NUREG-0170 and Modal Study

accident source terms. The comparisons demonstrate that both of these studies made a number

of very conservative assumptions about spent fuel and cask response to accident conditions,

which caused their estimates of accident source terms, accident frequencies, and accident

consequences to also be very conservative. The results of this study and the previous studies

demonstrate that the risks associated with the shipment of spent fuel by truck or rail are very

small.
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 CONTENTS

ABSTRACT...................................................................................................................................iii

ACKNOWLEDGEMENTS ........................................................................................................xvii

ACRONYMS ...............................................................................................................................xix

EXECUTIVE SUMMARY....................................................................................................... ES-1

1. INTRODUCTION ................................................................................................................1-1

1.1 NUREG-0170........................................................................................................................................... 1-1

1.2 NUREG-0170 Spent Fuel Transportation Risks ...................................................................................... 1-1

1.3 Need for Reevaluation of NUREG-0170 Spent Fuel Transportation Risks ............................................. 1-3

1.4 Study Objectives ...................................................................................................................................... 1-4

1.5 General Approach .................................................................................................................................... 1-5

1.6 References................................................................................................................................................ 1-6

2. METHODOLOGY OVERVIEW AND REPORT ROADMAP ..........................................2-1

2.1 Introduction.............................................................................................................................................. 2-1

2.2 RADTRAN .............................................................................................................................................. 2-1

2.3 RADTRAN Input ..................................................................................................................................... 2-2

2.3.1 Route Parameters ....................................................................................................................... 2-2

2.3.2 Weather Parameters ................................................................................................................... 2-3

2.4 Package Inventories and Surface Dose Rates........................................................................................... 2-4

2.5 Accident Source Terms ............................................................................................................................ 2-4

2.5.1 Source Term Probabilities.......................................................................................................... 2-5

2.5.2 Source Term Magnitudes........................................................................................................... 2-6

2.6 Response of Representative Casks to Accident Conditions...................................................................... 2-6

2.6.1 Finite Element Impact Calculations ........................................................................................... 2-7

2.6.2 Impacts onto Yielding Surfaces ................................................................................................. 2-8

2.7 Rod Failure Fractions............................................................................................................................... 2-8

2.8 Thermal Calculations ............................................................................................................................... 2-9

2.9 RADTRAN Calculations........................................................................................................................ 2-10

2.10 Report Roadmap..................................................................................................................................... 2-10

2.11 References.............................................................................................................................................. 2-11

3. RADTRAN INPUT ..............................................................................................................3-1

3.1 Fixed and Sampled Input Variables ......................................................................................................... 3-1

3.2 RADTRAN 1 and RADTRAN 5 Input Variables .................................................................................... 3-3
vi

3.3 Variables Selected for Sampling ............................................................................................................ 3-12

3.3.1 Incident-Free Variables Selected for LHS Sampling ............................................................... 3-12

3.3.2 Incident-Free Variables Not Selected for LHS Sampling ........................................................ 3-13

3.3.3 Accident Variables................................................................................................................... 3-22

3.4 Development of Distribution Functions ................................................................................................. 3-24

3.4.1 Route Characteristics ............................................................................................................... 3-24

3.4.2 Truck and Train Accident Statistics......................................................................................... 3-37

3.4.3 Development of Miscellaneous Distributions .......................................................................... 3-44

3.5 References.............................................................................................................................................. 3-50

4. SELECTION OF GENERIC CASKS...................................................................................4-1

4.1 Description of Casks ................................................................................................................................ 4-1

4.2 Conservatism in Cask Selection ............................................................................................................... 4-7

4.3 References................................................................................................................................................ 4-8

5. STRUCTURAL RESPONSE ...............................................................................................5-1

5.1 Finite Element Calculations for Impacts onto Rigid Targets.................................................................... 5-1

5.1.1 Introduction................................................................................................................................ 5-1

5.1.2 Assumptions for Finite Element Models.................................................................................... 5-2

5.1.3 Material Models......................................................................................................................... 5-7

5.1.4 Finite Element Results ............................................................................................................... 5-8

5.1.5 Benchmarking of Finite Element Calculations......................................................................... 5-15

5.2 Impacts onto Real Targets...................................................................................................................... 5-16

5.2.1 Introduction.............................................................................................................................. 5-16

5.2.2 Methodology............................................................................................................................ 5-16

5.2.3 Soil Targets.............................................................................................................................. 5-19

5.2.4 Concrete Targets...................................................................................................................... 5-20

5.2.5 Hard Rock Targets................................................................................................................... 5-24

5.2.6 Example Calculation................................................................................................................ 5-24

5.2.7 Results for Real Target Calculations........................................................................................ 5-24

5.2.8 Impacts onto Water.................................................................................................................. 5-26

5.2.9 Correlation of Results with Modal Study Event Trees............................................................. 5-26

5.3 Puncture Analyses .................................................................................................................................. 5-26

5.4 Failure of Rods....................................................................................................................................... 5-27

5.4.1 Rod Failure Strain Criterion..................................................................................................... 5-28

5.4.2 Estimation of the Fraction of Rods Failed During Impacts...................................................... 5-31

5.5 Conservatism in Calculating Structural Response.................................................................................. 5-31

5.6 References.............................................................................................................................................. 5-33

6. THERMAL ANALYSIS OF THE GENERIC CASKS

IN A LONG DURATION FIRE ...........................................................................................6-1

6.1 Introduction.............................................................................................................................................. 6-1

6.2 Generic Casks Modeled ........................................................................................................................... 6-1

6.3 PATRAN/PThermal Model...................................................................................................................... 6-4
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6.4 Thermal Modeling Results ....................................................................................................................... 6-5

6.4.1 Cask Initial Temperature Profiles ..............................................................................................6-5

6.4.2 Thermal Response to a Long Duration, 1000°C Fire.................................................................6-5

6.4.3 Thermal Response to a Long Duration 800°C Fire....................................................................6-7

6.5 Sensitivity Discussion .............................................................................................................................. 6-8

6.6 Summary .................................................................................................................................................. 6-9

6.7 References................................................................................................................................................ 6-9

7. SOURCE TERMS AND SOURCE TERM PROBABILITIES............................................7-1

7.1 Truck and Train Accident Scenarios ........................................................................................................ 7-1

7.1.1 Event Trees ................................................................................................................................ 7-1

7.1.2 Route Wayside Surface Characteristics ..................................................................................... 7-4

7.1.3 Truck Accident Data.................................................................................................................. 7-7

7.1.4 Train Accident Data................................................................................................................... 7-9

7.2 Source Term and Source Term Probability Expressions........................................................................ 7-13

7.2.1 RADTRAN Risk Equations ..................................................................................................... 7-13

7.2.2 Accident Source Terms............................................................................................................ 7-13

7.2.3 Cask Inventories....................................................................................................................... 7-14

7.2.4 Chemical Element Classes ....................................................................................................... 7-16

7.2.5 Release Fractions ..................................................................................................................... 7-18

7.2.6 Accident Cases......................................................................................................................... 7-24

7.2.7 Source Term Probabilities........................................................................................................ 7-27

7.2.8 Accident Severities .................................................................................................................. 7-27

7.3 Values for Release Fraction Parameters................................................................................................. 7-30

7.3.1 Fission Product Release from Failed Rods to the Cask Interior............................................... 7-30

7.3.2 Noble Gases ............................................................................................................................. 7-30

7.3.3 Particles.................................................................................................................................... 7-30

7.3.4 Cesium ..................................................................................................................................... 7-35

7.3.5 Release Following Fuel Oxidation........................................................................................... 7-45

7.3.6 CRUD ...................................................................................................................................... 7-48

7.3.7 Impact Failure of Spent Fuel Rods........................................................................................... 7-49

7.3.8 Fission Product Transport from the Cask Interior to the Environment .................................... 7-51

7.3.9 Expansion Factor Values ......................................................................................................... 7-54

7.4 Values for Severity Fraction Parameters ................................................................................................ 7-55

7.4.1 Introduction.............................................................................................................................. 7-55

7.4.2 Cask Involvement .................................................................................................................... 7-55

7.4.3 Values for Collision Conditional Probabilities ........................................................................ 7-56

7.4.4 Values for Fire Probabilities .................................................................................................... 7-63

7.5 Values for Release Fractions and Severity Fractions ............................................................................. 7-71

7.5.1 Introduction.............................................................................................................................. 7-71

7.5.2 Calculational Method............................................................................................................... 7-71

7.5.3 Source Term Severity Fraction and Release Fraction Values .................................................. 7-72

7.6 Conservatisms ........................................................................................................................................ 7-72

7.7 References.............................................................................................................................................. 7-77
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8. RADTRAN CALCULATIONS............................................................................................8-1

8.1 Calculations Performed ............................................................................................................................ 8-1

8.2 The RADTRAN 5 Computational Scheme .............................................................................................. 8-3

8.2.1 Latin Hypercube Sampling......................................................................................................... 8-3

8.2.2 Size of the LHS Sample ............................................................................................................. 8-3

8.3 Input Parameters and Results Calculated ................................................................................................. 8-4

8.4 Number of Cases Examined ..................................................................................................................... 8-5

8.5 Complementary Cumulative Distribution Functions ................................................................................ 8-6

8.6 Results for the Generic Steel-Lead-Steel and Steel-DU-Steel Truck Casks............................................. 8-6

8.7 Results for the Generic Steel-Lead-Steel and Monolithic Steel Rail Casks............................................ 8-18

8.8 Comparison of Truck and Rail Transport Mean Risks........................................................................... 8-24

8.9 Comparison of NUREG-0170 Incident-Free Doses to Those of This Study.......................................... 8-25

8.10 Illustrative Real Routes .......................................................................................................................... 8-28

8.10.1 Steel-Lead-Steel Truck Cask Results for Illustrative Routes ................................................... 8-29

8.10.2 Monolithic Steel Rail Cask Results for Illustrative Routes ...................................................... 8-37

8.10.3 Rod Strain Failure Criterion Sensitivity Calculation................................................................ 8-44

8.11 Rail Routes with Heavy-Haul Segments and Intermodal Transfers........................................................ 8-45

8.12 Loss of Shielding Accidents................................................................................................................... 8-47

8.12.1 Severity Fractions, Dose Rates, and Cask LOS Areas ............................................................. 8-48

8.12.2 Maximum Dimension of LOS Area ......................................................................................... 8-50

8.12.3 Final Calculation...................................................................................................................... 8-50

8.12.4 An Example of an LOS Calculation......................................................................................... 8-50

8.13 Population Dose Risks for Shipment of the Entire 1994 Spent Fuel Inventory...................................... 8-51

8.14 Individual Dose Estimates...................................................................................................................... 8-54

8.15 Effect of NUREG-0170 Source Term and Exposure Pathway Models on Dose Risk............................ 8-56

8.15.1 Source Term and Exposure Pathway Models in RADTRAN 1 and RADTRAN 5.................. 8-56

8.15.2 Comparison of Results Calculated with RADTRAN Versions 1, 4, and 5 .............................. 8-58

8.15.3 Effect of Treatments on RADTRAN 5 Accident Population Dose CCDFs ............................. 8-61

8.16 Population Dose Risk CCDFs from NUREG-0170, the Modal Study, and this Study........................... 8-64

8.16.1 CCDF Probability Axis Intercepts ........................................................................................... 8-64

8.16.2 CCDF Consequence Axis Intercepts........................................................................................ 8-69

8.17 References.............................................................................................................................................. 8-71

9. SUMMARY AND CONCLUSIONS ...................................................................................9-1
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APPENDIX A STRUCTURAL RESPONSE INFORMATION...........................................A-1

APPENDIX B ANALYTICAL DETERMINATION OF PACKAGE

RESPONSE TO SEVERE IMPACTS .......................................................... B-1

APPENDIX C ORIGEN2 CALCULATIONS ...................................................................... C-1

APPENDIX D SOURCE TERM SPREADSHEETS............................................................D-1

APPENDIX E ILLUSTRATIVE LHS AND RADTRAN INPUT

AND OUTPUT FILES.................................................................................. E-1
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Figures

Figure E.1 Mean truck accident population dose risk CCDFs for calculations that compared the source terms

developed by NUREG-0170, the Modal Study, and this study. Each RADTRAN 5 calculation assumed

transport in a steel-lead-steel truck cask over each of the 200 representative truck routes and each

calculation generated results for all of the 19 representative truck accident source terms............................. ES-7

Figure E.2 Mean rail accident population dose risk CCDFs for calculations that compared the source terms

developed by NUREG-0170, the Modal Study, and this study. Each RADTRAN 5 calculation assumed

transport in a steel-lead-steel rail cask over each of the 200 representative rail routes and each calculation

generated results for all of the 21 representative rail accident source terms.................................................. ES-8

Figure 3.1a Comparison of the cumulative distributions of route lengths for truck ................................................3-25

Figure 3.1b Comparison of the cumulative distributions of route rural fractions for truck ...................................3-25

Figure 3.1c Comparison of the cumulative distributions of route suburban fractions for truck ............................3-26

Figure 3.1d Comparison of the cumulative distributions of route urban fractions for truck...................................3-26

Figure 3.2a Comparison of the cumulative distributions of route lengths for rail...................................................3-27

Figure 3.2b Comparison of the cumulative distributions of route rural fractions for rail.......................................3-27

Figure 3.2c Comparison of the cumulative distributions of route suburban fractions for rail ................................3-28

Figure 3.2d Comparison of the cumulative distributions of route urban fractions for rail......................................3-28

Figure 3.3a Histogram of truck route lengths..........................................................................................................3-30

Figure 3.3b Histogram of rail route lengths ............................................................................................................3-30

Figure 3.4a Cumulative distribution of truck route lengths.....................................................................................3-31

Figure 3.4b Cumulative distribution of rail route lengths .......................................................................................3-31

Figure 3.5a Histograms of rural, suburban, and urban length fractions for truck routes .........................................3-32

Figure 3.5b Histograms of rural, suburban, and urban length fractions for rail routes............................................3-32

Figure 3.6a Cumulative distributions of rural, suburban, and urban length fractions for truck routes ....................3-33

Figure 3.6b Cumulative distributions of rural, suburban, and urban length fractions for rail routes.......................3-33

Figure 3.7a Histogram and cumulative distribution for rural population density for rural truck route

segments .........................................................................................................................................................3-34

Figure 3.7b Histogram and cumulative distribution for suburban population density

for suburban truck route segments..................................................................................................................3-34

Figure 3.7c Histogram and cumulative distribution for urban population density for

urban truck route segments .............................................................................................................................3-35

Figure 3.8a Histogram and cumulative distribution for rural population density for rural rail route

segments .........................................................................................................................................................3-35

Figure 3.8b Histogram and cumulative distribution for suburban population density for suburb

an rail route segments .....................................................................................................................................3-36

Figure 3.8c Histogram and cumulative distribution for urban population density for urban rail

route segments ................................................................................................................................................3-36

Figure 3.9a Accident rate versus rural population density ......................................................................................3-41

Figure 3.9b Accident rate versus suburban population density...............................................................................3-41

Figure 3.10a Cumulative distribution of rural accident rates ..................................................................................3-42

Figure 3.10b Cumulative distribution of suburban and urban accident rates ..........................................................3-42

Figure 3.11 Cumulative distribution of rail accident rates (used for all segments: Rural,

Suburban, and Urban).....................................................................................................................................3-43

Figure 3.12 Distribution of normal commercial truck stop times............................................................................3-45

Figure 3.13 Distribution of response team arrival plus evacuation times................................................................3-46

Figure 3.14 Histogram and cumulative distribution of rural interstate traffic density.............................................3-49

Figure 3.15 Histogram and cumulative distribution of interstate traffic density for urbanized areas......................3-49

Figure 3.16 Histogram and cumulative distribution of suburban interstate traffic density......................................3-50

Figure 4.1 Conceptual design of a generic steel-lead-steel truck cask ......................................................................4-2

Figure 4.2 Conceptual design of a generic steel-DU-steel truck cask .......................................................................4-3

Figure 4.3 Conceptual design of a generic steel-lead-steel rail cask .........................................................................4-4

Figure 4.4 Conceptual design of a generic monolithic steel rail cask........................................................................4-5
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Figure 4.5 Finite element representation of a typical closure lid for structural analysis,

showing the locations of the bolts.....................................................................................................................4-7

Figure 5.1 Geometry of the initial and pre-crushed impact limiter ...........................................................................5-2

Figure 5.2 Finite element model of the steel-lead-steel rail cask in the CG-over-corner drop orientation...............5-3

Figure 5.3 Detail of the end of the steel-lead-steel rail cask finite element model....................................................5-4

Figure 5.4 Typical model of a bolt used in the finite element analyses.....................................................................5-6

Figure 5.5 Modeling of the deformation in the bolts. The solid lines indicate the bolt position

after being deformed and the dashed lines indicate the initial bolt position .....................................................5-7

Figure 5.6 Deformed shape and plastic strain fringes for the steel-lead-steel truck cask following

a 120-mph impact in the side-on orientation. The maximum plastic strain (indicated by the asterisk)

occurs in the outer shell. The maximum strain in the inner shell is 0.27 ........................................................5-9

Figure 5.7 Seal region displacements for the 90-mph end impact of the monolithic steel rail cask .......................5-12

Figure 5.8 Time history for lid opening displacement for the 60 mph side-impact of the monolithic

steel rail cask ..................................................................................................................................................5-13

Figure 5.9 Slumping of lead and contents following a 120-mph end-on impact of the steel-lead-steel

rail cask...........................................................................................................................................................5-15

Figure 5.10 Kinetic energy time histories for the steel-lead-steel truck cask from 120-mph impact

analyses in the end, side, and corner orientations ...........................................................................................5-17

Figure 5.11 Force-deflection curves for the steel-lead-steel truck cask from the 120-mph impact

analyses in the end, side, and corner orientations ...........................................................................................5-18

Figure 5.12 Force-deflection curves for impact onto hard desert soil.....................................................................5-20

Figure 5.13 Comparison of test force-deflection curves with those derived from the empirical equations............5-22

Figure 5.14 Force-deflection curves for concrete target impacts of the steel-lead-steel truck cask at 120 mph......5-23

Figure 5.15 Fraction of railroad tank cars involved in puncture-type accidents that failed because

of puncture......................................................................................................................................................5-27

Figure 6.1 A generic, steel-lead-steel truck cask.......................................................................................................6-1

Figure 6.2 A generic, steel-DU-steel truck cask........................................................................................................6-1

Figure 6.3 A generic, steel-lead-steel rail cask..........................................................................................................6-2

Figure 6.4 A generic, monolithic steel rail cask ........................................................................................................6-2

Figure 6.5 Generic wall cross section used in the 1-D axisymmetric, thermal modeling ..........................................6-3

Figure 6.6 Internal surface temperature histories of the generic casks in an 1000°C long duration fire ..................6-6

Figure 7.1 Modal Study truck accident event tree.....................................................................................................7-2

Figure 7.2 Modal Study train accident event tree......................................................................................................7-3

Figure 7.3 Modified Modal Study truck accident event tree...................................................................................7-10

Figure 7.4 Modified Modal Study train accident event tree....................................................................................7-12

Figure 7.5 Fracture particle size distribution for depleted UO2 ..............................................................................7-32

Figure 7.6 Schematic of the CONTAIN Model for the HBU-7 rod blowdown test................................................7-38

Figure 7.7 CONTAIN predictions for the pressures in the HBU-7 experiment ......................................................7-41

Figure 7.8 CONTAIN predictions for the temperature in Cell 3 and the flow velocity

from Cell 3 to Cell 4 .......................................................................................................................................7-41

Figure 7.9 Variation with temperature of the concentrations of Cs vapor species predicted

by the VICTORIA code..................................................................................................................................7-43

Figure 7.10 Size distributions of the particles sourced into the TN-12 cask from failed spent fuel rods,

and of the particles that escaped from the cask through 4 and 100 mm2

 cask failures....................................7-52

Figure 7.11 Dependence of Cask-to-Environment Release Fractions (1.0 – Retention Fraction)

on the Size of the Cask Failure (leak area) .....................................................................................................7-52

Figure 8.1 Two hundred truck accident population dose risk CCDFs, one CCDF for each representative

truck route. Each RADTRAN 5 calculation examined all 19 representative truck accident source terms

and assumed transport of PWR spent fuel in the generic steel-lead-steel truck cask........................................8-7

Figure 8.2 Truck accident population dose risk CCDFs for transport of PWR spent fuel in the generic

steel-lead-steel truck cask over the 200 representative truck routes. Each underlying RADTRAN 5

calculation generated results for all of the 19 representative truck accident source terms................................8-8

Figure 8.3 Truck accident population dose risk CCDFs for transport of BWR spent fuel in the generic

steel-lead-steel truck cask over the 200 representative truck routes. Each underlying RADTRAN 5

calculation generated results for all of the 19 representative truck accident source terms..............................8-10
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Figure 8.4 Truck accident population dose risk CCDFs for transport of PWR spent fuel in the generic

steel-DU-steel truck cask over the 200 representative truck routes. Each underlying RADTRAN 5

calculation generated results for all of the 19 representative truck accident source terms..............................8-11

Figure 8.5 Truck accident population dose risk CCDFs for transport of BWR spent fuel in the generic

steel-DU-steel truck cask over the 200 representative truck routes. Each underlying RADTRAN 5

calculation generated results for all of the 19 representative truck accident source terms..............................8-12

Figure 8.6 Comparison of truck accident population dose risk CCDFs for transport of PWR or BWR

spent fuel in generic steel-lead-steel or steel-DU-steel truck casks over the 200 representative

truck routes. Each underlying RADTRAN 5 calculation generated results for all of the

19 representative truck accident source terms ................................................................................................8-13

Figure 8.7 Rail accident population dose risk CCDFs for transport of PWR spent fuel in the generic

steel-lead-steel rail cask over the 200 representative rail routes. Each underlying RADTRAN 5

alculation generated results for all of the 21 representative rail accident source terms ..................................8-19

Figure 8.8 Rail accident population dose risk CCDFs for transport of BWR spent fuel in the generic

steel-lead-steel rail cask over the 200 representative rail routes. Each underlying RADTRAN 5

calculation generated results for all of the 21 representative rail accident source terms.................................8-20

Figure 8.9 Rail accident population dose risk CCDFs for transport of PWR spent fuel in the generic

monolithic steel rail cask over the 200 representative rail routes. Each underlying RADTRAN 5

calculation generated results for all of the 21 representative rail accident source terms.................................8-21

Figure 8.10 Rail accident population dose risk CCDFs for transport of BWR spent fuel in the generic

monolithic steel rail cask over the 200 representative rail routes. Each underlying RADTRAN 5

calculation generated results for all of the 21 representative rail accident source terms.................................8-22

Figure 8.11 Comparison of rail accident population dose risk CCDFs for transport of PWR or BWR

spent fuel in generic steel-lead-steel or monolithic steel rail casks over the 200 representative

rail routes. Each underlying RADTRAN 5 calculation generated results for all of the

21 representative rail accident source terms ...................................................................................................8-23

Figure 8.12 Truck accident population dose risk CCDFs for transport of PWR spent fuel in the generic

steel-lead-steel truck cask over the Crystal River to Hanford illustrative truck route. Each underlying

RADTRAN 5 calculation generated results for all of the 19 representative truck accident source terms.......8-30

Figure 8.13 Truck accident population dose risk CCDFs for transport of PWR spent fuel in the generic

steel-lead-steel truck cask over the Maine Yankee to Skull Valley illustrative truck route. Each

underlying RADTRAN 5 calculation generated results for all of the 19 representative truck

accident source terms......................................................................................................................................8-31

Figure 8.14 Truck accident population dose risk CCDFs for transport of PWR spent fuel in the generic

steel-lead-steel truck cask over the Maine Yankee to Savannah River Site illustrative truck route.

Each underlying RADTRAN 5 calculation generated results for all of the 19 representative truck

accident source terms......................................................................................................................................8-32

Figure 8.15 Truck accident population dose risk CCDFs for transport of PWR spent fuel in the generic

steel-lead-steel truck cask over the Kewaunee to Savannah River Site illustrative truck route. Each

underlying RADTRAN 5 calculation generated results for all of the 19 representative truck

accident source terms......................................................................................................................................8-33

Figure 8.16 Truck accident population dose risk CCDFs for transport of PWR spent fuel in the generic

steel-lead-steel truck cask over the NUREG-0170 representative truck route. Each underlying

RADTRAN 5 calculation generated results for all of the 19 representative truck accident source terms.......8-34

Figure 8.17 Comparison of truck accident population dose risk CCDFs for transport of PWR spent

fuel in the generic steel-lead-steel cask over four illustrative truck routes and the NUREG-0170

representative truck route. Each underlying RADTRAN 5 calculation generated results for all

of the 19 representative truck accident source terms ......................................................................................8-35

Figure 8.18 Rail accident population dose risk CCDFs for transport of PWR spent fuel in the generic

monolithic steel rail cask over the Crystal River to Hanford illustrative rail route. Each underlying RADTRAN

5 calculation generated results for all of the 21 representative rail accident source terms..............................8-38

Figure 8.19 Rail accident population dose risk CCDFs for transport of PWR spent fuel in the generic

monolithic steel rail cask over the Maine Yankee to Skull Valley illustrative rail route. Each

underlying RADTRAN 5 calculation generated results for all of the 21 representative rail

accident source terms......................................................................................................................................8-39
xiii

Figure 8.20 Rail accident population dose risk CCDFs for transport of PWR spent fuel in the generic

monolithic steel rail cask over the Maine Yankee to Savannah River Site illustrative rail route. Each

underlying RADTRAN 5 calculation generated results for all of the 21 representative rail accident

source terms....................................................................................................................................................8-40

Figure 8.21 Rail accident population dose risk CCDFs for transport of PWR spent fuel in the generic

monolithic steel rail cask over the Kewaunee to Savannah River Site illustrative rail route. Each underlying

RADTRAN 5 calculation generated results for all of the 21 representative rail accident source terms .........8-41

Figure 8.22 Rail accident population dose risk CCDFs for transport of PWR spent fuel in the generic

monolithic steel rail cask over the NUREG-0170 representative rail route. Each underlying

RADTRAN 5 calculation generated results for all of the 21 representative rail accident source terms .........8-42

Figure 8.23 Comparison of rail accident population dose risk CCDFs for transport of PWR spent fuel in the generic

monolithic steel cask over four illustrative rail routes and the NUREG-0170 representative

rail route. Each underlying RADTRAN 5 calculation generated results for all of the 21 representative

rail accident source terms ...............................................................................................................................8-43

Figure 8.24 Representation of spent fuel surface for dose rate calculation for LOS scenarios ..............................8-49

Figure 8.25 Mean truck accident population dose risk CCDFs for calculations that examined the impact

on dose risks of NUREG-0170 source terms and exposure pathway models. Each RADTRAN 5

calculation assumed transport in a steel-lead- steel truck cask over each of the 200 representative

truck routes and each calculation generated results for all of the 19 representative truck accident

source terms....................................................................................................................................................8-63

Figure 8.26 Mean truck accident population dose risk CCDFs for calculations that compared the source terms

developed by NUREG-0170, the Modal Study, and this study. Each RADTRAN 5 calculation assumed

transport in a steel-lead steel truck cask over each of the 200 representative truck routes and each calculation

generated results for all of the 19 representative truck accident source terms ................................................8-66

Figure 8.27 Mean rail accident population dose risk CCDFs for calculations that compared the source terms

developed by NUREG-0170, the Modal Study, and this study. Each RADTRAN 5 calculation assumed

transport in a steel-lead steel rail cask over each of the 200 representative rail routes and each calculation

generated results for all of the 21 representative rail accident source terms...................................................8-67

Tables

Table E.1 Comparison of NUREG-0170 Incident-Free Doses (person-rem) to the Incident-Free

Doses Developed by this Studya .................................................................................................................... ES-5

Table E.2 Comparison of Mean Accident Population Dose Risks (person-rem) Calculated Using

NUREG-0170 Model I and Model II Source Terms and Modal Study Source Terms to Those

Calculated Using the Source Terms Developed by this Study....................................................................... ES-6

Table 1.1 NUREG-0170 Spent Fuel Truck and Train Route Data............................................................................1-2

Table 1.2 NUREG-0170 Annual Incident-Free Spent Fuel Transportation Doses (person-rem)..............................1-2

Table 1.3 Expected (Mean) Latent Cancer Fatalities Predicted in NUREG-0170 to be Caused

by Truck and Train Accidents that Occur during Spent Fuel Transport ...........................................................1-2

Table 1.4 Inventory (Ci) Assumed in NUREG-0170 to be Released to the Environment

from a Type B Spent Fuel Cask as a Result of an Accident..............................................................................1-3

Table 1.5 NUREG-0170 Model I and Model II Severity and Release Fractions for Spent

Fuel Transport by Truck and Rail.....................................................................................................................1-4

Table 3.1 Results of Sensitivity Calculations: Changes in Total Accident Risk Produced

by Changes in the Values of Several Input Variables.......................................................................................3-2

Table 3.2 Comparison of RADTRAN 1 and RADTRAN 5......................................................................................3-4

Table 3.3 Comparison of RADTRAN 1 and RADTRAN 5 Input Variables that Affect Incident-Free Dose...........3-5

Table 3.4 Comparison of RADTRAN 1 and RADTRAN 5 Input Variables that Affect Accident Risk.................3-10

Table 3.5 Definition of Population Density Categories (persons/km2

) ...................................................................3-29

Table 3.6 Truck Accident Rates (Accidents per Million Vehicle-Kilometers) .......................................................3-39

Table 3.7 Rail Accident Rates per Million Rail Car km .........................................................................................3-43

Table 3.8 Distribution of Normal Commercial Truck Stop Times..........................................................................3-44
xiv

Table 3.9 Distribution of Pasquill Categories .........................................................................................................3-46

Table 3.10 Distribution of Dose Rate at 1 m (RADTRAN parameter TI) for Truck Casks....................................3-47

Table 3.11 Distribution of Dose Rate at 1 m (RADTRAN parameter TI) for Rail Casks.......................................3-47

Table 3.12 Distribution of Persons per Vehicle on Highway Routes......................................................................3-48

Table 4.1 Steel-Lead-Steel Truck Casks ...................................................................................................................4-2

Table 4.2 Steel-DU-Steel Truck Casks .....................................................................................................................4-3

Table 4.3 Steel-Lead-Steel Rail Casks......................................................................................................................4-4

Table 4.4 Monolithic Rail Casks...............................................................................................................................4-5

Table 5.1 Impact Limiter Geometry (in inches) ........................................................................................................5-2

Table 5.2 Material Properties Used in the Finite Element Analyses .........................................................................5-8

Table 5.3 Maximum Plastic Strain in the Inner Shell of the Sandwich Wall Casks..................................................5-9

Table 5.4 Maximum Plastic Strains on the Inside of the Monolithic Rail Cask......................................................5-10

Table 5.5 Maximum True Strain in the Closure Bolts ............................................................................................5-11

Table 5.6 Seal Closure Displacements, in Inches, at the End of the Analysis.........................................................5-13

Table 5.7 Calculated Rail Cask Closure Leak Path Areas.......................................................................................5-14

Table 5.8 Peak Contact Force from Impacts Onto Rigid Targets (Pounds) ............................................................5-19

Table 5.9 Equivalent Diameters for Concrete Impacts............................................................................................5-23

Table 5.10 Real Target Equivalent Velocities (mph) for the Steel-Lead-Steel Truck Cask....................................5-24

Table 5.11 Real Target Equivalent Velocities (mph) for the Steel-DU-Steel Truck Cask......................................5-25

Table 5.12 Real Target Equivalent Velocities (mph) for the Steel-Lead-Steel Rail Cask.......................................5-25

Table 5.13 Real Target Equivalent Velocities (mph) for the Monolithic Steel Rail Cask.......................................5-25

Table 5.14 Calculation of Reactor-Years Producing High Burnup Fuel.................................................................5-29

Table 5.15 Calculation of Mass Weighted Sum of Burnup Dependent Rod Strain Failure Levels.........................5-30

Table 5.16 Peak Accelerations from Rigid Target Impacts without Impact Limiters, Gs.......................................5-31

Table 5.17 Peak Strains in Fuel Rods Resulting from a 100 G Impact ...................................................................5-32

Table 6.1 Generic Cask Dimensions (m) ..................................................................................................................6-3

Table 6.2 Assumed Loading of PWR and BWR Assemblies for the Generic Casks ................................................6-3

Table 6.3 Internal Heat Loads for Each of the Generic Casks for Three-Year-Old High Burnup Spent Fuel ..........6-4

Table 6.4 Internal and External, Steady State, Cask Surface Temperatures..............................................................6-5

Table 6.5 Time (hours) Required for the Generic Cask Internal Surface to get to the Three

Characteristic Temperatures in a Long Duration Engulfing, Optically Dense, 1000°C Fire ............................6-7

Table 6.6 Cask Internal Surface Temperatures (°C) for Four Characteristic Times in a Long

Duration, Engulfing, Optically Dense, 1000°C Fire .........................................................................................6-7

Table 6.7 Time (hours) Required for the Generic Cask Internal Surface to get to the Two

Characteristic Temperatures in a Long Duration Engulfing, Optically Dense, 800°C Fire ..............................6-7

Table 6.8 Cask Internal Surface Temperatures for Four Characteristic Times in a Long

Duration Engulfing, Optically Dense, 800°C Fire ............................................................................................6-7

Table 7.1 Wayside Hard Rock on Modal Study Segments of I-5 and I-80 ...............................................................7-5

Table 7.2 Wayside Surfaces on Modal Study Segments of I-5 and I-80...................................................................7-6

Table 7.3 Wayside Surface Characteristics for Three Illustrative Shipping Routes..................................................7-7

Table 7.4 Fractional Occurrence Frequencies for Route Wayside Surfaces Selected for Use in This Study............7-7

Table 7.5 Conditional Probabilities of Occurrence of Various Truck Accident Scenarios (%) ................................7-8

Table 7.6 Truck Accidents that Initiate Fires (Percentages) .....................................................................................7-9

Table 7.7 Conditional Probabilities of Occurrence of Various Train Accident Scenarios (%)...............................7-11

Table 7.8 Summary of ORIGEN Calculations, Total Curies per Assembly for All Radionuclides ........................7-15

Table 7.9 Generic High Burnup, Three-Year Cooled, Fuel Assembly Inventories for RADTRAN

Calculations (Ci/assembly) .............................................................................................................................7-17

Table 7.10 Truck Accident Cases ...........................................................................................................................7-25

Table 7.11 Train Accident Cases ............................................................................................................................7-26

Table 7.12 Experimental Release Fractions for Fuel Fines.....................................................................................7-31

Table 7.13 Granular Bed Lengths that Provide 99 Percent Filtering Efficiencies...................................................7-33

Table 7.14 Parameter Values for Lorenz Release Expressions for Cs ....................................................................7-36

Table 7.15 Comparison of Cs Release Fractions for Rod Burst Rupture and Diffusive Release ...........................7-37

Table 7.16 Initial Conditions and Volumes for the CONTAIN Model Cells..........................................................7-38

Table 7.17 Flow Junction Characteristics in the CONTAIN Model .......................................................................7-40
xv

Table 7.18 PWR and BWR Rod Failure Fractions (percent) for Four Generic Casks............................................7-50

 a. PWR Fuel Assembly .......................................................................................................................................7-50

 b. BWR Fuel Assembly.......................................................................................................................................7-51

Table 7.19 Seal Leak Areas and Values of FCE for Rail Casks ...............................................................................7-53

Table 7.20 Values of fdeposition for Rail Casks ..........................................................................................................7-54

Table 7.21 Expansion Factor Values ......................................................................................................................7-55

Table 7.22 Probability of Occurrence and Average Number of Cars Derailed

for Train Derailment Accidents by Accident Speed Range ............................................................................7-56

Table 7.23 Impact Speeds (mph) onto Real Yielding Surfaces that are Equivalent

to 30, 60, 90, and 120 mph Impacts onto an Unyielding Surface ...................................................................7-58

Table 7.24 Truck Accident Velocity Distributions .................................................................................................7-61

Table 7.25 Train Accident Velocity Distributions ..................................................................................................7-62

Table 7.26 Durations (hr) of Co-Located, Fully Engulfing, Optically Dense, Hydrocarbon

Fuel Fires that Raise the Temperature of Each Generic Cask to Ts, Tb, and Tf ..............................................7-65

Table 7.27 Truck Accident Fire Durations..............................................................................................................7-66

Table 7.28 Train Accident Fire Durations ..............................................................................................................7-67

Table 7.29 Comparison of Modal Study Cumulative Fire Durations for Various Truck

Accidents to Those Developed by Weighted Summation of Data from Clauss, et al. [7-5] ...........................7-68

Table 7.30 Truck and Train Commodity Flow Statistics for 1993..........................................................................7-69

Table 7.31 Source Term Severity Fractions and Release Fractions ........................................................................7-73

Table 8.1 Characteristics of Sets of RADTRAN Calculations..................................................................................8-2

Table 8.2 RADTRAN 5/LHS Accident-Risk Results versus Number of Observations ............................................8-4

Table 8.3 RADTRAN 5/LHS Accident-Risk Results for 200 Observations versus “Seed”......................................8-4

Table 8.4 Incident-Free and Accident Population Dose Risks for Truck Transport ...............................................8-15

Table 8.5 Incident-Free Population Dose Risks for Rail Transport ........................................................................8-24

Table 8.7 NUREG-0170 and Illustrative Real Truck and Rail Routes....................................................................8-29

Table 8.8 Incident-Free Population Dose Risks for Truck Transport of PWR Spent Fuel in

a Generic Steel-Lead-Steel Truck Cask over Illustrative Routes....................................................................8-36

Table 8.9 Incident-Free Population Dose Risks for Rail Transport of PWR Spent Fuel in a

Generic Monolithic Steel Rail Cask over Illustrative Routes .........................................................................8-44

Table 8.10 Route Parameters for Heavy-Haul Truck Transport Segments .............................................................8-46

Table 8.11 Heavy-Haul Incident-Free and Accident Population Dose Risks..........................................................8-47

Table 8.12 Values of Severity Fractions, LOS Fractions, .......................................................................................8-50

and Source-Strength Multipliers for Ten LOS Accident Cases ......................................................................8-50

Table 8.13 Results of Loss of Shielding Risk Calculation ......................................................................................8-52

Table 8.16 RADTRAN 1, RADTRAN 4, and RADTRAN 5 Estimates of the Mean Latent Cancer

Fatality Risks Associated with Shipment of Spent Fuel According to the NUREG-0170 Standard

Shipment Model for 1975...............................................................................................................................8-60

Table 8.17 Mean Accident Population Dose Risks (person-rem) for Five RADTRAN 5 Calculations

that Used Different Source Terms and Exposure Pathways............................................................................8-62

Table 8.18 Modal Study Truck and Rail Accident Source Terms...........................................................................8-65

Table 8.19 Comparison of NUREG-0170 Model I and Model II and Modal Study Probability

and Consequence Axis CCDF Intercepts to Those Developed by this Study .................................................8-68

Table 8.20 Ratios of Probability Axis Intercepts ....................................................................................................8-68
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xvii

Acknowledgements

Thanks are owed to a number of people for the contributions they made to the performance of

this study or the preparation of this report. The ORIGEN, CONTAIN, and VICTORIA

calculations described in Section 7 were performed on short notice by J.D Smith, Nathan Bixler,

and Kenneth Murata, respectively. Philip Reardon ressurected the RADTRAN 1 code and

supported the analyses described in Section 7 of impact fracturing of spent fuel and also of

cesium release fractions. Mona Aragon prepared the conceptual design drawings of the generic

casks in Section 4 and almost all of the figures in Section 5.

Thanks are especially owed to the reviewers of this report. They identified many topics that

needed to be better explained and even more sentences that required rewriting. Without their

efforts, many parts of this report would be close to inscrutable. At Sandia National Laboratories,

David Harding reviewed Sections 4 and 5 of the report, Dana Powers reviewed Section 7, and the

entire report was reviewed by Robert Luna and Charles Massey. External review of the report

was performed by Brian Anderson, Moe Dehgahani, Larry Fisher, Edwin Jones, Mike Shaffer,

and Monika Witte of Lawrence Livermore National Laboratories assisted by Theo Theofanous of

the University of California at Santa Barbara. The report was also reviewed by a number of

technical experts at NRC. The NRC reviews were directed and partly performed by M. Wayne

Hodges and Earl Easton.

Lastly, we wish to acknowledge the support, guidance, encouragement, and patience of John

Cook, the NRC project manager for this study. Without his help, we would never have finished.
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xix

ACRONYMS

AAR American Association of Railroads

ANL Argonne National Laboratory

BDF building dose factor

BMCS Bureau of Motor Carrier Safety

BWR boiling water reactor

CCDF Complementary Cumulative Distribution Function

DOE Department of Energy

DOT U.S. Department of Transportation

DU depleted uranium

EIS Environmental Impact Statement

EQPS Equivalent Plastic Strain

G acceleration due to gravity

GES General Estimates System

GIS Geographic Information System

GWDt/MTU gigawatt-days thermal per metric ton of uranium

LCF latent cancer fatalities

LHS Latin Hypercube Sampling

LLNL Lawrence Livermore National Laboratory

LOS loss of shielding

MPC multi-purpose cask

NMSS Nuclear Material Safety and Safeguards

NRC Nuclear Regulatory Commission

PWR pressurized water reactor

RAM radioactive material

SETU Structural Evaluation Test Unit

SNL Sandia National Laboratories

TE total plastic elongation

TIFA Trucks Involved in Fatal Accidents

UE uniform plastic elongation

USGS U.S. Geologic Survey
xx

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ES-1

EXECUTIVE SUMMARY

Introduction

In September of 1977, the Nuclear Regulatory Commission (NRC) issued a generic

Environmental Impact Statement (EIS), titled “Final Environmental Statement on the

Transportation of Radioactive Material by Air and Other Modes,” NUREG-0170, that covered

the transport of all types of radioactive material by all transport modes (road, rail, air, and water)

[E-1]. That EIS provides the regulatory basis for issuance of general licenses for transportation

of radioactive material under 10 CFR 71. Based in part on the findings of NUREG-0170, the

NRC’s Commission concluded that “present regulations are adequate to protect the public

against unreasonable risk from the transport of radioactive materials” (46 FR 21629, April 13,

1981) and stated that “regulatory policy concerning transportation of radioactive materials be

subject to close and continuing review.”

In 1996 the NRC decided to reexamine the risks associated with the shipment of spent power

reactor fuel by truck and rail. The reexamination was initiated (1) because many spent fuel

shipments are expected to be made during the next few decades, (2) because these shipments will

be made to facilities along routes and in casks not specifically examined by NUREG-0170, and

(3) because the risks associated with these shipments can be estimated using new data and

improved methods of analysis. This report documents the methodology and results of the study

that performed this reexamination of the risks of transporting spent fuel from commercial reactor

sites to possible interim storage sites and/or permanent geologic repositories.

Overview of NUREG-0170

NUREG-0170 estimated the radiation doses and latent cancer fatalities that might be associated

with the transportation of 25 different radioactive materials by plane, truck, train, and ship or

barge. The estimates were made using Version 1 of the RADTRAN code (RADTRAN 1) [E-2],

that was developed specifically to perform the NUREG-0170 study. One of the 25 radioactive

materials examined by NUREG-0170 was spent power reactor fuel.

For spent fuel shipments that occur without accidents (incident-free transport), radiation doses

were estimated for two population groups: (1) shipment workers (e.g., the truck or train crew,

cask handlers, and persons who inspect the cask, truck, or train) and (2) members of the general

public who would be exposed to low levels of radiation, because they lived near the shipment

route or came near the cask while traveling on the route. For transportation accidents, release of

radioactive material from spent fuel to the environment, the probability of these releases, and the

population doses and radiation-induced latent cancer fatalities that such releases might cause

were estimated.

The influence of accident severity on accident consequences was examined by dividing all

accidents into eight categories according to their severity. Because “little information relating

the response of packages to accident environments” [E-3] was available in 1975, release of

radioactive materials to the environment as a result of accidents was examined using two release

models that were constructed largely by expert judgement. The first model, Model I [E-4],
ES-2

assumed [E-5] that “zero release occurs up to the regulatory test level and that the packaging fails

catastrophically in all environments that exceed that level.” Because the Model I cask release

behavior was considered to be unrealistic, a second release model (Model II) was formulated. In

Model II, for accidents that exceed the regulatory test level, release fractions increased more

gradually with accident severity [E-6], becoming equal for catastrophic accidents to the release

specified for all severe accidents by Model I.

Because the NUREG-0170 spent fuel accident source terms were not developed by examining

the response of spent fuel and spent fuel casks to severe accident conditions, NRC had the

response of generic steel-lead-steel truck and rail spent fuel casks to collision and fire accident

conditions examined by the performance of finite element impact and thermal heat transport

calculations. The results of these calculations were published in 1987 in NUREG/CR-4829,

“Shipping Container Response to Severe Highway and Railway Accident Conditions,” which is

usually called the Modal Study [E-7]. Although that study did not perform any consequence

calculations, comparison of the probabilities and magnitudes of the accident source terms

developed for that study to those developed for NUREG-0170 allowed the authors of the Modal

Study to conclude that the risks per spent fuel shipment for shipments by both truck and rail were

“at least 3 times lower that those documented in NUREG-0170” [E-1].

Methodology

The risks associated with the transport of spent nuclear fuel were estimated using Version 5 of

the RADTRAN code [E-8, E-9]. Risks were estimated (1) for incident-free transport, (2) for

transportation accidents so severe that they result in the release of radioactive materials from the

cask to the environment, and (3) for less severe accidents that cause the cask shielding to be

degraded but result in no release of radioactive material (Loss of Shielding accidents).

Based on prior sensitivity studies [E-10, E-11, E-12], RADTRAN 5 input parameters were

divided into three groups: (1) source term parameters (severity and release fractions); (2) other

input parameters that strongly influence RADTRAN estimates of radiation dose, which were

collectively called other “more important parameters”; and (3) RADTRAN input parameters that

have little impact on estimates of radiation dose, which were collectively called “less important

parameters.” Central (best) estimate values were selected for each of the “less important”

parameters, e.g., breathing rate.

For the source term parameters, review of studies of transportation accidents, in particular the

Modal Study [E-7], allowed representative sets of truck and train accidents and their impact and

fire environments to be defined. This analysis developed 19 representative truck accidents and

21 representative train accidents. Severity fraction and release fraction values were estimated for

each representative accident.

Severity fractions specify the fraction of all possible accidents that are represented by each of the

representative accidents. Severity fraction values were estimated by review of the accident event

trees, accident speed distributions, and accident fire distributions that were developed for the

Modal Study [E-7]. Because only impact onto a very hard surface can result in the release of

radioactive materials during a collision accident, new event tree frequencies of occurrence of
ES-3

route wayside surfaces (e.g., hard rock; concrete, soft rock, and hard soil; soft soil; water) were

developed using Department of Agriculture data [E-13] and Geographic Information System

(GIS) methods of analysis [E-14].

Release fractions were estimated as the product of (a) the fraction of the rods in the cask that are

failed by the severe accident, (b) the fraction of each class of radioactive materials (e.g., noble

gases, volatile, particulates) that might escape from a failed spent fuel rod to the cask interior,

and (c) the fraction of the amount of each radioactive material released to the cask interior that is

expected to escape from the cask to the environment. Rod failure during high speed collision

accidents was estimated by scaling rod strains calculated for relatively low speed impacts [E-15]

and then comparing the scaled rod strains to a strain failure criterion [E-15]. Heating of the cask

by a hot long duration fire to rod burst rupture temperatures was assumed to fail all unfailed rods

(those not failed by collision impact). Rod-to-cask release fractions were estimated by review of

literature data, especially the experimental results of Lorenz [E-16, E-17, E-18]. Cask-toenvironment release fractions were based on MELCOR [E-19] fission product transport

calculations [E-20] that estimated the dependence of these release fractions on the cross-sectional

area of the cask leak path through which the release to the environment occurs.

Specifications for generic steel-lead-steel truck and rail casks and for a generic steel-DU-steel

truck cask and a generic monolithic steel rail cask were developed from literature data [E-21].

The response of these generic casks to severe collisions (e.g., seal leak areas) was examined by

performing three-dimensional finite element calculations for impacts onto an unyielding surface

at various impact speeds. Unyielding surface impact speeds were converted to equivalent impact

speeds onto yielding surfaces (e.g., soft rock) by considering the energy that would be absorbed

by the yielding surface, increasing the energy of the unyielding surface calculation by that

amount, and converting the new total energy to an initial impact speed. Seal degradation and rod

burst rupture temperatures due to heating during fires were estimated from literature data. The

durations of engulfing, optically dense fires needed to produce seal leakage and rod burst rupture

were estimated by performing one-dimensional heat transport calculations.

For the other “more important” parameters (e.g., route lengths, population densities, accident

rates, durations of truck stops, and cask surface dose rates), distributions of parameter values

were constructed that reflected the likely real-world range and frequency of occurrence of the

value of each parameter. Next, 200 sets of parameter values were constructed by sampling these

distributions using a structured Monte Carlo sampling technique called Latin Hypercube

Sampling (LHS) [E-12, E-22]. This procedure generated one set of 200 parameter values for

spent fuel transportation by truck and a second set for transportation by rail. Each set included

parameter values for 200 representative highway or railway routes that spanned the length and

breadth of the continental United States but had no specific origins or destinations.

By taking all possible combinations of the single set of central estimate values for the “less

important” RADTRAN input parameters, the 200 sets of other “more important” truck parameter

values, and the 19 sets of representative truck accident severity and release fraction values, input

for 3800 single-pass RADTRAN 5 truck spent fuel transportation calculations was developed for

each generic truck cask. Similarly, by taking all possible combinations of the set of “less

important” parameter values, the 200 sets of other “more important” rail parameter values, and
ES-4

the 21 sets of representative rail accident severity and release fraction values, input for 4200

single-pass RADTRAN 5 rail spent fuel transportation calculations was developed. Finally,

application of standard statistical methods to the results of these 3800 truck or 4200 rail

transportation calculations then allowed the results to be displayed as Complementary

Cumulative Distribution Functions (CCDFs) and estimates of the expected (mean) result for

radiological consequences (e.g., population dose) to be calculated.

Results

Seven sets of RADTRAN calculations are described in the body of this report. Each set of

calculations developed estimates of the radiological consequences and risks that are associated

with the shipment of power reactor spent fuel. Two types of consequences and risks were

estimated, those that are associated with the occurrence of accidents during the shipment and

those associated with shipments that take place without the occurrence of accidents. The

calculations examine four generic cask designs, two shipment modes, two sets of routes, and

three sets of accident source terms. The four generic cask designs examined are steel-lead-steel

truck and rail casks, a steel-DU-steel truck cask, and a monolithic steel rail cask. The two

shipment modes are truck and rail. The two sets of routes are (a) 200 representative truck or rail

routes selected by LHS sampling of route parameter distributions and (b) for each mode, the four

illustrative real routes plus the NUREG-0170 shipment route. The three sets of accident source

terms are the NUREG-0170 [E-1] source terms, the Modal Study source terms [E-7], and the

new source terms developed by this study.

Calculational sets one and two examine spent fuel transportation by truck and rail using the 200

sets of other “more important” truck or rail input parameter values that were constructed by LHS

sampling of the real-world distributions of the values of these parameters. Sets three and four

examine transportation by truck and rail over four “illustrative” truck or rail routes and the

NUREG-0170 truck or rail route. Comparison of the results of these illustrative route

calculations to the results obtained for the calculations that used the 200 representative routes

showed that the results obtained for the “illustrative” real routes fall within the range of the

results obtained for the representative routes. Set five examined the influence of NUREG-0170

exposure pathway modeling on accident consequence predictions. And sets six and seven

compared the accident consequence predictions developed using the accident source terms

developed by this study to those developed using the accident source terms developed by the

Modal Study [E-7] and NUREG-0170 [E-1].

The full study provides results for transport of PWR and BWR spent fuel by truck or rail in four

generic casks. In this Executive Summary, results are presented only for the six RADTRAN 5

calculations that examined transport of PWR spent fuel in steel-lead-steel truck or rail spent fuel

casks. These results are typical of those obtained for BWR spent fuel and/or transportation in

other generic casks. Each of the six calculations discussed here used the set of “less important”

values for all RADTRAN 5 input parameters assigned central estimate values. Each calculation

used the other “more important” truck or rail parameter values, that were generated by LHS

sampling. Thus, these calculations differed only in the source terms used (i.e., NUREG-0170

source terms, Modal Study source terms, or the source terms developed by this study), and the set

of exposure pathways modeled (the calculations that used Modal study source terms or the source
ES-5

terms developed by this study examined all exposure pathways; the calculations that used

NUREG-0170 source terms calculated exposures only for the inhalation pathway because only

the inhalation pathway was examined by the NUREG-0170 study).

Table E.1 compares the NUREG-0170 incident-free truck and rail doses to the incident-free

doses developed by this study. Because the NUREG-0170 doses were developed for all of the

spent fuel shipments expected to occur in 1975 or 1985, doses for single shipments are calculated

by dividing the 1975 or 1985 doses by the number of spent fuel shipments that NUREG-0170

estimated would occur during these years. Table E.1 shows that for single shipments the sum of

the other incident-free doses (i.e., crew, on-link, off-link, and stop doses) developed by this study

for spent fuel transport by truck with two-person crews is about one-fourth of the sum of the

corresponding NUREG-0170 truck doses. It also shows that the sum of this study’s incident-free

doses for transport by rail is about two-thirds of the sum of the corresponding NUREG-0170 rail

doses. The similarity of these incident-free results is not surprising, because both studies assume

that the surface dose rates of spent fuel transportation casks are somewhat below the regulatory

limit and both use along-route population densities and the population densities at rest stops that

are not very different. Table E-1 also shows that shipment of the 1994 spent fuel inventory at a

constant number of shipments per year over 30 years leads to average yearly population doses for

transport by truck and rail that are respectively about half and one-tenth of the NUREG-0170

estimates for 1985.

Table E.1 Comparison of NUREG-0170 Incident-Free Doses (person-rem)

to the Incident-Free Doses Developed by this Studya

Doses (person-rem)

Multiple Shipments Single Shipment

Study Year Mode Number of

Shipments

Hand/Storb Otherc Hand/Storb Otherc

NUREG-0170 1975 Truck 254 52.06 41.74 0.205 0.164

NUREG-0170 1985 Truck 1530 313.6 251.4 0.205 0.164

This Study Truck 2489d Not Calc.e 110 Not Calc.e 0.0441

NUREG-0170 1975 Rail 17 7.227 0.553 0.425 0.0325

NUREG-0170 1985 Rail 652 277.4 20.60 0.425 0.0316

This Study Rail 100.5d Not Calc.e 2.040 Not Calc.e 0.0203

a. Modal Study incident-free doses are not presented because the Modal Study did not perform any consequence calculations.

b. Handler + storage doses.

c. Crew + on-link + off-link + stop doses.

d. Average number of shipments per year required to ship the full 1994 spent fuel inventory over 30 years in steel-lead-steel

truck and rail casks.

e. NUREG-0170 assumed that intermodal cask transfers and temporary storage of the cask would occur during cask shipments;

this study assumed that they would not occur and therefore did not calculate any handling/storage doses.
ES-6

Figures E.1 and E.2 present the CCDFs generated by these calculations. CCDFs are plots of the

chance of obtaining a result equal to or larger than the consequence value that corresponds to the

probability. For example, in Figure E.1, the NUREG-0170 Model I CCDF shows that the

probability per shipment of an accident that leads to a population dose ≥ 10 person-rem is

estimated to be 10-4 (0.0001). Figures E.1 and E.2 both present four CCDFs: the NUREG-0170

Model I CCDF, the NUREG-0170 Model II CCDF, the Modal Study CCDF, and the CCDF

developed by this study. In each figure, the highest lying CCDF is the NUREG-0170 Model I

CCDF, the next highest is the NUREG-0170 Model II CCDF, the next is the Modal Study

CCDF, and the lowest lying CCDF is the CCDF developed by this study.

The area under each CCDF represents the expected risk from a single shipment of spent fuel for

the calculation that generated the CCDF. Table E.2 presents these expected accident population

dose risks. Thus, Table E.2 allows the expected dose risks calculated using the new truck and

train accident source terms developed by this study to be compared to those calculated using

NUREG-0170 Model I and Model II and Modal Study source terms. Because source term

magnitudes directly reflect spent fuel and cask response to accidents, the results presented in this

table and in Figures E.1 and E.2 display the effects of the different treatments of spent fuel and

spent fuel casks made by each study.

Table E.2 Comparison of Mean Accident Population Dose Risks (person-rem) Calculated

Using NUREG-0170 Model I and Model II Source Terms and Modal Study Source Terms

to Those Calculated Using the Source Terms Developed by this Study

Study Truck Accidents Train Accidents

 NUREG-0170 Model Ia 1.3E-2 1.9E-2

 NUREG-0170 Model IIa 7.7E-4 4.9E-4

 Modal Studyb 1.3E-4 1.9E-3

 This Studyb 8.0E-7 9.4E-6

a. Calculated assuming exposures only by the inhalation pathway.

b. Calculated assuming exposures by all exposure pathways.

Comparison of the results presented in Tables E.1 and E.2 shows that the ratio of this study’s

estimates of single shipment mean incident-free dose risks to this study’s single shipment mean

accident dose risks is about are 5x104

 for truck and about 2x103 for rail. Thus, single shipment

incident-free dose risks, which are quite small, greatly exceed single shipment accident dose

risks.

Inspection of Table E.2 shows that the expected accident population dose risks stand in the

following order and have the following relative magnitudes when normalized to the NUREG0170 Model I result:

Truck Accidents: NUREG-0170 Model I (1.0) > NUREG-0170 Model II (0.06)

> Modal Study (0.01) > This Study (0.00006)

Rail Accidents: NUREG-0170 Model I (1.0) > Modal Study (0.1)

> NUREG-0170 Model II (0.03) > This Study (0.0005)
ck accident population dose risk CCDFs for calculations that compared the source terms developed by

odal Study, and this study. Each RADTRAN 5 calculation assumed transport in a steel-lead-steel truck

 200 representative truck routes and each calculation generated results for all of the 19 representative

e terms.

70 accident release inventory, NUREG-0170 Model I release fractions, only inhalation pathways

70 accident release inventory, NUREG-0170 Model II release fractions, only inhalation pathways

tory, 20 Modal Study source terms, all exposure pathways

tory, 19 truck accident source terms developed for this study, all exposure pathways

4 10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)
ES-8

l accident population dose risk CCDFs for calculations that compared the source terms developed by

odal Study, and this study. Each RADTRAN 5 calculation assumed transport in a steel-lead-steel rail

 200 representative rail routes and each calculation generated results for all of the 21 representative rail

s.

70 accident release inventory, NUREG-0170 Model I release fractions, only inhalation pathways

70 accident release inventory, NUREG-0170 Model II release fractions, only inhalation pathways

tory, 20 Modal Study source terms, all exposure pathways

tory, 19 truck accident source terms developed for this study, all exposure pathways

10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)
ES-9

The relative ordering of these accident results is entirely consistent with the assumptions made by

each study regarding the probability of radionuclide leakage from the cask during transportation

accidents and the magnitude of the source terms generated by accidents of differing severities.

Because both Model I and Model II in NUREG-0170 assumed that spent fuel casks might release

a portion of their contents when subjected to the loads that characterize minor accidents, the

fraction of all truck and train accidents predicted by these models to cause releases is very large

and extremely conservative. Similarly, because the NUREG-0170 Model I assumed that all cask

leaks led to the release of the entire NUREG-0170 accident inventory (the largest amount of

radioactive material expected to be released during a severe accident), the mean accident

population doses calculated using the NUREG-0170 Model I for truck and rail accidents are

quite large. When, as was done by the Modal Study, cask failure and thus source term

probabilities and magnitudes are estimated from the response of the cask shell to mechanical and

thermal loads, both source term probabilities and most source term magnitudes decrease.

Consequently, relative to the NUREG-0170 Model I result, mean accident population dose risks

for rail and truck are decreased respectively by one and two orders of magnitude. When, as was

done by this study, cask release and thus source term probabilities and magnitudes are estimated

by examining the response of cask closures and spent fuel rods to impact loads and the burst

rupture of spent fuel rods due to heating by fires, cask release is found to be even less likely and

retention of particles and condensable vapors by deposition onto cask interior surfaces is found to

be substantial. Accordingly, source term probabilities and most source term magnitudes, except

those for the most severe accidents examined, decrease further. Consequently, relative to the

Modal Study result, expected (mean) accident population dose risks for both rail and truck are

each further decreased by about two orders of magnitude.

Source term magnitudes for the most severe accidents examined by the Modal Study and this

study are larger than the largest source term magnitude postulated in NUREG-0170. They are

larger because the product of the cask inventory and the largest accident release fractions

developed by this study is larger than the largest source term examined by NUREG-0170.

Nevertheless, although the largest source terms developed by the analyses performed by the

Modal Study and this study are larger than the largest NUREG-0170 source term, the accident

risks posed by these source terms are substantially smaller because these source terms are so very

improbable.

Conclusions

The results described in detail in the body of this report lead to the following conclusions:

• The single cask truck shipment expected incident-free population doses developed by this

study are about one-quarter of those in NUREG-0170.

• The single cask rail shipment expected incident-free population doses developed by this study

are about two-thirds of those in NUREG-0170.

• The use of very conservative cask failure criteria in NUREG-0170 caused its estimates of the

fraction of all accidents that release radioactive materials to be much too large and thus very

conservative.
ES-10

• The NUREG-0170 estimate of the largest source term that might be released from a failed

spent fuel cask during an unusually severe transportation accident is significantly lower than

the largest source terms calculated using Modal Study release fractions or the release

fractions developed by this study. However, the risks associated with these source terms are

lower than the risk of the largest NUREG-0170 source term because these source terms are so

very improbable.

• The source terms developed by the Modal Study and by this study, which reflect the

complexities of rod failure and cask response to transportation accident impact and thermal

loads, yield estimates of expected (mean) spent fuel transportation accident population doses

that are orders of magnitude smaller than those developed by the NUREG-0170 study.

Overall, the results of this study confirm the validity of the NUREG-0170 estimates of spent fuel

incident-free population doses. The results also show that the NUREG-0170 estimates of spent

fuel accident population dose risks were very conservative, as was believed to be true when

NUREG-0170 was published [E-23].

References

[E-1] “Final Environmental Statement on the Transportation of Radioactive Material by Air

and Other Modes,” NUREG-0170, U.S. Nuclear Regulatory Commission, Washington,

DC, December 1977.

[E-2] J. M. Taylor and S. L. Daniel, “RADTRAN: A Computer Code to Analyze

Transportation of Radioactive Material,” SAND76-0243, Sandia National Laboratories,

Albuquerque, NM, April 1977.

[E-3] Ref. [E-1], p. 5-20.

[E-4] Ref. [E-1], p. 5-22.

[E-5] Ref. [E-1], p. 5-21.

[E-6] Ref. [E-1], p. 5-23.

[E-7] L. E. Fischer, et al., “Shipping Container Response to Severe Highway and Railway

Accident Conditions,” NUREG/CR-4829, Lawrence Livermore National Laboratory,

Livermore, CA, February 1987.

[E-8] K. S. Neuhauser and F. L. Kanipe, “RADTRAN 5, Technical Manual,” Sandia National

Laboratories, Albuquerque, NM (in preparation, draft available on request).

[E-9] K. S. Neuhauser and F. L. Kanipe, “RADTRAN 5, User Guide,” Sandia National

Laboratories, Albuquerque, NM (draft available on the RADTRAN web site).

[E-10] G. S. Mills, G. S., K. S. Neuhauser, and F. L. Kanipe, “RADTRAN 4 Truck Accident

Risk Sensitivity Analysis,” Proceedings of Waste Management 95, WM Symposia,

Tucson, AZ, 1995.
ES-11

[E-11] G. S. Mills and K. S. Neuhauser, “Sensitivity Analysis for RADTRAN 4 Input

Parameters,” 88th Annual Meeting of the Air & Waste Management Association., San

Antonio, TX, 1995.

[E-12] G. S. Mills, et al., “Application of Latin Hypercube Sampling to RADTRAN 4 Truck

Accident-Risk Sensitivity Analysis,” Proceedings of the 11th International Conference

on the Packaging and Transportation of Radioactive Materials (PATRAM ’95), IAEA,

Vol. 4, p. 705, 1995.

[E-13] State Soil Graphics (STATSGO) Data Base, available on the Internet at

ftp.ftw.nrcs.usda.gov/pub/statsgo.

[E-14] ARC/INFO Coverages and Arc View Project, K. C. Bayer Digital Map of the U.S.,

purchased from Geologic Data Systems, Inc., 1600 Emerson St., Denver, CO 80218.

[E-15] T. L. Sanders, et al., “A Method for Determining the Spent-Fuel Contribution to

Transport Cask Containment Requirements, Appendix III, Spent Fuel Response to

Transport Environments,” SAND90-2406, Sandia National Laboratories, Albuquerque,

NM, November 1992.

[E-16] R. A. Lorenz, et al., “Fission Product Release from Highly Irradiated LWR Fuel,”

NUREG/CR-0722, Oak Ridge National Laboratory, Oak Ridge, TN, February 1980.

[E-17] R. A. Lorenz, et al., “Fission Product Release from Simulated LWR Fuel,” NUREG/CR0274, Oak Ridge National Laboratory, Oak Ridge, TN, July 1978.

[E-18] R. A. Lorenz, et al., “Fission Product Source Terms for the LWR Loss-of-Coolant

Accident,” NUREG/CR-1288, Oak Ridge National Laboratory, Oak Ridge, TN, July

1980.

[E-19] R. M. Summers, et al., “MELCOR 1.8.0: A Computer Code for Nuclear Reactor Severe

Accident Source Term and Risk Assessment Analyses,” NUREG/CR-5531, SAND90-

0364, Sandia National Laboratories, Albuquerque, NM, January 1991.

[E-20] J. L. Sprung, et al., “Data and Methods for the Assessment of the Risks Associated with

the Maritime Transport of Radioactive Materials: Results of the SeaRAM Program,”

SAND97-2222, Sandia National Laboratories, Albuquerque, NM, August 1997.

[E-21] “Shipping and Storage Cask Data for Commercial Spent Nuclear Fuel,” JAI Corp., July

1996.

[E-22] G. D. Wyss and K. H. Jorgensen, “A User’s Guide to LHS: Sandia’s Latin Hypercube

Sampling Software,” SAND98-0210, Sandia National Laboratories, Albuquerque, NM,

1998.

[E-23] Ref. [E-1], p. ix.
ES-12

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1-1

1. INTRODUCTION

1.1 NUREG-0170

In September of 1977, the Nuclear Regulatory Commission (NRC) issued a generic

environmental impact statement (EIS), titled “Final Environmental Statement on the

Transportation of Radioactive Material by Air and Other Modes,” NUREG-0170, that covered

the transport of all types of radioactive material by all transport modes (road, rail, air, and water)

[1-1]. That EIS provided the regulatory basis for continued issuance of general licenses for

transportation of radioactive material under 10 CFR 71. Based in part on the findings of

NUREG-0170, NRC staff concluded (1) that “the average radiation dose to the population at risk

from normal transportation is a small fraction of the limits recommended for members of the

general public from all sources of radiation other than natural and medical sources and is a small

fraction of natural background dose” and (2) that “the radiological risk from accidents in

transportation is small, amounting to about one-half percent of the normal transportation risk on

an annual basis” [1-2]. In addition, the NRC Commission concluded that “present regulations

are adequate to protect the public against unreasonable risk from the transport of radioactive

materials” (46 FR 21629, April 13, 1981) and stated that “regulatory policy concerning

transportation of radioactive materials be subject to close and continuing review.”

1.2 NUREG-0170 Spent Fuel Transportation Risks

NUREG-0170 estimated the radiation doses and latent cancer fatalities that might be associated

with the transport of 25 different radioactive materials by plane, truck, train, and ship or barge.

The 25 materials were chosen to encompass 90 percent of all shipments in the United States and

90 percent of the activity contained in shipments. The estimates were made using Version 1 of

the RADTRAN code (RADTRAN 1) [1-3], which was developed specifically to support the

performance of the NUREG-0170 study.

One of the 25 radioactive materials examined by NUREG-0170 was spent nuclear power reactor

fuel. For spent fuel shipments that occur without accidents (incident-free transport), radiation

doses were estimated for members of the general public who would be exposed to radiation, for

example, because they lived near the shipment route, and also for workers (e.g., crew, handlers,

inspectors). Release of radioactive materials from spent fuel to the environment as a result of

transportation accidents, the probability of these releases, and the latent cancer fatalities that such

releases might cause were also estimated.

Spent fuel transport risks were estimated for shipment by truck and by train over a generic

highway and a generic rail route [1-4]. Table 1.1 describes attributes of these two generic routes.

Radiological consequences (population doses for incident-free transport and expected numbers of

latent cancer fatalities for transportation accidents) were estimated for spent fuel shipments

expected to occur during 1975 and 1985. Tables 1.2 and 1.3 respectively present the incidentfree and accident consequences estimated for these spent fuel shipments.
1-2

Table 1.1 NUREG-0170 Spent Fuel Truck and Train Route Data

Parameter Truck Route Rail Route

Route Length (km) 2530 1210

 Fraction Urban 0.05 0.05

 Fraction Suburban 0.05 0.05

 Fraction Rural 0.9 0.9

Population Densities (people km-2)

 Urban 3861 3861

 Suburban 719 719

 Rural 6 6

Shipments per year (single cask)

 1975 254 17

 1985 1530 652

Table 1.2 NUREG-0170 Annual Incident-Free

Spent Fuel Transportation Doses (person-rem)

Incident-Free Truck Train

Shipment Doses 1975 1985 1975 1985

 Crew 31.3 188 0.68 2.6

 Handlers 50.8 306 6.8 261

 Storage 1.26 7.6 0.427 16.4

 General Public

 Off-Linka 3.8 22.9 0.175 6.69

 On-Linkb 1.88 11.3 0.222 8.53

 Stopsc 4.82 29.0 0.089 3.44

 Total Population Dose 93.8 565 7.78 298

a. Residents living by the transport route.

b. Travelers exposed while traveling in cars, buses, or trains.

c. Travelers exposed at rest stops.

Table 1.3 Expected (Mean) Latent Cancer Fatalities Predicted in NUREG-0170

to be Caused by Truck and Train Accidents that Occur during Spent Fuel Transport

Year Release Model Truck Train Truck + Train

1975 I 0.047 0.021 0.068

1985 I 0.29 0.8 1.09

1975 II NA NA 0.0000356

1985 II NA NA 0.000422
1-3

For calculations of radiological consequences that might be caused by accidents, accidents were

divided into eight categories (Categories I through VIII) of increasing severity. Because “little

information relating the response of packages to accident environments” [1-5] was available in

1975 for spent fuel and other highly radioactive materials shipped in Type B packages, release of

radioactivity as a result of accidents was examined using two release models. The first model,

Model I [1-6], assumed [1-7] that “zero release occurs up to the regulatory test level and that the

packaging fails catastrophically in all environments that exceed that level.” The amounts of each

radionuclide that were assumed [1-8] to be released to the environment by this “catastrophic”

failure are presented in Table 1.4. Thus, Model I assumed that the radioactive release specified

in Table 1.4 would take place whenever a Type B spent fuel package was subjected to

mechanical or thermal loads in excess of the mechanical and thermal loads encountered during

package certification tests [1-9]. Because the Model I cask release behavior was considered to be

unrealistic, a second release model (Model II) was formulated. In Model II, for accidents that

exceed the regulatory test level, release fractions increased more gradually with accident severity

[1-10], becoming equal for catastrophic accidents to the release specified for all severe accidents

by Model I.

Table 1.5 shows that the Model I and Model II release fractions are used for both truck and train

accidents. Model I and Model II release fractions are the same for accident categories I, II, V, VI,

VII, and VIII and differ only for categories III, and IV. Finally, Table 1.3 shows that accident

consequences are substantially decreased if, as is done in Model II, release is assumed to increase

with increasing accident severity.

Table 1.4 Inventory (Ci) Assumed in NUREG-0170 to be Released to the Environment

from a Type B Spent Fuel Cask as a Result of an Accident

Fission Products Truck Cask Rail Cask

Kr-85 1700 10,900

I-131 0.022 0.138

Volatiles as Cs-137 200 1280

1.3 Need for Reevaluation of NUREG-0170 Spent Fuel Transportation

Risks

While NUREG-0170 was an important analysis that delineated transportation risks in the context

of the information available at that time, its results were developed using rather simple models

and limited data. In the interim, there has been significant growth in analytical capabilities and

data. While the casks and the specific routes for spent fuel movements have not yet been

designated, it is clear that the generic cask and routes used in NUREG-0170 are now less than

typical. For example, spent fuel may soon be shipped in the dual-purpose or multi-purpose

canisters (MPCs) from commercial reactors to Interim Spent Fuel Storage Installations and/or

Centralized Storage Facilities in addition to shipment to a permanent geologic repository. In fact,

the Office of Nuclear Material Safety and Safeguards (NMSS) has received several applications

for dual-purpose (storage and transport) spent fuel casks, and additional applications
1-1

Table 1.5 NUREG-0170 Model I and Model II Severity and Release

Fractions for Spent Fuel Transport by Truck and Rail

Severity Fractionsa Release Fractions

Accident Models I and II Truck and Rail

Category Truck Rail Model I Model II

I 0.55 0.50 0.0 0.0

II 0.36 0.30 0.0 0.0

III 0.07 0.18 1.0 0.01

IV 0.016 0.018 1.0 0.1

V 0.0028 0.0018 1.0 1.0

VI 0.0011 1.3×10-4 1.0 1.0

VII 8.5×10-5 6.0×10-5 1.0 1.0

VIII 1.5×10-5 1.0×10-5 1.0 1.0

a. Fraction of accidents that fall into this severity range

are expected in the near future. In addition, many improvements have been made to the risk

assessment models implemented in the RADTRAN code since the initial version of that code

was used to estimate spent fuel transportation risks for NUREG-0170, and a major study of the

response of spent fuel casks to severe transportation accidents, “Shipping Container Response to

Severe Highway and Railway Accident Conditions,” NUREG/CR-4829, often called the Modal

Study, has been published [1-11].

Because new data and analytical methods were now available to apply to the analysis of power

reactor spent fuel transportation risks, and because spent fuel is likely to be shipped to facilities

along routes and in casks not specifically examined by NUREG-0170, the NRC decided the

conclusions reached in NUREG-0170 should be reexamined in order to determine if the risks of

the spent fuel shipments that are expected to take place during the next few decades are bounded

by the risk estimates published in NUREG-0170. Accordingly, this report documents the

methodology and results of a reevaluation of the risks of transporting spent fuel from commercial

reactor sites to possible interim storage sites and/or permanent geologic repositories.

1.4 Study Objectives

This study had three objectives:

• Estimation of the radiological and non-radiological, routine and accident, transportation

risks associated with the anticipated spent fuel shipments and determination of whether

those risks are bounded by the estimates and projections of spent fuel shipment risks

published in 1977 in NUREG-0170.

• Examination of any outstanding spent fuel transportation issues or environmental

concerns not resolved by NUREG-0170 and the Modal Study.
1-2

• Documentation of the approach, data, and computational methods used to reestimate

spent fuel transportation risks in detail sufficient to allow other transportation experts to

fully understand the analyses performed, and preparation of a summary of the results in a

form accessible to concerned citizens.

1.5 General Approach

The risks associated with the transport of spent fuel were estimated using Version 5 of the

RADTRAN code [1-12, 1-13]. As in NUREG-0170, risks were estimated for incident-free

transport and also for transportation accidents severe enough to cause radioactive material to be

released from the cask to the environment.

Based on prior sensitivity studies [1-14, 1-15, 1-16], RADTRAN 5 input parameters were

divided into three groups:

• Source term parameters (accident severity fractions and their corresponding accident

release fractions),

• Other “more important” parameters that strongly influence RADTRAN estimates of

radiation dose (for values within their likely range), and

• “Less important” parameters which have little impact on estimates of radiation dose (for

values within their likely range).

For each of the “less important parameters,” e.g., breathing rate, central (best) estimate values

were selected. For each of the more important parameters (e.g., route lengths, population

densities, accident rates, durations of truck stops, and cask surface dose rates), distributions of

parameter values were constructed that reflected the likely real-world range and frequency of

occurrence of the value of each parameter. Next, for both truck and rail analyses, 200 sets of the

other “more important” parameter values were constructed by sampling these distributions using

a structured Monte Carlo sampling technique called Latin Hypercube Sampling [1-16, 1-17].

For the source term parameters, review of studies of actual transportation accidents, in particular

the Modal Study [1-11], allowed representative sets of truck and train accidents and their impact

and fire environments to be defined. This analysis developed 19 representative truck accidents

and 21 representative train accidents. Severity fraction and release fraction values were

estimated for each representative accident.

Severity fraction values were developed by a review of the accident event trees, accident speed

distributions, and accident fire distributions that were published in the Modal Study [1-11]. New

event tree frequencies of occurrence of route wayside surfaces (e.g., hard rock; concrete, soft

rock, and hard soil; soft soil; water) were developed using Department of Agriculture data [1-18]

and Geographic Information System (GIS) methods of analysis [1-19].

Release fractions were estimated as the product of (a) the fraction of the rods in the cask that are

failed by the severe accident, (b) the fraction of each class of radioactive materials (e.g.,

particulates) that might escape from a failed spent fuel rod to the cask interior, and (c) the
1-3

fraction of the amount of radionuclides released to the cask interior that is expected to escape

from the cask to the environment. Rod failure during high speed collision accidents was

estimated by scaling rod strains calculated for low speed impacts and then comparing the scaled

rod strains to a strain failure criterion [1-20]. Heating of the cask by a fire to rod burst rupture

temperatures was assumed to fail all unfailed rods. Rod-to-cask release fractions were estimated

by review of literature data, especially the experimental results of Lorenz [1-21, 1-22, 1-23].

Cask-to-environment release fractions were based on MELCOR fission product transport

calculations [1-24] that estimated the dependence of these release fractions on the size (crosssectional area) of the cask failure that allows the release to the environment to occur.

Specifications for two generic truck and two generic rail spent fuel casks were developed from

literature data [1-25]. Cask damage (e.g., seal leak areas) during severe collisions was estimated

from the results of finite element calculations that modeled impacts onto an unyielding surface at

various impact speeds. Unyielding surface impact speeds were converted to equivalent impact

speeds onto yielding surfaces (e.g., soft rock) by considering the energy that would be absorbed

by the yielding surface, increasing the energy of the unyielding surface calculation by that

amount, and converting the new total energy to an initial impact speed. Seal leakage and rod

burst rupture temperatures due to heating during fires were estimated from literature data. The

durations of engulfing optically dense fires needed to produce large seal leak areas and rod

failure by burst rupture were estimated by performing one-dimensional heat transport

calculations.

By taking all possible combinations of the single set of central estimate values for the “less

important” RADTRAN input parameters, the 200 sets of other “more important” truck parameter

values, and the 19 sets of representative truck accident severity and release fraction values, input

for 3800 single-pass RADTRAN 5 truck spent fuel transportation calculations was developed for

each generic truck cask. Similarly, by taking all possible combinations of the set of “less

important” parameter values, the 200 sets of other “more important” rail parameter values, and

the 21 sets of representative rail accident severity and release fraction values, input for 4200

single-pass RADTRAN 5 rail spent fuel transportation calculations was developed. Application

of standard statistical methods to the results of these 3800 truck or 4200 rail transportation

calculations then allowed the results to be displayed as Complementary Cumulative Distribution

Functions (CCDFs) and estimates of the expected (mean) result for radiological consequences

(e.g., population dose) to be calculated. Finally, the results of these RADTRAN 5 calculations

were compared to the results of RADTRAN 5 calculations that used the spent fuel source terms

(severity fractions and release fractions) developed by the NUREG-0170 study [1-1] and those

developed by the Modal Study [1-11] and differences in predicted risks are discussed.

1.6 References

[1-1] “Final Environmental Statement on the Transportation of Radioactive Material by Air

and Other Modes,” NUREG-0170, U.S. Nuclear Regulatory Commission, Washington,

DC, December 1977.

[1-2] Ref. [1-1], Summary and Conclusions, p. vii.
1-4

[1-3] J. M. Taylor and S. L. Daniel, “RADTRAN: A Computer Code to Analyze

Transportation of Radioactive Material,” SAND76-0243, Sandia National Laboratories,

Albuquerque, NM, April 1977.

[1-4] Ref. [1-1], Vol.1, pp. 1-17, 4-16, 4-23, A-13, and E-4.

[1-5] Ref. [1-1], p. 5-20.

[1-6] Ref. [1-1], p. 5-22.

[1-7] Ref. [1-1], p. 5-21.

[1-8] Ref. [1-1], p. A-14.

[1-9] Code of Federal Regulations, Volume 10, Part 71.73 (10 CFR 71.73).

[1-10] Ref. [1-1], p. 5-23.

[1-11] L. E. Fischer, et al., “Shipping Container Response to Severe Highway and Railway

Accident Conditions,” NUREG/CR-4829, Lawrence Livermore National Laboratory,

Livermore, CA, February 1987.

[1-12] K. S. Neuhauser and F. L. Kanipe, “RADTRAN 5, Technical Manual,” Sandia National

Laboratories, Albuquerque, NM (in preparation, draft available on request).

[1-13] K. S. Neuhauser and F. L. Kanipe, “RADTRAN 5, User Guide,” Sandia National

Laboratories, Albuquerque, NM (draft available on the RADTRAN web site).

[1-14] G. S. Mills, K. S. Neuhauser, and F. L. Kanipe, “RADTRAN 4 Truck Accident Risk

Sensitivity Analysis,” Proceedings of Waste Management 95, WM Symposia, Tucson,

AZ, 1995a.

[1-15] G. S. Mills and K. S. Neuhauser, “Sensitivity Analysis for RADTRAN 4 Input

Parameters,” 88th Annual Meeting of the Air & Waste Management Assoc., San

Antonio, TX, 1995.

[1-16] G. S. Mills, et al., “Application of Latin Hypercube Sampling to RADTRAN 4 Truck

Accident-Risk Sensitivity Analysis,” Proceedings of the 11th International Conference on

the Packaging and Transportation of Radioactive Materials (PATRAM ’95), IAEA, Vol.

4, p. 705, 1995.

[1-17] G. D. Wyss and K. H. Jorgensen, “A User’s Guide to LHS: Sandia’s Latin Hypercube

Sampling Software,” SAND98-0210, Sandia National Laboratories, Albuquerque, NM

1998.

[1-18] State Soil Graphics (STATSGO) Data Base, available on the Internet at

ftp.ftw.nrcs.usda.gov/pub/statsgo.
1-5

[1-19] ARC/INFO Coverages and Arc View Project, K. C. Bayer Digital Map of the U.S.,

purchased from Geologic Data Systems, Inc., 1600 Emerson St., Denver, CO 80218.

[1-20] T. L. Sanders, et al., “A Method for Determining the Spent-Fuel Contribution to

Transport Cask Containment Requirements, Appendix III, Spent Fuel Response to

Transport Environments,” SAND90-2406, Sandia National Laboratories, Albuquerque,

NM, November 1992.

[1-21] R. A. Lorenz, et al., “Fission Product Release from Highly Irradiated LWR Fuel,”

NUREG/CR-0722, Oak Ridge National Laboratory, Oak Ridge, TN, February 1980.

[1-22] R. A. Lorenz, et al., “Fission Product Release from Simulated LWR Fuel,” NUREG/CR0274, Oak Ridge National Laboratory, Oak Ridge, TN, July 1978.

[1-23] R. A. Lorenz, et al., “Fission Product Source Terms for the LWR Loss-of-Coolant

Accident,” NUREG/CR-1288, Oak Ridge National Laboratory, Oak Ridge, TN, July

1980.

[1-24] J. L. Sprung, et al., “Data and Methods for the Assessment of the Risks Associated with

the Maritime Transport of Radioactive Materials: Results of the SeaRAM Program,”

SAND97-2222, Sandia National Laboratories, Albuquerque, NM, August 1997.

[1-25] “Shipping and Storage Cask Data for Commercial Spent Nuclear Fuel,” JAI Corp., July

1996.
2-1

2. METHODOLOGY OVERVIEW AND REPORT ROADMAP

2.1 Introduction

NUREG-0170 [2-1] documents estimates of the radiological consequences and risks associated

with the shipment by truck, train, plane, or barge of about 25 different radioactive materials,

including power reactor spent fuel. The estimates were calculated using Version 1 of the

RADTRAN code [2-2], which was developed for the NRC by Sandia National Laboratories

(SNL) specifically to support the conduct of the NUREG-0170 study. When the NRC asked

SNL to reexamine the consequences and risks associated with the transport of spent fuel by truck

and train, RADTRAN Version 5 [2-3, 2-4], the most recent version of the RADTRAN code, was

the computational tool of choice.

The basic methodology employed in the RADTRAN code is widely accepted. Changes to the

code are tracked by a software quality assurance plan that is consistent with American National

Standards Institute guidelines. Two reviews of RADTRAN Version 4, in which the RADTRAN

calculations were benchmarked against hand calculations and other codes, have been published

[2-5, 2-6]. Because the models implemented in RADTRAN 5 are almost identical to those

implemented in RADTRAN 4, the benchmarking results for RADTRAN 4 also apply to

RADTRAN 5.

2.2 RADTRAN

The RADTRAN code calculates the radiological consequences and risks associated with the

shipment of a specific radioactive material (RAM) in a specific packaging along a specific route.

The code estimates consequences and risks (a) for shipments that proceed without incident, that

is, for shipments during which no serious accidents occur, and (b) for accident scenarios that

might occur during these shipments that could lead to a loss of package shielding or to the release

of radioactive material to the environment. Radiation doses caused by shipments that take place

without the occurrence of serious accidents are called “incident free.” The doses and risks

associated with accident scenarios are referred to as “accident consequences and accident risks,

respectively.”

For incident-free shipments, RADTRAN calculates the radiological doses that would be received

by workers (e.g., drivers, handlers, inspectors, escorts) and by members of the general public

(e.g., persons who live near the RAM transport route and travelers who pass near the RAM

transport vehicle while it traverses the transport route). For each accident scenario severe enough

to cause a release of radioactive material, RADTRAN estimates (a) the doses that might be

received by people who reside downwind of the assumed accident location during the passage of

the windborne radioactive plume and as a result of deposition of radioactive materials from that

plume onto the ground, (b) the probability of the hypothesized accidental release, and (c) the

radiological risks that would be caused by the release (i.e., the product of each radiological

consequence and the probability of the release that causes those consequences). RADTRAN can

also be used to estimate the radiation doses associated with loss of shielding accidents, that is,

with accidents that do not result release of radioactive materials from the package but do cause

the radiation shielding of the package to be degraded.
2-2

2.3 RADTRAN Input

To perform its calculations, RADTRAN requires values for a large number of input parameters.

For many of these parameters (e.g., breathing rates, stop times), appropriate values are available

in the RADTRAN User’s Guide [2-4]. However, the following parameters, all of which strongly

influence consequences and risks, have values that vary greatly with route, radioactive material,

or packaging characteristics: (a) route lengths; (b) the fractions of those lengths that are urban,

suburban, or rural; (c) the population densities and accident rates that characterize those route

fractions; (d) the number of people in other vehicles traveling on the route (e) the durations of

stops taken while traveling the route; (f) the weather conditions that might prevail at the time of

an accident; (g) the surface dose rate of the package; (h) the amount of each radionuclide in the

package inventory that might be released to the atmosphere as the result of an accident; (i) the

probability of the release; and (j) the time required to conduct an evacuation should a release

occur. Because each of these parameters can take on a wide range of values, representative sets

of parameter values were developed for each of these parameters. The following sections discuss

the more complicated development methods.

2.3.1 Route Parameters

In the summer of 1996, when this study was initiated, power reactor spent fuel was stored at 79

locations. Although DOE was required by law [2-7] to begin accepting this spent fuel in early

1998 and overseeing its shipment to temporary and/or permanent storage sites, these shipments

have yet to begin because no temporary or permanent storage sites have yet been built. Because

the locations of the temporary and permanent storage sites that must eventually be built are not

known, this study could not examine a specific set of routes that were certain to be used

whenever spent fuel shipments actually take place.

The study could have examined a few specific highway and rail routes that connect some of the

sites where spent fuel is presently stored to a few sites that have been mentioned as possible

interim or permanent storage site locations. However, because such a minimal set of

hypothetical routes could not be shown to be representative (i.e., could not be shown to include

routes with characteristics that span the full range of possible routes), a different approach to

route construction was adopted.

First, six hypothetical interim storage site locations were selected. Each location selected had

been mentioned at some time as a possible site for interim storage of spent fuel and each site was

located in a different geographic region of the continental United States, i.e., in the northeast,

north-central, northwest, southeast, south-central, and southwest portions of the country. In

addition, three possible permanent repository locations (three of the nine sites that entered the

Yucca Mountain down-select process [2-8]) were selected, one each in the southeast, south

central, and southwest portions of the country. HIGHWAY [2-9] and INTERLINE [2-10] route

calculations were then performed that developed route lengths and urban, suburban, and rural

route fractions and population densities for 492 routes for each transport mode. Four hundred

seventy four of these routes connect the 79 current spent fuel storage locations to each of the 6

hypothetical interim storage site locations. The remaining 18 routes connect these hypothetical

interim site locations to the 3 hypothetical permanent storage site locations. These sets of 492
2-3

truck or rail routes were then substantially increased in size by adding the results of 249

HIGHWAY and 249 INTERLINE route calculations that had been developed for a prior spent

fuel transportation study [2-8]. Thus, route parameter values were available or were developed

for a total of 741 different truck and 741 different rail routes.

Next, for both highway and rail routes, distributions of route lengths as well as length fractions

and populations densities for the urban, suburban, and rural portions of these routes were

constructed using the pooled route data. Then sets of 200 highway and 200 rail routes were

generated by sampling these distributions using structured Monte Carlo sampling (Latin

Hypercube Sampling [2-11]) methods. Because this sample of routes was constructed by

sampling distributions of route parameters based on the characteristics of 741 real truck or 741

real rail routes located throughout the length and breadth of the continental United States, they

are believed to constitute a representative set of hypothetical spent fuel shipment routes, even

though none of the routes constructed by sampling these route parameter distributions

corresponds exactly to any specific real truck or rail route and none has a specific origin or a

specific destination.

Because route segment accident rates are not calculated by HIGHWAY or INTERLINE, accident

rate distributions had to be developed separately. Heavy truck accident rates on interstate

highways and mainline rail accident rates were compiled by Saricks and Kvitek [2-12] for each

of the 48 states in the continental United States. For truck accidents (but not train accidents),

separate accident rates were reported for accidents that occurred within and outside of

incorporated areas. Inspection of state population data for the unincorporated (i.e., rural) and

incorporated (i.e., suburban and urban) regions of each state allowed the truck accident rates to

be divided into sets of urban, suburban, and rural accident rates. The sets of suburban and rural

truck accident rates developed by this procedure were large enough to support the construction of

distributions. Because the set of urban accident rates was small, these rates were averaged and

the resulting single average urban heavy truck accident rate was applied to all urban route

segments.

Because mainline rail accident rates were not developed separately for incorporated and

unincorporated areas, a single mainline rail accident rate distribution was constructed using all of

the state rail accident rates reported by Saricks and Kvitek [2-12]. Accident rates selected by

sampling the resulting distribution were applied to each of the rail route segments in the

representative set of 200 rail routes regardless of the population density of the segment. Because

mainline rail route traffic densities are determined principally by regional shipping schedules

(local shipments are made by truck), they should be largely independent of local wayside

population densities. Thus, the use of rail accident rates that do not vary with route segment

population density is believed to be reasonable.

2.3.2 Weather Parameters

Should a spent fuel shipment be involved in an accident (a collision and/or a fire) that releases

radioactive materials to the atmosphere, the radiological consequences of the accident would be

determined principally by the amount released, the degree of dilution during downwind transport

of the radioactive plume produced by the release, and the size of the exposed population. The
2-4

degree to which the plume is diluted during downwind transport is determined by the turbulence

of the air through which the plume passes, which in turn is determined by the prevailing weather

conditions. Because plume dilution is a strong function of atmospheric turbulence, RADTRAN

develops accident consequences for six sets of prevailing weather conditions that correspond to

the six Pasquill-Gifford atmospheric stability classes [2-13] using national average frequencies of

occurrence for each of the classes.

The population exposed to significant levels of radiation is determined principally by the

direction in which the wind is blowing at the time of the accident. Because accident locations

cannot be predicted and, for most locations, wind speed and direction data (wind roses) would be

unavailable, the probability of a specific initial wind direction could not be determined.

Therefore, for accident calculations, RADTRAN assumes that all wind directions are equally

probable and uses a uniform population density for each route segment selected by sampling the

population density distributions developed from the HIGHWAY and INTERLINE results.

Although accident consequences would be larger, when the wind is blowing from the accident

site toward a small population center then when it is blowing away from that population center,

the absence of wind direction data means that this effect could not be modeled. The use of

uniform population densities for route segments means that the population densities of small

population centers are smeared out, which ensures that the plume always encounters population

no matter which way the wind is blowing, even for accidents that occur on lightly populated rural

route segments. Thus, the neglect of wind direction, when combined with the use of the uniform

segment population densities, is expected to yield a reasonable estimate of mean (expected)

accident consequences, even for rural route segments.

2.4 Package Inventories and Surface Dose Rates

Although the surface dose rate of a package can be calculated from the package inventory and

package design data, this calculation is not performed by the RADTRAN code. Instead surface

dose rate and package inventory are both RADTRAN input parameters. Because they are both

input parameters, a package inventory may be specified that will not generate the specified

package surface dose rate. This study uses package inventories calculated by the ORIGEN code

and a distribution of package surface dose rates. To be consistent with regulations, the

distribution of package surface dose rates had its maximum value set equal to the regulatory limit

for package surface dose rates. Then, in order to assure that accident source terms were

conservative, all accident calculations used PWR or BWR ORIGEN [2-14] inventories calculated

for high burnup fuel that had cooled for only three years, even though these inventories, if

shipped in the generic casks examined by this study, would produce surface dose rates that would

exceed the regulatory limit.

2.5 Accident Source Terms

Representative accident source terms are developed for discrete sets of truck and train accident

conditions. The conditions that define the representative accidents are cask impact speed onto an

unyielding surface, impact orientation, and fire duration. For each set of representative accident

conditions, the quantities of radionuclides available for release are calculated from the number of

rods that fail and the fraction of the rod inventory released upon failure. The amounts released to
2-5

the interior of the cask are reduced by deposition onto cask internal surfaces. The fraction of the

remaining gasborne radionuclides that are transported out of the cask is determined from the

fraction of the cask gases that escape from the cask after the cask is pressurized by rod failure

and heating of cask gases by accident initiated fires. Deposition times are estimated from cask

leak areas which are estimated from the results of finite element cask impact calculations. The

probabilities of these representative accident source terms are estimated from the probabilities of

the accident scenarios and the probabilities of the accident speeds, cask impact orientations,

impact surface hardnesses, occurrence of fires, and fire durations that can be associated with each

scenario. These probabilities are called severity fractions because they specify the fraction of all

accidents that have characteristics like those that define each representative accident.

2.5.1 Source Term Probabilities

The probability of occurrence of a representative accident source term is the product of the

chance that an accident of any severity occurs during shipment of the spent fuel and the fraction

of all of the possible accidents that yield source terms similar to that source term. Severity

fractions were calculated as follows. First, the accident scenarios depicted on the Modal Study

[2-15] truck and train accident event trees were determined by inspection to encompass the full

spectrum of possible accidents. Next, each scenario probability on these trees was multiplied by

the chance that the accident speed falls within one of four speed ranges and/or the chance that the

scenario involves a fire that heats the cask to temperatures in one of three temperature ranges.

This was done because the conditional scenario probabilities do not reflect the chance that the

accident scenario occurs at some particular speed or leads to a fire of some particular severity.

Because Modal Study event trees specify impact surfaces for all collision scenarios, the product

of a Modal Study event tree collision scenario conditional probability and the chance that the

accident speed falls within one of four speed ranges yields the severity fraction for that collision

scenario and speed range. If the collision can also initiate a fire, the product of the scenario

probability and the speed range probability is multiplied by the chance that a fire ensues and then

by the chance that the fire falls within one of three severity ranges that specify the chance that the

fire is an engulfing, optically dense fire that burns hot enough and long enough to cause or

increase the release of radioactive materials from the cask to the environment. For non-collision

accidents that initiate fires, the chance that a fire of a particular severity ensues is simply the

chance that the fire is a severe fire as defined in the preceding sentence. Finally, because

accidents of a given severity can be initiated by several different accident scenarios, the

probabilities of all scenario, speed, and fire combinations that lead to accidents having similar

severities are summed, which gives an estimate of the severity fraction for that set of accidents.

The chance that the accident speed falls within a given speed range is calculated as the difference

of the probabilities of the two speeds that define the speed range. These probabilities are read

from the accident speed distributions presented in the Modal Study using the impact speeds onto

the yielding surface specified for each scenario that are equivalent to one of the four speeds (30,

60, 90, and 120 mph after crushing of the impact limiter, which is equivalent to impact speeds of

42, 67, 95, and 124 mph for an uncrushed impact limiter) examined by the finite element

calculations of cask impacts onto unyielding surfaces. The chance that the fire duration is long

enough to heat the cask to the temperature where its elastomer seal develops a substantial leak or
2-6

rods not failed by impact are failed by burst rupture is read from the fire duration distributions

presented in the Modal Study.

2.5.2 Source Term Magnitudes

The amount of radioactive material that might be released from a failed spent fuel Type B cask as

a result of a collision and/or a fire is called the accident source term. The source term can be

expressed as the product of four parameters: (1) the inventory of each important radionuclide

being transported in the spent fuel cask, (2) the fraction of the fuel rods in the cask failed by the

accident, (3) the fraction of the inventory of a single rod that is released from the failed rod to the

cask interior, and (4) the fraction of the material that is released from the rods to the cask interior

that also is released from the cask interior to the environment. Because cask radionuclide

inventories can be precisely calculated by ORIGEN [2-14], development of reasonable estimates

of accident source term magnitudes depends on the development of reasonable estimates of rod

failure fractions and rod-to-cask and cask-to-environment release fractions for each

representative accident examined.

Release of fission products from segments of real and surrogate spent fuel rods has been

examined experimentally by Lorenz [2-16, 2-17, 2-18] and Burian [2-19]. A critical review of

these experimental results allowed rod-to-cask release fractions to be developed for noble gases,

cesium (Cs) compounds, ruthenium (Ru) compounds, and particulates and also for cobalt (Co) in

the CRUD [2-20] deposits on fuel rod external surfaces. The values developed reflect blowdown

of the rods upon failure, release of Cs and Ru compounds both as vapors and as constituents of

particulates, impact fracturing of fuel pellets, formation of particle beds in pellet crack networks

and in the pellet-cladding gap, and filtering of particles by these beds during particle transport

toward the rod failure location.

Transport of fission products released to the interior of a TN-125 spent fuel cask has been

examined by MELCOR [2-21] calculations [2-22]. These calculations show that the efficiency

of vapor and particle deposition processes inside of the cask is determined principally by the rate

at which the cask depressurizes after pressurization by the failure of spent fuel rods. The

calculations also show that depressurization times are determined by the cross-sectional area of

the leak path. Because a large leak leads to short depressurization times while a small leak leads

to long depressurization times, cask-to-environment release fractions increase as cask leak areas

increase. Accordingly, cask-to-environment release fractions can be estimated using the

MELCOR results provided the cross-sectional areas of the leaks can be estimated by other

methods.

2.6 Response of Representative Casks to Accident Conditions

Cask leak areas will depend on cask design and on accident conditions. Specifications (materials

of construction and the dimensions of the cask body, lid, and closure) for four generic Type B

spent fuel casks (a steel-lead-steel truck cask, a steel-lead-steel rail cask, a steel-DU-steel truck

cask, and a monolithic steel rail cask) were developed by review of the characteristics of existing

Type B spent fuel cask designs.
2-7

The response of these four generic casks to collision and fire accident conditions was then

examined by performing finite element calculations and one-dimensional heat transport

calculations. The finite element calculations examined cask response to impacts. The heat

transport calculations estimated the heating times in engulfing fires that would lead to seal failure

due to thermal degradation and rod failure by burst rupture. In addition, the probability of cask

puncture during collision accidents was estimated by review of rail tank car accident data.

2.6.1 Finite Element Impact Calculations

The response to end, center-of-gravity over corner, and side impacts onto an unyielding surface at

30, 60, 90, and 120 mph of each generic cask, with its impact limiter already fully crushed, was

modeled using a version of the PRONTO 3D finite element code [2-23] that runs on a parallel

processing computer. PRONTO 3D is a three-dimensional, transient solid-dynamics code that

models the large deformations produced in highly nonlinear materials when these materials are

subjected to extremely high strain rates. Thus, PRONTO 3D can model the material and

geometric non-linearities associated with the large deformations of cask structures that would be

produced by high-speed cask impacts. In PRONTO 3D, the modeling of contact between distinct

structures allows the various components of the cask to properly transmit loads from one

structure to a neighboring structure. This is especially important for modeling the behavior of the

cask closure (the cask lid, lid well, and lid bolts). Material failure was not included in any of the

models, but accurate depictions, for example, of the deformations and loads on bolts, allows the

failure of any single bolt to be predicted although sequential failure of bolts cannot be reliably

predicted. The PRONTO code has been validated by comparison of analysis and test results for a

wide range of problems, comparison to other finite element analysis results and to theoretical

solutions for problems of simple geometry1

. Many of the validation problems have been

developed to exercise the code in regimes typical of impact analyses of spent fuel casks. For

example, the Structural Evaluation Test Unit Program [2-24] performed by SNL involved

comparison of experimental and analytical results for cask impacts of up to 60 mph. Thus,

impacts at speeds as great as 120 mph should be realistically modeled.

Regardless of impact speed and orientation, the strains in truck and rail cask bodies predicted by

the PRONTO 3D calculations were always too small to suggest failure of the cask body or of any

penetrations that enter the cask through its body. Cask seal leakage and leakage areas were

estimated by examining radial and circumferential displacements of the cask closure (i.e.,

separation of the lid from the lid well). The calculations suggest that truck cask seals are not

compromised by impacts at any orientation onto an unyielding surface at 30, 60, and 90 mph and

may not leak even after impacts at any orientation at speeds as high as 120 mph. Nevertheless,

all 120 mph truck cask impacts were arbitrarily assumed to cause seal leaks with 1 mm2

 cross-

________

1. A Validation and Verification Manual is being prepared, personal communication, M. Blanford, Sandia National

Laboratories, 1999.
2-8

sectional areas. The results obtained using the finite element models of the two generic rail casks

suggest seal leakage may occur for some impact orientations at speeds as low as 60 mph and

certainly occurs for some or all impact orientations for impact speeds of 90 and 120 mph.

2.6.2 Impacts onto Yielding Surfaces

For any impact speed and orientation, the damage done to the cask by impact onto an unyielding

surface would be greater than the damage done by impact onto a yielding surface (hard and soft

rock, hard and soft soils, concrete, water, drainage ditches, and road and rail beds). Because

unyielding surfaces rarely occur in the real world, the impact speeds onto real world yielding

surfaces, that are equivalent (cause the same cask damage) to each impact speed used for the

unyielding surface, finite element calculations (30, 60, 90, and 120 mph) had to be calculated.

This was done as follows.

First, for each unyielding surface impact calculation, a cask velocity time-history was calculated

from the kinetic energy time-history. Next, the displacement of the center of gravity of the cask

and the cask’s rigid body acceleration were calculated respectively by numerical integration and

differentiation of the velocity time-history. A force time-history was now calculated assuming

that the contact force between the cask and the unyielding surface is equal to the rigid-body

acceleration times the mass of the cask. Combination of the force time-history and the

displacement time-history for any cask impact then produced a force-deflection curve for that

unyielding surface impact calculation.

Impact of a cask onto a real yielding surface will produce damage equivalent to that observed for

impact onto an unyielding surface only if the peak contact force for cask impact onto the yielding

surface equals the peak contact force on the force-deflection curve developed for impact onto an

unyielding surface. The energy absorbed by the yielding surface during each impact that

developed a peak-contact force of this magnitude was now added to the initial kinetic energy of

the unyielding surface impact. The velocity that corresponds to this total kinetic energy is the

velocity for impact onto the yielding surface that is equivalent to the unyielding surface impact

velocity (i.e., the velocity that would produce the same cask damage as that predicted for the

unyielding surface impact at the specified impact velocity and orientation).

2.7 Rod Failure Fractions

The fraction of the fuel rods in each generic cask that are failed by end, corner, and side impacts

of the cask at 30, 60, 90, or 120 mph onto an unyielding surface after crushing of the cask impact

limiter was estimated from the peak rigid-body accelerations predicted by finite element analysis

at each speed and impact orientation. First, the rod cladding strains calculated by Sanders, et al.

[2-25] for 100 G side impacts onto an unyielding surface by a spent fuel cask carrying a typical

pressurized water reactor or a typical boiling water reactor assembly were scaled to match the

peak rigid-body accelerations predicted by the finite element impact analyses for each generic

cask at each impact speed and impact orientation. Then, the fraction of rods that fail was

estimated by comparing the scaled cladding strains to the 4 percent strain level predicted by

Sanders, et al. to lead to cladding failure in typical spent fuel rods. Because rod strains generated

by side impacts were used to evaluate all of the finite element results, the fraction of rods
2-9

estimated to be failed by end and corner impacts is conservative as rod damage for these impacts

is expected to be less than that produced by side impacts with the same cask acceleration.

2.8 Thermal Calculations

Rod failure by burst rupture and times to failure for fire accident scenarios were estimated using

the PATRAN/PThermal [2-26] analysis code, which is available commercially [2-27].

PATRAN/PThermal models all of the heat transfer processes (i.e., conduction, convection, and

thermal radiation) that determine the heating rates of structures. Thus, the code can be used to

perform one-, two-, and three-dimensional simulations of the effects of ambient conditions and

fire conditions on the temperatures of spent fuel packages. PATRAN/Pthermal, formerly called

Q/TRAN, has been validated by comparison of its results to analytic solutions and to predictions

made by other thermal transport codes widely used in the transportation industry [2-28, 2-29].

PATRAN/PThermal results were developed for each of the four generic spent fuel casks

examined by the finite element calculations. For these thermal calculations, the cask’s neutron

shield material compartment was assumed to be empty. The compartment was modeled as empty

because, after the shield material in the compartment drains or burns away, as would be expected

to happen during a severe fire accident, radiative and convective heat transport to the cask body

through the empty compartment will significantly influence the rate of temperature rise of the

cask body.

For each generic cask, the PATRAN/PThermal calculations determined the duration of a fully

engulfing, optically dense, hydrocarbon fuel fire that would heat the cask to the temperature at

which spent fuel rods would fail by burst rupture. The probability of fires of this duration was

then used as an input to the calculation of accident severity fractions. During the calculation of

release fractions, it was assumed that any fire that raised cask internal temperatures to rod burst

rupture temperatures would also cause the failure of all unfailed rods in the cask. To assure that

the calculated fire durations were conservative (shorter than the times actually required to reach

seal leakage or rod burst rupture temperature), all of these calculations used a heat flux to the

inner surface of the shell of the cask that was appropriate for high burnup fuel that had cooled for

only three years.

The temperatures that cause seal leakage and the cross-sectional leak areas produced by thermal

degradation of cask seals are estimated from literature data as follows. About 70 percent of the

mass of elastomeric seal materials, including Viton, was lost during thermogravimetric analysis

(TGA) experiments [2-30] during which these seal materials were heated to 500oC at heating

rates like those predicted here for heating of the four generic casks in engulfing optically dense

hydrocarbon fires. Thus, heating a spent fuel cask to 500oC is assumed to cause the cask’s

elastomeric seals to fail completely due to extensive thermal degradation. If a cask containment

is lost due to thermal degradation of its elastomeric seal, the cask depressurization time will be

determined by the leak rate of cask gases through the metal-to-metal gap between the cask lid

and the lid well. Because bolt softening during cask heating by a hot, long-duration fire is

expected to essentially eliminate the compression between the lid and the lid well around the

entire circumference of the cask closure, the resulting leak area is assumed to equal the product

of the surface roughness of the closure and the closure circumference.
2-10

2.9 RADTRAN Calculations

Seven sets of RADTRAN calculations were performed. Most of the calculations were performed

with RADTRAN Version 5. A few calculations in the fifth set of calculations were performed

with RADTRAN Version 1.

Sets one and two used the 200 representative truck and rail routes that were developed by Latin

Hypercube Sampling of the route parameter distributions. The results of these calculations

depict the possible range of spent fuel transportation consequences and risks.

Sets three and four developed results for ten specific shipment routes, five truck and five rail

routes. Two of the ten routes were the national average spent fuel shipment truck and train

routes constructed for the NUREG-0170 study [2-1]. The other eight routes were the truck and

train routes that connect reactor sites to hypothetical interim storage locations. This set of

calculations was performed in order to show that the results obtained for real routes fall within

the envelope of results developed using the 200 representative routes constructed by sampling

route parameter distributions.

Set five compared the consequences and risks predicted for spent fuel shipments by RADTRAN

Version 1, the version of RADTRAN used during the NUREG-0170 study [2-1], to those

predicted for this study using RADTRAN Version 5. These calculations depict the influence of

cask inventory, spent fuel release fractions, and exposure pathway models on spent fuel

transportation consequences and risks.

Sets six and seven compared the consequences and risks obtained using the cask inventory and

release assumptions developed for the NUREG-0170 study [2-1], the Modal Study [2-15], and

this study. These calculations illustrate the influence of the chemical and physical phenomena

modeled on source term magnitudes and thus on consequences and risks.

2.10 Report Roadmap

The methods briefly outlined in this section are fully described in the following sections of this

report. RADTRAN input parameter values are discussed in Section 3. Section 3.1 describes the

selection of the RADTRAN parameters for which distributions are developed, Section 3.2

specifies values for the RADTRAN parameters for which central estimate values are used and

provides a brief description of the basis for each value, and Section 3.3 describes how the

parameter distributions were constructed.

The review of spent fuel transportation cask properties and the development of specifications for

the four generic casks examined by this study is described in Section 4. Section 5 presents the

results of the finite element unyielding surface impact calculations performed using the finite

element model of each generic cask and the extrapolation of these results to yielding surfaces.

The thermal analyses of the four generic casks are presented in Section 6.

The development of accident source terms is described in Section 7. Section 7.1 reexamines the

truck and train accident scenarios depicted by the accident event trees constructed for the Modal

Study [2-30]. Severity fraction and release fraction expressions are developed in Section 7.2.
2-11

Sections 7.3 and 7.4 respectively develop values for the parameters in these severity and release

fraction expressions. Section 7.5 then presents the source terms (sets of release fractions and the

severity fraction to which they correspond) calculated using these parameter values.

The RADTRAN calculations performed for this study and the results (spent fuel transportation

incident free and accident consequences and risks) of these calculations are described and

discussed in Section 8. Section 8.1 presents the results of the calculations that used the route

samples of size 200 that were constructed by Latin Hypercube Sampling of route parameter

distributions; Section 8.2 presents the results obtained for the ten specific routes for which

calculations were performed; Section 8.3 compares the estimates of consequences and risks

obtained using the source terms developed for the NUREG-0170 study, the Modal Study, and

this study; and Section 8.4 examines the effects of changing the inventory, release fraction, and

pathways modeled during the NUREG-0170 study to those used during this study.

Finally, Section 9 briefly discusses the results of the study and presents the study’s conclusions.

2.11 References

[2-1] “Final Environmental Statement on the Transportation of Radioactive Material by Air

and Other Modes,” NUREG-0170, U.S. Nuclear Regulatory Commission, December

1977.

[2-2] J. M. Taylor and S. L. Daniel, “RADTRAN: A Computer Code to Analyze

Transportation of Radioactive Material,” SAND76-0243, Sandia National Laboratories,

Albuquerque, NM, 1977.

[2-3] K. S. Neuhauser and F. L. Kanipe, “RADTRAN 5, Technical Manual,” Sandia National

Laboratories, Albuquerque, NM (in preparation, draft available on request).

[2-4] K. S. Neuhauser and F. L. Kanipe, “RADTRAN 5, User Guide,” Sandia National

Laboratories, Albuquerque, NM (draft available on the RADTRAN web site).

[2-5] J. J. Hancox and H. L. Wilkinson, “A Review of INTERTRAN/RADTRAN and

Associated Codes,” SRD/RMD 93/37/REP, SRD, UK Atomic Energy Authority,

Culcheth, Cheshire, UK, 1993.

[2-6] S. Maheras, “Validation of the Transportation Computer Codes HIGHWAY,

INTERLINE, RADTRAN 4, and RISKIND,” DOE/ID-10511, Idaho National

Engineering Laboratory, Idaho Falls, ID, 1995.

[2-7] Nuclear Waste Policy Act of 1982, and its 1987 amendments.

[2-8] J. W. Cashwell, et al., “Transportation Impacts of the Commercial Radioactive Waste

Management Program,” SAND85-2715, Sandia National Laboratories, Albuquerque,

NM, April 1986.
2-12

[2-9] P. E. Johnson, et al., “Highway 3.1 - An Enhanced Highway Routing Model: Program

Description, Methodology, and Revised User’s Manual,” ORNL/TM-12124, Oak Ridge

National Laboratory, Oak Ridge, TN, March 1993.

[2-10] P. E. Johnson, et al., “Interline 5.0 – An Expanded Railroad Routing Model: Program

Description, Methodology, and Revised User’s Manual,” ORNL/TM-12090, Oak Ridge

National Laboratory, Oak Ridge, TN, March 1993.

[2-11] G. D. Wyss and K. H. Jorgensen, “A User’s Guide to LHS: Sandia’s Latin Hypercube

Sampling Software,” SAND98-0210, Sandia National Laboratories, Albuquerque, NM

1998.

[2-12] C. Saricks and T. K. Kvitek, “Longitudinal Review of State-Level Accident Statistics for

Carriers of Interstate Freight,” ANL/ESD/TM-68, Argonne National Laboratory,

Argonne, IL, 1994.

[2-13] F. A. Gifford, “Use of Routine Meteorological Observations for Estimating Atmospheric

Dispersion,” Nuclear Safety 2, 47 (1961).

[2-14] A. G. Croff, “ORIGEN2 - A Revised and Updated Version of the Oak Ridge Isotope

Generation and Depletion Code,” ORNL-5621, Oak Ridge National Laboratory, Oak

Ridge, TN, July 1980.

[2-15] L. E. Fischer, et al., “Shipping Container Response to Severe Highway and Railway

Accident Conditions,” NUREG/CR-4829, Lawrence Livermore National Laboratory,

Livermore, CA, February 1987.

[2-16] R. A. Lorenz, et al., “Fission Product Release from Highly Irradiated LWR Fuel,”

NUREG/CR-0722, Oak Ridge National Laboratory, Oak Ridge TN, February 1980.

[2-17] R. A. Lorenz, et al., “Fission Product Release from Simulated LWR Fuel,” NUREG/CR0274, Oak Ridge National Laboratory, Oak Ridge TN, July 1978.

[2-18] R. A. Lorenz, et al., “Fission Product Source Terms for the LWR Loss-of-Coolant

Accident,” NUREG/CR-1288, Oak Ridge National Laboratory, Oak Ridge TN, July

1980.

[2-19] R. J. Burian, et al., “Response of Spent LWR Fuel to Extreme Environments,”

Contractor Report, SAND85-7213, Battelle Columbus Laboratories, Columbus, OH,

August 1985.

[2-20] R. P. Sandoval, et al., “Estimate of CRUD Contribution to Shipping Cask Containment

Requirements,” SAND88-1358, Sandia National Laboratories, Albuquerque, NM,

January 1991.
2-13

[2-21] R. M. Summers, et al., “MELCOR 1.8.0: A Computer Code for Nuclear Reactor Severe

Accident Source Term and Risk Assessment Analyses,” NUREG/CR-5531, SAND90-

0364, Sandia National Laboratories, Albuquerque, NM, January 1991.

[2-22] J. L. Sprung, et al., “Data and Methods for the Assessment of the Risks Associated with

the Maritime Transport of Radioactive Materials: Results of the SeaRAM Program,”

SAND97-2222, Sandia National Laboratories, Albuquerque, NM, August 1997.

[2-23] L. M. Taylor and D. P. Flanagan, “PRONTO 3D: a Three-Dimensional Transient Solid

Dynamics Program,” SAND87-1912, Sandia National Laboratories, Albuquerque, NM,

1987.

[2-24] J. S. Ludwigsen and D. J. Ammerman, Analytical Determination of Package Response to

Severe Impacts, Proceedings of PATRAM ’95, Las Vegas, NV, December 1995.

[2-25] T. L. Sanders, et al., “A Method for Determining the Spent-Fuel Contribution to

Transport Cask Containment Requirements,” SAND90-2406, Sandia National

Laboratories, Albuquerque, NM, November 1992

[2-26] PATRAN Thermal User Guide and Model Description Manual

(http://www.macsch.com/support/support.html).

[2-27] The MacNeal Schwindler Corp., 2975 Redhill Ave., Costa Mesa, CA,

(http://www.macsch.com/cgibin/MSCStore.storefront/1771903604/Catalog/DOC&2AM

SC&2FPATRAN).

[2-28] R. E. Glass, “Sample Problem Manual For Benchmarking of Cask Analysis Codes,

SAND88-0190,” Sandia National Laboratories, Albuquerque, NM, February 1988.

[2-29] R. E. Glass, et al, “Standard Thermal Problem Set for the Evaluation of Heat Transfer

Codes Used in the Assessment of Transportation Packages,” SAND88-0380, Sandia

National Laboratories, Albuquerque, NM, August 1988.

[2-30] P. J. Nigrey, “Prediction of Packaging Seal Life Using Thermoanalytical Techniques,”

Proceedings of the 12th International Conference on the Packaging and Transportation of

Radioactive Materials (PATRAM ’98), IAEA, Vol. 4, p. 1730, 1998.
2-14

Page intentionally left blank.
3-1

3. RADTRAN INPUT

The RADTRAN code [3-1, 3-2] calculates estimates of the risks associated with the

transportation of radioactive materials, for example spent nuclear fuel. For a specific material,

package, and route, the code develops estimates of a variety of consequences and risks for both

incident-free transport and transport subject to accidents.

The RADTRAN code requires a very large quantity of data to describe the incident-free

transportation of a radioactive material and also the accident scenarios and the radiological doses

that might be received by population groups located along the shipment route. Selecting

appropriate values for all the parameters used by the RADTRAN code to estimate transportation

consequences and risks is a substantial undertaking. Selection of parameter values is further

complicated by the fact that the casks and routes that will be used in the real spent fuel shipping

campaigns are presently unknown. Fortunately, there is a large body of existing analyses that

provide guidance on ranges of variables and their importance to the result. This knowledge base

is significant in performing multiple analyses addressing a variety of conditions contained in this

document. Experience allows the analyst to focus on identifying the variables that affect the

results directly and getting their reasonable ranges correct while spending much less time (and

computing resources) on less important parameters.

3.1 Fixed and Sampled Input Variables

For spent fuel shipments, many RADTRAN input variables can take on a wide range of realworld values (e.g., route lengths, wayside population densities, evacuation times). Fortunately,

not all of these variables strongly influence predictions of the consequences and risks associated

with the transportation of spent nuclear fuel. Spent fuel transportation risks are strongly

influenced by a number of RADTRAN input variables [3-3, 3-4], some of which may take on a

wide range of values in the real world. For these variables, construction of distributions and

selection of values from these distributions by structured sampling methods offers an efficient

way to assure coverage of the full range of each variable and also of the many possible

combinations of the values of different variables that might be encountered in the real world.

RADTRAN input variables may be divided into two groups:

• those required for accident analysis, and

• those required for incident-free analysis.

Within each of these groups, RADTRAN input variables can be further divided into:

• variables that strongly affect incident-free or accident consequences or risks (More

Important Variables)

• variables that do not strongly affect incident-free or accident consequences or risks (Less

Important Variables)

Finally, the “More Important” RADTRAN variables can be divided into Source Term Variables

(i.e., accident severity fractions and release fractions) and other “More Important” Variables.
3-2

The difference between More Important and Less Important Variables may be conceptually

described as follows. Let R be incident-free dose or accident dose-risk, vi be a RADTRAN input

variable, and the fractional change in risk for a fractional change in the variable be

 

i

i

i

v

∆v k

R

∆R =

Then, ki ≈ 1.0 for More Important Variables and ki << 1.0 for Less Important Variables. Thus,

for More Important Variables, a fractional change (e.g., a 10 percent increase) in the value of the

variable produces about the same fractional change in risk (e.g., about a 10 percent increase or

decrease). Conversely, for Less Important Variables, a fractional change in the value of the

variable produces a much smaller fractional change in risk.

Central Estimates are Used for Less Important Variables

Although the values of nearly all RADTRAN input variables could be selected by sampling from

distributions, constructing distributions for Less Important Variables is pointless because

variation of the values of Less Important Variables influences consequence and risk results only

slightly, if at all. Several RADTRAN input variables had been shown previously to have little

influence on estimates of accident risk [3-5]. To verify the conclusions of this study specifically

for spent fuel, single parameter sensitivity calculations were performed to investigate the effect

of these variables on spent fuel transportation risks. Table 3.1 lists these variables, the trial

values of each variable used in these sensitivity calculations, and the corresponding changes in

total accident risk produced by the change. Table 3-1 shows that none of the five variables

examined by these sensitivity calculations strongly affect risk. Therefore, for these variables, and

all other variables known to have little effect on risk, central estimate values were used as input

to all calculations performed for this study.

Table 3.1 Results of Sensitivity Calculations: Changes in Total

Accident Risk Produced by Changes in the Values of Several Input Variables

Variable

Name

Variable

Definition

Base Case

Value

Base Case

Result

Sensitivity

Case Value(s)

Sensitivity

Case Result

BRATE Breathing rate 3.3E-4 5.5E-06 1.6E-04 3.9E-6

BDF Respirable aerosol fraction

inside buildings

0.05 5.5E-06 5.0E-03

0.5

5.4E-06

6.8E-06

RPD Ratio of pedestrian and

resident population

densities

6.0 5.5E-06 3.0

12.0

4.6E-06

7.4E-06

RU Urban shielding factor 0.018 5.5E-06 0.01

0.18

5.5E-06

5.5E-06

CULVL Clean-up level 0.20 5.5E-06 0.10

0.02

5.3E-06

4.8E-06

Central Estimates are Used for More Important Variables with Little Variation
3-3

Distributions need not be constructed for More Important Variables that have values that are

fixed or that only vary over a narrow range. For example, some Important Variables have

precisely defined values (e.g., radionuclide half lives) or have values that are fixed by

regulations. Thus, central estimate values were also used for all More Important Variables that

are invariant or that only vary over narrow ranges.

Central Estimates are Used for all Source Term Variables that can Vary Widely

RADTRAN source term magnitudes are specified by the product of the cask inventory, which

can be precisely determined by ORIGEN calculations [3-6], and an accident release fraction. The

probability of the release (the source term probability) is specified as the product of a severity

fraction, which specifies the fraction of all possible accidents that lead to the given source term,

and the probability that any accident occurs, which is calculated as the product of a route length

and an accident rate. Because insufficient information exists from which to construct

distributions for these important RADTRAN variables, as is described in Section 7, their

variation was treated by constructing representative sets of truck and train accident release and

severity fractions.

Distributions are Used for Other More Important Variables with Wide Value Ranges

Consequently, distributions were constructed only for other More Important Variables that have

real-world values spanning a wide range (e.g., route lengths, accident rates, route wayside

population densities, evacuation times). For these other More Important Variables, as is

discussed below, distributions were constructed, usually by analysis of historic data for the

variable, and then representative sets of values for each variable were selected from these

distributions by structured Monte Carlo Sampling using Sandia National Laboratories’ Latin

Hypercube Sampling (LHS) computer code [3-7].

3.2 RADTRAN 1 and RADTRAN 5 Input Variables

Although the exposure and dose models implemented in RADTRAN 5 are the same as those

implemented in RADTRAN 1, models for a variety of other phenomena have either been

modified or added. In particular, RADTRAN 5 allows considerably greater flexibility in the way

that transportation routes are modeled. The principal differences between these two versions of

the RADTRAN code are summarized in Table 3.2.

Tables 3.3 and 3.4 respectively describe the incident-free and accident analysis input variables

used in RADTRAN 1 and RADTRAN 5, and present the RADTRAN 1 and RADTRAN 5 names

of each variable, the location (array name and position in the array) of the variable in RADTRAN

5, the sensitivity of RADTRAN output to each variable, the RADTRAN 1 and RADTRAN 5

value used for each variable, and clarifying comments or explanations. In Tables 3.3 and 3.4, the

term “not in code” in the RADTRAN 1 or RADTRAN 5 variable name column indicates that no

model implemented in the indicated version of the code uses this variable, and “Distribution” in
3-4

Table 3.2 Comparison of RADTRAN 1 and RADTRAN 5

RADTRAN 1 RADTRAN 5

Route Entire route modeled in three segments

occurring in fixed proportions related to

population density designations

Route may be divided into up to 60

user-defined segments (links)

Right-of-way width Fixed for freeway, non-freeway, urban User-defined

Population density Rural, suburban, urbana – fixed densities User-defined

Population density distribution

along the route

Fraction of route that is rural = 0.9,

suburban = 0.05, urban = 0.05

Population density can be defined

for each link

Distribution of population

along the route

Population is distributed in bands 1⁄2 mile

(800 m.) wide on either side of the route

Band depth is user defined

Lane width Fixed for rural, suburban, urban User-defined

Vehicle speed Fixed for rural, suburban, urban User-defined for each link

Vehicle density (traffic count) Fixed for rural, suburban, urban User-defined for each link

Traffic distribution: rush

hour, non-rush

Fixed fractions for rural, suburban, urban Not needed, because speeds are

user-defined

Traffic distribution by road

type

Fixed fractions for rural, suburban, urban Road type is user-defined

Stop time, distance from

cargo, number of people

Fixed for rural, suburban, urban User defined: each stop can be

treated separately, like a link

Package shape factor Not used directly Used

Dose to close-in receptors approximately 1/r2 dependence approximately 1/r dependence

Dose to handlers Treated like stop dose Activity-specific parameters

(distance, etc.) are user defined

Dose to crew Fixed for various modes User-defined

LCF/person rem (incident-free

transportation)

2.57 × 10-4 LCF/person rem (accepted

regulatory value in late 1970s)

(disaggregated by target organ)

User-defined; current guidance is:

5 × 10-4 LCF/rem for public;

4 × 10-4 LCF/rem for workers

LCF (transportation accidents) 3.79 × 10-4 LCF/rem (disaggregated by

target organ)

User-defined; current guidance is:

5 × 10-4 LCF/rem for public;

4 × 10-4 LCF/rem for workers

Accident frequencies 1974-75 national average data User defined; 1988 state-by-state

data are most recent available

values

Accident severity categories 8 categories Up to 30 categories available;

number of categories and

frequencies both user-defined

Loss of shielding accidents Included Included

Atmospheric dispersion

meteorology

Fixed: national average meteorology User-defined combination of

stability classes

Ingestion model Model similar to WASH-1400 [3-8] COMIDA2 [3-9]

a. Rural, suburban, and urban areas are called low-density, medium-density, and high-density, respectively, in

NUREG-0170.
Comparison of RADTRAN 1 and RADTRAN 5 Input Variables that Affect Incident-Free Dose

Variable Name

RADTRAN 5

Input

Location Variable Value

RADTRAN 1 RADTRAN 5 Array Name

(position)

Sensitivity

of Dose to

Variable RADTRAN 1

(NUREG-0170)

RADTRAN 5

(this study)

Comments

IPKG Package Dose

Rate (DR)

PACKAGE(2nd)

Proportional (not used) Distribution

(See Sect.3.4.3.4)

For NUREG-0170, TIPKG was set to 1.0which forced the package dose rate factor Kto have a value of 1000 mrem-ft2/hr.

not in code) Vehicle Dose

Rate

VEHICLE(3rd)

Proportional Distribution (see

package doserate above)

The NUREG-0170 model did not treat thepackage and vehicle separately; for spentfuel, the package and vehicle dose rates wereassumed to be the same.

not in code) Gamma Fraction PACKAGE

(3rd)

Small (1.0) 1.0 NUREG-0170 model assumed 100% gamma

radiation, which is conservative.

not in code) Neutron

Fraction

PACKAGE(4th)

Small (0.0) 0.0 NUREG-0170 model assumed 100% gamma

radiation. Neutrons readily attenuated byconcrete, humidity, etc.

not in code) Gamma Fraction VEHICLE

(4th)

Small (1.0) 1.0 NUREG-0170 model assumed 100% gamma

radiation, which is conservative.

not in code) Neutron

Fraction

VEHICLE(5th)

Small (0.0) 0.0 NUREG-0170 model assumed 100% gamma

radiation. Neutrons readily attenuated byconcrete, humidity, etc.

KGOE Package

Size

PACKAGE(5th)

Proportional (not used) 5.2 for truck

4.8 for rail

Package dimension was not used by theNUREG-0170 spent fuel model. It was usedoffline to estimate the package dose ratefactor (see TIPKG above) Values are forcasks currently in service.

not in code) Vehicle Size VEHICLE

(6th)

Proportional 5.2 for truck

4.8 for rail

The NUREG-0170 model did not treat thepackage and vehicle separately.

not in code) Exclusive

Use

VEHICLE(modifies 2ndvalue in array)

N/A Exclusive Use Exclusive Use

PY Number of

Shipments

VEHICLE(7th)

Proportional For 1975, 254

for truck and 17for rail.

1 NUREG-0170 examined results per year

(1975); this study looks at results pershipment.
parison of RADTRAN 1 and RADTRAN 5 Input Variables that Affect Incident-Free Dose (continued)

Variable Name

RADTRAN 5

Input

Location Variable Value

RADTRAN 1 RADTRAN 5 Array Name

(position)

Sensitivity

of Dose to

Variable RADTRAN 1

(NUREG-0170)

RADTRAN 5

(this study)

Comments

st value

 DNORM

ray

Crew Size VEHICLE (8th) Proportional

(crew doseonly)

Truck: 2 Truck: 2 Because of distance from the cask rail car,

both studies assume the train crew receivesnegligible in transit exposures.

rd value

 DNORM

ray

CrewDistance

VEHICLE(9th)

Proportional(crew doseonly)

Truck: 3.0 m Truck: 7.4 m Dose calculated from package surface

nearest crew rather than from sourcelocation at geometric center of package.

not in code) Crew View VEHICLE

(11th)

Proportional Truck: 2 m See preceding comment on distance from

package to crew.

not in code) Crew

Modfac

VEHICLE(10th)

(1.0) 1.0 RADTRAN 5 allows cab shielding to be

modeled; however, no shielding of crew wasassumed in current calculations.

KGSHP Number of

Packages

VEHICLE Proportional 1 1

OPZON Population

Density

STOP(3rd)

Proportional(stop doseonly)

Rural: 6Suburban: 719Urban: 3861

Truck: 3E+04Rail: Rural, 8;Suburban, 340

For RADTRAN 5, truck value based onempirical data; rail value reflects fact that,even in cities, rail yards are not surroundedby urban population density.

ixed Value Minimum Dist.

Maximum Dist.

STOP(4th, 5th)

Proportional(stop doseonly)

10 ft2600 ft

Truck: 1, 10 mRail: 30, 800 mRail classification yard: 400,800 m

In NUREG-0170 model, the 10 & 2600 ftvalues could not be changed. RADTRAN 5values are for members of public; workerdoses are computed separately.

not in code) Shield Factor STOP

(6th)

Proportional(stop doseonly)

1.0 Not in NUREG-0170 model; assumed to be

1.0 (i.e., everyone is outdoors). Set to 1.0 inthis study for conservatism.

h, 9th, &

0th values

 DNORM

ray

Stop Time STOP

(7th)

Proportional(stop doseonly)

 Truck RailR: 1 24S: 5 0U: 2 0

Truck: Distribution (See Sect.3.4.3.1)Rail: classification yardstops, 60 hr; allother rail stops,0.033 hr/km.

In NUREG-0170 model, aggregate stop timefor rural, suburban, and urban travel wasentered. In RADTRAN 5, stop time can beaggregated or entered separately for eachstop. Because trucks transporting spent fueldo not make stops to sleep. A correctionfactor to the results calculated using thetruck stop time distribution is developed inSection 8.6.
parison of RADTRAN 1 and RADTRAN 5 Input Variables that Affect Incident-Free Dose (continued)

Variable Name

RADTRAN 5

Input

Location Variable Value

RADTRAN 1 RADTRAN 5 Array Name

(position)

Sensitivity

of Dose to

Variable RADTRAN 1

(NUREG-0170)

RADTRAN 5

(this study)

Comments

TSTOR (not in code) Small Truck: 2

Rail: 4

N/A RADTRAN 5 calculations assumed stops for

storage didn’t occur.

DSTOR (not in code) Small Truck: 896

Rail: 25

N/A RADTRAN 5 calculations assumed stops for

storage didn’t occur.

not in code) (not in code) Small (5 ft, 1000 ft) N/A RADTRAN 5 calculations assumed stops for

storage didn’t occur.Storage exposure distance range was fixed inRADTRAN 1.

FMPS] Dist. LINK

(3rd)

Proportional R: 2530 

× 0.09

S: 2530 

× 0.05

U: 2530 

× 0.05

Distribution(See Sect.3.4.1.2)

1975 Model used fixed route length (FMPS)and fixed fractions of rural, suburban, andurban travel as indicated.

Speed LINK

(4th)

Proportional Truck: 55 mph

Rail:R: 40 mphS: 25 mphU: 16 mph

Truck: 55 mphRail:R: 40 mphS: 25 mphU: 16 mph

Truck value (55 mph) is used for interstatesfor all population densities. Applies toincident-free only; accident speeds not adirect RADTRAN input (see Chapter 7).

6th value in

NORM array

Persons per Veh LINK

(5th)

Proportional(on-link doseonly)

2 Distribution

(See Sect.3.4.3.6)

OPZON Pop Den LINK

(6th)

Proportional(off-link doseonly)

R: 6S: 719U: 3861

Distribution(See Sect.3.4.1.4)

Values in NUREG-0170 Model were fixed.

3rd, 24th &

5th values in

NORM array

Vehicle Density LINK

(7th)

Proportional(on-link doseonly)

R: 470S: 780U: 2800

Distribution(See Sect.3.4.3.5)

not in code) Pop Zone LINK

(9th)

N/A 1,2, or 3, as

appropriate

Designation determines shielding factorused; rural, suburban, and urban populationdensity ranges are the same as in NUREG0170.

not in code) RD LINK

(10th)

Small Truck: 1

Rail: 3

NUREG-0170 model assumed 5% travel oncity streets and 10% on non-interstatehighways. This study used 0% for bothvalues.
parison of RADTRAN 1 and RADTRAN 5 Input Variables that Affect Incident-Free Dose (continued)

Variable Name

RADTRAN 5

Input

Location Variable Value

RADTRAN 1 RADTRAN 5 Array Name

(position)

Sensitivity

of Dose to

Variable RADTRAN 1

(NUREG-0170)

RADTRAN 5

(this study)

Comments

not in code) Farm Frac LINK

(11th)

Small(ingestiondose only)

No effect Used to calculate ingestion dose. Not

present in NUREG-0170 model; notcalculated for present study.

ixed Value Number of

Handlers perPackage

HANDLING(3rd)

Proportional(handler doseonly)

2 5 NUREG-0170 model only required number

of handlings to be entered (7th value inDNORM array); other variables that cannow be user-defined were fixed values inNUREG-0170 model. Number of handlershas been updated based on recent empirical

data.

ixed Value Handling Distance HANDLING (4th) Proportional (handler dose

only)

1 1 Value used in RADTRAN 5 based on

empirical data that confirm originalNUREG-0170 value.

ixed Value Handling Time HANDLING

(5th)

Proportional(handler doseonly)

0.5 0.5 Value used in RADTRAN 5 based on

empirical data that confirm originalNUREG-0170 value.

not in code) CAMPAIGN MODSTD None 20 yrs Not present in NUREG-0170 model.not in code) DDRWEF MODSTD Proportional

(crew/workerdose only)

0.0018 hr/km Not present in NUREG-0170 model; used to

calculate rail worker dose for crew changestops outside of classification yards.

not in code) DISTOFF MODSTD Inversely

Proportional

(Truck: 27, 30,& 800 m)

Truck: 27, 30, &800 m

Values were fixed in NUREG-0170 model.

ixed Values DISTON MODSTD Inversely Proportional Truck: 3 m, Rail: 3 m Truck: 3 m, Passing

car: 4 m,Rail: 3 m

NUREG-0170 model did not treat passingcars.

not in code) FMINCL MODSTD Proportional

(crew doseonly)

2 Used to calculate rail worker dose at

classification yards. Not present inNUREG-0170 model.
parison of RADTRAN 1 and RADTRAN 5 Input Variables that Affect Incident-Free Dose (continued)

Variable Name

RADTRAN 5

Input

Location Variable Value

RADTRAN 1 RADTRAN 5 Array Name

(position)

Sensitivity

of Dose to

Variable RADTRAN 1

(NUREG-0170)

RADTRAN 5

(this study)

Comments

ot in code) RPD MODSTD Proportional 6 Not present in NUREG-0170 model. Used to

calculate dose to unshielded persons in cities.

ot in code) RR MODSTD Small (1.0) 1.0 Recommended value reflects large fraction of

time spent outdoors on farms.

ot in code) RS MODSTD Small (1.0) 0.87 Recommended value for wood frame

construction. NUREG-0170 model assumedno shielding.

ot in code) RU MODSTD Small (1.0) 0.018 Recommended value for masonry

construction. NUREG-0170 model assumedno shielding.

ot in code) SMALLPKG MODSTD Small (0.5 and 1.0) 0.5 RADTRAN 5 model has only one threshold –

variables for large packages are defined byuser.

RGLCF LCFCON MODSTD Proportional 2.22E-05 lung,

1.34E-5 thyroid,1.21E-04 wholebody, 6.9E-6bone, 3.4E-6LLI

5E-04 generalpublic; 4E-04workers (doseequivalent towhole-body dose)

NUREG-0170 model used organ-level factorsrather than CEDE or dose-equivalent-basedfactors and did not distinguish public andworker populations. RADTRAN 5 model isbased on BEIR V and ICRP 60.

ot in code) INTERDICT MODSTD Proportional 8 NUREG-0170 model didn’t include cleanup/interdiction thresholds.

ot in code) UBF MODSTD Proportional

(urban doseonly)

Aggregateanalyses, 0.52Route-specificanalyses, 0.9

NUREG-0170 model did not account for

fraction of urban area not occupied bybuildings (aggregate analyses) or fraction ofpopulation in buildings (route-specificanalyses).

ot in code) USWF MODSTD Proportional

(urban doseonly)

0.1 NUREG-0170 model did not account for

fraction of urban area occupied by pedestrianson sidewalks (aggregate analyses) or fractionof persons out of doors (route-specificanalyses)
.4 Comparison of RADTRAN 1 and RADTRAN 5 Input Variables that Affect Accident Risk

Variable Name RADTRAN 5

Input

Location

Variable Value

RADTRAN 1 RADTRAN 5 Array Name

(position)

Sensitivity

of Dose to

Variable

RADTRAN 1

(NUREG-0170)

RADTRAN 5

(this study)

Comments

APM Accidents per

vehicle-km

LINK(8th)

Proportional Truck: 1.06E-6

Rail: 9.3E-7

Distributions(See Sect.3.4.2)

In RADTRAN 1, for each AccidentCategory, APM and γ were entered as

a product.

γ Severity SEVERITY Proportional 8 truck and 8 rail

AccidentCategories (SeeTable 1.5)

19 truck and 21rail AccidentCategories(See Table 7.31)

In RADTRAN 1, for each AccidentCategory, APM and γ were entered asa product.

y

RF RFRAC RELEASE Proportional 8 truck and 8 rail

AccidentCategories (SeeTable 1.5)

19 truck and 21rail AccidentCategories(See Table 7.31)

NUREG-0170 values give fraction ofinventory of largest release that isreleased for each Accident Category(see Table 1.4).

AER AERSOL RELEASE Proportional (1.0) 1.0 Not explicitly treated by NUREG0170 model.RESP RESP RELEASE Proportional (1.0) 1.0 Not explicitly treated by NUREG0170 model.

)

(not in code) Pasquill PARM Proportional Distribution

(See Sect.3.4.3.3)

RADTRAN 1 treats only a single setof weather conditions. RADTRAN 5treats 6 sets of weather conditions.

(not in code) BRATE MODSTD Small (3.3E-04) 3.3E-04 Treated as part of RADTRAN 1

inhalation dose model.

(not in code) EVACUATION MODSTD Proportional Distribution

(See Sect.3.4.3.2)

Because NUREG-0170 model did nottreat groundshine, evacuation was notmodeled.

(not in code) CULVL MODSTD Proportional 0.2 Because NUREG-0170 model did not

treat groundshine, decontaminationwas not modeled.

(not in code) INTERDICT MODSTD Proportional 8 Because NUREG-0170 model did not

treat groundshine, interdiction was notmodeled.
mparison of RADTRAN 1 and RADTRAN 5 Input Variables that Affect Accident Risk (continued)

Variable Name

RADTRAN 5

Input Location

Variable Value

RADTRAN 1 RADTRAN 5 Array Name

(position)

Sensitivity

of Dose to

Variable RADTRAN 1

(NUREG-0170)

RADTRAN 5

(this study)

Comments

s

LCF LCFCON MODSTD Proportional 2.22E-05 lung;

1.21E-04 wholebody

5E-04 generalpublic; 4E-04workers (doseequivalent towhole-body dose)

NUREG-0170 model used organ-levelfactors rather than CEDE or doseequivalent-based factors and did notdistinguish public and workerpopulations. RADTRAN 5 model isbased on BEIR V and ICRP 60.

(not in code) GECON MODSTD Proportional 1.00E-04 No genetic effects were computed in

NUREG-0170 model.

(not in code) Neutron

Emission

MODSTD Small (0.0) 0.0 NUREG-0170 model did not treat

neutron emission. This model was notused by this study. LOS exposureswere calculated from surface dose rateof an unshielded assembly.

RADIST RADIST MODSTD Inversely

Proportional

10, 20, 30, 40,50, 100, 200,300, 500, and1000 ft

3.05, 6.1, 9.1,12.2, 15.2, 30.5,61, 91.4, 152, 305m

Change in units only.

(not in code) RPCTHYROID MODSTD Small isotope values Used to estimate early effects.(not in code) SURVEY MODSTD Small 10 Post-accident survey and clean-up

activities were not treated in NUREG0170 model.

TIMENDE MODSTD Small 1.0 R: 0.67

S: 0.67U: 0.42

In NUREG-0170 model, this variablewas defined as exposure time.

n

(not in code) UBF MODSTD Proportional

(urban doseonly)

0.52 for aggregateanalyses;0.9 for routespecific analyses;

NUREG-0170 model did not accountfor fraction of urban area not occupiedby buildings (aggregate) or fraction ofpopulation in buildings (routespecific).

(not in code) USWF MODSTD Proportional

(urban doseonly)

0.1 for all analyses NUREG-0170 model did not account

for fraction of urban area occupied bypedestrians on sidewalks (aggregate)or fraction of persons out of doors(route-specific).
3-12

the RADTRAN 5 variable value column indicates that values for this variable were selected from

a real-world distribution of the values of this variable. A “fixed value” is one that was held

constant throughout this study, either because it was a Less Important Variable or for the other

reasons outlined previously in connection with Important Variables. If a variable that is not

explicitly modeled has an implicit value or a value that is not accessible through input (i.e., a

hard-wired variable), then that value is enclosed in parentheses in the RADTRAN 1 or

RADTRAN 5 variable value column. In the variable value columns, R, S, and U respectively

mean Rural, Suburban, and Urban. Finally, in the “Sensitivity” column, “Proportional” and

“Small” have the meanings given above in the discussion of Important and Less Important

Variables.

The rationale for the selection of RADTRAN incident-free and accident input variables for which

distributions are constructed and the data used to construct each distribution are each presented in

detail in Sections 3.3 and 3.4.

3.3 Variables Selected for Sampling

Less Important Variables are identified in Tables 3.3 and 3.4 by the word “Small” in column

five, the column that specifies the sensitivity of radiation dose estimates to changes in the value

of the indicated variable. Because these variables have little impact on calculated radiation

doses, a central estimate value (the value listed in column seven of these tables) was selected for

each of these variables and that value was used in all of the RADTRAN 5 calculations performed

for this study.

More Important Variables are identified in Tables 3.3 and 3.4 by the word “Proportional” in

column five. Although radiation doses are strongly affected by changes in the value of any More

Important Variable, not all More Important Variables have values that take on a wide range of

values in the real world. Thus, More Important Variables can be subdivided into two groups,

those that have values that are constant or that vary only slightly, and those that take on a wide

range of values in the real world.

3.3.1 Incident-Free Variables Selected for LHS Sampling

All variables that have proportional effects on the value of the result (i.e., Important Variables)

were initially candidates for probabilistic treatment. Variables were selected for probabilistic

treatment (selection of variable value by LHS sampling of the variable’s distribution) principally

by examination of the importance analysis performed in RADTRAN output, which shows the

magnitude of the effect that a specified value change (1 percent) has on the result. As described

in detail below, fixed values were assigned to those with a proportional effect but which

experience little actual variation or are problem-specific. For example, incident-free dose

calculations are highly sensitive to the Package Dimension variable (PKGOE in RADTRAN 1),

but the characteristic dimension used in the analyses in this study is invariant for a given cask.

Thus, fixed values were assigned to that variable, 5.2 m for the truck cask and 4.8 m for the rail

cask (see Section 4). In contrast, an equally important variable (Package Dose Rate at 1 m) was

selected for probabilistic treatment (construction of a distribution of parameter values and

selection of values by sampling from the distribution), because the variety of fuel ages and
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burnups that characterize spent fuel causes the external dose rate of spent fuel casks to vary over

a substantial range.

The incident-free variables for which distributions of parameter values were constructed are:

• Package Dose Rate at 1 m (mrem/hour)

• Link Length (km)

• Link Population Density (person/km2)

• Persons per Vehicle (truck only)

• Link Vehicle Density (one-way vehicles/hour)

• Stop Time (truck only)

The package dose rate variable has been discussed already. Link length is treated by constructing

distributions because dose to the general public residing near the road or railroad (off-link dose)

is directly proportional to distance traveled and because the distances to possible destinations

investigated in this study vary considerably. Link population density also directly influences risk

to the general public and varies from link to link. The persons per vehicle variable directly

influences dose to general public in vehicles that sharing the road with the spent fuel truck, and

sufficient high-quality data regarding vehicle occupancy are now available from the Department

of Transportation (DOT) to permit construction of a vehicle-occupancy distribution. Link

vehicle density has a similar influence on on-link dose, and distribution data are available. The

distributions used to characterize these variables are described below in Sections 3.4.1 and 3.4.3.

3.3.2 Incident-Free Variables Not Selected for LHS Sampling

The remaining variables, some of which can affect consequences or risks proportionally, include

those

• that exhibit little or no actual variation,

• that cause only small changes in consequences or risks,

• for which there are not adequate data to determine the variable’s distribution,

• that are problem-specific and thus have different values for specific casks (e.g., the

characteristic dimension of the cask), and shipping campaigns (e.g., the number of

shipments in the campaign), and

• that have no effect on truck or rail transport consequences or risks (e.g., variables used

only for other modes, such as number of flight attendants).

Variables with small effects on risk and variables that vary over small ranges will be considered

together.
3-14

3.3.2.1 Variables with Little or No Variation or with Small Impacts

The following variables fall into this category:

• Number of Crew Persons

• Average Distance of Crew from Package Surface (m)

• Crew Modification Factor

• Number of Railcar Inspections per Trip (FMINCL)

• Distance-Dependent Rail Worker Exposure Factor (DDRWEF)

• Number of Handlers

• Handling time per Package

• Package-to-Handler Distance (m)

• Threshold Dimension for Handling by forklift or crane (SMALLPKG) (m)

• Genetic Effects Conversion Factor (GECON)

• Latent Cancer Fatality Conversion Factor (LCFCON)

Each of these variables is now discussed even though several of them (all of the handling

variables, GECON, LCFCON) are not used in any of the risk calculations performed for this

study or are used only in sensitivity calculations.

The number of crew persons varies little because it is determined by trucking and rail industry

practices. The value of 2 for truck transportation is by far the most common [3-10]. There is

little variation in the value of this parameter, and the selected value is representative. No intransit crew dose is calculated for rail mode because of the large separation distances and large

amount of shielding between the crew and the package(s).

The average distance of crew from package surface is a new variable in RADTRAN 5.

Previously, the distance from the crew compartment to the geometric center of the package was

used and the same point-source model used to calculate off-link and on-link dose was used to

calculate crew dose. However, for cylindrical packages such as spent-fuel casks, where the crew

view of the package is from the end rather than the side, a modification of the basic point-source

model yields less conservative results. For a given cask design, there is still some variability in

this value because of variation in trailer length, but it is not large. The distance used is the old

value less half the cask length, which relocates the crew-view point source from the geometric

center of the package to the center of the side closest to the crew.

The crew modification factor is part of a new model in RADTRAN 5 intended to account for

crew shielding (e.g., shielded truck cabs) and is not present in RADTRAN 1. It is a fraction that,

when multiplied by the package dose rate, reflects the reduced dose rate to the crew from the

presence of shielding, if any. The crew dose is limited by the maximum permissible dose rate in

the crew area (2 mrem/hour). The contribution of crew dose to the total result consequently

cannot exceed a maximum value, which is determined for a given dose rate by the total time in
3-15

transit. Furthermore, the value of this variable has a relatively small effect on overall population

dose. It should be noted, however, that the effect of dose rate changes within the subgroup itself

is not necessarily small. The affected subgroup (in this case, truck or rail crew) is noted in

parentheses under the column titled Sensitivity of Dose to Variable in Table 3.2.

The value of 2 assigned to FMINCL is determined by rail-carrier business practices, which

require one inspection at the beginning of a trip and one at the end. The possibility of other

inspections en route cannot be ruled out, but the experience base is insufficient to permit

statistical treatment of this variable. Thus, the value is set to 2, the total number of inspections

that are known to always occur (i.e., 1 at the beginning and 1 at end of each trip).

The DDRWEF applies to rail mode only. It is used to calculate the component of rail-worker

dose that depends on distance traveled (e.g., engine changes and shift changes) rather than on

time spent in a classification yard. The value of 0.0018 hour/km was determined from industrysupplied data [3-11] and is relatively invariant because of the uniformity of industry practices,

union agreements, etc. Furthermore, it is a small component of total rail worker dose because the

majority of the worker dose is incurred in classification yards.

The number of handlers was originally fixed at 2 in RADTRAN 1. The number is user-definable

in RADTRAN 5, and the recommended value for spent-fuel handling is now 5. This

recommendation is based on data from observations of 12 spent-fuel off loadings at the Port of

Newport News, Virginia [3-12]. The value includes workers who guide the crane to the proper

orientation for casks enclosed in ISO containers both to pick up the cask and to lower it into

position on the vehicle. It also includes a spotter and workers who lock and check the tiedowns

after the cask is in place. There may be more than 5 individuals involved but no more than 5 in

proximity to the cask at any given time. The standardization of handling equipment means there

is little variation in this value in normal operations.

Handling time per package was also a fixed value in RADTRAN 1 and was set to 1/2 hour

(30 minutes). Empirical data on spent-fuel off-loadings has since confirmed that this is a

somewhat conservative estimate [3-12]. As is the case for the other handling-related variables,

standardization of handling equipment means there is little variation in this value in normal

operations. For spent fuel casks, which are lifted with cranes, the time during which workers are

in proximity to a cask is 30 minutes or less. This includes the time required to guide a crane into

position; attach the crane to cask trunnions or to an enclosing ISO container; lift the cask; move

it over to the transport vehicle (e.g., truck or rail car); lower it into place; fasten the tiedowns; and

detach the crane once the tiedowns have been fastened. The time required for the reverse process

is the same. It includes additional safety steps (e.g., checking that the tiedowns are properly

secured) and also includes the time between cask movements for multiple cask handlings. Time

is required, for example, for a truck to drive out of the loading zone and be replaced by a second

truck ready to receive a second cask. Time is also required to reposition the crane over the next

railcar, ship hold, etc. from which the next cask is to be lifted. If only one cask is being handled,

then the latter actions are not necessary, which reduces the total elapsed time and makes the 30-

minute value somewhat conservative.
3-16

Package-to-handler distance was fixed at 1 m in RADTRAN 1. This value has since been shown

to be somewhat conservative but generally correct on the basis of empirical data [3-12] and to

have little variation. It is the recommended value for RADTRAN 5.

SMALLPKG has no effect on the results for spent-fuel handling. It merely defines the minimum

dimension above which mechanical handling methods must be used [3-13]. That dimension is a

function of the capabilities of the package-handling machinery available and is not subject to

wide variation.

Values of GECON and LDFCON are based on the most recent radiological data available. The

values used must conform with federal guidance [3-14]. The values change with time, however,

as more and better data become available. That is clearly seen in the difference between the 1975

and 1999 values.

3.3.2.2 Variables Where Distribution Data is Not Available

Variables for which distributions have not been developed include

• Gamma and Neutron Dose-Rate Fractions

• Rural, Suburban, and Urban Shielding Factors (RR, RS, and RU, respectively)

• Shipment velocity (km/hour)

• Urban building fraction or fraction of persons indoors (UBF)

• Urban sidewalk fraction or fraction of persons out of doors (USWF)

• Array of distances for off-link dose calculation (DISTOFF)

• Minimum distances to on-link vehicles (DISTON)

• Population density at stops (persons/km2)

• Minimum and maximum radii of annular area around stopped vehicle (m)

• Shielding factor

• Ratio of Pedestrian Density (RPD)

Gamma and neutron dose rates vary considerably with fuel age and burn-up and the mix of fuel

ages and burn-ups in any given shipment. For these reasons, especially the currently

unpredictable mix of assemblies in any given shipment, no distribution of gamma/neutron ratios

has been developed, and the conservative point estimates of 100 percent gamma and 0 percent

neutron are used instead. This approach is conservative because neutrons are more rapidly

attenuated by air and other hydrogen-rich media (e.g., concrete, shrubbery) through which they

might pass during the course of normal transport prior to reaching human receptors.

The rural, suburban, and urban shielding factors were not present in RADTRAN 1 (i.e., no

shielding effects were accounted for in RADTRAN 1). The variables are present in RADTRAN

5, but no distribution of weighted-average shielding factor values for urban or other areas has

been developed. In lieu of such distributions, point estimates based on typical or representative
3-17

construction types in the population zones have been used [3-15]. The value recommended for

urban shielding (RU) in RADTRAN 5 is representative of masonry construction. The suburban

factor represents frame construction. Although some suburban structures are constructed of brick

or other materials, frame construction and its analogs (e.g., mobile homes) are common

throughout the country. In the absence of a distribution, the frame-construction assumption also

is conservative. The rural factor is set somewhat conservatively to 1.0 (i.e., no shielding) to

reflect the large amount of time spent outdoors by many rural residents. No actual data on time

spent indoors versus out of doors has been combined with construction-type data to generate a

rural shielding factor distribution. These values were developed for RADTRAN II [3-16].

All spent-fuel shipments are highly regulated. Truck shipments have armed escorts for much if

not all of their travel time. Although escorts are only required in urban areas, past experience

indicates that escorts will accompany spent-fuel shipments for greater distances (e.g., in Virgina,

shipments are escorted over the entire route within the state). While speeds in excess of 88 kph

(55 mph) are common for ordinary commercial trucking, it is anticipated that spent-fuel

shipments would not significantly exceed 55 mph. Current experience with Waste Isolation Pilot

Plant (WIPP) shipments confirms this assumption [3-17]. Rail shipments travel at speeds

controlled by the rail companies, and speeds for trains carrying hazardous materials are generally

lower than those for general freight, although trains generally traverse urban areas at reduced

speeds.

In the absence of adequate data from which to construct truck or train speed distributions, the

typical interstate truck speed and typical train speeds for hazardous material shipments were used

as point estimates. Thus, shipment velocity is set to 88 kph (55 mph) in all population zones for

interstate truck transportation. For rail transportation, different values were used for rural,

suburban, and urban route segments: 64.37 kph (40 mph) on rural segments; 40.3 kph (25 mph)

on suburban segments; and 24.1 kph (16 mph) on urban segments. Because these speeds are

believed to be somewhat conservative (lower than may actually occur), they should lead to a

small overestimation of incident-free dose. Because these speeds are not used to estimate cask

impact speeds during collision accidents, they have no effect on accident risks.

UBF and USWF were not present in RADTRAN 1. They were added in RADTRAN II. At that

time, aggregated population-density data was the only type of population information available.

The population density assigned to urban links, therefore, was treated as being uniform across the

entire bandwidth (area within 800 m on either side of the road or railroad). This would have led

to an overestimate of the off-link urban population if used without modification. The UBF and

USWF correction factors restricted population to areas occupied by buildings and sidewalks; the

values came from the Urban Study [3-18]. In current analyses, however, population densities are

derived from GIS-based systems with census-block population data. That is, they represent

actual counts that should not be reduced by any correction factors. Thus, the UBF and USWF

values are now used to simply designate what fraction of the population is indoors and what

fraction is out of doors. The sum of the two fractions must now be unity. The data indicating

what fraction of the urban population is out of doors at any given time are from the Urban Study,

which examined only New York City. The 0.1 estimate (10 percent), which applies only to a

weekday during working hours in Manhattan, has been used as a conservative point estimate; the

0.9 indoors value (90 percent) was obtained by subtraction from 1.0. The Manhattan value is
3-18

conservative because of the number of workers who are out of doors for significant portions of

the workday (e.g., garment-district carriers and messengers).

DISTOFF consists of an array of three distances, the first two of which define a pedestrian zone

adjacent to the road or railroad and the last of which establishes the maximum depth or

bandwidth for off-link dose calculation. These variables were present in RADTRAN 1 and have

not changed since 1975. There undoubtedly is variation in the minimum distance to the road at

which people may reside; it may frequently be greater than 30 m and occasionally may be less,

but no distribution for this variable is available in the literature. The maximum distance was set

at 800 m (0.5 mi) in the 1975 model to conform with the previously published Reactor Safety

Study [3-8] although dose rates drop below measurable values at much shorter distances from the

road or railroad. All analyses since then have used the same value, and, even though RADTRAN

5 allows the value to be altered, 800 m is used here to provide comparability with earlier studies.

The pedestrian zone width was set at 3 m in RADTRAN 1 on the basis of civil-engineering

standards for walkway widths, and in the absence of any data to support use of a distribution, the

3 m width also is used here to provide comparability.

DISTON is used in the calculation of on-link dose and is the minimum distance from the package

to traffic in nearby lanes. The user enters up to four values for interstate highways, secondary

roads, city streets, railroads, and passing vehicles, respectively. The interstate value is based on a

1986 model of a minimal four-lane configuration with an average lane width of 5 m. The

secondary and city-street values, which are smaller (3 m), are not used in this study. The railroad

value of 3 m is based on the minimum clearance between passing trains on double-rail route

segments. The value for passing vehicles (4 m) is the median value for all interstate and

secondary-road lane widths. These variables are not equally uncertain. The minimum interstate

lane width, for example, is determined by engineering standards that apply to all interstate

highways. However, no published data are available that indicate the range of magnitudes of

these variables, and the point estimates described above are used here.

Two population densities are used to calculate public dose at ordinary truck stops (rest and

refueling stops). The first population density is a derived value that yields approximately nine

persons fully unshielded within a 10-m radius in order to conform to the observations of Griego

et al. [3-19]. The second density is used to calculate exposures to more distantly located persons.

It is set equal to the suburban aggregate value used in the 1975 model since it is not possible to

predict exact stop locations in advance. The Griego et al. study [3-19] examined two separate

truck stops, one suburban and one rural in nature. Their data include many hours of observation

of truck-stop operations. The standard deviation of their data for persons within 10 m is small.

The reasons for this uniformity are that

• truck stops provide standardized services (refueling bays, restaurants, etc.),

• service area and refueling bay designs tend to be standardized, and

• truck parking parameters (average row spacing and average distance from the service

area) have low variability.
3-19

Thus, the mean value of the Griego et al. data [3-19] was used in this analysis for the inner

annulus of truck stops. For rail stops, public dose is also estimated using the suburban aggregate

population density. This is done because most rail yards are located in regions with suburban

population densities, and because a distribution for this variable can not be constructed without

knowing the actual locations of rail stops, which of course can only be specified for the real

routes used during a real shipping campaign.

The minimum and maximum radii in RADTRAN 1 established an annular area around a stop

location in which exposed persons were located. They were arbitrarily fixed at 10 ft (≈ 3 m) and

2600 ft (≈ 800 m). Recent observations of actual truck stops have shown that the minimum is

too large [3-19]. The minimum approach distance was in the 1 m range. These observations also

led to the partitioning of the surrounding population into two nested annular areas. The

innermost annulus has minimum and maximum radii of 1 and 10 m, and all persons within the

area are unshielded; the outer annulus has minimum and maximum radii of 10 and 800 m,

respectively. Proximity of the shipment to structures and other trucks provides some shielding

for this outer population. For calculation of public dose at rail stops in classification yards, the

minimum radius coincides with the typical classification-yard boundary (400 m) and the

maximum radius remains 800 m. For rail stops outside of classification yards, the minimum

radius is 30 m and the maximum radius remains 800 m. The maximum radius is set to 800 m

solely to provide calculational consistency between modes and between stop-related and intransit contributions to dose. In the absence of advance knowledge of stop locations, exact

minimum values cannot be used, and no distribution of population densities around possible

stops has been developed.

The shielding factor is set to 1.0 (no shielding) on the basis of the data in [3-19] for the inner

annular area at truck stops (radii of 1 m and 10 m). References [3-19] and [3-10] are the basis

for the selection of 0.2 as a shielding factor for the outer annular area. The shielding factor of 0.1

for rail classification stops was calculated in [3-11]. The shielding factor for rail stops outside of

classification yards has been set to a conservative 1.0 because of the lack of empirical

information on presence or absence of surrounding structures at intermediate rail stops. No

distribution that describes the frequency distribution of shielding factors for public exposure at

either truck or rail stops has been developed.

The ratio of pedestrian density allows the user to account for persons out of doors in urban areas

and persons who are not residents (shoppers, drivers, etc.). It acts as a direct multiplier for the

out-of-doors urban population. The value used in this study is 6 and it is taken from the Urban

Study [3-18], which examined only New York City. The value is generally conservative because

commercial districts remain robust, unlike many other American cities where much of the

business activity has relocated to suburban shopping centers and industrial parks. The ratio of

the number of retail businesses to the residential population is 6.95 for New York City, as

opposed to values near 1 for most other East Coast cities (e.g., 1.01 for Boston); it also is greater

than the same ratio for large West Coast cities such as Los Angeles (ratio = 5.65) [3-20]. No

distribution of values for this variable has been developed.
3-20

3.3.2.3 Problem-Specific Variables

Problem-Specific Variables include:

• Characteristic Package Dimension (m)

• Number of Shipments

• Number of Packages per Shipment

• DTSTOR (Storage time per shipment; hours)

• PDSTOR (Number of persons exposed during storage)

• RSTOR (Radial distances defining annular area within which persons are located around

storage location)

• Crew-view Package Dimension (m)

• Distance of crew from nearest package (m)

As noted in the introduction to this section, the characteristic package dimension is determined

by the choice of package for a given analysis. The values used in this study are 5.2 m for the

truck cask and 4.8 m for the rail cask (see Section 4).

The number of shipments is a variable found in all releases of RADTRAN. It clearly is problemspecific. All of the RADTRAN calculations performed for this study examined single shipments

that transport one spent fuel cask, i.e., the number of shipments was set to one, and the number of

shipments required to ship the entire on-site spent-fuel inventory (e.g., all of the spent fuel

assemblies that will have to be shipped from the sites where they are presently stored) to a

repository or intermediate storage facility is addressed in external calculations (spreadsheet). The

number of shipments needed to move the spent fuel inventory from on-site storage locations to

temporary or permanent storage facilities is discussed in Section 8.6.

The number of packages per shipment also is found in all releases of RADTRAN. For the

analyses performed for this study, it was assumed that each shipment carried only one Type B

spent fuel cask. This assumption is clearly correct for transport by truck. For transport by rail, it

is generally correct when transport is not by dedicated train (shipment by dedicated train was not

examined by this study).

The RADTRAN 1 variables DTSTOR, PDSTOR, and RSTOR are not present as distinct

variables in RADTRAN 5 because storage is modeled as a special type of stop in RADTRAN 5.

No en route storage is anticipated in the spent-fuel shipments analyzed in this study, so storage

variables are set to zero for RADTRAN 1 and no special storage stop is modeled in

RADTRAN 5.

The crew-view package dimension, like the basic package dimension variable, is determined by

the choice of cask and has no associated uncertainty. The values used in this study are 2 m for

the truck cask and 5 m for the rail cask.
3-21

3.3.2.4 Variables that Do Not Affect Truck or Rail Spent Fuel Transport

There are several variables that do not contribute to dose or risk calculation for spent-fuel

transportation by truck and rail modes. They are

• Number of Flight Attendants (FNOATT)

• Fraction of Land under Cultivation

• Exclusive-Use Flag (computer code “switch”)

• Population Zone

• Link Type

• CAMPAIGN

Some variables have no effect on the result in this study, regardless of what values are assigned

to them. One of these is the number of flight attendants; it applies only to modes of

transportation (air modes) not considered in this study. The term “No Effect” is entered for this

variable in the Variable Value column in Table 3.1, and no value is entered for FNOATT in the

input file. The fraction of land under cultivation variable has no effect on the result in this study

because ingestion dose is not computed.

Several flags and control variables found in RADTRAN 5 also should be mentioned. The first of

these is the flag for exclusive-use versus non-exclusive use. It is set to exclusive use in all cases

in this study. The population zone designation (rural, suburban, or urban) determines which

shielding factor is used and what column the link results are entered into in the output. The

designation is problem-specific. The designator was intended to allow use of non-standard

shielding factors (e.g., use of an “urban” shielding factor in non-urban links with high proportion

of masonry construction. However, such highly route-specific data are not employed in this

study and the designator thus depends on the definitions of rural, suburban, and urban population

densities. The latter are 0 through 66 person/km2

 for rural; 67 through 1,670 persons/km2 for

suburban; and greater than 1,670 persons/km2

 for urban. These ranges were derived from the

demographic model in NUREG-0170, and they have been used to develop population zone data

for all releases of RADTRAN. The letters R, S, and U are used to designated rural, suburban,

and urban zones in RADTRAN 5. A related variable is the Link Type designator. It is set to 1

for interstate highways, 2 for other highway types, and 3 for rail or other modes. These

designations are completely problem-specific, and there is no uncertainty as to what value is

entered for each link once the route has been established.

The CAMPAIGN variable has no direct effect on the result. It is used to calculate the total offlink population for multi-year campaigns by taking account of in-migration and out-migration of

population. It is based [3-21] on 1990 Census Bureau demographic data.
3-22

3.3.3 Accident Variables

This section gives information on RADTRAN variables required for accident-risk analysis

(Table 3.4). The format is the same as that used for incident-free variables. Variables were

selected for probabilistic treatment on the basis of sensitivity analyses performed to determine

the magnitude of change in the result associated with a fixed amount of change in an input value.

3.3.3.1 Accident Variables not Selected for LHS Sampling

The following accident-risk variables have been assigned point-estimate values

• Sidewalk Width in early effects calculation (m)

• Building Dose Factor

• Clean-up Level (CULVL) (microCi/m2)

• Threshold for Interdiction of Contaminated Land (microCi/m2)

• Time to Survey Contaminated Land (days)

• Breathing Rate (m3

/sec)

• Neutron Emission Factor for Loss of Shielding (LOS) Accidents

• One-year Dose to Thyroid (rem/rem inhaled)

• Radii of annular areas of exposure in an LOS Accident

• Time for Evacuation following an LOS Accident (hours)

Sidewalk width was a RADTRAN 1 variable and is no longer included as a variable in

RADTRAN 5. It was used only in calculation of dose to persons following an LOS accident on a

city street. Because travel on city streets during spent-fuel transportation historically has

occurred only in the case of overseas shipment into U.S. ports, no travel on city streets is

considered in this analysis, the model in which the variable is used in RADTRAN 1 is not

invoked and no correlation or adjustment is necessary.

The building dose factor is used to account for filtration of particulates from the air by building

heating/cooling systems. It was not included in RADTRAN 1. The recommended value of 0.05

for RADTRAN 5 is taken from [3-11]. This value is an average across a number of residential,

office, and industrial building types and represents the best available estimate in the absence of a

distribution.

Clean-up level (CULVL) was not a variable in RADTRAN 1. This variable is not treated

probabilistically because it is defined by regulation. Although there is currently no final

guidance for the value of the regulatory clean-up level, draft guidance issued by the U.S.

Environmental Protection Agency, recommends a value of 0.2 microCi/m2

 [3-22]. This value is

used in all of the RADTRAN calculations performed for this study. Like the clean-up level,

there is currently no final regulatory guidance for the Interdiction Threshold contamination level.

The value selected for use is 40 times higher than the value selected for CULVL, because the
3-23

decontamination factors achieved cleaning up two cases of weapons-related contamination [3-23]

suggest that decontamination of areas of moderate size by factors as large as 40 is achievable.

The actual time required to perform a contamination survey would likely be prolonged, but it is

not possible to predict because of regulatory and legal complexities [3-23]. The longer deposited

material remains on the ground, however, the more is (a) removed by radioactive decay and

(b) spread by forces such as wind and rain. In general, the shorter the elapsed time between an

accident occurrence and completion of a survey, the higher the survey results would be.

Furthermore, because of the rarity of actual contamination events, there is a paucity of empirical

data on which to base an estimate. For these reasons, the time to survey contaminated lands was

set at a radiologically conservative but practically unrealistic 10 days. The legal and practical

realities associated with post-accident response are discussed in Chanin and Murfin [3-23].

The generally accepted standard for breathing rate is used for calculation of inhalation and

resuspension doses. The breathing rate of the International Council on Radiation Protection

Reference Man (70-kg adult male at light work) is the recommended value; it is 3.3E-04 m3/sec

[3-24]. While not a quantity prescribed by regulation, this variable was developed by a

recognized international body (International Council on Radiation Protection) and is commonly

used in radiological consequence calculations. Thus, there is no need to treat this variable

probabilistically.

The dose-conversion factor for one-year dose to the thyroid is used to calculate thyroid dose via

the inhalation pathway. The factor is applied only to radioisotopes of iodine. Values specific to

I-131, I-129, and I-125 have been developed for this variable and they are: 1.26E-06, 5.77E+06,

and 9.25E+05 rem/Ci inhaled, respectively. These are radiological quantities and are not subject

to probabilistic treatment. Because none of the inventories used in this study contain significant

quantities of radioiodines, the value of this parameter is not important.

3.3.3.2 Accident Variables Selected for LHS Sampling

The accident variables selected for probabilistic treatment and the sections that describe the

treatments are:

• Accident Rate on a Link (accidents/vehicle-km) − Sections 3.4.2.2 and 3.4.2.3

• Evacuation Time − Section 3.4.3.2

• Atmospheric Stability − Section 3.4.3.3
3-24

3.4 Development of Distribution Functions

3.4.1 Route Characteristics

3.4.1.1 Introduction

The present study, which is intended to address the risk of transporting spent nuclear fuel from

all commercial power reactors to a repository, posed an unusual difficulty. While the locations

of the reactors where spent fuel is presently stored are known, final locations for interim storage

sites and for a permanent repository have not yet been selected and formally approved.

Therefore, specific spent fuel shipment routes could not be examined and small set of

hypothetical routes could be shown to be truly representative of all of the routes that might

someday be used. The method chosen to address this difficulty was to develop distributions of

shipment parameters and route characteristics using data for a very large number of real routes

that connect reactor sites to plausible interim storage site and permanent repository location, and

then to construct representative set of route parameter values by sampling these distributions

using LHS sampling methods. Provided that the distributions constructed represent the full

spectrum of possible routes and that sufficient sets of RADTRAN input variables (generated by

sampling the distributions) are analyzed, the mean risks and the risk ranges estimated using these

sets of route parameter values should accurately represent actual shipment risks.

The set of primary shipment origins is well known (commercial reactors with spent fuel in

holding pools). One possible interim storage site location was identified in the northeast, northcentral, northwest, southeast, south-central, and southwest portions of the continental United

States. In addition, three possible permanent repository locations, one of which was Yucca

Mountain, were also selected. The set of interstate truck routes or mainline rail routes that

connect each reactor site to each of the possible interim storage sites and each of these interim

storage sites to each of the three possible permanent repository locations were examined by

performing HIGHWAY [3-25] or INTERLINE [3-26] route calculations. In the case of truck

shipments, the routes were specified in compliance with HM-164 rules for “highway route

controlled quantity” shipments (49 CFR 177.825) such as the spent nuclear fuel shipments

considered here. For rail shipments, the routes conformed to rail carrier practice. For both types

of shipments, any NRC regulations (10 CFR 73.37) that would affect route selection were

considered.

After the routing calculations were completed, a data base of the lengths, and rural, suburban,

and urban length fractions was constructed using the data for the 492 truck or the 492 rail routes.

Sets of parameter values from each data base were ordered and aggregated to create cumulative

distributions for each of these route parameters. In Figures 3.1a through 3.1d, these NEW

distributions for truck routes are compared to OLD distributions constructed from similar sets of

route data tabulated in the Yucca Mountain down-select report [3-27]. Figures 3.2a through 3.2d

present a similar comparison of NEW and OLD rail-route parameter distributions. After visual

inspection of these distributions indicated that each NEW distribution was very similar to its

corresponding OLD distribution, the two data sets were combined thereby generating a larger,

statistically more comprehensive data base. The final set of route parameter distributions was

then constructed using the pooled data.
3-25

Figure 3.1a Comparison of the cumulative distributions of route lengths for truck.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 0.2 0.4 0.6 0.8 1

Rural Fraction

Cumulative Fraction

NEW

OLD

Figure 3.1b Comparison of the cumulative distributions of

route rural fractions for truck.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 1000 2000 3000 4000 5000

kilometers

Cumulative Fraction

NEW

OLD
3-26

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 0.2 0.4 0.6 0.8 1

Suburban Fraction

Cumulative Fraction

NEW

OLD

Figure 3.1c Comparison of the cumulative distributions of

route suburban fractions for truck.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 0.2 0.4 0.6 0.8 1

Urban Fraction

Cumulative Fraction

NEW

OLD

Figure 3.1d Comparison of the cumulative distributions of

route urban fractions for truck.
3-27

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 1000 2000 3000 4000 5000 6000

kilometers

Cumulative Fraction

NEW

OLD

Figure 3.2a Comparison of the cumulative distributions of route lengths for rail.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 0.2 0.4 0.6 0.8 1

Rural Fraction

Cumulative Fraction

NEW

OLD

Figure 3.2b Comparison of the cumulative distributions of route rural fractions for rail.
3-28

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 0.2 0.4 0.6 0.8 1

Suburban Fraction

Cumulative Fraction

NEW

OLD

Figure 3.2c Comparison of the cumulative distributions of route suburban fractions for rail.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 0.2 0.4 0.6 0.8 1

Urban Fraction

Cumulative Fraction

NEW

OLD

Figure 3.2d Comparison of the cumulative distributions of route urban fractions for rail.
3-29

3.4.1.2 Route Lengths

The length of any route is a key parameter in determining the risks associated with that route

because accident probabilities on the segments of a route are the products of the accident rate

(number per vehicle-km) and the length of each segment. In addition, incident-free doses are

proportional to route length (e.g., total stop time and driver exposure time for truck shipments)

and route-length multiplied by population-density (populations sharing and neighboring the

route). Histograms of route lengths derived from the combined route data are presented in

Figures 3.3a and 3.3b respectively for truck and rail routes. Integration of these histograms and

normalization to a total cumulative probability of 1.0 yielded the final cumulative route-length

distributions presented in Figures 3.4a and 3.4b.

3.4.1.3 Rural, Suburban, and Urban Route Fractions

The same data base described in Section 3.4.1.1 provided values for the aggregate fractions of

each route that traversed areas with Rural, Suburban, or Urban population densities. Table 3.5

presents the population densities ranges that were used in NUREG-0170 and in this study to

define urban, suburban, and rural route segments.

Table 3.5 Definition of Population Density Categories (persons/km2

)

Category Minimum Maximum Mean

Rural 0 66 6

Suburban 67 1670 719

Urban 1670 - - - 3861

Histograms of the Rural, Suburban, and Urban fractions, constructed from the combined data, are

shown in Figures 3.5a and 3.5b. The cumulative distribution functions derived from these

histograms, are presented in Figures 3.6a and 3.6b.

3.4.1.4 Rural, Suburban, and Urban Population Densities

As part of the route compilation described in Section 3.4.1.2, the distance-weighted average

population density values for the rural, suburban, and urban categories were also tabulated in the

route characteristics data base. Values for truck routes were sorted and aggregated, then

integrated and normalized to create the histograms and cumulative distributions shown in Figures

3.7a through 3.7c; similar processing of the rail route data yielded the plots in Figures 3.8a

through 3.8c. Note that the Urban values in Table 3.5 were influenced by the inclusion of citystreet route options while the present study is limited to interstate highways and loops that do not

traverse such high population-density areas.

3.4.1.5 Application Notes

Each of the cumulative distributions presented in the following figures serves as input to the LHS

sampling code. Sampled values of route length, route fractions, and segment population
3-30

0

10

20

30

40

50

60

70

80

90

100

040080012001600200024002800320036004000440048005200

kilometers

Frequency

Figure 3.3a Histogram of truck route lengths.

0

10

20

30

40

50

60

70

80

040080012001600200024002800320036004000440048005200560060006400

kilometers

Frequency

Figure 3.3b Histogram of rail route lengths.
3-31

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 1000 2000 3000 4000 5000 6000

kilometers

Cumulative Fraction

Figure 3.4a Cumulative distribution of truck route lengths.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 1000 2000 3000 4000 5000 6000 7000

kilometers

Cumulative Fraction

Figure 3.4b Cumulative distribution of rail route lengths.
3-32

0

50

100

150

200

250

300

Fraction

Rural

Suburban

Urban

Figure 3.5a Histograms of rural, suburban, and urban length fractions for truck routes.

0

50

100

150

200

250

00.10.20.30.40.50.60.70.80.91

Fraction

Frequency

Rural

Suburban

Urban

Figure 3.5b Histograms of rural, suburban, and urban length fractions for rail routes.
3-33

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 0.2 0.4 0.6 0.8 1

Fraction

Cumulative Fraction

Rural

Suburban

Urban

Figure 3.6a Cumulative distributions of rural, suburban, and

urban length fractions for truck routes.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 0.2 0.4 0.6 0.8 1

Fraction

Cumulative Fraction

Rural

Suburban

Urban

Figure 3.6b Cumulative distributions of rural, suburban, and

urban length fractions for rail routes.
3-34

0

20

40

60

80

100

120

140

160

Persons/sq km

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Frequency

Cumulative Fraction

Figure 3.7a Histogram and cumulative distribution for

rural population density for rural truck route segments.

0

20

40

60

80

100

120

140

Persons/sq km

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Frequency

Cumulative Fraction

Figure 3.7b Histogram and cumulative distribution for

suburban population density for suburban truck route segments.
3-35

0

20

40

60

80

100

120

140

160

Persons/sq km

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Frequency

Cumulative Fraction

Figure 3.7c Histogram and cumulative distribution for

urban population density for urban truck route segments.

0

10

20

30

40

50

60

70

Persons/sq km

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Frequency

Cumulative Fraction

Figure 3.8a Histogram and cumulative distribution for

rural population density for rural rail route segments.
3-36

0

10

20

30

40

50

60

70

80

90

100

Persons/sq km

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Frequency

Cumulative Fraction

Figure 3.8b Histogram and cumulative distribution for

suburban population density for suburban rail route segments.

0

20

40

60

80

100

120

140

160

180

Persons/sq km

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Frequency

Cumulative Fraction

Figure 3.8c Histogram and cumulative distribution for

urban population density for urban rail route segments.
3-37

densities from these distributions provide the necessary route-description inputs for a

RADTRAN calculation. The number of sets of sampled values (and the number of RADTRAN

calculations) is dependent on the number of individual parameter values to be selected by

sampling, and the requirements for statistically meaningful results (at least twice the number of

parameters). The size of the sample that is required to develop statistically meaningful results is

discussed in Section 8.2.2

3.4.2 Truck and Train Accident Statistics

3.4.2.1 Introduction

Table 3.2 in Section 3.2 indicates that one of the More Important (“Proportional”) parameters in

calculating accident risks is the LINK Accident Rate. RADTRAN 5 determines the probability

of an accident occurring on a particular truck- or train-route link (segment) by computing the

product of its length (in kilometers) and the accident rate (number of accidents per vehiclekilometer) for that link. In general, accident rates vary with highway or rail line classification,

e.g., Interstate, U.S. and State highways, or Main and Branch rail lines. The code RADTRAN

(version 1 or 5) also distinguishes between Rural, Suburban and Urban links, as defined by the

population density bordering the link. For maximum specificity, distinct accident-rate values

would be assigned to these distinct portions of a route as well. In reality, such detailed data are

not usually available and more generalized accident rates must be used. Regulations of the DOT

for truck transport of Highway Route Controlled Quantities of RAM, including spent nuclear fuel

specify that Interstate highways (HM-164) be used exclusively, except where not available.

Therefore, Interstate highway accident rates are of primary interest for the truck transport portion

of this study.

Rail accident data available from the DOT does not identify the character (urban, suburban, or

rural) of the region where the accident occurred or the population density of the accident

location. However, in DOT compilations of truck accident statistics, Interstate accident rates are

reported for accidents occurring in Urban and Rural areas. However, this division is not made on

the basis of population density as is done for RADTRAN route segments (0 to 66, 67 to 1670,

and greater than 1670 persons/km2

 for Rural, Suburban and Urban areas, respectively). Instead,

the DOT division distinguishes between incorporated areas (cities) and unincorporated areas.

Since there can be Suburban (or even Rural) population densities (as specified for RADTRAN)

within city limits or Suburban population densities outside of city limits, the DOT division of

accident statistics does not easily map into the division required by RADTRAN. Past practice

has been to use the DOT Urban accident rate for Interstate highway links identified as Urban in

RADTRAN and to use the DOT Rural accident rate for Interstate highway links identified as

Suburban or Rural in RADTRAN. For the present study, accident rates for the entire set of

routes examined, were used to construct cumulative probability distributions from which

representative samples of route parameters were selected, by LHS, for use as input for

RADTRAN calculations. This approach permitted an approximate separation of the tabulated

DOT data into Rural, Suburban and Urban accident rates for Interstate highways, as is described

in Section 3.4.2.2.
3-38

3.4.2.2 Truck Accident Data

Over the years since NUREG-0170 was published, several studies of truck accident rates were

performed by the DOT, the DOE, or their contractors and the results published in formats with

variable applicability to the needs of this present study. These studies are described briefly in

chronological order in the following paragraphs.

Urban Study. This was an investigation of actual accident experience on city streets in an urban

area (New York City) performed to answer criticisms of the single, point-estimate accident rate

used in NUREG-0170. The data were gathered in the mid-1970’s and the results were published

in 1980 [3-18]. The accident rates obtained are not applicable to Interstate highways but are

included here to indicate a potential upper limit to be reached by accident-rate distributions

employed in the current study.

California Highway Department Study. Highway accident rates for three truck types and

several highway types were derived from California collision reports. Data for 1980 and 1981

were extracted from individual accident files by the State of California Department of

Transportation in response to a request from SNL. The results were published in a SNL report

[3-28].

Modal Study. Lawrence Livermore National Laboratory (LLNL) performed an analysis of spent

nuclear fuel truck transport [3-29] in which truck accident rates were derived from three sources

of data: DOT Bureau of Motor Carrier Safety (BMCS, now Office of Motor Carriers), American

Petroleum Institute (API), and California Department of Transportation. For the Modal Study,

LLNL chose to use the API rate data because of the similarity of tanker-trucks to the trucks used

to transport spent nuclear fuel casks. However, the API data included light truck accidents,

which were atypical and inflated the accident rates. For this study, the BMCS accident rate data

are judged to be most appropriate because the data reflects trucks and highways like those that

will characterize spent fuel shipments.

SIS Project EIS. The DOE published an Environmental Impact Statement (EIS) on the Special

Isotope Separation Project in which a national average accident rate for combination trucks

(tractor/trailers) on Interstate highways was derived from DOT data [3-30]. Average accident

rates for the specific routes considered in the EIS were also calculated and found to be nearly the

same as the national average (48 states).

BMCS Data. Four years (1984 and 1986 through 1988) of accident data derived from reports

submitted to the DOT by commercial carriers have been tabulated for Interstate highways inside

and outside city limits (Urban and Rural by DOT definition) for each of the 48 contiguous United

States. Data for 1986 through 1988 were collected in a study performed by Argonne National

Laboratory (ANL Longitudinal Review) for the DOE [3-31]. BMCS data are biased (toward

more severe accidents compared to total accident statistics) by the reporting criteria imposed by

the DOT, but they apply most specifically to the vehicle and highway types employed in spent

nuclear fuel truck shipments.

Truck accident rates and the years from which data were obtained in these various reports are

presented in Table 3.6 together with the value quoted in NUREG-0170.
3-39

Table 3.6 Truck Accident Rates (Accidents per Million Vehicle-Kilometers)

Source Period

Urban or

Total Rate*

Non-Urban

Rate Comments

NUREG-0170 pre-1975 0.46

Urban Study (NY City) pre 1980 7.2 - 91 Depends on time of day

15 Average

Calif. Hwy. Dept. 1980 0.8 1.1 Truck/Trailers on Freeways

1981 0.7 1.0 Total Accidents

Modal Study

 BMCS 1960-72 1.6 Reportable Accidents

 Am. Petrol. Inst. 1968-81 4.0 Used in the Study

 Calif. Hwy. Dept. 1981-83 0.6 Limited Access

3.1 4-Lane

SIS Project** 1984 0.31 Tractor-Trailers

BMCS** 1984 0.20 0.28 Interstate Highways

ANL Long. Rev. 1986-88 0.36 0.20 Interstate Highways

* Urban rate if distinguished, otherwise Urban and Non-Urban rate

** Average over 48 states

It should be noted that these values are not necessarily based on the same accident definition,

truck type, highway type, or sample sizes. However, they give an indication of the range of

values that pertain to different types of highways, different demographic areas, and different

points in time. The data collection period was of particular concern because nearly all of these

data were collected when the national speed limit, which was recently cancelled, was 55 mph.

In April of 1999, an update of the ANL Longitudinal Review was published which analyzes

heavy combination truck accident data for 1994 to 1996 [3-32]. Because of changes in the way

truck accident data are currently reported, the data in this report are not directly comparable with

the data in the earlier ANL study [3-31]. Nevertheless, the average accident rate on Interstate

highways for the three-year period for the continental United States is 3.45 accidents per 10

million truck-kilometers which is quite similar to the means of the Rural and Suburban accidentrate distributions (respectively 2.2 and 4.1 accidents per 10 million truck-kilometers) that are

derived in the following paragraphs. In addition, the ANL report authors note that the accident

rate on Interstate highways increased by 37% in states which increased speed limits in 1995 or

1996. The authors caution that available data do not yet establish whether this is a sustained

change or a transient; in any case, it is not a large enough change to invalidate the accident-rate

distributions employed in the current analysis.

The most comprehensive and recent of the data sets available at the time accident-rate

distributions were developed were the BMCS accident-rate listings for all 48 states which related

directly to combination truck accidents on Interstate highways. However, they were not

separated into accidents within Rural, Suburban, and Urban portions of the Interstate highway

system, as required for RADTRAN input; they were distinguished only according to whether

accidents occurred inside incorporated areas (“Urban,” referred to as City in the following
3-40

discussion) or outside incorporated areas (“Rural,” referred to as non-City in the following

discussion). A method for separating these sets of accident-rate data into the required

population-density groups, based on correlations between non-City or City accident rates with

state population densities outside or inside incorporated areas (as determined by the U.S. Bureau

of the Census for 1990) for each state, was developed.

For each of the 48 states, the BMCS Interstate-highway city accident rates from 1984 and the city

accident rates in the ANL Longitudinal Review (1986-88), were averaged; this was also done for

the non-city accident rates. In Figure 3.9a, the non-City average state accident rates that

correspond to rural population densities, as defined for RADTRAN calculations (i.e., ≤ 67

persons/km2

), are plotted versus the population densities of the state’s unincorporated areas (state

population minus incorporated population divided by state area minus incorporated area). In

Figure 3.9b, the average City accident rates for each state that correspond to suburban or urban

population densities, as defined for RADTRAN calculations (i.e., > 67 persons/km2), are plotted

versus the average population densities of incorporated areas (cities with populations ≥ 25,000).

This plot also contains six non-city accident rate points because they correspond to RADTRAN

suburban population densities (densities greater than 67 persons/km2). This figure also contains

three points that correspond to RADTRAN urban population densities (densities greater than

1670 persons/km2

). After dropping the three urban points, histograms of the accident rates in

Figures 3.9a and 3.9b were separately computed, summed, and normalized, thereby generating

cumulative distributions of accident rates for accidents on Rural Interstate Highways and also on

Suburban plus Urban Interstate highways in areas that have population densities that fall within

the RADTRAN population density range for rural or suburban regions. These cumulative

distributions are presented in Figures 3.10a and 3.10b.

These two cumulative distributions were sampled, using LHS, to provide accident-rate values for

the Rural and Suburban fractions of the 200 routes in the LHS sample of More Important

parameter values. Because of the lack of data for accidents in Urban areas, the three points in

Figure 3.9b that have Urban densities (> 1670 persons/km2 ) were averaged to provide a pointestimate accident rate of 5.2 accidents per 107 vehicle-kilometer for the relatively small Urban

fractions of the 200 representative routes. Although less than the highest accident rate depicted

in Figure 3.9b, this rate is considered reasonable for urban regions, since interstate highway

speeds within the densely populated urban areas are generally lower than they are in suburban or

rural regions, therefore there should be fewer reportable accidents and consequently a lower

frequency of reportable accidents.

3.4.2.3 Train Accident Data

The additional sources of rail accident-rate data, that have become available since NUREG-0170

was published, are not as numerous as those for truck accident-rate data. The sets of data that

were used for this study are a subset of the sources described in Section 3.4.2.2; these sets of data

are listed in Table 3.7.
3-41

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0 10 20 30 40 50 60 70

Population Density (persons/sq km)

Accidents per 107 veh-km

Figure 3.9a Accident rate versus rural population density.

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0 1000 2000 3000 4000 5000

Population Density (persons/sq km)

Accidents per 107veh-km

Figure 3.9b Accident rate versus suburban population density.
3-42

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

012345

Accidents per 107

 veh-km

Cumulative Fraction

Figure 3.10a Cumulative distribution of rural accident rates.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 2 4 6 8 10 12

Accidents per 107

 veh-km

Cumulative Fraction

Figure 3.10b Cumulative distribution of suburban and urban accident rates.
3-43

Table 3.7 Rail Accident Rates per Million Rail Car km

Source Date Urban or Total* Comments

NUREG-0170 pre-1975 0.9 Per Rail Car km

Modal Study

 Fed. Rail Admin. 1975-82 7.5

 [0.11]

Per Train km, All trains & tracks

Per Rail Car km @68 cars/train

 ANL Long. Rev.** 1985-88 0.06 Per Rail Car km, All tracks

 0.03 Per Rail Car km, Main Line Only

 * Urban rate if distinguished, otherwise Urban and Non-Urban rate

** Average over 48 states

Note that the rate from the Modal Study is per train-km which must be corrected to car-km for

comparison to the other values. Comparing car-miles to train-miles on Class I railroads for 1980

and 1990, as obtained from the DOT Internet Web page, indicates that the approximate number

of cars per train is 68. This value leads to a Modal Study accident rate of 0.11E-6 per car-km

which lies between the NUREG-0170 and ANL values in Table 3.7.

A histogram and cumulative distribution of data for accidents on main lines by state, as compiled

in the ANL study, were computed and the distribution is presented in Figure 3.11. The ANL

study did not distinguish accidents on the basis of population densities; therefore, this

distribution was sampled, using LHS, to provide accident rates for all portions of the rail routes

analyzed.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 5 10 15 20 25

Accidents per 108

 railcar-km

Cumulative Fraction

Figure 3.11 Cumulative distribution of rail accident rates

(used for all segments: Rural, Suburban, and Urban).
3-44

3.4.3 Development of Miscellaneous Distributions

In addition to route parameters (length, population zone fractions, population densities and

accident rates), several additional parameters were selected as suitable input for LHS. In this

section, the development of distributions for the remaining LHS parameters is described.

3.4.3.1 Truck Stop Time

Fueling, eating, and other stops were characterized in a study of commercial truck stops serving a

major truck transport route (Interstate 40) [3-19]. The study provided a tabulation of individual

stop times (in minutes) versus number of observed stops suitable for constructing a histogram

and a cumulative distribution. The results of the study were adapted to represent the totality of

stops made during a typical spent nuclear fuel shipment by scaling up the observed times to

values appropriate for the length of the shipment. The parameter employed in previous

RADTRAN versions for estimating total stop time (0.011 hours per km of shipment length) and

the average distance from the distribution of shipment distances (~1800 km) yielded an average

total stop time per truck shipment of: 1800 × 0.011 = 19.8 hours. The individual stop times (from

the study, in hours) were scaled up to yield a stop time of 20 hours at the peak of the histogram

(Number of Observed Stops = 10). Table 3.8 lists the original stop times in minutes (first

column), the original stop times in hours (second column), the scaled stop times in hours (third

column) and the corresponding stop counts (fourth column). The cumulative distribution (fourth

and fifth columns of Table 3.8) is shown in Figure 3.12; this distribution was added to the LHS

input file. Note that the value of 0.011 hours of stop time per km of shipment length is

descriptive of normal commercial trucking operations and includes time required by regulations

for sleep.

Table 3.8 Distribution of Normal Commercial Truck Stop Times

Stop

Time (min)

Stop Time

(hr)

Scaled Stop

Time (hr)

Number of

Observed Stops

Cumulative

Distribution

00 0 0 0

8 0.13 7 3 0.06

11 0.18 10 6 0.17

14 0.23 12 8 0.33

17 0.28 15 9 0.50

20 0.33 17 8 0.65

23 0.38 20 10 0.85

26 0.43 23 2 0.88

29 0.48 25 2 0.92

32 0.53 28 2 0.96

35 0.58 30 1 0.98

50 0.83 43 1 1.00
3-45

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

05101520253035404550

Scaled Stop Time (hours)

Cumulative Fraction

Figure 3.12 Distribution of normal commercial truck stop times.

As is discussed in Section 8.6, industry practice for spent fuel shipments under exclusive use

conditions is to use two-man crews and to minimize stop time by not making stops to sleep. As

is shown in Section 8.6, when spent fuel shipments are made under these special operating

conditions, the incident-free risks calculated using the stop times specified by the distribution in

Table 3.8 and Figure 3.12 are found to be conservative by a factor of approximately 28. In

Section 8.6, this factor is used to correct by scaling the incident-free doses that are calculated

using the stop time distribution presented in Table 3.8 and Figure 3.12.

3.4.3.2 Evacuation Time

The elapsed time between an accident occurrence and completed evacuation of the area around

an accident site was set at 24 hours in RADTRAN I. A study of evacuation times [3-33], in

which news reports of accidents requiring evacuations (e.g., transportation, refinery, and

chemical plant accidents) were followed up by telephone interviews of the authorities involved in

handling the accident/evacuation, provided a distribution of the times required to evacuate an

accident site and the surrounding area threatened by release of hazardous materials. The data

from this study were subsequently supplemented [3-34] by Department of Transportation data

describing elapsed time between accidents and arrival of first-responders (Emergency Medical

Service personnel) [3-35]. A histogram and cumulative distribution were constructed from the

combined elapsed-time data sets. As Figure 3.13 shows, the points of the cumulative distribution

are fit with high precision by a log-normal distribution. This log-normal distribution of

evacuation times in days was incorporated into the LHS input files for truck and rail shipments.
3-46

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0.000.100.200.300.400.500.600.700.800.901.00

Time in Days

Cumulative Fraction

Combined Data

Lognormal

Distribution

Figure 3.13 Distribution of response team arrival plus evacuation times.

3.4.3.3 Pasquill Stability Category

The relative speed of dispersion of a cloud of aerosols is related to atmospheric stability as

indicated by Pasquill Stability categories A through F (in order of increasing stability). Table 3.9

presents the occurrence frequencies of these six atmospheric stability classes as calculated from

national average observed stability conditions for the continental United States [3-36] and the

cummulative distribution of these frequencies. This discrete cumulative distribution was used to

select one of the six Pasquill atmospheric stability categories for use in each of the 200 sets of

More Important parameter values selected by LHS sampling.

For risk assessment purposes, the distribution of stability class frequencies of occurrence must be

very broadly based because the site of a transportation accident cannot be pre-determined nor can

the atmospheric stability at a random location be reliably specified by measurements available

from a distant weather station. Regional stability class occurrence statistics could be used but,

for these calculations, the additional precision their use might produce was not expected to be

worth the effort required to gather and process the data.

Table 3.9 Distribution of Pasquill Categories

Pasquill Category Occurrence Frequency Cumulative Distribution

A 0.043 0.043

B 0.190 0.233

C 0.190 0.423

D 0.216 0.639

E 0.241 0.88

F 0.120 1.00
3-47

3.4.3.4 Truck and Rail Transportation Index

Values of cask dose rates at one meter from the cask surface (RADTRAN input parameter, TI)

have been calculated for truck and rail spent fuel casks by Parks et al. [3-37] for spent fuel with

various cooling times. Pairing of these values, with the number of PWR and BWR assemblies in

the 1994 spent fuel inventory [3-38] that have cooling times equal to the time that produced the

calculated surface dose rate at 1 m from the surface, allowed cumulative distributions of cask

surface dose rates to be constructed for PWR and BWR spent fuel for both truck and rail casks.

Tables 3.10 and 3.11 present these distributions. Because the upper limits of these distributions

were less than the regulatory limit for cask dose rates (10 mrem/hour at 2 m from the cask

surface), in order to be conservative, the calculated dose rates at 1 m were scaled so that the

upper limits of both distributions equaled 13 mrem/hour at 1 m, which for a cask with a

maximum dimension of 5 meters is equivalent to the regulatory cask dose rate limit. Finally,

because the difference between the PWR and BWR distributions was insignificant compared to

the expected accuracy of the model, a single distribution of TI values was constructed by pooling

the truck cask or rail cask PWR and the BWR data. These distributions are presented in the last

column of Tables 3.10 and 3.11.

Table 3.10 Distribution of Dose Rate at 1 m (RADTRAN parameter TI) for Truck Casks

Cooling TI BWR PWR

Time

(yr)

Assys. of

that Age

Cumulative

Distribution

Assys. of

that Age

Cumulative

Distribution

Distribution

Used in

Calculations

5 13.0 3781 1.000 2824 1.00 1.00

10 6.39 3832 0.725 2785 0.711 0.72

15 4.57 2735 0.447 1937 0.427 0.44

20 3.49 2131 0.248 1662 0.229 0.24

25 2.76 1290 0.094 575 0.059 0.08

Table 3.11 Distribution of Dose Rate at 1 m (RADTRAN parameter TI) for Rail Casks

Cooling TI BWR PWR

Time

(yr)

Assys. of

that Age

Cumulative

Distribution

Assys. of

that Age

Cumulative

Distribution

Distribution

Used in

Calculations

3 13.0 1900 1.000 1400 1.000 1.00

5 6.72 3781 0.879 2824 0.875 0.87

10 3.95 3832 0.637 2785 0.622 0.63

15 3.03 2735 0.393 1937 0.373 0.38

20 2.43 2131 0.218 1662 0.200 0.21

25 1.99 1290 0.082 575 0.051 0.08
3-48

3.4.3.5 Highway Traffic Density

Traffic density information is used in calculating On-LINK incident-free doses in RADTRAN 5.

Distributions of this parameter (in units of vehicles per hour per lane) for rural and suburban

areas were developed from Department of Transportation publications tabulating miles of rural

interstate highway together with vehicle-miles per year for each state [3-39] and daily freeway

traffic per lane for 377 urbanized areas [3-40], respectively. For the rural distribution, the annual

vehicle-miles value for each state was converted to vehicles per hour (dividing by the state’s

miles of interstate and the number of hours per year). The value of vehicles per hour per lane (as

required by RADTRAN) was approximated by assuming that rural interstate highways typically

have two lanes in each direction. These values were used to construct the histogram and

cumulative distribution shown in Figure 3.14. The data for urbanized areas included population

density for each area. In an effort to separate the data into suburban and urban groups, the traffic

densities were plotted versus their respective population densities (Figure 3.15). Nearly all of the

data points lie in the suburban range (67 to 1670 persons/km2

); the points within the range were

used to construct the suburban traffic density histogram and cumulative distribution shown in

Figure 3.16. The 200 values of rural and suburban truck traffic density incorporated into the 200

sets of More Important parameter values were selected from these distributions using LHS

sampling methods.

Because there were so few points in the urban population density range (> 1670 persons/km2

),

the value of the largest traffic density, 930 vehicles per hour per lane, was assumed to be a

conservative point-estimate for urban portions of the truck shipment routes.

3.4.3.6 Persons per Vehicle Sharing a Highway Route

Persons per vehicle data are used in RADTRAN 5 to calculate On-LINK incident-free doses. A

tabulation of private vehicle occupancy in the United States for 1990 [3-41] derived from the

1990 Census of Population by the Journey-to-Work and Migration Statistics Branch, Population

Division, U.S. Bureau of the Census was converted to a discrete cumulative distribution for LHS

input (Table 3.12). Because the original tabulation did not distinguish vehicle occupancy

according to population density, the same distribution was used in the LHS input for rural,

suburban, and urban portions of the truck shipment routes.

Table 3.12 Distribution of Persons per Vehicle on Highway Routes

Persons per

Vehicle

Fraction of

Vehicles

Cumulative

Distribution

1 0.846 0.846

2 0.121 0.967

3 0.02 0.987

4 0.007 0.994

5 0.002 0.996

6 0.001 0.997

>6 0.003 1
3-49

0

2

4

6

8

10

12

14

16

18

0100200300400500600More

Veh/hr/lane

Frequency

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Cumulative Fraction

Frequency

Cumulative %

Figure 3.14 Histogram and cumulative distribution of rural interstate traffic density.

0

10

20

30

40

50

60

70

80

90

Veh/hr/lane

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Figure 3.15 Histogram and cumulative distribution of interstate traffic density

for urbanized areas

Cumulative Fraction
3-50

0

10

20

30

40

50

60

70

80

90

0100200300400500600700800More

Veh/hr/lane

Frequency

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

Cumulative Fraction

Frequency

Cumulative %

Figure 3.16 Histogram and cumulative distribution of suburban interstate traffic density.

3.5 References

[3-1] K. S. Neuhauser and F. L. Kanipe, “RADTRAN 5, Technical Manual,” Sandia National

Laboratories, Albuquerque, NM (in preparation, draft available on request).

[3-2] K. S. Neuhauser and F. L. Kanipe, “RADTRAN 5, User Guide,” Sandia National

Laboratories, Albuquerque, NM (draft available on the RADTRAN web site).

[3-3] G. S. Mills and K. S. Neuhauser, “Sensitivity Analysis for RADTRAN 4 Input

Parameters,” 88th Annual Meeting of the Air & Waste Management Association, San

Antonio, TX, 1995.

[3-4] G. S. Mills, K. S. Neuhauser, and F. L. Kanipe, “Application of Latin Hypercube

Sampling to RADTRAN 4 Truck Accident-Risk Sensitivity Analysis,” Proceedings of

PATRAM ’95, Las Vegas, NV, 1995.

[3-5] G. S. Mills, K. S. Neuhauser, and F. L. Kanipe, “RADTRAN 4 Truck Accident Risk

Sensitivity Analysis,” Proceedings of Waste Management 95, WM Symposia, Tucson,

AZ, 1995a.

[3-6] A. G. Croff, “ORIGEN2 - A Revised and Updated Version of the Oak Ridge Isotope

Generation and Depletion Code,” ORNL-5621, Oak Ridge National Laboratory, Oak

Ridge, TN, July 1980.
3-51

[3-7] G. D. Wyss and K. H. Jorgensen, “A User’s Guide to LHS: Sandia’s Latin Hypercube

Sampling Software,” SAND98-0210, Sandia National Laboratories, Albuquerque, NM,

1998.

[3-8] U.S. Nuclear Regulatory Commission, “Reactor Safety Study,” WASH-1400,

Washington, DC, 1975.

[3-9] M. L. Abbott and A. S. Rood, “COMIDA: A Radionuclide Food-Chain Model for

Acute Fallout Deposition,” EGG-GEO-10367, Idaho National Engineering Laboratory,

Idaho Falls, ID, 1994.

[3-10] M. M. Madsen, and E. L. Wilmot, “Truck Transportation of Radioactive Materials,”

Proceedings of the 7th International Conference on the Packaging and Transportation of

Radioactive Materials (PATRAM ‘83), Vol. I, p. 724, New Orleans, LA, 1983.

[3-11] R. M. Ostmeyer, “A Revised Rail-Stop Exposure Model for Incident-Free Transport of

Nuclear Waste,” SAND85-1722, Sandia National Laboratories, Albuquerque, NM,

1986.

[3-12] K. S. Neuhauser and R. F. Weiner, “Intermodal Transfer of Spent Fuel,” Proceedings of

the 10th International Conference on the Packaging and Transportation of Radioactive

Materials (PATRAM ’92), Vol. I, p. 427, Yokohama, Japan, 1992.

[3-13] H. S. Javitz, et al., “Transport of Radioactive Material in the United States: Results of a

Survey to Determine the Magnitude and Characteristics of Domestic, Unclassified

Shipments of Radioactive Materials,” SAND84-7174, Sandia National Laboratories,

Albuquerque, NM, 1985.

[3-14] K. F. Eckerman and J. C. Ryman, Federal Guidance Report No. 12, “External Exposure

to Radionuclides in Air, Water, and Soil,” Oak Ridge National Laboratory, Oak Ridge,

TN, 1993.

[3-15] R. J. Engelman, “Effectiveness of Sheltering in Buildings and Vehicles for Plutonium,”

DOE/EH-0159T, U.S. Department of Energy, Washington, DC, 1990.

[3-16] J. M. Taylor and S. L. Daniel, “RADTRAN II: Revised Computer Code to Analyze

Transportation of Radioactive Materials,” SAND80-1943, Sandia National

Laboratories, Albuquerque, NM, 1982.

[3-17] Waste Isolation Pilot Plant Disposal Phase Final Supplemental Environmental Impact

Statement, Volume II Appendices, DOE/EIS-0026-S-2, U.S. Department of Energy,

Carlsbad, NM, 1997.

[3-18] N. Finley, et al., “Transportation of Radionuclides in Urban Environs: Draft

Environmental Impact Assessment,” Volumes 1 and 2, NUREG/CR-4829, Nuclear

Regulatory Commission, Washington, DC, 1980.
3-52

[3-19] N. R. Griego, J. D. Smith, and K. S. Neuhauser, “Investigation of RADTRAN Stop

Model Input Parameters for Truck Stops,” Conference Proceedings, Waste

Management 96, Tucson, AZ, 1996.

[3-20] County and City Data Book, 1988, U. S. Department of Commerce, Washington DC,

1988.

[3-21] J. D. Smith, K. S. Neuhauser, and F. L. Kanipe, “Expected Residence Time Model,”

Conference Proceedings, Waste Management ‘96, Tucson, AZ, 1996.

[3-22] U.S. Environmental Protection Agency, Proposed Guidance on Dose Limits for Persons

Exposed to Transuranic Elements in the General Environment, EPA-520/4-77-016,

U.S. Environmental Protection Agency, Washington, D.C., 1977.

[3-23] D. Chanin and W. B. Murfin, “Site Restoration: Estimation of Attributable Costs from

Plutonium-Dispersal Accidents,” SAND96-0957, Sandia National Laboratories,

Albuquerque, NM, 1996.

[3-24] International Council on Radiation Protection, “Limits on Intakes of Radionuclides by

Workers, Parts 1-3,” Annals of the International Council on Radiation Protection, Vol.

2 (3-4), 1979 through Vol. 8 (1-3), 1982), Pergamon Press, Oxford, England, 1979.

[3-25] P. E. Johnson, et al., “HIGHWAY 3.1 – An Enhanced Highway Routing Model:

Program Description, Methodology, and Revised User’s Manual,” ORNL/TM-12124,

Oak Ridge National Laboratory, Oak Ridge, TN, 1993.

[3-26] P. E. Johnson, et al., “INTERLINE 5.0 – An Expanded Railroad Routing Model:

Program Description, Methodology, and Revised User’s Manual,” ORNL/TM-12090,

Oak Ridge National Laboratory, Oak Ridge, TN, 1993.

[3-27] J. W. Cashwell, et al., “Transportation Impacts of the Commercial Radioactive Waste

Management Program,” SAND85-2715, Sandia National Laboratories, Albuquerque,

NM, April 1986.

[3-28] R. N. Smith and E. L. Wilmot, “Truck Accident and Fatality Rates Calculated from

California Highway Accident Statistics for 1980 and 1981,” SAND82-7066, Sandia

National Laboratories, Albuquerque, NM, 1982.

[3-29] L. E. Fischer, et al., “Shipping Container Response to Severe Highway and Railway

Accident Conditions,” NUREG/CR-4829 UCID-20733, Lawrence Livermore National

Laboratory, Livermore, CA, 1987.

[3-30] U.S. Department of Energy, “Final Environmental Impact Statement on Special Isotope

Separation Project,” DOE/EIS-0136, U.S. DOE, Washington, DC, 1988.
3-53

[3-31] C. Saricks and T. K. Kvitek, “Longitudinal Review of State-Level Accident Statistics

for Carriers of Interstate Freight,” ANL/ESD/TM-68, Argonne National Laboratory,

Argonne, IL, 1994.

[3-32] C. L. Saricks and M. M. Tompkins, “State-Level Accident Rates of Surface Freight

Transportation, A Reexamination,” ANL/ESD/TM-150, Argonne National Laboratory,

Argonne, IL, 1999.

[3-33] G. S. Mills, et al., “Study of Evacuation Times Based on General Accident History,”

Proceedings of the 11th International PATRAM Conference, Las Vegas, NV, 1995.

[3-34] G. S. Mills, et al., “Study of the Components of Evacuation Times,” Proceedings of the

12th International PATRAM Conference, Paris, France, 1998.

[3-35] “1992 Traffic Safety Facts Annual Report,” U.S. Department of Transportation, Bureau

of Transportation Statistics, BTS-CD-04-01.

[3-36] D. Bruce Turner, “Workbook of Atmospheric Dispersion Estimates,” PHS Publ.

No. 999-AP-26, U.S. Department of Health, 1969.

[3-37] C. V. Parks, et al., “Parametric Study of Radiation Dose Rates from Rail and Truck

Spent Fuel Transport Casks,” ORNL/CSD/TM-227, 1985.

[3-38] “Spent Nuclear Fuel Discharges from U.S. Reactors,” Energy Information

Administration, U.S. Department of Energy, SR/CNEAF/96-01, 1994.

[3-39] Federal Highway Administration, Combination of Tables HM-50 and VM-2 in Section

V of “Highway Statistics for 1997” derived from the Highway Performance Monitoring

System, U.S. Department of Transportation Web site.

[3-40] Federal Highway Administration, Table HM-72 in Section V of “Highway Statistics for

1997” derived from the Highway Performance Monitoring System, U.S. Department of

Transportation Web site.

[3-41] www.census.gov/population/socdemo/journey/usveh90.txt.
4-1

4. SELECTION OF GENERIC CASKS

4.1 Description of Casks

Generic casks were used in this study to relate the behavior of typical examples of a broad

packaging type to the risks that might be realized during a spent fuel shipping campaign.

Detailed analyses of these casks can be used to demonstrate differences (or similarities) among

various construction features for this type of package. Casks for the transportation of power

reactor fuel are generally available in three weight classes (legal weight truck, overweight truck,

and rail) and with three gamma-shielding materials (steel, lead, and depleted uranium). Casks

that are most likely to be used in future shipping campaigns only use four of the nine possible

combinations of weight and shielding. These are lead and depleted uranium (DU) shielded truck

casks and steel and lead shielded rail casks. A survey of currently licensed and proposed casks

was used to develop the generic casks used for this study. Tables 4.1 to 4.4 list the casks that

were examined to develop generic designs. Most of the information was obtained from

“Shipping and Storage Cask Data for Commercial Spent Nuclear Fuel,” by JAI Corporation

[4-1]. Other information was obtained from the certificates of compliance for the casks or from

safety analysis reports.

Tables 4.1 to 4.4 list the casks used in derivation of the generic casks and provide details about

the generic casks. Because of the way the generic casks were developed, they may not meet all

of the requirements of 10 CFR 71. Real packages must meet these requirements, and are

therefore, likely to be more robust than the generic casks used in this study. For the monolithic

steel rail casks, the currently licensed casks use some type of ferritic steel for the cask body and

lid. The current regulatory position favors the use of stainless steel or a ferritic steel with very

high ductility (requirements are given in NRC Regulatory Guide 7.12 [4-2]). For this reason, and

to be consistent with the sandwich wall casks, stainless steel was chosen as the material for the

monolithic cask. Figures 4.1 to 4.4 show artist renditions of the generic casks. Other features

that are typical of transportation casks but are not included in the generic casks are fill and drain

ports, lifting and tiedown trunnions, and personnel barriers. The omission of these features is not

believed to significantly effect the behavior of the casks. The personnel barrier absorbs energy

during an impact and acts as a thermal shield during a fire event. Therefore, omitting this feature

is conservative. For the extra-regulatory impacts considered in this report, impact onto a

trunnion is less damaging than impact onto the side of the cask, as the impact area is smaller and

the trunnion will act as an impact limiter. Therefore, omitting this feature is also conservative.

The fill and drain ports are generally in the very substantial base and lid structure of the cask.

These are regions with small deformations, and it is very unlikely that a failure will occur at these

points.
Table 4.1 Steel-Lead-Steel Truck Casks

Material

Closure

Bolts

(no./size)

Wall

Thickness (inches)

Outside

Diameter

(inches)

Cavity

Diameter

(inches)

Length

(inches)

Impact

Limiter

Design Heat

Rejection (kW)

Seal

Material C of C

stainless 12 1” 0.75,5.75,1.2 44.2 13.375 199.80 honeycomb 2.5 both 71-9225

stainless 6 1.25” 0.31,6.63,1.25 38 13.5 214 balsa 11.5 elast. 71-9183

stainless 12 1” 0.5,2.125Pb,

2.75DU,0.875

47.125 13.375 195.25 balsa 10.6 metal 71-9010

steel 16 1.25” 0.23,5.32,0.79 67.6 ~30 217.2 balsa 35.5 elast. 71-9015steel 16 1.25” 0.23,5.04,0.79 67.6 ~21 226.6 balsa 24.5 elast. 71-9016

stainless 12 1” 1.12,3.44,1.5 31.0 18.0 207 wood 0.36 elast. 71-9253

stainless N.A. 0.5,5.25,1.25 27.5 13.5 193 yes 0.8-5.4 N.A. -

stainless 12 1” 0.5,5.5,1.0 27.5 13.5 205 yes 2.5 elast. -

U-steel wall configuration and was therefore not used in the determination of the generic cask.

t-truck casks and were therefore not used in the determination of the generic cask.

Figure 4.1 Conceptual design of a generic steel-lead-steel truck cask.
Table 4.2 Steel-DU-Steel Truck Casks

Material

Closure

Bolts

(no./size)

Wall

Thickness (inches)

Outside

Diameter

(inches)

Cavity

Diameter

(inches)

Length

(inches)

Impact

Limiter

Design Heat

Rejection (kW)

Seal

Material C of C

stainless 24 1.25” 0.67,3.5,0.91 28.0 17.7 208 yes 4.1 elast. 71-6346

stainless 12 1” 0.375,2.64,1.5 39.75 18.16 sq. 187.75 honeycomb 2.47 elast. 71-9226

stainless 12 1” 0.25,2.45,1.75 39.75 18.16 sq. 198.3 honeycomb 2.12 elast. -

stainless 12 1” 0.5,2.125Pb,

2.75DU,0.875

47.125 13.375 195.25 balsa 10.6 metal 71-9010

stainless 12 1” 0.5,3.5,0.9 28 18 200 yes 2.5 elast. -

U-steel wall configuration and was therefore not used in the determination of the generic cask.

Figure 4.2 Conceptual design of a generic steel-DU-steel truck cask.
Table 4.3 Steel-Lead-Steel Rail Casks

Material

Closure

Bolts

(no./size)

Wall

Thickness

(inches)

Outside

Diameter

(inches)

Cavity

Diameter

(inches)

Length

(inches)

Impact

limiter

Design Heat

Rejection (kW)

Seal

Material C of C

stainless 42 1.5” 1.5,3.7,2.65 87.0 71.0 193 wood 22.3 metal 71-9235

stainless N.A. N.A. 87.0 67.0 210.0 honeycomb 26 metal -

stainless 32 1.5” 1.0,3.88,2.0 65.5 51.25 207.5 foam 0.7 elast. 71-9200

ferritic

steel

N.A. N.A. 83.23 32.8 200.5 yes N.A. N.A. -

stainless 16 .75,6,2 96.0 45.0 204.5 balsa 70 both 71-9023

stainless 32 2.5” 1.0,4.5,1.75 82 58.5 202 wood 15 elast. -

stainless N.A. 0.5,5.25,1.5 52 37.5 193 yes 3.4-24 N.A. -

stainless 24 1.75” 1.0,4.5,2.0 80 65 200 yes 24 elast. -

Figure 4.3 Conceptual design of a generic steel-lead-steel rail cask.
Table 4.4 Monolithic Rail Casks

Material

Closure

Bolts

(no./size)

Wall

Thickness

(inches)

Outside

Diameter

(inches)

Cavity

Diameter

(inches)

Length

(inches)

Impact

Limiter

Design Heat

Rejection (kW)

Seal

Material C of C

SA-350 N.A. 9.5 92.4 57.25 186.8 none 24 metal 72-1005

SA-350 48 1.625” 9.25 90.25 71.25 180 redwood 2.7 both 71-9206

SA350 LF3 48 1.625” 9.62 83.25 64 190.5 redwood 3.1 both 71-9202

ferritic steel N.A. 13.6 95.9 68.75 202.9 ? 23.4 N.A. 71-9261*

Steel N.A. 12.7 90.0 64.6 196.9 none N.A. N.A. -

ferritic steel 40 1.65” 15.9 78.74 33.2 210 wood 120 elast. -

NCI N.A. 15.0 93.9 60.1 192.4 none 28 metal 72-1000

stainless steel 24 1.75” 10 85 65 190 yes 24 elast. -

sed for storage in the U.S. but are used for transportation in other countries.

Figure 4.4 Conceptual design of a generic monolithic steel rail cask.
4-6

The capacity of the generic casks was assumed to be 24 pressurized water reactor (PWR) or

52 boiling water reactor (BWR) assemblies for the steel-lead-steel and monolithic steel rail

casks, 1 PWR or 2 BWR assemblies for the steel-lead-steel truck cask, and 3 PWR or 7 BWR

assemblies for the steel-DU-steel truck cask. No attempt was made to specify a generic basket.

It may not be physically possible to fit the assumed number of assemblies in the cavity volume of

the generic casks. It may also be possible that the generic casks would not be suitable for the

assumed number of assemblies for all conceivable fuel types that may be shipped. For example,

the surface dose rate or internal temperatures may be too high for short-cooled high-burnup fuel.

The wall thickness listed in the tables does not include neutron shielding, which is generally in

the central region of the cask and outside of the containment system of the walls. The neutron

shielding does not contribute significantly to the strength of the cask. Therefore, ignoring it will

have little effect on the results of the structural modeling discussed in the following chapter. In

the structural finite element model, the weight of the neutron shielding and its liner are added to

the contents so that the total weight of the package is correct. For the thermal analyses a neutron

shield consisting of 4.5 inches of water (considered empty in the analyses) contained by a

0.25-inch steel shell is assumed for all of the casks. Even though most modern casks use a solid

neutron-shielding material, the thermal analyses assumed that an empty neutron-shielding layer

would provide a more conservative assessment of the heating of the cask for cases where the fire

does not follow a severe impact that collapses the neutron shielding tank, thereby eliminating the

4.5 inch air gap.

In other aspects of the cask construction where there is a major difference between older casks

and newer casks, the generic casks specifications more closely simulated the newer designs.

Many of the older casks are of designs where additional packages cannot be built, so a fleet of

these casks will not be used for a major transportation campaign. For all casks to be used in

transportation it is assumed there will be an impact limiter. The information available about the

impact limiters was not sufficient to develop a generic design, but it will be assumed that the

regulatory impact (9-m free drop onto an unyielding target) uses the full amount of energy

absorbing capacity of the impact limiter prior to the lock-up region of the force-deflection curve.

For all of the structural analyses, the finite element model includes an impact limiter that has

been fully crushed in all directions.

All of the generic casks are assumed to have elastomeric o-ring seals inboard of the bolt location.

It is possible, using the results of the finite element analysis in the next section, to derive sourceterms for casks with metallic seals in addition to the source-terms derived for the casks with

elastomeric seals, but this has not been done. The closure on all of the casks is recessed into the

cask body, with a face-seal configuration. Figure 4.5 shows the lid of one of the casks and the

location of the bolts. This type of closure is the most common configuration used in spent fuel

casks, but other configurations are seen. For example, the 125-B cask uses bore seals instead of

face seals.
4-7

Figure 4.5 Finite element representation of a typical closure

lid for structural analysis, showing the locations of the bolts.

4.2 Conservatism in Cask Selection

The specifications of the generic casks for this study were defined with the intent of producing a

conservative analysis. That is, a design that is more likely to develop a leak path and lose

containment integrity than any of the certified/planned designs listed.

All of the sandwich wall generic casks have shell thicknesses that are less than those of modern

designs. Thicker shells result in smaller deformations, lower probabilities of puncture, and

reduced lead slump. For the rail casks the number of bolts chosen for the generic design is lower

than the number being used for modern designs. Increasing the number of bolts decreases the

closure openings, resulting in reduced probabilities for radioactive material release.

Although generic specifications are likely to lead to conservative results, it should not be

assumed that designs with similar dimensions could not be implemented in a real cask that could

gain certification by the NRC.
4-8

4.3 References

[4.1] JAI Corporation, “Shipping and Storage Cask Data for Commercial Spent Nuclear Fuel,”

JAI-421, Fairfax, VA, July 1996.

[4.2] US Nuclear Regulatory Commission, “Fracture Toughness Criteria of Base Material for

Ferritic Steel Shipping Cask Containment Vessels with a Wall Thickness Greater Than

4 inches (0.3m),” Regulatory Guide 7.12, June 1991.
5-1

5. STRUCTURAL RESPONSE

5.1 Finite Element Calculations for Impacts onto Rigid Targets

5.1.1 Introduction

To deter mine the respo nse of the gener ic casks , finit e eleme nt calcu lations for impac ts onto rigid 

targe ts were condu cted. For all of the analy ses in this repor t, the Sandi a-develope d non-l inear

trans ient dynam ics finit e eleme nt progr am PRONT O-3D [5-1, 5-2, 5-3] was used to deter mine

the damag e resul ting from each impac t. PRONT O is a shock -wave propa gation code, espec ially

devel oped for impac t probl em types . It uses a time march ing expli cit integ ration of the equat ion

of motio n to deter mine the respo nse of the struc ture. Input s to the code are geome try (incl uding

bound ary condi tions), mater ial prope rties, and initi al veloc ities. This type of code updat es the

posit ion of each node at each time step, which allow s for both mater ial and geome tric nonlinea rities. One resul t of this appro ach is that strai ns repor ted are true strai ns, rathe r than

engin eering strai ns that are based upon the undeforme d geome try. PRONT O has been

exten sively bench marked for analyses of cask respo nse [5-4, 5-5]. For each gener ic cask, 

calcu lations were perfo rmed for impac ts in end-o n, CG-ov er-corner, and side- on orien tations.

The respo nse of the casks at other orien tations is sufficie ntly simil ar to (or bound ed by) these 

resul ts to be envel oped by them. For impac t angle s betwe en end-o n and 5 degre es from verti cal,

the end-o n analy sis resul ts will be used. For impacts betwe en 5 degre es from verti cal to 70

degre es from verti cal the CG-ov er-corn er analy sis resul ts will be used. For impac ts betwe en 70

degre es from verti cal to horiz ontal, the side- on analy sis resul ts will be used. All impac ts are

assum ed to be onto a flat, rigid surfa ce with the initi al veloc ity perpe ndicular to the surfa ce.

While it is possi ble for a cask to impac t a surfa ce that is not flat (such as a bridg e colum n) in a

side impac t orien tation (such that the conta ct occur s betwe en the impac t limit ers), this type of

accid ent was not consi dered. An impac t of this type only provi des loadi ng and, there fore,

defor mation to the cylin drical porti on of the cask away from the closu re area. This part of the

cask is extre mely ducti le, and can withs tand defor mations great er than the cask diame ter witho ut

causi ng the cask to relea se radio active mater ial.

To short en the analy sis times and avoid calcu lation of the very large shear strai ns that occur in

the impac t limit er, at the start of all of the analy ses it was assum ed that the impac t limit er has

alrea dy been drive n into the lock- up regio n (the point at which the mater ial stops behavin g in a

crush able manne r). The initi al and crush ed size of the impac t limit ers for each cask are given in

Table 5.1. Figur e 5.1 shows the initi al and pre-c rushed geome try of an impac t limiter. The

amoun t of energ y absor bed by the impac t limit er prior to lock- up is equiv alent to the kinet ic

energ y from the regul atory drop test. Using the pre-c rushed impac t limit er, analy ses with impac t

veloc ities of 30, 60, 90, and 120 mph are condu cted for each cask and orien tation. If the energ y

requi red to crush the impac t limit ers is added to the initi al kinet ic energ y of the cask, these 

analy sis veloc ities corre spond to actua l impac t veloc ities of 42, 67, 95, and 124 mph. Howev er,

throughout this report the calculations will be identified as 30, 60, 90, and 120 mph impact cases.
5-2

Table 5.1 Impact Limiter Geometry (in inches)

Cask Cask

Diameter

Engagemen

t

Length

Initial End

Thickness

Crushed End

Thickness

Initial Side

Thickness

Crushed Side

Thickness

Steel-LeadSteel Truck 27.5 12 12 4 12 4

Steel-DUSteel Truck 28 12 12 4 12 4

Steel-LeadSteel Rail 80 14 14 4.67 14 4.67

Monolithic

Rail 85 14 14 4.67 14 4.67

Figure 5.1 Geometry of the initial and pre-crushed impact limiter.

5.1.2 Assumptions for Finite Element Models

While it is possi ble to creat e a finit e eleme nt mesh that accur ately model s all of the detai ls of the

gener ic cask model s, using these model s requi res too much compu tation time for the many cases 

consi dered in this work. For this reaso n, simpl ifying assum ptions were made. All of the

impac ts consi dered have a plane of symme try throu gh the long axis of the cask, so it is only

neces sary to model one-h alf of the struc ture. Figur e 5.2 shows the finit e eleme nt model used for

the lead shiel ded rail cask, typic al of the model s used for all of these analy ses.
5-3

Figure 5.2 Finite element model of the steel-lead-steel rail cask in the

CG-over-corner drop orientation.

For all of the sandw ich-wall casks the inner and outer steel layer s were model ed with zerothick ness shell eleme nts. This type of eleme nt accur ately captu res the bendi ng behav ior and axial

force s in the shell , but does not incor porate stres ses in the direc tion perpe ndicular to the shell 

surfa ce. Where this fact has the great est influ ence is in the conta ct betwe en the vario us layer s.

If the geome try of the conte nts and shiel ding layer are model ed corre ctly, it is impos sible for a

zero- thickness shell eleme nt to be conta cting both the conte nts and the shiel ding. In these finit e

eleme nt model s the shell eleme nts are locat ed at the mid-t hickness of the wall layer they

represent. This leave s a gap betwe en the conte nts and the shell and betwe en the gamma 

shiel ding and the shell . The gap betwe en the conte nts and the shell is typic al of spent fuel casks ,

but the gap betwe en the gamma shiel ding and the shell s resul ts in havin g the gamma shiel ding

(and the shell s) unsup ported for motio n in the direc tion trans verse to the shell s. This resul ts in

large r defle ctions and strai ns in the sandw ich wall for the model than would occur in reali ty. For

casks with lead gamma shiel ding the lack of later al suppo rt resul ts in a signi ficant overpredi ction of the amoun t of lead slump . Figur e 5.3 shows a detai led view of the end of the steel -

lead- steel rail cask. 
5-4

LID

CASK END FORGING

IMPACT LIMITER

CONTENTS

INNER SHELL

LEAD GAMMA SHIELDING

OUTER SHELL

Figure 5.3 Detail of the end of the steel-lead-steel rail cask finite element model.

The behav ior of the neutr on shiel ding and its liner has littl e effec t on defor mations to the

remai nder of the cask, but any effec t is benef icial. For this reaso n, these compo nents are not

model ed, but rathe r their mass is lumpe d with the mass of the conte nts to achie ve the corre ct

packa ge weigh t. The conte nts and baske t are treat ed as a homogeno us crush able mater ial. The

crush stren gth of this mater ial is chose n from the buckl ing stren gth of PWR fuel pins subje cted

to axial loads . The densi ty of this mater ial is adjus ted so that the total weigh t of the cask is equal 

to the speci fied weigh t from Chapt er 4. Model ing of the baske t and conte nts in this manne r does

not allow direc t determinat ion of the behav ior of the fuel rods, but provi des an asses sment of the

loads that these componen ts trans mit into the struc tural porti ons of the cask. Because the only

purpo se of the conte nts withi n the model is to provi de loadi ng onto the cask, varia tions in their 

mater ial prope rties has littl e effec t on the analy sis resul ts. A descr iption of how fuel behav ior is

deter mined from the finit e eleme nt resul ts is given in Secti on 5.4.

As indic ated earli er, the crush ing behav ior of the impac t limit ers is not model ed. They are precrush ed at the beginning of the analy sis. To accou nt for the post- crush behav ior of the impac t

limit ers they are treat ed as a solid with a densi ty equiv alent to a typic al densi ty for fully crush ed

alumi num honeycom b. The yield stren gth of this crush ed mater ial is typic al for fully crush ed

1000- psi aluminum honey comb. The finit e eleme nt model assum es that the entir e impac t limit er

has been fully crush ed, so the geome try in the model remai ns axi-s ymmetric. No attem pt is

made to model the attac hments of the impac t limit ers; they are held in place only by inert ia. If the

inert ial force s are not suffi cient to keep the impac t limit er in place durin g the impac t event , then

the cask body will impac t direc tly onto the rigid surfa ce. Real casks have impac t limit er

attac hments that are usual ly desig ned so the impac t limit ers stay attac hed durin g the regul atory

impac t tests .

For all of the analyses, the initi al veloc ity vecto r of the cask is assum ed to be perpe ndicular to the

rigid surfa ce. All of the inter ior conta ct surfa ces in the model (betw een the conte nts and the

inner shell , the gamma shiel ding and both shell s, the lid and the cask body, and the cask body

and the impac t limit er) are assum ed to be frict ionless. The conta ct betwe en the cask and the rigid 
5-5

surfa ce is also frict ionless. For most aspec ts of the probl em this assum ption is conse rvative, as

there is no loss of impac t energ y because of frict ional heati ng. Inclu ding frict ion at conta ct

surfa ces tends to cause the vario us parts of the model ed struc ture to behav e more like a singl e

piece (decr eases separ ation of the parts of the struc ture being model ed). Inclu ding frict ion would 

also decre ase the amoun t of impac t energ y avail able to cause struc tural defor mation, as some of

the energ y would be absor bed by frict ional heati ng. Lack of frict ion and the direc tion of the

initial veloc ity guara ntee that the displ acement, veloc ity, and accelera tion vecto rs will alway s be

in a direc tion that is perpe ndicular to the rigid surfa ce. This will be impor tant when deriv ing the

force -deflectio n curve s for the casks in Secti on 5.2.2 .

The closu re of the cask is expli citly model ed. The lid is reces sed into the body of the cask and

held in place with eithe r 12 (6 in the half- symmetric model ) 1-inc h diame ter bolts for the truck 

casks or 24 (12 in the half- symmetric model ) 1.75- inch diame ter bolts for the rail casks . The

bolt model cross -section is square with squar e heads . The area of the squar e bolt shank is the

same as the area of a round bolt. The edges of the heads are rigid ly attac hed to the cask lid, and

the botto m of the shank is rigid ly attac hed to the cask body. Figur e 5.4 shows the cross -section 

throu gh the cente r of a typic al bolt and an isome tric view of a singl e bolt. All of the conta cts are

tied via coincid ent nodes . The initi al prelo ad in the bolts cause d by the torqu e appli ed to them

when the cask is close d is negle cted. Negle cting this prelo ad is conse rvative becau se the prelo ad

must be overc ome by loadi ng from the conte nts befor e there is any defor mation to the bolts .

This facto r makes a prelo aded closu re have small er openi ngs than a closu re witho ut prelo ad.

 Model ing the bolt in this way force s all of the defor mation of the closu re to take place in the

short secti on that repre sents the shank of the bolt. Figur e 5.5 shows how this metho d of

model ing the bolt depic ts shear defor mations and tensi le defor mations. In a real closu re,

movem ent betwe en the lid and the cask body will be accom modated by defor mation of the bolt

head and seat, slidi ng in the clear ance hole, and stret ching over a longe r lengt h of the bolt. 

These diffe rences make the model ed bolts stiff er than the real bolts for tensi le defor mations,

which leads to an over- prediction of bolt strai n and an under -predictio n of bolt stret ch. Becau se

the bolts (in the model and in reality ) are much less stiff than the closu re, the over- prediction of

strai n is much more signi ficant than the under -predictio n of displ acement. The effec t on leak

area is discu ssed in secti on 5.1.4 .

The O-rin g groov es and O-rin gs for the seals are not inclu ded in the model , but the defor mations

in the seali ng surfa ces at the locat ions of the O-rin gs are track ed to deter mine when there is

sufficient openi ng to cause perma nent failu re of the seal. From tests perfo rmed at Sandi a on

closu re movem ents using 0.25- inch nomin al O-rin gs, it has been deter mined that elast omeric

O-rings can withs tand great er than 0.070 inche s of openi ng witho ut losin g their abili ty to conta in

heliu m at one atmos phere of diffe rential press ure [5-6] . These O-rin gs had an initi al precompr ession of about 0.075 inche s. For the large r O-rin gs (comp ared to the Sandi a study )

typic al of spent fuel casks , the large r amoun t of pre-c ompression impli es there shoul d be no

mater ial relea se for openi ngs up to 0.100 inche s.
5-6

BOLT

CASK BODY

CASK LID

NODES TIED

TO CASK LID

NODES TIED TO

CASK BODY

Figure 5.4 Typical model of a bolt used in the finite element analyses.
5-7

DEFORMATION

DUE TO TENSION

DEFORMATION

DUE TO SHEAR

BOLT

HEAD

BOLT

HEAD

BOLT

SHANK

Figure 5.5 Modeling of the deformation in the bolts. The solid lines indicate the bolt

position after being deformed and the dashed lines indicate the initial bolt position.

5.1.3 Material Models

The casks and conte nts model ed in this study consi st of six diffe rent mater ials. The lids, ends, 

and struc tural porti ons of the walls are 304L stain less steel . The bolts are a high- strength

stainless steel . The impac t limit ers are crush ed alumi num honey comb. The gamma shiel ding is

either lead, deple ted uranium , or stain less steel . The baske t and spent fuel are model ed as a

homogen ized crush able mater ial.

The stain less steel is model ed with a power -law harde ning mater ial model . This model treat s the

mater ial as elast ic up to the limit of propo rtionality and captu res the plast icity by the equat ion:

σσ ε ε = + 〈−〉 p pL

n A (1)

where σp is the stres s at the limit of propo rtionality , A is the harde ning const ant, εp is the

equiv alent plast ic strai n, εL is the Luder ’s strai n (the flat porti on of the stres s-strain curve 

immed iately after yield ing for low-c arbon steel s), 〈 〉 indic ates the Heavis ide funct ion where the

expre ssion enclo sed in the brack ets is uncha nged when posit ive and equal to zero when negat ive,

and n is the harde ning expon ent.

For 304L stain less steel the param eters used are σp = 28 ksi, A = 192.7 46 ksi, εL = 0, and

n = 0 .74819. For the elast ic part of the curve E = 28,00 0 ksi and ν = 0.27 [5-7] .

The high- strength bolts (SA-5 40 Grade B23 Class 5 [5-8] ) are model ed with a bi-li near elast icplast ic mater ial model . The param eters used are σy = 105 ksi, E = 30,00 0 ksi, ν = 0.3, and

Ep = 30 ksi. The crush ed alumi num honey comb impac t limit ers are model ed using the power -

law hardening model with σp = 4250 psi, A = 32.7 ksi, εL = 0, n = 0.325722, E = 9,900 ksi and

ν = 0.33. The lead is model ed using the power -law harde ning model with σp = 20 00 psi,
5-8

A = 8 00 psi, εL = 0, n = 0 .5, E = 2,000 ksi and ν = 0.27. These are the same mater ial

prope rties that were used in the bench marking analy ses of Ludwi gsen and Ammer man [5-4] .

The deple ted urani um is model ed with a bi-li near elast ic-plastic mater ial model with σy = 20 ksi,

E = 28,00 0 ksi, ν = 0.3, and Ep = 150 ksi [5-9] .

The homog enized baske t and spent fuel are model ed with a mater ial model origi nally devel oped

for low-d ensity polyu rethane foams . This model is defin ed by the initi al yield stren gth of the

mater ial (σy), initi al elast ic stiff ness (E) and Poiss on’s ratio (ν), the harde ning modul us (A), the

solid mater ial volum e fract ion (φ), the initi al gas press ure in the mater ial (po), and the stren gth of

the solid porti ons (poly ) [5-10 ]. For these analy ses the value s for the mater ial prope rties are σy

= 1700 psi, A = 1700 psi, poly = 30,00 0 psi, po = 14.7 psi, φ = 0.6, E = 1000 ksi, and ν =

0.0.

A summa ry of the mater ial prope rties for all of the mater ials used in the analy ses is given in

Table 5 .2. All of these mater ial model s accur ately captu re the three -dimension al state of stres s

and strai n withi n finit e eleme nt analy ses.

Table 5.2 Material Properties Used in the Finite Element Analyses

Item

Material

Model

E

(ksi) ν

σy or

σp

(ksi)

A or Ep

(ksi) n

poly

(ksi) φ

po

(psi)

Stainless

Steel

Power-law

hardening

28,000 0.27 28 193 0.7482

Bolts Elasticplastic30,000 0.30 105 30

Impact

Limiters

Power-law

hardening

9,900 0.33 4.25 32.7 0.3257

Lead Power-law

hardening

2,000 0.27 2 0.8 0.5

Depleted

Uranium

Elasticplastic28,000 0.3 20 150

Contents Crushable 1,000 0.0 1.7 1.7 30 0.6 14.7

5.1.4 Finite Element Results

Using finit e eleme nt analy ses to deter mine the abili ty of the casks to maint ain conta inment

require s inves tigation of all of the areas and facto rs that may resul t in a loss of conta inment. For

these casks the main facto rs to consi der are maxim um tensi le plast ic strai ns in the conta inment

bound ary, maxim um tensi le plast ic strai ns in the closu re bolts , and defor mations in the regio n of

the seals . For the sandw ich-wall casks the conta inment bound ary is the inner shell , but the

develop ment of a tear in this shell does not neces sarily imply a loss of conta inment if the outer 

shell remai ns intac t. None of the finit e element impac t analy ses indic ated strai ns above 70

percent in this shell , so no teari ng is predi cted to take place (the true strai n at failu re for 304L is
5-9

great er than 120 p ercent). Table 5.3 shows the maxim um level of plast ic strai n obser ved in the

inner shell for the three sandw ich wall casks . The strai n level s in the other porti ons of the cask

were lower than those in the shell s. A strai n fring e plot for the 120-m ph impac t of the steel -leadsteel truck cask is shown in Figur e 5.6. EQPS is the equiv alent plast ic strai n, and is the nondirec tional three -dimension al measu re of stret ching in the mater ial. Simil ar figur es for all of the

analy ses are given in Appendix A.

Table 5.3 Maximum Plastic Strain in the Inner Shell of the Sandwich Wall Casks

Cask Corner Impact

Speed Strain

 (%)

End Impact

Speed Strain

 (%)

Side Impact

Speed Strain

 (%)

Steel-Lead-Steel

Truck

30 mph 12

60 mph 29

90 mph 33

120 mph 47

30 mph 3.9

60 mph 12

90 mph 18

120 mph 27

30 mph n.a.

60 mph 16

90 mph 24

120 mph 27

Steel-DU-Steel Truck 30 mph 11

60 mph 27

90 mph 43

120 mph 55

30 mph 1.8

60 mph 4.8

90 mph 8.3

120 mph 13

30 mph 6

60 mph 13

90 mph 21

120 mph 30

Steel-Lead-Steel Rail 30 mph 21

60 mph 34

90 mph 58

120 mph 70

30 mph 1.9

60 mph 5.5

90 mph 13

120 mph 28

30 mph 5.9

60 mph 11

90 mph 15

120 mph n.a.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

* = 0.40

EQPS

Figure 5.6 Deformed shape and plastic strain fringes for the steel-lead-steel

truck cask following a 120-mph impact in the side-on orientation. The maximum

plastic strain (indicated by the asterisk) occurs in the outer shell. The maximum

strain in the inner shell is 0.27.
5-10

For the monol ithic rail cask the maxim um strai n on the inter ior surfa ce of the cask is less than

60 pe rcent for all analy ses. The maxim um occur s at the lid-c ask inter face for the 120-m ph side

impact case. At this locat ion most of the plast icity is cause d by compr ession, so there is no

possi bility of mater ial failu re. Table 5.4 lists the maxim um strai ns on the insid e of the cask for

these analy ses.

Table 5.4 Maximum Plastic Strains on the Inside of the Monolithic Rail Cask

Corner Impact

Speed Strain

 (%)

End Impact

Speed Strain

 (%)

Side Impact

Speed Strain

 (%)

30 mph < 10

60 mph < 20

90 mph < 30

120 mph < 50

30 mph < 2

60 mph < 5

90 mph < 10

120 mph < 17

30 mph < 10

60 mph < 30

90 mph < 50

120 mph < 60

The chanc e of a closu re failu re is direc tly relat ed to the defor mations betwe en the cask lid and

cask body and tensi le or shear failu re of the bolts . For the conse rvative bolt model used in these 

analyses, the maximum strain in any of the bolts is shown in Table 5.5. Several of these analyses

indic ate bolt strai ns that are high enoug h that failu re of the bolt is likel y (strains great er than 50

perce nt). The bolt mater ial has a speci fied perce nt elong ation great er than 15 perce nt and a

speci fied perce nt reduc tion of area great er than 50 perce nt [5-8] . This corre lates to a true strai n

at failu re of 69 perce nt. A value of 50 perce nt is conse rvatively chose n to indic ate bolt failu re

becau se the mater ial model used for the bolts has the true stres s in the bolts equal to the ultim ate

tensi le stres s (an engin eering stres s) at a strai n of 50 perce nt. Limit ing the bolt stres s to the

ultim ate tensi le stres s also assur es that the bolt threa ds will not fail. Bolt true strai ns that are

higher than 50 percent are shown in bold in the table. Several other analyses indicate bolt strains

that are high enoug h that failu re of the bolts is possi ble (true strai ns highe r than 25 pe rcent).

These bolt strai ns are shown in itali cs in the table . Analy sis for one of the cases where bolt

strai ns indic ate that bolt failu re could occur inclu ding a failu re model for bolts with strai ns

great er than 50 perce nt shows that even if some of the bolts fail, the remai ning bolts will hold the

lid in place . Compa rison of the closu re defor mations for this case with those for the same case

witho ut the bolt failu re model indic ates only minor diffe rences (less than 20% for the side impac t

and only a few perce nt for the corne r impac t). This is becau se the bolt loads are prima rily cause d

by a displ acement disco ntinuity betwe en the cask body and the lid.
5-11

Table 5.5 Maximum True Strain in the Closure Bolts

Cask Corner Impact

Speed Strain

 (%)

End Impact

Speed Strain

 (%)

Side Impact

Speed Strain

 (%)

Steel-Lead-Steel Truck 30 mph 3

60 mph 6

90 mph 9

120 mph 11

30 mph 1

60 mph 3

90 mph 5

120 mph 7

30 mph n.a

60 mph 2

90 mph 5

120 mph 10

Steel-DU-Steel Truck 30 mph 5

60 mph 9

90 mph 19

120 mph 22

30 mph 0

60 mph 3

90 mph 7

120 mph 9

30 mph 1

60 mph 4

90 mph 10

120 mph 18

Steel-Lead-Steel Rail 30 mph 19

60 mph 37

90 mph 60

120 mph 102

30 mph 6

60 mph 3

90 mph 9

120 mph 16

30 mph 14

60 mph 106

90 mph 151

120 mph n.a.

Monolithic Rail 30 mph 14

60 mph 40

90 mph 67

120 mph 80

30 mph 4

60 mph 14

90 mph 35

120 mph 58

30 mph 15

60 mph 32

90 mph 104

120 mph 170

The amoun t of defor mation betwe en the cask body and the lid at the locat ion of the O-rin g seals 

deter mines if a leak path from the cask is gener ated. Becau se the seal groov es were not expli citly

inclu ded in the model , the defor mation at a locat ion that is near where the O-rin gs would be

locat ed is used. For each model the displ acement of two sets (uppe r point and lower point ) of

two nodes on the cask lid and one node on the cask body are track ed for all times . Initi ally these 

three nodes are co-li near, with the body node lying betwe en the two lid nodes . From the

displ acement time histo ries, the amoun t of seal separ ation and seal slidi ng can be deter mined.

The seal separ ation is defin ed as the movem ent of the body node that is norma l to the line

betwe en the two lid nodes . The slidi ng is defin ed as the movem ent of the body node along the

line betwe en the two lid nodes . Figur e 5.7 shows these displ acements for the 90-mp h end

impac t of the monol ithic steel rail cask. Figure 5.8 shows a typic al time histo ry for openi ng

displ acement. Simil ar curves for all of the analy ses are inclu ded in Appen dix A. Table 5.6

shows the seal regio n displ acements at the end of the finit e eleme nt analy sis. Becau se the only

locat ion for leaka ge of radio active mater ials is at the closu re, and the high degre e of varia bilit y in

closu re desig ns, ident ical analy ses with less stiff bolts were perfo rmed for the 60 mph corne r

and side impac ts of the monol ithic steel rail cask. To perfo rm these analy ses the elast ic modul us

and strai n-hardenin g modul us of the bolt steel were reduc ed by a facto r of three . These analy ses

resul ted in nearl y ident ical openi ng displ acements as the origi nal analy ses. These resul ts suppo rt

the hypot hesis that the cask wall and lid are much stiff er than the closu re bolts , and the openi ng

displ acements are the resul t of displ acement disco ntinuities betwe en the cask body and lid, and

are not great ly affec ted by bolt clamp ing force .
5-12

For the end-o n impac t orien tation analy ses the displ acements at the end of the finit e eleme nt run

had not reach ed a stabl e value . For these analy ses a range of final displ acements is given in the

table . This oscil latory respo nse is cause d by the lack of friction and mater ial dampi ng withi n the

finit e eleme nt model . Numer ically these oscil lations will conti nue while the cask is rebou nding.

In reali ty, the frict ion and other dampi ng mecha nisms will quick ly cause these oscil lations to

stop, and the final displ acements will be at about the middle of the range shown in the table .

The many factors affecting closure opening and the way they interact can lead to surprising results.

For example, the maximum true strain in the closure bolts for the lead shielded rail cask is higher

for the 30-mph impact than it is for the 60-mph impact. In addition, for many of the impacts

increasing the impact velocity results in a decrease in closure opening as shown in Table 5.6.

Node A Node B

initial pos.

Node B

final pos.

Node C

Sliding displacement

Opening

displacement

Node A Node B

initial pos.

Node B

final pos.

Node C

Cask Lid

Cask

Body

Figure 5.7 Seal region displacements for the 90-mph end

impact of the monolithic steel rail cask.
5-13

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0 0.01 0.02 0.03 0.04 0.05

Time (sec.)

Opening Displacement (in.)

upper point

lower point

Figure 5.8 Time history for lid opening displacement for the 60 mph

side-impact of the monolithic steel rail cask.

Table 5.6 Seal Closure Displacements, in Inches, at the End of the Analysis

Cask Analysis Corner Impact End Impact Side Impact

Velocity Opening Sliding Opening Sliding Opening Sliding

Steel-Lead-Steel

Truck

30 mph

60 mph

90 mph

120 mph

0.02

0.02

0.02

0.04

0.01

0.03

0.06

0.04

0.000-0.002

0.001-0.003

0.000-0.002

0.002

0.000-0.002

0.001-0.004

0.003-0.005

0.02

-

0.01

0.02

0.02

-

0.02

0.02

0.01

Steel-DU-Steel

Truck

30 mph

60 mph

90 mph

120 mph

0.02

0.08

0.02

0.03

0.07

0.07

0.10

0.15

0.005-0.012

0.01-0.02

-

0.013

0.001-0.005

0.003-0.006

-

0.03

0.01

0.01

0.01

0.004

0.02

0.01

0.02

0.02

Steel-Lead-Steel

Rail

30 mph

60 mph

90 mph

120 mph

0.01

0.08

0.24

0.51

0.14

0.32

0.74

1.18

0.001-0.022

0.000-0.016

0.004-0.005

0.001-0.018

0.009-0.012

0.01-0.02

0.097-0.101

0.20-0.22

0.01

0.02

0.02

-

0.02

0.01

0.02

-

Monolithic Rail 30 mph

60 mph

90 mph

120 mph

0.04

0.10

0.22

0.44

0.20

0.36

0.48

0.59

0.007-0.053

0.04-0.12

0.03-0.13

0.09-0.16

0.04-0.05

0.09-0.10

0.38-0.39

0.668

0.01

0.04

0.08

0.12

0.01

0.01

0.09

-
5-14

To deter mine the leak area that resul ts from these openi ng displ acements, the influ ence of the

pre-c ompression of the elast omeric O-rin g and the width of the openi ng must be consi dered. For

cases with maxim um openi ngs of less than 0.100 inche s, the pre-c ompression of the O-rin g (as

much as 0.112 inche s for 3/8-i nch O-rin gs and 0.150 inche s for 1/2-i nch O-rin gs at 30 perce nt

compr ession for stati c face seal confi gurations [5-11 ]) will allow it to recov er suffi ciently to

maint ain an adequ ate seal to preve nt relea se of radio active mater ial. For openi ng displ acements

betwe en 0.100 and 0.200 inche s, the diffe rence in bolt strai ns indic ates that the openi ng only

occur s at the locat ion of one bolt. The width of the leak path is then equal to the bolt spaci ng

(6.38 inche s for the rail casks ). Howev er, for part of this width , the actua l openi ng

displ acement will be less than the O-rin g compr ession; there fore, the area of the resul ting hole is

calcu lated by trunc ating the base (the trunc ated part has a heigh t of 0.100 inche s) of an isosc eles

trian gle with a heigh t of the openi ng displ acement and a width of the bolt spaci ng. For openi ng

displ acements betwe en 0.200 and 0.300 inche s, the openi ng occurs over two bolt spaci ngs, and

for openi ng displ acements great er than 0.300 inche s, it is assum ed the openi ng occur s over three 

bolt spaci ngs. For openi ng displ acements great er than 0.300 inche s, the resul ting leak area is

suffi ciently large that incre asing the width of the openi ng has littl e or no effec t on the amoun t of

relea se. Table 5.7 summa rizes the leak path calcu lations for the analy ses where the maxim um

closu re openi ng is great er than 0.100 inche s.

Table 5.7 Calculated Rail Cask Closure Hole Sizes

Cask Velocity

(mph)

Orientation Opening

Displacement

(inches)

Opening

Width

(inches)

Leak Path

Area

(in2)

Steel-Lead-Steel Rail 90 Corner 0.243 12.76 0.54

120 Corner 0.512 19.14 3.2

60 Corner 0.103 6.38 0.00028

90 Corner 0.216 12.76 0.40

120 Corner 0.439 19.14 2.5

Monolithic Rail

120 Side 0.123 6.38 0.014

An addit ional resul t of impac t accid ents can be loss of shiel ding. For the two lead- shielded

casks , loss of shiel ding is a resul t of the slump ing of the lead. For the monol ithic steel rail cask

there is no loss of shiel ding, but there may be some radia tion strea ming throu gh the closu re. For

the steel -DU-steel truck cask, the model does not inclu de any gaps betwe en forge d DU

segme nts, so there is no loss of shiel ding. Lead slump occur s mostly in the end-o n impac t

orien tation, with a lesse r amoun t in the CG-ov er-corner orien tation. In the side- on orien tation

there is no signi ficant reduc tion in shiel ding. The zero- thickness shell eleme nts in the finit e

eleme nt model allow the lead addit ional space to flow to befor e conta cting the wall. This

incre ases the obser ved amoun t of lead slump . Figur e 5.9 shows the steel -lead-stee l rail cask

follo wing a 120-m ph end impac t.
5-15

Figure 5.9 Slumping of lead and contents following a 120-mph

end-on impact of the steel-lead-steel rail cask.

5.1.5 Benchmarking of Finite Element Calculations

Typic al analy ses used to certi fy a cask do not indic ate the large level s of strai ns seen in these 

analy ses. To be confi dent that analy ses of this type are captu ring the true respo nse of the

package they must be compa red to simil ar analy ses that have been demon strated to be accur ate.

In the mid 1990s Sandi a perfo rmed a serie s of tests and analy ses of the Struc tural Evalu ation

Test Unit (SETU ). End impac t tests of 30, 45, and 60 mph were perfo rmed. This test unit was

rough ly a 1/3-s cale model of a steel -lead-stee l walle d rail cask. In this progr am excel lent

agreement was obtai ned betwe en two-d imensional axi-s ymmetric finit e eleme nt analy ses and end

impact tests . In addit ion, a 7 degre es off-a xis impac t test at 60 mph was perfo rmed and

compa red to 3-D finit e eleme nt calcu lations. Again there was excel lent agree ment betwe en the

analy sis and test resul ts. The finit e eleme nt model s used in the SETU progr am were very simil ar
5-16

to those used here [5-4] . For the 3-D finit e eleme nt analy sis the inner and outer shell s were

model ed using the same shell eleme nts as this repor t. Howev er, in the SETU analy ses the

locat ion of the zero- thickness shell eleme nts was adjac ent to the lead because there was no

possi bility for 2-sid ed conta ct on the shell s. Appen dix B of this repor t gives a detai led

descr iption of the SETU analyses.

5.2 Impacts onto Real Targets

5.2.1 Introduction

The finit e eleme nt resul ts discu ssed in the previ ous secti on are all for impact s onto a rigid targe t.

For this type of impac t, the entir e kinet ic energ y of the impac t is absor bed by the cask. For finit e

eleme nt analy ses a rigid targe t is easil y imple mented by enfor cing a no displ acement bound ary

condi tion at the targe t surfa ce. In real life, the const ruction of a rigid targe t is impos sible, but it

is possi ble to const ruct a targe t that is suffi ciently rigid that incre asing its rigid ity does not

incre ase the amoun t of damag e to the cask. This is becau se in real impacts there is a shari ng of

energ y absor ption betwe en the cask and the targe t. If the targe t is much weake r than the cask, 

the targe t will absor b most of the energ y. If the targe t is much stron ger than the cask, most of

the energ y will be absor bed by the cask. In this secti on the parti tioning of the drop energ y

betwe en the four gener ic casks and sever al “real -world” targe ts will be devel oped in order to

obtai n impac t speed s onto real surfa ces that give the same damag e as impac ts onto rigid targe ts.

Impac ts onto hard deser t soil, concr ete highw ays, and hard rock are consi dered. Impac ts onto

water surfa ces are not expli citly treat ed, but are discu ssed. In addit ion, the proba bility of

punct ure of the cask cause d by impac t again st a non-f lat surfa ce (or impac t by a puncture probe )

is devel oped.

5.2.2 Methodology

The finit e eleme nt analy ses discu ssed in the prece ding secti ons were all condu cted assum ing the

impac t limit er had alrea dy been fully crush ed. As a resul t, it is not possi ble to use these analy ses

to deter mine real target impac t veloc ities that equat e to the regul atory impac t. Impac t limit ers are

typic ally desig ned to prote ct the baske ts and spent fuel in a cask from high accel erations. For

this reaso n, most spent -fuel casks have very simil ar impac t limit er desig ns. Cask behav ior for

regul atory impac ts is prima rily a funct ion of impac t limit er desig n, and not cask desig n. This

allow s the resul ts from the Modal Study [5-15 ] steel -lead-stee l casks (whic h inclu ded the impac t

limit ers for 30-mp h impac ts) to be used for the gener ic casks used in this study to deter mine

equiv alent real targe t impac t veloc ities at rigid targe t impac t veloc ities of 30 mph. There fore, for

impac ts onto real targe ts that equat e to the regul atory impac t, the resul ts from the Modal Study 

are used for all surfa ces excep t hard rock. For the hard rock impac ts it is assum ed the targe t

absor bs no energ y and the equiv alent veloc ity is equal to the rigid targe t veloc ity. For impac ts at

highe r veloc ities, the metho dology descr ibed below is used. 

For each finit e eleme nt calcu lation for impac t onto a rigid targe t the total kinet ic energ y of the

finit e eleme nt model is outpu t at 100 time- steps throu gh the analy sis. The total kinet ic energ y is

one half of the sum of the mass assoc iated with each node times the veloc ity of that node

squar ed. Figur e 5.10 shows kinet ic energ y time- histories for the steel -lead-stee l truck cask for
5-17

each orien tation from the 120-m ph impac t analy ses with pre-c rushed impac t limit ers. From the

time- history of kinet ic energ y, a velocity time histo ry is deriv ed. The rigid -body veloc ity for

each time- step is calcu lated assum ing that all of the kinet ic energ y of the model is cause d by

veloc ity in the direc tion of the impac t. Equat ion 2 shows this mathe matically. 

vt

2KE

mt

i

= ∑ (2)

where vt

 is the veloc ity at time t, KEt is the kinet ic energ y at time t, mI is the mass assoc iated

with node I, and the summa tion is over all of the nodes in the finit e eleme nt model .

0

5 106

1 107

1.5 107

2 107

2.5 107

0 0.01 0.02 0.03 0.04 0.05

Steel-lead-steel Truck Cask 120 mph Impact

Kinetic Energy Time Histories

End

Side

Corner

Kinetic Energy (ft-lbs)

Time (seconds)

Figure 5.10 Kinetic energy time histories for the steel-lead-steel truck cask from

120-mph impact analyses in the end, side, and corner orientations.
5-18

Numer ical integ ration of the veloc ity time- history gives the displ acement of the cente r-of-gravi ty

of the model . A large porti on of this displ acement is the resul t of the cente r-of-gravi ty movin g

down from the geome tric cente r of the cask due to lead and conte nts slump . Numer ical

diffe rentiation of the veloc ity time- history gives rigid -body accel eration. The conta ct force 

betwe en the rigid targe t and the cask at any time is assum ed to be equal to the rigid -body

accel eration times the mass of the cask. This resul ts in a force time- history. Combi nation of the

force time- history and the displ acement time- history resul ts in a force -deflectio n curve for each

cask and impact veloc ity. Figur e 5.11 shows the force defle ction curve s deriv ed from the kinet ic

energ y time- histories shown in Figur e 5.10. Numer ical integ ration of the force -deflectio n curve 

resul ts in energ y absor bed by the cask. At the end of the analysis the energ y absorbe d by the

cask is equal to the initi al kinet ic energ y.

0

5 106

1 107

1.5 107

2 107

2.5 107

3 107

3.5 107

012345

Steel-lead-steel Truck Cask 120 mph Impact

Force-Deflection Curves

End

Side

Corner

Contact Force (pounds)

Cask Deflection (feet)

Figure 5.11 Force-deflection curves for the steel-lead-steel truck cask from the 120-mph

impact analyses in the end, side, and corner orientations.
5-19

For each analy sis the peak conta ct force is deter mined. Table 5.8 lists these force s. For an

impact onto a real targe t to be as damag ing to the cask as the impac t onto the rigid targe t, the

targe t must be able to impar t a force equal to this peak force to the cask. 

The energ y absor bed by the targe t in devel oping this force is added to the initi al kinet ic energ y of

the cask. This total absor bed energ y is used to calcu late an equiv alent veloc ity by repla cing KEt

in Equat ion 2 with the total energ y.

Table 5.8 Peak Contact Force From Impacts Onto Rigid Targets (Pounds)

Cask Corner Impact End Impact Side Impact

Steel-Lead-Steel

Truck 30 mph 2.3E6

60 mph 5.0E6

90 mph 7.0E6

120 mph 1.0E7

30 mph 9.0E6

60 mph 1.3E7

90 mph 1.7E7

120 mph 2.0E7

30 mph 5.7E6

60 mph 1.4E7

90 mph 2.2E7

120 mph 3.4E7

Steel-DU-Steel Truck 30 mph 6.5E6

60 mph 1.1E7

90 mph 1.4E7

120 mph 1.7E7

30 mph 1.0E7

60 mph 1.3E7

90 mph 1.5E7

120 mph 1.7E7

30 mph 9.0E6

60 mph 2.3E7

90 mph 3.4E7

120 mph 4.9E7

Steel-Lead-Steel Rail 30 mph 1.3E7

60 mph 2.3E7

90 mph 3.6E7

120 mph n.a.

30 mph 3.8E7

60 mph 6.8E7

90 mph 8.3E7

120 mph 1.1E8

30 mph 1.8E7

60 mph 4.4E7

90 mph 6.2E7

120 mph n.a.

Monolithic Rail 30 mph 2.1E7

60 mph 3.9E7

90 mph 5.8E7

120 mph 7.5E7

30 mph 3.8E7

60 mph 9.5E7

90 mph 1.1E8

120 mph 1.3E8

30 mph 2.2E7

60 mph 5.4E7

90 mph 9.5E7

120 mph 1.1E8

5.2.3 Soil Targets

The force that hard deser t soil impar ts onto a cask follo wing an impac t was deriv ed from resul ts

of impac t tests perfo rmed by Gonza les [5-13 ], Waddo ups [5-14 ], and Bonzo n and Scham aun

[5-15]. The tests by Gonza les and Waddo ups used casks that were compa rable to the gener ic

casks of this study . The tests by Bonzo n and Scham aun were with casks that were less stiff than

the gener ic casks . This large amoun t of test data was used to devel op an empir ical soil targe t

force -deflectio n equat ion that is a funct ion of impac tor area. Figur e 5.12 shows the force -

defle ction curve s for impac t of the steel -lead-stee l truck cask. Corne r impac ts were assum ed to

have the same conta ct area on the soil targe t as the end impac ts, so only two curve s are shown .

Simil ar curve s were devel oped for each of the other casks . Compa rison of Figur e 5.12 with the

force s in Table 5.8 show that many of the impac ts will resul t in very large soil penet rations .

This is consi stent with the resul ts seen in Waddo ups’ tests , where casks were dropp ed 2,000 

feet from a helic opter. Penet ration depth s for these impac ts were up to 8 feet, and the equiv alent

rigid target impac t veloc ity was less than 30 mph. Integrati on of the force -deflectio n curve up to

the peak conta ct force deter mines the amoun t of energ y absor bed by the targe t.
5-20

0

5 106

1 107

1.5 107

2 107

2.5 107

3 107

0 2 4 6 810 12

Steel-Lead-Steel Truck Cask

End Impact

Side Impact

Contact Force (pounds)

Penetration Distance (feet)

Figure 5.12 Force-deflection curves for impact onto hard desert soil.

5.2.4 Concrete Targets

The force impar ted to a cask by impac t onto a concr ete targe t is deriv ed from test resul ts by

Gonzales [5-13 ]. In his serie s of tests , a cask- like test unit was impac ted onto two types of

concr ete targe ts, one 12 inche s thick and one 18 inche s thick , at veloc ities from 30 to 60 mph.

All of the impacts were in an end-o n orien tation. Based upon the resul ts of these tests and

engin eering mechani cs, an empir ical relat ionship betwe en the force and energ y absor bed was

deriv ed. For impacts onto concr ete slab targe ts there are two mecha nisms that produ ce large 

force s onto the cask. The first is the gener ation of a shear plug in the concr ete. The force 

requi red to produ ce this shear plug is linea rly relat ed to the impac t veloc ity, the diame ter of the

impac ting body, and the thick ness of the concr ete. Equati on 3 gives the empir ical equat ion for

the force requi red to produce the shear plug. 

F Cvdt s s e ic = (3)
5-21

where Fs is the force requi red to produ ce the shear plug, Cs is an empir ical const ant (16.8 4), ve

is the equiv alent impac t veloc ity, di is the diame ter of the impac tor, and tc is the thick ness of the

concr ete slab. 

The energ y absor bed in produ cing this shear plug is linea rly relat ed to the cask diame ter, the

squar e of the impac t veloc ity, and the fourt h root of the slab thick ness. Equat ion 4 gives the

empiric al equat ion for the energ y requi red to produ ce the shear plug. 

E Cdv t s eie

2

c

0.25 = (4)

where Es

 is the energ y requi red to produ ce the shear plug and Ce is an empir ical const ant

(0.00 676).

After the shear plug is forme d, furth er resistan ce to penet ration is achie ved by the behav ior of the

subgr ade and soil benea th the concr ete. This mater ial is being penet rated by the cask and the

shear plug. Gener ally, the shear plug forms with 45-de gree slope s on the side. There fore, the

diame ter of the soil being penet rated is equal to the cask diame ter plus twice the slab thick ness.

The behav ior of the subgr ade and soil is assum ed to be the same as the hard deser t soil used for

the soil targe t impac ts. Figur e 5.13 shows a compa rison of the empiric al relat ionship with one

of Gonza les’ tests . Figur e 5.14 shows the force -deflectio n curve for the steel -lead-stee l truck 

cask impac ting a 9-inc h thick concr ete roadw ay at 120 mph. For corne r and side impac ts an

equiv alent diame ter is calcu lated to fit with the empir ical equat ions. For each case the diame ter is

calculat ed by assum ing the shear plug forms when the concr ete targe t has been penet rated two

inche s. The area of the equiv alent diame ter is equal to the area of the concr ete in conta ct with the

cask when the penet ration depth is two inche s. To calcu late the equiv alent veloc ity for concrete 

targe ts the force requi red to gener ate the shear plug must be compa red to the peak conta ct force 

for the impac t onto the rigid targe t. The veloc ity requi red to produ ce this force can be calculat ed

from Equat ion 3. The kinet ic energ y assoc iated with this veloc ity is absor bed by a combinat ion

of produ cing the shear plug, penet ration of the subgr ade and soil benea th the concr ete, and

defor mation of the cask. The energ y absor bed in produ cing the shear plug is calcu lated by

Equat ion 4, the energ y absor bed by the cask is equal to the kinet ic energ y of the rigid targe t

impact, and the energ y absor bed by the subgr ade and soil is calcu lated in a manne r simil ar to that

for the soil impac t discu ssed above . If the amoun t of energ y to be absor bed by the soil is

sufficient ly high, the force in the soil will be highe r than the force requi red to produ ce the shear 

plug. In this case, an itera tive appro ach is neces sary to deriv e an equiv alent veloc ity so that the

maximum force gener ated in penet rating the subgr ade and soil benea th the concr ete is equal to the

peak conta ct force for the rigid targe t impac t.
5-22

0

5 105

1 106

1.5 106

2 106

2.5 106

3 106

3.5 106

0 0.2 0.4 0.6 0.8 1 1.2

Gonzales Impacts onto Highway Targets

Test 44 fps

Calc. 44 fps

Test 88 fps

Calc. 88 fps

Contact Force (pounds)

Penetration Distance (feet)

Figure 5.13 Comparison of test force-deflection curves

with those derived from the empirical equations.

The only orien tation of impac ts onto concr ete targe ts where test data is avail able is for end

impacts . In this orien tation the conta ct area betwe en the cask and the concr ete does not incre ase

with incre asing penet ration dista nce. In order to use the empir ical relat ionships devel oped for

end impac ts with other impac t orien tations, an equiv alent diame ter must be deter mined. For both

the side and corne r impac ts, the equiv alent diame ter was calcu lated to have an area equal to the

area of the cask two inche s above the conta ct point . For side impac t orien tations, this area is a

recta ngle. For corne r impac t orien tations this area is a trunc ated parab ola. Table 5.9 gives the

equiv alent diame ters used for each of the casks. For all of the casks , the equiv alent diame ter for

the corne r impac t is much small er than the cask diame ter. This is espec ially prono unced for the

rail casks . In reali ty, the failu re mode for a concr ete targe t being impac ted by a large cask in a

corne r orien tation is proba bly not gener ation of a shear plug, but rathe r a split ting tensi le failu re

and subse quent rotat ion of the slab to allow perfo ration by the cask. After penet ration of the

concr ete occur s, the area of the cask plus concr ete penet rating the soil is equal to the cask cross -

secti onal area (the same area used for the soil targe t impac ts).
5-23

0

5 106

1 107

1.5 107

2 107

2.5 107

3 107

3.5 107

0 2 4 6 810 12

Concrete Target Force-Deflection Curves

for 120 mph Steel-lead-steel Truck Cask Impacts

End

Corner

Side

Contact Force (pounds)

Target Deflection (feet)

Figure 5.14 Force-deflection curves for concrete target impacts

of the steel-lead-steel truck cask at 120 mph.

Table 5.9 Equivalent Diameters for Concrete Impacts

Cask Orientation Equivalent Diameter

(inches)

Corner 15.3

End 27.5

Steel-Lead-Steel Truck

Side 61.1

Corner 20.2

End 28.0

Steel-DU-Steel Truck

Side 60.6

Corner 13.6

End 80.0

Steel-Lead-Steel Rail

Side 79.8

Corner 13.0

End 85.0

Monolithic Rail

Side 79.0
5-24

5.2.5 Hard Rock Targets

For impac ts onto hard rock targe ts the targe t is assum ed to be a semi- infinite half plane . The

force and energ y absor bed by the targe t is deter mined by the volum etric behav ior of the rock. 

For hard rock surfa ces this behav ior is suffi ciently stiff that very littl e energ y is absor bed by the

target. For this reaso n these impac ts are treat ed as rigid targe t impac ts.

5.2.6 Example Calculation

In this secti on, the metho dology discu ssed in Secti on 5.2.2 will be applied to the steel -lead-stee l

truck cask using the soil targe t prope rties from Secti on 5.2.3 . For the 120 mph impac t in the

end-o n orien tation the peak conta ct force actin g on the cask is 20 × 106

 pound s (from Figur e 5-

11 or Table 5-8). For a soil targe t to gener ate this amoun t of force , the cask must penet rate

sligh tly over 12 feet (from Figur e 5.12) . The energ y absor bed by the soil targe t while it is being 

penet rated to this dista nce is equal to the integ ral under the force -deflectio n curve up to this

penet ration distance . For this case, this is equal to 136 × 106

 foot- pounds. The kinet ic energ y

of this 50,00 0 pound cask trave lling at 120 mph is 24.1 × 106

 foot- pounds. This is the amoun t

of energ y absor bed by the cask for impac t onto a rigid targe t. For the impac t onto the soil targe t,

the cask will there fore absor b 24.1 × 106

 foot- pounds of energ y and the soil will absor b

136 × 106

 foot- pounds of energ y for a total of 160 × 106 foot- pounds of energ y. The cask

veloc ity that is assoc iated with this amount of kinet ic energ y is 309 mph. This veloc ity is much

highe r than the 150-m ph top veloc ity in the accid ent veloc ity distr ibutions. Note that all of the

equiv alent veloc ities deter mined in this manne r negle ct the energ y absor bed by the impac t limit er.

5.2.7 Results for Real Target Calculations

Table s 5.10 to 5.13 summa rize the resul ts for impac ts onto soil and concr ete targe ts.

Table 5. 10 Real target Equivalent Velocities (mph) for the Steel-Lead-Steel Truck Cask

Target/Orientation Rigid Target Velocity

30 mph

w/o limiter

60 mph

w/o limiter

90 mph

w/o limiter

120 mph

w/o limiter

Soil

End >150 >>150 >>150 >>150

Side 70 >150 >>150 >>150

Corner 61 135 >150 >>150

Concrete Slab

End 123 >150 >>150 >>150

Side 35 86 135 >150

Corner 56 123 >150 >>150
5-25

Table 5. 11 Real Target Equivalent Velocities (mph) for the Steel-DU-Steel Truck Cask

Target/Orientation Rigid Target Velocity

30 mph

w/o limiter

60 mph

w/o limiter

90 mph

w/o limiter

120 mph

w/o limiter

Soil

End >150 >>150 >>150 >>150

Side 99 >>150 >>150 >>150

Corner 128 >150 >>150 >>150

Concrete Slab

End 134 >150 >150 >150

Side 56 142 >150 >>150

Corner 121 >150 >>150 >>150

Table 5. 12 Real Target Equivalent Velocities (mph) for the Steel-Lead-Steel Rail Cask

Target/Orientation Rigid Target Velocity

30 mph

w/o limiter

60 mph

w/o limiter

90 mph

w/o limiter

120 mph

w/o limiter

Soil

End >>150 >>150 >>150 >>150

Side 72 >150 >>150 >>150

Corner 68 133 >150 >150

Concrete Slab

End >150 >>150 >>150 >>150

Side 85 >150 >>150 >>150

Corner >>150 >>150 >>150 >>150

Table 5. 13 Real Target Equivalent Velocities (mph) for the Monolithic Steel Rail Cask

Target/Orientation Rigid Target Velocity

30 mph

w/o limiter

60 mph

w/o limiter

90 mph

w/o limiter

120 mph

w/o limiter

Soil

End >150 >>150 >>150 >>150

Side 92 >150 >>150 >>150

Corner 111 >150 >>150 >>150

Concrete Slab

End >150 >>150 >>150 >>150

Side 104 >>150 >>150 >>150

Corner >>150 >>150 >>150 >>150
5-26

5.2.8 Impacts onto Water

Equiv alent veloc ities for impac ts onto water targets for veloc ities great er than the regul atory

impact are assum ed to be above the range of possi ble impac t veloc ities (150 mph). The

incom pressible natur e of water makes perfe ctly flat impac ts quite sever e. As the impac t veloc ity

incre ases small er deviati ons from the perfe ctly flat orien tation are suffi cient to cause the lack of

shear stren gth in water to domin ate the respo nse. Becau se perfe ctly flat impac ts are very

impro bable, this appro ach is justi fied.

5.2.9 Correlation of Results with Modal Study Event Trees

The Modal Study [5-12 ] event trees speci fy impac t surfa ces for each accid ent type. Because 

these event trees are used in this study to deter mine accid ent proba bilities, this secti on will

discu ss which of the veloc ities deter mined above corre late to the surfa ces speci fied in the event 

trees . For this study the event tree surfa ce of railb ed/roadbed will be treat ed as soil. The soil

impac ted in the tests used to calib rate the model was very hard deser t soil, typic al of

Albuq uerque, New Mexic o. This soil is gener ally harde r than the soil found on railb eds and

roadb eds. For impac ts onto the event tree surfa ce of clay/ silt the equiv alent veloc ities will

alway s be highe r than the soil impac t veloc ity deriv ed here, but this veloc ity will be conse rvative

and is there fore used. For the event tree surfa ce of soft rock/ hard rock/ concrete the data from the

concr ete slab analy ses will be used. In the Modal Study the equiv alent veloc ities for the event 

tree surfa ces of colum n and abutm ents were the same as those for the soft rock/ hard soil/ concrete

surfa ce. This appro ach will be repea ted in this study . The event tree surfa ce of hard rock will

be treat ed as unyie lding at all veloc ities, becau se the amoun t of energ y absor bed by the rock is

only a small porti on of the impac t energ y. For all of the other impac t surfa ces the 30-mp h

equiv alent veloc ity is taken direc tly from the Modal Study .

5.3 Puncture Analyses

Revie w of data from the Assoc iation of Ameri can Railr oads (AAR) on the punct ure of railr oad

tank cars indic ates that cars with a shell thick ness great er than or equal to one inch rarel y

exper ience punct ure failu res1

. Becau se the steel -lead-stee l rail cask in this study has an outer 

shell thick ness of two inche s, it is highl y unlik ely that even the outer shell will be punctured in

any rail accid ent. The conta inment bound ary on the sandw ich-wall casks is the inner shell , so

punct ure failu re of the outer wall will not resul t in any relea se. The resid ual energ y neces sary to

punct ure the inner shell after the outer shell and shiel ding layer s have been perfo rated is similar

in magni tude to that requi red to punct ure the outer shell , makin g loss of conta inment in punct ure

accid ents even more unlik ely. Figur e 5.15 shows the relat ionship betwe en tanke r shell thick ness

and fract ion of cars invol ved in punct ure-type accid ents that were faile d becau se of punct ure.

Even the truck casks , which have thinn er outer shell s than rail casks , have a compo site wall

stren gth that is signi ficantly great er than the stren gth of the stron gest tank cars. The proba bility

that these casks will be faile d becau se of punct ure is extre mely low. This

_____________

1. Perso nal commun ication wi th D. J. Paste rnak and data from RPI-AAR Ra ilroad Tan k Car Safe ty Researc h

and T est Projec t, June 19 98.
5-27

0

0.02

0.04

0.06

0.08

0.1

0.4 0.6 0.8 1 1.2

Shell Thickness (inches)

Fraction of Tank Cars Punctured

Figure 5.15 Fraction of railroad tank cars involved in

puncture-type accidents that failed because of puncture.

is consi stent with recen t analy ses perfo rmed by the NRC in respo nse to quest ions from the

AAR. These analy ses concl uded that it would be impos sible for a rail coupl er or a regul atory

puncture spike to punct ure the wall of a rail cask [5-16].

5.4 Failure of Rods

The perce ntage of fuel pins damag ed for each impac t is estim ated based on the peak rigid -body

accel eration. The STACE repor t [5-17] provi des strai ns in the fuel pin cladd ing for a 100-G side

impac t for both PWR and BWR assem blies. In that repor t, it was shown that side impac t

provides the most sever e loadi ng to the fuel assem blies. Durin g end-o n impac ts, the fuel

assem blies are loade d by axial compr essive loads . This type of loadi ng will cause the indiv idual

rods to event ually buckl e. Becau se of the limit ed space for later al motio n that resul ts from this

buckl ing and the very slend er natur e of the fuel rods, relat ively low strai ns are produ ced.

There fore, in this repor t, the maxim um strai n gener ated in a fuel rod due to impac ts onto a rigid 

targe t at any of the four speed s and three impac t orien tations model ed by the finit e eleme nt

calcu lations will be estim ated using the peak accel eration of the impac t to scale the large st strai n

gener ated in a fuel rod by a 100-G side impac t. The rod will then be said to fail whene ver the

scale d strai n level equal s or excee ds the strai n failu re crite rion devel oped in the next secti on.
5-28

5.4.1 Rod Failure Strain Criterion

As of 1994, the U.S. comme rcial spent fuel inven tory conta ined about 49 perce nt low burnu p

(0 to 30 GWDt/ MTU) fuel, about 49 perce nt inter mediate burnu p (30 to 45 GWDt/ MTU) fuel, 

about 2 perce nt inter mediate to high burnu p (45 to 50 GWDt/ MTU) fuel, and only 0.2 perce nt

high burnu p (50 to 60 GWDt/ MTU) fuel [5-18 ]. Recen t data sugge st that, as of 1998, about 25

to 30 perce nt of PWRs and 15 to 20 perce nt of BWRs were produ cing high burnu p fuel1

. Since 

hardl y any high burnu p fuel was being produ ced in 1994, linea r extra polation of this data

sugge sts that by 2010 almos t all U.S. comme rcial react ors will be producin g high burnu p spent 

fuel and about half will be produ cing high burnu p fuel in 2002. 

In 1994, the 109 power react ors that were opera ting in the United State s gener ated 1883 MT of

spent fuel [5-18] or 17.28 MT per react or-year. If all of the U.S. comme rcial power react ors

opera ting in 1999 exten d their plant lives to 40 years , then data publi shed in Nucle ar News [5-

19] allow s the amoun ts of spent fuel that will be gener ated over the remai ning life of these 

react ors to be calcu lated. The rate of conve rsion to high burnu p fuel can be captu red by

assum ing that from 1995 throu gh 2001, all opera ting react ors will gener ate fuel with burnu ps of

40-45 GWDt/ MTU and from 2002 throu gh the end of their opera ting lives they will all gener ate

high burnu p fuel (fuel with burnu ps of 55-60 GWDt/ MTU). Thus, durin g the seven year perio d

from 1995 throu gh 2001, 13181 MTU = (7 yrs)(188 3 MTU per yr) of 40-45 GWDt/ MTU fuel

will be produ ced; and, after 2001, 33600 MTU = (17.2 8 MT per react or)(1945 react or-yrs) of

high burnu p fuel will be produ ced where , as Table 5.14 shows , 1945 is the numbe r of years of

react or opera tion after 2001 that will occur if all of the react ors operati ng in 1999 exten d their 

plant lives to 40 years .

The strai ns that cause rod failu re are expec ted to lie somew here betwe en the unifo rm plast ic

elong ation (UE) and total plast ic elong ation (TE) strai ns that produ ce rod failu re, proba bly well

below the total elong ation strai ns and not much above the unifo rm elong ation strai ns2

. For

avera ge burnu p fuel, the resul ts of Bauer and Lowry [5-20] sugge st that, when heate d to 200 to

300° C, avera ge burnu p spent fuel will fail when UE strai n level s reach 4 perce nt or TE strai n

level s reach 8 perce nt. For avera ge burnup fuel, Sande rs et al. [5-17 ] estim ate that the

proba bility of rod failu re due to an impac t that gener ates a biaxi al stres s ratio (pres surized fuel

under tensi on) of 0.9 is 50 perce nt when the ruptu re strai n is 4 perce nt. For high burnu p fuel,

the data of Smith et al . [5-21 ] and Garde et al. [5-22 ] indic ate that at 300° C high burnu p fuel

will fail when UE stain level s reach 1 perce nt or TE strai n level s reach 3.8 perce nt. Accor dingly,

1 perce nt and 4 perce nt strai ns respe ctively are assum ed to cause the cladd ing of high (55-6 0

GWDt/ MTU) and high inter mediate (40-4 5 GWDt/ MTU) burnu p spent fuel rods to fail, which 

sugge sts that the rod failu re strai n crite rion will incre ase 1 perce nt for each 5 GWDt/ MTU

incre ase in burnu p.

____________

1. Perso nal commu nications, J. Finuc ane, Coal, Nucle ar, and Renew able Fuels Divis ion, U.S. Depar tment of

Energ y, 1999. 

2. Perso nal commu nication, M. Billo ne, Argon ne Natio nal Labor atory, 1999. 
5-29

Table 5. 14 Cal culation o f Reactor- Years Prod ucing High Burnup Fu el

Start Years Start Years Start Years

Reactor Type Year >2001 Reactor Type Year >2001 Reactor Type Year >2001

Calloway PWR 85 23 Arkansas 1 PWR 74 12 Hope Creek BWR 86 24

Cook 1 PWR 75 13 Arkansas 2 PWR 80 18 Salem 1 PWR 77 15

Cook 2 PWR 78 16 Grand gulf BWR 85 23 Salem 2 PWR 81 19

Palo Verde 1 PWR 86 24 River Bend BWR 86 24 R.E. Ginna PWR 70 8

Palo Verde 2 PWR 86 24 Waterford 3 BWR 85 23 Virgil C. Summer PWR 84 22

Palo Verde 3 PWR 88 26 Davis Besse PWR 78 16 South Texas 1 PWR 88 26

Calvert Cliffs 1 PWR 75 13 Perry 1 BWR 87 25 South Texas 2 PWR 89 27

Calvert Cliffs 2 PWR 77 15 St Lucie 1 PWR 76 14 San Onofre 2 PWR 83 21

Pilgrim BWR 72 10 St Lucie 2 PWR 83 21 San Onofre 2 PWR 84 22

Brunswick 1 BWR 77 15 Turkey Point 1 PWR 72 10 Farley 1 PWR 77 15

Brunswick 2 BWR 75 13 Turkey Point 2 PWR 73 11 Farley 2 PWR 81 19

Robinson 2 PWR 71 9 Crystal River 3 PWR 77 15 Hatch 1 BWR 75 13

Shearon Harris PWR 87 25 Oyster Creek BWR 69 7 Hatch 2 BWR 79 17

Braidwood 1 PWR 88 26 Three Mile Island 1 PWR 74 12 Vogtle 1 PWR 87 25

Braidwood 2 PWR 88 26 Duane Arnold BWR 75 13 Vogtle 2 PWR 89 27

Bryon 1 PWR 85 23 Clinton BWR 87 25 Bellefonte1 PWR 95 33

Bryon 2 PWR 87 25 Cooper BWR 74 12 Bellefonte2 PWR 95 33

Dresden 2 BWR 70 8 FitzPatrick BWR 75 13 Browns Ferry 1 BWR 74 12

Dresden 3 BWR 71 9 Indian Point 3 PWR 76 14 Browns Ferry 2 BWR 75 13

LaSalle 1 BWR 84 22 Nine Mile Point 1 BWR 69 7 Browns Ferry 3 BWR 77 15

LaSalle 1 BWR 84 22 Nine Mile Point 1 BWR 88 26 Sequoyah 1 PWR 81 19

Quad Cities 1 BWR 73 11 Seabrook PWR 90 28 Sequoyah 1 PWR 82 20

Quad Cities 2 BWR 73 11 Millstone 2 PWR 75 13 Watts Bar 1 PWR 96 34

Indian Point 2 PWR 74 12 Millstone 3 PWR 86 24 Watts Bar 2 PWR 95 33

Palisades PWR 71 9 Monticello BWR 71 9 Comanche Peak 1 PWR 90 28

Fermi 2 BWR 88 26 Prairie Island 1 PWR 73 11 Comanche Peak 2 PWR 93 31

Catawba 1 PWR 85 23 Prairie Island 2 PWR 74 12 Vermont Yankee BWR 72 10

Catawba 2 PWR 86 24 Fort Calhoun PWR 73 11 North Anna 1 PWR 78 16

McGuire 1 PWR 81 19 Susquehanna 1 BWR 83 21 North Anna 2 PWR 80 18

McGuire 2 PWR 84 22 Susquehanna 1 BWR 85 23 Surry 1 PWR 72 10

Oconee 1 PWR 73 11 Diablo Canyon 1 PWR 85 23 Surry 2 PWR 73 11

Oconee 2 PWR 74 12 Diablo Canyon 2 PWR 86 24 WPN-2 BWR 84 22

Oconee 3 PWR 74 12 Limerick 1 BWR 86 24 Point Beach 1 PWR 70 8

Beaver Valley 1 PWR 76 14 Limerick 2 BWR 90 28 Point Beach 2 PWR 72 10

Beaver Valley 2 PWR 87 25 Peach Bottom 1 BWR 74 12 Kewaunee PWR 74 12

Peach Bottom 2 BWR 74 12 Wolf Creek PWR 85 23

Reactor-Years at High Burnup 1945
5-30

Use of the combi nation of the extra polated amoun ts of inter mediate and high burnu p fuel with

the 1994 data for metri c tons of spent fuel by burnu p range produ ces the basis for const ructing

an avera ge strai n failu re level as a weigh ted sum of strai n failu re level s weigh ted by the amount 

of spent fuel in each burnu p range . To do this, the cladd ing strai ns that produ ce rod failu re are

assum ed to incre ase rough ly linea rly with decre asing fuel burnu p. High burnu p (55 to 60

GWDt/ MTU) spent fuel is assum ed to fail at 1 perce nt strai n, interm ediate burnu p (40 to 45

GWDt/ MTU) spent fuel fails at 4 perce nt strai n, and low burnu p (0 to 25 GWDt/ MTU) spent 

fuel fails at 8 per cent strai n. As Table 5.15 shows , weigh ted summa tion of these cladd ing strai n

level s by burnu p range produ ces an avera ge failu re stain level of 3.6 perce nt. This avera ge is

proba bly somew hat low for three reaso ns: (a) becau se it is deriv ed using unifo rm elong ation

strai ns which are expec ted to under estimate somew hat the strai ns requi red to produ ce rod failu re,

(b) becau se not all opera ting reactor s will exten d their opera ting life to 40 years , and (c) becau se

not all opera ting react ors will conve rt to a fuel manag ement cycle that produ ces high burnu p fuel. 

Accor dingly, in agree ment with the STACE repor t [5-17 ] and consi stent with failu re strai ns

repor ted by Westi nghouse for several burst tests [5-23 ], an avera ge strai n failu re crite rion of

4 per cent seems reasonab le for the U.S. comme rcial power react or spent fuel inven tory even

after corre cting for the amoun ts of high- burnup fuel likel y to be produ ced durin g the remai nder

of the nucle ar fuel cycle in the Unite d State s. Final ly, a sensi tivity calcu lation descr ibed below 

in Secti on 8.10. 3, shows that, when rod failu re fract ions are set to 1.0 for all colli sion scena rios

regar dless of their sever ity, mean accid ent dose risks are incre ased by only a facto r of 2.0.

Thus, mean accid ent doses and dose risks are not parti cularly sensi tive to the avera ge value 

chose n for the strai n crite rion for rod failu re durin g colli sion accid ents. 

Table 5. 15 Cal culation o f Mass Wei ghted Sum

of Bu rnup Depen dent Rod S train Fail ure Levels 

Criterion GWDT

per MTU MTU Range Weighted

0-25 8437 8 0.88

25-30 6177 7 0.56

30-35 6815 6 0.53

35-40 5149 5 0.34

40-45 2570 4 0.13

45-50 636 3 0.02

50-55 44 2 0.00

55-60 5 1 0.00

AvBU 13181 4 0.69

HBU 33600 1 0.44

Total 76614 Sum 3.60
5-31

5.4.2 Estimation of the Fraction of Rods Failed During Impacts

If the cladd ing strai ns are scale d by the ratio of peak rigid -body accel erations calcu lated in

Secti on 5.2.2 to the 100-G accel eration used in the STACE repor t, the numbe r of pins with

cladd ing strai ns large r than 4 perce nt can be deter mined. These resul ts are used to provi de an

estim ate of fuel pin failu re percenta ges. Table 5.16 gives the peak rigid -body accel erations for

each of the analy ses. Table 5.17 gives the strai ns in the fuel rods resul ting from a 100-G impac t,

taken from Figur es III-6 0 and III-6 4 of the STACE repor t. Scali ng the strai ns in Table 5.17 by

the accel erations in Table 5.16 and count ing the numbe r of rods with strai ns great er than 4

perce nt resul ts in the fract ion of rods faile d given in Table 7.18 for each of the analy ses.

Table 5.16 Peak Accelerations from Rigid Target Impacts without Impact

Limiters, Gs

Cask Orientation 30 mph 60 mph 90 mph 120 mph

Corner 51.3 111.4 156.0 222.9

End 200.6 289.8 378.9 445.8

Steel-Lead-Steel

Truck

Side 127.0 312.1 490.4 757.8

Corner 132.6 224.3 291.6 346.7

End 203.9 254.9 297.8 346.7

Steel-DU-Steel Truck

Side 183.5 469.1 693.4 999.3

Corner 50.6 94.4 145.9 n.a.

End 167.3 303.0 371.1 483.6

Steel-Lead-Steel Rail

Side 73.3 178.8 349.7 n.a.

Corner 93.8 174.2 259.1 335.1

End 169.8 424.4 513.8 580.8

Monolithic Rail

Side 98.3 241.3 424.4 491.5

5.5 Conservatism in Calculating Structural Response

In this secti on the conse rvatism assoc iated with the vario us assum ptions in the deter mination of

the struc tural respo nse of the gener ic casks will be discu ssed in appro ximately the same order as

the secti ons of this chapt er.

Treat ing all corne r impac ts as if they were CG-ov er-corner force s all of the impac t energ y to be

absor bed on the prima ry impac t end. For corne r impac ts away from CG-ov er-corner, some of

the initi al kinet ic energ y of the cask will be conve rted into rotat ional kinet ic energ y at the end of

the prima ry impac t. This rotat ional kinet ic energ y will be absor bed by a secon dary impac t on the

oppos ite end of the cask. Anoth er conse rvatism in choos ing the impac t angle s to be analy zed is

the assum ption that all end and corne r impac ts occur on the closu re end of the cask. The

defor mations on the end away from the impac t are much small er, so if the impac t occur s on the

end away from the closu re there will only be small defor mations in the closu re regio n and no

relea ses for even the 120 mph impac ts. In addit ion, the veloc ity vecto rs for all of the accid ents

are assum ed to be perpe ndicular to the impac t surfa ce. In reali ty, there will be a distr ibution of

angle s betwe en the veloc ity vecto r and the impac t surfa ce, and only the compo nent of the
5-32

veloc ity vecto r that is perpe ndicular to the impac t surfa ce will cause damag e to the cask. If the

media n of the distr ibution is at 45 degre es, this resul ts in a 70% reduc tion, on avera ge, in the

compo nent of veloc ity that produ ces damag e.

Table 5.17 Peak Strains in Fuel Rods Resulting from a 100 G Impact

Fraction of

PWR Rods

Peak Strain,

%

Fraction of

BWR Rods

Peak Strain,

%

1/15 3.3 1/7 1.1

2/15 2.9 2/7 1

3/15 2.2 3/7 0.85

4/15 2 4/7 0.83

5/15 1.7 5/7 0.78

6/15 1.5 6/7 0.66

7/15 1.4 7/7 0.62

8/15 1.4

9/15 1.4

10/15 1.3

11/15 1.3

12/15 1.2

13/15 1.2

14/15 1.1

15/15 1.1

Treating the impact limiter material as completely locked-up from a 30-mph impact neglects the

design margin that cask designers include in their impact limiter designs. For most cask designs

the regulatory impact only uses about 50% of the energy absorbing capability of the impact limiter.

If the impact limiter can absorb twice as much energy (the energy from a 60-foot free drop) the

accident velocities associated with the 30, 60, 90 and 120 mph finite element calculations become

52, 73, 99, and 127 mph respectively instead of the 42, 67, 95, and 124 mph respectively used in

this report.

The use of zero-thickness shell elements to represent the structural portions of the sandwich walls

for the lead and DU shielded casks results in an overprediction of lead slump and strain in the

walls. Because none of the walls had strains that were sufficiently high to indicate tearing of the

stainless steel, the overprediction of these strains did not have any consequences. Therefore, the

only consequence of the zero-thickness shells is for loss-of-shielding analyses.

Omitting the neutron shielding and any liner that is outside of it ignores the energy that will be

absorbed by these components. During regulatory drops (30 mph) this is insignificant, but for

higher velocity side impacts it is possible for the neutron shielding and its liner to absorb enough

energy to reduce the damage to the remainder of the cask.
5-33

The seal leak path areas are only calculated at the location of one of the two o-rings typical in casks

(the one that is closest to the interior of the cask). In reality, the o-rings at both locations can

provide containment. For most of the analyses, the opening deflection at the location of the second

o-ring is about half of the deflection at the inner o-ring.

The use of minimum material properties for the closure bolts results in a reduction of bolt clamping

force and an over-estimation of bolt elongation. The specified bolt material (SA-540 Grade B23

Class 5) can have yield strengths more than 50% higher than the values used. Using more realistic

values for bolt material parameters would result in smaller openings.

For soil impacts all of the results are based upon soil properties around Albuquerque, NM. This

desert location has very hard soils (generally not tillable) compared to most of the rest of the

nation. For impacts onto more typical soils even higher velocities would be required to obtain the

damage levels from the rigid target finite element analyses. For impacts onto highway surfaces, all

of the surfaces are assumed to be concrete. Impacts onto asphalt highway surfaces would be less

severe. For impacts onto rock these analyses assumed the rock would absorb none of the impact

energy. In reality, if a spent fuel cask were to impact into solid rock there would be some cracking

and spalling of the rock surface as a result of the impact. This damage to the rock surface implies

that it is absorbing some amount of energy.

Although the puncture data given in this chapter indicate the probability for puncturing a cask with

a wall thickness greater than 1 inch is extremely remote, the risk analyses in this report assume the

truck casks are punctured in 0.1% of the accidents. Even more conservative is the assumption that

the rail casks are punctured in 1% of the rail-coupling impacts and 0.1% of all other impacts.

Scaling the strains in the spent fuel rods calculated for a 100 G impact by the accelerations for more

severe impacts significantly overestimates the rod strains. As the geometry of a spent fuel

assembly changes in the more severe impacts, the deformations become constrained due to limited

space. Once this happens, the strains will no longer increase with increasing load.

5.6 References

[5-1] L. M. Taylo r and D. P. Flana gan, “PRON TO 3D, A Three -Dimension al Trans ient Solid 

Dynam ics Progr am,” SAND8 7-1912, Sandi a Natio nal Labor atories, Albuq uerque, NM,

March 1989. 

[5-2] S. W. Attaw ay, “Upda te of PRONT O 2D and PRONTO 3D Trans ient Solid Dynam ics

Progr am,” SAND9 0-0102, Sandi a Natio nal Labor atories, Albuq uerque, NM,

Novem ber 1990. 

[5-3] V. L. Bergm ann, “Tran sient Dynam ics Analy sis of Plate s and Shell s with PRONT O

3D,” SAND9 1-1182, Sandi a Natio nal Labor atories, Albuq uerque, NM, Septembe r

1991. 

[5-4] J. S. Ludwi gsen and D. J. Ammer man, “Anal ytical Deter mination of Packa ge Respo nse

to Sever e Impac ts,” Proce edings of PATRA M 95, Las Vegas , NV, Decem ber 1995. 

[5-5] D. J. Ammer man, “Benc hmarking of Finit e Eleme nt Codes for Radioact ive Mater ial

Trans portation Packa ges,” in Devel opment, Valid ation, and Appli cation of Inela stic

Metho ds for Struc tural Analy sis and Desig n, PVP-V ol. 343, ASME, New York, NY,

1996. 
5-34

[5-6] D. J. Ammer man, “Effe ct of Closu re Movem ent and O-rin g Prope rties on Leak Rate, ”

Contr act repor t #2390 04, Sandi a Natio nal Labor atories, Albuq uerque, NM, Septe mber

1993. 

[5-7] G. W. Wellm an and R. Salzb renner, “Quas istatic Model ing and Testi ng of Exclu sion

Regio n Barri er Mock- Ups”, SAND9 2-0024, Sandi a Natio nal Labor atories,

Albuq uerque, New Mexic o, March 1992. 

[5-8] Ameri can Socie ty of Mecha nical Engin eers, “Spec ification for Alloy -Steel Bolti ng

Materia ls for Speci al Appli cations,” SA-54 0, ASME, New York, NY, 1998. 

[5-9] H. J. Rack and G. A. Knoro vsky, "An Asses sment of Stress -Strain Data Suita ble for

Finit e-Element Elast ic-Plastic Analy sis of Shipp ing Conta iners," NUREG /CR-0481,

SAND7 7-1872, Sandi a Natio nal Laborator ies, Albuq uerque, NM, Sept. 1978. 

[5-10 ] M. K. Niels en, H. S. Morga n, and R. D. Krieg , “A Pheno menologica l Const itutive

Model for Low Densi ty Polyu rethane Foams ,” SAND8 6-2927, Sandi a Natio nal

Laborator ies, Albuq uerque, NM, April 1987. 

 [5-11 ] Parke r Seal Group , “Park er O-Rin g Handb ook,” Parke r Hanni fin Corpo ration,

Cleve land, OH, 1992, pp. A4-7. 

[5-12 ] L. E. Fisher, et al., “Ship ping Conta iner Respo nse to Sever e Highw ay and Railw ay

Acciden t Condi tions,” NUREG /CR-4829, Lawre nce Liver more Natio nal Labor atory,

Liver more, CA, February 1987. 

[5-13 ] A. Gonza les, “Targ et Effec ts on Packa ge Respo nse: An Exper imental and Analy tical

Evalu ation,” SAND8 6-2275, Sandi a Natio nal Labor atories, Albuq uerque, NM, May

1987. 

[5-14 ] I. G. Waddo ups, “Air Drop Test of Shiel ded Radio active Mater ial Conta iners,”

SAND7 5-0276, Sandi a Natio nal Labor atories, Albuq uerque, NM, Septe mber 1975. 

[5-15 ] L. L. Bonzo n and J. T. Schau mann, “Cont ainer Damag e Corre lation with Impac t

Velocity and Targe t Hardn ess,” IAEA- SR-10/21, Trans port Packa ging for Radio active

Mater ials, IAEA, Vienn a, Austr ia, 1976. 

 [5-16 ] S. F. Shank man, Lette r to R. E. Fronc zak, Assoc iation of Ameri can Railr oads –

Respons es to AAR’s Febru ary 7, 1997 Quest ions, Nucle ar Regul atory Commi ssion,

May 23, 1997. 

[5-17 ] T. L. Sande rs, et al., “A Metho d for Determi ning the Spent -Fuel Contr ibution to

Trans port Cask Conta inment Requi rements,” SAND9 0-2406, Sandi a Natio nal

Labor atories, Albuq uerque, NM, Novem ber 1992. 

[5-18 ] Spent Nucle ar Fuel Disch arges from U.S. React ors, Energ y Infor mation

Admin istration, U.S. Depar tment of Energ y, SR/CN EAF/96-01, 1994. 
5-35

[5-19 ] “Worl d List of Nucle ar Power Plants ,” Nucle ar News, p. 52, March 1999. 

[5-20 ] A. A. Bauer and L. M. Lowry , Nucle ar Techn ology 41, 359 (1978 ).

[5-21 ] G. P. Smith , et al., The Evalu ation and Demon stration of Methods for Impro ved

Nucle ar Fuel Utili zation, DOE.E T/34013-15 , Combu stion Engin eering, Inc., Winds or,

CT, 1994. 

[5-22 ] A. M. Garde , et al., “Effe cts of Hydri de Preci pitate Local ization and Neutr on Fluen ce

on the Ducti lity of Irrad iated Zirco loy-4,” Zirco nium in the Nucle ar Indus try: 11th

Inter national Symp., ASTM STP 1295, Ameri can Socie ty for Testi ng and Mater ials,

1996, p. 407.

[5-23 ] M. G. Balfo ur, et al., “Fina l Repor t, EP80- 16, Hot Cell Exami nation of Zion Fuel

Cycle s 1 Throu gh 4,” WCAP- 10473, Westi nghouse Energ y Syste ms, Pitts burgh PA

15230 , April 1985. 
6-1

6. THERMAL ANALYSIS OF THE GENERIC

CASKS IN A LONG DURATION FIRE

6.1 Introduction

Thermal analyses were performed on the four generic casks defined in Section 4. The analyses

examined two fire environments, a 1000°C extra-regulatory fire environment and an 800°C

regulatory fire environment. Both fires were assumed to be fully engulfing and optically dense.

The analyses were performed with PATRAN/PThermal, a commercial heat transfer code [6-1],

that includes the conduction, convection and radiation heat transfer modes. The casks were

modeled as one-dimensional (1-D) axisymmetric cylinders, including a neutron shield. The heat

that would be released to the cask interior by the decay of radionuclides in the spent fuel that

each cask would be carrying was treated as an internal heat source.

6.2 Generic Casks Modeled

Figures 6.1 through 6.4 present schematic drawings of the four generic casks modeled in these

analyses. The two generic truck casks modeled were a steel-lead-steel cask (Figure 6.1) and a

steel-DU-steel cask (Figure 6.2), where DU refers to depleted uranium. The rail casks modeled

were a steel-lead-steel cask (Figure 6.3) and a monolithic steel cask (Figure 6.4). These casks

have dimensions similar to currently available casks, but have not been optimized for their

thermal properties for any particular fuel load. Figure 6.5 presents a radial cross section at the

center of these generic casks. The dimensions of these four generic casks, including the

thicknesses of the four shells labeled A, B, C, and D in Figure 6.5, are given in Table 6.1. The

maximum number of fuel assemblies assumed to be shipped in each cask is given in Table 6.2.

Figure 6.1 A generic, steel-lead-steel truck cask.

Figure 6.2 A generic, steel-DU-steel truck cask.
6-2

Figure 6.3 A generic, steel-lead-steel rail cask.

Figure 6.4 A generic, monolithic steel rail cask.
6-3

Figure 6.5 Generic wall cross section used in the 1-D axisymmetric, thermal modeling.

Table 6.1 Generic Cask Dimensions (m)

Wall Thicknesses

Cask A BCD

Neutron

Shield

Thickness

Outside

Diameter

Cavity

Diameter

Cask

Length

Steel-Lead-Steel

Truck Cask

0.0127

(0.5”)

0.1397

(5.5”)

0.0254

(1”)

0.006

(0.25”)

0.114

(4.5”)

0.94

(37”)

0.343

(13.5”)

5.207

(205”)

Steel-DU-Steel

Truck Cask

0.0127

(0.5”)

0.0889

(3.5”)

0.0229

(0.9”)

0.006

(0.25”)

0.114

(4.5”)

0.953

(37.5”)

0.457

(18”)

5.08

(200”)

Steel-Lead-Steel

Rail Cask

0.0254

(1”)

0.1143

(4.5”)

0.0508

(2”)

0.006

(0.25”)

0.114

(4.5”)

2.273

(89.5”)

1.651

(65”)

5.08

(200”)

Monolithic Steel

Rail Cask

0.254

(10”)

0.006

(0.25”)

0.114

(4.5”)

2.4

(94.5”)

1.651

(65”)

4.826

(190”)

Table 6.2 Assumed Loading of PWR and BWR Assemblies for the Generic Casks

Truck Casks Rail Casks

Cask Steel-Lead-Steel Steel-DU-Steel Monolithic Steel Steel-Lead-Steel

PWR 1 3 24 24

BWR 2 7 52 52
6-4

6.3 PATRAN/PThermal Model

The thermal effects of a long duration, external fire conditions on the casks were modeled in 1-D

with an axisymmetric model (see Figure 6.5). The simulations were done in two steps. First, a

steady-state simulation of the cask with its internal heat load from the fuel assemblies was done

to obtain initial conditions for the analysis. A transient analysis in the presence of a long

duration fire was then completed.

In the first stage, the neutron shield was assumed to be filled with water. Ambient temperature

was set at 38°C. The internal heat load in each cask, generated by the decay of radionuclides in

the spent fuel as calculated by ORIGEN [6-2], was set to the value presented in Table 6.3. Note

that the generic casks are similar to modern casks designed for ten-year-old, moderate-burn-up

fuel. This heat load was modeled as a flux onto the internal surface of each cask. Heat deposited

in the inner shell of the cask by this heat flux was transferred by conduction in the solid shells of

the cask, by conduction and convection in the water in the cask’s neutron shield compartment,

and by convection [6-3] and radiation in the air surrounding the cask. Thermal radiation was

calculated with the gray-body approximation. In all cases, a cask outer surface emittance of 0.8

and a fire emittance of 0.9, consistent with 10 CFR 71 and at the high end of the normal range of

surface emittances, were assumed. Thermal radiation across the neutron shield interior, when

empty, was calculated using a typical stainless steel surface emittance of 0.5. Conduction and

convection in the neutron shield water was modeled with a convection correlation that provided

an effective value for conductivity in the water [6-4]. This model provided a steady state

temperature profile in the cask characteristic of normal conditions of transport.

Table 6.3 Internal Heat Loads for Each of the Generic Casks for

Three-Year-Old High Burnup Spent Fuel

Fuel Rail Casks Truck Casks

Type

Assembly

Heat Load Monolithic Steel Steel-Lead-Steel Steel-Lead-Steel Steel-DU-Steel

PWR 2796 W 67104 W

(2289 W/m2

)

67104 W

(2190 W/m2)

2796 W

(482 W/m2)

8388 W

(1100 W/m2)

BWR 902.5 W 46930 W

(1600 W/m2

)

46930 W

(1532 W/m2)

1805 W

(312 W/m2)

6318 W

(828 W/m2)

The temperature profile from the steady state calculation was used as a starting point for a

transient calculation for the cask in the presence of an engulfing, optically dense, long duration

fire. In the transient calculation, the water was replaced with air, the ambient temperature was

increased from 38°C to 1000°C over one minute and held at 1000°C for 11 hours. Heat transfer

to the outer surface of the cask from the fire was calculated with convection and radiation,

through the air in the empty neutron shield compartment with conduction and radiation, and

through the cask shells to the interior surface of the cask by conduction. All of the calculations

used PWR decay heat loads, because these loads represent a conservative upper limit for the heat

flux from spent fuel to the cask’s internal surface.
6-5

6.4 Thermal Modeling Results

The PATRAN/PThermal analyses of the four generic casks determined the initial internal and

external temperatures of the cask shell during normal transport conditions and the temperature

response of the casks during a long duration, engulfing, optically dense fire.

6.4.1 Cask Initial Temperature Profiles

The steady state calculations determined the temperature profiles of the casks during the normal

conditions of transport. The temperatures of the internal and external cask surfaces calculated

for normal transport conditions are given in Table 6.4.

Table 6.4 Internal and External, Steady State, Cask Surface Temperatures

Cask Internal External

Steel-Lead-Steel Truck 72°C 69°C

Steel-DU-Steel Truck 113°C 104°C

Monolithic Steel Rail 215°C 193°C

Steel-Lead-Steel Rail 218°C 194°C

These temperatures are calculated for the generic casks that were not optimized for the

postulated thermal loading, and therefore do not meet the surface temperature requirements of

10 CFR 71.43g. However, these temperatures do represent a conservative set of baseline cask

temperatures for the purposes of this analysis.

6.4.2 Thermal Response to a Long Duration, 1000°C Fire

Figure 6.6 presents the time-dependent temperature change of the interior surface of each of the

four generic casks while the cask is exposed to a long-duration, engulfing, optically dense

1000°C fire. Changes in the slopes of these temperature curves occur because of internal phase

transitions in carbon steel (at 770°C) and depleted uranium (at 667°C and 775°C) and the

melting of lead (at 327.5°C).

The times to reach the following three characteristic temperatures are of interest: 350°C where

the rate of thermal degradation of elastomeric seals becomes significant, 750°C where spent fuel

rods can fail by burst rupture, and 1000°C where the cask has come into equilibrium with the

fire. The choice of the seal degradation and rod-burst temperatures is discussed in detail in

Section 7. The times at which the casks reach these temperatures when heated continuously by

an engulfing, optically dense, 1000°C fire are given in Table 6.5. Note that, because of thermal

lags, some cask temperatures would continue to rise if the fire went out at each of these times.

The times required to reach the indicated temperatures at the inside surface of the inner shell, as

shown in Figure 6.6, were used in Section 7.0 to estimate the probability of seal degradation and

rod burst during cask exposure to long duration hydrocarbon fueled fires. The temperature of the

inner surface of the cask body was used as an indicator of seal and rod response to heating in a

fire for several reasons. First, inspection of the results of these calculations indicates that, when
6-6

heated by a fire, temperatures in the lead or depleted uranium gamma shield are similar to,

though usually 10 to 20°C hotter than, the temperature of the cask’s inner surface. Second,

although seal location is dependent on cask design, seal well temperatures are also expected to

closely track cask inner surface temperatures. Thus, because a somewhat low seal degradation

temperature of 350°C was chosen, the uncertainty in the time to reach seal degradation

temperature is expected to be conservative, i. e., shorter than actual. Moreover, inspection of the

probability distributions for fire duration presented in Tables 7.26 and 7.27 indicate, as is

discussed below, that risk estimates will not be very sensitive to this choice. Through similar

arguments, fuel rod bundle temperatures are also expected to closely track the temperature of the

inside surface of the cask, although for “hot” fuel, the inner-fuel-assembly temperatures could be

significantly higher. However, the assumption is made that this temperature should be a

reasonable surrogate for average spent fuel rod temperatures.

There are four characteristic fire duration times of interest in a risk analysis: 10 minutes—the

duration of a typical automobile fire, 30 minutes—the duration of a regulatory fire, 60 minutes—

the typical duration of an experimental pool fire with fuel from one tanker truck, and 400

minutes—the typical duration of an experimental pool fire with fuel from one rail tank car.

Table 6.6 presents the temperatures reached by each of the generic casks at these times in a long

duration 1000°C fire.

0

200

400

600

800

1000

1200

0 2 4 6 8 10 12

Monolithic Rail Cask

Steel-Lead-Steel Rail Cask

Steel-Lead-Steel Truck Cask

Cask Internal Surface Temperature (°C)

Steel-DU-Steel Truck Cask

Time (hours)

Figure 6.6 Internal surface temperature histories of the

generic casks in an 1000°C long duration fire.
6-7

Table 6.5 Time (hours) Required for the Generic Cask Internal Surface to get to the Three

Characteristic Temperatures in a Long Duration Engulfing, Optically Dense, 1000°C Fire.

Temperature Truck Casks Rail Casks

(°C) Steel-Lead-Steel Steel-DU-Steel Steel-Lead-Steel Monolithic Steel

 350 1.04 0.59 1.06 1.37

 750 2.09 1.96 2.91 6.57

1000 5.55 5.32 6.43 >11

Table 6.6 Cask Internal Surface Temperatures (°C) for Four Characteristic Times

in a Long Duration, Engulfing, Optically Dense, 1000°C Fire.

Time Truck Casks Rail Casks

(minutes) Steel-Lead-Steel Steel-DU-Steel Steel-Lead-Steel Monolithic Steel

10 91 139 222 222

30 252 313 275 230

60 337 531 338 300

400 1000 1000 1000 750

6.4.3 Thermal Response to a Long Duration 800°C Fire

The regulatory requirements specify that thermal cask analysis be done with an 800°C fire. The

response of the generic casks to an 800°C fire is given here for comparison. Table 6.7 lists the

time required for the interior surface of each generic cask to climb to 350°C and 750°C in the

800°C fire and Table 6.8 presents the interior surface temperatures reached in that fire at each of

the four characteristic times.

Table 6.7 Time (hours) Required for the Generic Cask Internal Surface to get to the Two

Characteristic Temperatures in a Long Duration Engulfing, Optically Dense, 800°C Fire.

Temperature Truck Casks Rail Casks

(°C) Steel-Lead-Steel Steel-DU-Steel Steel-Lead-Steel Monolithic Steel

350 1.77 1.06 1.69 2.37

750 4.88 5.07 6.32 >11

Table 6.8 Cask Internal Surface Temperatures for Four Characteristic Times

in a Long Duration Engulfing, Optically Dense, 800°C Fire.

Time Truck Casks Rail Casks

(minutes) Steel-Lead-Steel Steel-DU-Steel Steel-Lead-Steel Monolithic Steel

10 79 123 220 216

30 161 211 256 231

60 289 341 314 265

400 793 775 766 562
6-8

6.5 Sensitivity Discussion

Three-year high burn-up spent fuel was used for the thermal calculations in contrast with the tenyear average burn-up fuel that will typically be transported in the casks of the design types

considered. The conservatism introduced by this assumption is large. For example, thermal

loads for a three-year high-burn-up PWR fuel assemblies are on the order of 2.8 kilowatts, while

the ten-year average-burn-up fuel assembly produces less than 600 watts of decay heat. With

thermal calculations, the three-year high burn-up spent-fuel assumption leads to conservative risk

estimates, because more rapid heating means that seal degradation and rod burst temperatures

can be reached with fires of shorter duration.

While conservative, the calculations in the report do not include some secondary effects that

would need to be considered if the cask designs were to be used for transport of three-year highburn-up fuel. For example, the use of the cask inner-surface temperature to estimate rod burstrupture temperature would not be acceptable with three-year spent fuel. This is because the

overall temperature increase from the cask inner surface to highest fuel rod temperature could

reach several hundred degrees Celsius for multiple three-year assemblies. For the ten-year

average burn-up fuel, the temperature increase from the cask inner surface to the center of the

fuel assemblies is typically less than 100°C [6-5]. Inspection of the calculations used in this

section demonstrated that the use of the three-year high burn-up fuel in the risk calculations

adequately compensates for the neglect of the temperature increase between the cask inner

surface and the fuel rods for ten-year average burn-up fuel.

In an additional conservatism, the phase change of the neutron shield material at the outside of

the cask is also neglected. The neutron shield can be water or a solid hydrogenous material. For

this analysis water is assumed. The neutron shield material thermal properties are changed in the

calculation instantaneously at the start of the fire from water to air. In the calculations, when the

neutron shield is voided instantaneously, the inner surface of the neutron shield rapidly reaches

fire temperature within one to two minutes. When the liquid remains, the increase to boiling

temperature and the boiling of the water limits the temperature increase of the cask interior to

100°C for several minutes, depending on the amount of water left in the collision-damaged

shield. For example, for a full shield on the SDUST cask, the boiling of water would limit the

shield-inner-surface temperature to near 100°C for about 20 minutes at the start of a fire. Similar

conservative results would be obtained if a solid neutron shield material were to be used.

To estimate the conservatism introduced with the three-year spent fuel assumption, an additional

1000°C long-duration fire calculation was performed for the most rapidly responding cask, the

steel-DU-steel truck cask. The time to reach the seal degradation temperature of 350°C, given in

Table 6.5 for three-year high burnup fuel, increased from 0.59 hours to 0.86 hours. Similarly,

the time to reach the rod burst temperature of 750°C increased from 1.96 to 2.68 hours. This

indicates that time-to-temperature increases on the order of 30 to 50 percent are anticipated if

ten-year average burn-up fuel is used in calculations rather than three-year high burnup fuel. The

effect of this change on overall risk probabilities is much smaller, however, because for the

assumed fuel, times-to-failure already fall into the low-probability tail of the fire duration

probability distribution curves (see Tables 7.26 and 7.27). Increasing these times simply places

the probabilities further out on the tail of these distribution curves.
6-9

6.6 Summary

Thermal analysis of the generic casks provided input for risk analysis of characteristic times at

which the casks may undergo elastomeric seal failure or rod burst/rupture. This analysis was

conservative for the following reasons:

• The casks, although similar in dimension to casks available from manufacturers, were not

optimized for their thermal response.

• The analysis assumed that the casks were uniformly engulfed in the fire.

• The fire temperature was assumed to be 1000°C.

• The water in the neutron shield was immediately replaced by air at the onset of the long

duration fire to simulate fluid loss as a result of puncture of the neutron shield.

6.7 References

[6-1] PATRAN Thermal User Guide and Model Description Manual

(http://www.macsch.com/support/support.html).

[6-2] A. G. Croff, “ORIGEN2: A Versatile Computer Code for Calculating the Nuclide

Compositions and Characteristics of Nuclear Materials,” Nuclear Technology 62, p. 335

(1983).

[6-3] B. V. Karlekar, and R. M. Desmond, Engineering Heat Transfer, West Publishing

Co., 1977.

[6-4] G. D. Raithby, and K. G. T. Hollands, “A General Method of Obtaining Approximate

Solutions to Laminar and Turbulent Free Convection Problems,” Advances in Heat

Transfer, Academic Press, NY, 1974.

[6-5] G. W. Thomas and R. W. Carlson, “Evaluation of the Use of Homogeneous Fuel

Assemblies in the Thermal Analysis of Spent Fuel Storage Casks,” UCRL-ID-134567,

Lawrence Livermore National Laboratory, Livermore, CA, July, 1999.
7-1

7. SOURCE TERMS AND SOURCE TERM PROBABILITIES

7.1 Truck and Train Accident Scenarios

7.1.1 Event Trees

To estimate accident source terms, the mechanical and thermal environments that a cask might

experience during truck and train accidents must be estimated. Because all of the variations of

all of the accidents in the historic record plus all plausible accidents not yet observed constitutes

far too many accidents to examine individually, a smaller representative set of accidents is

formulated and the frequencies of occurrence of each representative accident are estimated.

Representative sets of accidents can be developed by constructing accident event trees. Event

trees for truck and train accidents were developed during the course of the Modal Study [7-1].

Figures 7.1 and 7.2 present these event trees. Inspection of these figures shows that an event tree

depicts an accident scenario as a sequence of events and also gives the probability of each event

in the sequence. Thus, a path on the event tree constitutes a unique sequence of events and the

product of all of the probabilities of the events on a path (branch point probabilities) gives the

probability of that accident scenario. For example, in the truck accident event tree shown in

Figure 7.1, a truck accident that leads to a collision with a pedestrian is depicted by the

uppermost branches of the tree, specifically the branches labeled “Collision,” “Non-fixed object,”

and “Cones, animals, pedestrians.” Because the probabilities of these branches are 0.7412,

0.8805, and 0.0521, the chance that this accident scenario occurs (expressed as a percent), given

that any truck accident has been initiated, is 3.4002 = 100 [(0.7412)(0.8805)(0.0521)], where

3.4002 is called the path (scenario) probability and gives the fraction of all truck accidents that

follow this path. Because the probability of any accident occurring is not included in this

product, the resulting fraction is a conditional probability, that is conditional on the occurrence of

an accident of any severity and type. Further, because of the way the tree is constructed, each

probability on the tree is conditional on the branch point probabilities that precede it and many

branch point probabilities are represented by far more significant figures than is warranted by the

underlying data because the sum of the branch point probabilities for any single branch of the

tree must sum exactly to one.

Because each event tree path (accident scenario) defines a set of accident conditions (mechanical

and/or thermal environments), the impact of each scenario on a radioactive material

transportation cask can be estimated by hypothetically subjecting the cask to the conditions that

characterize the end point of the path. The Modal Study performed such an analysis for each

path on their truck and train accident trees. On these trees, paths that seemed capable of failing a

Type B spent fuel cask are indicated by placing an asterisk (*) after the path number (path

Accident Index). Thus, the Modal Study analyses found, for example, that collisions of a truck

with a train might generate mechanical loads large enough to fail a Type B spent fuel cask

thereby allowing radioactivity to be released from the cask to the environment. Accordingly, the

truck accident scenario, denoted by the Accident Index 5, which has a conditional chance of

occurring of 0.7701 percent (conditional on the occurrence of some truck accident), is tagged

with an asterisk.
7-2

Accident Type Speed Distribution Object/Surface Probability (%) Index

Cones, animals, pedestrians 3.4002 1

0.0521

Motorcycle 0.8093 2

0.0124

Automobile 43.1517 3

Non-fixed object Level Ground 0.6612

0.8805 Truck, bus 13.3201 4

0.2041

Train 0.7701 5*

0.0118

Other 3.8113 6

0.0584

Water 0.1039 7*

0.20339

Collision Railbed, Roadbed 0.3986 8*

0.7412 0.77965

Bridge Railing Clay, Silt 0.0079 9*

0.0577 0.015486

Hard Soil, Soft Rock 0.0006 10*

0.001262

Hard Rock 0.0001 11*

0.000199

Small 0.0299 12*

Column 0.8289

On road fixed object Level Ground 0.9688 Large 0.0062 13*

0.1195 0.0042 0.1711

Abutment 0.0011 14*

0.0382

Level Ground Concrete object 0.0850 15

0.0096

Level Ground Barrier, wall, post 4.0079 16

0.4525

Truck Level Ground Signs 0.5111 17

Accident 0.0577

Level Ground Curb, culvert 3.7050 18

0.4183

Clay, Silt 2.3063 19*

0.91370

Into Slope Hard Soil, Soft Rock 0.1881 20*

0.2789 0.07454

Hard Rock 0.0297 21*

0.01176

Clay, Silt 1.3192 22*

0.5654

Hard Soil, Soft Rock 0.1076 23*

Off road Over Embankment 0.0461

0.3497 0.2578 Hard Rock 0.0170 24*

0.007277

Drainage ditch 0.8894 25

0.381223

Non-collision Level Ground Trees 0.9412 26

0.2588 0.1040

Level Ground Other 3.2517 27

0.3593

Level Ground Overturn 8.3493 28

Impact roadbed 0.6046

0.5336 Level Ground Jackknife 5.4603 29

0.3954

Other mechanical 2.0497 30

0.0792

Fire only 0.9705 31

0.0375

Figure 7.1 Modal Study truck accident event tree.
7-3

Accident Type Collision Outcome Speed Distribution Impact Surface Probability (%) Index

Highway Grade Crossing 3.0400 1

0.0304

Remain on Track 8.5878 2

0.6404

Water 0.1615 3*

0.20339

Clay, Silt 0.0122 4*

0.015486

Collision Over Bridge Hard Soil, Soft Rock, Concrete 0.0010 5*

0.1341 0.0097 0.001262

Hard Rock 0.0002 6*

0.000199

Railbed, Roadbed 0.6192 7*

Collision Derailments 0.77965

0.3596 Drainage ditch 0.3433 8

0.3812

Clay, Silt 0.5092 9*

Over Embankment 0.5654

0.0110 Hard Soil, Soft Rock 0.0415 10*

0.04610

Hard Rock 0.0066 11*

Train 0.007277

Accident Clay, Silt 1.4437 12*

0.91370

All Derailments Into Slope Hard Soil, Soft Rock 0.1178 13*

0.818722 0.0193 0.07454

Hard Rock 0.0186 14*

0.01176

Small 0.0465 15*

Column 0.8289

0.0034 Large 0.0096 16*

Into Structure 0.1711

0.2016 Abutment 0.0017 17*

0.0001

Derailment Other 16.4477 18

0.7705 0.9965

Locomotive 3.2517 19

0.2305

Collision Car 10.0148 20

0.2272 0.7099

Rollover Coupler 0.8408 21*

0.7584 0.0596

Roadbed 15.9981 22

Non-Collision 0.3334

0.7728 Earth 31.9865 23

0.6666

Other 6.500 24

0.0650

Figure 7.2 Modal Study train accident event tree.

The suitability of an event tree depends on whether it depicts a suitable representative set of

accidents and on the whether the data used to estimate the event tree branch point probabilities,

and thus the probability of occurrence of each accident scenario, are still current. Inspection of

Figures 7.1 and 7.2 shows that early branches on these event trees define accident conditions

(e.g., on the truck event tree, a collision with a non-fixed object) while later branches provide

information that specifies the accident speed distribution (e.g., the branch labeled “Over

Embankment” on the train event tree) and the object (e.g., column or abutment on both trees) or

surface (e.g., hard rock, clay/silt on both trees) that is struck. Inspection of these trees suggests

that each tree depicts a comprehensive set of credible accidents (i.e., all probable accident

scenarios appear to have been included and no unusually severe but credible accident scenarios
7-4

appear to have been omitted). Accordingly, the structures of both trees seem appropriate.

Therefore, the suitability of these trees for use in this study depends principally on the currency

of the branch point probabilities. For each tree, this was investigated by comparing tree branch

point probabilities to similar but more recent data.

7.1.2 Route Wayside Surface Characteristics

The occurrence frequencies of route wayside surfaces (clay/silt, hard soil/soft rock, hard rock),

presented in the Modal Study were developed by performing visual surveys of two segments of

California interstate highways (Interstate 80 from Davis, California, to the Nevada border and

Interstate 5 from the San Diego County/Orange County line to the Los Angeles County/Kern

County line). Each survey classified visible wayside surfaces as hard rock, untilled soil (which

was equated to hard soil/soft rock), and tilled soil (which was equated to clay/silt). After

comparing the results of these visual surveys to data available from agricultural soil surveys and

geological highway maps, Modal Study analysts chose the following values for wayside route

surface frequencies of occurrence: clay/silt, 0.9137; hard soil/soft rock, 0.07454, and hard rock,

0.01176. Moreover, although developed by survey of interstate highway wayside surfaces,

because rail wayside surface data was not available, as the “Into Slope” branches on Figures 7.1

and 7.2 show, these surface occurrence frequencies were used for both the truck and the train

event trees.

Because the finite element cask impact calculations described in Section 5 showed that only

impact at a high speed onto an essentially unyielding surface (e.g., a large monolithic chunk of

rock that doesn’t fragment easily) was likely to cause the seal of a Type B spent fuel cask to leak,

the frequency of occurrence of wayside hard rock becomes an unusually important branch point

probability. But for high-speed impacts, shallow layers of soft soil will easily be penetrated

without significant expenditure of kinetic energy. Therefore, if only high-speed impacts onto

hard rock are likely to cause a spent fuel cask seal to leak, then not only is visible hard rock of

concern, but so is hard rock that lies beneath but close to the soil surface.

7.1.2.1 U.S. Geologic Survey Data

The amount of hard rock (expressed as a percent of the route length) traversed by the two

segments of I-80 and I-5 surveyed for the Modal Study was reestimated using data developed by

the U.S. Geologic Survey (USGS) [7-2]. To do this, a digital (electronic) USGS map of the

surface geology of the continental United States was analyzed using a Geographic Information

System (GIS). The analysis identified the number of kilometers of each interstate segment that

traverse plutonic and intrusive rock formations, the two hardest rock-types depicted on the USGS

map. Table 7.1 compares the Modal Study visual estimates of the percentage of each route

segment length that is hard rock to the results developed by GIS analysis of the USGS data.

The USGS data in the table suggest that substantially larger portions of the two interstate

segments traverse hard rock than was found by the Modal Study visual surveys of these two route

segments. However, because the USGS map does not indicate the depth of the soil layers that lie

over these hard rock layers, it is not possible to decide whether a cask impacting the overlying

soil would penetrate to and be damaged by impacting the underlying hard rock layer.
7-5

Table 7.1 Wayside Hard Rock on Modal Study Segments of I-5 and I-80

Route Segment Hard Rock (%)

Interstate 5

 Modal Study Visual Survey 0.0

 GIS Analysis of USGS Data 5.7

Interstate 80

 Modal Study Visual Survey 2.4

 GIS Analysis of USGS Data 22.9

7.1.2.2 U.S. Agricultural Department Data

Because the USGS data could not identify overlying soil layers thick enough to absorb most of

the cask impact energy before the layer was penetrated, the GIS analysis performed using the

USGS data was repeated using a digitized U.S. Agricultural Department map [7-3] that showed

the locations of coherent, monolithic rock formations in the continental United States that must

be removed by blasting (i.e., hard rock) and rock that can be removed by a backhoe because it

fragments relatively easily (i.e., soft rock), and also specified the amount of dirt that lies above

each type of rock. In addition, the map showed the locations of surface soil layers of various

depths (thicknesses) that contained rocks with average diameters (drock) larger than some

reference diameters (e.g., drock ≥ 3 inches, drock ≥ 10 inches). Given the information about the

character of near-surface soil and rock layers provided by the Agricultural Department map, the

following definitions were adopted for hard rock, soft rock, hard soil, and soft soil.

Hard Rock: Rock that must be removed by blasting that lies on average within 24 inches of

the route wayside surface (minimum distance to the rock layer ≤ 12 inches; maximum

distance to the rock layer ≤ 36 inches).

Soft Rock: Rock that can be removed by a backhoe that lies on average within 24 inches of

the route wayside surface (minimum distance to the rock layer ≤ 12 inches; maximum

distance to the rock layer ≤ 36 inches).

Hard Soil: Soil that contains ≥ 10 percent rocks with average diameters ≥ 3 inches.

Soft Soil: Everything else.

Four observations about these definitions are in order. First, rock layers that lie more than three

feet below the surface are not of concern because penetration by the cask of three feet of surface

soil will consume so much of the cask’s impact energy that impact onto a rock layer that lies

below this soil will be unlikely to cause the cask seal to leak. Second, a layer of soil that

contains rocks of a significant size (e.g., diameters ≥ 3 inches) that occupy a significant fraction

(e.g., ≥ 10 percent) of the volume of the layer will significantly increase the effective hardness of

the layer. Third, the preceding definitions mean that any wayside surface that isn’t hard or soft

rock will be hard soil if the surface soil layer contains ≥ 10 percent rocks with average diameters
7-6

≥ 3 inches; if it does not, it will be soft soil. And fourth, implicit in the definition of hard soil is

the assumption that a thin layer of surface soil that contains rocks is unlikely to lie over a thick

layer of rock-free soil. Thus, if the surface soil layer is thin, then the wayside surface character

will be determined by the near-surface underlying rock layer, and if the surface layer is not thin,

then its characteristics will be determined by the characteristics of the rocks that it contains.

The wayside surface characteristics of the two interstate highway segments surveyed for the

Modal Study were reanalyzed using GIS techniques to interrogate the digitized U.S. Agricultural

Department map. Table 7.2 presents the results (expressed as percentages) obtained for the two

California interstate segments and compares them to the results obtained by the visual surveys

conducted for the Modal Study. Inspection of Table 7.2 again suggests that the Modal Study

visual survey of wayside interstate highway surfaces significantly underestimated the presence of

hard rock, soft rock, and hard soil layers that lie close enough to the surface of the ground so that

cask penetration to and/or impact onto these layers will determine the extent of cask damage

during collision accident scenarios.

Table 7.2 Wayside Surfaces on Modal Study Segments of I-5 and I-80

I-80 I-5

Route Segment Modal Study US Ag. Data Modal Study US Ag. Data

Hard Rock 2.4 17.4 0.0 0.0

Hard Soil/Soft Rock 7.4 7.2

Soft Rock 13.4 20.3

Hard (rocky) Soil 21.0 0.0

Soft Soil 90.2 48.2 92.9 79.7

7.1.2.3 New Route Wayside Surface Occurrence Frequencies

Because of the importance of impacts onto hard rock and because the visual surveys of interstate

wayside surfaces conducted for the Modal Study appeared to significantly underestimate surface

or near-surface hard rock layers, new wayside surface occurrence frequencies were developed for

the four illustrative real truck and rail routes described in Section 8.3 (Crystal River to Hanford,

Maine Yankee to Skull Valley, Maine Yankee to the Savannah River Site, and Kewaunee to the

Savannah River Site) by GIS interrogation of the digitized U.S. Agricultural Department map.

Table 7.3 presents the results of these GIS analyses.

Finally, in order to be somewhat conservative with respect to the wayside occurrence of hard

rock and soft rock/hard soil, the average fractional frequencies of occurrence of hard rock and

soft rock/hard soil presented in Table 7.3, rounded up to the next integer, were chosen for use in

this study, and the frequency of occurrence of soft soil was calculated by subtraction of the sum

of these two occurrence frequencies from 1.0. Table 7.4 presents the frequencies of occurrence

obtained by this procedure.
7-7

Table 7.3 Wayside Surface Characteristics for Three Illustrative Shipping Routes

Route

Hard

Rock

Soft

Rock

Hard

(Rocky) Soil

Truck

Crystal River to Hanford 2.1% 4.0% 2.9%

Maine Yankee to Savannah River Site 5.4% 0.0% 6.9%

Kewaunee to Savannah River Site 2.7% 0.0% 0.9%

Rail

Crystal River to Hanford 2.5% 1.9% 3.9%

Maine Yankee to Savannah River Site 2.8% 0.0% 2.5%

Kewaunee to Savannah River Site 0.3% 0.0% 1.4%

Table 7.4 Fractional Occurrence Frequencies for Route Wayside Surfaces

Selected for Use in This Study

Mode Clay/Silt Hard Soil/Soft Rock Hard Rock

Truck 0.91 0.05 0.04

Rail 0.91 0.06 0.03

7.1.3 Truck Accident Data

The Modal Study truck accident event tree was constructed using Bureau of Motor Carrier Safety

(BMCS) accident data for the years 1973 through 1983 for all trucks (no accidents were

discarded based on truck size) and all types of roads (i.e., city streets, county roads, state

highways, interstate highways) [7-4]. The frequency with which various roadside structures

(e.g., bridge railings, columns, abutments, barriers, and signs) are struck during collisions was

developed from California Department of Transportation reports for the years 1975 through

1983. The sizes of columns and abutments next to highways, a distribution of highway bridge

heights and of the surfaces below highway bridges were all developed during the Modal Study by

counting these features while conducting the two surveys of segments of Interstate Highways 5

and 80.

Because the Modal Study truck event tree is based on data that is now more than 15 years old,

that data was compared to more recent accident data developed by Clauss, et al. [7-5]. The data

developed by Clauss, et al. was drawn from two databases, the TIFA (Trucks Involved in Fatal

Accidents) file maintained by the University of Michigan Transportation Research Institute, and

the GES (General Estimates System) file maintained by the National Highway Traffic Safety

Administration. TIFA file entries report data for medium and heavy duty truck accidents that

occurred on U.S. highways and caused fatalities. GES file entries report data extracted from
7-8

police reports for fatal and non-fatal accidents. Clauss, et al. used TIFA file data for the years

1980 through 1990, and GES file data for the years 1988 through 1990.

Table 7.5 compares the conditional probabilities of occurrence of Modal Study truck accident

scenarios to estimates of the probabilities of occurrence of the same type of accident drawn from

the study of Clauss, et al. Inspection of Table 7.5 shows that Modal Study conditional accident

probabilities are similar to TIFA and GES accident probabilities, usually differing from the TIFA

or GES result by about a factor of two. As the Modal Study examined all truck accidents (both

fatal and non-fatal) without any restriction on truck size, while the TIFA and GES data excludes

small truck accidents, the fact that the probabilities agree to about a factor of two suggests that

truck accidents that occurred during the 1980s are not substantially different in character from

those that occurred during the late 1970s and early 1980s. Thus, the Modal Study conditional

probabilities would seem to still be representative of current truck accidents. Accordingly, it was

concluded that the structure of the tree (set of scenarios embedded in the tree) reasonably

depicted the variety of possible truck accidents and did not omit important accident branches.

Table 7.5 Conditional Probabilities of Occurrence

of Various Truck Accident Scenarios (%)

Scenario/Accident

Modal

Study

TIFA

(fatal) GES (all) GES (fatal)

Collision Scenarios

Truck + Bus

Truck + Tanker

13.32

6.13 6.65 7.90

Car 43.15 68.83 66.05 74.88

Train 0.77 0.57 0.18 0.42

Water

Immersion

0.10

0.20

Hard Objecta 0.81 2.04 1.94 0.51

Soft Objectb 4.93 2.59 7.46 0.43

Non-Fixed Object 7.21 9.67 6.57 4.94

Non-Collision Scenarios

Overturn

Rollover

8.35

8.17 4.48 10.03

Fire 0.97 1.80 0.46 0.39

a. For Modal Study, sum of Hard Soil, Soft Rock, Hard Rock, and Columns and Abutments.

b. For Modal Study, sum of Clay, Silt, Railbed, Roadbed, and Drainage Ditch.

Both the Modal Study and the study of Clauss, et al. developed estimates of the probability that a

truck collision would initiate a fire. The Modal Study developed estimates of the fractions

(expressed as percentages) of various types of truck collisions (e.g., collision with a car) that

initiated fires. The study of Clauss, et al. developed estimates of the fractions (expressed as

percentages) of all truck accidents that were collisions with trucks, cars, tankers, or other objects

that also caused both fires and a fatality. Clauss, et al. also found that 1.7 percent of all fatal

truck collisions led to fires. Therefore, multiplication of the results of Clauss, et al. for fatal
7-9

collisions with cars, or trucks and tankers, or other objects that initiate fires and cause a fatality

by 1.7 percent (e.g., for truck collisions with cars, 37.5 × 0.017 = 0.6) yields a result directly

comparable with the results given in the Modal Study. Table 7.6 presents and compares these

estimates. Inspection of Table 7.6 shows that the Modal Study results and those of Clauss, et al.

differ by factors of two, which suggests that the Modal Study results are most likely still

representative.

Table 7.6 Truck Accidents that Initiate Fires (Percentages)

Clauss, et al. Modal Study

Fraction All Fatal Collisions

that Initiate Fires that

Impact Listed Object (%)

Fraction Accidents of this

Type that Initiate Fires (%)

Fraction Accidents of this

Type that Initiate Fires (%)

Collision with

 Car 37.5 0.6 0.3

 Truck, Tankers

 Truck

 Tanker

24.0

22.1

 1.9

0.4

 0.37

 0.03

 0.8

 Other Objects 38.6 0.7 1.3

Non-Collisions

 Ran off road 1.1

 Overturns 1.2

 Other 13.0

Finally, weighted summation of the Modal Study results in Table 7.6 using the probabilities of

occurrence of each accident type as given in Figure 7.1 shows that, in agreement with Clauss, et

al., 1.8 percent of all of the truck accidents examined by the Modal Study initiate fires, where

1.8 = 0.432(0.3) + 0.132(0.8) + 0.177(1.3) + 0.091(1.1) + 0.083(1.2) + 0.085(13.0)

Accordingly, as Figure 7.3 shows, the Modal Study truck accident event tree was used in this

study with only one modification, replacement of the Modal Study wayside route surface

frequencies of occurrence, that were developed by visual surveys of interstate highway segments,

by the frequencies developed by GIS analysis of three representative real spent fuel highway

transportation routes using U.S. Agricultural Department data.

7.1.4 Train Accident Data

The Modal Study train accidents event tree was constructed using data published in Federal

Railroad Administration Accident/Incident Bulletins for the years 1975 through 1982 [7-6].

Because no rail line wayside surface data were available and because rail and highway routes

were believed to traverse similar terrain [7-7], the Modal Study used the results of the survey of

California Interstates 5 and 80 to specify the branch point probabilities for the train derailment

accident branches labeled “Over Bridge,” “Over Embankment,” and “Into Slope,” and also for

the occurrence frequencies of the impact surfaces “Water,” “Clay, Silt,” “Hard Soil, Soft Rock,

Concrete,” “Hard Rock,” “Railbed, Roadbed,” and “Drainage Ditch.” In addition, although train

accident experts stated [7-8] that most train derailments leave the derailed cars upright or tipped
7-10

Accident Type Surface Probability (%) Index

Cones, animals, pedestrians 3.4002 1

0.0521

Motorcycle 0.8093 2

Non-fixed object 0.0124

0.8805 Automobile 43.1517 3

0.6612

Truck, bus 13.3201 4

0.2041

Train 0.7701 5*

0.0118

Other 3.8113 6

0.0584

Water 0.1039 7*

0.20339

Collision Railbed, Roadbed 0.3986 8*

0.7412 0.77965

Bridge Railing Clay, Silt 0.0079 9*

0.0577 0.015434

Hard Soil, Soft Rock 0.0004 10*

0.000848

Hard rock 0.0003 11*

0.000678

Small 0.0299 12*

Column 0.8289

On road fixed object Column, abutment 0.9688 Large 0.0062 13*

0.1195 0.0042 0.1711

Abutment 0.0011 14*

0.0382

Concrete Object 0.0850 15

0.0096

Barrier, wall, post 4.0079 16

0.4525

Truck Signs 0.5111 17

Accident 0.0577

Curb, culvert 3.7050 18

0.4183

Clay, Silt 2.2969 19*

0.91

Into Slope Hard Soil, Soft Rock 0.1262 20*

0.2789 0.05

Hard Rock 0.1010 21*

0.04

Clay, silt 1.3138 22*

 0.56309

Hard Soil, Soft Rock 0.0722 23*

Off road Over Embankment 0.03094

0.3497 0.2578 Hard Rock 0.0578 24*

 0.02475

Drainage Ditch 0.8894 25

 0.38122

Non-collision Trees 0.9412 26

0.2588 0.1040

Other 3.2517 27

0.3593

Overturn 8.3493 28

Impact roadbed 0.6046

0.5336 Jackknife 5.4603 29

0.3954

Other mechanical 2.0497 30

0.0792

Fire only 0.9705 31

0.0375

Figure 7.3 Modified Modal Study truck accident event tree.
7-11

over but only slightly damaged, the Modal Study train accident event tree does not divide

derailment accidents into minor derailments (those where the derailed cars remain upright or

simply tip over) and major derailments (those where at least some of the derailed cars are

severely damaged). Lastly, the Modal Study train accident event tree does not contain a branch

for fire-only accidents (i.e., fires not initiated by collisions or derailments).

Rail accident data for the years 1988 through 1995 were reviewed for this study by Department

of Transportation (DOT) Volpe Center staff. Table 7.7 compares the conditional occurrence

probabilities developed by the Modal Study for train accidents to those developed by the DOT

Volpe Center. Inspection of Table 7.7 shows that train accident scenario probabilities

constructed from recent data generally differ from the probabilities constructed during the Modal

Study by factors of two or less. Inspection of the Modal Study train accident event tree suggests

that the following three derailment paths probably lead only to minor damage: (1) derailments

that lead to impacts into structures other than columns or abutments, (2) rollover derailments that

do not lead to additional collisions, and (3) rollover derailments where the cars that roll over

bump into other cars or locomotives and that the fraction of all derailments that these paths

account for is 0.9490, where

0.9490 = (0.2016)(0.9965) + (0.7584)(0.2272)(0.2305+0.7095) + (0.7584)(0.7728)

Now, because (1) this fraction agrees well with the Volpe Center estimate of 0.9782 for the

frequency of occurrence of minor derailments, (2) the paths that contribute to this fraction were

all judged in the Modal Study to generate minor accidents, and (3) Table 7.7 shows that recent

train accident data are consistent with the data developed by the Modal Study, as Figure 7.4

shows, the Modal Study train accident tree is used with only two modifications. First, the Modal

Study wayside route surface frequencies of occurrence, that were developed by visual surveys of

Interstate Highway segments, were replaced by the frequencies developed by GIS analysis of

Table 7.7 Conditional Probabilities of Occurrence of

Various Train Accident Scenarios (%)

Scenario/Accident Modal Study DOT Volpe Center

Grade Crossing 0.0304 0.1298

Collision

 Remain on Track

 Collision Derailment

 0.1341

 0.6404

 0.3596

 0.0875

 0.4429

 0.5162

Derailment

 Minor Damage

 Severe Damage

 0.7705 0.6511

 0.9782

 0.0218

Other

 Fire/Explosion

 Obstruction/Other

 0.0650 0.1315

 0.0147

 0.1168
7-12

Accident Type Collision Outcome Speed Distribution Impact Surface Probability (%) Index

Highway Grade Crossing 3.0400 1

0.0304

Remain on Track 8.5878 2

0.6404

Water 0.1615 3*

0.20339

Clay, Silt 0.0121 4*

0.015433

Collision Over Bridge Hard Soil, Soft Rock, Concrete 0.0008 5*

0.1341 0.0097 0.001018

Hard Rock 0.0005 6*

0.000509

Railbed, Roadbed 0.6192 7*

Collision Derailments 0.77965

0.3596 Drainage Ditch 0.3433 8

0.3812

Clay, Silt 0.5071 9*

Over Embankment 0.5631

0.0110 Hard Soil, Soft Rock 0.0334 10*

0.03713

Hard Rock 0.0168 11*

Train 0.01857

Accident Clay, Silt 1.4379 12*

0.91

All Derailments Into Slope Hard Soil, Soft Rock 0.0948 13*

0.818722 0.0193 0.06

Hard Rock 0.0186 14*

0.03

Small 0.0465 15*

Column 0.8289

0.0034 Large 0.0096 16*

Into Structure 0.1711

0.2016 Abutment 0.0017 17*

0.0001

Derailment Other 16.4477 18

0.7705 0.9965

Locomotive 3.2517 19

0.2305

Collision Car 10.0148 20

0.2272 0.7099

Rollover Coupler 0.8408 21*

0.7584 0.596

Roadbed 15.9981 22

Non-Collision 0.3334

0.7728 Earth 31.9865 23

0.6666

Fire only 0.7300 24

0.0073

Obstruction, Other 5.7700 25

0.0577

Figure 7.4 Modified Modal Study train accident event tree.

three representative real spent fuel rail transportation routes using U.S. Agricultural Department

data; and second, consistent with Volpe Center results, the first-level branch on the Modal Study

train event designated “Other” that has an occurrence probability of 0.0650, is split into a “Fire

only” branch and an “Obstruction, Other” branch that have respectively the following occurrence

probabilities:

Fire only 0.0073 = (0.0650)(0.0147/0.1315)

Obstruction, Other 0.0577 = (0.0650)(0.1168/0.1315)
7-13

7.2 Source Term and Source Term Probability Expressions

Type B spent fuel trans portation casks are massi ve, extre mely stron g struc tures delib erately

designe d to withs tand large mecha nical and/o r therm al loads witho ut losin g conta inment

integri ty. Never theless, altho ugh unlik ely, it is possi ble that a truck or a train that is carry ing a

Type B spent fuel cask could be invol ved in an accid ent so sever e that both the cask and at least 

some of the spent fuel rods in the cask may fail. Were this to happe n, radio active speci es would 

be relea sed from the spent fuel into the cask inter ior and some of these speci es could be

transporte d from the cask inter ior throu gh the cask leak to the envir onment.

To estim ate the risks assoc iated with accid ents that might occur durin g the trans port of spent fuel

by truck or train , estim ates of the magni tude of the radio active relea ses that might be cause d by

sever e trans portation accid ents and of the proba bility of occur rence of these relea ses must be

develop ed for three broad class es of trans portation accid ents: fires withou t colli sions, colli sions

witho ut fires , and colli sions that lead to fires .

7.2.1 RADTRAN Risk Equations

By defin ition, risk is the produ ct of the magni tude (M) of an undes irable accid ent conse quence

and its proba bility of occur rence (P). Thus, risk = P×M where M is calcu lated using a

trans portation conse quence code, for examp le RADTR AN [7-9, 7-10] , and is a stron g funct ion

of the acciden t sourc e term, the preva iling meteo rology at the time of the hypot hesized accid ent,

the popul ation that might be expos ed to radia tion as a resul t of the accid ent, and the effec tiveness

of any actio ns taken to avoid radia tion expos ures, for examp le, evacu ation and/o r reloc ation of

popul ation, and decon tamination , tempo rary inter diction, and/o r conde mnation of conta minated

prope rty. The meteo rological, popul ation, and emerg ency respo nse input requi red by the

RADTRAN code are discu ssed in Secti ons 3.4.3 .3, 3.4.1 .4, and 3.4.3 .2. This secti on deriv es

expre ssions for accid ent sourc e terms and for their proba bilities of occur rence. Value s for the

param eters in these expre ssions are develop ed in subse quent secti ons.

7.2.2 Accident Source Terms

Accid ent sourc e terms (STjk) depen d on the accid ent scena rio (j) and on the cask (k) invol ved in

the accid ent. Here they are calcu lated as the product of the inven tory of each radio nuclide (i) in

the spent fuel being carri ed in the trans portation cask and two relea se fract ions, the fract ion of

that inven tory that is relea sed from each faile d rod to the cask inter ior, and the fract ion of the

invento ry that is relea sed to the cask inter ior that is trans ported throu gh the cask leak to the

environme nt. Thus, 

ST ST I f f I f f jk ijk ik release,ijk rod, jk ik RCijk CEijk

i i i

== = ∑∑ ∑

where STijk is the amoun t of radio nuclide i relea sed from cask k durin g accid ent scena rio j, Iik is

the numbe r of curie s of nucli de i in the inven tory of cask k, frelea se,ijk is the fract ion of the

inven tory of radio nuclide i in cask k that is relea sed to the envir onment durin g accid ent scena rio

j, frod,j k is the fract ion of the rods in cask k that fail durin g accid ent scena rio j, fRCijk is the fract ion
7-14

of nuclide i that is released during scenario j to the interior of cask k from each failed rod, and

fCEijk is the fraction of the amount of each radionuclide released to the cask interior that is

transported to the environment through the cask leak.

7.2.3 Cask Inventories

Spent fuel assemblies contain radionuclides that were produced by fissioning of uranium and by

activation of assembly hardware and of materials in deposits on assembly surfaces. For this

study, the ORIGEN code [7-11, 7-12] was used to calculate inventories for a generic pressurized

water reactor (PWR) assembly that contained 289 fuel rods and for a generic boiling water

reactor (BWR) assembly that contained 64 rods. As is described below, after dropping

radionuclides that do not contribute significantly to radiation doses and adding important

radionuclides formed by activation of deposits on assembly surfaces (e.g., Co-60), cask

inventories were calculated by multiplying the modified single assembly inventories by the

number of assemblies transported in each of the four generic casks defined in Tables 4.1 through

4.4.

7.2.3.1 Fuel Burnup

Because inventory size depends on fuel burnup, which is an ORIGEN input, and the length of the

fuel cooling time after fuel discharge from the reactor, which is an ORIGEN output, initially a

DOE report [7-13] was consulted to identify average and maximum BWR and PWR fuel

burnups, and then, for each burnup, an ORIGEN calculation was performed that depicted the

variation of inventory size with fuel cooling time. The DOE report contains data on spent fuel

that has been discharged from commercial power reactors located in the United States. Table 7

in that report presents a tabulation by fuel burnup ranges of the number of metric tons of uranium

in BWR and PWR spent fuel discharged during the years 1968 through 1994. This table showed

that the maximum burnups reported were about 45 to 50 GWDt/MTU (gigawatt-days thermal per

metric ton of uranium) for BWR spent fuel and about 55 to 60 GWDt/MTU for PWR spent fuel;

and that the most probable burnups were approximately 30 GWDt/MTU for BWR spent fuel and

35 GWDt/MTU for PWR spent fuel. In addition, extrapolation to 1998 of data in Table 5 in that

report showed that ten years was the quantity-weighted (weight in MTU) average age of all of the

tabulated spent fuel.

7.2.3.2 ORIGEN Calculations

ORIGEN calculations were performed for the most probable and the maximum PWR and BWR

fuel burnup levels, where these levels are 30 and 50 GWDt/MTU for BWR spent fuel and 35 and

60 GWDt/MTU for PWR spent fuel. Full descriptions of these calculations are presented in

Appendix C. Table 7.8 summarizes the results of these calculations. Table 7.8 shows that—for

both BWR and PWR spent fuel and for any fuel cooling time—the total number of curies in high

(maximum) burnup spent fuel is less than a factor of two greater than the number in spent fuel

having the most probable burnup. The table also shows that, due to decay, the number of curies

decreases rapidly during the first three years after discharge and rather slowly after five years of

cooling, and also that the number of curies at three years after discharge is approximately a factor

of two greater than the number of curies at ten years, which is the quantity-weighted average age
7-15

of the fuel. Nevertheless, even though most of the spent fuel that will eventually be shipped is

likely to be average burnup fuel that has cooled for about ten years, in order to be conservative,

the ORIGEN results for maximum burnup fuel after three years of cooling were chosen for use in

this study. This choice means that the total curie content of the inventories used in the

RADTRAN risk calculations described in Section 8 are most likely conservative by about a

factor of four.

Table 7.8 Summary of ORIGEN Calculations,

Total Curies per Assembly for All Radionuclides

Burnup Fuel Cooling Time (years)

(GWDt/MTU) At

Discharge 0.5 1.0 3.0 5.0 10.0 30.0

BWR

Most probable, 30 2.87E+07 5.66E+05 3.38E+05 1.40E+05 9.38E+04 6.60E+04 3.55E+04

Maximum, 50 2.99E+07 7.04E+05 4.52E+05 2.06E+05 1.44E+05 1.03E+05 5.61E+04

PWR

Most probable, 35 1.30E+08 2.29E+06 1.28E+06 4.60E+05 2.85E+05 1.93E+05 1.04E+05

Maximum, 60 1.07E+08 2.34E+06 1.47E+06 6.34E+05 4.32E+05 3.05E+05 1.68E+05

7.2.3.3 Elimination of Unimportant Radionuclides

An ORIGEN inventory contains approximately 800 radionuclides. This large set of

radionuclides was reduced to a much smaller set that contained only radionuclides that together

accounted for 99.9 percent of the health hazard posed by the total inventory using radionuclide

A2 values [7-14, 7-15] as a measure of radiation health hazard. The RADSEL code [7-16] was

used to perform this reduction. For each radionuclide in the total inventory, RADSEL computes

the ratio of the nuclide’s number of curies and its A2 value, sums and normalizes these ratios,

sorts the ratios according to magnitude, and then retains the smallest set of radionuclides whose

ratios sum to 0.999.

7.2.3.4 Radioactive Gases

Although tritium gas and tritiated water are very active biologically, the quantities per assembly

calculated by ORIGEN for three-year cooled PWR (482 Ci) and BWR (168 Ci) fuel are so small

compared to the A2 value for tritium (1080 Ci) that they contribute less than 0.1% to the health

hazard of the total inventory. Therefore, tritium was not included in the reduced, maximum

burnup, three-year cooled, BWR or the PWR inventories. However, although the relative

contribution to total health hazard of Kr-85 is also less than 0.1% for the three-year cooled fuel,

because Kr is the most important member of the non-condensible gas chemical element group, it

was retained in the reduced BWR and PWR assembly inventories despite its minor contribution

to health hazard. Accordingly, the following quantities per assembly of Kr-85 were added back

into the reduced BWR and PWR inventories generated by RADSEL: 5.87E3 Ci to the PWR

assembly inventory, and 1.74E3 Ci to the BWR assembly inventory.
7-16

7.2.3.5 CRUD

During reactor operation, corrosion products formed in the reactor’s primary cooling system

deposit on fuel assembly surfaces where elements in these deposits are activated by neutron

bombardment. The resulting radioactive deposits are called CRUD [7-17]. Due to vibratory

loads during incident free transportation, impact loads during collision accidents, and thermal

loads during accidents that lead to fires, portions of these radioactive deposits may spall from the

rods. Then, if some of these spalled materials become airborne during an accident, their release

to the atmosphere could contribute to the radiation exposures caused by the accident. Although

CRUD contains a number of radionuclides, only Co-60 would contribute significantly to these

radiation exposures. Since the CRUD deposits on typical PWR and BWR spent fuel rods contain

respectively 0.2 and 1.0 Ci of Co-60 per rod [7-17] and the generic PWR and BWR assemblies

for which ORIGEN inventories were calculated contain respectively 289 and 64 spent fuel rods,

the amounts of Co-60 produced by activation of deposits on assembly surfaces is 57.8 Ci for the

generic PWR assembly and 64 Ci for the generic BWR assembly.

7.2.3.6 Inventories for Generic PWR and BWR Assemblies

The final generic PWR and BWR assembly inventories were now constructed by adding the

amounts per assembly of Kr-85 and of the Co-60 in CRUD to the reduced generic assembly

inventories that were generated by eliminating all radionuclides shown by the RADSEL

calculation to contribute negligibly to radiation exposures from the full assembly inventories

calculated by ORIGEN. Table 7.9 presents these reduced modified generic assembly inventories.

7.2.4 Chemical Element Classes

To simplify the development of accident source terms, fission products are assigned to chemical

element classes that have similar physical and chemical properties and therefore are expected to

have similar transport characteristics. Each group is called a chemical element class and for

convenience each is denoted by one of the elements assigned to the class. After assignment to

classes, rod-to-cask and cask-to-environment release fractions are developed for each chemical

element class.

Fission products are usually assigned to one of three general chemical element classes: noncondensible gases, condensible gases, and particulates. Each class may be further subdivided if

the transport properties of its member elements differ widely. For example, because the volatile

forms of cesium and iodine, Cs, CsOH, CsI, I2, have very different volatilities and chemical

properties, Cs and I are usually assigned to different classes of condensible gasses. In addition,

elements with unique chemistries are placed in special chemical element classes. For

transportation accident analysis, Co and Ru are usually placed in special classes. Co is placed in

a special element class because it is the major constituent of the radioactive deposits called

CRUD that form on the outside of spent fuel rods during reactor operation. Ru is placed in a

special element class because, if exposed to oxygen while at elevated temperatures, involatile

RuO2 can be converted to RuO3 and RuO4, which are much more easily vaporized, thereby

greatly increasing the rate of release of Ru from fuel pellets.
7-17

Table 7.9 Generic High Burnup, Three-Year Cooled, Fuel Assembly Inventories

for RADTRAN Calculations (Ci/assembly)

Generic BWR Assembly Generic PWR Assembly

Nuclide Amount (Ci) Nuclide Amount (Ci)

Co-60 6.40e+01 Co-60 5.78e+01

Kr-85 1.74e+03 Kr-85 1.74e+03

Sr-90 1.59e+04 Sr-90 5.36e+04

Y-90 1.59e+04 Y-90 5.36e+04

Ru-106 1.42e+04 Ru-106 4.43e+04

Cs-134 2.15e+04 Cs-134 6.99e+04

Cs-137 2.59e+04 Cs-137 7.90e+04

Ce-144 1.03e+04 Ce-144 3.87e+04

Pm-147 8.49e+03 Pm-147 2.58e+04

Pu-238 1.67e+03 Eu-154 8.42e+03

Pu-239 7.44e+01 Pu-238 4.81e+03

Pu-240 1.36e+02 Pu-239 2.14e+02

Pu-241 2.91e+04 Pu-240 4.28e+02

Am-241 2.05e+02 Pu-241 6.52e+04

Am-242M 8.09e+00 Am-241 4.36e+02

Am-243 1.22e+01 Am-242M 1.33e+01

Cm-242 1.82e+02 Am-243 2.51e+01

Cm-243 1.42e+01 Cm-242 3.76e+02

Cm-244 2.95e+03 Cm-243 2.88e+01

Cm-244 5.62e+03

For this study, fission products are assigned to five chemical element classes. The five classes

and the representative element that denotes each class are:

Representative Element Description

Xe Noble (non-condensible) gases

Cs Condensible gases

Ru Single element group

Co Fission products found in CRUD

Part All other fission products

Condensible gases are not subdivided into a cesium (Cs) and an iodine (I) class because, by the

time spent fuel is removed from a reactor’s spent fuel pool and released for transport to an

interim or a permanent repository, almost all iodine nuclides except I-129 will have decayed

away and the remaining I-129 will have reacted with Cs to form CsI. Thus, an iodine chemical

element class is not needed. Finally, the class denoted by Part represents all fission products that

exist in chemical forms (usually refractory hydroxides and oxides, e.g., Sr which transports as

Sr(OH)2, Pu which transports as PuO2) that transport only as particles.
7-18

7.2.5 Release Fractions

This section develops expressions for accident release fractions. Expressions are developed for

four broad classes of accidents: collision accidents that do not initiate fires (Collision only),

collision accidents that initiate fires and generate mechanical or thermal loads that cause the cask

seal to leak (Collision + Fire, 1 leakage path), collision accidents that initiate fires and generate

mechanical or thermal loads that cause the cask seal to leak and also lead to failure of the cask

shell by puncture or shear (Collision + Fire, 2 leakage paths), and fire accidents that do not

involve collisions (Fire only). The first three of these four accident categories correspond to

accident categories 4, 5, and 6 in the six-category accident severity scheme that is frequently used

when performing RADTRAN calculations [7-18]. The last accident category, fires not initiated

by collisions, leads to accidents that have severities that are similar to those of Category 5

accidents, but release fraction expressions that are different than those used to calculate release

for accidents initiated by collisions that lead to fires. Because their release fraction expressions

are unique, they are here not lumped into Category 5, but are placed in a separate fire-only

category. Collisions that lead both to double cask failures and to fires are separated from

collisions that lead to fires, but only a single cask failure, because differential thermal heating of

a cask with a double failure may cause combustion gases, including some air, to flow through the

cask. Flow of gas through the cask could sweep most fission products released to the cask

interior out of the cask to the environment, thereby minimizing fission product retention in the

cask. Flow of air into the cask could also lead to the oxidation of UO2 to UO3 and of RuO2 to

RuO3 and RuO4 [7-19]. Because Cs diffuses though UO3 more easily than through UO2,

oxidation of fuel enhances Cs release rates. Because RuO3 and RuO4 are much more volatile

than RuO2, conversion of RuO2 to RuO3 and RuO4 substantially increases release of Ru.

7.2.5.1 Mechanical Failure of Cask Seals and Spent Fuel Rods.

The response of four generic Type B spent fuel casks—two truck casks and two rail casks—and

of the spent fuel rods carried in the casks, to high-speed impacts onto yielding real-world

surfaces (clay/silt, hard soil/soft rock, hard rock, water, railbed/roadbed) and objects (small

columns, large columns, abutments) is discussed in Section 5. Puncture and shear failures of rail

tank cars during collision accidents were also analyzed in that section.

The analysis of puncture and failures presented in Section 5.3 suggests that formation of a

puncture or shear probe during a collision accident depends only weakly on accident speed.

Therefore, probe formation is possible during any collision accident. But a probe, if formed (or

already present at the accident site), can puncture a cask only if the probe (a) is sharp enough and

so oriented upon impact with the cask that it initiates a puncture or tear in the cask shell (does not

glance off of the cask surface) and (b) has a stem that is sufficiently robust so that it does not

break before the cask shell is completely penetrated by the probe. Since these two conditions are

both improbable, the analysis concluded that failure of a cask by puncture or shear was possible

during any collision accident but also was most unlikely.

The finite element calculations described in Section 5 and their extrapolation to real-world

yielding surfaces strongly suggest that only extremely high-speed impacts onto slightly yielding

surfaces (e.g., hard rock) are likely to cause the seals of Type B steel-lead-steel and steel-DU-
7-19

steel spent fuel truck casks to leak. Specifically, the calculations show so little distortion of the

cask closures of the generic steel-lead-steel and steel-DU-steel spent fuel truck casks following

120 mph impacts onto an unyielding surface that seal leakage cannot be predicted with certainty

even for impacts this severe. Nevertheless, even though not large enough to predict that seal

leakage is certain to occur, because distortion of the cask closure is clearly discernable, 120 mph

impacts onto an unyielding surface are assumed to cause the seal of truck casks to leak and that

leak path is arbitrarily assumed to have a cross-sectional area of 1 mm2. Thus, if vseal is the speed

that produces a seal leak, then by definition vseal = 120 mph for impacts of truck casks onto an

unyielding surface at any orientation and vseal = v120 for impacts of truck casks at any orientation

onto real world yielding surfaces, where v120 is the impact speed for the specified impact

orientation onto the real yielding surface that causes the same damage to the truck cask and its

contents as is caused by a 120 mph impact at the same impact orientation onto an unyielding

surface.

For rail casks, the finite element calculations indicate that seal leakage occurs for impacts onto an

unyielding surface at some impact orientations at speeds as low as 60 mph. Specifically, for both

the steel-lead-steel and the monolithic steel generic rail casks, closure region distortions are

sufficiently large for 60 mph impacts onto an unyielding surface in the center of gravity over

corner impact orientation to allow seal leakage to be predicted (i.e., the predicted separation of

the lid well from the cask lid is larger than the compliance of the O-ring seal, which means that

sealing function should be lost). Closure region distortion also appears to be large enough to

predict seal leakage for side impacts of the monolithic steel generic rail cask onto an unyielding

surface at 60 mph.

The finite element calculations also show that, for some yielding surfaces, many impact

accidents, that do not cause the cask seal to leak, will cause slumping of cask contents or inward

collapse of the cask shell that is sufficiently severe so that fuel rods would be expected to fail

either by buckling or tearing and also that the impact speed that produces failure of some fraction

of the rods in the cask will be different for end, corner, and side impacts. Thus, the impact

speeds that cause rod to fail or seals to leak depend on both the nature of the impact surface and

the cask orientation at the time of impact.

Although failure of some fuel rods is expected for most severe collision accidents, the finite

element analyses described in Section 5.1 do not predict the fraction of rods failed. They did,

however, provide estimates of the peak rigid body accelerations that the fuel rods would

experience as a result of cask impacts onto unyielding surfaces. This allowed results from an

analysis of the strains generated in PWR and BWR fuel rods carried in a typical PWR or BWR

assembly [7-20] for regulatory impacts to be scaled to match the accelerations produced by

impacts onto unyielding surfaces at 60, 90, and 120 mph. Comparison of the scaled rod strains to

the rod failure criterion developed for the analysis of regulatory impacts [7-21] then allowed the

fraction of the rods in a typical PWR or BWR assembly failed by 30, 60, 90, and 120 mph

impacts onto an unyielding surface to be estimated.

Accordingly, for each impact orientation examined in Section 5.1 and each class of real-world

yielding surfaces, four speeds were determined, v30, v60, v90, and v120, where v30, v60, v90, and v120

are the impact speeds for the stated impact orientation (end, corner, or side) onto the real yielding
7-20

surface that inflict damage onto the cask and its contents equivalent to the damage caused by 30,

60, 90, and 120 mph impacts onto an unyielding surface. These four speeds define four speed

ranges, v30 ≤ v < v60, v60 ≤ v < v90, v90 ≤ v < v120 and v120 ≤ v, where v is the cask impact speed

onto the real yielding surface or object at the stated impact orientation.

7.2.5.2 Thermal Failure of Cask Seals and Spent Fuel Rods

During normal transport under ambient conditions, the peak temperature of spent fuel in a Type

B spent fuel cask is about 300°C [7-22]. Because the average temperature of free burning

hydrocarbon fuel fires is about 1000°C [7-23], elastomeric cask seals and spent fuel rods can

both fail if the cask that contains them is heated long enough by a hot fire.

Type B spent fuel casks are usually equipped with elastomer seals (e.g., Viton O-rings). When

heated to temperatures above 350°C at rates comparable to the heating rates of engulfing

hydrocarbon fuel fires, these seal materials degrade thermally losing about 5 percent of their

mass if heated to 380°C, 10 percent if heated to 400°C, and 70 percent if heated to 450°C [7-24].

Elastomeric O-rings lose sealing function, as measured by helium leak detection, if heated to

about 400°C, but can be repeatedly cycled from ambient temperatures to temperatures

approaching 380°C without loss of sealing function [7-25]. Loss of mass without loss of sealing

function upon heating to 380°C occurs because elastomeric O-rings usually contain or are coated

with volatile organics (e.g., oils). Thus, the mass loss that occurs first upon heating is due to the

vaporization of these volatile organics and not to thermal decomposition of rubber matrix

materials, which causes the O-ring to shrink and, when shrinkage is appreciable, sealing function

to be lost. Accordingly, heating of elastomeric cask seals to temperatures above 400°C is

probably required, if loss of sealing function is to be large enough to allow significant quantities

of gasborne aerosols to escape from the cask through the failed seal. Nevertheless, it is here

assumed that elastomeric cask seals begin to leak when heated to 350°C and, in order to be

consistent with the treatment of seal failures caused by impacts, it is also assumed that the seal

leak produced by heating to 350°C has a cross-sectional leak area of about 1 mm2

 (because no

credit is taken for vapor and particle deposition during most of the 60 to 80 minutes that is

required for an engulfing fire to heat a cask to seal failure temperatures, source term magnitudes

and thus accident consequences are relatively insensitive to seal failure temperatures). Finally,

the substantial mass loss that is caused by heating to 450°C is assumed to cause O-ring sealing

function to be lost around the entire circumference of the cask closure producing a leak area that

is determined by the roughness of the surfaces of the cask lid and lid well where they contact

each other and the length of the closure circumference.

When heated to elevated temperatures, spent fuel rods fail by burst rupture. During the

experiments of Lorenz, et al. [7-26], sections of spent fuel rods that had been heated to 900°C

failed by burst rupture when rod pressures reached 275 psig. Wilmot’s analysis of release of

fission products from spent fuel rods during transportation accidents assumes rod failure by burst

rupture occurs at 850°C [7-27]. The critical review of spent fuel transportation accident

conditions by Sanders, et al. [7-28] indicates that rod burst rupture is expected to occur at

temperatures near 725 to 750°C. And, after correcting for differences in burnup and internal

pressure, data in the Cask Designers Guide suggest that spent fuel rods may fail due to creep
7-21

ruptu re occurs at 850°C [7-27 ]. The criti cal revie w of spent fuel trans portation accid ent

condi tions by Sande rs, et al. [7-28 ] indic ates that rod burst ruptu re is expec ted to occur at

tempe ratures near 725 to 750°C. And, after corre cting for diffe rences in burnu p and inter nal

press ure, data in the Cask Desig ners Guide sugge st that spent fuel rods may fail due to creep 

ruptu re at tempe ratures as low as 700°C [7-29 ]. Becau se the relea se of Cs vapor s will be great er

when rods fail at highe r rathe r than lower tempe ratures, the tempe rature at which rods fail by

therm al burst ruptu re is assum ed to be 750°C, the middl e of this range , rathe r than 700°C, the

botto m of the range .

Let the inter nal tempe rature of a Type B spent fuel cask durin g norma l trans port under ambie nt

condi tions be Ta = 300°C, the tempe rature where elast omeric spent fuel cask seals begin to leak

throu gh a leak path with a cross -sectional area of 1 mm2

 be Ts = 350°C, the tempe rature where 

spent fuel rods fail by burst ruptu re be Tb = 750°C, and the avera ge tempe rature of hydro carbon

fuel fires be Tf

 = 1000°C. These four tempe ratures defin e three tempe rature range s, Ta ≤ Tcask

≤ Ts, Ts < Tcask < Tb, and Tb ≤ Tcask ≤ Tf, where Tcask is the inter nal tempe rature of the cask. 

7.2.5.3 Collision-Only Scenarios

Colli sions that do not initi ate fires must be unusu ally sever e if seal leakage is to cause d by

impact. For impac ts onto an unyie lding surfa ce at 60 mph by a Type B rail cask and at 120 mph

by a Type B truck cask, the finit e eleme nt cask impac t calcu lations descr ibed in Secti on 5 indic ate

that, even thoug h slump ing of cask inter nal struc tures is so great that many of the rods in the

cask are likel y to fail, disto rtion of the cask seal regio n is not great enoug h to concl ude that seal

leaka ge defin itely occur s. Despi te this, here it is assum ed that (a) leaka ge of the cask’ s

elast omeric seals is produ ced by all colli sions that lead to impac t of a Type B spent fuel cask

onto a yield ing surfa ce at a veloc ity that subje cts the cask to mecha nical loads equal to those 

gener ated by impac ts onto an unyie lding surfa ce at 60 mph for rail casks and at 120 mph for

truck casks , (b) the leaka ge area produ ced by these impac ts is about 1 mm2

, and (c) such impac ts

cause at least some of the rods in the cask to fail. 

MELCO R calcu lations [7-30 ] indic ate that, when cask leak path cross -sectional areas are small 

(∼ 1 mm2

), the mass depos ition rate of vapor s and parti cles onto cask inter ior surfa ces is rapid 

compa red to the mass rate of their relea se from the cask to the envir onment. Thus, unles s cask

depre ssurizatio n is rapid , depos ition of vapor s and large parti cles onto cask inter ior surfa ces will

be effic ient which means that depos ition of radio active mater ials will also be effic ient.

There fore, for colli sion accid ents that do not initi ate fires , depos ition of parti cles and vapor s onto

cask inter ior surfa ces durin g rod depre ssurizatio n is assum ed to be appre ciable whene ver cask

seal leaka ge areas are small . Thus, for Collision- Only scena rios (Cate gory 4 accid ents), frelea se,

the total relea se fract ion for relea se of fissi on produ cts from faile d rods to the envir onment, is

given by

f f f 1f 1 p

p release rod,impact RC deposition

atm

Imp

= − ( ) − 









÷ (1)
7-22

where frod,impact = 1.0 is the fraction of the rods in the cask that are failed by the collision impact,

fRC is the fraction of the materials in a spent fuel rod that is released to the cask interior upon rod

failure, fdeposition is the fraction of those materials that rapidly deposit onto cask interior surfaces

upon release from the failed spent fuel rods, patm is atmospheric pressure, and pImp is the cask

internal pressure after depressurization of the fuel rods that failed as a result of the collision

impact. Note that although the values of fRC and fdeposition will depend on the physical and

chemical properties of the materials (radionuclide species) being released from the failed fuel

rods, for simplicity in this and subsequent equations, they are written without attachment of the

radionuclide species subscript i (e.g., as fRC rather than fRCi).

7.2.5.4 Collision Plus Fire Scenarios

Consider a collision accident that is severe enough to fail some of the rods in the spent fuel cask,

but not the cask seal, and that also initiates a fire that heats the cask to the temperature Ts where

the cask seal fails due to thermal degradation causing the cask to depressurize. Now let patm be

atmospheric pressure, pImp be the cask internal pressure after depressurization of the fuel rods that

failed as a result of the collision impact, Ta be the cask internal temperature during normal

transport under ambient conditions, Vcask be the internal free volume of the cask, Vexpansion be the

volume that the gases initially in the cask plus the gases released to the cask by rod failure would

occupy at Ts and atmospheric pressure, and fCE be the fraction of the gasborne radioactive

materials that escape from the cask to the environment when the cask seal fails due to thermal

degradation. But

expansion

cask

CE V

V 1f −= and 

s

atm expansion

a

caskImp

T

Vp

T

Vp = and therefore 

sImp

aatm

expansion

cask

Tp

Tp

V

V =

So, if deposition of particles and vapors is neglected during the time required for the fire to heat

the cask from Ta to Ts,

sImp

aatm

expansion

cask

CE Tp

Tp 1

V

V 1f −= −=

By extending this approach, a conservative expression can now be developed for release due to

failure of some rods by an impact that does not fail the cask seal followed by heating of the cask

in a fire first to the temperature Ts where the cask seal begins to leak, then to the temperature Tb

where the remaining rods fail by burst rupture, and finally to the temperature of the fire Tf. As

before, let pImp be the cask pressure after rod failure due to impact and patm be atmospheric

pressure. In addition, let fimp be the fraction of the rods failed by impact, fbur be the fraction of

rods failed by thermal burst rupture, pb be the cask pressure after rod failure due to burst rupture,

fRCimp be the release fraction for fission products to the cask interior from a rod failed by impact,

fRCf be the release fraction for fission products to the cask interior from a rod failed by thermal

burst rupture due to a fire, and fdep be the fraction of the materials released from failed rods to the

cask interior that deposits rapidly onto cask internal surfaces. Then, the total release fraction frel
7-23

for relea se of fissi on produ cts from faile d rods to the environme nt durin g Categ ory 5 accid ents is

given by

f ff 1f 1 p

p

T

T

p

p

T

T

1 T

T

p

p

T

T

1 p

p

T

T

ff 1f

rel imp RCimp dep

atm

imp

a

s

atm

imp

a

s

s

b

atm

imp

a

b

atm

b

b

f

bur RCf dep

= − ( ) − 















+















 − 



 



 +















 − 



 

























+ − ( ) 1− 



 

















p

p

T

T

atm

b

b

f

(2)

where fbur = 1−fimp, becau se all rods not faile d by impac t are assum ed to fail when the rod burst 

ruptu re tempe rature is reach ed, and the expre ssion is conse rvative becau se depos ition of partic les

and vapor s is assum ed to occur only immed iately follo wing rod failu re and not durin g the time

perio ds durin g which the cask is heate d by the fire to eleva ted tempe ratures .

Inspe ction of Equat ion 2 shows that the first term in the equat ion gives the relea se fract ion for

mater ials relea sed due to rod failu re cause d by colli sion impac ts and the secon d term gives the

relea se fract ion for mater ials relea sed due to rod failu re cause d by therm al burst . In addit ion, the

three parts of the first term respe ctive ly refle ct the effec t on relea se of (1) cask press urization due

to rod depre ssurizatio n upon impac t failu re follo wed by heati ng of cask gases to the tempe rature

where seal leaka ge begin s, (2) heati ng of cask gases from the tempe rature of seal leaka ge almos t

to the temperat ure of rod burst ruptu re, and (3) cask press urization due to burst ruptu re of the

remai ning unfai led rods follo wed by heati ng of cask gases from the burst ruptu re tempe rature to

the temperat ure of the engulfi ng fire. 

Equat ion 2 also is used to calcu late the relea se fract ion for Categ ory 6 accid ents, colli sions that

initi ate fires and fail not only the cask seal by impac t but also the cask body by punct ure or

shear . For these accid ents, fdep in the last term of the equat ion is set to zero, becau se the flow of

gases throu gh the cask durin g these accid ents is assum ed to trans port all mater ials relea sed to the

cask inter ior from the faile d rods throu gh the cask failu res to the envir onment.

Final ly, for Categ ory 5 and Categ ory 6 accid ents that heat the cask to tempe ratures ≥ Tb, all Cs in

parti cles depos ited on cask inter nal surfa ces is assum ed to volat ilize. Volat ilization of all Ru in

parti cles depos ited on cask inter nal surfa ces is also assum ed to occur durin g all Categ ory 6

accidents since, durin g these accid ents, air is assum ed to be flowi ng throu gh the faile d cask

which would cause involat ile RuO2 to be oxidi zed to volat ile RuO4.

7.2.5.5 Fire-only Scenarios

For fires not initi ated by colli sions (Cate gory Fire- only accid ents), when the inner wall of the

cask shell reach es a tempe rature of 350°C = Ts, therm al degra dation of the cask’ s elast omeric

seal is assum ed to cause the cask seal to begin to leak throu gh a leak path that has a cross -

secti onal area of 1 mm2

. In addit ion, whene ver the cask shell tempe rature excee ds 450°C,

decom position of the elast omeric seal is assum ed to be so exten sive that the effec tive leak path

has a cross -sectional area equal to the produ ct of the closu re circu mference and the rough ness

heigh t of the lid and the lid well where they conta ct insid e of the closu re. In addit ion, all of the
7-24

rods in the cask are assum ed to fail by burst ruptu re when the cask inner shell tempe rature

reaches 750°C = Tb, and, whenever rod failure occurs, the fire is assumed to burn long enough to

heat the cask to Tf

 = 1000°C, the avera ge tempe rature Tf of a hydro carbon fuel fire which is here

assum ed to be 1000°C. There fore, for Categ ory Fire- only accidents ,

f ff 1f p

p

T

T rel bur RCf dep

atm

b

b

f

= − ( ) − 



 



 1 (3)

where fbur = 1.0 is the fract ion of rods in the cask that fail when the cask inter nal tempe rature

reach es the rod burst tempe rature Tb.

7.2.5.6 Expansion Factor Ratios

Now let fe1 = (patm/pimp)(Ta/Ts), fe2 = Ts/Tb, fe3 = (patm/pimp)(Ta/Tb), fe4 = (patm/pb)(Tb/Tf), and fe5 =

(patm/pImp). After subst itution of these expan sion facto r symbo ls, the equat ions for relea se cause d

by colli sions that do not initi ate fires , by colli sions that do initi ate fires , and fires not initi ated by

colli sions reduce to:

Accid ent Categ ory Term Part Failu re

Mode

Temperat ure

Range 

Colli sions that do not initi ate Fires 

 frel = fimpfRCimp (1−fdep)(1−fe5) 1 Impac t Ta

Colli sions that initi ate Fires 

 frel = f,impfRCimp (1−fdep)(1−fe1) 1 1 Impac t Ta ≤ Tcask ≤ Ts

 + fimpfRCimp (1−fdep)(fe1)(1−fe2) 1 2 Ts < Tcask < Tb

 + fimpfRCimp (1−fdep)(fe3)( 1−fe4) 1 3 Tb ≤ Tcask ≤ Tf

 + (1−fimp)fRCfir e(1-fdep)(1−fe4) 2 Ruptu re Tb ≤ Tcask ≤ Tf

Fires witho ut Colli sions

 frel = (1−fimp)fRCfir e(1−fdep)(1−fe4) 1 Ruptu re Tb ≤ Tcask ≤ Tf

7.2.6 Accident Cases

The four accid ent categ ories, the four veloc ity range s, and the three tempe rature range s defin ed

above allow 18 truck accid ent cases and 20 train accid ent cases that lead to relea se of

radio nuclides to be defin ed (beca use RADTR AN requi res that the proba bilities of the cases 

suppl ied as input sum to one, befor e being input to RADTR AN, these accid ent cases are

augme nted by one case that inclu des shipm ents not subje ct to accid ents and shipm ents that

invol ve accid ents that do not lead to a relea se of radio nuclides, i.e., 19 total truck cask and 21

total train cases ). For truck accidents , the 18 accid ent cases consi st of one Categ ory 4 case, 

twelv e Categ ory 5 cases , four Category 6 cases , and one Categ ory Fire- only case. Table 7.10
7-25

presents the characteristics (cask failure mechanism, impact velocity range, and temperature

range) of each truck accident case.

In Table 7.10, the single Category 4 accident case represents collisions that do not initiate fires

but are so severe that the impact forces cause the cask seal to leak and all of the rods in the truck

cask to fail. The twelve Category 5 accident cases occur in four groups of three accident cases.

The first three groups represent collisions that are not severe enough to cause seal leakage but

initiate fires that heat the cask to temperatures greater than the temperature where the cask seal

begins to leak due to thermal degradation. The fourth group of three Category 5 accident cases

represents collisions that both initiate fires and are also so severe that the impact causes the cask

seal to leak. Because for these three cases vseal  v120, the initial impact also fails all of the rods

in the cask. Cases 14 through 17, the Category 6 accident cases, are the same as Cases 4, 7, 10,

and 13 except that a second failure of the cask by puncture or shear is assumed. Because of the

Table 7.10 Truck Accident Cases

Category Case Cask Seal Failure by Velocity Range Temperature Range

Impact Fire v30-v60 v60-v90 v90-v120 ≥ v120 Ta-Ts Ta-Tb Ta-Tf

4 1 X X

5 2 X X X

 3 X X X

 4 X X X

 5 X X X

 6 X X X

 7 X X X

 8 X X X

 9 X X X

10 X X X

11 X X X

12 X X X

13 X X X

6 14 X X X

15 X X X

16 X X X

17 X X X

Fire Only 18 X X

No Release 19

double failure of the cask, it is also assumed first that flow of combustion gases or air through the

cask carries out to the environment all fission products released from the rods to the cask interior

while the cask is hot, and second that oxidation of fuel and of RuO2 enhances the releases of Cs

and Ru compared to the releases that characterize Case 4, 7, 10, and 13 accidents. Finally, the

single case in the Fire Only category represents fires not initiated by collisions that heat the cask

to temperatures high enough to fail all of the spent fuel rods by burst rupture and also the cask

seal by thermal degradation.

If a term for the deposition of particles and vapors, while a fire is heating the cask to elevated

temperatures, were added to Equation 2, then Category 5 accident Cases 8, 9, and 10 would have

slightly smaller release fractions than Category 5 accident Cases 11, 12, and 13. Because particle

and vapor deposition during periods of cask heating by a fire is neglected, the release fractions
7-26

calculated for accident Cases 11, 12, and 13 will be the same as those calculated for accident

Cases 8, 9, and 10. Finally, because the rod failure fractions (frod,impact) for the four Category 6

accident cases (Cases 14, 15, 16, and 17) are ordered as follows,

frod,impact,Case 14 frod,impact,Case 15 frod,impact,Case 16 = frod,impact,Case 17

the release fractions for these four accident cases have the following order:

frelease,Case 14  frelease,Case 15  frelease,Case 16 = frelease,Case 17

Increasing the fraction of rods failed by impact decreases the release fraction for Category 6

accidents because for this accident category, deposition processes are assumed to be effective for

materials released to the cask interior when rods are failed by impact but is neglected when rods

fail by burst rupture. Deposition is neglected following burst rupture because the combustion

gases that are assumed to be flowing through the cask during Category 6 accidents are also

assumed to carry all materials released to the cask interior out to the environment without

significant depletion by deposition to cask interior surfaces.

For train accidents, because rail cask seals may leak after impacts onto an unyielding surface at

some orientations at speeds as low as 60 mph, the train accident matrix consists of 20 accident

cases, three Category 4 cases, twelve Category 5 cases, four Category 6 cases, and one Category

Fire-only case. Table 7.11 presents the characteristics (cask failure mechanism, impact velocity

range, and temperature range) of each train accident case.

Table 7.11 Train Accident Cases

Category Case Cask Seal Failure by Velocity Range Temperature Range

Impact Fire v30-v60 v60-v90 v90-v120 ≥ v120 Ta-Ts Ta-Tb Ta-Tf

4 1 X X

 2 X X

 3 X X

5 4 X X X

 5 X X X

 6 X X X

 7 X X X

 8 X X X

 9 X X X

10 X X X

11 X X X

12 X X X

13 X X X

14 X X X

15 X X X

6 16 X X X

17 X X X

18 X X X

19 X X X

Fire Only 20 X X

No Release 21
7-27

7.2.7 Source Term Probabilities

For trans portation accid ents, the proba bility P that an accid ent is so sever e that it gener ates a

sourc e term that leads to conse quences with magni tude M is expre ssed as the produ ct of the

proba bility that any accid ent occur s (Paccid ent), the proba bility that the truck or rail car carry ing the

cask is invol ved in the accid ent (Pvehic le), and the fract ion of all possi ble accid ents (Fsever ity) that

lead to relea ses of radio activity that cause conse quences of magni tude M. Therefore, 

P = Paccid ent Pvehic le Fsever ity (4)

7.2.7.1 Accident Probabilities

The proba bility that a truck or train is invol ved in an accid ent of any sever ity while trave ling a

route of lengt h L is usual ly expre ssed as the sum of the chanc es that an accid ent occur s on the

urban , subur ban, and rural porti ons of the route . Thus, 

P Lf Rate accident m accident,m

m 1

3

= =

∑

where m is a link index , which is here used to denot e the urban , subur ban, and rural porti ons of

the route , Rateaccid ent,m is the accid ent frequ ency, witho ut regar d to sever ity, per unit dista nce

traveled on the urban , subur ban, and rural porti ons of the route , and fm is the fract ion of the

route lengt h that is urban , subur ban, or rural . Value s for L, fm, and Rateaccid ent,m were devel oped

in Sections 3.3.1 and 3.3.2 .

7.2.7.2 Vehicle Involvement

Value s for Pvehic le, the proba bility that the vehic le carry ing the spent fuel cask is invol ved in the

accid ent, are devel oped in Secti on 7.4.2 direc tly from accid ent data. Thus, Pvehic le is not

formulated as an algeb raic combinatio n of other varia bles.

7.2.8 Accident Severities

The massi ve natur e and robus t const ruction of Type B spent fuel casks mean that only an

extreme ly sever e colli sion and/o r a hot, long- durati on fire can cause both the cask and a

signi ficant fract ion of the spent fuel rods being trans ported in the cask to fail. The sever ity of a

colli sion acciden t depen ds on accid ent type, accid ent speed , cask impac t angle , the hardn ess of

the impac t surface, the fract ion of the accid ent energ y that is consu med damag ing struc tures other 

than the cask, the size of the cask leak, and the fract ion of the rods in the cask that are faile d by

the impact loads . Becau se only a hot, long durat ion fire can heat a spent fuel cask to

tempe ratures that are high enoug h to cause both the cask seal and spent fuel rods to fail, the

sever ity of fire accidents depen ds on fuel type (comb ustion chara cteristics ), the amoun t of fuel

avail able to be burne d, the effec ts of fuel runoff and of adsor ption of fuel by the groun d, fuel

avail ability and rate of combu stion, the stand -off dista nce of the fire from the cask, and the size

of the cask leak. 
7-28

7.2.8.1 Severity Fraction Expressions

Let Pscenario,j be the probability that an accident follows accident scenario j (the probability of path

j on the truck or rail accident event trees depicted in Figures 7.3 and 7.4). For collision

accidents, let Ppuncture/shear be the conditional probability that during the collision the cask shell is

failed by puncture or shear and Pspeed,j be the probability that the cask impact speed v for collision

accident scenario j is large enough to cause consequences of magnitude M by itself for collisiononly accidents or in conjunction with the effects of any ensuing fires for collision accidents that

initiate fires. For accidents that involve fires (collisions that initiate fires and fire-only

accidents), let Pfire/scenario,j be the probability that accident scenario j initiates a fire and Psevere fire,k

be the probability that the fire raises the temperature of cask k high enough to cause the

additional damage (seal leakage due to thermal degradation and rod failure by burst rupture)

required to produce consequences of magnitude M.

Given these definitions and assuming that these probabilities are largely independent, for

collisions that don’t initiate fires (Category 4 accidents),

Fseverity,j = Pscenario,j Pspeed,j (5)

where Pscenario,j is the probability of accident scenario j and Pspeed,j is the probability that the cask

impact speed for accident scenario j is large enough to cause consequences of magnitude M, and

all of the probabilities are conditional probabilities that are conditional on the occurrence of an

accident and each probability in this and subsequent expressions is also conditional on the

probabilities in the expression that precede it.

For Category 5 accidents that involve collisions that initiate fires,

Fseverity,j = Pscenario,j Pspeed,j Pfire/scenario,j Psevere fire,k (6)

For Category 6 accidents that involve collisions sufficiently severe to fail the cask shell by

puncture or shear and its seal by warping of the seal seat,

Fseverity,j = Pscenario,j Pspeed,jm Pfire/scenario,j Psevere fire,k Ppuncture/shear (7)

And for Category Fire-only accidents that don’t involve collisions,

Fseverity,j = Pscenario,j Psevere fire,k (8)

because by definition Pfire/scenario,j = 1.0 for fire-only accidents.

7.2.8.2 Accident Velocity Probabilities

In Section 7.2.5.1, four ranges for the cask impact speed v were defined, v30 ≤ v < v60, v60 ≤ v <

v90, v90 ≤ v < v120, and v120 ≤ v, where v30, v60, v90, and v120 are the impact speeds for end, corner,

or side impact orientations onto real yielding surfaces that cause the same damage to the cask and

its contents (spent fuel) as is caused respectively by end, corner, and side impacts at speeds of 30,

60, 90, and 120 mph onto an unyielding surface. Thus, Pspeed,j, the probability that the cask
7-29

impac t speed v for colli sion accid ent scena rio j is large enoug h to cause conse quences of

magni tude M has four value s, one for each speed range . Specific ally,

P v ,v P P v P v speed, j 30 60 orientation,m speed, jm 60 speed, jm 30

m 1

3

( ) = [ ] ( ) − ( ) =

∑

P v ,v P P v P v speed, j 60 90 orientation,m

m 1

3

( ) = [ ] speed, jm 90 speed, jm 60 ( ) − ( ) =

∑

P v ,v P P v P v speed, j 90 120 orientation,m

m 1

3

( ) = [ ] speed, jm 120 speed, jm 90 ( ) − ( ) =

∑

 P v P 1.0 P v speed, j 120 orientation,m

m 1

3

( ) ≥ = − [ ] speed, jm 120 ( ) =

∑

where v30, v60, v90, and v120 have diffe rent value s for each cask/ surface combi nation, Porien tation,m

is the proba bility that the cask impac t is an end, corne r, or side impac t and Pspeed ,jm(v30),

Pspeed ,jm(v60), Pspeed ,jm(v90), and Pspeed ,jm(v120) are respe ctively the cumul ative proba bilities for

impac t orien tation m and accid ent scena rio j that the cask impac t speed v is ≤ v30, ≤ v60, ≤ v90,

and ≤ v120.

7.2.8.3 Accident Fire Probabilities

In Secti on 7.2.5 .2, the inter nal tempe rature of the cask under ambie nt condi tions Ta, the cask

seal leaka ge tempe rature Ts

, the rod burst ruptu re tempe rature Tb, and the avera ge tempe rature of

hydroca rbon fuele d fires Tf were used to defin e three tempe rature range s: Ta ≤ Tcask ≤ Ts, Ts <

Tcask < Tb, and Tb ≤ Tcask ≤ Tf . Now, for fire- only accid ents or colli sions that initi ate fires , let

Pco-lo cated be the proba bility that the cask and the fire are co-lo cated (i.e. , that the cask is not

signi ficantly offse t from the fire) , Poptic ally dense be the proba bility that the fire diame ter is large 

enoug h to make the fire optic ally dense to loss of energ y from the cask (i.e. , the fire diame ter is

about 3 m large r than the fire diame ter that just engul fs the cask) , Pflame temp be the proba bility that

the flame temperat ure of the fire is high enoug h to raise the tempe rature of the cask inter nals to a

tempe rature that falls withi n one of the three tempe rature range s, and Pdurat ion be the proba bility

that the fire burns long enoug h so that the cask inter nals actua lly reach a tempe rature in that

tempe rature range . Final ly, for colli sions that initi ate fires , let Pfire/ scenario,j be the condi tional

proba bility that scena rio j initi ates a fire. 

Given these defin itions

Psever e fire, k = Pco-lo cated Poptic ally dense Pflame temp Pdurat ion,k (9)

where Pco-located, Poptically dense, Pengulfing, Pflame temp, and Pduration,k will have different cask-specific values

for each of the three temperature ranges, Ta ≤ Tcask ≤ Ts

, Ts < Tcask < Tb, and Tb ≤ Tcask ≤ Tf.
7-30

7.3 Values for Release Fraction Parameters

7.3.1 Fission Product Release from Failed Rods to the Cask Interior

When a spent fuel rod is failed during a transportation accident, depressurization of the rod

causes particles (fuel fines) and fission product gases, for example, noble gases and condensible

vapors such as Cs atoms, gasborne at the time of rod failure, to be carried into the cask by the

flow of He out of the failed rod. Release of fuel fines may be increased if fines on pellet surfaces

are entrained into the depressurization flow of rod gases and might be decreased if these fines

must flow through and thus be filtered by a bed of larger fines before they reach the location of

the rod failure. Release of vapors may be increased if exposure of fuel pellets to the cask

atmosphere upon rod failure leads to changes that increase the rate of release of fission product

species from the pellets (e.g., oxidation of UO2 or RuO2).

7.3.2 Noble Gases

Because spent fuel rods are usually pressurized with He to about 30 atm, when a rod fails,

depressurization to 1 atm causes 29/30 of the He in the rod to flow into the cask. Thus, the rodto-cask release fraction FRC for noble gases is 29/30 = 0.97 ≈ 1.0.

7.3.3 Particles

When first removed from a reactor, spent fuel rods contain particles of UO2 called fuel fines. If

during a transportation accident a spent fuel rod is subjected to large impact forces, fracturing of

fuel pellets will generate additional particles of UO2. If these impact forces or heating of the rod

by a fire cause the rod to fail, the rush of rod gases over pellet surfaces during rod

depressurization will cause some of the UO2 particles to be entrained into the depressurization

flow of gases which may then transport them to and through the rod failure into the cask interior.

Transport of particles through the gap to the rod failure will be inefficient for particles with

diameters similar to the gap width. In addition, if the large fuel fines in the gap act as a granular

bed, then transport of particles with diameters smaller than the gap width may also be inefficient

if these particles are efficiently captured by the bed of larger fuel fines.

Significant transport of particles from failed rods to the cask interior will occur only during rod

depressurization. Once rod depressurization has occurred, deposition of particles still gasborne

within the failed rod onto cladding and pellet surfaces will be much more rapid than transport by

diffusion out of the rod to the cask interior, and entrainment of particles off of fuel pellet and

cladding surfaces into diffusive gas flows will not occur as the velocities of diffusive flows are

much to small to cause particle entrainment.

Release of particles (fuel fines) from H. B. Robinson one-foot-long spent fuel rod sections upon

rod failure due to burst rupture was examined experimentally by Lorenz, et al. [7-26] during high

temperature tests. Most of the particles released from the rod were found to be of sizes that

deposited very rapidly onto surfaces inside of the furnace tube used to heat the test sections to

burst rupture temperatures. Examination of five radioactive particles by scanning electron

microscopy indicated that the particles deposited in the furnace tube were large (range of

diameters, 140 to 210 μm) while the particles that escaped from the furnace tube had diameters
7-31

≤ 10 μm. Lorenz, et al. calculated release fractions for fuel fines (particles of UO2) for release

into the furnace and for escape from the furnace. Table 7.12 summarizes these experimental

release fractions and shows that the fraction of respirable particles (particles with diameters

≤ 10 μm) that escaped from H. B. Robinson spent fuel rod test sections during the burst rupture

tests of Lorenz, et al. was about 3.1 × 10-6 = (2.4 × 10-4)(0.013).

Table 7.12 Experimental Release Fractions for Fuel Fines

Test

Fraction UO2 Released

from the Test Section to

the Furnace Tube

Fraction of UO2 Mass

Released to the Furnace Tube

that

Escapes from Furnace Tube

HBU-7 1.6 × 10-4 ∼ 0.02

HBU-8 4.1 × 10-4 < 0.01

HBU-9 1.8 × 10-4 ∼ 0.01

HBU-10 2.2 × 10-4 ∼ 0.02

Average 2.4 × 10-4 ∼ 0.013

Release of particles (fuel fines) from one-foot-long sections of Turkey Point spent fuel rods upon

rod failure due to burst rupture was examined experimentally by Burian, et al. [7-31, 7-32] during

high temperature tests. In a typical test, the fraction of UO2 mass released upon rod rupture was

4.2 × 10-5 and about 90 percent of this particle mass deposited onto surfaces inside of the furnace

used to heat the test sections to burst rupture temperatures. The particles that constituted the

remaining 10 percent of the particle mass escaped from the furnace and were collected on the

stages of a bank of downstream impactors. These particles had aerodynamic diameters of 4 μm

or less. Thus, the fraction of respirable particles that escaped from Turkey Point spent fuel rod

test sections during the burst rupture tests of Burian, et al. was about 4.2 × 10-6 = (4.2 × 10-

5

)(0.1), which is quite similar to the results obtained by Lorenz, et al. and suggests the use of this

value to estimate release from the one-foot portion of a real spent fuel rod that contains the rod

rupture.

During collision accidents, the impact forces should lead to the production of additional fuel

fines due to fracturing of fuel pellets. In 1994, DOE published a Handbook of airborne release

fractions for nuclear materials [7-33]. The handbook presents the following relationship between

the fraction Frespirable of a brittle material that is converted to respirable particles upon impact onto

a hard surface.

Frespirable = Aρgh

where A = 2 × 10-11 cm3

/g cm2sec-2 is an empirical constant determined by impact tests on glass

and ceramic specimens, ρ is the material (specimen) density, g is the acceleration due to gravity,

and h is the fall-height. But mgh = 0.5m(vimpact)

2

 where vimpact is the impact velocity of the

specimen onto the hard surface. So Frespirable = 0.5Aρ(vimpact)

2

. Therefore, because fuel pellet

densities are about 10 g/cm3

, for 30, 60, 90, and 120 mph pellet impacts onto cladding surfaces,
7-32

one might expect the following fractions of the pellet mass to be converted to respirable particles,

1.8 × 10-4 at 30 mph, 7.2 × 10-4 at 60 mph, 1.6 × 10-3 at 90 mph, and 2.9 × 10-3, at 120 mph.

The distribution of particle sizes produced by impact fracturing of depleted UO2 pellets has been

determined experimentally [7-34]. Figure 7.5 presents the experimental cumulative distribution

of particle sizes. The figure shows that almost 99.99 percent of the particles produced by impact

fracturing of depleted UO2 pellets have diameters ≥ 10 μm. This data suggests that, during

impact accidents, pellet fracturing would be expected to generate a bed of particles with

diameters ≥ 10 μm that fills the pellet cladding gap in the spent fuel rod and any internal crack

network in the fuel pellets.

Figure 7.5 Fracture particle size distribution for depleted UO2.

Capture of particles by a granular bed has been examined by Otani, et al. [7-35] who find that

interception is the dominant removal mechanism for particles that are somewhat smaller than the

average diameter of the bed particles. For such particles, Otani, et al. state that the single particle

interception removal efficiency ηR is

ηR = [Re/(Re2 ])1 33/116 − + R

and the total bed removal efficiency E is
7-33

η = −  −



 



 − 2

3

1 1 α

α

d

L

E g ln( )

where R = dp/dg, dp is the diame ter of the particle s entra ined in the gases flowi ng throu gh the

granu lar bed, dg is the diame ter of the parti cles that compr ise the granu lar bed; Re = ρfdgui/μ is

the Reyno lds numbe r of the gas flowi ng throu gh the bed (He for spent fuel rods) ; ui

 = us/α; ρf,

ui

, us, and μ are the densi ty, inter stitial veloc ity, super ficial veloc ity, and dynam ic visco sity of

the gas flowi ng throu gh the bed; α is the parti cle volum etric packi ng densi ty, and L is the bed

lengt h.

Now, if η is equat ed to ηR (i.e. , all remov al mecha nisms other than inter ception are negle cted),

then for a fixed value of E, for examp le 0.99, L incre ases as ηR decre ases. Thus, use of large r

value s for dg and Re will gener ate large r value s for L. Accor dingly, since the exper iments of

Lorenz, et al. show that the large st parti cles that escap ed from the spent fuel rod secti ons upon

burst ruptu re had diame ters of about 200 μm, let dg = 200 μm. A CONTA IN calcu lation

descr ibed below indic ates that us

 = 6 x 102 cm s-1 for He flow throu gh a one-f oot secti on of a

spent fuel rod that has a 20 μm gap and is press urized to 18.6 atm. Becau se us shoul d be

incre ased by highe r press ures and decre ased by longe r flow lengt hs, this value is reaso nable for

a full lengt h rod pressuriz ed to 30 atm. Thus, ui

 = 1.2 x 103 cm s-1. Because a bed of 200 μm

parti cles forme d in the 20 μm pelle t cladd ing gap must look somet hing like a singl e layer of

spher es, α = (4/3) πr

3

/(2r) 3 = 0.5. For He at 750 C, the likel y burst ruptu re tempe rature for

spent fuel rods press urized to 30 atm, Re = 77 and thus ηR = 16R1.47. For He at 350°C, the

appro ximate tempe rature of spent fuel rods durin g norma l trans port and thus the rod

depre ssurizatio n tempe rature when failu re is cause d by colli sion impac t rathe r than burst ruptu re,

Re = 311 and ηR = 16R1.34.

Now, let the bed effic iency E = 0.99, where upon L = 6.14 x 10-2/ηR. Table 7.13 prese nts, for

sever al parti cle diame ters dp of inter est, value s of ηR and L for a singl e layer bed of 200 μm

particles with He Reyno lds numbe rs of Re = 77 or 311. The table shows that this bed will

remov e parti cles with diame ters ≥ 1 μm with an effic iency of 0.99. Thus, respi rable fines with

diame ters of 1 to 10 μm shoul d also be remov ed with simil ar effic iencies from the

depre ssurizatio n flow of He throu gh the gap of a full lengt h spent fuel rod that occur s when the

rod fails due to impac t loads or therm al burst rupture. 

Table 7.13 Granular Bed Lengths that Provide 99 Percent Filtering Efficiencies

Re = 77 Re = 310

dp(μm) ηR L(cm) ηR L(cm)

30 1.00 0.06 1.00 0.06

10 0.20 0.31 0.29 0.21

 1 6.6 x 10-3 9.3 1.3 x 10-2 4.7

 0.1 8.4 x 10-5 728 6.0 x 10-4 102
7-34

Table 7.13 indicates that beds with lengths of 0.06, 0.31, and 9.26 cm would be expected to

provide 99 perce nt filte ring effic iency respe ctively for parti cles with diame ters ≥ 30, ≥ 10, and

≥ 1 μm. Thus, it seems reasonable to conclude that only about one percent of the respirable fuel

fines in a spent fuel rod will be able to be transported by depressurization gas flows through a rod

gap filled with fuel fines with diameters of order 50 to 200 μm.

Based on the prece ding discu ssion, a rod not subje ct to impac t (no parti cle produ ction by

fracturin g of UO2) might be expec ted to gener ate durin g depre ssurizatio n a plug (bed) of fuel

fines in the rod gap that would cause fines not in the one-f oot secti on of the rod that conta ins the

rod ruptu re to be filte red while the fines in the one-f oot secti on would escap e with negli gible

dimin ution due to filte ring. There fore, a reaso nable estim ate for FRC, the rod to cask relea se

fract ion for respi rable fuel fines (part iculates), for a rod not subje cted to impac t (no parti cle

produ ction by fract uring of UO2) is

F 4.2 10 1

12

11

12 RC (0.01) 3.9 10 6 7 = × ( ) + 



 



 = × − −

and becau se an 0.3 cm long bed of 200 μ parti cles will captu re 99 perce nt of the respir able fuel

fines that enter the bed, reaso nable estim ates for rods subje ct to impac t fract uring are

F 4.2 10 2.9 10 0.25

144

143.75

144 RC 3.4 10 -6 -3 -5 = × ( ) + × + ( ) 



 



 0 01 . = × for 120 mph impac ts,

F 4.2 10 1.6 10 0.25

144

143.75

144 RC 1.9 10 -6 -3 -5 = × ( ) + × + ( ) 



 



 0 01 . = × for 90 mph impac ts,

F 4.2 10 7.2 10 0.25

144

143.75

144 RC 8.5 10 -6 -4 -6 = × ( ) + × + ( ) 



 



 0 01 . = × for 60 mph impac ts,

F 4.2 10 1.8 10 0.25

144

143.75

144 RC 2.2 10 -6 -4 -6 = × ( ) + × + ( ) 



 



 0 01 . = × for 30 mph impac ts,

where the first term in the brack ets in these expre ssions repre sents parti cle relea se from the

0.25 inch (0.25 inch = 2 x 0.3 cm) porti on of the rod that conta ins the ruptu re and the secon d

term repre sents parti cle release from the other 143.7 5 inche s of the rod, 0.01 repre sents the

fract ion of respi rable fines that will pass throu gh a plug or a bed of large r fuel fines , the relea se

fract ion value of 4.2 x 10-6 refle cts the exper imental relea se fract ions for respi rable fuel fines 

measu red for the one-f oot-long exper imental test secti ons of Loren z, et al. [7-26 ] and Buria n, et

al. [7-31 ], and 2.9 x 10-3, 1.6 x 10-3, 7.2 x 10-4, and 1.8 x 10-4 are estim ates of the fract ions of

UO2 mass in fuel pellets conve rted to respi rable fuel fines by impac t fract uring as a resul t of 120,

90, 60, and 30 mph impac ts. Final ly, given the preci sion of this analy sis, use of value s of

4 x 1 0-7

 and 3 x 10-5 respe ctivel y for FRC for relea se of parti cles durin g non-i mpact and impac t

accid ents seems appropriat e.
7-35

7.3.4 Cesium

The amoun t of a conde nsible vapor (e.g. , Cs atoms ) carri ed from a faile d rod to the cask inter ior

shoul d be deter mined by the free volum e of the rod (the sum of the rod plenu m volum es, the

cladd ing gap volum e, and the volum e of the inter nal netwo rk of crack s in the fuel pelle ts

containe d in the rod) and by the parti al press ure of the conde nsible vapor at the rod tempe rature

at the time of rod failu re. If rod depre ssurizatio n leads to the adiab atic expan sion of rod gases ,

signific ant cooli ng of those gases and of the cladd ing and pelle t surfa ces that they conta ct could 

take place . If this happe ns and if the conde nsible vapor s in the rod heliu m encou nter a coole d

surfa ce befor e they are carri ed out of the rod into the cask, signi ficant conde nsation onto fuel

pelle t and rod inter nal cladd ing surfa ces may take place which would signi ficantly decre ase the

amoun ts of conde nsible vapor s relea sed to the cask. Thus, one might expec t relea se fract ions for

conde nsible vapor s to refle ct the partial press ure of the vapor at eithe r the burst ruptu re

tempe rature of the rod or the tempe rature of pelle t and/o r cladd ing surfa ces that have been

subst antially coole d by adiab atic expan sion of gases durin g rod depre ssurization. 

After a faile d rod has depressu rized, if the cask and rods are heate d by a fire to eleva ted

temperat ures, fissi on produ cts volat ile at fire tempe ratures may vapor ize from pelle t surfa ces and

then diffu se out of the rod into the cask inter ior. Thus, conde nsible vapor s could be released

both by trans port in rod depre ssurizatio n gas flows and, after rod depre ssurizatio n, by diffu sion

from the rod free volum e throu gh the rod failu re into the cask. 

7.3.4.1 Cs Release Fractions for Burst Rupture and Diffusion

Loren z, et al. exami ned relea se of Cs from heate d secti ons of simul ated [7-36 ] and real [7-26 ]

spent fuel rods by diffu sion and durin g depre ssurizatio n follo wing rod failu re due to burst 

ruptu re. By fitti ng their exper imental resul ts, Loren z, et al. devel oped empir ical model s for the

relea se of volat ile fissi on produ cts due to burst ruptu re of press urized spent fuel rods and

diffu sion subsequent to burst ruptu re [7-37 , 7-38] . For burst ruptu re, the follo wing model 

appli es,

F M

M

V M

F

A exp C

burst T

burst

inventory

burst inventory

0.2 gap

clad

0.8

= = 



 



÷ [ ] −( ) − α (10)

where Mburst is the mass (g) of the volatile fissi on produ ct relea sed due to ruptu re of the fuel rod

while press urized, Minven tory is the mass (g) of the total inven tory of the fissi on produ ct in the rod,

Vburst is the volum e (cm3) of rod gases relea sed from the rod due to rod ruptu re calcu lated at 0°C

and system pressure (0.3 MPa in the experiments of Lorenz, et al.), Fgap is the fraction of the total

inven tory of the fissi on produ ct that was in the fuel- clad gap at the time the rod ruptu red, Aclad is

the area (cm2

) of the clad with which the fissio n produ cts in the fuel- clad gap are assoc iated (the

surfa ce area of the activ e lengt h of the fuel rod), T is the tempe rature (K) of the gap gases at the

time of rod ruptu re, and α and C are adjus table const ants deter mined exper imentally for each

fission produ ct.
7-36

For release by diffusion after rod failure, the following model applies,

{ } exp[1 ] gap gapo inventory

inventory

diffusion

diffusion F MFtR

M

M

F = −−=

(11)

o = δ ( )( ) gap inventory AMFPWR clad exp[ ] − ( ) γ T 8.0

where R0 is the initial rate of diffusive release (g/hr), T is the diffusion temperature (K), t is the

time at the diffusion temperature (hr), W is the width of the fuel-cladding gap (μm), P is the

system pressure (MPa), and δ and γ are adjustable constants determined experimentally for each

fission product.

Table 7.14 presents the values determined experimentally for Cs by Lorenz, et al. for the

adjustable constants in Equations 10 and 11.

Table 7.14 Parameter Values for Lorenz Release Expressions for Cs

Parameter Cesium

α (g/cm3)(g/cm2)

-0.8 3.49

C K-1 7420

δ (g MPa/μm hr)(g/cm2)

-0.8 1.90 × 103

γ K-1 1.98 × 104

7.3.4.2 Relative Importance of Cs Release by Burst Rupture and Diffusion

Table 7.15 presents release fractions for Cs from spent fuel for several temperatures of interest

for release due to burst rupture and for 24 hours of release by diffusion. These release fractions

were calculated by Sanders et al. [7-39] using Equations 10 and 11 and the values of the

adjustable constants presented in Table 7.14.

Table shows (1) that, relative to burst release, release by diffusion is not significant at or below

600°C and (2) that, during a long duration (24 hours) engulfing hydrocarbon fuel fire, diffusion

increases total release by a factor of about three over release by burst rupture:

(burst rupture + diffusion)/(burst rupture) = (5.7 × 10-4 + 9.8 × 10-4)/(5.7 × 10-4) = 2.7

The thermal analyses presented in Section 6 showed that it takes about six hours for an engulfing

hydrocarbon fire to heat a spent fuel cask to the average temperature of the fire (1000°C) and the

fire statistics presented in Section 7.4.4.1 show that hydrocarbon fires with durations of 6 hours

or more are quite rare. Therefore, only a highly improbable fire will be able to heat a cask to

average hydrocarbon fire temperatures for more than a few hours. Now, because the exponent in

Equation 11 is small, diffusive release for 2 hours at 1000°C will be about 1/12 of the diffusive
7-37

release produced by 24 hours at 1000°C. Therefore, the diffusive release fraction for a 6-hour

fire during which the cask is at 1000°C for 2 hours will be about 0.8 × 10-4 or about 1/7 of the

burst rupture release fraction. So for almost all fires, diffusive release will not be important

compared to burst release. Consequently, release of Cs by diffusion is neglected.

Table 7.15 Comparison of Cs Release Fractions for

Rod Burst Rupture and Diffusive Release

Temperature Release Fraction

Value (C) Condition

Burst

Rupture

Diffusion

(for 24 hours)

 300 Normal Transport 4.6 × 10-7 1.3 × 10-11

 530 Regulatory Maximum 1.9 × 10-5 1.7 × 10-7

 600 3.9 × 10-5 1.1 × 10-6

 800 Regulatory Fire 1.9 × 10-4 6.4 × 10-5

1000 Hydrocarbon Fuel Fire 5.7 × 10-4 9.8 × 10-4

7.3.4.3 Rod Cooling During Burst Rupture

The influence of adiabatic expansion of rod gases during rod depressurization on the temperature

of those gases was examined by performing CONTAIN code [7-40] calculations that modeled

the temperatures of the rod gases during depressurization upon burst rupture of the HBU-7 spent

fuel test section examined by Lorenz, et al. [7-41]. The analysis focused on the thermalhydraulic conditions of the helium fill gas in the test section during the blowdown from the initial

test section pressure, after rod failure caused by induction heating.

7.3.4.3.1 HBU-7 Test Section Model

The six-cell model used to represent the HBU-7 rod test section during these calculations is

depicted in Figure 7.6. Table 7.16 presents the identities, volumes, and initial conditions of these

six cells just prior to rod failure. As Figure 7.6 and Table 7.16 show, the helium reservoir

attached to the 30.48-cm-long HBU-7 test segment was modeled by one cell, the rod test segment

by four cells, and the bulge formed in the test segment cladding just prior to segment failure by

one cell. Upon failure of the bulge by burst rupture, gases in the test section were vented through

the failure to the environment, which was thus in effect a seventh cell. Three of the six cells

described in Figure 7.6 and Table 7.16, Cells 3, 4, and 5, represent those sections of the rod test

section that were directly heated by induction during the burst rupture experiment. Because they

were not directly heated, the temperatures in Cells 1, 2, and 6 were much lower than the

temperatures in Cells 3, 4, and 5. The volumes assigned in Table 7.16 to the cells include an

estimate of the effects of clad swelling, as described in Reference 1. The volumes are several

times larger than the volumes implied by the hydraulic diameter, DH = 43.2 μm, of the annular

gap in the rod test segment, a value that was deduced from the steady-state rod blowdown

measurements [7-42].
7-38

Figure 7.6 Schematic of the CONTAIN Model for the HBU-7 rod blowdown test.

Table 7.16 Initial Conditions and Volumes for the CONTAIN Model Cells

Test Section Cells

Cell Name Reservoir Left End Left Middle Bulge Right Middle Right End

Cell No. 1 2 3 4 5 6

Rod Length in Cell (cm) 0 8 12 2* 4 6.48

Initial Pressure (bars) 18.66 18.66 18.66 18.66 18.66 18.66

Initial Temperature (K) 303 742 1181 1181 1181 742

Cell Volume (cm3) 4.33 0.44 0.45 1.9 0.15 0.36

*Heat sinks were not modeled in the bulge.

As indicated in Figure 7.16, Zr and UO2 heat sinks were modeled in Cells 2, 3, 5, and 6. Each of

the Zr and UO2 sinks in a cell were assumed to have an effective heat transfer area πDL, where D

is the fuel pellet diameter (0.932 cm), and L is the length of the rod section represented by the

cell. These heat sinks are expected to be important during the blowdown of the test segment,
7-39

because they tend to offset the cooling effects caused by gas expansion. Note that the heat

transfer areas of the UO2 heat sinks were calculated assuming that the gas in the rod test section

is confined to the rod’s annular gap. Because this assumption neglects the surface area of any

internal crack network in the fuel pellets, the UO2 heat sink areas are minimums.

The time constant th for heating of gas within the annular gap can be estimated by

k4Nu

ρDC

t

2

Hp

h =

where Cp is the specific heat of the gas, ρ is the gas density, k is the gas conductivity, and Nu is

the heat transfer Nusselt number. Here, Nu is taken to be Nu = 8.32, the Nusselt number

appropriate for fully developed laminar flow in an annular gap [7-43]. This value corresponds to

the case with equal heat flux from the inner and outer walls into the gap. As discussed below, an

order of magnitude result, not a precise value, is of interest here. For this Nusselt number, the

above equation gives very small values for the time constant, e.g., th = 5.5 × 10-7 s at 1180°K.

This value for th implies nearly instantaneous equilibration between the heat sinks and the gas

passing through the annular gap. However, it also indicates that the timesteps required for

stability in the CONTAIN calculation would be much less than the code was designed for.

Therefore in the CONTAIN results discussed below, Nu was taken to be 1,000 times smaller (Nu

= 0.00832), a value that allows reasonable calculation times but still demonstrates the isothermal

nature of the blowdown at late time. 

Along with the heating time constant, the time constant tm for equilibration of volatile fission

product concentrations in the gap is also needed. From the heat and mass transfer analogy

[7-44], this time constant is given by

f

2

H

m D4Nu

D

t =

where Df is the diffusivity of the fission product in helium. One can estimate this time constant

from kinetic theory. For I2, for example, at 1180°K and a total pressure of 20 atm, one obtains tm

= 2.9 × 10-6 s, which is also a very short time.

In the CONTAIN calculation, flow between cells was assumed to be governed by a combination

of laminar and turbulent losses of the form

2

2

FC

ρA

W P υ∆ W += CK

where ν is the gas kinematic viscosity, K is the laminar loss coefficient (m-3), W is the mass flow

rate, CFC is the CONTAIN turbulent loss coefficient, and A is the flow area. To determine K, the

effective hydraulic diameter DH for the annular gap was used. From the standard expression for
7-40

laminar flow, this corresponds to a coefficient K equal to 4.07 × 1016 L, where L is in meters. In

the CONTAIN model, the laminar loss along the rod was allocated to the flow junctions so that

one-half of the laminar loss within a cell was assigned to each junction involving that cell. The

flow junction characteristics are summarized in Table 7.17.

Table 7.17 Flow Junction Characteristics in the CONTAIN Model

Junction Cells 1-2 Cells 2-3 Cells 3-4 Cells 4-5 Cells 5-6 Cells 4-7

Flow Area (cm2) 0.0198 0.00632 0.00632 0.00632 0.00632 0.02

K (m-3) 1.63

×1015

4.07×1015 2.44×1015 8.14×1014 2.13×1015 0

CFC 1.35 0 0 0 0 1.35

7.3.4.3.2 CONTAIN Calculation Results

Figures 7.7 and 7.8 present the CONTAIN predictions for the HBU-7 rod burst rupture test.

Figure 7.7 gives the pressures in the cells along the principal blowdown path, starting with Cell 1

(the reservoir) and ending with the bulge region (Cell 4) where the rod failure occurred. This

figure indicates that the bulge region depressurizes on a very short time scale. The reservoir, on

the other hand, blows down on a much longer time scale. There is reasonable agreement between

the measured depressurization rate and the CONTAIN prediction. Note that somewhat higher

experimental depressurization rate may be the result of clad swelling effects, which would lead to

a larger DH than was deduced from the steady-state experiments. Figure 7.8 indicates that gas

initially in the bulge cools rapidly due to adiabatic expansions. However, as gas from the rest of

the system refills the bulge, there is a rapid temperature rise, and after the initial transient, the

blowdown is essentially isothermal. The gas velocity in the flow junction between Cells 3 and 4,

based on the gap flow area from the steady-state experiments, is also shown in Figure 7.8. The

indicated velocities are consistent with an isothermal process, given the time constant for gas

equilibration in the annular gap as discussed above.

Since the temperature behavior shown in Figure 7.8 corresponds to a Nusselt number that is three

orders of magnitude smaller than it should be, there is ample margin to accommodate factors

such as clad swelling that were ignored in this analysis. The discrepancy between the measured

and calculated depressurization rates indicates that clad swelling could have been important.

Because the laminar loss coefficient (which depends on DH to the third power) is somewhat more

sensitive to DH than the time constant for equilibration (which depends on DH squared), one can

conclude that the effect on gap heat transfer would be at most comparable to that in the

depressurization rate. The clad swelling would therefore not be large enough to change the

essentially isothermal nature of the blowdown at late time.

These results suggest that the work done expanding the gases in the plenum region of the rod

causes the gases in the plenum region to cool significantly. However, during transport of plenum

gases through the gap region of the rod to the burst rupture location, heat transfer from cladding

and fuel pellets to the gases flowing through the gap region heats these gases back to the

temperatures near to the rod burst rupture temperature. Therefore, since the characteristic time
7-41

0123

Time (s)

Pressure (kPa)

Cell 1

Cell 2

Cell 3

Cell 4

Experiment

0

20

40

60

80

100

120

140

160

180

200

Figure 7.7 CONTAIN predictions for the pressures in the HBU-7 experiment.

0123

Time (s)

700

800

900

1000

1100

1200

Temperature (K)

0

2

4

6

8

10

12

14

16

18

20

Flow Velocity (m/s)

Flow Velocity (Cell 3 to Cell 4) 

Gas Temperature (Cell 3)

Figure 7.8 CONTAIN predictions for the temperature in

Cell 3 and the flow velocity from Cell 3 to Cell 4.
7-42

for heat transfer to these gases during flow through the gap region is significantly shorter than the

time required to flow through the gap region, when these gases reach the burst rupture location,

they will again be saturated with Cs vapor species at the burst rupture temperature of the rod.

7.3.4.4 Burst Rupture Release Expressions for Vapors that Contain Cs

Release of a vapors that contain Cs from a failed spent fuel rod, when depressurization does not

lead to significant cooling of the gases escaping from the rupture, should be determined by the

vapor pressure of the Cs containing vapor at the temperature (Tb) of the rod at the time burst

rupture occurs. For this case, the mass of elemental Cs released (MR) is given by combining an

experimental or theoretical expression for the vapor pressure of the Cs species (Log P = −a/T+b)

with the ideal gas equation (PV = nRT) to obtain the following expression:

ba/T

b

rod

b

RR

b 10

RT

V MW

RT

PV MWMWnM +− == = (12)

where nR is the moles of Cs vapors released, MW is the molecular weight of Cs (133 g mole-1), P

is the saturation vapor pressure of the Cs vapor at the rod burst rupture temperature Tb, Vrod is the

free volume of the spent fuel rod, and R is the gas constant.

7.3.4.4.1 Cs Vapor Species

Condensible Cs vapors likely to exist in the free volume of a spent fuel rod (or rod section) at

burst rupture temperatures were identified using the VICTORIA equilibrium thermodynamics

code [7-45], which models chemical equilibrium between 288 chemical species. Of these 288

species, 27 were active during these VICTORIA calculations.

The initial molar abundances for active species were taken from the output of the ORIGEN

calculation described in Section 7.2.3.2. In addition, all of the calculations assumed that:

• The spent fuel rod (or rod section) is moisture free.

This assumption is consistent with manufacturing specifications which limit moisture

in fuel pellets to 1 ppm by mass and moisture in rod gases to 115 ppm by volume1

.

• All cesium and iodine had migrated to the surfaces of the fuel pellets.

This is a conservative assumption, because only a few percent of the cesium and

iodine in a fuel pellet would be present on or would migrate to the surface of the

pellet under transportation accident conditions. Moreover, the calculation of

equilibrium is insensitive to the abundances of species on fuel surfaces as long as

there are sufficient amounts of the equilibrating species to establish an equilibrium

between species that exist in both the condensed and vapor phases.

______________

 1. Personal Communication, J. Clauss, 1998.
7-43

• All iodine is initially present as cesium iodide (CsI).

• Excess cesium not initially present as CsI is initially present as Cs2UO4.

• CsI and Cs2UO4 form an ideal solution.

• The gas phase (free volume of the rod) is initially pure helium.

Figure 7.9 shows the variation with temperature of the concentrations of Cs vapor species

predicted by the VICTORIA code to exist in the rod free volume. The figure shows that the

important cesium species are predicted to be Cs2I2, CsI, Cs, and Cs2O. The figure also shows

that at 750°C (1023°K), the likely burst rupture temperature of intact spent fuel rods, CsI(g) is

the dominant Cs vapor.

Finally, to test the importance of the assumptions that the rod was dry and that Cs not initially

present CsI is present as Cs2UO4, calculations were performed with Cs2U2O7 as the initial

dominant cesium species and with about 0.01 mole-percent steam in the gas phase. The net

effect of these changes was to reduce the vapor pressures of Cs species.

Figure 7.9 Variation with temperature of the concentrations of

Cs vapor species predicted by the VICTORIA code.
7-44

7.3.4.4.2 Exponential Terms in Release Expressions

Becau se

gapMF inventory Mgap =

where Mgap is the mass of a radio nuclide, for examp le Cs, on surfa ces in the gap of the spent fuel

rod or rod test secti on, Equat ion 10 can be rearr anged to yield 

M V

M

A exp C

burst burst T

gap

clad

0.8

= 



 

 α ÷ [ ] −( ) (13)

The experiments of Lorenz, et al. yielded a value of 7240 K-1 for C. Now, if the exponential term

in this equat ion expre sses the depen dence of Cs vapor s on tempe rature, then one might expec t

that C/2.3 03 = 7240/ 2.303 = 3144 K-1 to be simil ar in magni tude to the value of a for CsI(g ) in

Equat ion 12. But for CsI(g ), a = 7960 K-1. Thus, the value of C deter mined by Loren z, et al.

does not seem to be consi stent with relea se of Cs princ ipally as CsI(g ). Howev er, as the

follo wing deriv ation shows , the Loren z value of C is quite consi stent with the relea se of vapor 

forms of Cs that are comprise d princ ipally of CsI(g ), provi ded relea se of Cs in parti cles is also

consi dered.

As was state d above , Cs shoul d be relea sed both as a const ituent of Cs conta ining vapor s and

also as a constituent of fuel fines blown out of the failed rod or rod section upon burst rupture. If

Equat ion 13 is equat ed to the sum of a vapor relea se term and a parti cle relea se term, then the

follo wing equat ion resul ts

α V

M

A exp C

T MW V

RT burst 10 M F gap

clad

0.8

b

rod

b

a/T b

inventory particles b 



 



÷ −

  



 



 = + − + (14)

where Fparticles is the fraction of the mass of the fuel pellets in the rod or rod section that is released

as fuel fines. But for the 900°C burst rupture tests conducted by Lorenz, et al. using sections of

spent fuel rods, α = 3.49, Vburst = 97 cm3

, Vrod = Vtest section = 2.5 cm3, Mgap/Aclad = 12.4 x 10-6 g, Tb =

1173°K, Minventory = 0.456 g Cs, and Fparticles = 2.4 x 10-4; and for Cs, MW = 133 g, and, when P is

expressed in MPa, R = 8.2 cm3

 MPa K-1 mole-1, a = 7960 K-1, and b = 4.18. Substitution of these

values into Equation 14 followed by solving for C now yields a value of 6250 K-1 for C, which

agrees quite well with the value determined experimentally by Lorenz, et al., which suggests that

Cs release at temperatures like those examined by Lorenz, et al. (700 to 900°C) can be treat ed as

the sum of a term for relea se of vapor s that conta in Cs, princ ipally CsI(g ), and a term for relea se

of fuel fines that conta in Cs atoms . Accor dingly, divis ion of the right hand side of Equat ion 14

by Minven tory yield s a pheno menologica lly reaso nable expre ssion for the rod-t o-cask relea se

fract ion for Cs that is consi stent with the exper imental resul ts of Loren z, et al. There fore, for Cs
7-45

particles

ba/T

b

rod

inventory

RC F10

RT

V

M

MW F b = + +− (15)

A maximum value for FRC for Cs can be calculated by substituting values of a and b for CsI(g)

into this expression and using the values for Fparticles calculated above for impact and non-impact

events. Accordingly, because MWCs = 133 g mole-1, Vrod = 30 cm3

, MCs,rod = 8.0 g, Tb = 1023°K,

Fparticles = 4 × 10-7 and 3 × 10-5 respectively, for non-impact and impact events, and for CsI(g) a

= 7960 K-1 and b = 4.18 when P is in MPa, FRC = 1.5 × 10-5 + 4 × 10-7 = 1.5 × 10-5 for fire-only

events and 1.5 × 10-5 + 3 × 10-5 = 4.5 × 10-5 for impact events that initiate fires. As a check, if

the CONTAIN result for the molar concentration of Cs in Cs vapors (e.g., CsI, Cs, Cs2O, and

Cs2I2) in the free volume of a PWR fuel rod at T = 1025°K is used to calculate FRC, then for nonimpact and impact events, respectively, FRC = 1.3 × 10-5 and 4.3 × 10-5. Therefore, to be slightly

conservative, use of FRC = 2 × 10-5 for fire-only events and 5 × 10-5 for impact events that initiate

hot, engulfing, optically dense, long-duration fires seems appropriate. Finally, to ensure that

these release fractions for cesium vapors are somewhat conservative, for fire scenarios that heat

the cask to rod burst rupture temperatures, no credit is taken for deposition of cesium vapors onto

cool cask surfaces (say at the ends of the cask), and for collision scenarios that initiate fires,

revaporization of cesium from particles that deposited onto cask interior surfaces following

release to the cask due to impact failure of rods is modeled whenever cask internal temperatures

equal or exceed rod burst rupture temperatures.

7.3.5 Release Following Fuel Oxidation

Lorenz, et al. found [7-46] that the diffusive release of Cs, I, and Ru at 700°C was increased

respectively by factors of 54.6, 22.4, and 2.02 × 104

 during tests that lasted 5 hours, when the

experimental atmosphere was dry air (test HBU-6) rather than steam (test HBU-1). Increased

release of Cs and I was attributed to the substantial increase in UO2 surface area that

accompanies the oxidation of UO2 to UO2+x when UO2 is exposed to air while at elevated

temperatures. Increased release of Ru was attributed to the oxidation of non-volatile asymmetric

RuO2 to volatile symmetric RuO4.

Assume that release of Cs and Ru from the test segment is complete (release fraction = 1.0) for

that region of the test segment that is subject to extensive fuel oxidation. Let Fdiffusion be the

release fraction per hour for Cs or Ru caused by diffusive release in a steam atmosphere, Foxidized

be the release fraction per hour for Cs or Ru caused by extensive oxidation of a portion of the test

segment, and Rair/steam be the ratio of the total release fraction from the test segment per hour in

air to that in steam. Then,

air/steam

diffusion

oxidized

diffusion

oxidized diffusion R1

F

F

F

FF

=+=

+ (16)

The diffusive release fractions for Cs and Ru in steam were found by Lorenz, et al. [7-47] to have

the following experimental values for test HBU-1: 2.62 × 10-7 for Cs and 3.6 × 10-10 for Ru.

Substitution of values for Fdiffusion and Rair/steam into Equation 16 allows the following values to be

calculated for Foxidized: 1.40 × 10-5 for Cs and 7.27 × 10-6 for Ru. Now, given the precision of the
7-46

experimental data, these two values are essentially the same, which suggests that the enhanced

release of Cs and Ru does occur from the same volume, the volume of the fuel which is

extensively oxidized as a result of the exposure to air while at elevated temperatures, and that

release of volatile species from this small volume of fuel that becomes extensively oxidized is

essentially complete. Now, because Foxidized is referenced to the total volume of the test segment

(VT) rather than to the portion of the test segment that is extensively oxidized due to exposure to

air while at elevated temperatures (Voxidized),

Foxidized VT = 1.0 Voxidized (17)

Because the test segment has a length of 12 inches and the fuel pellets that occupy that length

have a diameter of 9.32 mm, the total volume of the test segment (VT) is 2.08 × 104

 mm3.

Therefore, use of the larger value for Foxidized, the value for Cs, yields Voxidized = 0.29 mm3

. Now,

assume that the enhanced release of Cs and Ru occurs from a disc of oxidized fuel that lies just

under the hole predrilled in the cladding of the test segment used in test HBU-6, the test that

measured diffusive release in air at 700°C through a predrilled hole with a diameter of 1.6 mm.

Thus, if the diameter of the disc is 2doxidized + dhole, then

[ ] ( ) oxidized

2 Voxidized = π 2doxidized + hole d2d (18)

whereupon substitution of 1.6 mm for dhole and 0.29 mm3

 for Voxidized gives doxidized = 0.11 mm

and doxidized + dhole = ddisc = 1.71 mm. Since the rate of weight gain by UO2 powder, when

oxidized by exposure to low partial pressures of oxygen ( mm 1pO2 = ) at 500 or 1000°C, is 0.3

mg min-1 [7-48], oxidation of the amount of UO2 in a disc of sintered UO2 powder having a

diameter of 1.61 mm and thickness of 0.11 mm should occur in less than a minute, provided that

diffusion of oxygen into the surface layer of a sintered UO2 pellet isn’t extremely slow.

Accordingly, oxidation of a disc of sintered UO2 with dimensions similar to those considered

here, and also of all of the Ru in that disc, seems quite reasonable if the disc is exposed to oxygen

for several hours while at elevated temperatures (500 to 1000°C).

Fuel pellet surfaces can be exposed to an oxidizing agent (oxygen or carbon dioxide) while at

elevated temperatures only during accidents that involve fires. For Category 5 and Fire-only

accidents, air can enter the cask through the single cask leakage path only after the fire dies out

and cask cooling causes air to flow into the cask. Because cooling will cause any fission product

vapors (e.g., CsI or RuO4) to condense onto cask interior surfaces before they can diffuse out of

the cask to the atmosphere, oxidation of fuel during accidents that fall into either of these fire

accident categories is not of concern. However, fuel oxidation during Category 6 accidents is of

concern because these accidents by definition lead to double failures of the cask. Because of the

double failure, differential heating of the cask could induce a buoyant flow of gases through the

cask. While the fire is burning, the gases flowing through the cask would be combustion gases,

which should contain little molecular oxygen. After the fire dies out, the gas flow would be air.

Because fuel cladding is a getter and UO2 is more easily oxidized the RuO2, oxidation of Ru and

RuO2 to RuO4 will not be significant until all of the cladding and all of the UO2 near the burst

rupture hole in the cladding has been oxidized. Nevertheless, because hydrocarbon fuel fires

with durations of several hours may occur, if the collision that initiates these fires also causes a
7-47

double failure of the cask, then any sizeable buoyancy driven flow of combustion gases or air

through the cask would be expected to significantly oxidize exposed spent fuel surfaces, which

would substantially increase the release of fission products from these oxidized fuel regions.

Finally, if combustion gases or air is flowing through the cask, any fission products released to

the cask interior would be transported to the environment by the gases that are flowing through

the cask with little deposition onto cask interior surfaces.

By definition, Category 6 accidents fail all of the rods in the cask. The finite element cask

impact calculations described in Section 5.1.4 show (see Figure 5.6) that severe impacts onto

hard surfaces cause substantial slumping of the materials carried in the cask, that is, slumping of

the fuel baskets and the rods they contain. Severe slumping means that most of the rods in the

cask will be subjected to significant bending. Rod failure mechanisms due to rod bending have

been discussed by Sanders, et al., who identified three failure modes, transverse tearing,

longitudinal tearing, and rod breakage [7-49]. Assume that tearing of clad produces a crack with

a width (wcrack) of 1 mm and a length equal to half the circumference of the rod. Then, since

typical PWR and BWR rods have inside diameters respectively of about 0.9 and 1.2 cm [7-50],

typical cladding tears will expose about 15 mm2

 of pellet surface area to the cask atmosphere,

where 15 mm2

 = πdpelletwcrack/2 = π(10 mm)(1 mm)/2. By comparison, a full rod break will

expose at least the ends of two fuel pellets to the cask atmosphere (more if pellets spill from the

broken rod) and thus at least 160 mm2

 = 2π(dpellet/2)2 of pellet surface area. So, rod breakage will

expose much more pellet surface area to the cask atmosphere than will be exposed by a single

cladding tear.

In typical spent fuel baskets, the PWR and BWR rods carried in the baskets are supported by six

or seven spacers. Thus, the rods will have seven or eight regions between spacers that might

undergo bending during a severe accident. Since all of the unsupported portions of a single rod

will not undergo the same amount of bending and different rods will be bent in different ways,

most rods will fail by cracking or tearing, usually at a single location, some rods may fail by

cracking or tearing at more than one location, and a few rods may experience full circumferential

breaks. Here, it is assumed that the average set of failures per rod exposes an amount of pellet

surface equal to three times the cross-sectional area of a fuel pellet, which is equivalent to

assuming that each rod suffers three full rod breaks. But Equation 17 shows that Foxidized =

Voxidized/VT. So if rod failure exposes on average an amount of pellet surface equal to six pellet

ends, then Voxidized = 6π(dpellet/2)2

doxidized and VT = π(dpellet/2)2Lactive, where Lactive is the total

length of the all of the pellets in the fuel rod (the active length of the rod), typical values of Lactive

for PWRs and BWRs are 3.6 and 3.0 m, respectively [7-50], and doxidized = 0.11(2/5) = 0.044 mm

when fuel oxidation occurs over a two-hour rather than a five-hour time period. Therefore, a

maximum value for Foxidized for a full spent fuel rod subject to multiple breaks and exposed to air

for about two hours is

5

3

active

oxidized

active

2

pellet

oxidized

2

pellet

T

oxidized

oxidized 108.8

mm103

6(0.044mm)

L

6d

L/2)(d

d/2)(d6

V

V F − ×=

× == == π

π

and, given the approximate nature of this analysis, rounding up to the next order of magnitude is

appropriate. Therefore, Foxidized = 10-4 and thus for Category 6 accidents FRC,6 = FRC,5 + Foxidized
7-48

which means that for Cs FRC,6 = 5 × 10-5 + 10-4 = 1.5 × 10-4, and for particles FRC,6 = 3 × 10-5 +

10-4 = 1.3 × 10-4.

7.3.6 CRUD

The formation of radioactive deposits called CRUD on the surfaces of spent fuel rods and the

release to the cask interior by spallation of these materials during transportation in a spent fuel

cask has been critically reviewed by Sandoval, et al. [7-17]. Sandoval, et al. state that “CRUD is

a mixture of reactor primary cooling system corrosion products that have deposited on fuel rod

surfaces,” that the “deposits contain neutron-activated nuclides,” and that during transport in a

spent fuel cask portions of the deposits “may spall from the rods, become airborne in the cask

cavity, and be released to the environment should a leak develop in the cask....” During routine

(accident free) transportation of spent fuel, CRUD spallation from rod surfaces is principally

caused by vibration of the rods. However, should an accident occur during the course of the trip,

the mechanical loads experienced by the rods during the accident might cause large fractions of

the CRUD on the rods to spall from the rod surfaces forming flakes and particles, some of which

would become gasborne in the cask interior. To develop an expression for STCRUD,i, the

contribution of radionuclide i in CRUD to a transportation accident source term, let ICRUD,i be the

inventory of radionuclide i in all of the CRUD on all of the spent fuel rods in the spent fuel

transportation cask, FCRUD,RCi be the fraction of the CRUD on an average rod that spalls from the

rod surface during an accident to form particles that become gasborne in the cask interior, and

FCEi be the fraction of the gasborne CRUD particles that is transported from the cask interior to

the environment through the cask leak. Then, STCRUD,i = ICRUD,iFCRUD,RCiFCEi.

Sandoval, et al. measured surface concentrations of radionuclides in CRUD on rod surfaces upon

discharge from the reactor [7-51]. They found that the following radionuclides accounted for

most of the radioactivity at the time of fuel discharge: 58Co, 60Co, 54Mn, 51Cr, 59Fe, 95Zr, 125Sb

and 65Zn. However, because all of these radionuclides except 60Co decay rapidly, after storage

for 5 years, 60Co accounts for 92 percent of the radioactivity in CRUD on PWR rods and 98

percent on BWR rods. The measurements also showed that maximum 60Co activity densities at

discharge ranged from 2 to 140 μCi/cm2

 on rods from U.S. PWRs and from 11 to 595 μCi/cm2

on rods from U.S. BWRs. Now given that PWR and BWR spent fuel rods have total surfaces

areas of approximately 1200 and 1600 cm2

, respectively [7-50], maximum 60Co CRUD

inventories per rod are respectively about 2 × 105 μCi = (1200 cm2

)(140 μCi/cm2) for PWRs and

1 × 106 μCi = (1600 cm2

)(595 μCi/cm2) for BWRs. Finally, multiplication of these maximum

60Co inventories per rod by the number of rods per cask will yield maximum values for 60Co for

ICRUD,i.

Scanning Electron Microscopic examination of CRUD shows [7-52] that CRUD deposits are not

solid films but instead consist of agglomerates comprised of irregularly shaped particles with

diameters that range from approximately 0.1 to 10 μm. The agglomerates have a log-normal size

distribution that has a number geometric mean diameter of 3.0 μm and a geometric standard

deviation of 1.87. The CRUD layer has a density of 1.1 g cm-3 and a void fraction of 0.8. Thus,

the density of the CRUD particles is about 5.5 g cm-3, which means that the aerodynamic

equivalent Geometric Mass Median Diameter of the particles is about 22.8 μm and the fraction of

the mass of the CRUD layer that is in particles with sizes ≤ 10 μm is about 0.094.
7-49

Spallation of CRUD from spent fuel rods was reviewed by Sandoval, et al. [7-53]. That review

found data for CRUD spallation (a) from rods exposed to flowing gases (air, nitrogen, argon) for

long periods of time at ambient or moderately elevated temperatures (230°C), (b) from rods

heated to elevated temperatures (300 to 450°C) for short time periods (0.5 to 2.0 hours), but no

data for spallation of CRUD from rods subjected to impact loads. Heating of PWR and BWR

rods to 230°C for 0.5 hours caused at least 5 to 6 percent of the CRUD on the rods to be removed

by spallation and possibly 8 percent when experimental uncertainties are considered. Heating to

300°C for 0.5 hours, then to 400°C for 1.0 hour, and finally to 450°C for 2.0 hours was estimated

to cause 12 to 15 percent of the CRUD on the rods to be removed by spallation.

The following equation gives the fraction Frespirable of a brittle material that is converted to

respirable particles upon impact onto a hard surface,

Frespirable = Aρgh

where A = 2 × 10-11 cm3

/g cm2sec-2 is an empirical constant determined by impact tests on glass

and ceramic specimens, ρ is the material (specimen) density, g is the acceleration due to gravity,

and h is the fall-height [7-33]. But mgh = 0.5m(vimpact)

2

 where vimpact is the impact velocity of the

specimen onto the hard surface. So Frespirable = 0.5Aρ(vimpact)

2

. Therefore, because the density of

CRUD is 5.5 g/cm3

, if CRUD behaved like a brittle solid, it would have a spallation fraction for

respirable particles of about 1.6 × 10-3 for a 120 mph impact onto a hard surface. Because

CRUD spallation fractions when subjected to thermal loads are so much larger than this value, it

seems likely that CRUD spallation fractions during collisions will also be much larger than 10-3,

probably similar to the values found for spallation due to thermal loads, and thus of order 10-1.

Therefore, since citation and key-word searches identified no additional CRUD spallation data

other than that presented by Sandoval, et al., the following values were used for FCRUD,RC, the

CRUD spallation fraction: for fires not initiated by collisions, FCRUD,RC = 0.15; for collisions that

don’t initiate fires, FCRUD,RC = 0.1; and for collisions that lead to fires, FCRUD,RC,impact = 0.1 and

FCRUD,RC,fire = 0.05.

7.3.7 Impact Failure of Spent Fuel Rods

In Section 5.4, estimates of the fraction of rods failed by end, corner, and side impacts onto an

unyielding surface at four speeds, 30, 60, 90, and 120 mph, were developed for each of the four

generic casks being examined by this study when each cask is carrying PWR or BWR fuel

assemblies. Table 7.18 presents these fractions (expressed as percents), the average result for

each impact orientation, and a weighted summation of these average results using as weights the

expected frequencies of end (0.056), corner (0.722), and side (0.222) impacts that are defined

below in Section 7.4.3.2.

Inspection of Table 7.18 shows that failure of all of the rods in a PWR assembly is predicted for

60 mph corner impacts onto an unyielding surface by steel-DU-steel truck casks and 60 mph end

impacts onto an unyielding surface by monolithic steel rail casks. For BWR assemblies, failure

of all of the rods is not predicted at 60 mph for any cask or impact orientation but is predicted for

corner impacts at 90 mph onto an unyielding surface by steel-DU-steel truck casks.

Nevertheless, because the finite element calculations show that slumping of cask internal
7-50

structures (i.e., the fuel assemblies being carried in the cask) is substantial for 90 mph impacts

onto an unyielding surface, failure of all of the rods in PWR or BWR assemblies is assumed for

any impact onto an unyielding surface by any cask at any orientation whenever the impact speed

is ≥ 90 mph, and thus failure of all rods is also assumed for any impact onto a real yielding

surface at a speed that is equivalent to a 90 mph impact onto an unyielding surface (i.e., for

impacts onto any real yielding surface, frod,impact = 1.0 whenever vcask ≥ v90 where v90 is the impact

speed onto the real surface that is equivalent to a 90 mph impact onto an unyielding surface). For

the speed ranges, v30 to v60 and v60 to v90, frod,impact is assumed to equal the midpoint value of the

range of values given in Table 7.18. Thus, for PWR assemblies, frod,impact = 0.25 when v30 ≤ vcask

< v60, 0.59 when v60 ≤ vcask < v90, and 1.0 when v90 ≤ vcask < v120 or whenever vcask ≥ v120. And

for BWR assemblies, frod,impact = 0.03 when v30 ≤ vcask < v60, 0.20 when v60 ≤ vcask < v90, and 1.0

when v90 ≤ vcask < v120 or whenever vcask ≥ v120.

Table 7.18 PWR and BWR Rod Failure Fractions (percent) for Four Generic Casks

a. PWR Fuel Assembly

Impact Speed (mph)

Cask

Impact

Orientation 30 60 90 120

Steel-Lead-Steel Truck end 27 60 100 100

corner 7 73 100 100

side 0 0 13 27

Steel-DU-Steel Truck end 27 33 60 87

corner 13 100 100 100

side 7 27 60 87

Steel-Lead-Steel Rail end 13 60 100 100

corner 0 13 33 100

side 0 0 13 87

Monolithic Steel Rail end 13 100 100 100

corner 0 33 100 100

side 0 13 33 73

All end 20.0 63.3 90.0 96.8

corner 5.0 54.8 83.3 100.0

side 1.8 10.0 29.8 68.5

All All 5.1 45.3 71.8 92.8
7-51

Table 7.18 PWR and BWR Rod Failure Fractions (percent) for Four Generic Casks

(continued)

b. BWR Fuel Assembly

Impact Speed (mph)

Cask

Impact

Orientation 30 60 90 120

Steel-Lead-Steel Truck end 0 0 14 29

corner 0 0 57 100

side 0 0 0 0

Steel-DU-Steel Truck end 0 0 0 0

corner 0 29 100 100

side 0 0 0 0

Steel-Lead-Steel Rail end 0 0 14 43

corner 0 0 0 43

side 0 0 0 0

Monolithic Steel Rail end 0 29 57 71

corner 0 0 29 57

side 0 0 0 0

All end 0 7.3 21.3 35.8

corner 0 7.3 46.5 75.0

side 0 0.0 0.0 0.0

All All 0 5.6 34.8 56.2

7.3.8 Fission Product Transport from the Cask Interior to the Environment

Transport of aerosols and fission product vapors, released to the interior of a Type B TN-125

cask, from the cask interior to the environment was modeled by Shaffer using the MELCOR code

[7-30]. Figures 7.10 and 7.11 present results from this study for a collision scenario that does not

initiate a fire.

Figure 7.10 compares the size distribution of the particles sourced into the cask from the spent

fuel rods upon failure due to impact to the distribution of the particles that escape from the cask.

The figure shows that for leak paths with cross-sectional areas of 4 and 100 mm2

, deposition

processes largely deplete the source distribution of particles with diameters larger than 10 μm.

Figure 7.11 displays the dependence of cask-to-environment release fractions (FCE) on the crosssectional area of the seal leakage path that was calculated for a TN-125 cask, when the cask is

pressurized to 5 atm by the failure of all of the rods in the cask during a high-speed collision and

then depressurizes to atmospheric pressure (patm) at a rate determined by the seal leak area.

Figure 7.11 shows that cask-to-environment release fractions (FCE) increase as cask leak areas

increase. This is to be expected since, after pressurization due to the failure of the fuel rods, cask

depressurization times decrease as cask leak areas increase. Thus, a large leak area means a short

depressurization time, little time for fission product deposition to cask interior surfaces, and
7-52

Figure 7.10 Size distributions of the particles sourced into

the TN-12 cask from failed spent fuel rods, and of the particles that

escaped from the cask through 4 and 100 mm2

 cask failures.

Figure 7.11 Dependence of Cask-to-Environment Release Fractions

(1.0 – Retention Fraction) on the Size of the Cask Failure (leak area).
7-53

consequently large cask-to-environment release fractions. In Figure 7.11, the curve for TeO

closely tracks the curve for fuel fines (i.e., UO2), while the curves for CsI and CsOH, which exist

partly as vapors at cask internal temperatures, diverge from the UO2 curve as hole sizes decrease.

The TeO curve tracks the UO2 curve because TeO is released and transports as a constituent of

particles. The CsI and CsOH curves diverge from the UO2 curve as hole sizes decrease because,

when hole sizes are small and there is significant time for deposition to occur, deposition onto

cool interior cask surfaces of the small fraction of CsI and CsOH that is initially released as

vapors is significantly more efficient than is deposition of CsI and CsOH that is released as a

constituent of particles.

As was stated in Sections 7.2.5.1 and 7.2.5.2, leakage of elastomeric truck and train cask seals

due to heating by fires to 350oC and of elastomeric rail and truck cask seals due to cask impacts

onto yielding surfaces at speeds equivalent respectively to 60 and 120 mph impacts onto an

unyielding surface are assumed to produce 1 mm2

 leak areas. In Section 7.2.5.2, it was

concluded that, when heated above 450oC, elastomeric seals will fail catastrophically causing

seal leak areas to be set by the space between the contacting surfaces of the cask lid and the cask

lid well. In Section 5.1.4, the closure region distortions in rail casks produced by impacts onto an

unyielding surface at speeds of 60, 90, and 120 mph were used to estimate the seal leak areas that

these impacts would cause. Table 7.19 presents the estimates of rail cask seal leak areas

developed by this analysis, the values selected for use in developing release fractions, and the

values of the cask-to-environment release fractions for particles and CsI(g) that Figure 7.11

shows correspond to these leak areas.

Table 7.19 Seal Leak Areas and Values of FCE for Rail Casks

Cask Impact Leak Area (mm2) FCE

Calculated Values Analysis Values

Speed Orientation Steel-LeadSteel Cask

Monolithic

Steel Cask

All Rail

Casks

Particles CsI(g)

 60 Corner 0.18 1a,b 0.02 0.0008

 90 Corner 346 256 300c 0.6 0.4

120 Corner 2046 1616 1800d 0.8 0.8

120 Side 9 10 0.2 0.06

a. Rounded to 1 mm2 so as to be consistent with treatment of truck cask leak areas.

b. The oblong nature of seal leak cross sections and the log-normal character of particle size distributions means

that leaks with areas significantly smaller than 1 mm2

 need not be considered. For example, an 0.1 mm2 leak

that is one bolt spacing (35 to 60 mm) long is only 1.5 to 3 μm wide and thus will not transmit significant

quantities (by mass) of respirable particles (particles with diameters ≤ 10 μm).

c. Average of steel-lead-steel and monolithic steel rail cask results.

d. Scaled by a factor of six, the average of the ratios of calculated 120 and 90 mph results.

Let fdeposition be the fraction of the particles or vapors, released to the interior of a RAM transport

cask upon rod failure, that deposit onto cask interior surfaces before they can escape from the

cask to the environment. This fraction is related to FCE by the following equation:

FCE = (1 − fdeposition)(1 − patm/pImp)
7-54

Since patm =1.0 and pImp = 5.0 for the TN-125 cask calculation, values for fdeposition can be

calculated for the rail cask leak areas presented in Table 7.19 by substitution of the values for FCE

that correspond to these leak areas. Then weighted summation of the resulting orientationdependent leak areas using as weights the expected frequencies of end (0.056), corner (0.722),

and side (0.222) impacts that are defined below in Section 7.4.3.2 yields the values for fdeposition

for the indicated speed ranges listed in Table 7.20.

Table 7.20 Values of fdeposition for Rail Casks

Speed Range fdeposition

(mph) Particles CsI(g)

 60 to 90 0.98 0.999

 90 to 120 0.45 0.64

  120 0.2 0.26

Finally, because elastomeric cask seal leakage caused by heating by a fire to 350oC and

elastomeric truck cask seal leakage caused by cask impacts at 120 mph and any orientation onto

an unyielding surface are assumed to produce 1 mm2

 seal leak areas, for these seal leak, fdeposition

equals 0.98 for particles and 0.999 for CsI(g). However, no credit is taken for deposition of Cs

vapor species during scenarios that involve fires that heat the cask to temperatures ≥ 750oC.

Thus, whenever release of Cs as a vapor (e.g., CsI) is significant, deposition of that vapor species

onto cool cask interior surfaces is neglected (e.g., fdeposition,CsI = 0.0). Thus, Cs vapor deposition is

treated when rod failure is caused by impact but not when it is caused by burst rupture.

7.3.9 Expansion Factor Values

Transport of radioactive species from the cask to the environment during depressurization of the

cask or due to heating of cask gases by a fire was discussed in Sections 7.2.5.4 and 7.2.5.5. In

Section 7.2.5.6, expansion factor expressions were derived that allowed the fraction of the cask

gases that escape from the cask to the environment during cask depressurization or heating by a

fire to be calculated. Table 7.21 presents the values of the parameters that enter each expansion

factor and the value of the expansion factor produced by these parameter values. Values of pImp

and pb, which are respectively the pressure of the cask after some fraction of the rods in the cask

are failed by impact and by burst rupture, are calculated using the following equations:

)(F atm 0.4atm 0.1pImp += impactrod, and )F0.1( atm 0.4atm 0.1pb += − impactrod,

where 1.0 atm is the internal pressure of the cask during normal transport and 4.0 atm is the

pressure rise produced by the failure of all of the rods in the cask. Thus, for example, pimp = 3.36

atm = 1.0 + 4.0(0.59), when 59 percent of the rods in the cask fail upon impact and pb = 4.20 atm

= 1.0 + 4.0(1.0 0.20), when the 80 percent of the rods not failed by collision impact are later

failed by burst rupture due to heating by an ensuing fire.
7-55

Table 7.21 Expansion Factor Values

Expansion Factor Frod,impact Temperatures (K) Pressures (atm) Value

PWR BWR Ta Ts Tb Tf patm pImp pb

fe1 = (patm/pImp)(Ta/Ts) 1.00 1.00 573 623 1.0 5.00 0.184

0.59 573 623 1.0 3.36 0.274

0.25 573 623 1.0 2.00 0.460

0.20 573 623 1.0 1.80 0.511

0.03 573 623 1.0 1.12 0.821

fe2 = (Ts/Tb) all 623 1023 0.609

fe3 = (patm/pimp)(Ta/Tb) 1.00 1.00 573 1023 1.0 5.00 0.112

0.59 573 1023 1.0 3.36 0.167

0.25 573 1023 1.0 2.00 0.280

0.20 573 1023 1.0 1.80 0.311

0.03 573 1023 1.0 1.12 0.500

fe4 = (patm/pb)(Tb/Tf) 1.00 1.00 1023 1273 1.0 1.0 0.804

0.59 1023 1273 1.0 2.64 0.304

0.25 1023 1273 1.0 4.00 0.201

0.20 1023 1273 1.0 4.20 0.191

0.03 1023 1273 1.0 4.88 0.165

0.0 0.0 1023 1273 1.0 5.00 0.161

fe5 = (patm/pimp) 1.00 1.00 1.0 5.00 0.200

0.59 1.0 3.36 0.298

0.25 1.0 2.00 0.500

0.20 1.0 1.80 0.556

0.03 1.0 1.12 0.893

7.4 Values for Severity Fraction Parameters

7.4.1 Introduction

Severity fraction expressions were formulated in Section 7.2.8. In this section, values are

developed first for the parameters that enter those expressions and then for the severity fractions

themselves by substitution of the parameter values into the individual severity fraction

expressions.

7.4.2 Cask Involvement

When a spent fuel cask is transported by truck, the truck is always a tractor semi-trailer. Trucks

that haul more than one trailer are never used. Therefore, for truck accidents, Pcask = 1.0, because

the vehicle that is carrying the cask, the tractor semi-trailer, is always involved in the accident.

Train accident data for 1972 were reviewed by Clarke, et al. [7-54] who found that freight trains

typically contain about 66 cars, that on average 10 cars are involved in side or raking collisions,

and that the number of cars involved in derailment accidents is speed dependent. For derailment

accidents, Clarke, et al. determined the average number of cars derailed during derailment

accidents that had derailment speeds that fell into the following four speed ranges: 0 to 10, 10 to

30, 30 to 60, and 60 to 80 mph. Now because the Modal Study [7-55] developed a cumulative

distribution of derailment accident speeds, the chance that a derailment accident occurs at a speed
7-56

that falls withi n each of these four speed range s can be calcu lated. Table 7.22 prese nts, for each

derailm ent accid ent speed range , the proba bility of occur rence of derai lment accid ents with

derai lment speed s that fall in each speed range and the avera ge numbe r of cars derai led durin g

those accidents .

Table 7.22 Probability of Occurrence and Average Number of Cars

Derailed for Train Derailment Accidents by Accident Speed Range

Speed Range (mph) 0 to 10 10 to 30 30 to 60 30 to 60

Probability of Occurrence 0.402 0.4079 0.1829 0.0050

Average Number of Cars Derailed 5 6 11 17

If the derai lment data of Clark e, et al. is weigh ted using the cumul ative speed distr ibution data

for derai lment accid ents prese nted in the Modal Study [7-55 ], the follo wing weigh ted summa tion

results :

N W N 5(0.402) 6(0.4079) 11(0.1829) 17(0.0050) 6.6 cars/derailment i i

i

==+ + + = ∑

where the four speed ranges are respectively 0 to 10, 10 to 30, 30 to 60, and 60 to 80 mph. Thus,

about six or seven cars will derai l durin g a typic al derai lment accid ent. But derailme nt accid ents

that occur at speed s < 30 mph will fail neith er the cask seal nor any of the spent fuel rods being 

carri ed in the cask. So if these accid ents are ignor ed, const ruction of a weigh ted sum for the

speed range s 30 to 60 and 60 to 80 mph shows that the avera ge numbe r of cars invol ved in

derailm ent accid ents of conce rn is

Ncars/derailment W N 11(0.9734) 17(0.0266) 11.2 i i

i

== + = ∑

There fore, becau se the avera ge numbe r of cars invol ved in side and rakin g colli sions is usual ly

about ten and the avera ge numbe r of cars invol ved in derailm ent accid ents that occur with speed s

≥ 30 mph is about 11, 0.17 = 11/66 is a reaso nable estim ate for Pcask for train accid ents.

7.4.3 Values for Collision Conditional Probabilities

Truck and train accid ent scena rios were discu ssed in Secti on 7.1. That section prese nted event 

trees that depic ted possi ble accid ent scena rios, where a speci fic scena rio is a uniqu e path on the

tree. Inspe ction of the truck and rail event trees depic ted in Figur es 7.3 and 7.4 shows that each

tree lists the condi tional proba bilities of occur rence of each scena rio (path ) on the tree, ident ifies

the scena rios that may lead to cask failu re (the paths marke d with an aster isk), and for colli sion

scena rios speci fies an assoc iated accid ent speed distr ibution and an impac t surfa ce. Accor dingl y,

the value of the condi tional proba bility of truck or train accid ent scena rio j, Pscena rio,j is read from

the appro priate event tree. 
7-57

7.4.3.1 Accident Velocity Probabilities

For colli sion accid ents, Pspeed ,j(v30,v60), Pspeed ,j(v60,v90), Pspeed ,j(v90,v120), and Pspeed ,j(≥v120) are

calculated using the followin g equat ions:

P v ,v P P v P v speed, j 30 60 orientation,m speed, jm 60 speed, jm 30

m 1

3

( ) = [ ] ( ) − ( ) =

∑

P v ,v P P v P v speed, j 60 90 orientation,m

m 1

3

( ) = [ ] speed, jm 90 speed, jm 60 ( ) − ( ) =

∑

 P v ,v P P v P v speed, j 90 120 orientation,m

m 1

3

( ) = [ ] speed, jm 120 speed, jm 90 ( ) − ( ) =

∑

 P v P 1.0 P v speed, j 120 orientation,m

m 1

3

( ) ≥ = − [ ] speed, jm 120 ( ) =

∑

where v30, v60, v90, and v120 are the impact speeds for end, corner, or side impact orientations onto

real yield ing surfa ces that would cause the same damag e to the cask and its conte nts (spen t fuel) 

as is predi cted respe ctively for end, corne r, and side impac ts at speed s of 30, 60, 90, and 120

mph onto an unyieldi ng surfa ce; v30, v60, v90, and v120 have diffe rent value s for each cask/ surface

combinat ion; Porien tation,m is the proba bility that the cask impac t is an end, corne r, or side impac t;

and Pspeed ,jm(v30), Pspeed ,jm(v60), Pspeed ,jm(v90), and Pspeed ,jm(v120) are respe ctively the cumul ative

proba bilities for impac t orien tation m and accid ent scena rio j that the cask impac t speed v is ≤

v30, ≤ v60, ≤ v90, and ≤ v120.

In Secti on 5.1, cask- specific value s for the impac t veloc ities, v30, v60, v90, and v120, were

determined by finit e eleme nt analy ses for impac ts onto an unyie lding surfa ce for each of the four

generic casks being exami ned by this study . In Secti on 5.2, these unyie lding surfa ce impac t

veloc ities were extra polated to yield ing surfa ces by parti tioning the impac t energ y betwe en the

cask and the yield ing surfa ce. Table 7.23 prese nts the cask speci fic real surfa ce impac t veloc ities

determined by those analy ses.

7.4.3.2 Cask Impact Orientation Probabilities

The finit e eleme nt cask impac t calcu lations descr ibed in Secti on 5 exami ned three cask impac t

orien tations, side, corne r, and end, where the cask impac t orien tation is speci fied by the angle 

betwe en the cask axis and the plane of the impac t surfa ce. By defin ition, side impac ts have

impac t angle s betwe en 0 and 20 degre es, corne r impac ts have impac t angle s betwe en 20 and 85

degre es, and end impac ts have angle s betwe en 85 and 90 degre es. Thus, for examp le, a cask

must strik e an impac t surfa ce nearl y end-o n for the impac t orien tation to be class ed as an end

impac t. Now, altho ugh the proba bility of occur rence of each of these impac t orien tations is
7-58

Table 7.23 Impact Speeds (mph) onto Real Yielding Surfaces that are

Equivalent to 30, 60, 90, and 120 mph Impacts onto an Unyielding Surface

a. Type B Steel-Lead-Steel Spent Fuel Truck Cask

Impact Surface Impact Impact Speed

Orientation v30 v60 v90 v120

Hard Rock End 30 60 90 120

Corner 30 60 90 120

Side 30 60 90 120

Soft Rock/Hard Soil/Concrete (slab, column, abutment) End 38* 177 232 273

Corner 35* 123 172 245

Side 32* 86 135 209

Clay/Silt End 84* >277 >367 >448

Corner 58* >135 >195 >279

Side 32* >170 >273 >426

Railbed/Roadbed End 38* 277 367 448

Corner 35* 135 195 279

Side 32* 170 273 426

Water End 78* ∞∞∞

Corner 150* ∞∞∞

Side 42* ∞∞∞

* From the Modal Study, driven by impact limiter response, rather than cask response.

b. Type B Steel-DU-Steel Spent Fuel Truck Cask

Impact Surface Impact Impact Speed

Orientation v30 v60 v90 v120

Hard Rock End 30 60 90 120

Corner 30 60 90 120

Side 30 60 90 120

Soft Rock/Hard Soil/Concrete (slab, column, abutment) End 38* 167 196 228

Corner 35* 204 266 316

Side 32* 142 210 303

Clay/Silt End 84* >253 >303 >360

Corner 58* >223 >298 >360

Side 32* >263 >394 >575

Railbed/Roadbed End 38* 253 303 360

Corner 35* 223 298 360

Side 32* 263 394 575

Water End 78* ∞∞∞

Corner 150* ∞∞∞

Side 42* ∞∞∞

* From the Modal Study, driven by impact limiter response, rather than cask response.
7-59

Table 7.23 Impact Speeds (mph) onto Real Yielding Surfaces that are

Equivalent to 30, 60, 90, and 120 mph Impacts onto an Unyielding Surface (continued)

c. Type B Monolithic Spent Fuel Rail Cask

Impact Surface Impact Impact Speed

Orientation v30 v60 v90 v120

Hard Rock End 30 60 90 120

Corner 30 60 90 120

Side 30 60 90 120

Soft Rock/Hard Soil/Concrete (slab, column, abutment) End 38* 419 507 573

Corner 35* 1129 1679 2171

Side 32* 256 451 522

Clay/Silt End 84* >521 >632 >750

Corner 58* >218 >321 >418

Side 32* >230 >394 >505

Railbed/Roadbed End 38* 521 632 750

Corner 35* 218 321 418

Side 32* 230 394 505

Water End 78* ∞∞∞

Corner 150* ∞∞∞

Side 42* ∞∞∞

* From the Modal Study, driven by impact limiter response, rather than cask response.

Table 7.23 Impact Speeds (mph) onto Real Yielding Surfaces that are

Equivalent to 30, 60, 90, and 120 mph Impacts onto an Unyielding Surface (continued)

d. Type B Steel-lead-steel Spent Fuel Rail Cask

Impact Surface Impact Impact Speed

Orientation v30 v60 v90 v120

Hard Rock End 30 60 90 120

Corner 30 60 90 120

Side 30 60 90 120

Soft Rock/Hard Soil/Concrete (slab, column, abutment) End 38* 319 391 509

Corner 35* 640 990 >990

Side 32* 207 289 >289

Clay/Silt End 84* >386 >480 >635

Corner 58* >133 >208 >223

Side 32* >180 >256 >262

Railbed/Roadbed End 38* 386 480 635

Corner 35* 133 208 >223

Side 32* 180 256 >262

Water End 78* ∞∞∞

Corner 150* ∞∞∞

Side 42* ∞∞∞

* From the Modal Study, driven by impact limiter response, rather than cask response.
7-60

likely to depend on accident scenario, because such scenario dependencies cannot be easily

estimated, it is assumed that impacts at any angle are equally probable. Therefore, the

probabilities of side, corner, and end impacts (values of Porientation,m) are Pside = 20/90 = 0.222,

Pcorner = 65/90 = 0.722 and Pend = 5/90 = 0.056.

7.4.3.3 Modal Study Accident Velocity Distributions

The Modal Study developed eight cumulative velocity distributions for truck and train accidents,

four truck accident and four train accident distributions. These distributions are presented in

Tables 7.24 and 7.25. Values of Pspeed,jm were calculated by linear interpolation using the data

presented in these tables.

The cumulative velocity distributions presented in Tables 7.24 and 7.25 are of three types: (1) a

velocity distribution for accidents that occur on level ground, which means that the velocity at

accident initiation of the cask and the truck or train is assumed to be the cask impact velocity,

(2) a velocity distribution for accidents where the cask and the truck or train plunge off of a

bridge and fall to the ground below and thus have an impact velocity that depends on the height

of the bridge, and (3) a velocity distribution for accidents where the cask and the truck or train

plunge down an embankment and then strike an object or a surface. As stated in the Modal

Study, the velocity distributions for truck accidents on level ground (velocity distribution v1)

reflect a reduction in velocity due to braking, the velocity distribution for train accidents that

occur on level ground (velocity distribution Tv1) take no credit for braking, and the velocity

distributions for accidents where the cask and the truck or train plunge down an embankment

were developed by constructing the vector sum of the level ground and bridge height velocity

distributions[7-56].

7.4.3.4 Puncture/Shear Probability

Collision accidents may generate sharp objects that could fail a cask by puncture or shearing of

the cask shell. Puncture and shear failure data for rail tank cars was reviewed in Section 5.3.

The review developed an estimate for the probability that a probe capable of causing puncture or

shear failures of a Type B spent fuel cask will be both formed during a collision accident, will

strike the cask in an orientation that might allow it to cause a cask failure, and will not break

before it causes the failure. The review concluded that a sharp probe capable of failing a cask by

puncture or shear might be formed during any collision accident, that probe formation would be

possible at any accident speed, and that formation was most unlikely at any speed. Accordingly,

although there are no data on the frequency of formation of very sharp very robust puncture/shear

probes during truck or train accidents, because spent fuel casks have two 1 inch steel shells and

only about 4 tank car puncture accidents in 100 lead to puncture of tank cars with 1 inch shells, it

is assumed that Ppuncture/shear = 0.001 = (0.04)2

 for all truck accidents and also for all train

accidents except train pileup accidents during which the cask is struck by a train car coupler. For

train pileup accidents, where the cask is struck by a coupler and therefore puncture or shear is

more likely to occur, it is assumed that Ppuncture/shear = 0.01.
7-61

Table 7.24 Truck Accident Velocity Distributions

v1

Initial Truck Velocity

Adjusted for Braking

v2

Impact Velocity Based

on Bridge Heights

v3

Vector Sum of First and

Second Distributions

v4

Train Grade Crossing

Accident Velocities

Velocity

(mph)

Cumulative

Probabilitya

Velocity

(mph)

Cumulative

Probabilitya

Velocity

(mph)

Cumulative

Probabilitya

Velocity

(mph)

Cumulative

Probabilitya

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

2.0 0.03834 7.74 0.00621 5.0 0.0 2.0 0.06014

6.0 0.12916 10.94 0.01550 10.0 0.00141 6.0 0.17906

10.0 0.23508 15.48 0.04754 15.0 0.00821 10.0 0.29398

14.0 0.34886 18.95 0.1051 20.0 0.03387 14.0 0.40255

18.0 0.46237 21.89 0.1952 25.0 0.11129 18.0 0.50280

22.0 0.56877 24.47 0.3178 30.0 0.28292 22.0 0.59331

26.0 0.66345 26.81 0.4629 35.0 0.51279 26.0 0.67319

30.0 0.74353 28.95 0.6124 40.0 0.70110 30.0 0.74210

34.0 0.80877 30.95 0.7464 45.0 0.81951 34.0 0.80022

38.0 0.86020 32.83 0.8508 50.0 0.89168 38.0 0.84814

42.0 0.89961 34.61 0.9217 55.0 0.93543 42.0 0.88676

46.0 0.92881 36.29 0.9635 60.0 0.96178 46.0 0.91718

50.0 0.95009 37.91 0.9849 65.0 0.97751 50.0 0.94062

54.0 0.96547 39.46 0.9945 70.0 0.98680 54.0 0.95826

58.0 0.97634 41.67 0.9991 75.0 0.99227 58.0 0.97125

62.0 0.98383 43.08 0.9998 80.0 0.99547 62.0 0.98060

66.0 0.98908 44.45 0.9999 85.0 0.99766 66.0 0.98717

70.0 0.99261 56.86 1.0 90.0 0.99901 70.0 0.99169

74.0 0.99503 95.0 0.99961 74.0 0.99473

78.0 0.99670 100.0 0.99985 78.0 0.99672

82.0 0.99825 105.0 0.99995 82.0 0.99800

86.0 0.99910 110.0 0.99998 86.0 0.99881

90.0 0.99956 115.0 0.99999 90.0 0.99930

94.0 0.99979 150.0 1.0 94.0 0.99960

98.0 0.99990 98.0 0.99977

102.0 0.99995 102.0 0.99987

106.0 0.99998 106.0 0.99993

110.0 0.99999 110.0 0.99996

150.0 1.0 114.0 0.99998

118.0 0.99999

150.0 1.0

a. Probability that the accident or impact velocity is less than or equal to the listed velocity.
7-62

Table 7.25 Train Accident Velocity Distributions

Tv1

Collision Accident

Train Velocities without

Braking

Tv2

Derailment Accident

Train Velocities without

Braking

Tv3

Impact Velocity Based

on Bridge Heights

Tv4

Vector Sum of Second

and Third Distributions

Velocity

(mph)

Cumulative

Probabilitya Velocity

(mph)

Cumulative

Probabilitya Velocity

(mph)

Cumulative

Probabilitya Velocity

(mph)

Cumulative

Probabilitya

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

2.0 0.09385 2.0 0.07543 7.74 0.00621 5.0 0.0

6.0 0.26286 6.0 0.22036 10.94 0.01550 10.0 0.00232

10.0 0.40788 10.0 0.35480 15.48 0.04754 15.0 0.01244

14.0 0.53042 14.0 0.47634 18.95 0.1051 20.0 0.04814

18.0 0.63240 18.0 0.58341 21.89 0.1952 25.0 0.14919

22.0 0.71598 22.0 0.67534 24.47 0.3178 30.0 0.35837

26.0 0.78345 26.0 0.75225 26.81 0.4629 35.0 0.60624

30.0 0.83709 30.0 0.81495 28.95 0.6124 40.0 0.77834

34.0 0.87908 34.0 0.86477 30.95 0.7464 45.0 0.87230

38.0 0.91147 38.0 0.90385 32.83 0.8508 50.0 0.92649

42.0 0.93606 42.0 0.93246 34.61 0.9217 55.0 0.95855

46.0 0.95446 46.0 0.95386 36.29 0.9635 60.0 0.97727

50.0 0.96801 50.0 0.96920 37.91 0.9849 65.0 0.98792

54.0 0.97784 54.0 0.97991 39.46 0.9945 70.0 0.99379

58.0 0.98486 58.0 0.98720 41.67 0.9991 75.0 0.99692

62.0 0.98980 62.0 0.99204 43.08 0.9998 80.0 0.99852

66.0 0.99323 66.0 0.99516 44.45 0.9999 85.0 0.99932

70.0 0.99557 70.0 0.99713 56.86 1.0 90.0 0.99970

74.0 0.99714 74.0 0.99834 95.0 0.99987

78.0 0.99818 78.0 0.99906 100.0 0.99995

82.0 0.99886 82.0 0.99948 105.0 0.99998

86.0 0.99929 86.0 0.99972 110.0 0.99999

90.0 0.99957 90.0 0.99985 150.0 1.0

94.0 0.99974 94.0 0.99992

98.0 0.99985 98.0 0.99996

102.0 0.99991 102.0 0.99998

106.0 0.99995 106.0 0.99999

110.0 0.99997 150.0 1.0

114.0 0.99998

118.0 0.99999

150.0 1.0

a. Probability that the accident or impact velocity is less than or equal to the listed velocity.
7-63

7.4.4 Values for Fire Probabilities

For fires that are initiated by collisions, the probability that a fire of concern occurs is the product

of the conditional probability that the collision scenario j initiates a fire, Pfire/scenario,j, and the

fraction of these fires, Psevere fire,k, that are severe enough to cause the cask seal to leak and/or the

spent fuel rods being transported in the cask k to fail. Of course, if the accident in question is a

fire not initiated by a collision (a fire-only accident), then Pfire/scenario,j = 1.0.

Because of the large mass of Type B spent fuel transportation casks, only a hot, co-located, fully

engulfing, optically dense, long-duration fire can heat one of these casks to temperatures where

spent fuel rods being transported in the cask will fail by burst rupture. Therefore, the fraction of

all fires that can cause thermal burst rupture of spent fuel rods (heat a cask to temperatures in the

temperature range Tb ≤ Tcask ≤ Tf ) is given by

Psevere fire,k = Pco-located Poptically dense Pflame temp Pduration,k (9)

where Pco-located is the probability that the cask and the fire are co-located (i.e., that the cask is not

significantly offset from the fire), Poptically dense is the probability that the fire diameter is large

enough to make the fire optically dense to loss of energy from the cask to the atmosphere (i.e.,

the fire diameter is about 3 m larger than the fire diameter that just engulfs the cask), Pflame temp is

the probability that the average temperature of the fire is high enough to heat the cask to a

temperature ≥ Tb, the temperature at which intact spent fuel rods fail by thermal burst rupture,

Pduration,k is the probability that the fire will burn long enough to heat generic cask k to that

temperature, Tcask is the temperature of the cask internals, and Tf is the average flame temperature

of a hydrocarbon fuel fire.

It is important to note that the four probabilities that enter the preceding expression for Psevere fire,k

should usually be largely independent. For example, large truck fires can occur only if more than

one vehicle is involved in the accident and train fires always involve more that one rail car as the

car carrying the spent fuel cask carries no fuel. So fire size and fire location should not be

correlated for large fires. Similarly, fuel character and thus fire temperature should not depend

on fire location or fire size or fire duration (smoldering smoky fires are probably optically dense

but are not likely to be large enough or hot enough to be of concern). And although fire duration

might be expected to be inversely proportional to fire size, runoff or soaking of fuel into the

ground will cause the seeming correlation to be greatly weakened. So, although some of these

four probabilities may be weakly correlated, for this analysis they are treated as though they are

uncorrelated.

Although only an unusually severe long-duration fire can heat the internals of a spent fuel cask to

rod burst rupture temperatures, less severe fires should be easily able to heat a spent fuel cask to

lower temperatures. To capture the lessened fire severity needed to heat a cask to lower

temperatures, some of the probabilities in the preceding formula can be relaxed by assuming that

all fires meet the requirement represented by that probability. For example, because elastomeric

cask seals begin to leak at about 350oC, a temperature only 50 to 100oC above normal cask

internal temperatures, it would seem that most fires that burn hot enough and long enough to heat

a spent fuel cask to 350oC would be able to do so even if they were somewhat offset (not co-
7-64

located) and weren’t optically dense (smoldering fires, very small collocated fires, and large

offset fires located far from the cask are exceptions to this statement). Accordingly, the fraction

of all fires that can heat a spent fuel cask to a temperature in the temperature range Ta ≤ Tcask ≤

Ts, where Ta is the cask internal temperature under ambient (normal transport) conditions and Ts

is the cask seal leakage temperature, is here taken to be

Psevere fire,k = Pco-located Poptically dense Pflame temp Pduration,k = Pflame temp Pduration,k

since for this temperature range it is assumed that Pco-located = Poptically dense = 1.0.

Similarly, any moderately large fire not well-separated from the cask that burns hot enough and

long enough should be able to heat the cask to a temperature greater than the temperature that

cause the cask seal to leak but not to the temperature where rods fail by burst rupture, that is, to

some temperature in the temperature range Ts<Tcask<Tb. Thus, the fraction of all fires that can

heat a spent fuel cask to a temperature in the temperature range Ts<Tcask<Tb is taken to be

Psevere fire,k = Pco-located Poptically dense Pflame temp Pduration,k = Pco-located Pflame temp Pduration,k

or

Psevere fire,k = Pco-located Poptically dense Pflame temp Pduration,k = Poptically dense Pflame temp Pduration,k

since, for a fire to heat a cask to temperature in this temperature range, the fire must either be

fairly large (i.e., Poptically dense = 1.0) but not colocated (i.e., Pco-located < 1.0) or it must be co-located

(i.e., Pco-located = 1.0) but not optically dense (Poptically dense < 1.0).

Finally, the conditional probability, Pduration,k, that the fire burns long enough so that generic cask

k is heated to a temperature that falls within one of the three temperature ranges, Ta ≤ Tcask ≤ Ts,

Ts < Tcask < Tb, and Tb ≤ Tcask ≤ Tf, is calculated using the following expressions:

)(tP)TT(TP Tk,kduration, s scaskakduration, =≤≤

)(tP)(tP)TT(TP Tk,kduration, b Tk,kduration, s bcaskskduration, =<< −

)(tP1.0)TT(TP Tk,kduration, b fcaskbkduration, −=≤≤

where for example Tk, s t is the time that it takes an optically dense, co-located, hydrocarbon

fueled fire to heat generic cask k to its seal leakage temperature Ts given that the normal internal

temperature of the cask is Ta, and (tP ) Tk,kduration, s and (tP ) Tk,kduration, b are respectively the

cumulative probabilities that the fire duration is Tk, s ≤ t and Tk, b ≤ t .

Cask-specific values for the heating times, Tk, s t , Tk, b t , and Tk, f t , were determined by 1-D

thermal calculations for each of the four generic casks being examined by this study. Those

calculations were described in Section 6. Table 7.26 presents the cask specific heating times

determined by those calculations.
7-65

Table 7.26 Durations (hr) of Co-Located, Fully Engulfing, Optically Dense, Hydrocarbon

Fuel Fires that Raise the Temperature of Each Generic Cask to Ts, Tb, and Tf

Temperature (°C)

Cask Ts = 350 Tb = 750 Tf = 1000

Steel-Lead-Steel Truck 1.04 2.09 5.55

Steel-DU-Steel Truck 0.59 1.96 5.32

Steel-Lead-Steel Rail 1.06 2.91 6.43

Monolithic Steel Rail 1.37 6.57 11

7.4.4.1 Modal Study Fire Duration Distributions

The Modal Study developed eight cumulative fire duration distributions for truck and train fires,

five truck fire distributions and three train fire distributions. Tables 7.27 and 7.28 present these

cumulative fire duration distributions. Values of ) (tP Tk,kduration, s , ) (tP Tk,kduration, b , and

)(tP Tk,kduration, f were determined by linear interpolation using the data in these tables.

7.4.4.2 Optically Dense Fire Size

The four generic casks being examined by this study all have lengths of about 5 m (200 inches).

Therefore, if engulfed by a fire, the fire must have a diameter of about 8 m (26.7 ft) if it is to be

optically dense with respect to the engulfed cask (large enough so that the cask doesn’t lose heat

by radiation through the fire plume to the atmosphere) [7-57,7-58].

7.4.4.3 Truck Collision Fire Statistics

Cumulative distributions of fire temperatures, diameters, stand-off distances, and durations for

fires initiated by collisions of trucks with other vehicles, with trains, or with fixed and non-fixed

objects have been developed by Clauss, et al. [7-5]. Clauss, et al. find that

• essentially all fires have average fire temperatures greater than 650oC, which agrees

well with the results of Lopez, et al. who found [7-59] that essentially all fires have

average flame temperatures greater than 725oC,

• only one fire in two reaches average fire temperatures of 1000oC,

• no more than one fire in two is an engulfing fire,

• 80 percent of all fires not caused by train collisions have diameters < 25 ft,

• all fires caused by train collisions have diameters > 25 ft,

• fires with diameters ≥ 25 ft initiated by truck collisions with other trucks, with cars,

and with fixed or non-fixed objects all have fire durations < 60 minutes (i.e., there is

not enough fuel available to support fires of longer durations),
7-66

• 85 percent of all fires initiated by truck collisions with tankers have durations longer

than 60 minutes, and

• only 25 percent of all fires initiated by the collision of a train with a truck have

durations longer than 60 minutes (this is because most train fires are so large, i.e.,

have such large diameters, that they do not burn very long).

Table 7.27 Truck Accident Fire Durations

Duration

(hr)

NonCollision

Accidents

Off-Road Accidents

and Collisions with

Fixed Objects

Truck/Truck

Collisions

Truck/Car

Collisions

Train Grade

Crossing

Accidents

0. 0. 0. 0. 0. 0.

0.083 0.3311 0.0321 0.0035 0.0131 0.00238

0.167 0.6596 0.2821 0.0451 0.1653 0.07222

0.250 0.8551 0.5860 0.1572 0.4179 0.16427

0.333 0.9625 0.7754 0.3488 0.6516 0.31099

0.417 0.9801 0.8769 0.5001 0.7878 0.43757

0.500 0.9897 0.9358 0.6034 0.8725 0.54957

0.583 0.9944 0.9643 0.6771 0.9161 0.64690

0.667 0.9970 0.9800 0.7322 0.9456 0.73075

0.750 0.9985 0.9902 0.7750 0.9662 0.80265

0.833 0.9992 0.9949 0.7960 0.9761 0.86416

0.917 0.9996 0.9973 0.8123 0.9838 0.87612

1.0 0.9998 0.9989 0.8257 0.9898 0.88589

1.083 0.99991 0.9995 0.8367 0.9936

1.167 0.99996 0.9998 0.8459 0.9964 0.89828

1.250 0.99999 0.99995 0.8535 0.9984

1.333 1.0 0.99998 0.8596 0.9993 0.90934

1.417 0.99999 0.8652 0.9997

1.500 1.0 0.8696 0.9999 0.91874

1.583 0.8737 0.99996

1.667 0.8779 0.99997 0.92730

1.750 0.8812 0.99999

1.833 0.8847 1.0 0.93452

1.917 0.8882

2.0 0.8917 0.94126

3.0 0.9287 0.96792

4.0 0.9503 0.98247

5.0 0.9641 0.99056

6.0 0.9773 0.99643

7.0 0.9905 1.0

8.0 1.0
7-67

Table 7.28 Train Accident Fire Durations

Duration

(hr)

Collision

Accidents

Derailment

Accidents

Fire-Only

Accidents

0.083 0.00238 0.01009 0.00943

0.167 0.07222 0.09213 0.09180

0.250 0.16427 0.17603 0.17574

0.330 0.31099 0.29164 0.29183

0.417 0.43757 0.39717 0.39789

0.500 0.54957 0.49517 0.49648

0.583 0.64690 0.58120 0.58291

0.667 0.73075 0.65917 0.66075

0.750 0.80265 0.72958 0.73139

0.833 0.86416 0.79154 0.79373

0.917 0.87612 0.80544 0.80765

1.0 0.88589 0.81870 0.82036

1.167 0.89828 0.83308 0.83454

1.333 0.90934 0.84752 0.91874

1.500 0.91874 0.86071 0.86292

1.667 0.92730 0.87388 0.87564

1.833 0.93452 0.88537 0.88704

2.0 0.94126 0.89665 0.89792

3.0 0.96792 0.94290 0.94342

4.0 0.98247 0.96790 0.96821

5.0 0.99056 0.98166 0.98239

6.0 0.99643 0.98868 0.98941

7.0 1.0 0.99380 0.99403

8.0 0.99702 0.99754

9.0 0.99910 0.99928

10.0 0.99978 0.99985

11.0 1.0 1.0

Now because only hydrocarbon fuel (or liquid chemical) fires will have average fire temperatures

≥ 1000oC, while essentially all fires will have average fire temperatures > 650oC, for trucks, Pflame

temp(Ta ≤ Tcask ≤ Tb) = 1.0 and Pflame temp(Tb ≤ Tcask ≤ Tf) = 0.5. Since only fully engulfing fires

with diameters > 25 ft will be optically dense and all truck/train accident fires have diameters >

25 ft, Poptically dense/train = 1.0. Because 80 percent of all other truck accidents lead to fires with

diameters < 25 ft, Poptically dense/not train = 0.2. Because one truck fire in two is an engulfing fire, Pcolocated = 0.5. Substitution of these values into Equation 9 yields the following expressions for the

probability of fires sufficiently severe to heat a truck spent fuel cask to a temperature in the

indicated temperature range.
7-68

Psever e fire,k(Tb ≤ Tcask ≤ Tf = Poptic ally dens e Pco-lo cated Pflame temp(Tb ≤ Tcask ≤ Tf) Pdurat ion,k(Tb ≤ Tcask ≤ Tf)

= (0.2) (0.5)(0.5) Pdurat ion,k = 0. 05 Pdurat ion,k(Tb ≤ Tcask ≤ Tf)

for t ruck accidents that don’ t involve trains

= (1.0) (0.5)(0.5) Pdurat ion,k = 0. 25 Pdurat ion,k(Tb ≤ Tcask ≤ Tf)

for t rain collisions with truc ks

Psever e fire,k(Ts ≤ Tcask ≤ Tb) = Poptic ally dens e Pco-loca ted Pflame temp(Ts ≤ Tcask ≤ Tb) Pdurat ion,k(Ts ≤ Tcask ≤ Tb)

= (0.2) (1.0)(1.0) Pdurat ion,k = 0. 2 Pduration, k(Ts ≤ Tcask ≤ Tb)

for t ruck accidents that don’ t involve trains

= (1.0) (1.0)(1.0) Pdurat ion,k = Pdurat ion,k(Ts ≤ Tcask ≤ Tb)

for t rain collisions with truc ks at grad e crossing s

since , for fires in this tempe rature range , it is assum ed that Pco-lo cated = 1.0.

 Psever e fire,k(Ta ≤ Tcask ≤ Ts) =Poptic ally dense Pco-loca ted Pflame temp(Ta ≤ Tcask ≤ Ts) Pdurat ion,k(Ta ≤ Tcask ≤ Ts)

= (1.0) (1.0)(1.0) Pdurat ion,k = Pdurat ion,k(Ta ≤ Tcask ≤ Ts)

for a ll truck a ccidents 

since , for fires in this tempe rature range , it is assumed that Poptic ally dense = Pco-lo cated = 1.0.

Final ly, Claus s et al. devel oped cumul ative distr ibutions of fire diame ters for truck colli sions

with cars, trucks, trains, and off-road objects. In addition, for each of these classes of collisions,

they also devel oped cumul ative distr ibutions of fire durat ion for fires of diffe rent sizes (rang es of

fire diame ters). Now, if Pdi is the proba bility that a truck colli sion with anoth er truck leads to a

fire with a diame ter d that lies in the diame ter range di

 to di+1, and Pi is the proba bility that fires in

this size range have durat ions ≤ 1 hour, then the chanc e PT that a truck colli sion will produ ce a

fire of any size that has a durat ion ≤ 1 hour is

P PP T di i

i

= ∑

Table 7.29 compa res the value s of cumul ative fire durat ion proba bilities for fires of any size with

durat ions ≤ 1.0 hour for vario us truck colli sions devel oped using this summa tion and the data of

Claus s, et al. to the value s developed by the Modal Study .

Table 7.29 Comparison of Modal Study Cumulative Fire Durations for Various Truck

Accidents to Those Developed by Weighted Summation of Data from Clauss, et al. [7-5]

Collision With Car With Truck With Train Off-Road

Clauss, et al. 0.99 0.80 0.94 0.995

Modal Study 0.9898 0.8257 0.8859 0.9989
7-69

Inspection of the table suggests that the results of Clauss, et al. are quite consistent with those

presented in the Modal Study. Accordingly, use of values of Poptically dense, Pco-located, and Pflame temp

developed from the data of Clauss, et al. with Modal Study fire duration data and truck accident

event tree probabilities seems appropriate.

7.4.4.4 Train Collision Fire Statistics

Because a modern study of train collision fire statistics was not identified, estimates of Poptically

dense, Pco-located, and Pflame temp for fires initiated by train collisions had to be developed by

considering other data. The results of Clauss, et al. show that fires initiated by the collision of a

train with a truck almost always have diameters ≥ 25 ft and that half of these fires have diameters

≥ 30 ft. Because these collisions are unlikely to lead to train derailments, the fires they initiate

may involve the fuel that powers the diesel engine that was hauling the train but are not likely to

involve liquid chemicals in tank cars further back in the train’s consist (the set of cars that make

up the train). Accordingly, because train accidents that lead to derailments that also initiate fires

frequently involve more than one car in the consist, the cumulative probability distribution of the

sizes of fires initiated by train derailments should lie higher than the distribution found for fires

initiated by train collisions with trucks. Therefore, because (a) fires with diameters ≥ 25 ft will

be optically dense to a cask that is engulfed by the fire, (b) fires initiated by train derailments are

likely to be larger than fires initiated by the collision of a train with a truck, and (c) essentially all

fires initiated by train collisions with a truck have diameters ≥ 25 ft, for all train fires it is

assumed that Poptically dense = 1.0.

Data on truck and train cargoes, specifically commodity flow statistics, has been compiled by the

Department of Transportation for the year 1993. Table 7.30 presents the ton-miles and ton-mile

fractions of highly combustible cargoes (commodities) that were transported over long distances

by trucks and by trains during 1993.

Table 7.30 Truck and Train Commodity Flow Statistics for 1993

Highly Combustible Cargo Train Truck

Ton-miles

(millions)

Fraction Ton-miles

(millions)

Fraction

w Coal w/o Coal w Coal w/o Coal

Coal 3.93×105 0.417 7.24×103 0.012

Petroleum na na na na na na

Chemicals 1.13×105 0.120 0.205 5.73×104 0.091 0.092

Petroleum Products 4.76×104 0.050 0.087 3.00×104 0.048 0.048

Rubber, Plastics 1.11×103 0.001 0.002 1.94×104 0.031 0.031

Lumber, Wood Products 3.04×104 0.032 0.055 2.29×104 0.036 0.037

Pulp, Paper 3.77×104 0.040 0.069 4.74×104 0.075 0.076

All Highly Combustible – w Coal 6.23×105 0.661 4.28×105 0.680

All Highly Combustible – w/o Coal 2.30×105 0.418 4.21×105 0.677

All – w Coal 9.43×105 6.29×105

All – w/o Coal 5.50×105 6.22×105
7-70

Table 7.30 shows that, when coal is excluded from consideration, the number of ton-miles of

highly combustible cargoes transported by truck is about twice that transported by train, and that

the relative amounts of the types of combustibles carried by the two transport modes are quite

similar, differing principally in that trains carry more chemicals and petroleum products than

trucks while trucks carry more rubber and plastics than trains. Because, when shipped by train,

most coal is hauled in unit trains, and because little petroleum is transported by train (long

distance transport of gaseous and liquid hydrocarbons is almost always done by pipeline), while

petroleum fuels (diesel, gasoline) are almost always transported from tank farms to gasoline

stations by truck, it is clear that large quantities of petroleum are transported by truck but little by

train. Therefore, derailments of regular trains which haul little coal or petroleum should be less

likely to initiate fires fueled by highly combustible fuels than are fires initiated by truck

collisions. Accordingly, the chance that a train derailment will initiate a fire that has an average

temperature ≥ 1000°C should be smaller than the chance that a fire initiated by truck collision

initiates such a fire. But Pflame temp(Tb ≤ Tcask ≤ Tf) = 0.5 for fires initiated by truck collisions.

Therefore, for fires initiated by train derailments, use of Pflame temp(Tb ≤ Tcask ≤ Tf) = 0.5 should be

conservative.

The discussion presented in Section 7.4.2 above suggests that side and raking collisions and train

derailments typically involve about ten rail cars. Inspection of Table 7.30 shows that about 42

percent of all cargo in regular trains (not unit trains such as coal trains) is highly combustible. So

a typical train accident will involve four cars that are carrying highly combustible cargo. Now,

given that the train accident has led to a fire and that the car carrying the spent fuel cask is one of

the cars involved in the accident, an upper bound on the chance that the ensuing fire engulfs the

cask can be calculated as the ratio of the 50 percentile fire area to the minimum area occupied by

the ten cars. Thus,

( )

( )

( )

( ) 3.0

21ftx10ft10

π ft 15

lw10

π r P

2

carcar

2

fire

engulfing = = =

where 10 ft and 21 ft are the width and length of a typical flat bed rail car.

Substitution of the values developed for Poptically dense, Pflame temp, and Pco-located for train fires into

Equation 9 yields the following expressions for the probability of train fires sufficiently severe to

heat a rail spent fuel cask to a temperature in the indicated temperature range.

 Psevere fire,k(Tb ≤ Tcask ≤ Tf) = Poptically dense Pco-located Pflame temp(Tb ≤ Tcask ≤ Tf) Pduration,k(Tb ≤ Tcask ≤ Tf)

= (1.0)(0.3)(0.5) Pduration,k = 0.15 Pduration,k(Tb ≤ Tcask ≤ Tf)

 Psevere fire,k(Ts ≤ Tcask ≤ Tb) = Poptically dense Pco-located Pflame temp(Ts ≤ Tcask ≤ Tb) Pduration,k(Ts ≤ Tcask ≤ Tb)

= (1.0)(0.3)(1.0) Pduration,k = 0.2 Pduration,k(Ts ≤ Tcask ≤ Tb)

since, for fires in this temperature range, it is assumed that Pflame temp = 1.0.

 Psevere fire,k(Ta ≤ Tcask ≤ Ts) = Poptically dense Pco-located Pflame temp(Ta ≤ Tcask ≤ Ts) Pduration,k(Ta ≤ Tcask ≤ Ts)

= (1.0)(1.0)(1.0) Pduration,k = Pduration,k(Ta ≤ Tcask ≤ Ts)

since, for fires in this temperature range, it is assumed that Pflame temp = Pco-located = 1.0.
7-71

7.5 Values for Release Fractions and Severity Fractions

7.5.1 Introduction

Severity fraction values can now be calculated by substituting the severity fraction parameter

values developed in Section 7.4 into the severity fraction expressions developed in Section 7.2.

When this is done, four sets of severity fractions are obtained, one for each of the four generic

casks, the steel-lead-steel and steel-DU-steel truck casks, and the steel-lead-steel and monolithic

steel rail casks, for which specifications were developed in Section 4.

Similarly, release fraction values can now be calculated by substituting the release fraction

parameter values developed in Section 7.3 into the release fraction expressions developed in

Section 7.2. When this is done, because low to moderate impact loads are estimated to fail more

PWR rods than BWR rods, two sets of release fractions are obtained for each generic cask, one

for PWR spent fuel and another for BWR spent fuel. Thus, eight sets of release fractions are

constructed, four sets of PWR release fractions (one set for each generic cask) and four sets of

BWR release fractions (again one set for each generic cask).

7.5.2 Calculational Method

Release fractions and severity fractions were calculated using spreadsheets. Copies of these

spreadsheets are presented in the Appendix D. Calculation of release fraction values was done

using a single spreadsheet. Four linked spreadsheets were used to calculate the severity fraction

values for each generic cask.

The first of the four severity fraction spreadsheets is the truck or train accident event tree that

gives constructs values for individual accident scenarios, Pscenario,j values. The second severity

fraction spreadsheet calculates values for Pspeed,j (v30,v60), Pspeed,j (v60,v90), Pspeed,j (v90,v120), and

Pspeed,j (≥ v120), where v30, v60, v90, and v120 are the cask impact speeds for accident scenario and

accident surface j that are equivalent to 30, 60, 90, and 120 mph impacts onto an unyielding

surface, and for example Pspeed,j (v30,v60) is the chance that the cask impact velocity onto that

surface falls within the speed range (v30,v60). These speed range probabilities are calculated by

linear interpolation using the appropriate Modal Study cumulative accident velocity distribution

and the real-surface values of v30, v60, v90, and v120 developed from the finite element cask impact

results for unyielding surfaces described in Section 5.1 by partitioning of the impact energy

between the cask and the real yielding surface as described in Section 5.2.

The third severity fraction spreadsheet calculate values for Pduration,k (Ta,Ts), Pduration,k (Ts,Tb), and

Pduration,k (Tb,Tf), where Ta, Ts, and Tf are respectively the normal internal temperature of the spent

fuel cask, the temperature at which cask elastomeric seals begin to leak due to thermal loads, and

the average temperature of a hydrocarbon fuel fire, and for example Pduration,k (Ta,Ts) is the chance

that the fire initiated by the accident burns long enough to raise the temperature of cask k into the

temperature range (Ta,Ts). As was done for cask impact velocities, these fire duration

probabilities are calculated by linear interpolation using the appropriate Modal Study cumulative

accident fire duration distribution and the values of Ta, Ts, and Tf that were developed in Section

6 for each of the four generic casks. Finally, the fourth severity fraction spreadsheet calculates
7-72

individual severity fraction values for each combination of one of the 31 truck accident scenarios

with one of the 18 truck accident cases, or one of the 25 train accident scenarios with one of the

20 rail accident cases, and then sums the results for each accident case over all of the accident

scenarios that contribute to that accident case thereby producing a set of 18 truck accident

severity fractions for each generic truck cask or 20 train accident severity fractions for each

generic rail cask.

7.5.3 Source Term Severity Fraction and Release Fraction Values

Finally, Table 7.31 presents the severity fraction and release fraction values developed by the

process outlined in the preceding section.

7.6 Conservatisms

Some of the source term models developed in this section use treatments of phenomena or

parameter values that are significantly conservative. The more significant of these conservatisms

are:

• the use of high burnup, three year cooled cask inventories rather than average burnup, ten

year cooled cask inventories that would better represent the average characteristics of the

spent fuel generated to date;

• the assumption that during collision accidents all of the pellets in a fuel rod fracture and the

calculation of the degree of fracturing assuming that the pellets are subjected to forces

equal to those generated by a 120 mph impact onto an unyielding surface;

• the assumption that the particle size distribution produced by spallation of CRUD from rod

surfaces due to mechanical or thermal loads is identical to the size distribution of the

agglomerated crystalites that comprise the CRUD deposits on the rod surfaces;

• the treatment of particle and vapor deposition onto cask interior surfaces only during the

short time period that immediately follows rod failure (e.g., during collisions accidents that

lead to fires, particle and vapor deposition is neglected during the long time periods

between the failure of some of the rods due to impact and the failure of the rest of the rods

due to burst rupture, and the neglect of vapor deposition onto cooler cask interior surfaces

following rod failure by burst rupture); and

• the neglect of plugging of small seal leak paths (leaks with cross sectional areas of order

1 mm2

) which are likely to be cracks that are much longer (at least one bolt spacing) than

they are wide (< 30 μm) and thus easily subject to plugging by larger particles entrained in

the cask’s blowdown gas flow.
Table 7.31 Source Term Severity Fractions and Release Fractions

el-DU-Steel Truck Cask Steel-DU-Steel Truck Cask

 of PWR Fuel Assemblies: 3 Number of BWR Fuel Assemblies: 7

PWR Release Fractions BWR Release Fractions

r Cs Ru Particulates CRUD

Case Severity

Fraction Kr Cs Ru Particulates CRUD

-01 2.4E-08 6.0E-07 6.0E-07 2.0E-03 1 1.53E-08 8.0E-01 2.4E-08 6.0E-07 6.0E-07 2.0E-03-01 4.1E-09 1.0E-07 1.0E-07 1.4E-03 2 5.88E-05 5.4E-03 1.6E-10 4.0E-09 4.0E-09 4.5E-04-01 5.4E-09 1.3E-07 1.3E-07 1.8E-03 3 1.81E-06 1.5E-02 4.5E-10 1.1E-08 1.1E-08 1.3E-03-01 3.6E-05 3.8E-06 3.8E-06 3.2E-03 4 7.49E-08 8.4E-01 4.1E-05 4.9E-06 4.9E-06 3.1E-03-01 1.3E-08 3.2E-07 3.2E-07 1.8E-03 5 4.65E-07 9.8E-02 2.9E-09 7.3E-08 7.3E-08 1.2E-03-01 1.5E-08 3.7E-07 3.7E-07 2.1E-03 6 3.31E-09 1.4E-01 4.1E-09 1.0E-07 1.0E-07 1.7E-03

-01 2.7E-05 2.1E-06 2.1E-06 3.1E-03 7 0.00E+00 8.4E-01 3.7E-05 4.0E-06 4.0E-06 3.2E-03

-01 2.4E-08 6.1E-07 6.1E-07 2.0E-03 8 1.13E-08 8.2E-01 2.4E-08 6.1E-07 6.1E-07 2.0E-03-01 2.7E-08 6.7E-07 6.7E-07 2.2E-03 9 8.03E-11 8.9E-01 2.7E-08 6.7E-07 6.7E-07 2.2E-03

-01 5.9E-06 6.8E-07 6.8E-07 2.5E-03 10 0.00E+00 9.1E-01 5.9E-06 6.8E-07 6.8E-07 2.5E-03

-01 2.4E-08 6.1E-07 6.1E-07 2.0E-03 11 1.44E-10 8.2E-01 2.4E-08 6.1E-07 6.1E-07 2.0E-03-01 2.7E-08 6.7E-07 6.7E-07 2.2E-03 12 1.02E-12 8.9E-01 2.7E-08 6.7E-07 6.7E-07 2.2E-03

-01 5.9E-06 6.8E-07 6.8E-07 2.5E-03 13 0.00E+00 9.1E-01 5.9E-06 6.8E-07 6.8E-07 2.5E-03

-01 9.6E-05 8.4E-05 1.8E-05 6.4E-03 14 7.49E-11 8.4E-01 1.2E-04 1.1E-04 2.4E-05 6.5E-03

-01 5.5E-05 5.0E-05 9.0E-06 5.9E-03 15 0.00E+00 8.4E-01 1.0E-04 8.9E-05 2.0E-05 6.4E-03-01 5.9E-06 6.4E-06 6.8E-07 3.3E-03 16 0.00E+00 9.1E-01 5.9E-06 6.4E-06 6.8E-07 3.3E-03-01 5.9E-06 6.4E-06 6.8E-07 3.3E-03 17 0.00E+00 9.1E-01 5.9E-06 6.4E-06 6.8E-07 3.3E-03

-01 1.7E-05 6.7E-08 6.7E-08 2.5E-03 18 5.86E-06 8.4E-01 1.7E-05 6.7E-08 6.7E-08 2.5E-03

0.0 0.0 0.0 0.0 0.0 19 0.99993 0.0 0.0 0.0 0.0 0.0

1.00000

Aerosolized Fraction = 1.0Respirable Fraction = 1.0
Table 7.31 Source Term Severity Fractions and Release Fractions (continued)

l-Lead-Steel Truck Cask Steel-Lead-Steel Truck Cask

 of PWR Fuel Assemblies: 1 Number of BWR Fuel Assemblies: 2

PWR Release Fractions BWR Release Fractions

r Cs Ru Particulates CRUD

Case Severity

Fraction Kr Cs Ru Particulates CRUD

-01 2.4E-08 6.0E-07 6.0E-07 2.0E-03 1 1.53E-08 8.0E-01 2.4E-08 6.0E-07 6.0E-07 2.0E-03-01 4.1E-09 1.0E-07 1.0E-07 1.4E-03 2 6.19E-05 5.4E-03 1.6E-10 4.0E-09 4.0E-09 4.5E-04-01 5.4E-09 1.3E-07 1.3E-07 1.8E-03 3 2.81E-07 1.5E-02 4.5E-10 1.1E-08 1.1E-08 1.3E-03-01 3.6E-05 3.8E-06 3.8E-06 3.2E-03 4 6.99E-08 8.4E-01 4.1E-05 4.9E-06 4.9E-06 3.1E-03-01 1.3E-08 3.2E-07 3.2E-07 1.8E-03 5 4.89E-07 9.8E-02 2.9E-09 7.3E-08 7.3E-08 1.2E-03-01 1.5E-08 3.7E-07 3.7E-07 2.1E-03 6 9.22E-11 1.4E-01 4.1E-09 1.0E-07 1.0E-07 1.7E-03-01 2.7E-05 2.1E-06 2.1E-06 3.1E-03 7 3.30E-12 8.4E-01 3.7E-05 4.0E-06 4.0E-06 3.2E-03-01 2.4E-08 6.1E-07 6.1E-07 2.0E-03 8 1.17E-08 8.2E-01 2.4E-08 6.1E-07 6.1E-07 2.0E-03-01 2.7E-08 6.7E-07 6.7E-07 2.2E-03 9 1.90E-12 8.9E-01 2.7E-08 6.7E-07 6.7E-07 2.2E-03

-01 5.9E-06 6.8E-07 6.8E-07 2.5E-03 10 0.00E+00 9.1E-01 5.9E-06 6.8E-07 6.8E-07 2.5E-03

-01 2.4E-08 6.1E-07 6.1E-07 2.0E-03 11 1.49E-10 8.2E-01 2.4E-08 6.1E-07 6.1E-07 2.0E-03-01 2.7E-08 6.7E-07 6.7E-07 2.2E-03 12 2.41E-14 8.9E-01 2.7E-08 6.7E-07 6.7E-07 2.2E-03

-01 5.9E-06 6.8E-07 6.8E-07 2.5E-03 13 0.00E+00 9.1E-01 5.9E-06 6.8E-07 6.8E-07 2.5E-03

-01 9.6E-05 8.4E-05 1.8E-05 6.4E-03 14 6.99E-11 8.4E-01 1.2E-04 1.1E-04 2.4E-05 6.5E-03-01 5.5E-05 5.0E-05 9.0E-06 5.9E-03 15 3.30E-15 8.4E-01 1.0E-04 8.9E-05 2.0E-05 6.4E-03

-01 5.9E-06 6.4E-06 6.8E-07 3.3E-03 16 0.00E+00 9.1E-01 5.9E-06 6.4E-06 6.8E-07 3.3E-03-01 5.9E-06 6.4E-06 6.8E-07 3.3E-03 17 0.00E+00 9.1E-01 5.9E-06 6.4E-06 6.8E-07 3.3E-03

-01 1.7E-05 6.7E-08 6.7E-08 2.5E-03 18 5.59E-06 8.4E-01 1.7E-05 6.7E-08 6.7E-08 2.5E-03

0.0 0.0 0.0 0.0 0.0 19 0.99993 0.0 0.0 0.0 0.0 0.0

1.00000

Aerosolized Fraction = 1.0Respirable Fraction = 1.0
Table 7.31 Source Term Severity Fractions and Release Fractions (continued)

Monolithic Rail Cask Monolithic Rail Cask

of PWR Fuel Assemblies: 24 Number of BWR Fuel Assemblies: 52

PWR Release Fractions BWR Release Fractions

r Cs Ru Particulates CRUD

Case Severity

Fraction Kr Cs Ru Particulates CRUD

-01 1.2E-08 2.5E-07 2.5E-07 1.4E-03 1 4.49E-09 8.9E-02 2.7E-09 5.3E-08 5.3E-08 8.9E-04-01 8.6E-06 1.3E-05 1.3E-05 4.4E-02 2 1.17E-07 8.0E-01 8.6E-06 1.3E-05 1.3E-05 4.4E-02-01 1.8E-05 1.9E-05 1.9E-05 6.4E-02 3 4.49E-09 8.0E-01 1.8E-05 1.9E-05 1.9E-05 6.4E-02-01 4.1E-09 1.0E-07 1.0E-07 1.4E-03 4 3.05E-05 5.4E-03 1.6E-10 4.0E-09 4.0E-09 4.5E-04-01 5.4E-09 1.3E-07 1.3E-07 1.8E-03 5 1.01E-06 1.5E-02 4.5E-10 1.1E-08 1.1E-08 1.3E-03-01 3.6E-05 1.4E-05 1.4E-05 5.4E-03 6 1.51E-08 8.4E-01 4.1E-05 1.8E-05 1.8E-05 5.4E-03-01 1.3E-08 2.6E-07 2.6E-07 1.5E-03 7 7.31E-08 9.8E-02 2.9E-09 5.9E-08 5.9E-08 9.8E-04-01 1.5E-08 2.9E-07 2.9E-07 1.7E-03 8 2.43E-09 1.4E-01 4.1E-09 8.3E-08 8.3E-08 1.4E-03-01 2.7E-05 6.8E-06 6.8E-06 4.5E-03 9 3.61E-11 8.4E-01 3.7E-05 1.5E-05 1.5E-05 4.9E-03

-01 8.8E-06 1.3E-05 1.3E-05 4.5E-02 10 9.93E-10 8.2E-01 8.8E-06 1.3E-05 1.3E-05 4.5E-02-01 9.6E-06 1.5E-05 1.5E-05 4.9E-02 11 3.30E-11 8.9E-01 9.6E-06 1.5E-05 1.5E-05 4.9E-02-01 1.4E-05 1.5E-05 1.5E-05 5.1E-02 12 4.91E-13 9.1E-01 1.4E-05 1.5E-05 1.5E-05 5.1E-02-01 1.8E-05 2.0E-05 2.0E-05 6.5E-02 13 3.82E-11 8.2E-01 1.8E-05 2.0E-05 2.0E-05 6.5E-02-01 2.0E-05 2.1E-05 2.1E-05 7.1E-02 14 1.27E-12 8.9E-01 2.0E-05 2.1E-05 2.1E-05 7.1E-02-01 2.2E-05 2.2E-05 2.2E-05 7.4E-02 15 1.88E-14 9.1E-01 2.2E-05 2.2E-05 2.2E-05 7.4E-02-01 9.6E-05 8.4E-05 1.8E-05 6.4E-03 16 5.69E-11 8.4E-01 1.2E-04 1.1E-04 2.4E-05 6.5E-03-01 5.5E-05 5.0E-05 8.9E-06 5.4E-03 17 3.61E-14 8.4E-01 1.0E-04 8.9E-05 2.0E-05 5.9E-03-01 1.4E-05 1.8E-05 1.5E-05 5.1E-02 18 4.91E-16 9.1E-01 1.4E-05 1.8E-05 1.5E-05 5.1E-02-01 2.2E-05 2.3E-05 2.2E-05 7.4E-02 19 1.88E-17 9.1E-01 2.2E-05 2.3E-05 2.2E-05 7.4E-02-01 1.7E-05 2.5E-07 2.5E-07 9.4E-03 20 6.32E-06 8.4E-01 1.7E-05 2.5E-07 2.5E-07 9.4E-03

0.0 0.0 0.0 0.0 0.0 19 0.99996 0.0 0.0 0.0 0.0 0.0

21 1.00000

Aerosolized Fraction = 1.0Respirable Fraction = 1.0
Table 7.31 Source Term Severity Fractions and Release Fractions (continued)

el-Lead-Steel Rail Cask Steel-Lead-Steel Rail Cask

of PWR Fuel Assemblies: 24 Number of BWR Fuel Assemblies: 52

PWR Release Fractions BWR Release Fractions

r Cs Ru Particulates CRUD

Case Severity

Fraction Kr Cs Ru Particulates CRUD

-01 1.2E-08 2.5E-07 2.5E-07 1.4E-03 1 8.20E-06 8.9E-02 2.7E-09 5.3E-08 5.3E-08 8.9E-04-01 8.6E-06 1.3E-05 1.3E-05 4.4E-02 2 5.68E-07 8.0E-01 8.6E-06 1.3E-05 1.3E-05 4.4E-02-01 1.8E-05 1.9E-05 1.9E-05 6.4E-02 3 4.49E-09 8.0E-01 1.8E-05 1.9E-05 1.9E-05 6.4E-02-01 4.1E-09 1.0E-07 1.0E-07 1.4E-03 4 2.96E-05 5.4E-03 1.6E-10 4.0E-09 4.0E-09 4.5E-04-01 5.4E-09 1.3E-07 1.3E-07 1.8E-03 5 8.24E-07 1.5E-02 4.5E-10 1.1E-08 1.1E-08 1.3E-03-01 3.6E-05 1.4E-05 1.4E-05 5.4E-03 6 1.10E-07 8.4E-01 4.1E-05 1.8E-05 1.8E-05 5.4E-03-01 1.3E-08 2.6E-07 2.6E-07 1.5E-03 7 6.76E-08 9.8E-02 2.9E-09 5.9E-08 5.9E-08 9.8E-04-01 1.5E-08 2.9E-07 2.9E-07 1.7E-03 8 1.88E-09 1.4E-01 4.1E-09 8.3E-08 8.3E-08 1.4E-03-01 2.7E-05 6.8E-06 6.8E-06 4.5E-03 9 2.51E-10 8.4E-01 3.7E-05 1.5E-05 1.5E-05 4.9E-03

-01 8.8E-06 1.3E-05 1.3E-05 4.5E-02 10 4.68E-09 8.2E-01 8.8E-06 1.3E-05 1.3E-05 4.5E-02-01 9.6E-06 1.5E-05 1.5E-05 4.9E-02 11 1.31E-10 8.9E-01 9.6E-06 1.5E-05 1.5E-05 4.9E-02-01 1.4E-05 1.5E-05 1.5E-05 5.1E-02 12 1.74E-11 9.1E-01 1.4E-05 1.5E-05 1.5E-05 5.1E-02-01 1.8E-05 2.0E-05 2.0E-05 6.5E-02 13 3.70E-11 8.2E-01 1.8E-05 2.0E-05 2.0E-05 6.5E-02-01 2.0E-05 2.1E-05 2.1E-05 7.1E-02 14 1.03E-12 8.9E-01 2.0E-05 2.1E-05 2.1E-05 7.1E-02-01 2.2E-05 2.2E-05 2.2E-05 7.4E-02 15 1.37E-13 9.1E-01 2.2E-05 2.2E-05 2.2E-05 7.4E-02-01 9.6E-05 8.4E-05 1.8E-05 6.4E-03 16 4.15E-10 8.4E-01 1.2E-04 1.1E-04 2.4E-05 6.5E-03-01 5.5E-05 5.0E-05 8.9E-06 5.4E-03 17 2.51E-13 8.4E-01 1.0E-04 8.9E-05 2.0E-05 5.9E-03-01 1.4E-05 1.8E-05 1.5E-05 5.1E-02 18 1.74E-14 9.1E-01 1.4E-05 1.8E-05 1.5E-05 5.1E-02-01 2.2E-05 2.3E-05 2.2E-05 7.4E-02 19 1.37E-16 9.1E-01 2.2E-05 2.3E-05 2.2E-05 7.4E-02-01 1.7E-05 2.5E-07 2.5E-07 9.4E-03 20 4.91E-05 8.4E-01 1.7E-05 2.5E-07 2.5E-07 9.4E-03

0.0 0.0 0.0 0.0 0.0 21 0.99991 0.0 0.0 0.0 0.0 0.0

1.00000

Aerosolized Fraction = 1.0 Respirable Fraction = 1.0
7-77

7.7 References

[7-1] L. E. Fischer, et al., “Shipping Container Response to Severe Highway and Railway

Accident Conditions,” NUREG/CR-4829, Lawrence Livermore National Laboratory,

Livermore, CA, February 1987.

[7-2] ARC/INFO Coverages and Arc View Project, K. C. Bayer Digital Map of the U.S.,

purchased from Geologic Data Systems, Inc., 1600 Emerson St., Denver, CO 80218.

[7-3] State Soil Graphics (STATSGO) Data Base, available on the Internet at

ftp.ftw.nrcs.usda.gov/pub/statsgo.

[7-4] Accidents of Motor Carriers of Property (for the years 1973 through 1983), Bureau of

Motor Carrier Safety, Federal Highway Administration, U.S. Department of

Transportation, Washington, DC, 1975-1984.

[7-5] D. B. Clauss, et al., “A Statistical Description of the Types and Severities of Accidents

Involving Tractor Semi-Trailers,” SAND93-2580, Sandia National Laboratories,

Albuquerque, NM, June 1994.

[7-6] Accident/Incident Bulletins Nos. 145 through 151, Office of Safety, Federal Railroad

Administration, U.S. Department of Transportation, Washington, DC, 1977-1983.

[7-7] Ref. [7-1], p. 2-30.

[7-8] Comments by meeting attendees at the Rail Accident Event Tree Meeting held at the

American Association of Railroads Offices in Washington, DC, November 3, 1997.

[7-9] K. S. Neuhauser and F. L. Kanipe, “RADTRAN 4, Volume II, Technical Manual,”

SAND89-2370, Sandia National Laboratories, Albuquerque, NM, May 1994.

[7-10] K. S. Neuhauser and F. L. Kanipe, “RADTRAN 4, Volume III, User Guide,” SAND89-

2370, Sandia National Laboratories, Albuquerque, NM, January 1992.

[7-11] A. G. Croff, “ORIGEN2 - A Revised and Updated Version of the Oak Ridge Isotope

Generation and Depletion Code,” ORNL-5621, Oak Ridge National Laboratory, Oak

Ridge, TN, July 1980.

[7-12] ORIGEN2 Isotope Generation and Depletion Code, CCC-371, Oak Ridge National

Laboratory, Oak Ridge, TN, 1991.

[7-13] Spent Nuclear Fuel Discharges from U.S. Reactors, Energy Information Administration,

U.S. Department of Energy, SR/CNEAF/96-01, 1994.

[7-14] International Atomic Energy Agency, Safety Series No. 7, IAEA Safety Guides,

Explanatory Material for the IAEA Regulations for the Safe Transport of Radioactive

Material (1985 Edition), 2nd Edition, Vienna, 1987.
7-78

[7-15] Code of Federal Regulations, Volume 49, Part 173.435 (49 CFR 173.435).

[7-16] RADSEL, unpublished Sandia code, available upon request.

[7-17] R. P. Sandoval, et al., “Estimate of CRUD Contribution to Shipping Cask Containment

Requirements,” SAND88-1358, Sandia National Laboratories, Albuquerque, NM,

January 1991.

[7-18] “Environmental Assessment of Urgent-Relief Acceptance of Foreign Research Reactor

Spent Nuclear Fuel,” DOE/EA-0912, U.S. Department of Energy, Washington, DC,

April 1994, Table E-7, p. E-12.

[7-19] D. A. Powers, et al., “A Review of the Technical Issues of Air Ingression During Severe

Reactor Accidents,” NUREG/CR-6218, Sandia National Laboratories, Albuquerque,

NM, September 1994.

[7-20] T. L. Sanders, et al., “A Method for Determining the Spent-Fuel Contribution to

Transport Cask Containment Requirements, Appendix III, Spent Fuel Response to

Transport Environments,” SAND90-2406, Sandia National Laboratories, Albuquerque,

NM, November 1992.

[7-21] Ref. [7-20], p. III-48.

[7-22] Ref. [7-20], p. II-138.

[7-23] J. J. Gregory, et al., Thermal Measurements in Large Pool Fires, J. Heat Transfer 111,

446 (1989).

[7-24] P. J. Nigrey, “Prediction of Packaging Seal Life Using Thermoanalytical Techniques,”

Proceedings of the 12th International Conference on the Packaging and Transportation of

Radioactive Materials (PATRAM ’98), IAEA, Vol. 4, p. 1730, 1998.

[7-25] H.-P. Weise, et al., “Untersuchung der Sicherheitreserven von Dichtsytemen für

Umschliessungen zum Transport und zur Lagerung Radioaktiver Stoffe,” Research

Project BMU/St. Sch. 1081, Final Report, 1992.

[7-26] R. A. Lorenz, et al., “Fission Product Release from Highly Irradiated LWR Fuel,”

NUREG/CR-0722, Oak Ridge National Laboratory, Oak Ridge, TN, February 1980, pp.

48-80.

[7-27] E. L. Wilmot, “Transportation Accident Scenarios for Commercial Spent Fuel,”

SAND80-2124, Sandia National Laboratories, Albuquerque, NM, February 1981.

[7-28] Ref. [7-20], p. II-149.

[7-29] L. B. Shappert, et al., “Cask Designers Guide,” ORNL-NSIC-68, Oak Ridge National

Laboratory, Oak Ridge TN, February 1970, p. 156.
7-79

[7-30] J. L. Sprung, et al., “Data and Methods for the Assessment of the Risks Associated with

the Maritime Transport of Radioactive Materials: Results of the SeaRAM Program, Vol.

2, Appendix IV, Cask-to-Environment Release Fractions,” SAND97-2222, Sandia

National Laboratories, Albuquerque, NM, August 1997.

[7-31] R. J. Burian, et al., “Response of Spent LWR Fuel to Extreme Environments,” SAND85-

7213, Sandia National Laboratories, Albuquerque, NM, August 1985 (unpublished

contractor report prepared by Battelle Columbus Laboratories; available on request).

[7-32] R. P. Sandoval, R. J. Burian, et al., “Response of Spent LWR Fuel to Extreme

Environments,” Proceedings of International Symposium on the Packaging and

Transportation of Radioactive Materials (PATRAM ’86), IAEA, Vol. 2, p. 695, 1987.

[7-33] Airborne Release Fractions/Rates and Respirable Fractions for Nonreactor Nuclear

Facilities, DOE-HDBK-3010-94, U.S. Department of Energy, Washington, DC, Vol. 1,

p. 5-23.

[7-34] Ref. [7-20], p. IV-13.

[7-35] Y. Otani, Aerosol Science Technol. 10, 463 (1989).

[7-36] R. A. Lorenz, “Fission Product Release from Simulated LWR Fuel,” NUREG/CR-0274,

Oak Ridge National Laboratory, Oak Ridge, TN, October 1978.

[7-37] R. A. Lorenz, et al., “Fission Product Source Terms for the Light Water Reactor Loss-ofCoolant Accident, Nuclear. Technology. 46, 404 (1979).

[7-38] R. A. Lorenz, et al., “Fission Product Source Terms for the Light Water Reactor Loss-ofCoolant Accident,” NUREG/CR-1288, Oak Ridge National Laboratory, Oak Ridge, TN,

July 1980.

[7-39] Ref. [7-20], p. IV-5.

[7-40] K. K. Murata, et al., “Code Manual for CONTAIN 2.0: A Computer Code for Nuclear

Reactor Containment Analysis,” NUREG/CR-6533, SAND97-1735, Sandia National

Laboratories, Albuquerque, NM, December 1977.

[7-41] Ref. [7-26], p. 48.

[7-42] Ref. [7-26], p. 128.

[7-43] F. P. Incropera and D. P. DeWitt, Fundamentals of Heat and Mass Transfer, John Wiley

& Sons, New York, 1985.

[7-44] R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, John Wiley &

Sons, New York, 1960.
7-80

[7-45] N. E. Bixler, “VICTORIA 2.0: A Mechanistic Model for Radionuclide Behavior in a

Nuclear Reactor Coolant System Under Severe Accident Conditions,” NUREG/CR6131, Sandia National Laboratories, Albuquerque, NM, 1998.

[7-46] Ref. [7-26], p. 104.

[7-47] Ref. [7-26], pp. 18-22.

[7-48] S. R. Dharwadkar and M. D. Karkhanavala, Indian J. Chem, 13, 685 (1975).

[7-49] Ref. [7-20], p. III-51.

[7-50] Ref. [7-20], Table I-3, p. I-10.

[7-51] Ref. [7-20], Table I-17, p. I-51.

[7-52] Ref. [7-20], Figures I-10 through I-12, p. I-36.

[7-53] Ref. [7-20], p. I-30.

[7-54] R. K. Clarke, et al., “Severities of Transportation Accidents, Vol. IV, Train,” SLA-74-

0001, Sandia National Laboratories, Albuquerque, NM, July 1976, pp. 15-17.

[7-55] Ref. [7-1], Table 5.2, p. 5-10.

[7-56] Ref. [7-1], Table 5.1, p. 5-8 and Table 5.2, p. 5-10.

[7-57] 10CFR71.73

[7-58] L. A. Gritzo, et al., “Transient Measurements of Radiative Properties, Soot Volume

Fraction and Soot Temperature in a Large Pool Fire,” Combust. Sci. and Tech. 139, 113

(1998).

[7-59] A. R. Lopez, et al., “Risk Assessment Compatible Fire Models (RACFMs),” SAND97-

1562, Sandia National Laboratories, Albuquerque, NM, July 1998.
8-1

8. RADTRAN CALCULATIONS

8.1 Calculations Performed

Seven sets of RADTRAN calculations and three RADTRAN sensitivity calculations are

described in this section. Each calculation develops estimates of the radiological consequences

and risks that are associated with the shipment of a single generic Type B cask that contains

power reactor spent fuel. Two types of consequences and risks are estimated—those that are

associated with the occurrence of accidents during the shipment and those associated with

shipments that take place without the occurrence of accidents.

The seven sets of RADTRAN calculations examine four cask designs, two shipment modes, two

sets of routes, and three sets of accident source terms. The four generic cask designs examined

are steel-lead-steel truck and rail casks, a steel-DU-steel truck cask, and a monolithic steel rail

cask. The two shipment modes are truck and rail. The two sets of routes are (a) 200

representative routes selected by Latin Hypercube Sampling (LHS) of route parameter

distributions and (b) four illustrative real routes plus the NUREG-0170 shipment route (Illus).

The three sets of accident source terms are the NUREG-0170 [8-1] source terms, the Modal

Study source terms [8-2], and the new source terms developed by this study.

Table 8.1 lists the seven sets of RADTRAN calculations that were performed and the defining

characteristics of each individual calculation. Table 8.1 shows that

• the first set of calculations examines the risks associated with shipping PWR and BWR

spent fuel by truck (T) in steel-lead-steel (SLS T) and steel-DU-steel (SDUS T) casks;

• the second set examines the risks of performing these shipments by rail (R) in steel-leadsteel (SLS R) and monolithic steel (Mono R) casks;

• the third set examines the risks of shipping PWR spent fuel by truck in a steel-lead-steel

cask over the following five illustrative (Illus) shipment routes: Crystal River Nuclear

Plant in Florida to Hanford, Washington (C/H), Maine Yankee Nuclear Plant in Maine to

Skull Valley, Utah (M/SV), Maine Yankee Nuclear Plant to the Savannah River Site in

South Carolina (M/SR), Kewaunee Nuclear Plant in Wisconsin to the Savannah River

Site (K/SR), and the representative truck route examined by NUREG-0170 [8-1];

• the fourth set repeats these PWR spent fuel shipment calculations for rail shipments in a

monolithic steel cask;

• the fifth set examines the influence on spent fuel truck accident risks of the inventory,

source term, and exposure pathway models that were used in NUREG-0170;

• the sixth set calculates spent fuel truck accident shipment risks using Modal Study and

NUREG-0170 Model I (Mod I) and Model II (Mod II) source terms; and

• the seventh set repeats the sixth set for spent fuel rail shipments.

The three sensitivity calculations examine the dependence of accident risks on rod failure

fractions, the risks associated with heavy haul truck transport of spent fuel, and the risks posed

by Loss of Shielding (LOS) accidents during spent fuel transport. These sensitivity calculations

are described in Sections 8.10.3, 8.11 and 8.12 respectively.
Table 8.1 Characteristics of Sets of RADTRAN Calculations

Routes Inventorya Severity and Release Fractions Exp. Paths

This Study This Study NUREG-0170

SLS T SDUS T SLS R Mono R Mod 1 Mod 2

Modal

Study

Illus

PWR BWR

0170

PWR BWR PWR BWR PWR BWR PWR BWR T R T R T R

All Inhal

Section

where

calculation

discussed

X

X

X

X

X

X

X

X

X

X X X

Sect. 8.6

X

X

X

X

X

X

X

X

X

X X X

Sect. 8.7

C/HX X

X

M/SV X

X

X

M/SR X

X

X

K/SR X

X

X

0170 X X

X

Sect. 8.10.1

C/H X

X

X

M/SV X

X

X

M/SR X

X

X

K/SR X

X

X

0170 X X X

Sect. 8.10.2

X X XX X X

X

X

X

X X X

Sect. 8.13

X

X

X

X X X

X

X

X

X X X

X X X

Sect. 8.14
8-3

Table 8.1 also shows that (a) calculations, that do not examine a single specific real route,

examine the representative set of 200 truck or rail routes constructed by LHS sampling of route

parameter distributions and (b) four of the five calculations, that use the NUREG-0170

inventory, model only radiation exposures occur via inhalation pathways (Inhal).

8.2 The RADTRAN 5 Computational Scheme

The core computation embedded in the RADTRAN 5 code estimates the risks associated with

the shipment of a single radioactive material along a single route. Given a radioactive material,

package specifications, route data, prevailing weather conditions, an accident source term, and

emergency response actions (i.e., population evacuation and decontamination and/or

condemnation of contaminated property), RADTRAN 5 calculates the population dose that

would result if the specified accident occurs (the accident dose) and if the accident does not

occur (the incident-free dose). RADTRAN’s computational scheme allows this core calculation

to be repeated by looping over additional route segments, weather conditions, and accident

source terms. The number of cases that can be examined using this internal loop structure is

limited. Therefore, when a very large number of cases needs to be examined, the examination is

accomplished using code’s Latin Hypercube Sampling computational shell [8-3], which allows

large sets of parameter values, selected by sampling from distributions, to be sequentially

provided to RADTRAN 5 as separate input files.

8.2.1 Latin Hypercube Sampling

LHS is a structured Monte Carlo sampling method that produces results comparable to those

obtained with random Monte Carlo sampling methods using samples that are much smaller than

those required by the random sampling methods. Although originally developed to support

uncertainty and sensitivity studies, Latin Hypercube Sampling was used in this study to generate

representative sets of values for a number of RADTRAN 5 input parameters, for example, route

parameters, that can take on a wide range of values in the real world.

8.2.2 Size of the LHS Sample

The size of the LHS sample that provides adequate coverage of the sampled distributions was

determined by comparing results calculated (a) with samples of different sizes and (b) with

samples of the same size selected using different random seed values. Table 8.2 compares the

accident population dose risks (maximum value, minimum value, and the mean value and its

standard deviation) obtained for a particular spent fuel shipment calculation using 100, 200, 300,

400, and 500 sets of RADTRAN 5 input selected by LHS sampling. Table 8.2 shows that mean

result and its standard deviation are quite stable for samples of size 200 or larger (for example,

the mean and standard deviation for the samples of size 200 and 500 are nearly identical), and

that increasing sample size beyond 200 principally affects the values of the largest (maximum)

and smallest (minimum) observations in the sample. The adequacy of a sample of size 200 was

further examined by varying the value of the random seed used to generate the LHS sample.

Table 8.3 shows that for samples of size 200, changing the value of the random seed principally

affects the values of the maximum and minimum observations in the sample and has little effect

on the value of the mean or its standard deviation. Thus, the results presented in these two tables

indicate that an LHS sample of size 200 (a sample that contains 200 sets of RADTRAN 5 input
8-4

values for the parameters sampled) will develop a representative set of values for each sampled

parameter (e.g., for the parameters that define the truck and rail routes used in the calculations

that examine representative rather than illustrative routes), and consequently reasonable

estimates of the mean values for calculated results.

Table 8.2 RADTRAN 5/LHS Accident-Risk Results versus Number of Observations

Observations 100 200 300 400 500

Mean 2.73E-7 2.87E-7 2.90E-7 2.82E-7 2.86E-7

Standard Deviation 2.45E-7 2.83E-7 3.06E-7 2.94E-7 2.85E-7

Maximum 1.13E-6 1.79E-6 1.70E-6 2.34E-6 2.00E-6

Minimum 5.3E-9 1.68E-9 3.42E-9 2.70E-9 1.14E-9

Table 8.3 RADTRAN 5/LHS Accident-Risk Results for 200 Observations versus “Seed”

Random Seed #1 #2 #3 #4 #5

Mean 2.87E-7 2.96E-7 2.80E-7 2.85E-7 2.78E-7

Standard Deviation 2.83E-7 3.20E-7 2.89E-7 3.13E-7 2.70E-7

Maximum 1.79E-6 1.64E-6 1.71E-6 1.92E-6 1.38E-6

Minimum 1.68E-9 4.17E-9 4.40E-9 8.88E-11 4.47E-9

8.3 Input Parameters and Results Calculated

All of the RADTRAN 5 calculations performed for this study examined spent fuel transported in

a Type B cask. All of the routes examined had three aggregate segments, one urban, one

suburban, and one rural. Thus, all of the RADTRAN 5 calculations used the following input:

• the cask’s spent fuel inventory (three-year cooled, high-burnup PWR and BWR inventories

with respective burnups of 60 and 50 gigawatt-days per metric ton of uranium) or the

NUREG-0170 inventory that specifies the curie amounts released to the atmosphere during

spent fuel transportation accidents of the three radionuclides (Kr-85, I-131, and Cs-137) used

to represent all radionuclides contained in the cask inventory;

• 200 representative routes, 1 illustrative route, or the NUREG-0170 route, each having three

segments;

• traffic densities and speeds, average vehicle occupancy, accident rates, population densities,

and lengths for each of the three aggregate route segments;
8-5

• the number of times the spent fuel transport vehicle (the truck or train) stops (e.g., rest stops

or stops for inspections), while traversing each segment, the duration of each stop, and the

number of people that might be exposed to radiation as a result of the stop;

• the dose rate 1 m from the surface of the spent fuel cask (the package dose rate);

• the weather conditions that prevail while the segment is traversed (the Pasquill-Gifford

atmospheric stability class that characterizes the prevailing weather conditions at the time of

any hypothetical accident);

• the 19 sets of truck accident release fractions or the 21 sets of train accident release fractions

developed for this study, the 8 sets of NUREG-0170 Model I or Model II release fractions, or

the 20 sets of Modal Study release fractions;

• the fraction of all possible accidents estimated to cause each set of release fractions (the

severity fraction of this type of accident);

• an evacuation time (time after the occurrence of an accident when evacuation of possibly

exposed population is completed); and

• values for all of the other RADTRAN 5 input parameters (the parameters that have values

that do not depend on the nature of the radioactive material being shipped, the shipment

route, the accident source term, prevailing weather, or emergency response actions).

Given this input, each RADTRAN 5 calculation performed for this study calculated

• the incident-free doses incurred by various population groups (e.g., inspectors, persons living

along the route, persons traveling in other vehicles on the route) while the spent fuel

shipment traveled along each aggregate route segment and the sum of these doses for each

population group and for all population groups together (i.e., the total incident-free dose);

and

• the accident doses that would result if, during the course of the shipment, the spent fuel truck

or train were to be involved in an accident that causes some of the rods in the cask to fail, the

cask containment to be compromised, and consequently some radioactive material to be

released to the environment.

8.4 Number of Cases Examined

For each route modeled, the number of cases, Ncases, examined (core calculations performed) by

each RADTRAN 5 calculation is given by Ncases = NsegmentsNrelease fraction sets, where Nsegments = 3

and Nrelease fraction sets = 8 when NUREG-0170 source terms are used; Nrelease fraction sets = 20 when

Modal Study source terms are used; and as Table 7.31 shows, Nrelease fraction sets = 19 for truck

transport and 21 for rail transport when the new source terms developed by this study are used.

The number of sets of new release fractions examined can be less than the total number of sets of

release fractions developed in Section 7, because, as Table 7.31 shows, some of the sets of

accident release fractions developed in Section 7 have associated severity fraction values of zero,
8-6

which means that the accident conditions that lead to the specified set of release fractions are

estimated to have zero probability of occurrence (i.e., are estimated to be unattainable during

credible accidents). For example, when the steel-DU-steel truck cask is carrying PWR spent

fuel, 6 of its 19 sets of release fractions have severity fraction values of zero. Thus, for each

route modeled, all of the RADTRAN 5 calculations that used this set of severity fractions and

release fractions examined 39 cases where 39 = Ncases = NsegmentsNrelease fraction sets = 3 × 13.

In summary, for each route modeled, the number of cases examined (core calculations

performed) by each RADTRAN 5 calculation were as follows: 24 = 3 × 8 for calculations that

used NUREG-0170 source terms; 60 = 3 × 20 for calculations that used Modal Study source

terms; and 39 = 3 × 13, 45 = 3 × 15, and 63 = 3 × 21 for calculations that used respectively the

steel-DU-steel truck cask source terms, the steel-lead-steel truck cask source terms, and the steellead-steel and monolithic steel rail cask source terms developed for this study.

8.5 Complementary Cumulative Distribution Functions

The results calculated for the sets of 24, 60, 39, 45, or 63 cases are displayed as Complementary

Cumulative Distribution Functions (CCDFs), which are plots of the probability of occurrence of

an accident population dose of a given size or larger (i.e., the probability associated with each

consequence value is the sum of the probabilities of that and all larger consequence values). In

addition, the area under any of these CCDFs is the expected (mean) population dose risk in

person-rem for the set of accidents represented by that curve.

Because 200 different sets of input were examined during each RADTRAN 5 calculation, each

of these calculations generated 200-accident dose CCDFs. Figure 8.1 displays the 200 CCDFs

that were calculated for the steel-lead-steel cask when that cask was transporting one PWR spent

fuel assembly. Because of the density of the CCDF curves plotted in this figure, this plot depicts

poorly the information that is embedded in the set of 200 CCDFs that are plotted on the figure.

To better depict the spread of possible consequences and their probabilities of occurrence, four

compound CCDFs are constructed. These four compound CCDFs are the expected (mean)

result, and the 5th, 50th (median), and 95th percentile results, where for any specific single

consequence value the corresponding 5th and 95th percentile probabilities are the probabilities of

the CCDFs that lie 10 up from the bottom and 10 down from the top of the set of 200 CCDFs,

the corresponding median percentile probability is the average of the probability values for

CCDF 100 and CCDF 101, and the expected (mean) result is the average of all of the CCDF

probability values that correspond to the specified consequence value.

8.6 Results for the Generic Steel-Lead-Steel and Steel-DU-Steel Truck

Casks

The four compound CCDFs that correspond to Figure 8.1 are plotted in Figure 8.2. Specifically,

Figure 8.2 presents the expected (mean) CCDF and the CCDFs that represent the 5th, 50th

(median), and 95th percentile values of the set of 200 CCDFs that were calculated using the PWR

source terms developed for the generic steel-lead-steel truck cask and the representative LHS

input sample of size 200. Each element in this LHS sample specified values for all route related
10-4 10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

dred truck accident population dose risk CCDFs, one CCDF for each representative truck route. Each

tion examined all 19 representative truck accident source terms and assumed transport of PWR spent

eel-lead-steel truck cask.
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

ident population dose risk CCDFs for transport of PWR spent fuel in the generic steel-lead-steel truck

presentative truck routes. Each underlying RADTRAN 5 calculation generated results for all of the

ck accident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
8-9

parameters (e.g., segment length, segment population and segment vehicle densities, and average

segment vehicle occupancy and speed), a type of prevailing weather (Pasquill-Gifford stability

category), a package dose rate, a set of STOP parameter values, and the time after accident

initiation when any evacuation of downwind population is completed. Because the LHS sample

contained 200 sets of input data, the compound CCDF for the expected (mean) population dose

is based on (derived from) 200 × 45 = 9000 cases (core calculations) that each examine one route

segment, one prevailing weather, and one value for all of the other sampled parameters. Because

the 15 source terms examined by this calculation are not specified in the LHS sample, the effect

of the range of source term sizes on accident population dose is depicted by the curvature of each

of the four compound CCDFs while the effects of the parameters that are varied within the LHS

sample are depicted by the range (spread) of the four compound CCDFs at any single value of

accident population dose.

The CCDF in Figure 8.2 and all subsequent CCDFs contain a second y-axis scale that was not

present in the CCDF in Figure 8.1. That scale gives an estimate of the expected time between

accidents that have consequences that exceed the corresponding x-axis value (consequences >

C). Thus, an accident that has an expected time between accidents of 100 years would be

expected on average to occur about once every 100 years, although there is a slight chance that

two of these accidents could occur within a few years of each other. For example, inspection of

the figure shows that an accident that produces a population dose that exceeds 1 rem is expected

to occur about once every million years .

The values on the left-hand y-axis, the probability axis, are converted to those on the right-hand

y-axis, the expected time between accidents axis, by taking the reciprocal of the product of the

probability axis value and an estimate of the number spent fuel shipments likely to occur each

year, i.e., years per accident = [(accidents per shipment)(shipments per year)]-1. The following

qualitative arguments allow an order-of-magnitude estimate of the number of spent fuel

shipments per year to be developed.

An interim or permanent storage facility can probably receive at most a few casks per day or

perhaps several hundred per year. The U.S. DOE has estimated [8-4] that during the first decade

of spent fuel shipments, about 900 MTU will be shipped per year, which is equivalent to about

80 rail shipments per year. If 900 MTU are shipped per year by truck, about 1000 shipments per

year would be needed; however, because rail is the preferred shipment mode, many fewer truck

shipments are likely to be made per year. The entire spent fuel inventory can be shipped by rail

over thirty years at a rate of about 200 shipments per year. Forty rail casks making a round-trip

by regular freight once every two weeks can handle about 200 shipments per year. Therefore,

because it is easy to scale (e.g., at 200 rather than 100 shipments per year, all of the right-hand

y-axis values would be halved), an order-of-magnitude value of 100 shipments per year was used

to convert the probability axis values to the values on the expected time between accidents axis.

Figures 8.3 through 8.5 respectively present sets of compound CCDFs for the generic steel-leadsteel truck cask carrying BWR spent fuel, for the generic steel-DU-steel truck cask carrying

PWR spent fuel, and for the generic steel-DU-steel truck cask carrying BWR spent fuel, that are
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

cident population dose risk CCDFs for transport of BWR spent fuel in the generic steel-lead-steel truck

presentative truck routes. Each underlying RADTRAN 5 calculation generated results for all of the 19

accident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

cident population dose risk CCDFs for transport of PWR spent fuel in the generic steel-DU-steel truck

presentative truck routes. Each underlying RADTRAN 5 calculation generated results for all of the 19

accident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

cident population dose risk CCDFs for transport of BWR spent fuel in the generic steel-DU-steel truck

presentative truck routes. Each underlying RADTRAN 5 calculation generated results for all of the 19

accident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

son of truck accident population dose risk CCDFs for transport of PWR or BWR spent fuel in generic

el-DU-steel truck casks over the 200 representative truck routes. Each underlying RADTRAN 5

d results for all of the 19 representative truck accident source terms.

), and Highest 95th ( ) and Lowest 5th ( ) quantiles
8-14

exactly analogous to those presented in Figure 8.2. The expected (mean) CCDFs from

Figures 8.2 through 8.5 and the highest 95th percentile and lowest 5th percentile CCDF in these

four figures are plotted together in Figure 8.6. Thus, this figure depicts the likely range of truck

accident population doses for accidents that are severe enough to cause a Type B spent fuel cask

to lose containment and to fail some of the rods in the cask.

The area under the expected (mean) CCDF in Figures 8.2 through 8.5 is the expected value of

truck accident population dose for the entire set of RADTRAN 5 spent fuel truck transport

calculations performed for each generic truck cask and type of spent fuel. Table 8.4 presents

these expected truck accident population doses and compares them to the expected (average)

values of three incident-free population doses (stop, other, and total incident-free dose) that were

developed by the same set of calculations. Because all incident-free doses have a probability of

occurrence of one (i.e., if the spent fuel shipment is completed without an accident occurring, the

estimated incident-free doses presented in Table 8.4 will be incurred), the value of any incidentfree population dose is also the value of the corresponding incident-free population dose-risk,

and the average of all of the values of any specific incident-free population dose is the expected

(mean) value of that incident-free dose.

In Table 8.4, two values for Stop Dose are presented for each metric. The first value, the “Sleep”

value, was calculated assuming that the one-person truck crew makes stops for inspections, to

eat, to refuel, and to sleep. Because of these stops, on average the truck stops for 0.011 hour for

each kilometer traveled [8-5], where this value was developed by surveying the types of stops

and stop times made by typical commercial tractor semi-trailer trucks [8-5]. The second stop

dose value, the “No Sleep” value, was calculated by dividing the first value, the “Sleep” value,

by 28. This was done after phone calls to shippers of Hazardous materials [8-6] indicated that

trucks transporting spent fuel casks have two-person crews, do not make sleep stops, and thus

have a stop time per kilometer of travel much smaller than 0.011 hours per kilometer.

The phone calls [8-6] to shippers of Hazardous Material developed the following picture of the

types of stops and stop times made by trucks transporting spent fuel casks. First, the 2-person

crews of these trucks alternate driving on 4-hour shifts. During each 12-hour period, one driver

drives for eight hours and sleeps for four hours and the other driver drives for four hours, sleeps

for four hours, and rides as an escort for four hours. During the second 12-hour period in each

day, this pattern is reversed. Two types of stops are made, food/refueling stops and inspection

stops. Inspection stops are made every 100 miles or every two hours, whichever comes first.

Since average truck speeds on interstate highways are greater than 50 mph, an inspection stop is

made once every 100 miles, preferably at a truck stop, sometimes on a freeway exit ramp, or, if

necessary, on the freeway shoulder. Regulations stipulate that the first inspection stop should be

made after 25 miles of travel so that the cask tiedowns can be checked. Additional inspection

stops are then made after each additional 100 miles of travel. After each 800 miles of travel, a

stop is made for refueling and to eat or buy food. These stops may last as long as an hour, but

typically take only 30 minutes. Because the inspections are “walk-around” inspections, they take

at most 15 minutes and usually about 10 minutes. Thus, industry practice for spent fuel

shipments under exclusive use conditions is to use two-man crews and to minimize stop time by

not making stops to sleep.
8-15

Table 8.4 Incident-Free and Accident Population Dose Risks for Truck Transport

Population Dose Risks (person-rem)

Incident-Free

Stopsa Total Metric

Sleepc No Sleepd,e OtherbSleepc No Sleepd Accident

PWR Spent Fuel; Steel-Lead-Steel Cask; 1 Assembly

Mean = 0.427 0.0153 0.0288 0.456 0.0441 8.00E-07

Standard Deviation = 0.296 0.0106 0.0238 0.297 0.0261 8.53E-07

Maximum = 1.840 0.0657 0.1340 1.974 0.1997 4.38E-06

Minimum = 0.017 0.0006 0.0024 0.019 0.0030 4.06E-08

PWR Spent Fuel; Steel-DU-Steel Cask; 3 Assemblies

Mean = 0.427 0.0153 0.0288 0.456 0.0441 2.29E-06

Standard Deviation = 0.296 0.0106 0.0238 0.297 0.0261 2.44E-06

Maximum = 1.840 0.0657 0.1340 1.974 0.1997 1.24E-05

Minimum = 0.017 0.0006 0.0024 0.019 0.0030 1.14E-07

BWR Spent Fuel; Steel-Lead-Steel Cask; 2 Assemblies

Mean = 0.427 0.0153 0.0288 0.456 0.0441 3.30E-07

Standard Deviation = 0.296 0.0106 0.0238 0.297 0.0261 3.61E-07

Maximum = 1.840 0.0657 0.1340 1.974 0.1997 1.99E-06

Minimum = 0.017 0.0006 0.0024 0.019 0.0030 1.68E-08

BWR Spent Fuel; Steel-DU-Steel Cask; 7 Assemblies

Mean = 0.427 0.0153 0.0288 0.456 0.0441 1.08E-06

Standard Deviation = 0.296 0.0106 0.0238 0.297 0.0261 1.20E-06

Maximum = 1.840 0.0657 0.1340 1.974 0.1997 6.51E-06

Minimum = 0.017 0.0006 0.0024 0.019 0.0030 5.22E-08

a. Exposures at rest, food, and refueling stops.

b. Sum of on-link, off-link, and crew doses.

c. Sleep means that the truck makes a rest stop of 8 hours once every 24 hours so the crew can sleep.

d. No Sleep means that the truck doesn’t make any rest stops to allow the crew to sleep.

e. The No Sleep stop dose is obtained by dividing the Sleep stop dose by 28.

The pattern of spent fuel shipment stops described above suggests that seven 10 minute

inspection stops and one 30 minute food/refueling stop will be made during each 1280 kilometer

= 800 mile portion of a truck spent fuel shipment. Thus, the total stop time for each 1280

kilometers of travel when no stops to sleep are made will be 1.67 hrs = [7(10 minutes) +1(30

minutes)]/60 minutes hr-1.

The effect on stop doses of eliminating sleep stops is now developed for two spent fuel shipment

routes. The first route, Crystal River to Hanford, is one of the four illustrative real routes

examined below in Section 8.10, while the second route has route parameter values that are set to
8-16

the means of the distributions of route parameter values that were used to construct the LHS

sample of size 200. The lengths and urban, suburban, and rural length fractions and population

densities of these two routes are given below in Table 8.7.

The stop model implemented in RADTRAN 5, the version of RADTRAN used in this study,

calculates stop doses to people in two radial intervals centered on the stopped truck that is

transporting the spent fuel cask, 1 to 10 m and 10 to 800 m. The population density of the first

interval is assumed to be 30,000 people per square kilometer (0.03 people per square meter).

The population density of the second interval is set equal to the average population density of the

suburban portions of the route. No shielding is assumed for persons in the first interval.

Because of intervening trucks and buildings, a shielding factor of 0.2 is assumed for persons in

the second interval.

When stops to sleep are assumed to occur, the total stop time for the Crystal River-to-Hanford

route, which has a length of 4818.5 km, is 53 hours = (4818.5 km)(0.011 hr km-1). Using this

total stop time, RADTRAN predicts that the aggregate stop dose received by persons in these

two intervals aggregated over all stops will be 0.128 person-rem to persons exposed in the first

interval, the area immediately adjacent to the spent fuel truck, and 5.4x10-4 person-rem to other

persons at the truck stop and residents of the area that immediately neighbors the truck stop.

An estimate of the stop doses that would result for the Crystal River-to-Hanford route if the route

is traveled without making stops to sleep can be developed by scaling these two stop doses using

scale factors that reflect (a) the smaller stop times incurred when stops to sleep are not made, (b)

changes in the densities of the exposed populations, and (c) changes in the shielding factors that

apply to each exposed population group. To do this let

D1 = the dose to persons exposed in the first radial interval = 0.128 person-rem

D2 = be the dose to persons exposed in the second radial interval = 5.4x10-4 person-rem

fshielding = the shielding factor assumed for persons in the second radial interval = 0.2

trest,sleep = the stop time at rest stops when sleep stops are made = 53 hrs

trest,no sleep = the stop time at rest stops when sleep stops are made = 1.9 hrs = 0.5 hrs (4818.5 km/1280 km)

tinspections = the time spent at inspection stops = 4.4 hrs = (70 min/60 min per hr)(4818.5 km/1280 km)

ρrest = the population density of the first radial interval = 3x104

 persons/km2

ρurban = the population density of urban portions of the Crystal River-top-Hanford route = 2190 persons/km2

ρsuburban = the population density of suburban portions of the Crystal River-top-Hanford route = 331 persons/km2

ρrural = the population density of rural portions of the Crystal River-top-Hanford route = 7.5 persons/km2

furban = the urban length fraction of the Crystal River-top-Hanford route = 0.01

fsuburban = the suburban length fraction of the Crystal River-top-Hanford route = 0.15

frural = the rural length fraction of the Crystal River-top-Hanford route = 0.84

Given these definitions, the population dose for transit of the Crystal River-to-Hanford route if

no sleep stops are made is

 Dose D D

t

t

D D 1

f

t

t no sleep 1 2 F rest,no sleep

rest,sleep

1

suburban

rest

2

shielding

inspections

rest,sleep

= + ( ) population











÷ +





 



 +



























÷











÷

ρ

ρ
8-17

where

 Ff f f population urban

urban

suburban

suburban

suburban

suburban

rural

rural

suburban

= 



 



÷ + 



 



÷ + 



 



÷

ρ

ρ

ρ

ρ

ρ

ρ

In the first equation, the factor (trest,no sleep/trest,sleep) corrects D1 + D2, the rest stop dose for travel

with sleep stops, for the decrease in time spent at rest stops when travel takes place without sleep

stops; the factor (ρsuburban/ρrest) adjusts D1, the dose in the first radial interval, to the dose that

would be received if the first radial interval had a suburban population density; the factor

( 1 / f sh ie ld in g ) co r r ect s D2 , th e dos e rec ei ve d i n the sec ond radi al i nt e r v al , whi ch is as su m e d t o hav e

a suburban population density, to the dose that would be received by the population of this

interval if their shielding factor had a value of 1.0, the value used in RADTRAN for persons who

a r e ou t d oo r s ; an d t h e f a c t or ( t i n sp e c t i o n s / t r e st , s l e e p ) F p o p u l a t i o n = ( t i n sp e c t i o n s / t r e st , s l e e p ) Σ f i ρ i / ρ s u b u r b a n , wh e r e i 

= urban, suburban, or rural, scales this adjusted rest stop dose for travel with sleep stops for the

fraction of time spent at inspection stops in urban, suburban, and rural areas and also for the ratio

of the population density of each of these regions to that of the suburban region, which is the

reference population density for the adjusted rest stop dose.

Finally, substitution of the values for the parameters that enter these two equations into the

equations yields Doseno sleep = 4.69x10-3 person-rem (note that this value is essentially unchanged

if the first radial interval at inspection stops is assumed to be devoid of population, which would

likely be true for inspection stops conducted on freeway offramps or shoulders). Accordingly,

 Dosesleep/Doseno sleep = (0.128 person-rem + 5.4x10-4 person-rem)/4.69x10-3 person-rem = 27.4

A nearly identical scale factor can be derived using the mean values of the distributions of route

lengths and urban, suburban, and rural length fractions and population densities, that were

sampled to produce the LHS sample of size 200. Thus, for an 800 mile = 1280 km portion of

this route,

 Dose

Dose

person hours

person hours

1280 km 0.011 hr km

t Nt

sleep

no sleep

sleep

no sleep

rest

1

inspection stop i i rest stop rest

i

= ( ) −

( ) − = ( )( )

+

−

∑

ρ

ρ ρ

where tinspection stop = 0.17 hr = 10 min/60 min, trest stop = 0.5 hr = 30 mi/60 min, as before i = urban,

suburban, or rural, Ni = the number of inspection stops in each portion of the route, and, given

the fractions of the route length that are urban, suburban, and rural, Nurban = 0, Nsuburban = 2, and

Nrural = 5. Substitution of parameter values into this equation now yields

 Dosesleep/Doseno sleep = 4.36x105 person-hrs/1.51x104 person-hrs = 28.9

Since the average of this value and the value for the Crystal River-to-Hanford route is 28.2, stop

doses for travel without sleep stops was estimated by dividing the stop dose calculated by

RADTRAN for travel with sleep stops by 28.
8-18

Table 8.4 shows that all four truck spent fuel transport calculations yield the same set of

incident-free population doses. Each calculation yields the same set of incident-free doses

because the incident-free portion of these calculations each used the same set of 200 routes and

200 cask dose rate values. Table 8.4 also shows (a) that incident-free population dose incurred at

stops exceeds all other incident-free population doses by a factor of 15 if sleep stops are assumed

to be taken, (b) that other incident-free doses exceed stop dose by about a factor of 2 if transport

is assumed to occur without sleep stops, and (c) that for any combination of a cask and a type of

spent fuel (e.g., the steel-lead-steel cask carrying PWR spent fuel) the expected value of the total

incident-free population dose risk exceeds the expected value of the accident population dose

risk by at least a factor of 2x104

 = 0.0441/2.29x10-6, if no stops for sleep are taken, or as much as

1.4x106

 = 0.456/3.3x10-7, were sleep stops to be taken. Thus, for any truck shipment, incidentfree dose risks greatly exceed accident dose risks.

Division of the dose risk values presented in Table 8.4 by the number of assemblies that

produced those dose risks shows that, on a per assembly basis, the expected accident population

doses for PWR and BWR spent fuel are respectively about 7.8E-7 and 1.6E-7 person-rem. Thus,

the expected accident population dose per assembly for truck transport of PWR spent fuel is

about 5 times greater than that for BWR spent fuel, which was to be expected because the rod

failure fractions for PWR spent fuel during accidents are about twice those of BWR spent fuel

and the curie amounts of those radionuclides that drive population dose in three-year cooled,

high-burnup PWR assemblies are about three times greater than those for three-year cooled,

high-burnup BWR assemblies.

8.7 Results for the Generic Steel-Lead-Steel and Monolithic Steel Rail

Casks

Figures 8.7 through 8.11 and Table 8.5 present for the generic steel-lead-steel and monolithic

steel rail casks the same set of results that were developed for the generic truck casks.

Figures 8.7 through 8.10 present the CCDFs of expected, 95th, median, and 5th percentile values

of accident population dose that were calculated for each generic rail cask using first a PWR and

then a BWR cask inventory. Figure 8.11 plots the four expected value CCDFs and compares

them to the highest lying 95th and the lowest lying 5th percentile CCDF found in Figures 8.7, 8.8,

8.9, or 8.10. Thus, this figure depicts the likely range of rail accident population doses for

accidents that are sufficiently severe to fail a Type B spent fuel rail cask and at least some of the

rods in the cask.

Table 8.5 compares the expected values of incident-free population doses to the expected value

of the corresponding accident population dose. Table 8.5 shows that, as was true for truck

transport, each of the four spent fuel rail transport calculations yields the same set of incidentfree doses (again because each calculation uses the same set of routes and cask dose rate values)

and that the value of total incident-free rail transport population dose risk again greatly exceeds

(by factors of approximately 103

 to 104) the four values of rail transport accident population dose

risk. However, in contrast to the result obtained for truck transport, other rail incident-free doses

are larger than rail incident-free stop doses (by a factor of 3.6) because in general rail stops

expose fewer people to radiation than truck stops, e.g., there are more people at truck rest stops

and they are closer to the spent fuel cask and less shielded than at rail classification yards.
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

dent population dose risk CCDFs for transport of PWR spent fuel in the generic steel-lead-steel rail cask

ntative rail routes. Each underlying RADTRAN 5 calculation generated results for all of the 21

ccident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

dent population dose risk CCDFs for transport of BWR spent fuel in the generic steel-lead-steel rail cask

ntative rail routes. Each underlying RADTRAN 5 calculation generated results for all of the 21

ccident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

ent population dose risk CCDFs for transport of PWR spent fuel in the generic monolithic steel rail cask

ntative rail routes. Each underlying RADTRAN 5 calculation generated results for all of the 21

ccident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

ident population dose risk CCDFs for transport of BWR spent fuel in the generic monolithic steel rail

presentative rail routes. Each underlying RADTRAN 5 calculation generated results for all of the 21

ccident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

ison of rail accident population dose risk CCDFs for transport of PWR or BWR spent fuel in generic

nolithic steel rail casks over the 200 representative rail routes. Each underlying RADTRAN 5 calculation

 all of the 21 representative rail accident source terms.

Mean CCDFs ( ), and Highest 95th ( ) and Lowest 5th ( ) quantiles
8-24

Table 8.5 Incident-Free Population Dose Risks for Rail Transport

Population Dose Risks (person-rem)

Incident-Free

Metric Stopsa Otherb Total Accident

PWR Spent Fuel; Steel-Lead-Steel Cask; 24 Assembly

Mean = 4.37E-03 1.59E-02 2.03E-02 9.43E-06

Standard Deviation = 2.58E-03 1.38E-02 1.40E-02 1.18E-05

Maximum = 1.29E-02 8.26E-02 9.55E-02 6.32E-05

Minimum = 1.73E-03 3.57E-04 2.08E-03 3.39E-08

PWR Spent Fuel; Monolithic Steel Cask; 24 Assemblies

Mean = 4.37E-03 1.59E-02 2.03E-02 1.99E-06

Standard Deviation = 2.58E-03 1.38E-02 1.40E-02 2.47E-06

Maximum = 1.29E-02 8.26E-02 9.55E-02 1.35E-05

Minimum = 1.73E-03 3.57E-04 2.08E-03 8.08E-09

BWR Spent Fuel; Steel-Lead-Steel Cask; 52 Assemblies

Mean = 4.37E-03 1.59E-02 2.03E-02 9.23E-06

Standard Deviation = 2.58E-03 1.38E-02 1.40E-02 1.18E-05

Maximum = 1.29E-02 8.26E-02 9.55E-02 6.19E-05

Minimum = 1.73E-03 3.57E-04 2.08E-03 2.97E-08

BWR Spent Fuel; Monolithic Cask; 52 Assemblies

Mean = 4.37E-03 1.59E-02 2.03E-02 1.46E-06

Standard Deviation = 2.58E-03 1.38E-02 1.40E-02 1.86E-06

Maximum = 1.29E-02 8.26E-02 9.55E-02 9.94E-06

Minimum = 1.73E-03 3.57E-04 2.08E-03 4.87E-09

a. Exposures at rest and refueling stops.

b. Sum of on-link, off-link, and crew doses.

Table 8.5 also shows that when shipped in the same cask, the expected accident population dose

risk per assembly for shipping PWR spent fuel exceeds that for BWR spent fuel by factors of

about 2 to 3. This ratio is smaller than what might have been expected given that rod failure

fractions for PWR spent fuel during accidents are about twice those of BWR spent fuel and the

curie amounts of those radionuclides that drive population dose in three-year cooled, highburnup PWR assemblies are about three times greater than those for three-year cooled, highburnup BWR assemblies.

8.8 Comparison of Truck and Rail Transport Mean Risks

Comparison of the incident-free doses (incident-free risks and incident-free doses are the same

because the probability of occurrence of the incident-free dose is unity) presented in Tables 8.4

and 8.5 shows that, for shipment of a single truck or train spent fuel cask, truck stop doses

exceed train stop doses by a factor of 100, if trucks make sleep stops, and by a factor of 35, if
8-25

truck sleep stops are not taken; other truck doses exceed other train doses by only a factor of two;

and total truck incident-free doses exceed total train incident-free doses by a factor of 22.5, if

truck sleep stops are made, and by a factor of 2, if trucks do not make sleep stops. Other truck

and other train doses are similar because truck and train spent fuel casks, when undamaged, have

similar surface dose rates, so people who reside by the route or are traveling on the route, when

the cask passes by, receive similar radiation exposures. Even though rail casks carry many more

fuel assemblies than are carried by truck casks, truck and train cask surface dose rates are similar

because in rail casks, inner assemblies are shielded by outer assemblies and because cask surface

dose rates are limited by regulation. However, because typical truck casks carry either 1 or 3

PWR assemblies or 2 or 7 BWR assemblies, while typical rail casks carry 24 PWR or 52 BWR

assemblies, it will take at least 8 = 24/3 and possibly 24 = 24/1 times as many truck shipments as

train shipments to transport any given quantity of PWR spent fuel, and at least 7.4 = 52/7 and

possibly 26 = 52/2 times as many truck shipments as train shipment to transport a given quantity

of BWR spent fuel. Therefore, on a campaign basis, truck incident-free doses might be expected

to exceed rail incident-free doses by factors of about 180 = 8 × 22.5 to 585 = 26 × 22.5.

Although this factor seems large, it is really of no concern, since all individual incident-free

doses will be within regulatory limits and also small when compared to normal yearly

background radiation doses.

Because truck casks carry fewer assemblies than rail casks, should a truck cask and a rail cask

both be involved in accidents that inflict the same damage on both casks (i.e., both accidents fail

the same fraction of the rods in each cask and both fail each cask in the same way, e.g., seal

failures of the same size), the overall impact from a train accident would be expected to be larger

because the radioactive release from the rail cask would be larger than that from the truck cask.

Comparison of Tables 8.4 and 8.5 shows that, depending on the casks used, mean train accident

dose risks are either about the same as or about ten times greater than mean truck accident dose

risks. Because, for any shipment campaign, transport by truck will require 8 to 26 more

shipments than transport by rail on a campaign basis, truck accident dose risks will exceed train

accident dose risks by factors of at least 8 = 8 × 1 and possibly as much as 260 = 26 × 10.

8.9 Comparison of NUREG-0170 Incident-Free Doses to Those of This

Study

NUREG-0170 [8-1] developed estimates of incident-free doses for eight population groups:

passengers, crew, attendants (e.g., flight attendants), handlers, population that resides along the

route (off-link population), persons traveling on the route (on-link population), persons exposed

at stops, and persons exposed at en route storage locations. For transport by truck or freight

train, there are no passenger or attendant doses. Storage doses and handler doses were not

examined during this study. Storage doses were not examined because direct shipment from the

reactor to the temporary or permanent storage site without storage at any intermediate location

was assumed. Handler doses were not examined because the doses incurred by workers loading

the spent fuel cask at the reactor site and unloading the spent fuel cask at the temporary or

permanent storage site are treated by most recent National Environmental Policy Act analyses as

facility doses, not transportation doses. Therefore, incident-free doses were limited to those

doses incurred while en route.
8-26

Table 8.6 compares the NUREG-0170 expected incident-free truck and rail doses presented in

Table 1.2 to the expected incident-free doses presented in Tables 8.4 and 8.5 that were developed

by this study. Because the NUREG-0170 doses were developed for all of the spent fuel

shipments expected to occur in 1975 or 1985, doses for single shipments are calculated by

dividing the 1975 or 1985 doses by the number of spent fuel shipments that NUREG-0170 [8-1]

estimated would occur during these years.

Table 8.6 Comparison of NUREG-0170 Incident-Free Doses to the

Incident-Free Doses Developed by this Study

Mode Truck Rail

Study NUREG-0170 This Study NUREG-0170 This Study

Year 1975 1985 1975 1985

Number of Shipments 254 1530 2489a 17 652 100.5a

Expected Dose (person-rem)

Multiple Shipments

 Handlers + Storage 52.06 313.6 Not Calc. 7.227 277.4 Not Calc.

 Stops 4.82 29.0 38 0.089 3.440 0.442

 Otherb 36.92 222.4 72 0.464 17.16 1.598

 Stops + Other 41.74 251.4 110 0.553 20.60 2.040

Single Shipment

 Handlers + Storage 0.205 0.205 Not Calc. 0.425 0.425 Not Calc.

 Stops 0.0190 0.0190 0.0153c 0.0052 0.0053 0.0044

 Otherb 0.145 0.145 0.0288 0.02729 0.02632 0.0159

 Stops + Other 0.164 0.164 0.0441 0.0325 0.0316 0.0203

a. Average number of shipments per year required to ship the full 1994 spent fuel inventory over 30 years in steellead-steel truck and rail casks.

b. Sum of crew, on-link, and off-link doses.

c. Result for truck shipments that proceed without taking sleep stops.

Table 8.6 shows that for truck transport the single shipment incident-free other doses (i.e., crew,

on-link, and off-link doses) calculated for NUREG-0170 are about 5 times larger than those

calculated for this study, that the single shipment incident-free stop doses calculated for

NUREG-0170 are about 25 percent larger than those calculated for this study, and thus the single

shipment total incident-free doses calculated for NUREG-0170 are about 3.7 times those

calculated for this study. NUREG-0170 other doses exceed those calculated by this study by a

factor of five because the average population density over the entire NUREG-0170 truck route

exceeds the average population density of the set of 200 truck routes examined by this study by

about a factor of 2.5 and the NUREG-0170 spent fuel cask surface dose rate is about twice the

mean of the surface dose rate distribution used in this study.

The fact that NUREG-0170 truck stop doses exceed those developed by this study by 25 percent

can be qualitatively explained as follows. Truck stop doses, Dstop, are proportional to the product

of the cask surface dose rate, the population density at the truck stop, ρpop, the exposure time of

that population, ∆t, and the following slowly varying function of radial distance, f(r), that

expresses the variation of radiation intensity with distance over the annular area of interest:

 f(r) 2 r e B(r)

r

dr

r

2

a

b

=

−

∫ π

μ
8-27

where μ is the absorption coefficient for radiation by air and B(r) is the Berger buildup factor in

air. When stops are made at locations that have different population densities, for example,

urban, suburban, and rural rest stops, Dstop is proportional to the product of the cask dose rate,

f(r), and Σ(∆tρpop)i, where ∆t and ρpop are the exposure time and the population density that

characterize each stop made on the route.

The NUREG-0170 value for f(r) differs from the value used in this study because different

integration limits are used for the function. For NUREG-0170, f(r) is evaluated from 3 to

800 meters and that annulus is assumed to have a population density that is the same as the

population density of the urban, suburban, or rural region in which the stop is made. For this

study, stop doses are evaluated over two concentric annuli with inner and outer radii of 1 and

10 meters and 10 and 800 meters. Because the population density of the inner annulus is taken

to be 0.03 persons per square meter (3x104

 persons per square kilometer) while the population

density of the outer annulus is assumed to be that of a suburban route segment, the dose

accumulated in the inner annulus dominates the stop dose. Therefore, the integration limits for

f(r) for the calculations performed for this study are effectively 1 and 10 meters.

Since the values of TI, f(r), and Σ(∆tρpop)i are respectively 9.5, 27.3, and 1.1x104

 where

 1.1x104 = (∆tρpop)urban stops + (∆tρpop)suburban stops + (∆tρpop)rural stops

= (2 hr)(3861 km-2) + (5 hr)(719 km-2) + (1 hr)(6.0 km-2)

when NUREG-0170 data is used, and 4.5, 14.2, and 3x104

 where

 3x104

 = ∆t ρ1-10 m = (1 hr)(3x104 km-2)

when data from this study is used, the ratio of NUREG-0170 truck stop doses to those estimated

by this study should be approximately 1.49 = [(9.5)(1.1x104

)(27.3)/[(4.5)(3x104)(14.2)], which is

in reasonable agreement with the actual ratio of 1.25.

Table 8.6 also shows that the NUREG-0170 single shipment incident-free stop and other doses

for transport by rail are larger than the corresponding doses calculated by this study by factors of

1.2 = 0.0052/0.0044 and 1.7 = 0.0263/0.0159, and therefore, NUREG-0170 total rail incidentfree doses exceed those calculated for this study by about a factor of 1.6 = 0.0316/0.0203. The

fact that the NUREG-0170 other incident-free rail doses exceed by a factor of 1.7 those

calculated for this study is explained as follows. Other incident-free population dose is

proportional the product of the cask dose rate and Σ(∆t ρpop)i where ∆t = Lfi/vi, L is the route

length, fi is the fraction of the length that is urban, suburban, or rural, and vi is the train speed in

these regions. Substitution of the values of these parameters used for the NUREG-0170

calculations and the means of the distributions of values used for the calculations performed for

this study yields, in good agreement with the actual result, an estimate of 1.8 for this dose ratio,

where
8-28

 

1 8

9 5 1210 0 9

64

6 0 05

40

719 0 05

24

3861

4 5 2560 0 75

64

9 6 0 22

40

356

.

.( ) .. .

.( ) . . .

=

=





 









 





=

( ) + ( ) + ( ) 



 





( ) + (

∑

∑

−

D

D

 

(TI)(L) f

v

(TI)(L) f

v

other incident-free, NUREG-0170

other incident-free, this study

i

i i NUREG 0170

i

i i this study

ρ

ρ

i

i ) + ( ) 



 





0 03

24

2280 .

8.10 Illustrative Real Routes

All of the results presented in Sections 8.6 and 8.7 were calculated using 200 sets of RADTRAN

5 input (an LHS sample of size 200) that contains data for 200 different representative truck or

rail routes, none of which exactly matches any real truck or rail route located in the continental

United States. In this section, results for four illustrative real truck or rail routes and also for the

NUREG-0170 representative truck or rail route are compared to the results developed using the

200 representative truck or rail routes embedded in the LHS samples that provided the input for

the calculations described in Sections 8.6 and 8.7. All of the truck calculations examined

transport of spent high-burnup PWR fuel in the generic steel-lead-steel truck cask, and all of the

rail calculations examined transport of spent high-burnup PWR fuel in the generic monolithic

steel rail cask.

Table 8.7 presents route parameter values for the four illustrative real truck and rail routes and

also for the NUREG-0170 representative truck and rail routes that were examined by this set of

RADTRAN 5 calculations. Also presented in the table are the mean values of the distributions

of route parameters that were sampled in order to construct the 200 representative routes that

were examined by the calculations described in Sections 8.6 and 8.7.

The four illustrative routes were chosen for the following reasons. The truck and rail routes from

the Crystal River nuclear plant to Hanford are about the longest routes possible in the continental

United States. Because they traverse the Boston-Washington urban corridor, the routes from the

Maine Yankee nuclear plant to the Savannah River Site have urban length fractions and

population densities that are about as high as is possible in the continental United States. The

routes from the Maine Yankee nuclear plant to Skull Valley represent long routes to the Yucca

Mountain area that traverse the urban Midwest. Finally, as Table 8.7 shows, the routes from the

Kewaunee nuclear plant to the Savannah River Site have route parameter values (especially the

urban parameter values) similar to the means of the route parameter distributions used to

construct the 200 representative truck and rail routes contained in the LHS sample of size 200.
8-29

Table 8.7 NUREG-0170 and Illustrative Real Truck and Rail Routes

Fraction of Total Length Population Densitya

Origin Destination

Length

(km) Rural Suburban Urban Rural Suburban Urban

Stop

Timeb

Truck Routes

Crystal River, FL Hanford Site, WA 4818.5 0.84 0.15 0.01 7.5 331 2190 53.0

Maine Yankee, ME Skull Valley, UT 4228.7 0.74 0.24 0.02 9.2 296 2286 46.5

Maine Yankee, ME Savannah River Site, SC 1917.5 0.52 0.43 0.05 18.3 282 2565 21.0

Kewaunee, WI Savannah River Site, SC 1765.0 0.63 0.32 0.05 16.3 358 2452 19.4

NUREG-0170 2530.0 0.90 0.05 0.05 6.0 719 3861 8.0

Route Parameter Distribution Mean Values 2550.0 0.76 0.23 0.01 10.1 336 2195 28.0

Rail Routes

Crystal River, FL Hanford Site, WA 5178.6 0.83 0.15 0.02 7.9 360 2063 231

Maine Yankee, ME Skull Valley, UT 4488.7 0.75 0.22 0.03 8.9 337 2429 208

Maine Yankee, ME Savannah River Site, SC 2252.7 0.52 0.38 0.10 14.3 325 2738 134

Kewaunee, WI Savannah River Site, SC 1917.2 0.64 0.32 0.04 14.1 351 2268 122

NUREG-0170 1210.0 0.90 0.05 0.05 6.0 719 3861 24

Route Parameter Distribution Mean Values 2560.0 0.75 0.22 0.03 9.6 356 2280 144

a. People per square kilometer.

b. Sum of all stop durations (hours) for the entire shipment. For truck shipments, includes stop time for sleep stops.

8.10.1 Steel-Lead-Steel Truck Cask Results for Illustrative Routes

Figures 8.12 through 8.17 present the accident population dose risk and Table 8.8 presents the

incident-free population dose risk results of the RADTRAN 5 calculations that examined spent

fuel transport in the generic steel-lead-steel truck cask over the four illustrative truck routes and

the NUREG-0170 truck route. Figures 8.12 through 8.15 present the results obtained for the four

illustrative real truck routes, and Figure 8.16 presents the results obtained for the NUREG-0170

truck route. Each of these figures presents CCDFs of the expected, 95th, median, and 5th

percentile values of accident population dose risks that were calculated for the generic steel-leadsteel truck cask carrying spent PWR high-burnup fuel along the indicated illustrative real truck

route or along the NUREG-0170 representative truck route. In Figure 8.17, the mean (expected)

CCDFs from each of these calculations are plotted together and compared to the 5th and 95th

percentile CCDFs depicted in Figure 8.6. Thus, Figure 8.17 compares the expected accident

population dose risks for the illustrative truck and NUREG-0170 truck route calculations to the

range of the accident population dose risks developed using the 200 representative truck routes

that were constructed by LHS sampling from truck route parameter distributions. Comparison of

Figure 8.17 to Figures 8.12 through 8.16 shows (a) that the CCDFs for the four illustrative truck

routes are quite similar, (b) that they all lie below the CCDF of 95th percentile values for the LHS

calculations that examined the 200 representative truck routes, and (c) that the CCDF for the

NUREG-0170 truck route calculation lies below the four illustrative truck route CCDFs when

accident population dose risks are below 100 person-rem but then crosses these CCDFs and
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

ccident population dose risk CCDFs for transport of PWR spent fuel in the generic steel-lead-steel truck

l River to Hanford illustrative truck route. Each underlying RADTRAN 5 calculation generated results

esentative truck accident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

ccident population dose risk CCDFs for transport of PWR spent fuel in the generic steel-lead-steel truck

Yankee to Skull Valley illustrative truck route. Each underlying RADTRAN 5 calculation generated

19 representative truck accident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

ccident population dose risk CCDFs for transport of PWR spent fuel in the generic steel-lead-steel truck

Yankee to Savannah River Site illustrative truck route. Each underlying RADTRAN 5 calculation

 all of the 19 representative truck accident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

ccident population dose risk CCDFs for transport of PWR spent fuel in the generic steel-lead-steel truck

nee to Savannah River Site illustrative truck route. Each underlying RADTRAN 5 calculation generated

19 representative truck accident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

ccident population dose risk CCDFs for transport of PWR spent fuel in the generic steel-lead-steel truck

G-0170 representative truck route. Each underlying RADTRAN 5 calculation generated results for all of

 truck accident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

ison of truck accident population dose risk CCDFs for transport of PWR spent fuel in the generic steel

our illustrative truck routes and the NUREG-0170 representative truck route. Each underlying

tion generated results for all of the 19 representative truck accident source terms.

Mean CCDFs ( ), and Highest 95th ( ) and Lowest 5th ( ) quantiles
8-36

Table 8.8 Incident-Free Population Dose Risks for Truck Transport of PWR

Spent Fuel in a Generic Steel-Lead-Steel Truck Cask over Illustrative Routes

Population Dose Risks (person-rem)

Incident-Free

Stopsa Total Metric

Sleepc No Sleepd,e OtherbSleepc No Sleepd Accident

Crystal River Nuclear Plant to Hanford Site

Mean = 1.470 0.0525 0.0581 1.530 0.111 9.53E-07

Standard Deviation = 0.722 0.0258 0.0281 0.722 0.038 5.92E-07

Maine Yankee Nuclear Plant to Skull Valley

Mean = 1.300 0.0464 0.0524 1.350 0.099 1.29E-06

Standard Deviation = 0.637 0.0228 0.0252 0.637 0.034 7.81E-07

Maine Yankee Nuclear Plant to Savannah River Site

Mean = 0.585 0.0209 0.0252 0.610 0.046 1.14E-06

Standard Deviation = 0.288 0.0103 0.0122 0.288 0.016 6.73E-07

Kewaunee Nuclear Plant to Savannah River Site

Mean = 0.541 0.0193 0.0231 0.564 0.042 1.01E-06

Standard Deviation = 0.257 0.0092 0.0112 0.257 0.011 5.93E-07

NUREG-0170 Truck Route

Mean = 0.779 0.0321 0.0304 0.810 0.063 1.28E-06

Standard Deviation = 0.383 0.0137 0.0147 0.383 0.020 6.68E-07

a. Exposures at rest, food, and refueling stops.

b. Sum of on-link, off-link, and crew doses.

c. Sleep means that the truck makes a rest stop of 8 hours once every 24 hours so the crew can sleep.

d. No Sleep means that the truck doesn’t make any rest stops to allow the crew to sleep.

e. The No Sleep stop dose is obtained by dividing the Sleep stop dose by 28.

thereafter lies near to or above the 95th percentile CCDF. Thus, Figure 8.17 shows that the four

illustrative truck routes yield accident population dose risks that lie toward the top of the range of

accident population dose risks obtained using the LHS sample that contained 200 representative

truck routes and, for accident population dose risks that exceed 100 person-rem, below the

CCDF obtained using the NUREG-0170 truck route. The NUREG-0170 truck route CCDF lies

generally higher than the illustrative truck routes CCDFs because, as Table 8.7 shows, the

NUREG-0170 truck route has suburban and urban population densities that are substantially

larger than those that characterize the illustrative truck routes.

Finally, Table 8.8 presents the mean (expected) incident-free population doses calculated by

RADTRAN 5 for transport of PWR spent fuel in the generic steel-lead-steel cask along the

illustrative routes. Table 8.8 shows that, as was true for the LHS calculations that examined

truck transport of spent fuel using the representative set of 200 truck routes for specific real truck

routes, total incident-free population dose risks again exceed accident population dose risks by

factors of at least 3x104

 = 0.042/1.29x10-6, if no sleep stops are made, to as much as
8-37

2x106 = 1.530/9.53x10-7, if sleep stops are made; and that population doses incurred when the

truck stops, for example to refuel, are quite similar, when no sleep stops are taken, and exceed all

other incident-free population doses (e.g., on-link and off-link doses) by factors of about 25, if

sleep stops are taken. Comparison of the results in Table 8.8 to those in Table 8.4 shows that all

of the incident-free doses for illustrative truck routes, both those calculated with sleep stops and

those calculated without sleep stops, fall within the range (defined by the maximum and

minimum values calculated) of results obtained for incident-free doses using the LHS sample

that contains 200 representative truck routes.

8.10.2 Monolithic Steel Rail Cask Results for Illustrative Routes

Figures 8.18 through 8.23 present the accident population dose risks and Table 8.9 presents the

incident-free population dose risks for the RADTRAN 5 calculations that examined spent fuel

transport in the generic monolithic steel rail cask over the four illustrative rail routes and the

NUREG-0170 rail route. Figures 8.18 through 8.21 present the results obtained for the four

illustrative real rail routes, and Figure 8.22 presents the results obtained for the NUREG-0170

rail route. Each of these figures presents CCDFs of the expected, 95th, median, and 5th percentile

values of accident population doses that were calculated for the generic monolithic Steel rail cask

carrying spent PWR high-burnup fuel along the indicated illustrative real rail route or for the

NUREG-0170 representative rail route. In Figure 8.23, the mean (expected) CCDFs from each

of these calculations are plotted and compared to the 5th and 95th percentile CCDFs depicted in

Figure 8.11. Thus, Figure 8.23 compares the expected accident population dose results of the

illustrative rail and NUREG-0170 rail route calculations to the range of the accident population

doses results developed using the 200 representative rail routes that were constructed by LHS

sampling from rail route parameter distributions. Figure 8.23 shows that (a) the CCDFs for the

four illustrative rail routes are quite similar, (b) they all lie below the CCDF of 95th percentile

values for the LHS calculation that examined the 200 representative rail routes, and (c) the

CCDF for the NUREG-0170 rail route calculation lies below the illustrative route CCDFs until

accident population doses exceed 1000 person-rem and then lies among them until the highest

accident population doses are reached, whereupon it crosses all of the illustrative route CCDFs

and even crosses the 95th percentile CCDF. Thus, Figure 8.23 shows that the four illustrative rail

routes yield accident population doses that lie toward the top of the range of accident population

doses obtained using the LHS sample that contained 200 representative rail routes and at all but

the very highest population doses above the CCDF of mean population doses obtained using the

NUREG-0170 rail route. The NUREG-0170 rail route lies generally lower than the illustrative

rail route CCDFs because it is only half as long and because its suburban route fraction is 4 to 6

times smaller than those of the illustrative rail routes.

Finally, Table 8.9 presents the mean (expected) incident-free population doses calculated by

RADTRAN 5 for transport of PWR high-burnup spent fuel in the monolithic steel rail cask along

the illustrative rail routes. Table 8.9 shows that, as was true for the LHS calculations that

examined truck transport of spent fuel using the representative set of 200 rail routes for specific

real rail routes, incident-free population dose risks exceed accident population dose risks by

factors of about 104

, and other incident-free population doses (e.g., on- link and off-link doses)

are larger than the population doses incurred when the train stops, for example in a classification

yard, by factors of 2 to 3. Comparison of the results in Table 8.9 to those in Table 8.5 shows that
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

ident population dose risk CCDFs for transport of PWR spent fuel in the generic monolithic

he Crystal River to Hanford illustrative rail route. Each underlying RADTRAN 5

d results for all of the 21 representative rail accident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

ident population dose risk CCDFs for transport of PWR spent fuel in the generic monolithic

he Maine Yankee to Skull Valley illustrative rail route. Each underlying RADTRAN 5

d results for all of the 21 representative rail accident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

ident population dose risk CCDFs for transport of PWR spent fuel in the generic monolithic

he Maine Yankee to Savannah River Site illustrative rail route. Each underlying RADTRAN

ed results for all of the 21 representative rail accident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

ident population dose risk CCDFs for transport of PWR spent fuel in the generic monolithic

he Kewaunee to Savannah River Site illustrative rail route. Each underlying RADTRAN 5

d results for all of the 21 representative rail accident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

ident population dose risk CCDFs for transport of PWR spent fuel in the generic monolithic

he NUREG-0170 representative rail route. Each underlying RADTRAN 5 calculation

 all of the 21 representative rail accident source terms.

Mean ( ) CCDF, and 95th ( ), 50th (. . . . . . . . . .), and 5th ( ) quantiles
10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

ison of rail accident population dose risk CCDFs for transport of PWR spent fuel in the

eel cask over four illustrative rail routes and the NUREG-0170 representative rail route.

DTRAN 5 calculation generated results for all of the 21 representative rail accident source

Mean CCDFs ( ), and Highest 95th ( ) and Lowest 5th ( ) quantiles
8-44

Table 8.9 Incident-Free Population Dose Risks for Rail Transport of PWR Spent Fuel

in a Generic Monolithic Steel Rail Cask over Illustrative Routes

Population Dose Risks (person-rem)

Incident-Free

Metric

Stopsa Otherb Total Accident

Crystal River Nuclear Plant to Hanford Site

Mean = 9.70E-03 2.89E-02 3.86E-02 2.44E-06

Standard Deviation = 5.71E-03 1.71E-02 1.80E-02 2.08E-06

Maine Yankee Nuclear Plant to Skull Valley

Mean = 1.19E-02 2.75E-02 3.69E-02 3.25E-06

Standard Deviation = 7.00E-03 1.62E-02 1.77E-02 2.77E-06

Maine Yankee Nuclear Plant to Savannah River Site

Mean = 1.02E-02 1.66E-02 2.70E-02 3.79E-06

Standard Deviation = 6.05E-03 9.84E-03 1.15E-02 3.27E-06

Kewaunee Nuclear Plant to Savannah River Site

Mean = 7.61E-03 1.33E-02 2.09E-02 1.95E-06

Standard Deviation = 4.50E-03 7.87E-03 9.06E-03 1.68E-06

NUREG-0170 Rail Route

Mean = 2.05E-03 6.46E-03 8.51E-03 1.11E-06

Standard Deviation = 1.21E-03 3.82E-03 4.01E-03 1.03E-06

a. Exposures at rest and refueling stops.

b. Sum of on-link, off-link, and crew doses.

the mean incident-free dose risks for illustrative rail routes fall largely within the range (defined

by the maximum and minimum values calculated) of results obtained for mean incident-free dose

risks using the LHS sample that contains 200 representative rail routes.

8.10.3 Rod Strain Failure Criterion Sensitivity Calculation

Because of radiation-induced hardening and hydride formation, the impact strains that cause

spent fuel rods to fail during collision accidents decrease significantly as fuel burnup increases.

In Section 5.4.1, a 4 percent average strain failure criterion for rod failure due to impact was

developed by constructing a weighted summation of strain failure criteria by fuel burnup ranges

using the fractional amounts of fuel in each burnup range as the weighting factors. The weighted

summation assumed that high burnup spent fuel rods fail when subjected to 1 percent strains and

that high average burnup fuel fails when subjected to 4 percent strains. The rod failure fractions

presented in Table 7.18 were then developed by comparing the rod strains developed in Section

5.4.2 to this 4 percent strain criterion.
8-45

In order to examine the effect of the rod strain failure criterion on accident risks, one of the

illustrative route calculations, the Crystal River to Hanford rail calculation that assumed spent

fuel transport in a monolithic steel rail cask, was repeated assuming that all of the rods in the

cask would fail during any collision accident, rather than some failing during collision accidents

with speeds between 30 and 60 mph, more failing at speeds between 60 and 90 mph, and all

failing when accident speeds exceed 90 mph. Because high burnup fuel rods will fail whever

subjected to strains greater than 1 percent, besides examining the sensitivity of the accident risk

analyses to rod failure strain criterion, this calculation also develops a result for high burnup fuel

rods which are expected to fail during all collisions that exceed regulatory conditions (a 30 mph

impact onto an unyielding surface).

Table 8.9 shows that, when a 4 percent average rod strain failure criterion was assumed, the

mean accident risk for the Crystal River to Hanford rail route for a monolithic steel rail cask was

calculated to be 2.44E-6 person-rem. When this calculation was repeated assuming rod failure

fractions of 1.0 for all accident speed ranges, the calculated mean accident risk was found to be

4.69E-6 person-rem. Thus, even if all of the rods in a spent fuel cask were assumed to fail

during any collision accident with a speed greater than 30 mph, accident risk estimates would

increase by only a factor of two.

Accident risks increase by only a factor of two for two reasons. First, as the tables in Appendix

D show, 10 of the 20 rail accident cases that lead to radioactive releases already have rod failure

fractions for collision accidents that have values of 1.0, and 2 of the 10 that have failure fractions

for collisions that are less than 1.0 lead to fires that fail all remaining unfailed rods. Second,

although failing more rods increases the release of particulates (fuel fines), it decreases the

release of Cs vapors because, once generated by heating by a fire, these vapors can now escape

from failed rods only by diffusion, which is a very inefficient transport process. Thus, failing all

of the rods on impact decreases the total release of Cs (Cs release in particulates increases but

not enough to compensate for the virtual elimination of Cs release in vapors). Therefore,

accident source terms increase much less than might be expected given the strong dependence of

rod failure on rod strain levels. Finally, the fact that accident risks are increased by only a factor

of two, when rod failure fractions are set to 1.0, shows that the approximate nature of the

analysis used in Section 5.4.1 to develop the 4 percent average rod failure strain criterion was

entirely justified.

8.11 Rail Routes with Heavy-Haul Segments and Intermodal Transfers

Transport of spent fuel by rail in a rail cask will require special heavy-haul truck transport over

short route segments when either the nuclear power plant (e.g., the Maine Yankee and Kewaunee

nuclear plants) or the storage site (e.g., the proposed Skull Valley interim storage site) are not

serviced directly by a rail spur. Because the need for heavy-haul truck transport to or from rail

route termini was neglected in all of the rail route calculations described in Sections 8.7 and

8.10.2, the magnitude of the incident-free dose risks (including handler dose risks incurred

during intermodal transfers) and accident population dose risks that might result during heavyhaul truck transport to or from railheads was investigated for three real heavy-haul route

segments:
8-46

1. the Maine Yankee nuclear plant to the railhead at Pejepscot Mills, Maine;

2. the Kewaunee nuclear plant to the railhead at Kewaunee, Wisconsin; and

3. the railhead at Timpie, Utah, to the proposed Skull Valley, Utah, interim storage site.

This section describes these calculations and compares the population dose risks calculated for

these heavy haul segments to the population dose risks calculated for the specific real rail route

that each heavy-haul segment would service.

For each heavy-haul route segment, route parameters for three aggregate segment links (urban,

suburban, and rural link distances; population densities; and accident rates) were developed.

Segment lengths and population densities were calculated for the non-interstate road segments

from 1990 census data using the ArcView GIS software system. Rural and suburban accident

rates were set to the means of the accident rate distributions developed in Section 3.4.2.3, and the

value used for the urban accident rate was the value used in the LHS truck route calculations.

Table 8.10 presents these route parameter values.

Table 8.10 Route Parameters for Heavy-haul Truck Transport Segments

Aggregate

Link

Length

(km)

Population Density

(persons per km2

)

Accident Rate

(accidents per km)

Maine Yankee Nuclear Plant to the Railhead at Pejepscot Mills

 Rural 15 31.6 2.2E-7

 Suburban 21 318 4.1E-7

 Urban 4.0 2570 5.2E-7

Kewaunee Nuclear Plant to the Railhead at Kewaunee

 Rural 17 38.5 2.2E-7

 Suburban 1.0 90.8 4.1E-7

 Urban 0.0 NA NA

Railhead at Timpie to the Proposed Skull Valley Interim Storage Site

 Rural 46 0.21 2.2E-7

 Suburban 0.0 NA NA

 Urban 0.0 NA NA

Next, the set of PWR truck accident severity fractions and release fractions in Table 7.31 was

modified by eliminating accidents (setting severity fractions to zero) that can not occur given the

characteristics of heavy-haul transport (movement under escort at low speeds). Specifically,

severity fractions were set to zero for all of the accident categories that describe accidents that

occur with speeds greater than 60 mph (Accident Categories 1, 5 through 13, and 15 through 17).

In addition, because the formation of a robust puncture probe during very-low-speed accidents is

extremely improbable, the severity fraction for Accident Category 14 was also set to zero. Thus,

rail cask failure during heavy-haul transport was assumed to be possible only for the three lowspeed collision accident categories (Categories 2 through 4) that initiate fires and also for the

fire-only accident category (Category 18). Then, because heavy-haul transport speeds are almost

always  30 mph (the calculation assumed 25 mph), the severity fractions for the remaining four
8-47

accident categories were each decreased by a factor of ten. Finally, given this input data,

RADTRAN 5 was used to calculate the population dose risks associated with heavy-haul truck

transport over each of the three heavy-haul routes defined in Table 8.10. The results of these

calculations are presented in Table 8.11.

Table 8.11 shows that, for these three heavy-haul route segments, other incident-free dose risks

are about 103

 to 106 times larger than the incident-free stop doses, and about 104 to 107 times

larger than the accident dose risks. Comparison of these dose risks to the same dose risks listed

in Tables 8.5 and 8.9 for transport over rail routes indicates that incident-free and accident dose

risks for heavy haul transport to or from railheads will be negligible when compared to the

population dose risks associated with transport over the rail portion of any route that requires

both transport by heavy-haul truck and by train. Finally, comparison of the intermodal transfer

handler population dose risks in this table to the total incident-free dose risks presented in Tables

8.5 and 8.9 shows that adding intermodal transfers to any rail route will significantly increase

total population dose risks because the handlers must work close to the cask for significant

periods of time while attaching lifting hardware, inspecting the cask, and performing other

transfer operations.

Table 8.11 Heavy-Haul Incident-Free and Accident Population Dose Risks

Population Dose Risks (person-rem)

Incident-Free

Metric Stopsa,b Otherc Total Accident Handlingd

Maine Yankee Nuclear Plant to the Railhead at Pejepscot Mills

Mean = 3.8E-07 5.1E-04 5.1E-04 8.0E-08 1.4E-02

Standard Deviation = 2.2E-07 3.0E-04 3.0E-04 4.4E-08 8.5E-03

Kewaunee Nuclear Plant to the Railhead at Kewaunee

Mean = 2.1E-07 1.7E-04 1.7E-04 2.2E-09 1.4E-02

Standard Deviation = 1.2E-07 1.1E-04 1.1E-04 1.4E-09 8.5E-03

Railhead at Timpie to the Proposed Skull Valley Interim Storage Site

Mean = 4.5E-10 4.2E-04 4.2E-04 2.6E-11 1.4E-02

Standard Deviation = 2.6E-10 2.7E-04 2.7E-04 1.8E-11 8.5E-03

a. Intermodal transfer stop dose to members of the public.

b. Short segment lengths mean no stops are made for inspections or to refuel, eat, or sleep.

c. Sum of on-link, off-link, and crew doses.

d. Intermodal transfer dose risk to cask handlers.

8.12 Loss of Shielding Accidents

The loss of shielding (LOS) accident model uses the entire radionuclide content of the material

to determine source strength because it was built for less robust (Type A) packages (e.g.,

radiopharmaceutical shipments) that could lose all or part of their shielding in serious accidents.

With spent-fuel casks, however, loss of shielding is expected to be localized to a small fraction

of the total surface area of the cask.
8-48

Although the STOP subroutine is generally used to evaluate incident-free doses at stops, it is also

suited to spent fuel cask LOS scenarios because the subroutine requires only dose rate, source

dimension, and exposure duration as input values. These are used to construct a point source of

the appropriate source strength to estimate radiation exposure fields, as is used for the

RADTRAN incident-free exposure model. Population may be modeled as being uniformly

distributed around the source in one or more annular areas with user-defined radii and population

densities. Exposure duration is taken to be the time that passes before emergency responders

establish an exclusion area around the accident site. In the absence of specific information for

this variable, 25 minutes in urban areas and 40 minutes in rural and suburban areas were the

values used.

To use the RADTRAN STOP model to assess LOS consequences for accidents involving casks,

three factors must be calculated for each accident severity category:

• Severity fraction for each LOS accident case.

• Dose rate (dose rate at 1 m from surface of cask after the LOS accident has occurred).

• Maximum dimension and geometry of the unshielded area.

8.12.1 Severity Fractions, Dose Rates, and Cask LOS Areas

Severity fractions for ten LOS accident cases are developed by combining the train accident

cases presented in Table 7.11 into 6 groups as follows: Cases 4, 5, and 6 which have accident

speeds from 30 to 60 mph, Cases 1, 7, 8, and 9 which have accident speeds from 60 to 90 mph,

Cases 2, 10, 11, 12, and 13 which have accident speeds from 90 to 120 mph, Cases 3, 13, 14, 15,

and 16 which have speeds > 120 mph, Case 20 which is all fire only accidents that produce lead

slump by melting, and Cases 16, 17, 18, and 19 which are collision accidents during which the

cask shell is punctured, which also lead to large fires and thus to the loss of melted lead out the

shell puncture. Severity fractions for these ten LOS accident cases are developed by summing

the severity fractions for the accident cases which contribute to each LOS case and multiplying

by the chance that the accident is an end or a corner impact (the finite element calculations do

not show LOS for side impact accidents).

The maximum exposed length of a spent-fuel assembly (at least for end drops where lead slumps

and separates from one end of the cask) is determined from the finite element analyses of cask

shielding damage for each scenario. This exposed length is then expressed as a fraction of the

length of a full PWR assembly (200 inches).

The LOS fraction is then used to calculate a Source-Strength Multiplier, which is the number by

which the maximum dose rate at 1 m from an unshielded fuel assembly must be multiplied to

yield the maximum dose rate 1 m from the cask on the centerline of the field of view of the

shielding damage. Because lead slump often occurs at the ends of the cask where the fittings are

and where the lowest burnup fuel is located, neglect of this consideration increases the

conservatism of the source strength estimates.
8-49

To calculate the Source-Strength Multiplier of a steel-lead-steel train cask, the following

approach was used. As is shown in Figure, 8-24, the dose rate at 1 m in the center of the zone of

shielding damage was modeled as the integrated sum of dose rate contributions from the fuel

surface extending in an arc from 0 degrees to approximately 60 degrees multiplied by 2 to

account for symmetry. The fuel surface was modeled as being a section of a cylinder with a

diameter equal to 1.65 m (the same as the cask ID) and a width equal to the maximum exposed

length.

Figure 8.24 Representation of spent fuel surface for dose rate

calculation for LOS scenarios.

Table 8.12 presents the severity fractions, LOS fractions, and source strength multipliers used in

the LOS accident calculations. The following comments qualify the development of the values

of these parameters:

1. For LOS Cases 1 through 8, impact forces are modeled as causing lead slump, and the

maximum length of exposed fuel for each of these cases was taken from the appropriate

finite element analysis.

2. For LOS Cases 9 and 10, the accident leads to a fire. Case 10 involves lead melt combined

with puncture that allows some of the lead to flow out of the cavity between the inner and

outer cask shells. Because the location of the puncture with respect to the ground surface

cannot be predicted, on the average it is assumed to allow approximately one-half of the lead

to flow out. Thus, a value of 0.5 for fractional exposure was assigned to this accident case.

3. In all cases, the approximately 3 inches of steel that comprise the inner and outer shell are

modeled as remaining in place, and the shielding they continue to provide is accounted for in

this model.

4. The Source-Strength Multiplier is calculated by expressing the result from the integration

(Step 1) as a fraction of the dose rate from a single fully exposed assembly and multiplying

by the total number of assemblies exposed.

5. This value is then entered as a modifier (shielding factor) into the RADTRAN STOP model,

and the package dose rate is replaced by the dose rate for the fully exposed fuel. The product

of these two variables yields dose rate in area of LOS.

Max. Dose Rate at 1 m

from surface (DRmax) at

LOS location

Maximum angle for contribution

to DRmax = 60°
8-50

Table 8.12 Values of Severity Fractions, LOS Fractions,

 and Source-Strength Multipliers for Ten LOS Accident Cases

LOS

Case

Accident

Type

Accident

Conditions

Train

Accident

Cases

Sum Case

Probabilities

Severity

Fraction

LOS

Fraction

SourceStrength

Multiplier

1 Collision end 4,5,6 3.049E-05 1.707E-06 0.052 0.215

2 Collision end 1,7,8,9 8.273E-06 4.633E-07 0.158 0.637

3 Collision end 2,10,11,12 5.730E-07 3.209E-08 0.264 1.017

4 Collision end 3,13,14,15 4.524E-09 2.534E-10 0.368 1.336

5 Collision corner 4,5,6 3.049E-05 2.201E-05 0.033 0.137

6 Collision corner 1,7,8,9 8.273E-06 5.973E-06 0.096 0.394

7 Collision corner 2,10,11,12 5.730E-07 4.137E-07 0.158 0.637

8 Collision corner 3,13,14,15 4.524E-09 3.266E-09 0.255 0.986

9 Fire Only T > 350° 20 4.905E-05 4.905E-05 0.029 0.120

10 Fire T > 350°C &

puncture

16,17,18,19 4.150E-10 1.660E-09 0.500 1.668

11 No LOS 9.999E-01 0.000

8.12.2 Maximum Dimension of LOS Area

The maximum LOS area is obtained in a relatively conservative manner by using the product of

LOS fraction and fuel assembly length as one dimension of a rectangle. The second dimension

is set equal to the ID of the cask. The diagonal of this rectangle is entered into RADTRAN as

the maximum characteristic dimension, which is used internally to calculate a shape factor (k0)

for a point source.

8.12.3 Final Calculation

The dose rate and dimension values entered as described above allow the user to calculate

population dose for persons, who remain at specified distances from the LOS accident location

for specified lengths of time, by treating the results of the LOS event as a point source. For real

LOS accidents, cask orientation combined with shielding by the undamaged portions of the cask

shell and also by nearby buildings would mean that radiation exposures would be limited in

extent by the view factor to the spent fuel through the damaged portions of the cask shell that

now provide no shielding. However, because the exact geometry of an accident cannot be

predicted in advance, a point-source model and a uniformly distributed surrounding exposed

population was used. Accordingly the estimates of the LOS accident dose risks should be

somewhat conservative.

8.12.4 An Example of an LOS Calculation

As an example of an LOS risk estimate, a steel-lead-steel rail cask containing PWR fuel

assemblies was considered. For an approximate surface dose rate of 50,000 rem/hr for five-year

cooled spent fuel, the dose rate at 1 m from the surface of one face at mid-length of the assembly

was calculated by modeling the assembly as a line source 5 m long. The resulting value,

3500 rem/hour, was then attenuated by 3 inches of steel using an approximate photon spectrum
8-51

derived from the isotopic inventory for PWR spent fuel before subtracting insignificant isotopes

relative to their A2 values [8-7]. Since the source of the surface dose rate quoted above did not

specify neutron and gamma fractions, the attenuation due to 3 inches of steel treats the radiation

as 100% gamma; this yields a conservative result for radiation outside the cask. The

radionuclides that account for 97 percent of the resulting dose rate are Co-60, Cs-134, Cs-137,

and Eu-154, as may be expected from the their photon energies. The result, 20 rem/hr,

representing the dose rate from a single PWR fuel assembly in a steel-lead-steel rail cask without

the lead shielding, was then multiplied by the appropriate Source-Strength Multiplier in Table

8.12 to provide the required RADTRAN 5 input. The source dimension used in modeling the

cask as a point source in RADTRAN 5 was taken to be the diagonal of the rectangular exposed

area (viewed at right angles to the cask axis) for each case in Table 8.12. These two sets of

parameters were used to define ten “VEHICLEs” in RADTRAN 5, one for each of the ten cases

in Table 8.12.

The RADTRAN 5 stop model was used to define three LOS accident locations, i.e. rural,

suburban, and urban. Population densities for these three stop definitions were assumed to equal

the means of the respective population density distributions for each region (i.e., 10.1, 336, and

2195 persons per square kilometer, respectively). The area occupied by these populations was an

annulus with a 10 m inner radius and an 800 m (1/2 mile) outer radius; the latter yields a dose

rate well below 10 mrem/hour in each case. The standard shielding factors (1.0, 0.87 and 0.018)

and emergency response times (0.67, 0.67, and 0.42) for rural, suburban, and urban areas,

respectively, were applied to the three stop definitions. Table 8.13 presents route-portion

lengths, mean rail accident rates, the severity fractions given in Table 8.13, the consequences

calculated by RADTRAN 5, and the risks (probability times consequence) for each of the ten

cases defined. The total LOS risk of 9.1E-11 person-rem may be compared with the PWR steellead-steel rail cask results given in Table 8.5 to see that this risk is much smaller than the

dispersion accident value. In addition, the sum of the two risks (representing an accident in

which there is loss of shielding and dispersion of cask contents) is well within the variability of

the dispersion value alone.

8.13 Population Dose Risks for Shipment of the Entire 1994 Spent Fuel

Inventory

The incident-free and accident population dose risks reported in the previous sections were

calculated for single shipments of one Type B spent fuel cask by truck or by train. In this

section, the results of those calculations are used to estimate the population dose risks that would

be associated with the shipment of the entire 1994 inventory of commercial BWR and PWR

spent fuel [8-2]. Table 8.14 presents the total numbers of BWR and PWR assemblies in the 1994

spent fuel inventory, the number of truck or rail shipments required to ship all of the BWR or all

of the PWR assemblies in each of the four generic casks examined by this study, and the

incident-free and accident population dose risks associated with the shipment of all of the BWR

assemblies, all of the PWR assemblies, and their sums (i.e., the population dose risks for

shipping the entire 1994 inventory). The population dose risks for transport by rail presented in

this table do not include any doses to handlers that might be incurred during intermodal transfers

(e.g., from heavy haul truck to rail car).
8-52

Table 8.13 Results of Loss of Shielding Risk Calculation

Case Pop. Zone Length

(km)

Acc. Rate

(per km)

Sev. Frac. Probability Consequence

(dose, rem)

Dose

Risk

1 Rural 1777 4.40E-08 1.71E-06 1.34E-10 0.0021 2.81E-13

Suburban 541 4.40E-08 1.71E-06 4.07E-11 0.06 2.44E-12

Urban 35 4.40E-08 1.71E-06 2.63E-12 0.0051 1.34E-14

2 Rural 1777 4.40E-08 4.63E-07 3.62E-11 0.0071 2.57E-13

Suburban 541 4.40E-08 4.63E-07 1.10E-11 0.206 2.27E-12

Urban 35 4.40E-08 4.63E-07 7.13E-13 0.0175 1.25E-14

3 Rural 1777 4.40E-08 3.21E-08 2.51E-12 0.0133 3.34E-14

Suburban 541 4.40E-08 3.21E-08 7.64E-13 0.385 2.94E-13

Urban 35 4.40E-08 3.21E-08 4.94E-14 0.0326 1.61E-15

4 Rural 1777 4.40E-08 2.53E-10 1.98E-14 0.0221 4.37E-16

Suburban 541 4.40E-08 2.53E-10 6.02E-15 0.639 3.85E-15

Urban 35 4.40E-08 2.53E-10 3.90E-16 0.0541 2.11E-17

5 Rural 1777 4.40E-08 2.20E-05 1.72E-09 0.0013 2.24E-12

Suburban 541 4.40E-08 2.20E-05 5.24E-10 0.0373 1.95E-11

Urban 35 4.40E-08 2.20E-05 3.39E-11 0.0032 1.08E-13

6 Rural 1777 4.40E-08 5.97E-06 4.67E-10 0.004 1.87E-12

Suburban 541 4.40E-08 5.97E-06 1.42E-10 0.115 1.63E-11

Urban 35 4.40E-08 5.97E-06 9.19E-12 0.0097 8.92E-14

7 Rural 1777 4.40E-08 4.14E-07 3.24E-11 0.0071 2.30E-13

Suburban 541 4.40E-08 4.14E-07 9.85E-12 0.206 2.03E-12

Urban 35 4.40E-08 4.14E-07 6.38E-13 0.0175 1.12E-14

8 Rural 1777 4.40E-08 3.27E-09 2.56E-13 0.013 3.32E-15

Suburban 541 4.40E-08 3.27E-09 7.78E-14 0.377 2.93E-14

Urban 35 4.40E-08 3.27E-09 5.04E-15 0.032 1.61E-16

9 Rural 1777 4.40E-08 4.91E-05 3.84E-09 0.0011 4.22E-12

Suburban 541 4.40E-08 4.91E-05 1.17E-09 0.0331 3.86E-11

Urban 35 4.40E-08 4.91E-05 7.55E-11 0.0028 2.12E-13

10 Rural 1777 4.40E-08 1.66E-09 1.30E-13 0.035 4.54E-15

Suburban 541 4.40E-08 1.66E-09 3.95E-14 1.01 3.99E-14

Urban 35 4.40E-08 1.66E-09 2.56E-15 0.0858 2.19E-16

Total 9.12E-11
8-53

Table 8.14 shows that, for shipment of the entire 1994 spent fuel inventory, accident dose risks

are negligible when compared to incident-free dose risks, and that the magnitude of these risks

changes significantly depending on the mode of shipment (truck or rail) and the type of cask

Table 8.14 Incident-Free and Accident Population Dose Risks for

Shipment of the Entire 1994 Spent Fuel Inventory (person-rem)

Spent Rail Shipments Truck Shipments

Fuel

Type

Monolithic

Steel Cask

Steel-LeadSteel CaskSteel-LeadSteel CaskSteel-DU-Steel

Cask

Assemblies in Total 1994 Inventory

BWR 60144

PWR 44598

Assemblies per Cask

BWR 52 52 2 7

PWR 24 24 1 3

Required Number of Shipments

BWR 1157 1157 30072 8592

PWR 1858 1858 44598 14866

Total 3015 3015 74670 23458

Incident-Free Stop Dose Risksa,b,c

BWR 5.1 5.1 460 130

PWR 8.1 8.1 680 230

Total 13.2 13.2 1140 360

Other Incident-Free Population Dose Risksa,b

BWR 18.4 18.4 870 250

PWR 29.5 29.5 1280 430

Total 47.9 47.9 2150 680

Total Incident-Free Population Dose Risksa,b

BWR 24 24 1330 380

PWR 37 37 1960 660

Total 61 61 3290 1040

Accident Population Dose Risksa

BWR 0.0017 0.011 0.010 0.0093

PWR 0.0037 0.018 0.036 0.034

Total 0.0054 0.028 0.046 0.043

a. Values have been rounded to two significant figures.

b. Because the probability of occurrence of incident-free doses is 1.0, incidentfree doses and incident-free dose risks have the same values.

c. Truck stop dose risks assume shipment without stops to sleep.
8-54

used for the shipments. The dependence of incident-free doses on shipment mode and cask type

means that the incident-free doses for each year in the full spent fuel shipment campaign could

vary significantly depending on the mix of assemblies shipped and the mode and cask used for

each shipment made during a given year. For example, if the shipments take place over 20 years,

the ratio of PWR to BWR assemblies shipped each year is the same as the ratio in the total

inventory, all shipments are by rail in monolithic steel and/or steel-lead-steel rail casks, and

handler doses during any intermodal transfers are neglected, then the total incident-free

population dose per year would be about 1.3 person-rem. Conversely, if the shipments take

place over 20 years, the ratio of PWR to BWR assemblies shipped each year is the same as the

ratio in the total inventory, and all shipments are by truck in steel-lead-steel truck casks (the

smaller capacity truck cask), then the total incident-free population dose per year would be about

130 person-rem, which is 100 times larger than the incident-free population dose for rail

shipments.

8.14 Individual Dose Estimates

Besides the population dose estimates that are the basis of the CCDF’s described above,

RADTRAN estimates dose within areas downwind of the accident site. Individuals who might

be within these areas at various distances from the accident site are counted as having received

the dose predicted for that area. These doses are directly dependent on the magnitude of the

source term for the specific representative accident being considered and assume that the

individual remains outdoors directly in the path of the passing radioactive plume for the entire

period of the accident/release event. Under these unlikely conditions and the very unlikely

sequence of events that yield a source term at all, there is a potential for persons close to the

accident location to receive a relatively large radiation dose. These accident conditions are

associated with the population doses at the extreme right edge of the CCDF’s in the preceding

figures.

As an example of the doses that might be received from accidents involving spent fuel

shipments, results from the RADTRAN calculations for rail shipment from Maine Yankee to

Skull Valley, one of the illustrative routes discussed earlier, will examined in greater detail. For

this discussion, a rail shipment was used because it presented the largest possible source term

(because of the large number of spent fuel assemblies a rail cask contains). Generally speaking,

the dose that could be received by a person decreases rapidly with distance from the point of

release and the highest doses are received at the points closest to the accident. Similarly dose

decreases with lateral distance from the maximum dose point (centerline) at any distance, i.e., as

the distance from the center of a radioactive plume increases the inhalation/immersion dose

decreases. As a result, the areas in which the highest doses could be received have a relatively

small area. In addition, locations very close to the site of the accident are unlikely to be occupied

by people for any length of time after an accident because of evacuation and crowd control

measures by first responders. Thus, the shortest distance at which individuals might be expected

to receive doses should be beyond 100 to 200 meters (330 to 660 feet) from the accident site.

In the distance range given, doses that could be received by individuals standing outdoors and

directly under the passing radioactive plume for the entire time of passage range from 3 to

500 rem (50 yr CEDE) for the extremely unlikely collision/fire events (on the order of 1 x 10-10

per shipment) estimated to result in a significant release of material from a cask. The doses
8-55

associated with these extremely unlikely events are relatively high but not so large that any early

fatality is predicted (as is true for all RADTRAN calculations completed for this report) nor

would an early fatality from radiation actually be expected to result. The largest of these doses,

if received, could pose a significant, though not life threatening, health hazard to anyone so

exposed, but there are many conservative factors in the RADTRAN calculations that come into

play to make the likelihood of experiencing such doses very small, given that the representative

accident producing the dose could even occur (which in itself is a very implausible event).

The principal RADTRAN conservatisms that make it unlikely that these large doses would ever

be realized are as follow:

• RADTRAN uses a ground level plume formulation, i.e., the highest concentration point

of the plume containing the release material moves along the ground from the release

point to the farthest point of the calculation. However, in 17 of the 20 representative

accidents that produce high population doses, the source term is the result (in part) of a

significant fire event. These fires are hot, fully engulfing, and of duration exceeding

1 hour. In reality, a fire of sufficient duration and temperature to cause a release would

cause the released plume to be lofted to an altitude in which the centroid is hundreds of

meters off the ground surface. In such situations, zero or extremely low doses will be

realized inside of distance that are 10 or more times the lofted height. Beyond that

distance the calculated maximum doses will approach those predicted by RADTRAN ,

but certainly are below 5 rem. The remaining three doses also result from release plumes

that are likely to be lofted, though not by the presence of a major fire, though it is likely

that there will be fires present near accidents with these collision/impact magnitudes.

Lofting for these plumes is a result of the fact that the major component of the gas

pressurizing the cask is helium which has a density one seventh that of air. Thus, the

plumes from these accidents (even in the absence of a fire) will also be lofted and the

resultant dose will be lower than predicted.

• RADTRAN assumes that no measures will be taken by emergency response personnel to

limit the progression of the accident. In urban and suburban and most rural areas where

people could be exposed, emergency response actions will limit the chain of events that

produce many of the source terms and thus act to preclude such releases. In remote areas

where there are few people, it is unlikely that there will be any one within the relatively

small area of high dose to receive it. Even more unlikely is that individuals would

remain close to the scene of an accident and stay outside directly in the passage of a

radioactive plume (that looks like a fire cloud/smoke) for the entire passage of the plume.

Thus, in spite of the predicted high doses realized for the high severity accident cases, it is

deemed unlikely that the predicted doses would ever be realized in an accident situation. More

importantly, it is assumed in this analysis that such accidents can occur, but, in fact, the

combination of circumstances needed to release material from a modern spent fuel cask are so

improbable as to be impossible.
8-56

8.15 Effect of NUREG-0170 Source Term and Exposure Pathway Models on

Dose Risk

The treatments of spent fuel accident source terms and exposure pathways used in RADTRAN 5

differ markedly from those used in RADTRAN 1. This section describes these treatments and

the effects they have on predictions of population dose risks in three steps. First, the inventories,

accident source term equations, and exposure pathways models used in NUREG-0170 are

contrasted with those used in this study. Second, results of RADTRAN 4 and RADTRAN 5

calculations are compared to RADTRAN 1 results in order to show that these codes can be made

to mimic RADTRAN 1 results. Finally, a series of RADTRAN 5 calculations are performed that

depict the effect of the NUREG-0170 source term and exposure pathway treatments on

predictions of population dose risks.

8.15.1 Source Term and Exposure Pathway Models in RADTRAN 1 and RADTRAN 5

Both RADTRAN 1 and RADTRAN 5 calculate spent fuel accident source terms (STi) as the

product of an inventory (Iinventory,i) of radionuclide I and the fraction (frelease,i) of that inventory

that could be released to the atmnosphere should the spent fuel cask fail during a severe accident.

Thus, STi = Iinventory,i frelease,i.

In Section 1.2, it was stated that, as it was used in NUREG-0170, Iinventory,i is not a cask

inventory. Instead, it is the number of curies of radionuclide i estimated to be released from the

spent fuel cask to the atmosphere should the cask fail during a severe accident. Thus, for the

RADTRAN 1 calculations performed for NUREG-0170, Iinventory = STsevere accident,i, where values

for STsevere accident,i were developed largely on the basis of conservative engineering judgment and

STsevere accident,i is the source term for a severe spent fuel accident. Accordingly, as used for

NUREG-0170, frelease,i is the fraction of the severe accident source term that is released during

accidents of lessor severity.

For this study, the number of curies of radionuclide i that is released from a Type B spent fuel

cask should the cask and some of the rods in the cask both fail during an accident is calculated as

the product of five numbers: the number of assemblies in the cask (Nassemblies), the inventory of

radionuclide i in a single fuel assembly (Ii), the fraction of the number of rods in an assembly

that fail (frods), the fraction of the inventory of radionuclide i in a single rod that escapes to the

cask interior upon rod failure (frod-to-cask,i), and the fraction of the amount of radionuclide i that

reaches the cask interior that escapes from the cask interior through the cask leak to the

environment (fcask-to-environment,i). Thus, for this study, the source term for radionuclide i (STi) is

calculated as

STi = NassembliesIifrodsfrod-to-cask,ifcask-to-environment,i

where Iinventory,i = NassembliesIi and frelease,i = frodsfrod-to-cask,ifcask-to-environment,i.

Table 7.9 shows that the single assembly BWR and PWR inventories used in this study contain

19 and 20 radionuclides, respectively. In marked contrast to Table 7.9, Table 1.4 shows that the

truck and rail cask accident “inventories” used with RADTRAN 1 for the NUREG-0170 spent

fuel calculations contain only three radionuclides, Kr-85, I-131, and Cs-137. Here “inventories”
8-57

is in quotes to emphasize the fact that the NUREG-0170 meaning for this term is different from

the common meaning. That is, in NUREG-0170 [8-1], “inventory” means the amount of each

radionuclide released to the environment upon package failure and not the amount of each

radionuclide that is contained (carried) in the package, here the Type B spent fuel cask.

Table 7.9 shows that the BWR and PWR inventories developed for this study do not contain

I-131. They do not contain I-131 because the RADSEL code calculation described in Section

7.2.3.3 showed that iodine radionuclides in three-year cooled, high-burnup spent fuel do not

contribute significantly to radiation health hazards at the level of one-tenth of one percent.

Table 7.31 shows that the source term analysis performed for this study developed 19 source

terms for a steel-lead-steel Type B spent fuel truck cask, one of which, Case 19, represents the

fraction of all truck accidents that do not lead to a release of radioactivity from the cask because

either the cask containment is not compromised or because none of the rods in the cask fail. The

table also shows that for a steel-lead-steel Type B spent fuel rail cask, 21 source terms were

developed, one of which represents accidents that do not lead to any release of radioactivity. As

described in Section 1.2, the source term scheme used in NUREG-0170 [8-1] had eight

categories and two release models, Models I and II. Categories I and II represented accidents

that respectively do not result in releases from Type A and Type B packages. Categories III

through VIII represented accidents that are severe enough to cause radionuclides to be released

from a Type B package. Both release models assumed that all materials released from the cask

were respirable, that is they were either gases, vapors, or respirable aerosols. Thus, all solid

materials released from the cask were assumed to be aerosols with sizes (aerodynamic mass

median diameters) 10 . Model I assumed that 100 percent of the NUREG-0170 truck and rail

accident “inventories” of Kr-85, I-131, and Cs-137 was released by any accident that fell into

Categories III through VIII. Model II tempered this conservative assumption by decreasing the

fraction of the NUREG-0170 accident “inventories” released for Categories III and IV accidents

from 100 percent to 1 and 10 percent respectively.

RADTRAN 5 models radiation exposures caused by transportation accidents that are delivered

via four pathways: direct exposure to the passing radioactive airborne plume (cloudshine),

exposures caused by inhalation of radioactive materials in the passing airborne plume (direct

inhalation), exposures to radioactivity deposited onto the ground from the passing airborne

plume (groundshine), and exposures caused by inhalation of radioactive materials that are

resuspended from contaminated ground into the air (resuspension inhalation). In marked

contrast to this, RADTRAN 1 only modeled inhalation exposures (both direct inhalation and

resuspension inhalation).

Two sets of calculations were performed to examine the impact on estimates of accident

consequences calculated with RADTRAN 1 and RADTRAN 5 of these differing treatments of

accident source terms and exposure pathways. The first set of calculations compared the mean

accident population doses and the mean number of latent cancer fatalities that are obtained when

the NUREG-0170 spent fuel transport accident calculation is run using RADTRAN 1,

RADTRAN 4, and RADTRAN 5. The second set of calculations examined the impact of

various combinations of these treatments on RADTRAN 5 steel-lead-steel truck cask accident

CCDFs.
8-58

8.15.2 Comparison of Results Calculated with RADTRAN Versions 1, 4, and 5

When this study was initiated, RADTRAN 1, the first version of the RADTRAN code that was

developed to support the performance of NUREG-0170 [8-1], existed only as a listing on

microfiche appended to the Sandia National Laboratories report that describes RADTRAN 1

[8-8]. Thus, for this study, in order to compare RADTRAN 1 results to results obtained with

later versions of the RADTRAN code, RADTRAN 1 had again to be made operational.

Reference [8-9] describes the resurrection and verification of RADTRAN 1.

Ideally, RADTRAN 1 results would be compared directly to results obtained using RADTRAN

5, the version of the RADTRAN code used to support this study. This was not done for the

following reasons. RADTRAN 1 is able to examine only one radionuclide at a time.

Accordingly, three RADTRAN 1 calculations must be performed to develop results for the three

radionuclides (Kr-85, I-131, and Cs-137) in the NUREG-0170 spent fuel accident “inventory.”

RADTRAN 4 and RADTRAN 5 can examine many radionuclides during a single calculation.

However, while RADTRAN 4 can output the accident population dose attributable to each

radionuclide examined, RADTRAN 5 outputs only the total population dose and not the doses

attributable to the individual radionuclides in its package inventory. Further, differences in code

input mean that essentially identical input can be developed for RADTRAN 1 and RADTRAN 4

or for RADTRAN 4 and RADTRAN 5, but not for RADTRAN 1 and RADTRAN 5. Because

RADTRAN 4 and RADTRAN 5 yield essentially identical results for the NUREG-0170 spent

fuel calculation (i.e., total truck and train accident population doses respectively of 2.12E+02

versus 2.13E+02 person-rem), RADTRAN 4 results are an excellent surrogate for RADTRAN 5

results. Therefore, because identical input could be developed for RADTRAN 1 and

RADTRAN 4 and because RADTRAN 4 generates population dose results for each radionuclide

examined, the calculations that compared accident doses compared RADTRAN 1 results to those

obtained with RADTRAN 4.

Replication of RADTRAN 1 input data in the formats required by RADTRAN 4 and RADTRAN

5 was not simple for all input parameters. For example, in RADTRAN 4, the fraction of land

occupied by buildings is 0.52, fixed values are used for the fractions of the population that are

outdoors and in buildings, and doses for people in buildings are calculated by multiplying the

dose for people outdoors by a building dose factor (BDF) which accounts for the lower doses

that are received by people in buildings because of particle filtering during air infiltration into

buildings. Because RADTRAN 1 does not model the particle filtration during air infiltration into

buildings, in order to force RADTRAN 4 to mimic RADTRAN 1, the value of BDF used in the

RADTRAN 4 calculations was chosen so 0.52 × BDF = 1.0, which made RADTRAN 4 doses for

people in buildings the same as the doses received by people outside of the buildings. For

RADTRAN 5, because the fraction of land occupied by buildings and the BDF are both input

parameters, RADTRAN 5 could be made to mimic RADTRAN 1 by setting both of these

parameters equal to 1.0. RADTRAN 4 and RADTRAN 5 but not RADTRAN 1 calculate

pedestrian doses in urban areas. Therefore, for the RADTRAN 4 and RADTRAN 5 calculations,

this dose was forced to zero by setting the value of RPD, the ratio of pedestrian density to region

population density, to zero. Finally, the value of the inhalation dose conversion factor currently

used for RADTRAN 4 and RADTRAN 5 calculations, which is somewhat larger than the value

used in RADTRAN 1, was reset to the RADTRAN 1 value.
8-59

Table 8.15 presents the mean accident population dose risks predicted by RADTRAN 1 and

RADTRAN 4 for the NUREG-0170 truck and rail calculations when each code was run using

the same truck or rail route and the same truck or rail accident source terms (i.e., the NUREG0170 truck or rail route, the NUREG-0170 truck or rail accident “inventory” specified in Table

1.4, and the NUREG-0170 Model II severity and release fractions specified in Table 1.3). Two

sets of RADTRAN 4 results are presented. The first set models only inhalation exposures (both

the dose from inhalation of radioactive materials directly from the passing plume and the dose

caused by inhalation of radioactive materials that are resuspended from the ground), while the

second set models not only direct and resuspension inhalation exposures but also exposures from

cloudshine and groundshine. Thus, the first set of results is directly comparable to the results

generated by RADTRAN 1 while the second set reflects the more complete treatment of

exposure pathways as currently modeled in both RADTRAN 4 and RADTRAN 5.

Table 8.15 Mean Accident Population Dose Risks Calculated by

RADTRAN 1 and RADTRAN 4 (person-rem)

Code (Exposure Pathways)

Radionuclide

RADTRAN 1

(only inhalation

and resuspension)

RADTRAN 4

(only inhalation

and resuspension)

RADTRAN 4

(all pathways)

NUREG-0170 Truck Route and Truck Accident Model II Source Terms

 Kr-85 1.05E-04 1.83E-04 4.20E-01

 I-131 2.68E-03 2.66E-03 2.69E-03

 Cs-137 1.32E+00 4.34E+00 1.79E+02

NUREG-0170 Rail Route and Rail Accident Model II Source Terms

 Kr-85 2.32E-05 3.73E-05 8.52E-02

 I-131 5.76E-04 5.29E-04 5.33E-04

 Cs-137 2.89E-01 8.78E-01 3.20E+01

Table 8.15 shows that

• that the doses caused by the quantities of Kr-85 and I-131 in the NUREG-0170 truck and

train accident “inventories” contribute negligibly to the total accident population doses

(sum of the doses caused by each radionuclide), which are essentially equal to the dose

caused by Cs-137;

• that the RADTRAN 4 total inhalation truck and rail accident population doses are

respectively 3.3 and 3.0 times larger than the corresponding RADTRAN 1 doses; and

• that the truck and rail accident population doses calculated by RADTRAN 4, when all

exposure pathways are modeled, are respectively about 41 and 36 times larger than the

doses calculated when only the direct inhalation and resuspension inhalation pathways

are modeled.
8-60

Differences between the RADTRAN 1 and RADTRAN 4 inhalation dose models explain the

second result. Specifically, in the RADTRAN 1 and RADTRAN 4 equations for Dinh, the total

inhalation dose (sum of the direct and resuspension inhalation pathway doses) are formed into a

ratio and common parameters that have the same value are cancelled, the following expression

results

3.3

RESUSP(RAD 1)TRAN

RESUSP(RAD 4)TRAN

22.223E

BRxIF

D (RADTRAN1)

D (RADTRAN4)

inh

inh × = − =

This expression equals 3.3 because in RADTRAN 4, the time-integrated atmospheric dilution

factor, IF = 66.2 Ci s/m2

 for Cs-137, the breathing rate, BR = 3.3E-4 m3/s, and the resuspension

factor, RESUSP = 5.41, while in RADTRAN 1 the constant 2.223E-2 represents the product of a

time integrated atmospheric dilution factor and a breathing rate, and RESUSP = 1.62. Thus, the

fact that RADTRAN 4 truck and rail accident population doses are respectively 3.3 and 3.0 times

larger that the same doses calculated with RADTRAN 1 is almost entirely caused by the

differences in the parameter values used in the nearly identical RADTRAN 1 and RADTRAN 4

inhalation dose models.

RADTRAN 1, RADTRAN 4, and RADTRAN 5 all estimate the radiation induced latent cancer

fatalities (LCFs) that may occur among a population exposed to radiation due to the transport of

a radioactive material, for example spent fuel. Because RADTRAN 1 and RADTRAN 4 use

different models to calculate LCF values, comparison of the LCF predictions of these two

versions of RADTRAN is not straightforward. However, because both RADTRAN 1 and

RADTRAN 5 calculate LCFs from population dose using a simple multiplicative cancer fatality

risk factor, the cancer fatality models in these two versions of RADTRAN can be made the same

by setting the value of this factor in RADTRAN 5 to 2.220E-05 LCFs/person-rem, the hardwired

value that is used in RADTRAN 1 to calculate cancer fatalities caused by inhalation dose to the

lungs, or to 1.216E-4 LCFs/person-rem, the value used to calculate cancer fatalities from the

dose delivered to the whole body by all exposure pathways.

Table 8.16 presents the predictions of LCF risks for the NUREG-0170 standard spent fuel

shipment model for the year 1975 (i.e., 17 rail shipments of length 1,210 km and 254 truck

shipments of length 2,530 km) obtained using RADTRAN 1, RADTRAN 4, and RADTRAN 5,

the NUREG-0170 truck and rail accident “inventories,” and the NUREG-0170 Model II Severity

Table 8.16 RADTRAN 1, RADTRAN 4, and RADTRAN 5 Estimates of the Mean Latent

Cancer Fatality Risks Associated with Shipment of Spent Fuel According to the

NUREG-0170 Standard Shipment Model for 1975

Code Version

(pathways modeled)

Mean Latent Cancer

Fatality Risk

RADTRAN 1 (only direct and resuspension inhalation) 3.57E-05

RADTRAN 4 (only direct and resuspension inhalation) 1.15E-04

RADTRAN 5 (only direct and resuspension inhalation) 1.16E-04

RADTRAN 4 (all pathways) 2.50E-02

RADTRAN 5 (all pathways) 2.54E-02
8-61

and Release Fractions. Table 8.16 shows that the RADTRAN 5 and RADTRAN 1 LCF

predictions differ by a factor of 3.3 when RADTRAN 5 is made to model only the direct and

resuspension inhalation pathways, while the RADTRAN 5 result when all exposure pathways are

modeled is 700 times larger than the result obtained using RADTRAN 1, which models only

inhalation pathways.

Because RADTRAN 4 inhalation doses exceed those predicted by RADTRAN 1 by factors of

approximately 3.3, the mean latent cancer fatality prediction of RADTRAN 4 also exceeds that

of RADTRAN 1 by about 3.3. Because the dosimetric models in RADTRAN 4 and 5 are

essentially identical, and their cancer risk models are equivalent, RADTRAN 4 and RADTRAN

5 yield essentially identical predictions of latent cancer fatalities when these fatalities are based

only on inhalation dose and also when they are based on dose delivered by all exposure

pathways.

The preceding results demonstrate that RADTRAN 4 and RADTRAN 5 yield nearly identical

latent cancer fatality predictions when both run the same problem. Therefore, because

RADTRAN 4 inhalation doses exceed those predicted by RADTRAN 1 by a factor that is almost

entirely explicable in terms of differences in a few inhalation dose parameter values, the fact that

RADTRAN 4 and RADTRAN 5 yield identical results for the same problem means that

RADTRAN 5 is a reasonable surrogate for RADTRAN 1. Accordingly, RADTRAN 5 was used

to examine the impact that the various components of the NUREG-0170 treatments of source

terms and exposure pathways have on population dose CCDFs.

8.15.3 Effect of Treatments on RADTRAN 5 Accident Population Dose CCDFs

Because the accident source terms developed for NUREG-0170 [8-1] are very different from

those developed for this study and because RADTRAN 1 models only inhalation exposures

while RADTRAN 5 models cloudshine and groundshine exposures in addition to inhalation

exposures, five RADTRAN 5 truck transport calculations were performed to illustrate the effect

of these different treatments on accident population dose risk. Except for source terms, the input

data used in these five calculations (the LHS sample and the values for all other parameters

except source term parameters) was identical. Thus, each calculation used the same set of 200

representative routes and route characteristics, and each used the same set of values for all other

input parameters except severity fractions and release fractions. Table 8.17 lists for each

calculation the source term used, the exposure pathways modeled, and the resulting Mean

Accident Population Dose Risk.

Figure 8.25 presents the five Accident Population Dose Risk CCDFs developed by these

calculations. Figure 8.25 shows that the five Accident Population Dose Risk CCDFs are ordered

as follows:

Calc. 19 CCDF  Calc. 20 CCDF  Calc. 21 CCDF  Calc. 22 CCDF  Calc. 1 CCDF

where  means “lies above.” Calculation 1 in Tables 8.1 and 8.17 is the RADTRAN 5

calculation that examined the risks associated with the transport of a single PWR assembly in the

generic steel-lead-steel truck cask and used as input (a) the LHS sample of size 200 that
8-62

Table 8.17 Mean Accident Population Dose Risks (person-rem) for Five RADTRAN 5

Calculations that Used Different Source Terms and Exposure Pathways

Inventory

Severity and Release

Fractions

Exposure

Pathways

0170c

Calculation

Number

from

Table 8.1

PWRa 0170b

Model I Model II

SLS-Td All Inhalation

Only

Mean

Accident

Population

Dose Risk

19 X X X 1.2E+4

20 X X X 7.0E+2

21 X X X 2.2E-2

22 X X X 7.7E-4

1 X X X 8.0E-7

a. See Table 7.9.

b. See Table 1.4.

c. See Table 1.3 in this report and Table 5-8 in Reference [8-1].

d. See Table 7.31.

contained the set of 200 representative truck routes and (b) the set of 19 new steel-lead-steel

truck cask source terms developed by this study. Calculation 22 in these tables is the

RADTRAN 5 calculation that best replicates, when 200 representative routes are examined, the

NUREG-0170 accident population dose risk results for the shipment of a single spent fuel truck

cask. Although the CCDFs for these two calculations cross at a population dose of about 2E+3

person-rem, Table 8.17 shows that the mean accident population dose risk for Calculation 22, the

calculation that used the NUREG-0170 truck accident source term and modeled only inhalation

exposures, is 1000 times larger than the mean accident population dose risk predicted by

Calculation 1, the steel-lead-steel truck transport calculation that used the 19 truck accident

source terms developed for this study and modeled all exposure pathways. Comparison of the

mean accident population dose risk results for Calculations 22 and 21, 21 and 20, and 20 and 19

then shows, respectively, that modeling cloudshine and groundshine increases mean accident

population dose risks by about a factor of 30; using the PWR cask inventory instead of the

NUREG-0170 truck accident “inventory,” which represents the radioactivity released to the

environment by the most severe accidents examined by NUREG-0170 [8-1], greatly increases

mean accident population dose risks by a factor of about 30,000; and finally, replacing the

NUREG-0170 Model II severity and release fractions by the Model I severity and release

fractions pushes the knee of the CCDF up a bit and further increases mean accident population

doses by a factor of about 20. Mean accident population dose risks increase by a factor of

30,000 when the NUREG-0170 accident “inventory” is replaced by the PWR truck cask

inventory, because the NUREG-0170 Models I and II treat all solid materials released as 100

percent aerosolized and 100 percent respirable. Thus, use of a real cask inventory with these

assumptions means that all of the actinides in spent fuel contribute to inhalation doses, which

greatly increases direct inhalation doses and very greatly increases long-term resuspension

inhalation doses.
100 101 102 103 104 105 106 107 108 109 1010 1011

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)

uck accident population dose risk CCDFs for calculations that examined the impact on dose risks of

 terms and exposure pathway models. Each RADTRAN 5 calculation assumed transport in a steel-lead

 each of the 200 representative truck routes and each calculation generated results for all of the 19

accident source terms.

tory, NUREG-0170 Model I release fractions, all exposure pathwaystory, NUREG-0170 Model II release fractions, all exposure pathways

70 accident release inventory, NUREG-0170 Model II release fractions, all exposure pathways

170 accident release inventory, NUREG-0170 Model II release fractions, only inhalation pathways

tory, 19 truck accident source terms, all exposure pathways
8-64

8.16 Population Dose Risk CCDFs from NUREG-0170, the Modal Study,

and this Study

Because the spent fuel risk assessment methodology developed by the Modal Study [8-2] was the

basis for all of the analyses conducted by this study, it is of interest to compare accident

population dose risk CCDFs and mean accident population doses calculated by RADTRAN 5

using NUREG-0170 Model I and Model II source terms, Modal Study source terms, and the

source terms developed by this study. Each of these calculations examined transport of PWR

spent fuel in a steel-lead-steel spent fuel cask and used the LHS sample of size 200 that

contained the representative set of 200 truck or rail routes. Except for inhalation dose and source

term parameters, each calculation used the same set of parameter values for all parameters that

had fixed values. Thus, the calculations differed only in the sets of source terms used and in

their treatments of exposure pathways (the NUREG-0170 calculations modeled only inhalation

dose while the Modal Study calculation and the calculation that used the source terms developed

for this study modeled all exposure pathways). Accordingly, these calculations compare the

NUREG-0170 result to the Modal Study result and to the result developed by this study.

The NUREG-0170 Model I and Model II source terms were presented in Table 1.5. Table 8.18

presents the Modal Study truck and rail accident source terms developed for generic steel-leadsteel casks. The source terms developed by this study for generic steel-lead-steel casks were

presented in Table 7.31.

Figures 8.26 and 8.27 present respectively the truck and rail accident population dose risk

CCDFs generated by these calculations. Each figure presents four CCDFs: the NUREG-0170

Model I CCDF, the NUREG-0170 Model II CCDF, the Modal Study CCDF, and the CCDF

developed by this study. In each figure, the highest lying CCDF is the NUREG-0170 Model I

CCDF, the next highest is the NUREG-0170 Model II CCDF, the next is the Modal Study

CCDF, and the lowest lying CCDF is the CCDF developed by this study. The impact of the

differences in the source term models used to generate these CCDFs can best be understood by

comparing the probability and consequence axis intercepts of these CCDFs and the mean

population dose risk associated with each CCDF (the area under each CCDF). The values of the

CCDF intercepts and the areas under each CCDF (the mean accident population dose risk) are

presented in Table 8.19.

8.16.1 CCDF Probability Axis Intercepts

The probability axis intercepts of the CCDFs in Table 8.19 can each be viewed as the product of

an average accident probability per shipment (averaged over the 200 representative truck or rail

routes examined) and one minus the chance that the shipment occurs without an accident severe

enough to cause the spent fuel cask to fail and release radioactivity to the atmosphere. Tables

1.5, 8.18, and 7.31 show that the chance that an accident will not be severe enough to fail a spent

fuel cask was estimated by NUREG-0170 [8-1], the Modal Study [8-2], and this study to be 0.91,

0.994316, and 0.99993, respectively, for truck accidents, and 0.80, 0.993962, and 0.99996,

respectively, for rail accidents. But all of the truck calculations used the same set of truck route

data and all of the train calculations used the same set of rail route data. So the average accident

probability per truck shipment was the same for all truck calculations and the average accident

probability per rail shipment was the same for all train shipments. Therefore, ratios of
8-65

Table 8.18 Modal Study Truck and Rail Accident Source Terms

Release Fractions (Table 8.3a 

) Source Term Fractions = F(rod) × Release Fractions Severity Fraction

Cs Ru Particulates CRUD Kr Cs Ru Particulates CRUD Truck

(Fig. 7-10)a

Rail

(Fig. 7-11)a

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.994316 0.993962

2.0E-04 2.0E-05 2.0E-06 2.0E-06 6.0E-03 6.0E-07 6.0E-08 6.0E-08 6.0E-07 3.8192E-03 2.7204E-032.0E-04 2.0E-05 2.0E-06 2.0E-06 6.0E-03 6.0E-07 6.0E-08 6.0E-08 6.0E-07 1.7984E-03 5.5450E-04

1.0E-06 6.7E-06 2.0E-06 2.0E-06 1.3E-02 1.0E-07 6.7E-07 2.0E-07 2.0E-07 1.6870E-05 1.2275E-031.0E-06 6.7E-06 2.0E-06 2.0E-06 1.3E-02 1.0E-07 6.7E-07 2.0E-07 2.0E-07 2.3300E-07 5.0110E-071.0E-06 6.7E-06 2.0E-06 2.0E-06 1.3E-02 1.0E-07 6.7E-07 2.0E-07 2.0E-07 1.5740E-07 1.0210E-072.0E-04 2.7E-05 2.0E-06 2.0E-06 3.3E-01 2.0E-04 2.7E-05 2.0E-06 2.0E-06 2.3620E-05 7.9511E-042.0E-04 2.7E-05 2.0E-06 2.0E-06 3.3E-01 2.0E-04 2.7E-05 2.0E-06 2.0E-06 3.0080E-07 3.2550E-072.0E-04 2.7E-05 2.0E-06 2.0E-06 3.3E-01 2.0E-04 2.7E-05 2.0E-06 2.0E-06 2.0340E-07 6.6340E-082.0E-04 4.8E-05 2.0E-06 2.0E-06 3.9E-01 2.0E-04 4.8E-05 2.0E-06 2.0E-06 1.5250E-05 6.1400E-042.0E-04 4.8E-05 2.0E-06 2.0E-06 3.9E-01 2.0E-04 4.8E-05 2.0E-06 2.0E-06 1.5920E-07 2.5310E-072.0E-04 4.8E-05 2.0E-06 2.0E-06 3.9E-01 2.0E-04 4.8E-05 2.0E-06 2.0E-06 1.0760E-07 5.1620E-082.0E-03 4.8E-04 2.0E-05 2.0E-05 6.3E-01 2.0E-03 4.8E-04 2.0E-05 2.0E-05 1.5320E-07 1.7860E-092.0E-03 4.8E-04 2.0E-05 2.0E-05 6.3E-01 2.0E-03 4.8E-04 2.0E-05 2.0E-05 3.9260E-14 3.2900E-132.0E-03 4.8E-04 2.0E-05 2.0E-05 6.3E-01 2.0E-03 4.8E-04 2.0E-05 2.0E-05 1.4950E-14 2.1370E-132.0E-03 4.8E-04 2.0E-05 2.0E-05 6.3E-01 2.0E-03 4.8E-04 2.0E-05 2.0E-05 7.6810E-16 1.6440E-132.0E-03 4.8E-04 2.0E-05 2.0E-05 6.3E-01 2.0E-03 4.8E-04 2.0E-05 2.0E-05 9.5700E-06 1.2490E-042.0E-03 4.8E-04 2.0E-05 2.0E-05 6.3E-01 2.0E-03 4.8E-04 2.0E-05 2.0E-05 7.2010E-08 1.0750E-082.0E-03 4.8E-04 2.0E-05 2.0E-05 6.3E-01 2.0E-03 4.8E-04 2.0E-05 2.0E-05 4.8370E-08 5.2960E-082.0E-03 4.8E-04 2.0E-05 2.0E-05 6.3E-01 2.0E-03 4.8E-04 2.0E-05 2.0E-05 1.0000E-16 3.4500E-14

 in the Modal Study, Reference [8-2].
8-66

uck accident population dose risk CCDFs for calculations that compared the source terms

G-0170, the Modal Study, and this study. Each RADTRAN 5 calculation assumed transport

ruck cask over each of the 200 representative truck routes and each calculation generated

19 representative truck accident source terms.

70 accident release inventory, NUREG-0170 Model I release fractions, only inhalation pathways

70 accident release inventory, NUREG-0170 Model II release fractions, only inhalation pathways

tory, 20 Modal Study source terms, all exposure pathways

tory, 19 truck accident source terms developed for this study, all exposure pathways

10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)
8-67

il accident population dose risk CCDFs for calculations that compared the source terms

G-0170, the Modal Study, and this study. Each RADTRAN 5 calculation assumed transport

ail cask over each of the 200 representative rail routes and each calculation generated

21 representative rail accident source terms.

70 accident release inventory, NUREG-0170 Model I release fractions, only inhalation pathways

70 accident release inventory, NUREG-0170 Model II release fractions, only inhalation pathways

tory, 20 Modal Study source terms, all exposure pathways

tory, 19 truck accident source terms developed for this study, all exposure pathways

10-3 10-2 10-1 100 101 102 103 104 105 106

Accident Consequence Value, C (person-rem)

10-110010110210310410510610710810910101011101210131014

Expected Years between Accidents Exceeding 

Consequence Value, C (100 shipments/yr.)
8-68

Table 8.19 Comparison of NUREG-0170 Model I and Model II and Modal Study

Probability and Consequence Axis CCDF Intercepts to Those Developed by this Study

Truck Accident

CCDFs

Train Accident

CCDFs

Probability Axis Intercepts

 NUREG-0170 Model I 1.5E-4 4.8E-4

 NUREG-0170 Model II 1.5E-4 4.8E-4

 Modal Study 3.6E-6 6.8E-7

 This Study 4.4E-8 9.4E-9

Consequence Axis Intercepts

 NUREG-0170 Model I 1.8E+3 1.2E+4

 NUREG-0170 Model II 1.8E+3 1.2E+4

 Modal Study 6.0E+4 1.0E+6

 This Study 3.0E+4 7.7E+5

Mean Accident Population Dose Risk

 NUREG-0170 Model I 1.3E-2 1.9E-2

 NUREG-0170 Model II 7.7E-4 4.9E-4

 Modal Study 1.3E-4 1.9E-3

 This Study 8.0E-7 9.4E-6

probability intercepts ought to qualitatively equal ratios of the differences from one of the chance

that the shipment takes place without a severe accident occurring. As the ratios in Table 8.20

show, within a factor of about two, this prediction holds true.

Table 8.20 Ratios of Probability Axis Intercepts

Truck Rail

Ratio

Probability

Intercepts

Ratio Values of

1- fnot severe accident

Ratio

Probability

Intercepts

Ratio Values of

1- fnot severe accident

NUREG-0170/Modal Study 42 16 71 33

Modal Study/This Study 82 81 70 151

This simple analysis shows that the values of the probability axis intercepts on the truck or train

accident population dose risk CCDFs are primarily determined by the substantially different

estimates developed by each study of the chance that an accident will not be severe enough to

cause radionuclides to be released from a spent fuel cask.

The estimates of the fraction of all accidents that lead to radionuclide release from a spent fuel

cask differ greatly because whenever cask failure was examined in greater detail, first by the

Modal Study [8-2] and then by this study, the chance of encountering impact or thermal loads

able to fail a spent fuel cask was found to decrease substantially. For example, the eightcategory accident scheme used in the NUREG-0170 analyses derives its severity fraction values
8-69

from analyses performed by Clarke, et al. [8-10], who estimated the fraction of all truck and train

accidents that were “minor, moderate, severe, extra severe, or extreme.” For NUREG-0170, the

probabilities of the accidents assigned to each of these five severity categories were

reapportioned into two categories that did not lead to cask failure and six that did (the NUREG0170 Categories I through VIII). When this was done, some of the accidents that fell into the

“minor” accident category of Clarke, et al. were judged to be able to cause cask failure, and the

“extra severe” and “extreme” categories were split into three categories that became NUREG0170 Categories VI, VII, and VIII. Inspection of the boundaries between the “minor” and

“moderate” truck and rail accident categories of Clarke, et al. shows that some “minor” accidents

might involve fires with durations less than 10 minutes, punctures with impact speeds of only a

few miles per hour, and crush loadings less than 20,000 pounds. Because some “minor”

accidents were apportioned into NUREG-0170 accident Category III, these conditions for the

boundary between “minor” and “moderate” accidents show that NUREG-0170 [8-1] made very

conservative assumptions about the accident conditions that might produce cask failure. Because

of these conservative assumptions, NUREG-0170 found that 9 percent of all truck accidents and

20 percent of all rail accidents were severe enough to fail a spent fuel cask.

The finite element and thermal analyses of cask response to impact and thermal loads performed

by the Modal Study [8-2] allowed the NUREG-0170 estimates of the chance of failure of spent

fuel truck and rail casks to be lowered respectively by factors of 16 and 33 to 0.57 and 0.60

percent. Moreover, when the Modal Study methodology was extended by this study to allow

examination of the response of the cask closure to mechanical and thermal loads, the chance that

a severe accident would fail a truck or a rail cask was estimated to be even smaller, specifically,

0.007 percent for truck casks and 0.004 percent for rail casks.

8.16.2 CCDF Consequence Axis Intercepts

Consequence axis intercept values give the largest accident population dose calculated during

any of the many trials (cases) examined by a single RADTRAN run. In the absence of

decontamination or interdiction of contaminated property, the largest population dose calculated

would be expected to be approximately proportional to the size of the radioactive release.

However, because the RADTRAN code interdicts ground that (a) is contaminated above an input

contamination criterion and (b) cannot be decontaminated to levels less than or equal to the

criterion, the maximum population dose calculated (i.e., the consequence axis intercept) may not

be caused by the largest set of release fractions examined during the calculation. Despite the

complications introduced by decontamination and interdiction, the relative values of the

consequence axis intercepts presented in Table 8.17 are instructive.

As Table 8.17 shows, the maximum values of the accident population doses listed in Table 8.17

and depicted in Figures 8.25 and 8.26 are ordered as follows: Modal Study value > value from

this study > NUREG-0170 value. As the table shows, the maximum accident population doses

calculated by the Modal Study [8-2] and by this study for truck accidents and also for rail

accidents differ only slightly (by a factor of two or less). This was to be expected because both

accident population dose calculations used the same cask inventory, both assumed failure of all

of the rods in the cask for the most severe accidents, both used rod-to-cask release fractions

based on the experimental results of Lorenz, and both assumed no deposition onto cask surfaces

of materials released to the cask interior from failed spent fuel rods (the Modal Study assumed
8-70

fcask-to-environment = 1.0 for all accidents; this study assumed fcask-to-environment = 1.0 for the most

severe accidents, i.e., for all Category 6 accidents, which by definition involve a double cask

failure).

Although NUREG-0170 source terms contain only Kr-85, I-131, and Cs-137, NUREG-0170

accident population doses are essentially caused exclusively by the Cs-137 in the source term.

Therefore, one would expect the ratio of the maximum NUREG-0170 rail accident population

dose and the maximum NUREG-0170 truck accident population dose (the NUREG-0170

consequence axis intercepts listed in Table 8.17) to about equal the ratio of Cs-137 in the

NUREG-0170 source terms. The NUREG-0170 Cs-ratio (rail/truck) is 6.4 = 1280 Ci/200 Ci and

the NUREG-0170 population dose ratio is 15. So again, the predicted and observed results agree

to about a factor of two. However, because interdiction would be expected to perturb the dose

caused by the larger release more than that caused by the smaller release, the ratio of the train

accident maximum population dose to the truck accident population dose might have been

expected to be less than rather than, as is observed, greater than 6.4.

Because the NUREG-0170 accident population doses are entirely caused by Cs-137 and because

the maximum amount of Cs-137 that can be released by these source terms is fixed at 200 Ci for

truck accidents and 1280 Ci for rail accidents, maximum NUREG-0170 accident population

doses are in effect capped. In contrast to this, because the Modal Study source terms and the

source terms developed for this study are both calculated as the product of a PWR cask inventory

that contains 19 radionuclides, a rod failure fraction, and a set of rod-to-cask and cask-toenvironment release fractions, the source term constructs developed by the Modal Study [8-2]

and by this study allow larger releases (larger source terms) to occur than are allowed to occur by

the NUREG-0170 source term construct. Accordingly, the fact that both the Modal Study

calculation and the calculation of this study both predict maximum accident population doses

that are larger than those predicted by the NUREG-0170 calculation was to be expected.

Comparison of the expected (mean) accident population dose risks and dose risk CCDFs

obtained using NUREG-0170 Model I and Model II source terms shows that, although both

calculations yield CCDFs that have identical probability and consequence axis intercepts, the

Model I expected accident population dose risk is about 17 times greater for truck accidents and

about 39 times greater for rail accidents than the Model II dose risk. This clearly shows that

dose risk is determined by the area under the CCDF in the region where the CCDF bends over

and then plunges toward the consequence axis.

Each of these calculations examined transport of PWR spent fuel assemblies in steel-lead-steel

spent fuel casks and each used the same PWR assembly inventory. For truck and rail transport,

the cask was assumed to carry, respectively, 1 and 24 assemblies. Therefore, because the release

fractions for the largest truck and train accident source terms of this study and the Modal Study

are very similar, the ratio of the maximum accident population doses predicted using these

source terms (the consequence axis intercepts of the CCDFs generated by these calculations)

should be approximately equal 24, the ratio of the number of assemblies carried by a rail cask to

the number carried by a truck cask. In fact, as Table 8.17 shows, the ratio of these maximum

doses for the Modal Study is 17 = 1E6/6E4, and the ratio for this study is 26 = 7.7E5/3.0E4.
8-71

Lastly, Table 8.17 shows that the expected accident population dose risks stand in the following

order and have the following relative magnitudes when normalized to the NUREG-0170 Model I

result:

Truck Accidents: NUREG-0170 Model I (1.0) > NUREG-0170 Model II (0.06)

> Modal Study (0.01) > This Study (0.00006)

Rail Accidents: NUREG-0170 Model I (1.0) > Modal Study (0.1)

> NUREG-0170 Model II (0.03) > This Study (0.0005)

Thus, the detailed analysis of the mechanical and thermal response of the cask shell performed

by the Modal Study [8-2] shows that spent fuel cask failure is significantly less probable and

spent fuel source terms substantially smaller than was estimated by NUREG-0170. In addition,

the analysis of closure behavior performed by this study by extending the Modal Study

methodology suggests that the probability of spent fuel cask failure and the magnitudes of spent

fuel accident source terms are both much smaller than the estimates developed by the Modal

Study.

8.17 References

[8-1] “Final Environmental Statement on the Transportation of Radioactive Material by Air

and Other Modes,” NUREG-0170, U.S. Nuclear Regulatory Commission, December

1977.

[8-2] L. E. Fischer, et al., “Shipping Container Response to Severe Highway and Railway

Accident Conditions,” NUREG/CR-4829, Lawrence Livermore National Laboratory,

Livermore, CA, February 1987.

[8-3] G. S. Mills et al., “Application of Latin Hypercube Sampling to RADTRAN 4 Truck

Accident-Risk Sensitivity Analysis,” Proceedings of the 11th International Conference

on the Packaging and Transportation of Radioactive Materials (PATRAM ’95), IAEA,

Vol. 4, p. 705, 1995.

[8-4] “Acceptance Priority Ranking and Annual Capacity Report,” DOE/RW-0457, U.S.

Department of Energy, Washington DC 20585, March 1995.

[8-5] N. R. Griego, J. D. Smith, and K. S. Neuhauser, “Investigation of RADTRAN Stop

Model Input Parameters for Truck Stops,” Conference Proceedings, Waste Management

96, Tucson, AZ, 1996.

[8-6] Personal Communications, B. Jody (Davis Transport, November 23, 1999); R. Ledford

(TriState, November 24, 1999); and Blake Williams (NAC, November 30, 1999).

[8-7] Regulations for the Safe Transport of Radioactive Material, Safety Standard Series No.

ST-1/Requirements, 1996, International Atomic Energy Agency (IAEA), Vienna,

Austria (reproduced in Code of Federal Regulations, Volume 10, Part 71, Appendix A).
8-72

[8-8] J. M. Taylor and S. L. Daniel, “RADTRAN: A Computer Code to Analyze

Transportation of Radioactive Material,” SAND76-0243, Sandia National Laboratories,

Albuquerque, NM, 1977.

[8-9] P. C. Reardon, “RADTRAN 1 Release 1: Retrieval and Verification from Archive,”

SAND99-1149, Sandia National Laboratories, Albuquerque, NM, to be published, copy

available on request.

[8-10] R. K. Clarke, et al., “Severities of Transportation Accidents, Volume III – Motor

Carriers and Volume IV – Train,” SLA-74-0001, Sandia National Laboratories,

Albuquerque, NM, 1976.
9-1

9. SUMMARY AND CONCLUSIONS

Risk assessment is inherently an attempt to anticipate the impact of future events. Because the

events that might take place sometime in the future are infinite, no risk analysis can examine all

of the possible sequences of events that might characterize the activity of interest, here the

transport of spent fuel. Risk analysts address this problem by constructing representative sets of

data for each important characteristic of the activity of interest. Then, by estimating the

outcomes for all possible combinations of the representative sets of data, a set of outcomes (here

the radiological consequences associated with the transport of spent fuel) is developed that is

expected to adequately explore the range and variability of the space that contains the infinity of

possible outcomes.

Cask design, route characteristics (e.g., accident rates and on-route and wayside population

densities), package external dose rates, prevailing weather, accident source terms, and evacuation

times are the principal characteristics of spent fuel shipments that affect the radiological

consequences associated with spent fuel shipments. For this study, three representative sets of

data were developed. The first set developed generic design data for four representative casks,

steel-lead-steel truck and rail casks, a steel-DU-steel truck cask, and a monolithic steel rail cask.

The second set contained 200 sets of representative truck or rail route data. Associated with each

representative set of route data was one possible set of prevailing weather conditions, an external

package dose rate, and an evacuation time. The values of these parameters were selected by

structured Monte Carlo (Latin Hypercube) sampling from distributions of these parameter values

that were derived from actual routes that might be used in spent fuel shipping campaigns. The

third set contained 19 representative truck or 21 representative train accident source terms

developed by analysis of the

• response of spent fuel casks, including the cask closure, and of the spent fuel rods being

transported in the cask to the mechanical and thermal environments that the cask might

experience during collision and fire accidents;

• size of the cask leak and the numbers of spent fuel rods that might fail due to these

mechanical and thermal environments; and

• amounts of radioactive materials that would escape from the failed rods to the cask

interior and then be released through the cask leak path to the environment before being

deposited onto cask interior surfaces.

Cask response to mechanical (collision) loads was estimated from the results of finite element

calculations. These calculations examined the impact of each of the four generic casks onto an

unyielding surface at three impact orientations. The impact speed onto a yielding surface that

would cause the same cask damage as was predicted for the impact onto the unyielding surface

was then estimated by partitioning the available impact energy between the cask and the yielding

surface. Cask response to thermal loads, specifically the times required to heat the cask seal to

seal decomposition temperatures and spent fuel rods to burst rupture temperatures, were

estimated by performing one-dimensional thermal analyses of the cask shell that took account of
9-2

the cask neutron shield compartment and the decay heat load produced by the spent fuel being

carried in the cask.

These impact and thermal results were used to estimate the dependence of cask leak areas on

collision speed and on the heating times required for an engulfing hydrocarbon fuel fire to heat

the cask to temperatures where elastomeric seals are seriously degraded or rods burst rupture.

Leak areas were used to estimate cask depressurization times following pressurization due to

failure of spent fuel rods. The depressurization time estimates then allowed cask-to-environment

release fractions to be estimated from the results of another study that examined transport of

noble gases, condensible vapors, and aerosols from a TN-12 cask through leak paths with various

cross-sectional areas to the environment. The results of that study show that, when cask leak

areas are small, cask depressurization is slow. Thus, considerable time is available during which

particles and condensible vapors can deposit onto cask interior surfaces. Conversely, when cask

leak areas are large, the rapid flow of gases out of the cask carries most materials released from

failed rods out to the environment before they can deposit onto cask interior surfaces. Total

release fraction values were calculated by combining the values estimated for cask-toenvironment release fractions with rod-to-cask release fraction values based on the experimental

results of Lorenz.

The fraction of all accidents that might produce a given source term was estimated using the

Modal Study truck and rail accident event trees, accident speed distributions, and accident fire

duration distributions. Because only impact onto hard rock at high speed appears to be able to

cause a spent fuel cask to leak, the Modal Study event trees were updated to reflect the

frequencies of occurrence of hard rock along three long interregional transportation routes as

determined by GIS analyses.

Given this input data, the radiological consequences associated with the shipment of spent fuel

were then estimated by performing RADTRAN calculations. Two types of radiological

consequences were examined: (1) consequences attributable to the population exposures that

result from the external dose rate of the undamaged package (incident-free consequences), and

(2) consequences caused by accidents that lead to the release of radioactive materials from the

damaged cask (accident consequences). Consequences were calculated for PWR and BWR spent

fuel shipped in each generic cask via each of the 200 routes in the representative sets of input

data, for four illustrative real truck and real rail routes, and for the NUREG-0170 truck and rail

routes. All of these calculations used the representative sets of 19 truck and 21 rail accident

source terms developed by this study.

The results obtained for the four generic casks using the 200 representative routes and the

representative truck and rail accident source terms showed that accident dose risks are negligible

when compared to incident-free dose risks, that truck transport stop doses exceed all other truck

incident-free doses, and that all other rail incident free doses are comparable in magnitude to rail

stop doses. These calculations also showed that for each transport mode the results obtained for

the illustrative routes and the NUREG-0170 route fall within the range of results generated by the

representative sets of 200 truck or rail routes.
9-3

The dependence of accident consequences on accident source terms was examined further by

comparing the results of calculations that differed only in the source terms used. Four sets of

truck and four sets of rail accident source terms were examined: the NUREG-0170 Model I and

Model II source terms, the Modal Study sets of 20 truck and 20 rail accident source terms, and

the sets of 19 truck and 21 rail accident source terms developed by this study. Comparison of the

mean (expected) accident population dose risks produced by these calculations indicates that, for

truck accidents, the NUREG-0170 Model I risks are about 17 times larger than NUREG-0170

Model II risks, which are about 6 times larger than the risks estimated using Modal Study truck

accident source terms, which in turn are about 160 times larger than the risks estimated using the

truck accident source terms developed by this study. For rail transport, NUREG-0170 Model I

accident population dose risks are about 10 times larger than the rail accident risks estimated

using Modal study rail accident source terms, which are about 4 times larger than the risks

estimated using NUREG-0170 Model II source terms, which are about 50 times larger than the

risks estimated using the rail accident source terms developed by this study.

The relative ordering of these accident results is entirely consistent with the assumptions made by

each study regarding the probability of radionuclide release during transportation accidents and

the magnitude of the source terms generated by accidents of differing severities. Because

NUREG-0170 assumed that spent fuel casks might fail when subjected to the loads that

characterize minor accidents, the fraction of all truck and train accidents estimated to lead to cask

failure is very large and extremely conservative. Similarly, because the NUREG-0170 Model I

assumed that all cask failures allowed the entire NUREG-0170 accident inventory (the maximum

amount of radioactivity that could be released during an accident) to be released, NUREG-0170

Model I mean accident population doses for truck and rail accidents are quite large. The Modal

Study estimated cask leakage from the response of the cask shell to mechanical and thermal

loads. As a result, both source term probabilities and source term magnitudes decrease and the

accident population dose risks calculated using these source terms are one or two orders of

magnitude below those calculated using NUREG-0170 source terms. In this study, source term

probabilities and magnitudes were estimated by examining the response of cask closures and

spent fuel rods to impact loads, and the burst rupture of spent fuel rods due to heating by fires.

Based on this more detailed analysis, cask leakage is found to be even less likely than the

estimates of the Modal Study, and retention of particles and condensible vapors by deposition

onto cask interior surfaces is found to be substantial. Accordingly, both source term probabilities

and magnitudes decrease further, and consequently accident population dose risks are reduced

further by factors of 10 to 100.

This summary and the detailed analyses described in Sections 2.0 through 9.0 lead to the

following conclusions:

• The single cask truck shipment expected incident-free population doses developed by this

study are about one-quarter of those in NUREG-0170.

• The single cask rail shipment expected incident-free population doses developed by this study

are about two-thirds of those in NUREG-0170.
9-4

• The use of very conservative cask failure criteria in NUREG-0170 caused its estimates of the

fraction of all accidents that release radioactive materials to be much too large and thus very

conservative.

• The NUREG-0170 estimate of the largest source term that might be released from a failed

spent fuel cask during an unusually severe transportation accident is significantly lower than

the largest source terms calculated using Modal Study release fractions or the release

fractions developed by this study. However, the risks associated with these source terms are

lower than the risk of the largest NUREG-0170 source term because these source terms are so

very improbable.

• The source terms developed by the Modal Study and by this study, which reflect the

complexities of rod failure and cask response to transportation accident impact and thermal

loads, yield estimates of expected (mean) spent fuel transportation accident population doses

that are orders of magnitude smaller than those developed by the NUREG-0170 study.

Consequently, the results of this study show that the NUREG-0170 estimates of spent fuel

transportation incident-free doses are somewhat conservative and the NUREG-0170 estimates of

accident population dose risks are very conservative. Since the NUREG-0170 dose and risk

estimates were not large enough to require regulatory action, the fact that the incident-free doses

estimated by this study are significantly smaller than the NUREG-0170 estimates and the

accident dose risks estimated by this study are orders of magnitude smaller than those estimated

by NUREG-0170 confirms that spent fuel transportation regulations adequately protect public

health and safety.